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Properties of localised charge carriers in vanadium and manganese garnets Citation for published version (APA): Oversluizen, G. (1983). Properties of localised charge carriers in vanadium and manganese garnets. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR124979 DOI: 10.6100/IR124979 Document status and date: Published: 01/01/1983 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 29. Aug. 2021
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Page 1: Properties of localised charge carriers in vanadium and … · Theo Kuijpe:PB die binnen het kade: ... Ruisendaal (typewe:Pk), Gerard Schepens (tekenwe:Pk) en L.J. HoPbaah (foto(JI'afie).

Properties of localised charge carriers in vanadium andmanganese garnetsCitation for published version (APA):Oversluizen, G. (1983). Properties of localised charge carriers in vanadium and manganese garnets. TechnischeHogeschool Eindhoven. https://doi.org/10.6100/IR124979

DOI:10.6100/IR124979

Document status and date:Published: 01/01/1983

Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:[email protected] details and we will investigate your claim.

Download date: 29. Aug. 2021

Page 2: Properties of localised charge carriers in vanadium and … · Theo Kuijpe:PB die binnen het kade: ... Ruisendaal (typewe:Pk), Gerard Schepens (tekenwe:Pk) en L.J. HoPbaah (foto(JI'afie).

PROPERTIES OF LOCALISED CHARGE CARRIERS

IN VANADIUM AND MANGANESE GARNETS

GERRIT OVERSLUIZEN

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Cover: 1. a conglomerate of flux-grown yttrium iron garnet single

crystals 2. the remnants of flux-grown vanadium garnet single crystals

(chapt. IV)

3. a natural garnet crystal fotmd in Nepal.

DISSERTA TIE DRUKKEfll ' u.ibru HELMOND

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PROPERTIES OF LOCALISED CHARGE CARRIERS IN VANADIUM AND MANGANESE GARNETS

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PROPERTIES OF LOCALISED CHARGE CARRIERS IN VANADIUM AND MANGANESE GARNETS

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN MN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. S.T.M. ACKERMANS, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DECANEN IN HET OPENBMR TE VERDEDIGEN OP VRIJDAG

9 SEPTEMBER 1983, TE 14.00 UUR

DOOR

GERRIT OVERSLUIZEN

GEBOREN TE VLAARDINGEN

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I Dit proefschrift is goedgekeurd door de promoto~n:

Prof.Dr. R. Metselaar en

Prof.Dr. F. van der Maesen.

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Aan mijn oudePs

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VOO:r'WOOI'd

Gmag wil ik op deze plaats al diegenen bed.an.ken die aan de totstand­

koming van dit p:Poefsah!'ift hebben meegewe:Pkt.

Alle leden van de vakgPoep fysisahe ahemie voo:P de pPettige manie:P

Waa!'Op z.ij mij gedUJ'ende het onde:Pz.Oek met Paad en da,aiJ tePzijde

hebben gestaan. In het bijzondeP wil ik hie:P noemen:

mijn di:Peate begeleideP en pPomoto:P Ruud MetselaaP die mij op de

hem eigen voo:Ptvarende wijze dooP de moeilijke stadia heeft geloodst;

de disaussies met hem Vo!'men de basis van dit pPoefsahI'ift.

Giel Bastin; zijn voo:PtdUI'ende belangatelling en de BamenuJePking

bij vooPkomende "mia:Poprobe" analyses heb ik als een (JI'Ote stimulans

e!'Varen.

Theo Kuijpe:PB die binnen het kade:P van zijn afstudeel"We:Pk het onde:P­

zoek aan de mangaan (J:Panaten Voo:P zijn Pekening heeft genomen.

D.C. Koningsbe:PgeP en J.H.M.C. van Wolput van de vak(JI'oep ano:Pganisahe

ahemie (THE) en M. Glasbeek en medeUJerkePs van de vak(JI'oep fysisahe

ahemie (U.v.A.) voor de UJaardevolle disaussiea en de ezpel'imentele

steun bij de ESR metingen.

D.L. Vogel van de vakgroep anorganisahe ahemie (THE) voor het op­

nemen van de I.R. speat!'a,

J. Sahoonman en P. B:Peddels van de Vak(JI'Oep natuUI'kunde en saheikunde

van de vaste stof (RUU) voo:P het besahikbaa:P stellen van de foto-

ge leidingsappa!'atuUI'.

V.A.M. Brabe:Ps, L. de Bont en W.C. van de Vleuten van de afdeling

vaste stof (THE) voo:P de hulp bij het ontwikkelen van de thermo­

k:Pacht opstelling.

C.R. van de Laan, P.W. van de Hoogen van de aentrale teahnisahe

dienst (THE) voor het maken van de thermok!'aahtael.

De vormgeving van dit pPoefsahI'ift UJePd Ve:PZO:P(Jd doo:P Charlotte

Ruisendaal (typewe:Pk), Gerard Schepens (tekenwe:Pk) en L.J. HoPbaah

(foto(JI'afie). Hiervoor mijn dank.

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1he investigations presented in this thesis have also been published

in the following papers:

G. Oversluizen and R. Metselaar,

ESR and optical absorption spectra of reduced vanadil..Dll ions in Ca.2Na

Mg2v3o12 garnet, J. Phys. C: Solid State Phys. ~. 4869 (1982).

G. Oversluizen and R. Metselaar, Photoinduced reduction of v4+ ESR

signal intensity in ca2NaMg2v3o12 garnet, J. Phys. C: Solid State Phys.

~. 355 (1983).

G. Oversluizen and R. Metselaar, Transport properties of Ca2NaMg2v3o12 garnet, "Solid State Chemistry 1982" eds. R. Metselaar, H.~.M. Heijli­

gers and J. Schoonman (Amsterdam, Elsevier) p. 353 (1983).

G. Oversluizen and R. Metse~aar, 1hennopower and conductivity in

Ca.2NaMg2v3o12 garnet, submitted to J. Solid State Chern.

G. Oversluizen, T.H.J.M. Kuijpers and R. Metselaar, 1hennopower and

conductivity in ~-xYxMn2Ge3o12 garnet, submitted to J. Arn. Cerarn. Soc.

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CXlNTENTS

· CllAVfER I INfRODUCTION

1.1. HistoPy of photoinduced effeats in YIG

1.2. The present investigation

Referenaes

OiAPTER II CRYSTAL a-JEMISTRY 2.1. Introduation

2.2. The gaz>net structure

2.3. Cation substitution

2.4. Single arystals

Referenaes

OiAPTER III POI.ARON TiiEORY

3.1. Introduction

3.2. The many-body SehPtJdinger equation;

the breakdOUJn of fundamental

approximations

3. 3. Po laPonie eonduetion

3.4. Thermoeleetria power in eleetroniaally

aondueting solids

3.5. The influenee of disorder; an

e::ctm term H e-inrp 3.6. Optiaal properties of polaPons bound

to a eentre

3.7. SumnaPy

Referenaes

OiAPTER IV ESR AND OPTICAL ABSORPTION SPECTRA OF REOOCED •

VANADIUM IONS IN Ca2NaMgzVP12 GARNET 4.1. Introduetion

4.2. FPepamtion and eharuaterisation

4.3. Experimental details

4. 4. Results

4.lJ.1. Optieal absorption

4.4.2. Eleatron spin resonanee

4.5. Interpretation of the speetra

4.5.1. Tetrahedral v4+

4.5.2. Oatahed.Pal v'+

page

1

2

5

5

5

7

9

11

11

11

16

17

19

22

22

25

25

25 28

28

28

29

32

32

36

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page

4.5.3, Pola:Ponia absorption

4.6. Disaussion

4.7. Conalusions

Referenaes

ClfAPTER V PHOIDINDUCED REDUCTION OF v4+ ESR SIGNAL

INTENSITI IN CazNaMgzV3012 GARNET 5.1. Introduation

15. 2. Experimental details

15. 3. Results

5.3.l, Photosensitivity of the v4+ ESR

signals

5.3.2. Photoaonduativity a:nd reflea-

ta:nae speatra

5.4. Disaussion

5.5. Conalusions

Referenaes

ClfAPTER VI lliEIMJPOWER AND CONJJJCTIVITI OF CazNaMgz v 301 z

GARNET· 6.1. Introduation

6. 2. Preparation of partially reduaed samples

6.3. Experimental details

6.4. Results a:nd disaussion

6.5. Sumnary a:nd aonalusions

Referenaes

ClfAPTER VII 'IHERMJPOWER AND coNtiJcriviTI OF Ca3-xY:itJnzGe3012 GARNET 7 .1 Introduation

7.2. Preparation a:nd aharaaterisation

7.3. Experimental details

7.4. Results a:nd disaussion

7.5. Sumnary a:nd aonalusions

39

39

41

44

44

44 45

45

47

49

53

56

56-

56

58 59

68

69

69

69

70

70

78

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Cl:IAPI'ER VIII CONCLUDING REMARKS

SUM\1ARY

SAMENVATIING

LEVENSBERIO:IT

8.1. General conclusions

8.2. Photomagnetio effects at room

temperature:

page

80

80

83

86

88

90

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rnAPTER.I

INfRODUCTION

1.1. History of photoinduaed effeats in YIG

Yttrium Iron Gamet (YIG), Y3Fe5o12 , is a ferrimagnetic compound. The physical properties can be adjusted over a wide range, to satisfy the requirements of specific applications, by introducing different ions in the original YIG stnicture. This possible change of proper­ties by so called chemical engineering has stinrulated a great amount of garnet research of both basic and applied character.

In 1967, Teale and Temp1i1)discovered a new and interesting phenomenon in Si-doped YIG. It was observed that the magnetocrystalline anisotropy varied under irradiation with infrared light. Since, many observations of photoinduced changes in magnetic properties of several compounds were reported in the literature(Z). The possible application of this effect in optical memory devices has resulted in several patents. However, generally the effect is observed at temperatures far below room temperature which would require a constant cooling of the device with liquid nitrogen. Therefore IIRlch work has been devoted to the temperature dependence of the photoinduced changes and the influence of dopants in various concentrations has been considered. Especially YIG has been extensively studied in this respect(3,4). The observed features and the model proposed to explain the photoinduced changes are reviewed in more detail in chapter V.

The cOIDIOOn factor in materials in which photoinduced changes have been observed, is that they always contain cations that can asstmM:l different valences. For instance, in donor doped Y3Fe5o12 the observed photomagnetic effects are explained in tenns of electron transfer between Fe3

+ ions. Such an electron transfer is equivalent to an ion displacement; in this example a displacement of an Fe2

+ ion. If the lattice sites involved in the electron transfer are inequivalent with respect to the physical property considered, the necessary conditions for the occurrence of photoinduced changes are met. Photo induced transitions of electrons between cations on different lattice sites, resulting in a redistribution of centres, are the

origin of the photoinduced changes.

1

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A prerequisite is, of course, that the electrons are localised, which usually requires temperatures below ambient. If the temperature is sufficiently low the change may be persistent due to the low mobility of the electrons, while at higher temperatures competition occurs between photo:induced transitions and thermal electron 100tion.

The electrical transport properties of doped and tmdoped YIG have been the subject of a great Ill.IJllber of investigations. However, the results and conclusions of these studies often seem contradictory. Apart from the trivial difficulty of preparing well-defined samples in the case of high-ohmic materials, the presence of transition metal ions in two or three sublattices fonns an extra complication especially in the tmderstanding of the charge transport mechanism and photo-conductivity results(S,6). The :m.miber of studies on the electrical transport properties of ''non-iron" gamets has been, rather limited and none have been per­fonned with respect to possible photoinduced effects in these materials.

In view of the above it seemed worthwhile to extend the inves­tigations to other gainet materials where preferably transition metal ions are only fOLmd in one sublattice.

1.2. The present investigation

The investigations presented in this thesis concem two different garnet series, the vanadium gamets and the manganese gamets, named

after the transition metal involved in the charge transport. In the

vanadium gamets, with formula ea2NaMg2vtzx~~o12_x, a number of y4+ centres could be introduced by a reduction reaction at elevated temperatures. The manganese garnets constitute a series of solid solutions, ca3_xYxt.ht/h;+Ge3o12 with 0 ..$. x ~ 2, where the amount of lower valent manganese is controlled chemically by yttrium substitution. The vanadil.Dll gainet was chosen because it is known that small concen­trations of v4+ ions can be present in the v5+ sub lattice C7J • Thus paramagnetic y4+ ions can be introduced in the diamagnetic host lattice providing the possibility of using ESR as an extra tool for the study of the defect centres. This is considered to be an advantage in comparison with the ferrimagnetic garnets where only the bulk magnetic properties can be studied. Further, the optical

2

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and electrical properties can be studied, and compared with those of the iron garnets. In the case of the manganese gamets the synthesis of the end members, with x = 0 and x = 2, was reported by Mill (S) and

Geller(9) indicating the existence of a complete series of solid solutions. This is of great interest, since it allows a study of the behaviour of charge carriers in a concentrated system. In both gamet systems transition metal ions occupy only one sublattice and the ratio of higher and lower valent ions can be varied where the vanadate garnets cover the low concentration region with xmax"' s.10-2 and the manganese gamets cover the high con­centration region with~ = 2. Therefore, within the limitations imposed by the complexity of the structure, these particular gamets can be considered as model systems for the study of the charge transport mechanism in relation to the occurrence of photoinduced phenomena.

Next a short outline will be given of the subjects dealt with in the subsequent chapters of this thesis. Chapter II is devoted to the crystal chemistry of gamets, where possible substitutions, single crystal synthesis and crystal struc­ture are considered. A knowledge of the structure is essential considering the physical properties of any solid since local symnetry and inter-atom separations predominantly determine the applicability of existing theories. In chapter III the relevant theory with respect to charge transport in narrow-band materials is reviewed. The equations appropriate for the evaluation of thennopower and conductivity data from the above gamets are derived. The chapters IV, V and VI deal with the vanadium gamets where successively the characterisation of centres by means of FSR and optical absorption spectrometry (chapter IV) , the photo induced intensity reduction of the v4+ FSR signal (chapter V) and the deter­mination of the charge transport mechanism through the combined results of conductivity and thennopower measurements (chapter VI), are discussed. Chapter VII contains the results and the interpretation of thenoo­power and conductivity measureirents on the series of polycrystalline

3

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manganese garnets.

A suumary of the experimental results and the conclusions drawn,

is given in chapter VIII.

REFERENCES

1. R.W. Teale"and D.W. Temple, Phys. Rev. Lett. ~' 904 (1967).

2. R. Metselaar, "Interaction of radiation with condensed matter"

(Vienna, I.A.E.A.) Vol. II, p 159 (1977).

3. R • .Metselaar and M.A.H. Huyberts, Philips Res. Repts. 29, 453 (1974).

4. F.K. Lotgering, J. Phys. Chem. Solids 36, 1183 (1975).

5. R • .Metselaar and P.K. Larsen, ''Physic of magnetic garnets" ed. A.

Paoletti (New York, North-Holland) p 417 (1978).

6. R. Suryanarayanan and R. Krishnan, Phys. Stat. Sol. K177 (1974).

7. V. Havlicek, P. Novak and M. Vichr, Phys. Stat. Sol. b44, K21 (1971).

8. B.V. Mill, Zhur. Strukt., Khim.~. 471 (1965).

9. S. Geller, C.E. Miller and R.G. Treuting, Acta Crystallogr. 1

179 (1960).

4

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rnAPTER II

QlYSTAL OIEMISTRY

2.1. Introduction

As illustrated on the cover of this thesis the synthesis of garnets is not restricted to laboratories. Natural garnets form

. 2+·,,3+ 4+ a large group of compounds with general fo111Ula M3 '''2 Si3 012 , where for example J+ = Ca and -J+ = AL Some of these mineral garnets like pyrope and aJ.mandite are considered as gem stones. Their characteristic colour is caused by the incorporation of small ammmts of transition metal ions. The structure of these silicate garnets was first elucidated by Men­zer in 1925(1•2). However, it was the discovery of the ferrimagnetic iron garnets in 1956, by two independent research grrups from Bell Telephone Companies and the "Laboratoire du Magnetisioo" in Grenoble, that boosted garnet research (3 ' 4) • Since numerous studies on the · possible substitutions, magnetic properties etc. have appeared.

2. 2. The garnet structure

According to Geller(5) the garnets belong to the cubic system with space grrup oii0. There are three kinds of cation sites all of which are usually occupied. The general fo111Ula is {C:,}[~] (D3Jo12 , in which {C} denotes ions on dodecahedral sites, [A] ions on octa­hedral sites and (D) ions on tetrahedral sites. The cations are located at the centre of the respective polyhedra which however are distorted. Therefore the site Syninetry is lower than cubic. The coordination about the anions is such that each oxygen ion has

frur nearest neighbours: two C sites, one A and one D site. In Table 2.1. the features characteristic for the garnet stnicture are suimnarised. Stnicture refinements have supplied the anion positions for many garnets and from these equations have been derived relating the positional parameters to the ionic radii of the constituent cations(6). The anion positions for the vanaditun garnet and the end members of the series of manganese garnets, calculated· accordingly, using the ionic radii of Shannon and Prewitt (cf. Table 2.3. ), are given in Table 2.2.

\

5

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Space group Ia.3d-O~O Typical (ideal) for.nula {Ca3} [Alzl (Si3) 012 Space group position 24c 16a 24d 96h

Location 0 48 000 0 48 xyz

Point synrootry (intern.) 222 3 4

Coordination to oxygen 8 6 4

Type of polyhedron aoaecaliearon octahedron tetrahedron (distorted cube)

Tabl-e 2.2. Anion positions

COlllpOl.Dld x y z

CazNaMg2V3°12 0.0376 0.0510 0.6545

Ca..31-h2Ge3012 0.0345 0.0470 0.6516

CaYzt-hzGe3012 0.0372 0.0565 0.6580

Figure 2.1. shows a three-dimensi911al representation of the struc­ture. In figure 2.2. an impression is shown of the spatial connection of the different polyhedra. The octahedra and tetrahedra do not share edges. Therefore the relative sizes of these polyhedra can be widely different and almost all metal ions can be used as substituents(9). Of course a number of garnet compounds exhibit a spontaneous magnetic polarisation and thus cannot be exactly cubic(5). Indeed, in some cases forbidden reflections have been observed(lO) and Olenavas et al(9) argued that the structure should be described in the centro­synrootrical space group R.3. However, the departure from cubic S}11111letry is generally very small and most of the structure refine­ments have been performed in the rubic space group.

6

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Fig. 2.1. Crystal struature of Y?e5o12 (yttrium iron garnet).

The piature shOUJs one oatant of the unit aeU. The indi­

aated diagonal aoinaides bYith the 'loaal threefoU a:r;is.

The full dots at the aorners and in the aentre of the aell

a:!'e Fe3+ ions oatahedra.Uy aoordinated by siz oxygen

ions (sma'l'l dots and airales). The la:!'ger rings a:!'e tetra­

hedraUy aoordinated FeJ+ ions. The la:!'ger fuU dots a:!'e

y 3+ ions (After Enz and Teal)71 ).

