Vol. 16, No. 3/4 193 Review of the EPR Data on ns^Centers in Crystals S. V. Nistor 1 and D. Schoemaker Physics Department University of Antwerp (U.I. A.) B-2610 Wilrijk-Antwerpen, Belgium I. Ursu 1 International Center for Theoretical Physics 34100 Trieste, Italy Contents I. Introduction II. Production and Structure of the ns^Centers 193 194 III. Theory of the EPR Spectra 196 A. The spin Hamiltonian of the ns 1 -centers 196 B. The superhyperfine interaction 200 IV. EPR Results 201 A. Trapped electron ns^centers 201 1. The IB-group (Cu°, Ag°, Au°) 201 2. The IIB-group (Zn+, Cd+, Hg+) 205 B. Trapped hole ns 1 -centers 209 1. The IIIA-group (Ga 2+ , In 2+ , Tl 2+ ) 209 2. The IVA-group (Ge 3+ , Sn 3+ , Pb 3+ ) 211 V. Concluding Remarks 216 VI. References 219 I. Introduction Several reviews concerning the EPR of the para- magnetic transition-metal ions in crystals are now available, either as periodic reports published in the Magnetic Resonance Review, or in books [1,2,3] and review papers [4, 5]. Such paramagnetic centers are usually observed in the as grown crystals, the para- magnetic state being the normal valency state of the impurity in the crystal-host lattice. The present review focuses on a different type of paramagnetic centers, the so-called ns^centers. 1 On leave from the Institute of Atomic Physics, Bucuresti, Roumania. Such centers, consisting mainly of a paramagnetic ion with the ns 1 (n > 2) outer electron configura- tion (Table 1), are seldom observed in the as grown crystals. They are produced in crystals containing cationic impurities by the trapping of electrons or holes induced by irradiation, as well as by additive or electrolytic coloring. In many cases several para- magnetic centers with different spin Hamiltonian parameters were reported for the same impurity- crystal host system. The differences are due to the various locations of the paramagnetic ion in the crystal lattice, as well as to the presence of neigh- boring defects such as vacancies, interstitials or im- purity anions.
Transcript
Vol. 16, No. 3/4 193
Review of the EPR Data on ns^Centers in Crystals
S. V. Nistor1 and D. Schoemaker
Physics DepartmentUniversity of Antwerp (U.I. A.)
B-2610 Wilrijk-Antwerpen, Belgium
I. Ursu1
International Center for Theoretical Physics34100 Trieste, Italy
Contents
I. Introduction
II. Production and Structure of the ns^Centers
193
194
III. Theory of the EPR Spectra 196A. The spin Hamiltonian of the ns1-centers 196B. The superhyperfine interaction 200
IV. EPR Results 201A. Trapped electron ns^centers 201
1. The IB-group (Cu°, Ag°, Au°) 2012. The IIB-group (Zn+, Cd+, Hg+) 205
B. Trapped hole ns1-centers 2091. The IIIA-group (Ga2+, In2+, Tl2+) 2092. The IVA-group (Ge3+, Sn3+, Pb3+) 211
V. Concluding Remarks 216
VI. References 219
I. Introduction
Several reviews concerning the EPR of the para-magnetic transition-metal ions in crystals are nowavailable, either as periodic reports published in theMagnetic Resonance Review, or in books [1,2,3] andreview papers [4, 5]. Such paramagnetic centers areusually observed in the as grown crystals, the para-magnetic state being the normal valency state of theimpurity in the crystal-host lattice.
The present review focuses on a different typeof paramagnetic centers, the so-called ns^centers.
1On leave from the Institute of Atomic Physics, Bucuresti,Roumania.
Such centers, consisting mainly of a paramagneticion with the ns1 (n > 2) outer electron configura-tion (Table 1), are seldom observed in the as growncrystals. They are produced in crystals containingcationic impurities by the trapping of electrons orholes induced by irradiation, as well as by additiveor electrolytic coloring. In many cases several para-magnetic centers with different spin Hamiltonianparameters were reported for the same impurity-crystal host system. The differences are due tothe various locations of the paramagnetic ion in thecrystal lattice, as well as to the presence of neigh-boring defects such as vacancies, interstitials or im-purity anions.