2.3. Cation substitution

The three cation sublattices in C3AzD3o12 may accOJllllOdate a variety of ions like C =rare-earth ions, Y,Ca,Na,Sr,Pb A= Fe, Al, Mg,Ni,Ga and D = Fe,Al,Si,Ge,V. Usually, the largest ions with J'\.O. 129-0. 096 nm oca.ipy dodocahedral sites, the medilDll sized ions with r ~ 0.083-0.053 nm oca.ipy octahedral sites and the smallest ions with r ~ 0.047-0.026 nm occupy tetrahedral sites. But to evalu­ate the site occupations in specific cases a knowledge of the ionic radii of the constituent ions alone is not sufficient. An other important parameter for instance is the coordination tendency towards oxygen. Also distributions over several sites are possible depending on the thermal history of the samples. An instructive review of

7

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existing garnets and the possible sublattice occupations is given by Geller(S). Further it should be noted that if, for example, an aJOOllllt of trivalent ions is replaced by fourvalent ions charge balance requires an equal am01.mt of divalent crunterdope. If the col.lllterdope is omitted, the system reacts by formation of lower valent ions amongst the original constituents. This effect is used to produce the photoinduced effects (cf. chapter I,V).

In this thesis chapters IV, V and VI will be devoted to the garnet {CazNal[Mg2] (V3)o12• In the stoichiometric crystal vanaditml ions are present as vs+ on tetrahedral sites exclusively, Mg2+ ions preferably occupy octahedral sites, ca2+ and Na+ dodecahedral sites. It should be remarked, however, that Mg2+ ions also can be substi­tuted on dodecahedral sites. In chapter VII results are presented for solid solutions {Ca3_xYx} [Ml2]Ge3o12• A complete series of solid solutions is possible between the end members {ca~+} [Mn~+] (Ge3)o12•

Fig. 2. 2. Spatial, connection of oxygen po'lyhedra in garnet. The

fPa;rnel,1ork of a'lternating tetrahedra and octahedra (shaded

portion) and of 8-foU dndecahedra (distorted cubes) is

presented. La.rge open circ'les represent o:x:ygen anions,

mnaZZ circles cations (after Novak and Gibbs{BJ).

8

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and {CaZ+~+}[Mn~+] (Ge3)o12 , clearly demonstrating the flexibility

of the garnet structure. The ionic radii of the relevant ions are summarised in Table 2.3.

Table 2. 6. Ionic radii • (11) (after Shannon and Preun. tt ) .

dodecahedral sites octahedral sites tetrahedral sites

ion r(run) ion r (run) ion r (run)

. Na+ 0.1180 Mn3+ 0.0645 VS+ 0.0355 eaz+ 0.1124 Mn2+ 0.0830 v4+ ? Mg2+ 0.089 Mg2+ 0.072 Ge4+ 0.0390 y3+ 0.1016 v3+ 0.064 Pb2+ 0.129

2.4. Single crystals

In the case of materials with very high or incongruent melting points a convenient way to prepare single crystals is the so-called flux-growth method, where an inorganic melt containing a solution of the component oxides at high temperatures is slowly cooled over a temperature range of several hundred degrees. After cooling down to room temperature the crystals fonned upon saturation can be separated from the solute by leaching the entire mass in hot diluted acids or bases. The method has several disadvantages. Since phase diagrams usually do not exist the composition of the melt has to be determined experimentally. Further, the size of the obtained crystals is generally rather small because the number of nucleation centres is large (cru­cible wall, melt surface, byproducts) Lead oxide is often one of the main melt constituents because of its low viscosity and high soluting power at elevated temperatures, which is essential to obtain and retain a homogeneous melt. However, under these conditions, some lead is also incorporated in the crystals (see par. 2.3., chapt. IV).

Garnet crystals exhibit a facetting 'Which predominantly consists of [110] and [211] faces. The prevailing fom of mineral garnet crystals

is the rhombododecahedron (cf. Fig. 2. 3 •• cover) fonned from .12 regular [110] faces.

9

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·"

Fig. 2.3. Rhombododeaahedron

REFERENCES

1. G. Menzer, Min. [A] 344 (1925). 2. G. Menzer, Z. Kristallogr. 69, 300 (1928). 3. F. Bertaut and F. Forrat, C'.omp. Rend. 242, 382 (1956). 4. S. Geller and M.A. Gilleo, Acta Crystallogr . .:!..Q_, 239 (1957). 5. S. Geller, z. Kristallogr. 125, 1 (1967). 6. F.C. Hawthonie, J. Solid State Chem. 37, 157 (1981). 7. U. Enz and R.W. Teale, Philips Tech. Rev. ~' 33 (1970). 8. G.A. Novak and G.V. Gibbs, .Amer. Mineral. 56, 791 (1971). 9. J. Chenav:as, J.C. Joubert, M. lvhrezio and B. Ferrand, J. Less­

Conmon Met. 62, 373 (1978). 10. T.J.A. Popma, A.M. van Diepen and J.M. Robertson, Mat. Res. lbll.

2_, 699 (1974). 11. R.D. Shannon and C.T. Prewitt, Acta Crystallogr. b25, 929 (1969).

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CHAPTER III

POLARON THEORY

3.1. Introduction

A large amount of literature exists concerning the charge trans­port mechanism in narrow band materials. The observation of extremely low carrier mobilities in some transition metal oxides is incompatible with conventional band theory. Therefore the polaron model was deve­loped in which a charge carrier becomes localised due to electron­phonon coupling. Other mechanisms for localisation can be found in electron-electron and electron-impurity interactions. The purpose of this chapter is to show that as a result of (all) these interactions the charge carriers in the vanadate and manganese garnets IID.lSt be considered as small polarons. Thermopower and conductivity studies are usefull experimental tools to elucidate the electronic nature of a solid. A great deal of information has

been gathered from two extensive reviewpapers by .Austin and M:>tt, and Bosman and van Daal, frequently referred to. In section 3.2. the breakdown of fundamental approximations used in band theory is discussed. In section 3.3. the equations governing the motion of small polarons are recalled and in section 3.4. appropriate forIID.llas for the thermoelectric power in electronically conducting solids are derived. The influence of "impurities" and dopants is reviewed in section 3.5. and the optical absorption due to small polarons is considered in section 3.6. Finally, in section 3.7. the equations used to interpret the experimental results in chapter VI and VII are swrmarised.

3.2. The many-body SehrBdinger equation; the breakdown of fundamental

appro:i:imations

Any solid and especially an ionic solid can be viewed as a collection of rv 1025 cnt3 electrons and rv 1024 an-3 ion cores mutually interacting via Coulomb forces. Neglecting effects due to spin-orbit coupling, magnetic effects, core-polarisation corrections etc. all of which can be handled by means of perturbation theory, the many-body Hamiltonian Eq. (1) is the correct starting point for the description of solid systems.

11

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p.2 Pei e2 Z Z e2 H = E S-+ E + 1 E + ! E Cl. 6

¥ 2 lrj-rkl 1Ra.-R6i j Cl. Cl. j,k a.,6

Z e2 E Cl. (1)

j,a IRa-rjl

In equation (1), latin subcripts refer to electrons and greek to ion cores; rj and pj are the position and ~ntum operators of the j th electron, Ra and Pa. are the position and 1ll0lrenttml of the a th ion core, which has mass Ma and charge Za.• m is the electronic mass and e is the magnitude of the electronic charge. 1he sums over j

and k nm over all the outer electrons; the sums over a and 6 run over all the ion cores. However, the resulting Schr&linger equation

H 1jl . = E iJ1 • e,i e,i (2)

where the subscripts e and i refer to electrons and ion cores res­pectively, cannot be solved exactly. In order to separate eq.(2) into solvable equations two serious approximations are conmionly employed; the Born-Oppenheimer and the one-electron approximations.

In the Born-Oppenheimer approximation it is assumed that the product functions ijle,i = 1jle(r,R)1jli(R) represent solutions to eq.(2). Physically this means that the motions of the heavy ion cores do not depend on the position? of the individual electrons. It is then possible to separate eq.(2) into

p 2 and H. = E N- + !

1 a a,6

z e2 E a . r-r.­

J ,a. a J

(3)

(4)

(5)

(6)

Equation (4) describes the motions of the ion cores, ie. phonons, therefore the corresponding Hamiltonian will be referred to as Hph. Equation (1) has thus been separated into H = He + Hph and tenns

involving the coupled motions of electrons and ion core,, ·

accmmted for by He-ph in eq. 8 below, :rave been neglected.

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TI1e one-electron approximation further assumes that a many­electron wave function w can be written as an antisynmietrized product of one-electron wave functions w = w(r1)w(r2)w(r3) ••• 'Ibis is equivalent with the assumption that the tenn in eq.(5) acc0W1ting for the interactions between different electrons can be written as a simple sum over individual electrons:

H = ! l: c - 2 jk

2

jr.:rkl = ~ h(j) J J

In this way each electron is supposed to experience only an average c.l¥irge due to the other electrons in the solid. TI1e possibility that two electrons can correlate their motion in such a way as to keep away from each other spatially and thus lower their average repulsive energy is neglected.

Finally, if the ions reside at their equilibrium positions, the last tenn in eq. (5) representing the attraction between the electrons and the ions,

Za e2 U(rj) = - l: jr.-R I

a J a

is a periodic function for the case of a crystaliine solid:

thus U(rj) = U(rj +Ra) (7)

for all Ra. Equation (5) can now be rewritten

H = z: [p?/zm + h(j) + U(r.)] e j J J

and the SchrOdinger equation (3) separates into N equations each involving only a single coordinate. TI1e solutions to these equations are the well-known Bloch functions that extend throughout the crystal; i.e. the electrons are itinerant. TI1e effect of the periodic potential U(j) is to group the energy eigenvalues into bands between which no eigen states exist; at least if the periodic potential is large enough, otherwise the bands may overlap. In the

tight-binding approach the width of these bands is given by 2zw

where w is the overlap integral between atomic wave functions centered * on nearest neighbours, w = J .P H .P d v, and z is the coordination

number. TI1e above reasoning has been set up to show that from the original Hamiltonian, which could be written

(8)

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. only the first two tenns are retained in conventional solid state theory. The band theory of solids depends on Bloch's theorem,_ eq. (7) , which can be proved for perfectly periodic potentials only, and the approximations

regarding the terms He-ph and He. Next some arguments will be presented that illustrate how the

breakdown of the above approximations under certain conditions results in major modifications of the intinerant electron picture. The critical parameter is the rigid ion band width.

Considering transition metal ions located at lattice positions relatively far apart, the small overlap between the d-orbitals will result in narrow bands. If a collection of widely spaced rtoms with partly filled orbitals is brought together to form a solid the degenerate atomic energy levels spread into bands. The band being partly filled, the electrons can generally be placed in lower energy states than on the original atoms, resulting in a decrease of the total energy. The energy gain is proportional to the width of the band and, in the case of narrow band materials, may not overcome the increase of electrostatic repulsion brought about by the approach of the electrons as pointed out by Mott(1). This correlation energy is not important when the band is nearly empty and the electrons consequently do not approach each other or when the band is nearly filled and the electrons cannot avoid each other even when they are allowed to correlate their motion. However, in the intermediate concentration region the correlation terms have to be explicitly considered. In the Hubbard model the electronic structure of a solid is analysed as a flmction of the interatomic spacing(2). At a critical density an insulator-metal transition, known as a Mott-transition occurs. Unfortunately, in the transition regime the model is difficult to analyse and a des­cription adequate for an existing material is not available(3). Nevertheless the Coulomb repulsion can result in localisation of the charge carriers as argued by Thouless ( 4) • This mechanism has

been suggested in case of several transition metal mono-oxides and magnetite, where the inter-transition metal ion distance is smaller than in the garnets considered here(5•6•7).

The breakcbwn of the Born-()ppenheimer approximation provides an even more important, second mechanism for localisation of the charge carriers. Concomittant with narrow bands are large effective

14

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masses and low velocities of the charge carriers. In ionic solids

in which at least two types of atoms exist optical phanons llllSt be present. These phonons represent movements in opposite directions of positively and negatively charged ions creating local m:inima. in charge density with respect to the equilibrium values. If the velocity of the charge carrier is small enough compared to the optical phonon motions and strong-electron phonon coupling exists the lattice will defonn in such a way as to lower the total poten­tial energy. The electron (or hole) then becomes trapped in the potential well created by the distortion of the surrounding lattice and charge transfer is induced by thennal fluctuations that reduce the depth of this well and create an equal one on an adjacent atom. The quasiparticle consisting of the charge carrier and its associated lattice distortion is called a polaron. Polaron theory is quite complex and is generally based upon the above Hamiltonian (eq. 8) without the tenn H~8 • 9 • 10). In the next section the equations governing the thennally activated motion (hopping) of polarons will be recalled. Some basic features, easily derived from first principles will be considered here.

An upper limit for the polaron mobility can be estimated using the Einstein relation, µ = eD/kT, and the condition for the occurrence ofself-trapping, T ~ T

0, where T

0 is the time period of

a lattice vibration. The diffusive motion of a hopping charge carrier is described by D"' la2/'r., where a is the jump distance. Thus the maximum mobility is given by:

ea2 1 ea2 t.w o u ~ 7T1<'f = 4iT" T ---i<r C 9)

0

The infrared lattice spectra of many oxides exhibit absorptions in the wavenumber region 200-900 an-1 (cf. for instance figures 6.6 and 7.6). Thus, disregarding phonon dispersion,1\w '\, kT at

0 room temperature. With a"' 0.3 nm it follows thatµ~ 10-5 m2/Vsec.

According to Austin and Mott the polaron binding energy can be estimated as follows(ll). In the continuum approximation the

potential of another electron at large distance from the trapped one is e2/41re

0e;r, whereas if the ions could not move it would be

2 e /4me;0 e00r, where e; and e

00 are the relative static and high fre-

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quency dielectric constants respectively and e is the dielectric 0

constant of vacuum. The potential energy in the well due to the displacerent of the ions is thus: V(r) = -e2/47re e*rwhere 1/E* =

0 1/e

00 - 1/e:. If the electron becomes localised in the well the energy

required to polarize the medium is e2/Sne:0e*r and the net energy

decrease due to polaron formation is: Ep = -e2/sn~e*r (10) &it the localisation costs an energy given by half the rigid ion band­width !ti, Therefore stable polarons are only formed if e2 /41T e

0/ r >ti.

The activation energy measured in a conductivity experiment is half

the polaron binding energy % = l ~ = e2 /16n 'l:/ Ji, since an elec­tron hops only when its energy is identical on both the site it occupies and a nearest-neighbouring site.

It has been remarked that Jahn-Teller ions are particularly suited to fonn polarons ( 12) •

3. 3. Polaronia aonduation

As stated in the previous section a polaron consists of a charge carrier and its associated lattice distortion. Polaron theory has been frequently adopted to describe the charge transport properties of transition mtal oxides. Bosman and van Daal have reviewed the results of numerous studies and summarized the conditions that detennine the applicability regions of the derived expressions(13). Based on the extension of the lattice distortion one distinguishes between large and small polarons. If the lattice distortion is confined to distances of the order of the lattice constant the polaron is called small. The large polaron case where the distortion extends to distances greater than the lat­tice constant and the mobility is not thermally activated, will not be discussed here. Depending on the value of the electron transfer integral (J) with respect to the phonon energy (h 'b) two cases are considered. If J :;:. h 'b• the so called adiabatic case, an electron can tunnel several times between potential wells on adjacent atoms during an excited lattice state. At high temperatures T > }9, where

O is the characteristic temperature (h 'h = k0) , an approximate foI'llllla for the mobility reads:

2 µ = (1-c) ~ v

0 exp (-%/kT) (11)

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where c is the fraction of ocaipied sites, a is the intersite distance, :Bii is the hopping energy and the other symbols have their usual meaning. If J < h v

0, the non-adiabatic case, the mobility is of the form:

ea2 µ = (1-c) ,;-- (12)

introducing an extra T-! outside the exponential (T > !0). At low temperatures T "'< lO small -polaron band conduction is expected in both cases, though it should be noted that fluctuations in potential energy between neighbouring sites caused by impurities (section 3.5) may wash out the band entirely.

3.4. Thel'rnoeLeotrio power in eLeotronioaLLy oonduoting soLids.

Since the treatment of Onsager it has been finnly established that the Seebeck coefficient, defined as the open-circuit voltage l:N

developed across a material in a temperature gradient divided by the temperature difference AT in the limit AT+ 0, can be expressed asC14):

* _ AV S _ 1 - * a = - fi.'T = - e = - e (S + Q /T) (13)

* where S (= Js/Je), the ratio between the entropy flux (Js) and the particle flux (Je), is called the transported entropy, Sis the

* particle entropy and Q is the heat transferred by the particle.

In a non-degenerate broad-band semiconductor the conductivity (cr)

is detel1Ilined by thermal excitation of charge carriers into non-lo­calised states in the conduction band:

cr = neµ = cr0

exp (-E/kT) (14)

The temperature dependence of the mobility is described by a simple power law where the exponent is detel1Ilined by the dominant scattering mechanism. The charge carriers can then be viewed as an electron gas. The entropy can be evaluated via the small-partition ftnlction:

z = E P· exp (-s./kT) i ]. ].

using S = k ln Z + U/T and U = kT2 olnZ

oT

(15)

(16)

(17)

where pi is the level degeneracy, t:i is the level energy, U is the total energy and Z zN/N! For an N electron gas enclosed in a volume V the grand partition function is given by(lS):

17

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ZN N * z = N.' = ~ { (2mn kT)"'"v}N N. ~

(18)

where the factor 2N accounts for the electron spin degeneracy and the * use of an effective electron mass m accotm.ts for the periodic poten-

tial in crystals as in band theory. Substitution in equations (16),(17)' and dividing by N to obtain the entropy per particle then yields:

s = ~k + k 1n c2nm;kr).l/,. + k 1n 2 - k 1n N/V 2 h

Asswning the heat of transport tenn to be negligible(l 5), the resul­

ting equation for the Seebeck-coefficient reads:

k Nc 5 k E 5 a = -e- cin n + 7) = - e-CK'f + z) (19)

* 2 Jl where n is the concentration of carriers and N = 2(2mn kT/h )~ c is the density of states at the bottom of the conduction band. The activation energy E is measured relative to the Fermi-level.

Neglecting minor tenns equations (14,19) imply an equal temperature dependence of a and log cr?

If electrical transport occurs via thennally activated hopping of a fixed number of localised charge carriers the entropy tenn is_ largely detennined by the entropy of mixing:

smix = k ln [(1-c)/c], where c is the fraction of occupied transport sites. There is consi­derable evidence fromboth practical and theoretical studies that the heat of transfer is negligible(11 •13 •17). The thennopower is tempe­

rature independent:

a = -(k/e) 1n [(1-c)/c] (20)

According to this relation, a < 0 for 0 < c < ! and a > 0 for ! < c < 1 where c is defined as c = n/N and n,N are the concentrations of carriers and available sites. With N = N

0, the total concentration

of transition metal ions concerned, eq. (20) is known as the ''Heikes" formula(lS).

It is important to note that in both n- and p-type materials electrical transport occurs by hopping of the same electrons over the same lattice sites. Consequently interaction effects are to be expec­ted at higher concentrations. This is to be contrasted with band-type

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conduction where electron and hole transport take place at different energy levels in independent bands and their contributions to the thennopower can be added according to the transport.numbers

(ti= cri/0 total): atotal = teae + ~~· (21)

3.5. The influenae of disorder; an eztra teI'lTI H . e-urrp

In the extrinsic regime, conductivity is controlled by impurities or deliberately introduced dopants or native defects. These lattice defects and foreign atoms often possess a net charge with res­pect to the lattice and since they do not normally build a superstlUC­ture, destroy the periodic potential. Apart from c~sitional disorder, so called positional disorder may exist in c~unds where different atoms are sinrultaneously present on one sublattice (cf. par. 5.4.). Other cases of positional disorder include interstitials, dislocations, cluster formation and amorphous systems. If the disorder is large enough localised states in the bandgap are fonned and Anderson esti­mated that above a critical value of the ratio of the disorder poten­tial (U) and the rigid ion bandwidth (LI.) U/ll.>2.8, all states are localised(l 9).

One should expect that electrons which are already localised due to disorder interact with phonons and fonn small polarons. However,

. because of the disorder potential the small polaron band regime will be absent and conduction takes place by hopping down to very low temperatures. Miller and Abrahams investigated the conductivity of heavily doped broad-band semiconductors(20). They introduced the concept of impurity hopping which, at low temperatures, leads to a conductivity of the fonn cr "'A exp -(C/T)l. Austin and M:>tt have applied this theory to polar materials and argue that, at the hlgh temperatures used in thls study, the conductivity behaves like o"' B exp(-EJkT) with E = 11i + iEd where Ed is the spread in energy levels caused by disorder and 11i is the hopping energy (cf. par. 3.3.).

From an electrostatic point of view it is obvious that the intro­duction of centres possessing a net charge with respect to the lattice will lead to an extra tenn H . in the Hamiltonian of sintl-

e-llllp lar magnitude as He (cf. 3.2) but of opposite sign. This tenn will tend to localise the charge carrier at a site neighbouring the im­purity and thuS causes an increase of the activation energy (Ea) obser-

19

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ved in a conductivity experiment. Assuming a random distribution of centres the contribution due to He-imp in the activation energy is e:x:Pected to decrease with increasing impurity content since at higher concentrations a jump away from one centre is equal to ~ jump towards the next. Such behaviour of the activation energy has been observed in many cases including ionic conductivity in fluorides and glasses and electronic conduction in several transition metal oxides(6•13•21 •22 •23). However, the concentration regions where the

major change in Ea is encountered, are widely different. Several mdels have been proposed to account for the concentration dependence of E • Lidiard applied the Debye-Hiickel approach,as developed for non­ide~ electrolyte solutions~ to ionic solids C24). The resulting

expression for Ea reads:

o e2i<: Ea = Ea - 41T ~£(l+1<'R) with

2 K=(2ex)!

V'lh£kT

where i<: is the Debye-Hiickel screening constant, R is the distance of closest approach for the free defect, v is the volume per nDlecule solvent and x is the free defect concentration. Wapenaar assumed a Gaussian distribution of activation energies where the average value depends linearly on x, i.e.: C25J

E = E0 - (h + i_ )x a a KT

where p = Clx is the width of the distribution and h a constant. Whereas M>tt derived the e:xpression(11 ):

2 E = e {1 _ (4'11X)1i} a 41r'be a T

where d is the distance between carrier and impurity centre. The above equations, which exhibit a different concentration dependence, describe satisfactorily the observed behaviour in respectively alkalihalides, fluorides and some doped transition metal oxides. However, the possibly complex defect structures are not explicitly taken into account. Yet, calculations have clearly demonstrated the importance of defect aggregation, even at low defect concentrations. For instance, according to calculations of Catlow and Stoneham in

*i-xo, a rapid change from almost 100% isolated vacancies to

20

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almost 100% so called [6:2] clusters occurs already at values of x between 10-4 and 10-3 (26}. The defect structure be:ing known, the derivation of expressions for the conductivity and the thennopower is a matter of percolation theory(27}.

In the absence of detailed infonnation with respect to the defect structure two limiting cases will be considered as schematical­ly depicted in Fig. 3.1a,b.

4 Ed ... _w 0 ......

c >-

Ill OJ

Ill c ltl OJ

"'O Ill

free energy E

- UJ 0 ....... c

>-.., Ill OJ

Ill c ltl OJ "'O Ill

free energy E

Fig. 3.la,b. Sehematie pol.aron site distributions; shaded areas

denote oeeupied levels (see text).

Fig. 3.1.a refers to the case where the energy levels of the transition metal ion sublattice are separated into discrete groups. The width of the energy level distribution within each group is supposed to be small with respect to kT whereas the intergroup separation is large with respect to kT. Charge transport involves all levels and the observed activation energy is predominantly detennined by jtUDps requiring the highest Ea. Since no electron redistributions between the different groups occur the entropy of mixing is temperature independent. Tirus the thennopower is temperature independent and the number of available polaron sites (cf. eq. (20} and subsequent discussion) is smaller than N

0, the total concentration of transition

metal ions.

21

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Fig. 3.1.b represents the case where a conti.rn.tous distribution of polaron sites exists, wide with respect to kT. If conduction takes place by jumps between states close to the Fermi-level the thenno­power can be evaluated using the ''metallic" fonnula (28) :

'112 k2T a=-3 e C51ncr(E)}

oE E=Ep

With cr(E) = cr0

(E) exp (-E/kT) this expression can be written as:

'112 k olncr0

(E) oEa a = - 3 e [kT ( oE )E=Ep - (~)E=Ep ] (22)

Although the differentials in eq. (22) are diffirult to evaluate in specific cases, a temperature independent thennopower is not to be

expected.

3.6. Opticai p!'OpePties of poZarons bound to a centpe

Sml:lll polaron transport can be induced both thennally and optically. Assuming equal potential wells for an occupied site and an adjacent unoccupied site, it has been shown that the energy required to transfer the electron at constant configurational coordinate (i.e. according to the Franck-Condon principle) is given by(ll):

(23)

In the presence of disorder, where the localisation of the electron is partly due to the tenn H . , additional energy is required

e-llllp for hops away from the impurity centre. Photon-assisted hopping

_ tlrus occurs at energies: ' i (lj = 2~ + /:J. (24) I

where Ep is the JOOdified polaron binding energy near an impurity. Since the electron is acted upon by a Coulomb field a series of exciton lines is to be expected. These however, will be broadened by temperature and zero-point motion resulting in a broad band.

3.7. Swrrnal'y

Evidently, if dictated by the structure the distance between transition metal ions on a sublattice is large and the rigid ion bandwidth is correspondingly small, the breakdown of the ftmdamental

22

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approximations as discussed in par. 3.2. causes a localisation of the charge carriers. Charge transport then occurs by thennally activated hopping.

In the vanadium and manganese garnets the shortest V-V and Ml-Ml

distances are large, viz. "' 0.38 respectively "' 0.54 nm. Further, the change in stoichiometry due to reduction in the vanadium garnets and the yttrium doping in the case of the manganese garnets will introduce tenIJS H . in the Hamiltonian. Therefore the charge

e-imp carriers are expected to be small polarons and the results from theI1110power and conductivity measurements (cf. chapt. VI, VII) will be interpreted using equations(11),(ZO)where N, the concentration of sites available for the polaron is reduced by defect interactions

(cf. Fig. 3.1.1), i.e.: Nc(1-c)e2a2v

cr = neµ = kT 0 exp (-Ea/kT) (25)

(26)

REFERENCES

1. N.F. t.btt, Proc. Phys. Soc. (London) a62, 416 (1949). 2. J. Hubbard, Proc. Roy. Soc. (London) a281, 401 (1964). 3. W.F. Brinkman and T.M. Rice, Phys. Rev. b2, 4302 (1970). 4. D.J. Thouless, J. Physique Colloq. 37, c4-349 (1976). 5. B.H. Brandow, Adv. Phys. 26, 651 (1977). 6. N.F. llitt, "Festkarper probleme XIX" ed. J. Treusch (Braunschweig,

Vieweg) p 331 (1979). 7. M.I. Klinger and A.A. Samokhvalov, Phys. Stat. Sol. b79 9 (1977). 8. J. Appel, "Solid state physics XXI" eds. F. Seitz, D. Turnbull

and H. Ehrenreich (New York, Academic) p 193 (1968). 9. T. Holstein, .Ann. Phys. ~. 325, 343 (1959).

10. D. Emin, "Electronic and structural properties of 3IOOrphous semiconductors" eds. P.G. Le Comber and J. llirt (London, Academic) p 261 (1973).

11. I.G. Austin and N.F. M:>tt, Adv. Phys. _1!, 41 (1969). 12. C. Crevecoeur and H.J. de Wit, J. Phys. Chem. Solids~. 783 (1970). 13. A.J. Bosman and H.J. v. Daal, Adv. Phys. ,.!2, 1 (1970).

23

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14. R.R. Heikes, '"lhennoelectricity" eds. R.R. Heikes and R.W. Ure (New York, Intersience) Chapt. 2 (1961).

15. R.P.H. Gasser and W.G. Richards, "Entropy and energy levels" (Oxford, Clarendon) p 33 (1974).

16. C. Wagner, "Progress in solid state chemistry'' eds. H. Reiss and J.O. M: Caldin (New York, Pergamon) Vol. 7, p 1 (1972).

17. H.L. Tuller and A.S. Nowick, J. Phys. Chem. Solids 38, 859 (1977), 18. R.R. Heilces, '"lhenooelectricity" eds. R.R. Heikes and R.W. Ure

(New York, Interscience) Chapt. 4 (1961). 19. P.W. Anderson, Phys. Rev. 1 1492 (1958). 20. A • .Miller and E. Abrahams, Phys. Rev. 120, 745 (1960). 21. K.E.D. Wapenaar, J. Phys. Colloq • .!!, c6-220 (1980). 22. A.M. Glass and K. Nassau, J. Appl. Phys.~. 3756 (1980). 23. A.J.M. IW.ipers, Electrical transport in the mixed series Fe3_xTix04,

Ph.D. Thesis, Eindhoven (1978), 24. A.B. Lidiard, ''Handbuch der physik XX" ed. s. Flligge (Berlin,

Springer Verlag) p 246 (1957). 25. K.E.D. Wapenaar, J.L. van Koesveld and J. Schoornnan, Solid

State Ionics ~. 145 (1981) . 26. C.R.A. Catlow and A.M. Stoneham, J. Am. Ceram. Soc. 64, 234 (1981). 27. J.D. Hodge and H.K. Bowen, J. Am. Ceram. Soc. 64, 431 (1981). 28. N.F. M:>tt and E.A. Davis, "Electronic processes in non-crystalline

materials" (Oxford, Clarendon) (1971).

24

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CHAPTER N

ESR AND OPI'ICAL ABSORPI'ION SPECTRA OF REOOGED VANADIUM IONS IN

CazNaMg2V3o12 GARNET

4.1. Introduation

In stoichiometric fonn the vanadilllll garriet {Ca~+Na+}[Mg~+]cv;+)o12 contains only ions with closed shell configurations. 11ru.s no ESR

signals are to be expected and apart from charge transfer transitions at relatively high energies no optical absorption in the visible spectral region should occur. However, it is known that small concen­trations of v4+ (3d1) ions can be present on the v5+ sublattice(l).

Other signals being absent, the presence of localised v4+ centres should be clearly observable in both ESR and optical spectrometry. M:>reover, the combined results of these techniques enable an tmam­

biguous detennination of the lattice site occupied by the v4+ ion and also valuable infonnation is obtained with respect to possible un­expected impurities and valence states.

In this chapter results of optical and ESR measurements on

ca2NaMg2v3o12 are presented. In section 4.2 the preparation of single crystals is described, together with the characterization by means of electron microprobe, x-ray analysis and weight loss measurements Section 4.3 gives experimental details. In sections 4.4 and 4.5 optical absorption spectra and ESR results are presented and discussed. TI:ie results are compared and discussed in relation to the literature data in section 4.6, and the conclusions drawn are summarised in section 4. 7.

4.2. Preparation and aha:eaaterisation

Polycrystalline Ca2NaMg2v3o12 has been prepared by solid state reaction following a synthesis first described by A. Durif(ZJ. TI:ie component oxides and carbonates, Na2co3, eaco3 and MgO,v2o5, were of at least p.a. purity grade. Weighed stoichiometric quantities were mixed by conventional ball-milling in agate mortars and fired in air at 700°c for 10 hours. Single crystals have been grown from v2o5 and PbO fluxes with molar compositions 1Ca2NaMg2v3o12 + 1.5V2o5, 1Ca2NaMg2v3o12 + 1.2v2o5 and 1Ca2NaMg2v3o12 + 1.2Pb0, respectively. Tightly covered platinum crucibles containing circa 30 cm3 of the

25

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melt were placed in the centre of a resistance furnace and heated to

1200°c in 6 hours. The furnace was cooled at 2 degrees/hour from 1200-800°c where the power was turned off. The resulting crystals were

separated from the flux by leaching in hot NH4Cfl. The greater part of the crystals had some well developed faces. Crystal dimensions were

typically of the order 1-2 mm and in individual cases 4-5 mm. Further reduction of the cooling rate did not increase the crystal dimensions. Similar synthesis have been described in the literature(3).

All diffraction lines present in the recorded x-ray patterns

could be indexed in the Ia3d group, as illustrated in Fig. 4.1.

16401

14441

(6]11

so

- 29(deg)

16111 CS32J

45

(4]11

!S!Ol

U.20J

(1.001

U221 C332)

12111

021) C220l

25 20

Fig. 4.1. A typiaal garnet x-ray diffraation pattern of Ca2Na.Mg2v3o12

The lattice parameters were accurately determined from Gu:j.nier pictures using Al2o3 as internal standard. The compositions of the•single crystals

were evaluated relative to the polycrystalline material by x-ray analysis on a Jeol 733 rnicroprobe. The lead content was calculated with respect to a PbO standard. Lead is known to be readily incorporated in garnets of this type(4). A method based on buoyancy was used to determine the crystal density(S).

Several characteristics of the prepared garnets are st.Dlllllarised in Table 4.1.

Thermogravimetric experiments perfonned in air indicated an irreversible weight loss starting at approximately 900°c and contilruing at a rate of about 3 x 10-4 wt%/hour at 1100°c. This

weight loss was accompanied by an increase of the lattice parameter and a reduced content of ions - mainly Ca, Na and Mg ions. Long heating periods at temperatures above 10so0c resulted in the formation of an

26

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Composition Lattice parameter x-ray density Experimental Colour Facetting (:!; 0.0001 Illl1) (gfcm3) density (g/ cm3)

Ca2NaMg2V3°12 1.2435 3.431 white powder

ca2.05Nao.6cffg2,11v2,99012 1.2423 3.406 3.40 reddish {211}>{110} s:i,ngle crystal

ea1.94Nao,91Pbo.1oMg1.92v2.99°12 1. 2453 3.511 3.52 transparent {211}>{110} single crystal

TabZe 4.2. Pa.T'ametere of the aziaZ spin hamiZtonian as deduaed from the ESR epeatra at ??K.

Composition g// g.,l. IAql (1 IA..cl (1

Caz.05Nao.60Mg2.11Vz.99°12 1.8569+0.0004 1.9801+0.0005 152.8:!;0.3 31.9+0.3

Ca1,94Nao,91Pbo.10Mg1.92v2.99°12 1.8549!0.0003 1.9785!0.0003 150.1+0.2 31.0;t0.2

nominal ca2NaMg2v3o12 (1) 1.856!0.002 1.979!0.001 152 31

N '1

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unidentified second phase. In this two-phase material the lattice parameter of the gamet remained constant at 1 • 2439 nm. Near 1100°c a reversible reduction reaction occurred simultaneously, producing v4+ centres. In the single crystals y4+ centres were pro­duced by a heat treatment for 15 minutes at 1120-1140°c in air, followed by an air quench to room temperature. Similar results can be obtained in polycrystalline, sintered pellets; however, poly­crystalline powdered samples reoxidise already during quenching. All measurements reported in this ~sis were perfonned on homogeneous single-phase crystals as verified by optical microscopy, scanning microscopy and electron microprobe measurements.

4. 3. Experi.mental detail.8

Thin plane-parallel plates of 0. 5-1 mm thickness were prepared from the crystals by grinding and polishing with diamond discs. Room temperature optical absorption spectra were measured with a Zeiss ~ II spectrometer. ESR spectra were recorded on a Varian E-15 spectrometer operating at X-band frequencies with 100 kHz rf­modulation. The magnetic fields were measured with an N.M.R. probe to within 0.1 G and the frequency was monitored using a Hewlett­Packard model 2590 B transfer oscillator and a model 5245 L electronic cowiter. The samples were placed in the centre of a T102 cavity equipped with a liquid helilDll continuous-flow cryostat (OX:ford Instn.mmts). The temperature was controlled to within 0.5 K by means of a Cryoson VC30 temperature controller. Preliminary crystallographic orientation of the single ctystals was perfonned by the x-ray Laue back-reflection technique. Then the crystals were glued to a holder with the (100) or (110) planes perpendiatlar to the axis of rotation. Final orientation was carried out, according to the extreme value of the magnetic resonance field of the low-field lines.

4.4. Re8ults

4,4.1. Optical abaol'Ption

Absorption spectra recorded before and after heat treatment of the crystals are shown in Fig. 4.2. The gamet as grown from the PbO flux is transparent up to a strong absorption edge situated at 25500 cm-l. After the heat treatment a double absorption band in

28

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"' z

"' Q

.... <(

u

Q.

0

1.5

1.0

IS

I I

I

a

I ,~

I I

/ ,, ... -... ~--"""'

,,,,.,,. ... I

I

--I

/I --

I I

I I

I I

I I

I I

I

/

b

I I

I I

I

,,.-.. 1' ,.,.,,,,, ' ... __ ,.

//~~~~~~~~~~~

10 15 20 25 10 I 5

WAVENUMBER c1o'crii'l

I I

I

I I

I

I I

I I

I

20

I

I I

I

/

I I

I I

I I

25

Fig. 4. 2. Absorption speatra at room temperature of

a) ca1•94Na0•91Pb0•1cJ1f11•92v2_99o12, sample thiakness

1. 7 mm, and

b) Ca2• 0~a0 • 6cJ1f12 • 11 v2 • 99o12, sample thiakness 1.0 mm.

Full aurve as grOUJn.; broken aUPve after heat treatment.

the infrared, with maxima at 11900 an-1 and13500 an-1, is seen, together with an increased absorption in the (16-25)103 an-1 region. The absorption spectra of crystals grown from a v2o5 flux show essentially the same features, apart from the weakly structured absorption responsible for the reddish colour of the untreated crystals. Tentatively this absorption may be decomposed into two

bands at 14000 an-1 and 22000 cm-1• An attempt to obtain a better resolution at liquid nitrogen temperature was not successful. In

crystals grown from a v2o5 flux the double band in the near infrared is shifted to slightly higher energies in comparison with crystals grown from a PbO flux.

4.4.2. Electron spin resonance

In the untreated crystals no ESR signal could be detected in the available field range 0-104 G, even at 4.2 K. After heat treatment the response of three, for a general direction of the field inequivalent, S=l/2 centres was detected, with a characteristic hyperfine splitting due to an I=7/2 isotope.

29

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a

1508 4000 _.L__ ___ .

J

r

b

-+-rtta----

Fig. 4.3. ESR spectra of ca1•94Na0•91Pb0•1cJ'1g1•92v2•99o12 at 77 K

a) H//[111] b) H//[001].

30

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No change of resonance positions was observed with temperature.

Above 77 K the lines broaden, probably due to spin-lattice relaxation.

Below 77 K saturation becomes important and at 4. 2 K unsaturated

signals were only obtained at minimum klystron power.

Two spectra, recorded at special orientations of the magnetic field

(H) with respect to crystal synnnetry axes, are shown in Fig. 4. 3.

Fig. 4.4. shows the angular dependence at 77 K when the magnetic

field is rotated in a (110) plane.

4000

20"

Fig. 4. 4. Angula'J.' dependenee of ESR lines when the field is rotated

in the (110) plane; D° H//[001], 90°H//[110].

Evidently the spectra exhibit tetragonal local synnnetry with the

distortion axis coinciding with one of the cubic axes. With

coinciding principle axes of the g and A (hyperfine) tensors and

neglecting nuclear quadnipole interactions the appropriate spin

Hamiltonian is

31

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.An accurate fit with the experimental angular variation was obtained by considering the hyperfine interaction up to second order(6). The calwlated spin Hamiltonian parameters are given in Table 4.2. For ccoparison, data previously reported by Havlicek et al (1) have been included in this table.