194 Bulletin of Magnetic Resonance
Table 1: Paramagnetic ions with the ns1—1S1/2 electron configuration observed in crystals by EPR. The usualvalency state of the impurity ion in the as grown ionic crystals is shown between brackets.
The objective of the present article is to presenta comprehensive picture of the EPR studies of suchcenters in inorganic crystals. The review is based ona literature survey of various reference sources car-ried out during several years when the authors wereinvolved in the study of such centers. Although ef-forts have been made to include all relevant refer-ences until the end of 1992, it is still possible thatomissions due to inadvertent oversight may occur.
The paper is divided into four main parts. Thefirst is a short survey of the production and struc-ture of the ns1-centers, which is far from trivial,and is essential in understanding their structure andEPR spectral properties.
The second part contains a short review of thetheory of EPR spectra for systems with 5 = 1/2 andI > 1/2, including the case of a dominant hyperfineinteraction, which is the appropriate one in manycases. Although the case has been discussed in aunified form [6], several approaches are to be foundin the literature devoted to the ns1-centers. Thepresent survey is mainly an attempt to put togetherthe various approaches.
The third and main part is a presentation of theEPR studies on ns^centers reported so far, the ac-cent being not on chronology and priority aspectsbut on the general features connected with the for-mation and structure of the resulting centers un-der various conditions (temperature, optical treat-ments, etc.). The understanding of the structureand formation mechanism of the ns1-centers hasmarkedly improved in the last decade as a resultof the studies performed on the similar np1-centers,which are much more sensitive to the surroundingcrystal fields.
The paper also contains a set of tables in whichthe spin Hamiltonian parameters of the various ns1-centers in inorganic crystals reported until the endof 1992 are presented.
II. Production and Structure ofthe ns^Centers
The ns1-centers have been extensively studiedin alkali halides (mainly chlorides), where a largebody of data are available. The real understand-ing of their production started with the observation[7] that doping KC1 with certain impurities, such asTl+, Ag+ or Pb2+, strongly enhances both the rateof formation and the final concentration of the self-trapped hole centers (Vk centers) produced by irra-diation with ionizing radiation at low (T < 100K)temperatures. It has been suggested that such im-purity ions act as efficient electron-trapping centers(resulting in the trapped electron centers Tl°, Ag°or Pb+), strongly reducing the recombination of theelectrons and holes produced by irradiation. Manyof the impurity ions act as efficient hole traps too.Consequently, by warming such a low temperatureirradiated crystal to temperatures where the holesbecome mobile (T > 170K in KC1) it is possible toobtain high concentrations of the trapped-hole cen-ters Tl2+, Ag2+ or Pb3+. The various hole and elec-tron trapping reactions have been extensively stud-ied in KC1:T1+ and KCl:Ag+ crystals [8, 9]. Fur-ther evidence concerning the structure of these cen-ters has been obtained from the EPR studies of theisostructural np1-centers [8, 10, 11].
The formation and structure of the ns1-centersis determined to a large extent by the vacancies,
Vol. 16, No. 3/4 195
present in the host lattice before irradiation ascharge compensating cation vacancies of the diva-lent IIB or IVA impurity cations, or produced by ir-radiation in the form of anion vacancies. Their pres-ence in the neighborhood of the ns1 paramagneticions results in the lowering of the symmetry of thelocal crystal field, which is, however, little reflectedin the EPR spectra of the ns^centers, due to thes-like character of their wave function. The usualabsence of a resolved superhyperfine (shf) structurefor the vacancy-associated ns1-centers makes it anextremely difficult task to determine their structure.For this reason the structural models of the variousns1-centers are based, in many cases, on indirectevidence.