4.5. Intezrpretation of the spectra

4.5.1. Tetrahedral y4+

The v5+ isotope with nuclear spin !=7/2 has a natural abundance of 99.76%. Further it is known that the tetrahedral sites ii:t garnets are distorted along the cubic axis with site symmetry 4 (7). One therefore readily attributes the observed ESR spectrum to v4+ ions on tetrahedral sites. The splitting of 2n states in an axial field is shown in Fig. 4.5. The ground state can be inferred from the relative magnitude of the spin Hamiltonian parameters. Crystal field theory predicts g •< &i. if the tetrahedron is elongated and Kt < g /1 if the tetrahedron is compressed(8). By comparing these expressions with the experimental values, it is seen that the tetrahedron is elongated, corresponding to a d 2 2 ground state. This agrees with the results of crystallo­graphi~ ~ructure refineioonts in similar gamets(9).

2T 2E dxzdyz

29 I

dxv

(3d 1) 20

1:., t:..J..

free ion 2A1

2E dz2 29

cubic field dxlv2 tetragonal field

4+ l Fig. 4.5. Energy Level, saheme of V (3d ) ions on a tetrahedYa"l site

urith tetragonal, deforniation.

32

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As the ESR v4+ signal and the double band in the optical absorption

spectra appear and disappear simultaneously with reduction and reoxidation of the samples respectively, it seems natural to ascribe these features to the same centre. The observed"' 12000 an-1 and "' 13500 cm-1 absorptions are then assigned to transitions from the 2B1 ground state to the 2Bz and 2E levels. This assignment requires a crystal field parameter 10 Dq :{: 12000 cm-1 and a tetragonal field splitting of"' 1900 cm-

1• The above values are in agreement with those

reported by Weber(lO) for reduced vanaditm1. centres in Y3Al5o12 (YAG),

as shown in Table 4.3.

b~ . . . f d d d. • (lO) Ta ,,e 4.3. T:r.>ansi,ti,on ene:r.>gi,ee o :r.>e uae vana i,um aent:r.>es i,n YAG •

centre transition energy (10 cm-1) assignment

V + tetrahedral 12.5 2E +Zr 2

14.4 4+

V octahedral 20.2 2Tz + 2E

23.0

v3+ tetrahedral 8.0 3Az + 3rz

v3+ octahedral 16.3 3T1 + 3Tz

23.5 3T1 + 3T1

The ESR and optical absorption data can be correlated using oolecular orbital (M.O.) theory. Neglecting the usually small corrections due

to overlap integrals, the spin Hamiltonian parameters may be expressed as(ll):

gll = ge - (8;\ol3;2-y2 13;/l:,Q)

g4 = &e - (Z;\013;2-y2 13;z,yz/t,4)

and

A = -Pc c! + K) 132 . - Cg - g ) - 13 Cg - g ) J

ff ·1 ::c2"'y2 11 e 4 e

(2)

(3)

where 13 2 2, 13 , 13 are the fractions of d-like orbital in the ::c -y ::cy , ::cz,yz corresponding antibonding functions, ge = 2.0023 is the free-electron

33

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VI

""" Pab'le 4. 4. Ca'lcu'lated va'lues of PS2•

host lattice Ref. g II g...L IA11I IA.ti PS 2 (10-4 CJll-1)

c10-4an-1) (1o-4an-1) 8=1,A-'<O f3=1, A4 >0

A1P04 13 1.9168 1.9835 188 75 121 281

zncs2cso4)2.6H2o 14 1.935 1.986 182 73 119 178

MAG alum 15 1.939 1.976 174.2 67 118 165

Ge02 (amorphous) 16 1.929 1.976 175.5 68.2 117 165

Ge02 16 1.963 1.921 134 37 112 197

Ti02 17 1.956 1.914 142 37 121 207

SrTi03 18 1.9420 1.8945 146.8 44.0 117 218

ea.2.05Nao.60Mg2.11v2.99°12 this work 1.8569 1. 9801 152.8 31.9 122 186

ea1.94Nao.91Pbo.10Mg1.92v2.99°12 this work 1.8549 1.9785 150. 1 31.0 120 182

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spin g-factor, >.. = 248 cm-1 is the free-ion spin-orbit coupling constant(12), tJ. 11°and_ 8.Lare the optical transition energies indicated in Fig. 4. 5. IC is a term representing the Fenni contact interaction and Pis related to the average value of <r-3

>

for the free ion by

2$ µ P = -!Ji <r -3>

I

Taking~= 5.14 ~(6), I = 7/2 and <r-3> = 3.67 a.u:(l2), a theoretical estimate P = 172 x 10-4 cm-1 is obtained.

Elimination of IC from the hyperfine equations (3) yields

6 2 5 A,,- A.L.= -P[7 Sx2-y2 - (g,1 - ge) + T4 (g...l.- ge)]

(4)

(5)

Possible values of the coefficients a 2 2 are obtained by x -y ,xy,xz,yz

insertion of the spin Hamiltonian parameters (Table 4.2.) in Eqs. (5), (2). Since the computer fit to the e:xperimental data provides only the squares of the hyperfine parameters four possibilities have to be considered: A,,> 0, A.i_ < O; A 11 > 0, A.1. > O; A 11 < O; AJ..> O; A

11< O,

A.1. < 0. With A 11 > 0 negative values of a2 2 2 result, whereas

x -y the choices A 11 < 0 and A.1, > 0 or A /1 < 0 and A-1. < 0 result in either a_2 2 ~ 0.81 with S ~ 1.18 and$ ~ 0.97 or S 2 2 > 1. Such

w -y xy xz,yz x -y values of a are physically unrealistic as argued below. Therefore y4+ ESR data were gathered from the literature to obtain an e:xperimental estimate of P (cf. Table 4.4.). In what follows the M.O. coefficient of the

ground-state orbital appearing in equation (5) will be referred to as S because in the distorted octahedral sites also considered in Table 4.4. the ground state corresponds to a d orbital. For /J.g values of the order 0.1, the product PS2 is ra~r insensitive to the exact value chosen for a. The fact that p can only be positive reduces the sign possibilities to A 11 < O, A.J. < 0 and Ag < O, A.i_ > 0. The calcu­lated Pa2 values, assuming S = 1, for a number of tetragonal v4+ centres in different compounds are listed in Table 4.4. From the table we observe a striking correspondence between Pa2 values for v4+ in different compounds if it is assumed that Ag and A.1. are both negative. On the other hand the assumptions A 11 < 0, A..1.. > 0 lead to widely varying values of Pa2• If the maxilllllll value of Pa2 is considered to correspond to complete ionicity in the ground state, i.e. P =

122 x 10-4 cm-1, a recalculation of the M.O. coefficients yields

35

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0.92 < 6 < 1.0. Values close to one should indeed be expected because the selection of the ground state is essentially the result of the small interaction of the orbital conceni.ed with the surroundings(lO). M:>lecular orbital coefficients, obtained using P = 122 x 10-4 cm-1, band data and assignments are sun:marised in Table 4.5. The difference in transition energies between the two compoWlds, clearly demonstrates the reduction of the crystal field on enlargement of the lattice parameter (cf. Table 4.1.), whilst a marked difference between M.O. coefficients is not observed. Although the acruracy of the M.O. coefficients is limited by the inaccuracy of all other parameters involved in their determination, the above observation is felt to be indicative of the dimensional insensibility of M.O. coefficients.

However, the main conclusions to be drawn from these results are: (i) the assumption that the v4+ ion is situated at the tetrahedral sublattice is correct; (ii) the Fermi contact interaction contributes significantly to the hyperfine coupling parameters; (iii) the ground state may be regarded ionic whereas the 2E state has a higher degree of covalency. It is gratifying to note that the ionicity of the orbitals expressed by the 6-values shows the order expected from simple geometri­cal considerations.

4.5.2. Ootahedral v3+ To explain the absorption responsible for the reddish colour in the

Wltreated crystals grown from a v2o5 flux, the following possibilities will be considered: v3+ on octahedral sites, v3+ on tetrahedral sites and v4+ on octahedral sites. Optical absorption due to v3+ on tetrahedral sites should ocrur at energies lower than observed for v4

+ on tetrahedral sites. v4

+ on octahedral sites is expected to produce ESR signals at 4.2 K or even higher temperatures, considering the normally observed trigonal-field splittings. F-state ions like v3+ (3d2) in distorted octahedral synmetry do not produce ESR signals Wlder ordinary experimental conditions (S). The 3T1-state, which is the grOWld state in octahedral fields, is split by the axial field in a doublet and a singlet. Strong spin-orbit coupling between these states leads to a large zero-field splitting and a fast spin-lattice relaxation. Tlrus the Ms = :!: 1 levels are reiooved too far from the Ms = O state to permit observation of 6Ms = 1 transitions. fuuble quantum transitions may be observed, but fast spin-lattice

36

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Pabie 4.5. M.O. coefficients, band assignments and crystai-fieid parameters.

optical crystal field _1 compOlUld transition assignments parameters (cm )

ax2-y2 a. f3, K energy cubic tetrag. xy xz (103cm-1)

Caz.05Nao.6oMg2.11v2.99°12 11.9 2B1 + 2Bz 12200 2000 1.00 0.95 0.79 0.53

13.9 2B1 +

Ca1.94Na0.91Pb0.1~1.92v2.99°12 11.5 2B1 + 2B2 11800 1800 0.99 0.95 0.81 0.51

13.3 2B + 1

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relaxation makes it necessary to perfonn ESR measurements at 4 K or lower. Experimentally in the untreated crystals an optical absorption was observed in the region expected for v3+ on octahedral sites (cf.

Table 4.3), while ESR signals are absent. Therefore both v4+ on octa­hedral sites and tetrahedrally coordinated v3+ can be ruled out. An

energy level diagram for the 3d2 configuration of v3+ in octahedral sites is shown in Fig. 4.6(20). The proposed assignments and calculated crystal-field parameters are given in Table 4.6. In YAG: v3

+ the cor-

E/B 70

60 'T, •s 1T2

50 3T1

40 3T2 •A.

30

!T, --~--~~...._.__....._~__,

0 2 3 4 Oq/B

Fig. 4.6. Enez>gy levels of yS+ (Jd2J in an oatahed:r-al aZ'ystal field.

The best fit urith the expeZ'imental Z'esults is marked by a

dashed line.

responding transitions are f0tmd at 15800 on-1 and 23000 ~- 1 , in accordance with the smaller value of the lattice constantlin YAG (a

0 = 1.2000 nm) (21 ).

38

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TabZe 4.6. Optiaai data, assignments and aPysta.Z-fieZd pa:rametePB

of 0+ in oat;a.hed;mZ sites.

transition energy (1 o3Clll-1)

14

22

assigrunent

4. 5. 3. Po Za.I'onia absoPption

crystal field parameter_1 10 Dq (an )

15700

Racah parameter B (encl)

640

Apart from the double band near 12000 cm - l , an absorption peak is observed with a maximum at about 19500 an - l (2. 4 eV) • This broad peak cannot be assigned to crystal-field transitions. However, the fact that the v4+ crystal-field transitions and this broad absorption band appear and disappear sinn..tltaneously with reduction and reoxidation of the crystals respectively, does suggest that these features belong to the same centre. As argued in chapters III and VI the y4+ centres in ca2NaMg2V3o12 11U.1St be considered as small polarons. In that case a broad absorption band due to ''photon-assisted hopping" is expected at

I

energies: w = 41b + A (cf. par. 3.6.) where~ is the activation energy for electron hops between sites situated on energetically equivalent positions and A represents the energy differences caused by defect interactions. Assuming the minimum activation energy observed in the conductivity experiments, 0.26 eV (chapter VI), to be close to~.

·optical absorption should occur at w"' 8400 + A(Clll-l). The maximum

in optical absorption thus corresponds to site energy differences due to defect interactions of 11000 an-1 "' 1.36 eV. For comparison it is remarked that in neodymium doped yttrium aluminium garnet, Y3AI5o12 (Nd), an opti­cal absorption band centered at 2.35 eV and several eVwide has been attributed to polarons(22).

4.6. Disaussion

The compositions of the flux-grown crystals and the polycrystalline material differ considerably in the occupation of the octahedral and dodecahedral sublattices. To obtain the figures stated in Table 4.1.

39

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the composition of the polycrystalline material has been asstuned to correspond to the weighed stoichiometric fractions, which seems realistic in view of the low temperature of synthesis. This asslDllP­tion is supported by the good correlation between the different experimental results. The calrulated x-ray densities of the single crystals, using the compositions and lattice parameters detennined, agree well with the measured values. The total cationic charge is equal to twenty four within experimental error if the vanadium ions are present in the highest oxidation state. In crystals, grown from PbO fluxes, no reduced vanadium centres could be detected. The. results of optical absorption neasurements and electron microprobe analysis indicate the amotmt of triply charged vanadium present in crystals grown from v2o5-fluxes to be small. Therefore, in agreement with observations made by Ronniger et a1C23), it is concluded that in these garnets, as grown, the tetrahedral sublattice is mainly occupied by v5+ ions and any surplus of doubly charged ions is compen­sated by vacancies in the c and a sublattices i.e. the crystals used for this study have a composition:

{caz.osNl:lo.6~0.11°0.24 1 [Mg21 CV2.99)012 and

{ca1.94Nl:lo.91Pho.10°o.os1 (Mg1.92ao.os1 CVz.99J012 respectively.

In contrast to the results obtained in this study, Desvignes et al(Z4) have reported a large excess of vanaditun, 0.17 - 0.27 V per fol1lllla unit, to occur in this garnet, when grown from fluxes with similar compositions. To achieve charge balance in that case, a considerable quantity of reduced vanadium centres must be present, leading to optical absorptions in the visible region. Their assigmoont of bands seen at 18900 an-1 and 20000 an-1 to trivalent vanadilDll. at tetrahedral sites is incompatible with the interpretation of spectral data given in the previous sections. If, however, the absorptions are attributed to fourvalent vanadium at octahedral sites reasonable agreement is attained. The centre is then characteri­sed by a cubic splitting of 10 Dq % 19000 cm-1 and .a trigonal splitting of 1000 an - l . In comparison with YAG the bands are shifted towards lower energy due to the difference in lattice parameter and because in vanadate garnets the octahedral sites are al.Joost regular, the trigonal splitting is sma.11(9).

However, a large amount of the vanadium content reported by Desvignes

40

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et al might be due to the calculation procedure, since the total number of cations has been normalised to eight, which is incorrect if a vacancy mechanism occurs.

Some remarks should be made with regard to the difference between the P value of 172. 1 o-4 on - 1 predicted by Eq. ( 4) and the experimentally determined value of 122.10-4cm-1• The Hartree-Fock wave functions used by Malli et alC25) to calculate <r-3> are known to yield theoretical values of interaction constants that approximate the measured ones to within :!: 5% for the free ions. The discrepancy observed obviously exceeds these limits and nD.lSt have a physical origin. Q.iite probably the reduction of P reflects the extension of the wave :ftmction in the solid state. The same conclusion may be drawn from the results of a IJX)re complete description of y4+ centres in this and other garnets by I. Veltrusky(26). Although the analysis of Veltrusky was complicated by the fact that a number of additional M.O. coefficients had to be evaluated from the same experimental spin Hamiltonian parameters, and optical data were not available in many cases, a consistent set of ion para­meters like A, K etc was calculated using an iterative procedure. In his treatment the radial integral <r-3> and the spin-orbit coupling constant were used as adjustable variables. The best fit was obtained using a spin-,.orbit coupling constant hardly different from the free-ion value and a value of <r-3> of 1. 79 10-23

cm-3, i.e. P = 124 x 10-4 on-1, very close to our value. The strong rise in optical absorption above 25000 cm-1

has not been discussed so far. Because the absorption edge is also present in samples without y4+ centres it nD.lSt be attributed to v5+ ions. The origin of this absorption will be reconsidered in

. var 5.3. and par.5.4. where optical reflection measurements are disOJSsed.

Finally it is noted that the stoichiometric melting point, mentioned in the literature(1), is contradicted by the perfonned thennogravimetric experiments.

4.7. Conclusions

The Ca2NaMg2v3-012 single crystals contain a large concentration of vacancies on dodecahedral and octahedral sublattices. Some

lead, rv 4 wt%, is incorporated in the single crystals grown from

41

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PbO-fluxes. In the single crystals grown from v2o5 fluxes a small concentration of y3+ on octahedral sites is responsible for their reddish colour.

At high temperatures a reversible weight lossoccurs, which is accompanied by the fonnation of y4+ ions at tetrahedral sites. The optical transitions, interpreted in a crystal-field scheme, can be correlated to the ESR parameters, by means of M.O. theory, if a reduced value of the hyperfine interaction is used. The justification therefore is illustrated by the available literature data.

The y4+ centres also give rise to a broad polaronic absorption band, extending over the entire visible spectral region, with a maximum at rv 19000 on - 1 •

REFERENCES

1. V. Havlicek, P. Novak and M. Vichr, Phys. Stat. Sol. 044 K21 (1971).

2. A. Durif, "Int. conf. on phys. of the solid state and applications to electronics and teleconmmications", Brussels, Belgium, p. 500 (1958).

3. G. Ronniger, B. V. Mill and V. I. Sokolov, Sov. Phys. Crystallogr. _11, 219 (1974).

4. G. Ronniger and B.V. Mill, Sov. Phys. Crystallogr. _!!, 339 (1973). 5. D. Prokic, J. Phys. D.: Appl. Phys.'!_, 1873 (1974), 6. A. Abragam and B. Bleaney, "Electron paramagnetic resonance of

transition ions" (Oxford, Clarendon) p 167, p 416 (1970). 7. S. Geller, Z. Krist. 12S, 1 (1967). 8. J.E. Wertz and J.R. Bolton, "Electron spin resonance: elementary

theory and practical applications" (New York, Mc Graw-Hill) p. 287, p 277, p 329 (1972).

9. E.L. Dukhovskaya and B.V. Mill, Sov. Phys. Crystallogr. _11, 47 (1974).

10. M.J. Weber and L.A. Riseberg, J. Chem. Phys. SS, 2032 (1971). 11. D. Kivelson and R. Neiman, J. Chem. Phys. 1~9 (1961) • 12. S. Fraga, J. Karwowski and K.M.S. Saxena, ''Handbook of atomic

data" (New York, Elsevier) p 489 (1976) • 13. R.S. De Biasi, J, Phys. C.: Solid St. Phys.~, 6235 (1980). 14. V.K. Jain and T.M. Srinivasan, Z. Naturforsch a32, 1068 (1977). 1S. K.V.S. Rao, M. Dattatreya Sastry and Putcha Venkateswarlu,

J. Chem. Phys. ~. 812 (1969).

42

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16. I. Siegel, Phys. Rev. a134, 193 (1964) •

17. H.J. Gerritsen and H.R. Lewis, Phys. Rev. 119, 1010 (1960),

18. Th.W. Kool and M. Glasbeek, Solid St. Coll11l. 32, 1099 (1979).

19. D.S. Mc Clure, ''Electronic spectra of molerules and ions in

crystals" (New York, Academic) p 90 (1959).

20. S. Sugano, Y. Tanabe and H. Kamimura, ''Multiplets of transition-

metal ions in crystals" (New York, Academic) p 108 (1970).

21. F. Euler and J.A. Bruce, Acta Crystallogr • .!.Q., 971 (1965).

22. K. Cermlik, Czech. J, Phys. b31, 1172 (1981).

23. G. Ronniger and B.V. Mill, Sov. Phys. Crystallogr. ~. 187 (1973).

24. J.M. Desvignes, P. Feldman and H. Le Gall, J. Cryst. Growth

52. 650 (1981) '

25. G. Malli and S. Fraga, Theoret. Chim. Acta2_, 75 (1967).

26. I. Veltrusky, Czech. J. Phys. b28, 675 (1978).

43

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rnAPTER v

PHOI'OINDUCED REDUCTION OF v4+ ESR SIGNAL INTENSI1Y IN Ca2NaMg2v3o12 GARNET

5.1. Introduction

In the previous chapter it was demonstrated that a number of v4+ centres can be introduced in {Ca2Na} [Mg2] (V3)o12 garnet by a heat treatment at elevated temperatures. The localised character of these centres is proved by the observed ESR signals and optical crystal-field transitions. Further, a wide optical absorption band, extending over the entire visible spectral region, has been attributed to a light-induced electron transport within the vanadiwn sublattice. Since light-induced electron transitions between ions on different lattice sites are considered to be the origin of the reported photo­magnetic effects in many materials, and the v4+ centres are directly observed by means of ESR spectrometry, the investigation of possible photoinduced changes of the ESR signal seems a natural extension of the above research. Evidently additional infonnation in this respect can be expected from photoconductivity experiments.

In this chapter photoinduced changes in the v4+ ESR signal inten­sity are reported together with the results of photoconductivity and optical reflectance measurements. Section 5.2. gives experimental details. In section 5.3. some characteristics of the ESR photosensi­tivity, the optical reflectance and photoconductivity spectra are presented. The results are compared and discussed in relation to the literature in section 5.4. and the conclusions drawn are sunmarised in section 5.5.

5.2. Experimental details

Ca2NaMg2v3o12 single crystals were obtained from PbO and v2o5 fluxes. Polycrystalline material was prepared by solid state reaction. The v4+ centres were introduced by a heat treatment at "' 1130°C in air followed by an air quench to room t~eratute. Details concerning the preparation conditions and the ESR equipment have been given before (cf. par. 4.2.). Illring the illumination experiments light emitted by a 200W xenon lamp was focused on a dedicated Tl 02 measurement cavity.

44

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'.Che pho.toconductivity experiments were perfonned in a home-made cryostat operating at a fixed temperature. For the experiments reported here a temperature of 19SK, achieved by filling the cryostat with a dry-ice/acetone mixture, was suitable. The plane-parallel

polished single crystals were spring moi.mted in an Al2o3 insulated sample holder. Good electrical contact was achieved by silver­painted electrodes. Light emitted by a 450W xenon lamp was dispersed through Bausch and

Lomb high-intensity gratings and focused on the crystals in a direction perpendicular to the electric field, a mask preventing illumination of the contacts. In the visible spectral region UV

filters were employed to eliminate short-wavelength stray light. The current was measured with a Cary 401 vibrating-reed electrometer. The source consisted of a set of batteries that supplied voltages 0-300V. ilirrents as small as 10-15 A could be reliably measured.

The 45° reflectance spectra were recorded at room temperature with a Zeiss PJl.Q II spectrometer equipped with a RA2 reflectance i.mit. The

optical density was measured relative to a sodium fluoride standard.

5.J. Results

5.J.1. Photoaensitivity of the v4+ ESR signais

The v51 isotope with ruclear spin I = 7/2 has a natural abtmdance of 99. 76%. The y4+ ESR signals correspond to a S = L I = 7/2 centre

in tetragonal S}'llliletry (cf. par. 4.5.1.). The same centre causes optical absorption at .\,;13000 cm-1 due to 2B1 + 2B2, 2E crystal-field

transitions (cf. par. 4.5.1.). Photoinduced transitions of the electron between vanadium fons on different lattice sites result in an absorption band between 10000-25000 cm-1 with a maximum at 19000 an-1

(cf. par. 4.5.3.). It was observed that the measured ESR signal intensity decreased upon irradiation, while the line width and the line shape did not change.

Several features of this photoinduced effect - temperature dependence,

wavelength dependence, etc - will be outlined below.

The signal intensity reduction attained and the shape of the decay curve is the same for each hyperfine line and independent of the orientation of the magnetic field. In the temperature range 77-190K the intensity reduction decreases only slightly towards higher temperatures.

45

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Large differences in the reduction factor may exist however between different single crystals as is illustrated by figure 5. 1. , where two typical decay curves measured at 140K are shown •

"' t: QI

t:

l I I \ \ l

' ' I

\

f \ ' \

• I

l 1ght .... , on ",,

0

I I

',~ ; ...... _ I .. ________ ..J

2

time lmins.l

I I

I I

I

I I

I I

I

I I

I I

I

/ /

//,-'

/

4

.. ..,, ....... -

Fig. 5.1. Deaa:y aurves of v4+ ESR signal intensity in CafVaMg2v3o12 single arystals grObJn from v2o5 and PbO fluzes (see text).

Full aurve: {Cal. 94Nao. 91Pb 0.10 a o. 05} [Mgl. 92°0. 08 1(V2.99)012;

broken aUPVe: {Ca2.05Nao.6oAfgo.11°0.24}[Mg2](V2.99)012·

The height of the derivative signal of the first low field line S = ~. M1 = -7/2, when the magnetic field direction is along the tetragonal axis, is recorded as a function of time. The relative starting intensities of both lines have been normalised to one. COmparison of the curves relative to one another reveals that the maxinrum signal intensity reduction obtainable and the shape of the recovery curve are different for the two crystals. The difference in composition quoted in the figure caption is probably not responsible for the observed changes because even greater differences have been observed between crystals (non-oriented) grown from the same fluxJ Unfortunately the measurements performed at liquid helium temperature all concerned crystals which exhibited only a small, but stiH reversible, effect. Using Schott glass filters it was established that only light in

46

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the spectral region 10000-15000 an-1 was effective. Furthennore. it should be remarked that during illumination no other ESR signal could be detected in the field range 0-10 kG.

5.J.2. Photoaonductivity and refieatanae speatra

In figure 5.2. the room temperature reflectance spectra from ca2Na.Mg2v3o12 powders are shown together with the photoconductivity results obtained at 195K. This temperature was chosen because at 300K the photocurrents were too small to be detected as a function of wavelength, while at 77K only electrical polarisation effects could be measured due to the high resistance of the crystals. The resistance of the crystals at 195K was of the order 1016 ohm. The dark a.irrents were always at least one order of magnitude smaller than the maximum photocurrents and exhibited linear voltage characteristics.

1.2 ...-~~~~~~~~~~~~~~~~~-, m

.... m c: 0.8 QI

't:l -ltl u 0.4

a. 0

0 ----10

---/

/ __ ...

- --.: ....

-2 0 30 40

wavenumber l 1 o3c m-1 l

' ' \

50

-c: :::> .d .... ltl ...... -c: QI ... .... :::> u 0 -0 .c a.

Fig. 5.2. Photoaonductivity and powder refieatanae speatra of

· Ca2NaMg2v3o12. FuU aurve: after reduation;

broken aurve: before reduation.

Because no essential differences were observed neither between crystals grown from different fluxes nor before or after heat treatment, only one curve is shown. The plotted curve represents the current corrected for variations in the 18llq) intensity in quanta/wavenumber. The magnitude of the correction factor increases rapidly above 44000 an-1• The corresponding part of the photoconductivity curve,

47

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which is the product of the decreasing photocurrent and the increasing correction factor, therefore, becomes proportionally uncertain (dotted curve). Deliberate illumination of the electrical contacts did not change the observed behaviour. The photocurrents were proportional to the light intensity, I 'V GY with y = 1, where I is the photocurrent and G is the incident light intensity (Fig. 5.3.).

<(

.... z ·13 UJ10 a:: a:: ::> u 0 .... ·14 4 010 :r CL

10 100 L I G HT INT ENS I TV (0/o}

Fig. 5.3. Light intensity dependenae of the photoeurrent:

1) 150V, 240 nm 2) 150V, 200 nm 3) 50V, total lamp

speatrwn 4) 150V, total lamp apeatrum.

The reflectance spectra nicely reproduce the results previously obtained in transmission experiments on single crystals in the range 10000-26000 an-1• Partial reduction of the powder causes an increased absorption in the entire spectral region and the bands, due to v4+ crystal-field transitions, at 'V 13000 an-l are re-observed. The new infonnation obtainable from the reflectance spectra concel11S the wavelength range 400-200 run where transmittance measurements are impossible due to the high absorbance of the crystals. Th~ reported intrinsic absorption edge at 'V 26000 cm-l appears to be the side of a band peaked at 'V 29000 cm-1• A second maximum is seen at 'V

43000 an-1•

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5.4. Discussion

Photoeffects of the type to be discussed, have been observed in several magnetic compounds(1). Prior to a discussion of the results obtained with the vanadilUll garnet the physical mechanism of these photoinduced changes will be explained on the basis of observations made on partially reduced or Si-doped Y3Fe5o1z. Charge compensation in this material occurs by Fez+ centres and the electrical transport properties at low temperatures are described in tenns of thennally activated hopping of electrons between Fe ions. Many of the photoinduced changes observed in YIG concern the magnetic properties. They have been divided in two groups, class I respectively class II effects. Class I effects are observed in saturating magnetic fields and depend on the field direction relative to the crystal synmetry axes. Class II effects occur in low or zero magnetic fields and are independent of the direction of the field. The latter may also be observed in polycrystalline samples. Large differences have been reported with regard to the time scale and the temperature at which the experiments were perfonned. Teale et al(Z) have measured the ferromagnetic resonance field of Si-doped YIG single crystals as a flmction of Si content and temperature. Their results indicate that even at 4.ZK only a small fraction~ O.Z5 of the Fe2+ ions are frozen in their sites for longer than 5 minutes. On

the other hand changes in the initial magnetic penneability reported by Enz et al(3) are persistent at 77K. A phenomenological two-centre model was shown to fit the experimental data(4). Recently Wurlitzer and Franke C5) have argued that at least three types of sites are needed to explain the photomagnetic changes observed in polycrystalline YIG (Si). However, as is clearly revealed by e.g. dielectric loss measurements, these models are an oversimplification of the real situation because in practice the electrons are not distributed over just two or three types of sites. In fact a wide distribution of relaxation times exists(6). To account for this observation the model has been adapted(?)_ Although the new model only gives a qualitative description, it has the advantage that it also includes class I effects. In the extended model it is assumed that a range of grotmd­state energies of Fez+ ions, corresponding to different distances be­tween the centre and the lattice defects Si, v0 etc., characterises the system. In that case a measured relaxation time will be an average

49

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value weighted with the distribution of ferrous ions over the lattice at the temperature of measurement. The differences observ'.ed, are thus atrributed to differently situated electrons. Dedukh et al(S) have investigated the photomagnetic effect in irra-

diated and plastically deformed,undoped YIG single crystals. They

concluded, in line with the model state above, that YIG single crystals contain an inhomogeneous system of electron centres whose state can be altered by various types of electromagnetic radiation.

In the following the photoinduced intensity reduction of the v4+ ESR signal will be discussed. Although several questions regarding the detailed mechanism have to remain unanswered, certain similarities with the photoinduced changes encountered in YIG are obvious. Firstly, the effect observ'.ed must involve electron transport through the lattice because relaxations within the v4+ centre with a decay time of the order of mirrutes are physically unreasonable. Secondly, the di~ferences observed between samples from the same batch, in which no differences in composition were detected, must be due to the quenching procedure or be related to natural variables in flux-grown crystals such as dislocation density. The quenching procedure was not standardised. The crystals were removed from the furnace and allowed to cool in air. In this way the temperature interv'.al 1130-zo0 c was bridged in a few minutes. The conductivity experiments reported in chapter VI have revealed that v4+ centres are also fomed by annealing the samples at low oxygen partial

]:!ressures at "176ooc. The measured activation energies appeared to be a function of both the concentration of v4+ centres and the thermal history of the samples. It is thus evident that for crystals differing in size and geometry the above quenching procedure will result in variations in the concentration of v4+ centres and the distribution of vacancies. . Bacause of practical reasons the ESR experiments have been perfomed in a single cavity without DPPH intensity standard. The cal­culated intensities for different samples in that case are only a rough indication of the relative concentrations of centres. A correlation between the estimated concentrations and the magnitude of the photo­induced intensity reduction was not found. It is concluded that the Ca*NaMg2v3o12 single crystals contain an inhomogeneous system of v4 centres where concentration and distribution play a major role in the occurrence of the photoinduced intensity reduction. This conclusion is further substantiated by the inhomogeneous broadening

50

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of resonance lines that was first observed and thoroughly studied by Havlicek and Novak(9) and reproduced in our experiments. They suggested the source of this inhomogeneity to be the random distribution of Ca and Na ions over the dodecahedral sublattice. Indeed, recently reported NMR experiments on ca2NaMg2v3o12 samples have ascertained the existence of at least two types of y5+ ions(lO) due to differences in the local dodecahedral sublattice occupations. The above results indicate, however, that such a distribution alone cannot account for the observed behaviour and concentration-dependent tenns must be invoked in the description of the system. To account for the fact that during illumination no other ESR signal is detected two explanations will be considered. The electrons respon­sible for the intensity reduction are either moving too fast to be detected or are trapped in a diamagnetic state. Bipolaron fonnation is a well established phenomenon in various vanaditllll oxides(11 •12 •13l. However, there are two reasons to reject this mechanism in the present case. In the first place an electron-electron coupling of this kind may be expected to be strongly dependent on the distance between nearest vanaditllll ions. In the garnet this distance is far greater ('\J 0. 38 nm) than in the vanaditml oxides ('\J 0.29 mn). The second reason is the observed behaviour of the effect with temperature: namely, a certain stabilization energy has to be associated with the fonnation of bipolarons which is either large, so that the changes can be frozen in, or suffi­ciently small to result in a strong temperature dependence, neither of which occurs. Therefore the following process is assumed to represent best the actual situation: the energy absorbed in the optical transitions is sufficient to detach the electron from the vanaditml ion concerned and subsequently it wanders through the lattice at a rate high compared with the ESR resonant frequency until a vanaditml ion situated suitably for retrapping is encountered. Such a process is in agreement with the reversibility of the photoinduced changes observed. It is also concordant with the polaronic nature of the v4+ centres indicated by the observed optical absorption band (cf. par. 4. 5. 3.) and the results of conductivity and thennoelectric power experiments (cf. chapter VI). If polaron.s are concerned, the existence of a polaron band regime is to be expected at temperatures ~le, where e is the Debye temperature (cf. par. 3.3.). The width of this conduction band is little temperature dependent as long

51

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as the thennal energy is insufficient to notably excite optical phonons(14 •15). Generally optical phonon absorption is found at wavenumbers > 100 an-1 (0.012 eV) (cf. also par. 6. • where an infrared absorption spectrum of ca2NaMg2v3o12 is shown); i.e. appreciable changes in bandwidth do not occur below 150 K. Thus. in the temperature region where the photosensitivity experiments have been perfonned. 77-190K, the electron velocity in the polaron conduction band is nearly temperature independent, accounting for the nearly temperature indepen­dent decay time. Further it should be noted that the invocation of the polaron-band concept in the explanation of the photoinduced effects imposes additional constraints on the concentration and distribution of centres since disturbances of the lattice periodicity tend to wipe out the polaron band regime (cf. par. 3.5.).

Due to the overlap of the v4+ crystal-field absorptions and the tail of the polaronic absorption band it is impossible to decide which absorption causes the photoinduced effects. Polaronic transitions by definition involve different lattice sites, but also crystal-field transitions can induce electron transport (see below). First however. it will be considered why the optical transitions at wavenumbers > 15000 cm-1 • in the high energy part of the polaron absorption band. seem to be ineffective. A probable explanation is fmmd in the fact that the ESR signal is a bulk signal. Because of the increased absorption at higher wavenumbers, the penetration depth of the radiation decreases and therewith the number of active centres excited. where it is important to note that apparently only part of the photoinduced electron transfers result in observable changes since no changes in line shape were observed; in other words. the available light quanta are consumed by ineffective transitions between well localised centres whereas active centres cannot be reached. In the case of Si-doped YIG this effect is demonstrated by comparing the sensitivity of bulk crystals and thin films. In bulk crystals a maximum sensitivity occurs at ~ 8000 cm-1 (l) whereas in thin films the sensitivity is fol.Illd to increase continuously up to 20000 cm-l(l 6).

Returning to the crystal-field transitions. it is not clear at present how these transitions can bring about electron transport but in case of Cdcr2s4 and YIG such transport has been ascertained by the observation of photo-currents after excitation in the crystal-field levels of chromitm1 and iron respectivelyC17 •18).

52

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The photoconductivity experiments reported here, failed to provide a definite proof of the electron transport initiated by excitation in the v4+ crystal-field transitions. Instead small photocurrents "' 10"13 A were detected under ilh.nnina­tion at wavenumbers > 35000 an"1• There is ample evidence that the absorption in the region 25000-50000 an"1 must be attributed to the vanadate groups in the lattice. Blasse and Bril(l9) have studied the fluorescence of Eu3+-activated

CazNaMg2v3o12 where excitation in the vanadate groups is followed by energy transfer to the Pu3+ ion and subsequent emission of the characteristic Eu3+ spectrum. The excitation spectrum consisted of a broad band ranging from 25000-50000 an"1 with a maximLnn at "'29000 cm-1• In the reflectance spectrum reported here two maxima occur at 29000 and 43000 cm - l • The absorption spectrum of V 2o5 also contains two maxima"' 12000 cm"1 apart at 25000 and 37000 cm1-, while in Cao and MgO absorption starts at wavenumbers > 50000 crii 1 C20 • 21) •

In agreement with the relative magnitudes of the V-0 distances "'0.16 run in v2o5 and"' 0.19 run in the garnet, the bands are shifted to higher energies. M::>reover, the crystalfield splitting of the vana­ditun 3d levels is"' 12000 an"1 (cf. Table 4.5.). Therefore the maxima

in the reflectance spectrum at "' 29000 cm"3 and "' 43000 cm-1 are due to transitions from the oxygen 2p band to the vanadil.Dll 3d levels. Because of the localised character of these levels such transitions do not induce photoconductivity. The onset of photoconductivity at wavenumbers > 35000 cm"1 is attributed to electron transfer from the oxygen 2p band to the rela­tively broad vanaditun 4s band.

The dependence of the photocurrent on the light intensity has been calculated for some simple model systems(22). Considering an

insulator where Iphoto » Idark' as for CazNaMg2v3o12 , a linear dependence of the photocurrent on the light intensity is fmmd in the case of one-carrier transport in the presence of traps. Such a model agrees well with the inhomogeneous distribution of v4+ centres indicated by the ESR experiments.

f5.f5. Conatusions

When reduced Ca2NaMg2v3o12 is irradiated with light in the wave­length region 1000-600 run photoinduced changes in the v4+ ESR signal

53

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occur. These changes are analogous to photomagnetic effects in Y3Fe5o12 , in this respect that in both cases the effects are caused by photo­induced electron transfer between differently situated transition metal ions. The additional requirement in the case of the vanadate garnet is that the transfer must be towards a vanadium ion representing a delocalised polaron band state to be observable as a reduction of the v4+ ESR signal intensity.

Excitation in the oxygen (2p)-vanadium (4s) charge-transfer band produces a small photocurrent. Its dependence on the light intensity may be described by a one-carrier insulator model with traps.