The main bulk of data concerning the produc-tion and structure of the ns^centers refers to thealkali halides. As suggested from earlier EPR stud-ies on transition metal ions in alkali halides [4, 5],the monovalent cation impurities are located sub-stitutionally at cation sites of the cubic lattice. Inthe case of substitutional divalent cation impuritiesan equal number of charge compensating vacanciesare present in the lattice host, usually located inthe nearest- neighbor (NN) or next-nearest-neighbor(NNN) positions.
The irradiation of alkali halides at low temper-atures (T < 100K) with ionizing radiation, or evenwith UV-light close to the band gap value (5-10 eV),produces electrons, holes and excitons, the last be-ing subsequently involved in the production of anionvacancies and interstitials [12, 13]. The electrons(e~), which are mobile, are trapped either by theanion vacancies (va) resulting in F centers, or bythe monovalent or divalent cation impurities (M+
or Me2+). The holes (h+) are self-trapped forming\4 centers. The reactions of interest here are:
M+ + e~ -» M° (M = Cu, Ag, Au) (1)
(X = C1, Br, (2)
Me2c+vc + e' -f Me+vc (Me = Zn, Cd, Hg) (3)
where the subscript indicates the occupation siteof the ion/atom (c-cation site, a-anion site, i-interstitial), and vc represents the neighboringcation vacancy.
Upon warming the irradiated crystal several pro-cesses take place. The Vk centers become mobile(above 170K in KC1), a large fraction of them being
trapped at the impurity ions, resulting in trappedhole ns1-centers, according to the reactions:
(M = Ga, In, Tl) (4)
Mei+vc+Vk Me3c+vc+2X~ (Me = Ge, Sn, Pb)
(5)At even higher temperatures, where vacancies be-come mobile, they can be either trapped at or re-leased from the ns1-centers. In the case of the cationvacancies the following reactions can take place:
Mr + v.T>Ta M2c+vc
Me
(M = Ga, In, Tl) (6)
(Me = Zn, Cd, Hg) (7)
(Me = Ge, Sn, Pb)(8)
where Ta is the activation temperature for the move-ment of vacancies (Ta = 220K for both vc and va inKC1 or RbCl [10, 11, 14]).
As initially suggested [15, 16] in the case of theatomic Ag°(5s1) center in KC1, the atomic ns1-centers can trap anion vacancies forming the so-called A% centers:
M°c M°cva{A°F) (M = Cu, Ag, Au) (9)
Such centers are produced in even larger concen-trations by optically bleaching at T > Ta, in the-F-band, the crystals previously irradiated at lowertemperatures. The analogy with a similar processpreviously observed in alkali halide crystals dopedwith alkali impurities [17], by which FA centers, (i.e.F centers next to alkali impurities) were obtained,has been initially the main argument supporting thereaction (9). The direct demonstration of the va-lidity of reaction (9) came later from the studies[10, 18] of the isostructural M°(l)-np1 centers (M =Ga, In, Tl), which have shown that such centers canbe also produced by the reactions:
M+ T>Ta
M°cva = A% =
(10)
(11)Reaction (10) is also valid for M = Cd, resulting inthe co-called A~p centers. By irradiation with ion-izing radiation at temperatures where vacancies aremobile, besides the Ap centers, various other centersare produced. Of special interest are the negativeions. The existence of such ions, supposed to be
196 Bulletin of Magnetic Resonance
located at anionic sites of the lattice, has been ear-lier proposed [19, 20] from optical studies on addi-tively or electrolytically colored alkali halides dopedwith copper, silver or thallium. Their productionby X-ray irradiation at RT is now supported bythe EPR observation of the Sn" [11], Pb~ [21] andBi° [22, 23] centers in KC1 crystals. The mecha-nism through which they are produced has been un-der debate since then [24]. By optical bleaching at300K in the negative ions optical absorption band(B-band), a new ns1-center called Ag^ has been ob-served [15, 16] in KCl:Ag+ crystals. The proposedproduction mechanism of this center, suggested tobe a Ag° atom at an anion site, consists of a simpleionization step:
Ag" (12)
Based on the positive identification by EPR spec-troscopy of the Ag°, Ag^ and Ag° centers, thefollowing sequence of reactions has been proposed[15, 16] to explain the production of negative ions:
(A) Ag+ H
(B) Ag°H
(C) A g ^ a
(D) Ag-
hv{Ag°F)
—^Aga
(13)
where (A) and (B) correspond to reactions (1) and(9), respectively. Reactions (B) and (C) take placeby optical excitation in the F and Kg°F absorp-tion bands, respectively. Reactions (B) and (D)are thermally activated. Reaction (C) has beenfound to take place even at low temperatures, sug-gesting a tunneling process. The above set of re-actions exclude the interstitialization of the silveratom [25, 26, 27]. Its general character remains tobe confirmed from the study of other ions and lat-tice hosts. Although no Cu^ centers have been ob-served yet, the reactions (13) are considered to de-termine the formation of the Cu~ negative ions too[28]. Supporting evidence for the general characterof reactions (13) comes from the identification of theM°, M°F and M° centers (M = Ga, In, Tl) in KC1and NaCl crystals after X-ray irradiation at roomtemperature [18, 29].