REFERENCES

1. R. Metselaar, "Interaction of radiation with condensed matter" (Vienna, I.A.E.A.) Vol. II, p 159 (1977).

2. R. Teale, D.W. Temple and D.I. Weatherley, J. Phys. C.: Solid State Phys. ~. 1376 (1970).

3. U. Enz, W. Lems, R. Metselaar, P.J. Rijnierse and R.W. Teale, IEEE Trans-Magnetics MAG-5, 467 (1969).

4. W. Lems, R. Metselaar, P.J. Rijnierse and U. Enz, J. Appl. Phys • .!!_, 1248 (1970).

5. M. Wurlitzer and J. Franke, Phys. Stat. Sol. a64, 539 (1981) 6. C. Crevecoeur, unpublished (1969). 7. U. Enz, R. Metselaar and P.J. Rijnierse,J. Phys. Colloq. 32~ C1-703

(1971). 8. I.M. Dedukh, J.P. Kabanov and A.A. Polyanskii, Sov. Phys. Solid

State 22, 225 (1980). 9. V. Havlicek and P. Novak, Czech. J. Phys. b24, 188 (1974).

10. M. W6jcik, H. Le Gall and J.M. Desvignes, Phys. Stat. Sol. b112, 483 (1982).

11. T. Kawakubo, S. Kabashima and T. Goto, "Conduction in low mobility materials", eds. N. Klein, D.S. Tannhauser and M. Pollak (London, Taylor & Francis) p 101 (1971),

12. B.K. Chakraverty, M.J. Sienko and J. Bonnerot, Phys. Rev. b7, 3781 (1978).

13. T. Takahashi and M. Nagasawa, Solid State Comm. 39, 1125 (1981). 14. D. Adler, 1'Handbook on semiconductors", Vol. I ed. W. Paul

(New York, North-Holland) p 805 (1982). 15. A.J. Bosman and H.J. van Daal, Adv. Phys. ~. 1 (1970).

54

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16. R. Metselaar, M.A.H. Huyberts and H. Logmans, J. Appl. Phys. 46, 3171 (197S).

17. P.K. Larsen and S. Wittekoek, Phys. Rev. Lett. 29, 1S97 (1972). 18. R. Suryanarayanan and R. Krishnan, Phys. Stat. Sol. a22, K177 (1974). 19. G. Blasse and A. Bril, J. Electrochem. Soc.: Solid State Science

..!!j_, 2SO (1967). 20. D.C. Conlon and W.P. Doyle, J. Chem. Phys. 3S, 7S2 (1961). 21. V.I. Neeley and J.C. Kemp, J. Phys. Chem. Solids 24, 1301 (1963). 22. R.H. Bube, "Photoconductivity of solids" (New York, Wiley) p 72

(1960).

SS

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rn:API'.ER VI

6.1. Introduation

Concluding the chapters devoted to investigations of ea2NaMg2v3o12_x garnet this chapter deals with the influence of v4+ centres, introduced by a reduction reaction, on the electrical conductivity. E\ridently, a study of the charge transport properties of Ca2NaMg2v3o12_x should confinn the spatial localization of the surplus electrons on the vanadium sublattice, as indicated by the results from ESR and optical absorption measurements discussed in the chapters IV and V. Important information with respect to the charge transport mechanism may be obtained from the combined results of conductivity and theTillO­electric power measurements (cf. chapter III)(l, 2). Since conductivity is determined by the product of the number of charge carriers and their mobility and the thennopower is solely dependent on the :rrumber of charge carriers the mobility can be inferred from such measurements. This quantity is experimentally difficult to access directly. In low-mobility materials the use of theTillOpower measurements to evaluate the carrier concentration is advantageous in comparison with Hall-effect measurements, because the theTillOvol tage is measured nnder "zero-current" conditions. Thus the velocity of the carrier does not affect the signal magnitude. On the other hand the magnitude of the Hall-voltage is proportional to the carrier velocity resulting in small signals for small mobilities. Unfortunately the measurements of theTillOpower and conductivity of par­tially reduced ea2NaMg2v3o12_x reported in this chapter, are limited to temperatures above ambient due to the high resistivity of the samples.

In section 6.2. the preparation of reduced samples is described. Section 6.3. gives experimental details and the results are presented and diso.issed in relation to the literature in section 6.4. The con­clusions drawn are StnmJarised in section 6.5.

6.2. Preparation of partially reduaed samples

Apart from the infrared spectra, that were measured on powders, all the results reported in par. 6.4. were obtained on two of the largest single crystals grown from PbO and V 2o5 fluxes with dimensions of

56

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"-' 4x4x5 and 4:ic4x3 l1Bll3 respectively. The preparation and characterisa­

tion of powder and single crystals were discussed in chapter IV (par. 4.2.), where it was also noted that in the as-grown single

4+ crystals no V centres could be detected by means of ESR spectro-metry (par. 4.4.2.). Therefore the crystals were subjected to a reduction treatment at elevated temperatures in air or CO/co2 gas mixtures and subsequently quenched to room temperature (cf. Table 6.1.).

Table 6.1. l'ret:r-eatment aonditions (see text).

sample flux number composition

1Ca2NaMg2V3012 + 1.2 PbO

2 II

3 " 4 II

5 ft

6 II

7 II

8 " 9 1ca2NaMg2V3012

+ 1.2 v2o5 10 ti

quenching rate

as grown cf. par. 4.2.

fast + partially reoxidised at 1oooc medium

medium

slow

fast

slow

medium

. as .2l'O'Wil

cf. par. 4.2.

fast

temperature (OC)

1130

760

760

775

1130

775

760

1130

log Po2 (Pa)

+4.3

-11.3

-10.5

+4.3

-14.7

+4.3

At first the crystals were heated for "' 15 rnins. at 1130°c in air followed by an air quench to room temperature (fast quench, cf. also par. 4.2.). However, the photosensitivity experiments indicated a marked influence of the thennal history of the crystals on the observed physical properties (cf. par. 5.4.). Therefore it was attempted to standardise the pretreatment conditions by performing the

57

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reduction reaction in the conductivity cell in a CD/m2 atmosphere.

The relative large thennal mass in that case imposes slow quenching

rates and to avoid carbon deposition the m;m2 mixture had to be

replaced by purified argon before quenching. Finally some reduction experiments were perfonned in a Setaram type MTB 10-8 microbalance

(medium quenching rate). The samples were equilibrated to constant

weight in an oxygen atmosphere at 76o0 c. Although often reversible

and reproducible weight changes of the order of 10-200 µg were recorded after changing the oxygen partial pressure

in one nm., the results obtained with remounted samples were inco­

herent. The observed weight changes for single crystals and powder

also showed differences. No weight changes were observed after

replacement of o2 by N2• Since little experience has yet been

attained in our laboratory with the application of this microbalance

in the measurement of small defect concentrations, the correspondence

between the apparent weight loss and the oxygen deficiency is uncert~in.

A continuing weight loss at very low oxygen partial pressures

indicates the onset of sample decomposition. At weight losses ~ O. 2

wt% no steady state was attained which allows an estimation of an

upper limit for the oxygen deficiency in Ca2NaMg2v3o12_x of x ~ 5 x 10-2•

6.3. Experimental details

The quenched single crystals were spring-mounted between

platinum electrodes in an alumina sample holder with an ejnpty

cell resistance of~ 1011 n at room temperature. Good electrical

contact was achieved by platinum painting of the contact areas (Leitplatin 308A Demetron). Most of the conductivity measurements

have been perfonned with a Keithley 616 Digital Electrometer opera­ting in the resistance mode. Occasionally the systems were checked

for frequency dispersion in the range 0.05-104 Hz with a Solartron

Frequency Response Analyser 1174. The sample holder was furnished

with two platinum wire resistance heating elements, that could be

independently controlled, to supply the temperature gradient for

the thennopower measurements. Using two heating blocks the average

temperature is easily maintained constant within + 1°c, while also

the ~T range is effectively doubled without increase of ~Tmax because

58

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the temperatures can be inverted. The thennal response of the system is such that a few minutes after a change of settings the thenno­couple readings have stabilised within 1 µV •• To assure good corres­pondence, thermopower and conductivity measurements were performed directly after one another. The Seebeck coefficients were calculated by a least squares analysis from plots of AV versus AT consisting of 8 data points and the maximum temperature difference employed was limited to "' 10°c. These plots were linear and with an uncer­tainty of :!: 1°c always went through the origin apart from exceptions at high temperatures which are explicitly discussed in the following section. At low temperatures the measurement range is limited by the sample resistance. At resistance values higher than "' 5x106 olnn electrical noise caused by the heating coils and spurious voltages inevitably present, lead to erratic results. The reported Seebeck coefficients are not affected by the heating currents since operating the system at the scima average temperature but 3ooc ~espectively 1500C above the temperature of the main furnace resulted in identical thermopower values. To prevent reoxidation of the samples the cell was continuously purged with purified argon and the measurements were performed with increasing temperature contrary to COJJllDn practice. Infrared lattice spectra were recorded in the 100-1000 crn-1 region, using a Bruker Infrared Fouriertransform Spectrometer IFS. For the region 100-700 crn-1 the finely divided powder samples were embedded in polyethylene, for the 400-1000 crn-1 region the samples were embedded in KBr pressed pellets.

6.4. Resuits and disaussion

The samples exhibited linear current-voltage characteristics, for voltages 10-3-10 V, and no frequency dispersion of the conductivity was observed in the region 0.05-104 Hz. Therefore the experimental data are assumed to correspond to electronic bulk conductivities. In Figs. 6.1. and 6.2. the measured conductivities (cr) of several partially reduced ca2NaMg2v3o12_x single crystals are plotted as log crT versus reciprocal temperature. These results are representative of a larger body of. experimental data. Generally, reproducible values were recorded on thennal cycling up to 700K. Heating to higher temperatures however, resulted in the observation of too small

59

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.. TCK> 300 400 500 700 900

+1

::£ 0 7~

7c: _, ..... ...... ..... 'C -2 ....... (!)

0 -3 _. i _, -5

s

3.0 2.5 2.0 1.5 1.0 .. 103/T C K-1>

Fig. 6.1. Conductivity-temperature produot versus reoiprooal tempera­

ture of CagNal4g2v3o12 single orystats groum. frpm a PbO

flux; numbers oorrespond to pretreatment oondi'tions given

in Table 6.1.

conductivities, at subsequent measurements at lower temperatures, due to reoxidation of the samples (reoxidation region in Fig. 6.1.). The lines depicted in Figs. 6.1. and 6.2. represent a least squares fit of the data to an equation appropriate in the case of charge transport by means of adiabatic hopping of small polarons (cf, eq. 3.25.):

aT = Nc(1-c) v0

e2a2/k(e:xp(-Ea/kT)] (1) where N is the density of available polaron sites, c is the fraction of occupied transport sites, a is the jump distance, v

0 is an

optical phonon frequency and the other symbols have their usual meaning. The obtained values of pre-exponential factors and activation energies are summarised in Table 6.2. An interpretation of the data

60

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--"' TCK> 500 700 900

+1

0 ~

·~ -1

·~ -2 I-'O -3 (!)

0 -4 10 _J

-5

2.0 1.5 1.0

... 103/T CK-1)

Fig. 6.2. Conductivity-tempe:r.>ature product versus reciprocal temperature

of Ca/laMg2v3o12 single crystals grown from a v2o5 fZux;

numbers correspond to pretreatment conditions given in

Table 6.1.

Table 6.2. Parameters obtained by fitting conductivity data for

ca2NaMg2v3o12_~ samples to eq. (1).

curve number

2

3

4

5

6

7

8

9

10

Ea (eV)

1.19 1.24

0.75 o. 77

0.75

0.70 0.38 0.26

1.28

1. 10

log Nc(1-c)e a v0/k

-1 -1 (Q m 6.24 7.25 4.34 4. 71 4.84 5.96 2.90 2.56 6.82

7.33

61

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according to eq. (1) is suggested by the observed temperature dependence

of the measured Seebeck coefficients, shown in Figs. 6.3. and 6.4.

+1

0 e •

-1 ae

2.3 k -2

i -3

-4

3.0

----1., ... T ( K >

400 500 700 900

• • • :-----~

:.~ s.

6

.~Y • 2-

2.5 2.0 1.5 1.0

~ 10 3/T c K1>

Fig. 6.3. Reduaed Seebeak aoeffiaient versus reaiproaal temperature of

Ca:JVaMg2v3o12 single crystals groum from a PbO flux; numbers

aorrespond to pretreatment aonditions given in Table 6.1.

The arrows denote the onset of a rapid ahange of measured

a-values with inareasing temperature (see text).

The data were corrected for the thennopower of the platinum measurement leads(3). Inspection of the figures shows that the Seebeck coefficients

of most of the samples are temperature independent up to "' SOOK. This is a strong indication of a constant number of charge carriers; thus the thennally-activated conductivity is due to a thennally-activated mobility of the charge carriers. Unfortunately, the concentration of the carriers (Ne) in the individual samples cannot be evaluated from the Seebeck coefficients alone, since the concentration of available polaron sites (N) is not known. Nevertheless, from a comparison of the observed conductivities with the pretreatment conditions (cf. Table 6.1.) it can be concluded that generally an increased oxygen deficiency results in higher conductivities and lower activation energies. In Fig. 6.5. the conductivities are plotted as log crT versus activa­tion energy (Ea_>, illustrating the large variation of the resistivity with the reduction degree at 400, SOOand 667K. However, the most

62

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interesting feature of this figure is that these cross cuts through Figs. 6.1. and 6.2. at three temperatures demonstrate a linear dependence on the activation energy. The lines drawn correspond to log oT = (4.6 - 1/2.3 kT) Ea+ 1.33 .Apparently the pre-exponential factor in eq. (1) depends exponentially on Ea: Nc(l-c) v

0 rv exp(4.6 Ea)·

The fraction of occupied transport sites (c) can be evaluated from the Seebeck coefficients via a = - Smix/e·

Since every empty site can be occupied in two ways due to the electron spin degeneracy(4), the entropy of mixing is (see also par. 7.4.):

S . = k ln 2N(N-n) ! = k ln 2(1-c) (2) nux n. c

To obtain an estimate of the optical phonon frequency ( v0

) infrared lattice spectra were recorded (cf. Fig. 6.6.). Characteristic features of these spectra are a set of bands in the 800-600 cm - l

+1

0

-1 ae

2.3k -2

-3

-4

--•TCK) 700 900

1041 D Q g Q-

9~

1.S 1.0

.,...___ 103/T C K1>

Fig. 6.4. Reduced Seebeck coefficient vePBUB PecipPocai terrrpePatuPe

of Ca2Na}fg2v3o12 singie cr.ystais gPoum foPrn a v2o

5 fiux;

numbeP8 coTTespond to pPetPeatment conditions given in Tabie 6.1.

63

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+1

0

-1

-2 -~ .. ~ -3 -7c: - -4 -I-

t) -5 -(!)

0 -6 __J

400K 0

-7

-8 0

-9 0 0

0.5 1.0 ... EaCeV)

Fig. 6.5. Conduativity-temperature product versus activat~on energy

of severai partiaUy reduced Ca:!'aMg2v3o12 sing~e arystais at three temperatures.

64

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110. 0

t5 z g 85.0 !-­...... I: ({)

z er. a: ....

lil u z

60.0

100.0

g 50.0 !-.... I: en ~ a: I-

0.0

20 '±0 60 WAVENUMBERS CM-1

'* 0 6 0 B 0 WRVENUMBERS CM-1

1000

Fig. 6.6. InfPar>ed 'lattiae speatro of Catya14g2V3o12 powdeP

1.'eaoPded at 1.'0om tempePature; 100-700 am-1 1.'egion and

400-1000 am-1 1.'egion.

region and a strong band in the region around 400 on-1 • Similar spectra are known for rare-earth-aluminium and -iron gamets(S). The infrared spectra of the manganese garnets, discussed in the next chapter, again exhibit these features (cf. par. 7.4.). Raman spectra

65

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of ea.2NaMg2v3

o12

reported by White et a1(6) also show a series of peaks in the same spectral region. A peak around 850 Clll-

1 is assigned to a~ tetrahedral vibrational rode. Though there is no unambiguous assignment of the different vibrational modes, a value of v ~ 3.1013 s-1 seems a reasonable estimate.

0 The concentrations of available polaron sites calculated from the pre-exponential factors given in Table 6.2., using v

0 3.1013 s-1,

a = 0.38 run, the nearest neighbour V-V distance, and c-values obtained via the Seebeck coefficients, do increase exponentially from 2.1023 m-3 at E = 0.26 eV to 1031 m-3 at E = 1.24 eV. a a However, the maximum density of available polaron sites that is physically meaningful, is equal to the total vanadium ion concen­tration, 1.25 x 1028 m-3• Evidently an optical phonon frequency of ~ 1016 s-1 is impossible. Therefore, it is concluded that in these vanadate garnets, where coulombic defect interactions dominate the charge transport behaviour, illustrated by the large variation in activation energies, 0.26~ Ea~ 1.28 eV, the correct fraction of occupied transport sites is not obtained via eq. (2). In this respect it is instructive to reconsider the distribution of polaron sites schematically depicted in Fig. 3.la. If the density of polaron sites belonging to the partially filled group is too low to construct continuous conduction pathways through the crystal, charge transport will necessarily involve electron jumps over sites belonging to the other groups. In that case the conductivity will be predominantly determined by jumps requiring the highest activation energies. However, unlike the situation where parallel transport processes are occurring (cf. eq. 3.21), the Seebeck coefficient for a series circuit is a summation over individual terms a= ~ups ai. Therefore the fraction of occupied transport sites (c) in eq. 6.1 and the one determined via eq. 6. 2 are not identical. Nevertheless if the energy difference between the groups is large enough to prevent a redistri­bution of electrons over the groups at the temperatures of measure­ment, the observed thennopower is temperature independent. Tirus the above results ascertain that charge transport occurs by means of thennally activated hopping of electrons via the vanadium sublattice where defect interactions determine the number of different conduction paths and activation energies. Deviations between. the experimental Seebeck coefficients and those calculated via eq. (2), in cases where

66

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the deviation from stoichiometry or the dopant concentrations were known, have been reported repeatedly and are usually attributed to a complex defect stnictureC7-lo).

(1-c)ea2v Usingµ= kT 0 exp(-E/kT) (cf. eq. 3.11.)

with (1-c) ~ 1, a= 0.38 run and v0

= 3.1013 s-1, mobility estimates -7 2 -14 2

ofµ~ 3.10 m /Vs andµ~ 10 m /Vs for Ea= 0.25 eV and 1.0 eV respectively, are obtained at T = SOOK. With respect to the inter-vanadium distance it is noted that, considering the charge transport mechanism of a series of doped vanadium spinels, Goodenough observed a transition from itinerant to localised electron behaviour at an inter-vanadium distance of ~ 0. 29 run (7) • The shortest intervanadiwn separation in the vanadiwn garnet is nuch larger, 0.38 nm, favouring a localised behaviour. The number of other garnet materials where the charge transport mechanism has been established, is limited and mainly concerns doped and lllldoped yttriwn iron garnet. For this compolllld the majority of exper~ntal results favour the applicability of the large polaron model at high temperatures, T > 600K, and the small polaron model at low temperatures, T < 300K. On the other hand is gadolinium and dysprosium iron garnet the charge transport at elevated temperatures, T > 600K, has been ascribed to thennally activated hopping of holes via the iron lattice sites(12 ,13).

The arrows on the curves in Fig. 6.3., denoting the onset of a rapid change in the measured Seebeck coefficients with increasing temperature, have not been discussed sofar. The voltages obtained, correspond to physically unrealistic charge carrier concentrations whereas in the same temperature region no abrupt changes in the conductivity were observed. However, in this temperature region a displacement of the linear AV versus AT plots away from the origin (cf. par. 6.3.) was observed, indicating the appearence of additional voltages. The occurrence of an increased reoxidation rate at the same t~, is probably due to an increased_ ionic mobility. Therefore the additional voltages are attributed to rearranging defects. If these voltages and the electronic thennovoltages become comparable in magnitude, erratic a-values are to be expected. Similar effects are thought to be responsible for the curvatures of lines

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3 and 7; whereas the deviation of line 8 is due to reoxidation of the sanq>le, as was demonstrated by a decrease in conductivity (cf. Fig. 6.3.). Also in the manganese garnets, to be discussed in the following chapter, changes in the recorded thennopower values at high temperatures were observed, due to compositional relaxation in the temperature gradient. Finally it is noted that the differences in composition and impurity content between the crystals grown from PbO and v2o5 fluxes apparently do no affect the conductivity properties as demonstrated by the similarity of curves 1 and 9 (cf. Figs. 6.1. and 6.2.). Thus also in the untreated crystals the conductivity is probably determined by the oxygen deficiency.

6. 6. Summary and aono lusions

The thermopower of partially reduced CazNaMg2v3o12_x is temperature independent in the region 300-800K. The conductivity is thermally activated where large differences in activation energy, 0.26-1.28 eV, are observed with varying v4

+ content. The magnitudes of the measured Seebeck coefficients, for differently pretreated sanq>les, indicate a complex defect structure. Therefore, the charge transport in ea2NaMg2v3o12_x is attributed to thennally-activated hopping of small polarons via the vanadium sublattice where defect interactions deter­mine the number of different conduction paths and activation energies.

REFERENCES

1. I. Bransky and N.M. Tallan, "Conductivity in low-mobility materials" eds. N. Klein, D.S. Tannhauser and M. Pollak (London, Taylor &

Francis) p. 31 (1971). 2. J.M. Wimmer and I. Bransky, "Electrical conductivity in ceramics

and glass" ed. N.M. Tallan (New York, Dekker) Part A, p. 270 (1974). 3. J.P. M:>ore and R.S. Graves, J. Appl. Phys. 44, 1174 (1973). 4. P.M. Chaikin and G. Beni, Phys. Rev. b1 647 (1976). 5. N.T. Mc Devitt, J. Opt. Soc. Am. 59, 1240 (1969). 6. W.B. White and V.G. Kerarnidas, J. Am. Ceram. Soc. 54, 172 (1971). 7. J.B. Goodenough, Mat. Res. Bull.~. 621 (1970). 8. J.D. Hodge and H.K. Bowen, J. Am. Ceram. Soc. 64, 431 (1981). 9. H.L. 1\lller and A.S. Nowick, J. Phys. Chem. Solids 38, 859 (1977).

10. K. K01.nnoto and H. Yanagida, J. Am. Ceram. Soc. 64, C-156 (1981).

68

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11. R. Metselaar and P.K. Larsen, "Physics of magnetic game.ts", ed. A. Paoletti (New York, North Holland) p. 417 (1978).

12. V.R. Yadav and H.B. Lal, Can. J. Phys. 57, 1204 (1979). 13. V.R. Yadav and H.B. Lal, Jap. J. Appl. Phys • .:!!• 2229 (1979).

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CllAPI'ER VII.

7.1. Introduction

In this chapter the results are reported from thennopower and conductivity measurements on a series of polycrystalline {Ca3_xyx} [Mn2] (Ge3)o12 specimens with 0 ~ x ~ 2. This garnet system was chosen because the end members with x = 0 and x = 2 were known to exist(l,2). Because y3+ is very stable charge compensation occurs on the manganese sublattice. As compared to the vanadium garnets, discussed in chapters IV-VI, the manganese garnet system has the advantage that the amollll.t of Mn2+ is chemically controlled and can be varied from 0-100% (sublattice occupation).

In section 7.2. the preparation of the garnet powders is described together with the characterization by means of x-ray and electron microprobe analysis and section 7.3. gives experimental details. In section 7.4. the results are presented and discussed in relation to the literature and the conclusions drawn are summarised in section 7.5.

7.2. P!'eparation and characterisation

Ca3_xYxMn2Ge3o12 powders have been prepared by solid state reaction. The component oxides and carbonates, Y2o3,Ge02 and eaco3,Mnco3, were of at least p.a. purity grade. Weighed stoichiometric quantities were repeatedly fired at temperatures 1000-11S0°c. The mixing of the starting materials and the remixing between the firings was perfonned by conven­tional ball-milling in agate mortars. ea3Mn2Ge3o12 was fired in air, the samples with x > 0 were fired in nitrogen(l,2). After the first firing the samples with x I 0 usually contained Y 2Ge2o7' After refiring all diffraction lines present in the recorded x-ray patterns could be indexed in the Ia3d space group. The obtained powders were pelletised, using steel nwlds at pressures "' zx108 Pa and sintered in air (x=O) or nitrogen (xfO) at temperatures 1100-1200°c. The preparation condi­tions of the individual samples and the final densities obtained, expressed as percentage of the x-ray densities, are summarised in Table 7.1. The x-ray diffraction lines were slightly broadened in some cases, probably indicating inhomogeneities in the yttrium distribution. This

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could not be verified with the electron microprobe however. Though

the x-ray patterns did not show spurious lines, a few spots of a second

phase were detected by electron microscopy in the samples with x = 1.75 and x = 2. This second phase only contained Y and· Ge in equal amounts and is therefore probably the remainder of the Y2Ge2o7 phase which occurs at the beginning of the solid state reaction.

Because of the localised character and the small concentration this second phase is not expected to have a marked influence on the conductivity and thennopower data presented in section 7.4.

7.3. E:i:perimental details

The experimental equipment and the procedures used, are identical to those described in par. 6.3. Since the resistance of the manganese garnets is rather small at high temperature also four point measurements were perfonned using a Knick Precision-Current­

Voltage Source 7S 300 as current source and the platinum wires of the measurement thennocouples as voltage probes connected to a Keithley 616 electrometer. Most of the measurements were perfonned with decrea­

sing temperature in air.

7.4. Results and disaussion

Measurements on polycrystalline specimens are always hampered by possible grainbotnldary effects. Therefore the resistance was

checked on ohmic behaviour and occasionally the frequency dispersion characteristics were recorded. This should also reveal an ionic

contribution to the conductivity. Thus it was ascertained that the measured data correspond to electronic bulk conductivities. In Fig.

7.1. the results are plotted for a number of Ca3_xYxMn2Ge3o12 samples, with O~ x~ 2,as log crT versus reciprocal temperature. Only data points for x =O and x = 2 have been drawn to avoid confusion. The

a values have been corrected for porosity using a = crm(l-V)-3/ 2

where a is the measured conductivity and V is the volwne fraction of the ~ores(3). Inspection of the figure shows that the conductivi­ties can be fitted to a relation of the fonn:

Nc(1-c)e2a2v a = kT 0 exp (-Ea/kT) (1)

i.e. , assuming adiabatic hopping of small polarons where N is the density of transport sites, c is the fraction of occupied transport

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Tab'le 7.1. Pr'eparation aonditiona and final, densities of Ca3_3/:i/4n2Ge3o12

composition firing sintering final relative

(x) time (h) temp. (OC) time (h) temp.pc) density (%)

0 36 10SO 19 1100 67

o. 10 89 10SO 69 1100 S8

0.67 89 1 lSO 47 11 so 88 1.00 117 11 so 42 11SO 73 1.SO 134 11SO 89 1200 70 1. 7S 89 11 so 47 1200 72

2.00 134 1200 67 1200 70

sites, a is the jumpdistance, v0

is an optical phonon frequency and the other symbols have their usual meaning. The activation energies and pre-exponential factors, calculated by least squares analyses, are sumnarised in Table 7.2.

Tab ie 7. 2. Pa.rcuni:itera obtained by fitting aonduativi ty data for

Ca3-:r;YxMti2Ge3o12 aamp'les to Eq. (1).

composition Ea (x) (eV)

Nc(1-c)e a vik (106n-lm-1K) 1

µ(SOOK) c10-11m2v-1 s-1)

0 0.10 0.67 1.00

1.SO 1.7S 2.00

0.61 0.63 0.63 0.62 0.61 0.63 0.79

1.19 1.67 4.43 3.40 2.7S 1. Sl 1. 78

1. s 0.63 0.29 o. 18 0.080 0.0014

The above interpretation is supported by the thenwpower data shown in Fig. 7.2. These data represent values corrected for the thennopower of the plat:i.Jrum-measurements leads ( 4) • All samples exhibit a practically temperature ·independent thermopower apart from some high temperature data which will be disOJSsed separately below. This strongly suggests

71

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•TC K > 300 400 500 700 1000

+4

+3

+2

:IC .... +1 ·~ 7c:

0 I-

0 -1

(!)

0 _J -2

1 -3

-4

1,6,2 -s

3.0 2.0 1.0

10'lrc K1> ..

Fig. 7.1. Conduativity-temperat-uPe produat versus reaiproaal tempera­

ture for Ca3~YxMrt2Ge3o12 samples with: 1) x=O, 2) x=0.1,

3) x=0.67, 4) x=l, 5) x=l.5, 6) x=l.75, 7) x=2.

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• T ('c)

400 500 700 1000 I

• 2 ,.. • • • •• • 7 • • '

'

i ' ' ' ' ' ' 6 ' ' 0 0

0 0 0 6. tJ.f•

5 0 0 0 6. 6.

4 6. 6. 6. 6. 6. 6. .Jl.!L 0 2.3k 0 0 0 0 ¥.

3 0 0 0

'* 0 I I!

x ¥ 2 .x x x • 1 • •

-1

2.5 2.0 1.5 1.0

101/T ( l(f) ... Fig. ?.2. Reduaed Seebeak-aoeffiaient Vel'BUS PeaipPoaa'l temperutul'e

fol' ca3-:x:YxMri2Ge3o12 samp'les with: 1) x=O, 2) x=0.1,

3) x=0.6?, 4) x=l, 5) x=l.5, 6) x=l.?5, ?) x=2.

a constant number of carriers. In Fig. 7.3. the Seebeck coefficients measured at SOOK are plotted versus log[c/(1-c)], where it has been assumed that the Mn2+ concentration corresponds to the yttrium content (c=i)· Evidently the points do not fit the Heikes fonnula (cf. eq. 3.20.). In recent literature it has been argued that this fornD.lla should be adapted to include spin degeneracy of the carriers(5-9J. If the system is to remain electron-hole symmetric this results in 198 log [c/2(1-c)] for small values of x(n-type) and 198 log [2c/(1-c)] for large values of x (p-type) ; to our knowledge, no theory has been propo­sed yet for the intennediate concentration region. The dashed lines in Fig. 7.3. correspond to these equations. In then-type region the difference between experiment and theory is enlarged upon introduction of the spin degeneracy factor, whereas in the p-type region reasonable agreement is attained.

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-1

x

/

/ /

/

400

300 a. C)J V/K l ! 200

100 x

-200

-300

./

x

/ /

/

......_ 198 LOG [ C/Cl-C >]

Fig. ?.J. Compari8on of e:r:perimental Seebeek-eoeffieients at T=500K,

with theoretieal values: solid line - "Heikes" formula;

dashed line8 - Heikes formula ineluding an eleetron spin

degeneraey faetor (see text).

However, in our opinion, the dashed lines should be disregarded. The reason is that for a transition metal ion with a net spin in both valence states, the spin degeneracy should not contribute to the mixing entropy. A similar argument has been used for the case of Fe3o4 by Hodge and Bowen(lO). To reconcile the data with Eq. 3.20., we therefore propose that the number of possible transport sites is reduced due to defect interactions. This means that of the two Mn ions per formula unit only a number z = x/c is available for polaron transport. The effective number of transport sites (z) can be calculated from the known yttrium content (x) and the fraction of occupied transport sites (c), evfluated from the thermopower data using the Heikes fonrula. The results are shown in Table 7.3. Assuming equal activation energies and minor variations in v

0 upon incorporation of yttriUJ11 ions the conductivities should scale

with the product z(1-c)c. In view of the restrictions discussed below

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the scaling apparent from Fig. 7.4. is satisfactory. Tue deviation observed for the sample with x = 1.5 may be related to the fact that this sample was fired much longer than the other composi­tions. Annealing of samples during a week at 11 oo0c in air, indeed resulted in changes of thennopower and conductivity.

Table 7. S. Thel'fTlopower and effeative fraation of transport sites in

ca3_xYxMn2Ge3o12 as a funation of the yttriwn aontent.

composition a c z = x/c zc(l-c) x (µV/K)

0 -149 o. 151 0. 1 -135 0.173 0.58 0.083 0.67 54 0.651 1.03 0.234 1.0 113 0.788 1.27 0.212 1.5 139 0.834 1.80 0.248 1.75 232 0.937 1.87 0.110 2.0 347 0.983

•ZCC1-C) 5 lC 0

4 0.20

-. -~ 3 ~~ (.)

I •o .....

2 0.10 ..... (.)

0 N

i i 0 0

0 0.5 1.0 1.5 2.0 x _......,.

Fig. 7.4. Comparison of aomposition dependenaies at 300K of eleatriaal

aonduativity and the za(l-a) produat (see text) for

Ca3_xYxMn2Ge3o12 (lines are dra:iun to guide the eye).

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However, a very remarkable result is observed when the z-values from Table 7.3. are plotted against x (Fig. 7.5.). The figure shows that the number of Mn sites available for the polarons increases nearly linearly with x. z approaches the theoretical maximum z = 2 for x + 2. Thus for CaYzt.:tn2Ge3o12 the number of available sites is equal to the total m.nnber of Mn ions. From the value of the pre-exponential term in Eq. (1), as given in Table 7.2., the frequency v

0 can be calculated.

The lattice constants of the end members are a0

= 1.232 run for x = O and a

0 = 1.247 run for x = 2, in accordance with literature data(1•2). For

the intennediate compolUlds we folUld an approximately linear variation of a

0 with x, as measured from Gu:iAier _pictures. This corresponds to

a density of Mn-ions, N0

= 8.3 x 1027 m-3 and a nearest-neighbour M:l-Mn distance a = 1 a 13 = 0.54 run. The resulting frequency is

13 -1 ° v0

= 2.3 X 10 S •

2.0 z -2 max-

t 1.5

z 1.0

0.5

0 0.5 1.0 1.5 2.0 x--+

Fig. 7.5. Number of availabte Mn transport sites per formuta unit

of Ca3_xYxMn2Ge3o12 as a funation of x.

Fig. 7.6. gives the infrared spectnmi of a manganese garnet with x = 0.1. The spectn.nn shows the features typical for all garnets (cf. par. 6.4.). By comparison with the assignments for Y3Al5o12 and vana­diumgarnets (11•12) whose spectra show a close resew.blance with the man­ganese garnet spectn.un, it is seen that this value of v

0 is in excellent

agreement with the position of the longitudinal optical modes.

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w u z

100.0

g: 50.0 I-

I: in z a: a: I-

UJ u z

o.o

100.0

g so.a I-

t: Cl') z ~ I-

o.o

2 0 LJ: 0 WAVENUMBERS CM-1

\ 0 6 D B 0 10 0 WRVENUMBERS CM-1

Fig. ?.6. Infr:'ared absorption spe:;ra of ca2•9Y0_1Mn2Ge3o1g1at room

temperature: 100-?00 cm region and 400-1000 am region.

The correct magnitude of v0

sustains the applicability of the adiabatic

small polaron model since for the non-adiabatic case the apparent

frequency v = J 2/.1il?r (cf. F.qs. (3.11) and (3.12.) would be nruch smaller

because then J « hv0

• From F.q. (1) we can also calculate the polaron

mobility µ. Table I shows µ values calculated at T = SOOK. The low

values observed, also are consistent with the small polaron model.

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For a comparison with the charge transport mechanism in other garnets

see par. 6.4. Finally, the increase of the thermopower at high temperatures will

be discussed. The data for this temperature region are questionable because a correspondirig change in conductivity was not observed. Further,

annealing of the specimens for several hours in nitrogen did not affect the measured conductivity and thermopower values, so a change in defect concentration due to reduction can be ruled out. It was observed however, that with increasing temperature the linear thermovoltage ~V versus ~T plots tended to be displaced away from the origin, indicating additional voltages. Since at high temperatures the ionic defects will become

increasingly mobile, these additional voltages, that lead to erratic thermopower values, are probably caused by compositional relaxation in

the temperature gradient.

7. 5. Summary and aona lusion's

The conductivities of Ca3_xYxMn2Ge3o12 in the temperature region 30-1000°c are thermally activated with Ea~ 0.62 eV for 0 < x < 1.75

and Ea= 0.79 eV for x = 2. The corresponding thermopower values are temperature independent. These results are shown to be consistent with

adiabatic hopping of small polarons localised on the manganese sublattice, where defect interactions limit the nlUllber of available transport sites. In electronically conducting oxides with a fixed nlUllber of carriers, localised on a transition metal sublattice, the spin degeneracy does not contribute to the mixing entropy if the cation has a net spin in both valence states involved.

References 1. B.V. Mill, Zhur. Struct. Khim.~. 471 (1965). 2. S. Geller, C.E. Miller and R.G. Treating, Acta Crystallogr.

Q, 179 (1960). 3. D.A.G. Bruggeman, Ann. Phys.~. 645 (1936). 4. J.P. M:>ore and R.S. Graves, J. Appl. Phys. 44, 1173 (1973). 5. P.M. Chaikin and G. Beni, Phys. Rev. b13, 647 (1976). 6. D.P. Karim and A.T. Aldred, Phys. Rev. b20, 2255 (1979).

7. C.C. Wu and T.O. Mason, J • .Am. Ceram. Soc. 64, 520 (1981). 8. C.C. Wu, S. Kumarakrishnan and T.O. Mason, J. Solid State Chem.

37' 144 (1981).

78

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9. E. Gartstein and T.O. Mason, J. Am. Ceram. Soc. 65, c~24 (1982). 10. J.D. Hodge and H.K. Bowen, J. Am. Ceram. Soc. 64, 431 (1981). 11. J.P. lh.trrell, S.P.S. Porto, I.F. Chang, S.S. Mitra and R.P.

Bauman, Phys. Rev. 1 851 (1968). 12. W.B. White and V.G. Keramidas, J. Am. Ceram. Soc. 54, 472 (1971).

79

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C1lAPI'ER VI I I

OJNClllDING REMARKS

8.1. General conclusiona

The purpose of the present study is to examine the charge transport properties of some oxidic garnets in relation to the possible occurrence of photoinduced phenomena. f.:bre specifically, the following questions can be fonnulated: i) Which charge transport mechanism is to be expected in garnets where at least one sublattice is occupied by transition metal ions? ii) .Are irreversible changes of physical properties possible in these materials at room temperature? For reasons given in the introduction the garnet systems CazNaMg2v3o12_x and ea3_xY:}4n2Ge3o12 have been selected for investigation.

Vanadium garnet powders were prepared by conventional solid state synthesis. Vanadium garnet single crystals were obtained via flux growth. subsequent annealing of the materials at elevated tempe­ratures, in atmospheres with different oxygen partial pressures,

yielded partially reduced ea2NaMg2V~~2xvi:o12 samples. The physical properties thereof have been studied by means of electron microprobe, thennogravimetric, ESR, optical absorption, optical reflection, photoconductivity, electrical conductivity and thennopower measure­ments. The main results can be stmnnarised as follows: - A large amount of cation vacancies is possible in Ca2NaMgV3o12

garnet. - The maximum oxygen deficiency in Ca2NaMg2v3o12_x is x"' 5 x 10-2• - The ESR spectra exhibit an inhomogeneously broadened signal due

to an S = L I = 7/2 isotope in tetragonal symmetry. This signal is attributed to y4+ centres on tetrahedral sites.

- The v4+ centres give rise to optical crystal-field transitions in the infrared spectral region and photoinduced electron transfer between vanadium ions on different lattice sites results in a broad optical absorption band with a maximum at "' 2.4 eV.

- The v4+ signal intensity is found to decrease llll.der irradiation

with light in the energy region (1.2-2.1) eV. This effect is shown to be due to a photoinduced electron transfer from a well-localised v4

+ ion towards a vanadium ion representing a delocalised polaron band state.

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- A small photocurrent is observed after excitation in the oxygen (2p)-vanadium (4s) charge-transfer band at energies > 4.3 eV. Its dependence on the light intensity may be described by a one carrier insulator model with traps.

- The conductivities, measured at temperatures above ambient are thennally activated, whereas the thennopower is temperature indepen­dent. A large variation in activation energies, 0.26-1.28 eV, is observed for differently pretreated samples and the magnitudes of the measured Seebeck coefficients indicate a complex defect stIUcture. Therefore, it is concluded that charge transport occurs by means of thennally activated hopping of a fixed number of carriers where defect interactions detennine the nl.Ullher of different conduction paths and activation energies.

The above results clearly establish the polaronic nature of the excess electrons cv4+ centres) in Ca2NaMg2v3o12 since: i) A polaronic optical absorption band is observed. ii) The photosensitivity experiments indicate the existence of a

polaron band regime at low temperatures. iii)The electron DDbility at high temperatures is thennally activated. The existence of a distribution of centres over energetically different sites is sustained by the inhoDDgeneous broadening of the ESR signals. The spread in energylevels of the defects due to Coulomb interactions is also reflected in the width of the optical polaronic absorption band. The important contribution of these interactions (He-imp' cf. par. 3.5.) to the conductivity activation energies is illustrated by the large differences observed between differently pretreated sam­ples. Apparently at low defect concentrations, x < 5 x 10-2 in ca2NaMg2v3o12_x, widely varying site energies occur. !m upper limit for the part of the activation energy solely due to the tenn He-ph in eq~ 3.8 can also be estimated according to eq. 3.10:

2 . 1 . 1 1 f1i = ~E = e where - = - - -p 161T1,E:* r € * e:.., €

(cf. par. 3.2. for the definition of the symbols). Setting e:

00 -v 5, e -v 20 and r -v 0.2 nm a value -v 0.2 eV is obtained. Thus

a large part of the measured activation energies originates from defect

interactions, He-imp' A series of polycrystalline manganese garnets ea3_xYJb~~x~+Ge3o12 ,

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with 0~~2,was prepared by solid state synthesis. The charge transport properties of sintered specimens have been investigated by conductivity and thenoopower measurements. The conductivities, reasured in the temperature region 30-1000°c, are thennally activated with Ea~ 0.62 eV for O~x~1.75 and Ea= 0.79 eV for x = 2. The corresponding thennopower values are temperature independent. These results have been shown to be consistent with adiabatic hopping of small polarons localised on the manganese sublattice, where defect interactions limit the number of available transport sites. Again a considerable part of the observed activation energies must be due to defect interactions, H • , whereas

e-llllp in this concentrated system also correlation terms are probably important (see par. 3.2., par. 3.5. and above). Further it is noticed that apparently the preferred conduction path is the same for the specimens with O~~ 1 . 7 5, as indicated by the equal activation energies.

In the case of partial~y reduced or Si-doped YIG the charge transport at low temperatures is thought to occur by means of thennally activated hopping of electrons localised on the octahedral iron sub­lattice 1. To explain the various photomagnetic effects observed, it is assumed that a distribution of ground-state energies of ferrous ions exists, corresponding to different distances between the centre and the lattice defects Si, V

0 etc. (He-imp) 2• The charge transport mechanism

at temperatures above ambient has not been established unambugeouslybut the experimental results slightly favour the applicability of the large polaron model1•

On the other hand in DyIG and GdIG the charge transport at ele­vated temperatures, T > 600K, has been attributed to thermally acti­vated hopping of holes via the iron lattice sites with Ea~ 0.6 ev3•4• However, an interpretation of the data according to eqs. 3.20 and 3.25, assuming the density of available transport sites to be equal to the iron concentration, yields optical phonon frequencies of ~ 101 O sec - l, which are physically unrealistic. This probably indicates that also in these garnets defect interactions, limiting the number of transport sites, can not be neglected.

Thus, with respect to the questions fonm.ilated at the beginning of this chapter the following statements can be made: i) In many cases the small polaron model is applicable for the

description of the electrical properties of garnets where at least one sublattice is occupied by transition metal ions. It is important

82

;'•'

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to note that defect interactions predominantly detetmine the number of different conduction paths and activation energies.

ii) Irreversible photoinduced changes of physical properties occur if irradiation with light causes a pennanent redistribution of electrons over centres which are inequivalent with respect to the physical property considered. The activation energies for thennally induced electron motion may vary widely for different carrier concentrations or dopants. Also the occurrence of a photoinduced electron transfer between differently situated transition metal ions has been established in several cases. Therefore it can be concluded that irreversible photoinduced changes of physical properties of garnets at room temperature, should be possible.

It should further be remarked that for none of the garnets discussed, detailed infonnation concerning the actual defect structure(s) is available. Interesting results in this respect might be obtained from thennally stimulated (de-)polarisation current (T.S.P.C.) measurements.

8.2. Photomagnetia effeats at room temperatUX'e?

Next, the possible application of garnets in photomagnetic memory devices will be considered. For practical reasons this requires the occurrence of photomagnetic changes at room temperature. The question is then whether a garnet exhibiting such properties exists? The basic principle of the devi~e envisaged, is an irreversible change in coercive field under irradiation with light as is observed in Si­doped YIG at temperatures far below ambient. Such an effect imposes the following material requirements: i) The compotmd should possess a net magnetic moment at room temperature. ii) The compotmd should contain at least two types of sites, exhibiting

a marked difference in domain-wall pinning strenth, whose occupation degree can be irreversibly altered by irradiation with light at room temperature. Alternatively this condition is expressed in the reaction equation: hv

1~ weak wall pinning site f--- z strongwall pinning site

Lilith

where both processes, 1 and 2 , require electron transport over an energy barrier high in comparison with thermal energy at 300K.

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TI:te first requirement implies that both the octahedral (a) and the te­trahedral (d) lattice sites must be occupied by magnetic ions since in garnets only the (a-d) exchange interaction is strong enough to result in Curie temperatures> 300K. So called one-sublattice garnets exhibit very low Neel temperatures5• According to Geller et ai

6 iron and cobalt are the only magnetic ions which enter the tetrahedral sites in the garnet structure in substantial aioount. Numerous examples exist of garnets where the tetrahedral sublattice is completely occupied by iron ions whereas for cobalt a maximum of 0.44 Co per fornrula unit has been reported6• TI:terefore the number of suitable compounds is limited to iron garnets. It is thus not astonishing that the effects of dopants in various con­centrations on the photomagnetic effects (P.E.) observed in YIG have been studied extensively. Two classes of P.E. have been distinguished (cf. par. 5.4.) which are both associated with a photoinduced redistri­bution of excess electrons (Fe2

+ centres) over the iron lattice sites. TI:te photoinduced change in coercive field belongs to class II and is for instance found to occur in YIG containing small amounts of Si; < 0.05 Si per fonnula unit. TI:tis P.E. is attributed to a photoinduced electron transfer between iron lattice sites located near respectively at large distance from the Si ions, which implies low dopant concen­trations. A difference in wall pinning strength between these sites then results in the observed change in coercive field. TI:tus the magnitude of the effect can be influenced by changing the local environments of both types of sites. A comparatively large effect has been observed in In3+ -doped YIG7• Of course the tempera­ture dependence of the effect is also detennined by the thennal energy required to induce electron motion on both types of sites. Although large differences in magnitude of the P.E. have been reported for YIG containing different dopes, a marked increase of the temperature up to which the effect could be measured, was not observed7• Lotgering8

examined the electrical and photomagnetic properties of several YIG samples co-doped with some of the elements Ca, Co, V, Mn, Si, In. Although in Y3_2rCazrFe4_97_rsi0•06vro12 a change in conductivity activation energies (Ee) occurred, from Ee = 0.2 eV for r = 0.02 to Ee= 0.9 eV for r = 0.07, a corresponding change in the temperature dependence of the P .E. was not reported.

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These results can be explained, assuming that the dopants do change the m.unber of different conduction paths and activation energies, as in ca2NaMg2v3o12 , but do not affect the electron localisation at the sites situated at a large distance from the impurities. According to the above reasoning a ferrimagnetic garnet is required where the excess electrons are more strongly localised than in YIG. However, this localisation should not result fonn the tenn He-imp" Since any sublattice disorder will introduce such a tenn the hypo­thetical fonnula of the desired garnet can be written: {S+} [M.~+] (Fe~+)012 where ~+ nrust be a magnetic ion and no special conditions are imposed on the ion situated on dodecahedral lattice sites. However, the m.unber of triply charged magnetic ions is rather limited and only partial substitutions thereof on the octa­hedral sub lattice have been reported5 • 9• Therefore the existence of a garnet exhibiting the desired properties is doubted.

REFERENCES

1. R. Metselaarand P.K. Larsen, "Physics of magnetic garnets" ed. A. Paoletti (New York, North-Holland) p 417 (1978).

2. R. Metselaar, "Interaction of radiation with condensed matter" (Vienna, I.A.E.A.) Vol. II, p 159 (1977).

3. V.R. Yadav and H.B. Lal, Can •. J. Phys. 57, 1204 (1979). 4. V.R. Yadav and H. B. Lal, Jap. J. Appl. Phys. ~. 2229 (1979). 5. G. Winkler, ''Magnetic garnets" (Braunschweig, Vieweg) p 104,

p 46 (1981). 6. S. Geller, H.J. Williams, G.P. Espinosa and R.C. Sherwood,

Phys. Rev. 136A, 1650 (1964). 7. R. Metselaar and M.A.H. Huyberts, Philips Res. Repts. 29, 453 (1974). 8. F.K. Lotgering, J. Phys. Chem. Solids 36, 1183 (1975). 9. s. Geller, z. Kristallogr; 125, 1 (1967).

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The investigations presented in this thesis conce111 the proper­ties of localised electrons in two series of ga111ets, the vanadium

__ c;+ _ _4.+ 3+ ga111ets ca2NaMg2v3_2xvzxo12 and the manganese ga111ets ea3_xYxl>tlz-x .Mn;+Ge3o12 • The charge transport mechanism is studied in relation to the occurrence of photoinduced phenomena.

In the introduction the choice to investigate especially the above ga111ets in this repect is motivated.

The crystal chemistry of ga111ets is discussed in chapter II. In chapter III the relevant transport theory is reviewed. The

equations applicable for the interpretation of electrical conductivity and thermopower data are derived. It is argued that the localisation of excess electrons in ga111ets, where at least one sublattice is occupied by transition metal ions, results from the combined action of electron-phonon coupling, electron-impurity interaction and elec­tron-correlation tenns.

The chapters IV, V and VI deal with the experimental results obtained on vanadium ga111et single crystals. In chapter IV the results from ESR and optical absorption measurements on partially reduced crystals are presented. The spectra demonstrate the presence of y4+ centres on tetrahedral lattice sites. The occurrence of a photoinduced intensity reduction of the v4+ ESR signal is discussed in chapter V. This effect is attributed to a photoinduced electron transfer from a well-localised vanadium ion towards a vanadium ion representing a delocalised polaron band state. In chapter VI the results from conductivity and thermopower experiments at elevated temperatures are analysed. Charge transport is shown to occur by means of thennally activated hopping of electrons localised on the vanadium sublattice. Defect interactions predominantly deter­mine the number of different conduction paths and activation energies.

Chapter VII deals with the charge transport mechanism in a series of polycrystalline manganese ga111ets. The results from conductivity and thermopower measurements, performed in the temperature region 30-1000°C, are consistent with non-adiabatic hopping of small polarons localised at the manganese sublattice. Again defect interactions limit the number of available transport sites.

Chapter VIII contains the general conclusions. The small polaron model appears to be applicable for the description of the charge

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transport properties of many gatnets if the effects of defect interactions are taken into accotmt. Also it can be concluded that irreversible photoinduced changes of physical properties at room temperature should be possible in gatnets. However, the occurrence of irreversible photomagnetic effects at room temperature should not be expected.

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SAMENVAITING

Het onderzoek beschreven in dit proefschrift betreft de eigen­schappen van gelokaliseerde elektronen in twee series verbindingen

met de granaatstructuur, de vanadium granaten Ca2NaMg2~~Zx~;o12 3+ 2+ • en de mangaan granaten Ca3_2xY;t1z-xMI\: Ge3o12 • Het ladmgstransport mechanisme is bestudeerd in relatie tot het voorkomen van licht­geinduceerde effecten.

In de introductie wordt de keuze om juist bovengenoenrle granaten in dit verband te onderzoeken, gemotiveerd.

De kristal chemie van granaten wordt beschreven in hoofdstuk II. In hoofdstuk III wordt een overzicht gegeven van de betreffende

transport theorie. Er worden vergelijkingen afgeleid die toegepast kunnen worden bij de interpretatie van gegevens verkregen uit metingen van thennokracht en elektrische geleiding. Tevens wordt beargumenteerd dat de lokalisatie van extrinsieke ladingsdragers in granaten, waarin tenminste een subrooster wordt gevornd door over­gangsmetaal ionen, het gevolg is van elektron-fonon, elektron-elektron, en elektron-verontreiniging interacties.

De hoofdstukken IV, V en VI beschrijven de exper:imentele resul­taten gemeten aan gedeeltelijk gereduceerde vanadium granaat eenkris­tallen. In hoofdstuk IV worden de resultaten van ESR en optische absorptie metingen behandeld. De spectra tonen de aanwezigheid van v4+ centra op tetraeder posities aan. Een licht-geinduceerde intensiteitsvennindering van het v4+ ESR sig­naal wordt besproken in hoofdstuk V. Dit effect wordt toegeschreven aan een optisch ge!nduceerde elektron overdracht van een gelokaliseerd vanadium ion naar een vanadium ion dat een gedelokaliseerde toestand in een polaron band representeert. In hoofdstuk VI worden de resultaten van geleidings- en thennokracht metingen bij hoge temperaturen besproken. Het ladingstransport blijkt te geschieden via thennisch geactiveerd springen ("hoppen"), van elektronen die gelokaliseerd zijn op het vanadium subrooster. Daar­bij worden de verschillende transport routes en activeringsenergrnn voo:rnarnelijk bepaald door defectinteracties.

Hoofdstuk VII behandelt het ladingstransport mechanisme in een serie polykristallijne mangaan granaten. De resultaten van geleidings-

88

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en thennokracht metingen, uitgevoerd in het temperatuurgebied 30-100o0c, zijn in overeenstemming met niet-adiabatisch springen (''hoppen") van kleine polaronen Me gelokaliseerd zijn op het mangaan subrooster, waarbij het aantal rooster plaatsen dat beschikbaar is voor het transport proces beperkt wordt door defect interacties.

Hoofdstuk VIII bevat de algemene conclusies. Het klein-polaron model blijkt de elektrische transporteigenschappen van veel granaten te kunnen beschrijven als reken:i.ng gehouden wordt met defectinter­acties. Ook kan worden geconcludeerd dat in principe irreversibele licht-geinduceerde veranderingen van fysische eigenschappen bij kamer­temperatuur mogelijk zijn in granaten. Echter mag niet worden verwacht dat er bij kamertemperatuur irreversibele fotomagnetische effecten zullen optreden.

89

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LEVENSBERIGIT

02-12-1954

19-06-1972

26-0-6-1978

23-10-1978

01-06-1983

90

geboren te Vlaardingen eindexamen HBS-B, Baudartius College, Zlltphen doctoraal examen scheikunde, Rijks Universiteit Utrecht wetenschappelijk assistent in de vakgroep fysische chemie aan de Technische Hogeschool te Eindhoven, alwaar het in dit proefschrift beschreven onderzoek werd ver.cicht in dienst getreden als wetenschappelijk medewerker bij het Natuurkundig Laboratorium van de Nederlandse Philips Bedrijven B.V.

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STELLINGEN

behorend bij het proefschrift

PROPERfIES OF LOCALISED OIARGE CARRIERS IN VANADIUM .AND MANGANFSE

GARNETS.

1. Het is onjuist om anstenitisch roestvaste staalsoorten, wat betreft hun gevoeligheid voor spanningscorrosie, alleen op grond van de propagatiesnelheid van de scheuren te classificeren.

D. Desjardins, J. Daret, M.C. Petit and J.J. Pauthe, Corrosion Science, 20, 177 (1980).

2. De resultaten van door Reimers et al. uitgevoerde energiebere­keningen aan verschillende modificaties van ijs zijn aan twijfel onderhevig omiat niet is getest of de daarin voorkomende rooster­som van de elektrostatische energie voldoende convergeert bij het gekozen aantal tennen.

J.R. Reimers, R.O. Watts and M.L. Klein, Chem. Phys. 64, 95 (1982).

3. Ondat Bertoluzza et al. bij de interpretatie van hun Raman

metingen onvoldoende rekening houden met de adsorptie van water aan hun preparaten, krijgen zij een verkeerd beeld van de door hen onderzochte verdichting van Si02-gels.

A. Bertoluzza, c. Faguano, M. r.t:>relli, V. Gottardi and M. iliglielmi, J. Non-Crystalline Solids 48, 117 (1982).

4. De door Jackson et al. gevonden bandenstructuur in Ni-SiC diffusie koppels kan goed verklaard worden met het door Osinski voorge­stelde model.

M.R. Jackson, R.L. Mehan, A.M. Davis and E.L. Hall, Met. Trans. 14a, 355 (1983).

K. Osinski, The influence of Aluminium and Silicon on the reaction between Iron and Zinc, Proefschrift, Technische Hoge­school Eindhoven 1983.

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5. De bewering van Miyazawa et al. dat zij 3Bi2o3-ZM003 eenkristallen hebben bereid, stemt niet overeen met de door hen geanalyseerde chemische samenstelling daarvan.

Shintaro Miyazawa, Ahio Kawana, Hideo Koizumi and Hiroshi Iwasaki, Mat. Res. Bull. 2_, (1974).

6. Het verband tussen de gemeten dielektrische constante (£) en de dichtheid (f') van polykristallijne preparaten, dat door Dube et al. wordt gegeven, is strijdig met de door hen gesuggerebrde lineaire extrapolatie in een £ versus f graf iek.

D.C. Dube and A.K. Saraswat, J. Appl. ·phys. 53, 7095 (1982).

i 7. De interpretatie van metingen van thennokracht en elektrische

geleiding aan chroom(III)wolframa.at door Bharati et al. is i aanvechtbaar.

R. Bharati and R.A. Singh, Phys. Stat. Sol. 70a, K11 (1982).

8. In materialen waarin het ladingstransport plaatsvindt door middel van thermisch geactiveerd springen van ruimtelijk geloca~iseerde elektronen draagt de elektronenspin ontaarding niet bij tot de thennokracht als het betreffende ion in beide valentie tpestanden een netto spin-moment heeft.

Dit proefschrift hoofdstuk VII.

9. Het klein-polaron concept is een goed uitgangspunt bij de beschrij­ving van de elektrische transporteigenschappen van verbipdingen met de granaatstructuur waarin overgangsmetaalionen een hoofd­bestanddeel vormen.

Dit proefschrift hoofdstuk VIII.

G. Oversluizen; I

Eindhoven, 9 september ·1983.


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