us -centers have been also observed in mixed al-kali halides. Such centers exhibit a characteristic
shf pattern due to the presence in the first neigh-borhood of the second type of anion.
The production properties and structure of thens1-centers in other lattice hosts are less known.Such centers were observed after irradiation withionizing radiation, but very little effort has beendevoted towards the study of their production andstructural properties. It is, however, expected thatin other ionic crystals the accompanying lattice de-fects would behave in a similar way as in alkali chlo-rides. In certain oxides and semiconductors, thens1-type of paramagnetic centers have been alreadyobserved in the as grown crystals. In the latter casethe concentration of the ns1-centers could be dras-tically changed by illumination in the band gap as aresult of trapping the resulting free electrons/holes.
III. Theory of the EPR SpectraA. The spin Hamiltonian of the ns1-
centers
The EPR spectra of the ns1(15) paramagneticcenters can be described by the general spin Hamil-tonian
H = g-S + S - A - I - gNfiNH • I
(14)
with the usual notations [1, 2], Here 5 = 1/2 and /may have one or more values, corresponding to thenuclear isotopes of the ns2-impurity involved (Table2). In is the nuclear spin of the neighboring ligands.The spin Hamiltonian (14) contains terms describ-ing the electronic Zeeman, hyperfine (hf), nuclearZeeman, nuclear quadrupole (7 > l /2 ) and superhy-perfine (shf) interactions, respectively.
Due to the strong s—character of the electronwave function it is considered that the main con-tribution to the hf parameter A comes from theisotropic Fermi contact term
— (15)
where | 4>ns{ty |2 represents the ns-wave functiondensity at the central nucleus. A contribution to theisotropic hf parameter through the exchange polar-ization mechanism of the ns-electron with the innerelectronic shells is expected to occur [2]. However,
Vol. 16, No. 3/4 197
Table 2: Characteristic parameters of the naturally abundant nuclear isotopes with spin / ^ 0 occuring inthe ns^centers.
Nucleus63Cu65Cu67Zn69Ga71Ga73Ge107Ag109 A gm C dU3Cd113In
a Based on data published in Handb. of Chem. and Phys., 55th ed., CRC Press, Cleveland, 1974 and byVarian Assoc, Palo Alto, 1972.6 Reference [30].c Reference [31].d Calculated by multiplying the value for the other isotope with the ratio of the corresponding nuclear mo-ments.e Reference [32]./ Reference [33].9 Reference [34].h Reference [35].{ Reference [36].j Reference [37].k Reference [38].
in the analysis of the hf parameter of the ns1 centersthis contribution is not explicitely considered, beingeither neglected or formally included in the contactterm.
Theoretical evaluations, as well as experimental
data obtained from magnetic resonance measure-ments on ion beams or ions (atoms) trapped in in-ert gas matrices show (Table 2) that several I ^ 0isotopes exhibit large hf splittings (A 3> g/j,BH), atleast in the microwave X-band (9 GHz) in which the
198 Bulletin of Magnetic Resonance
EPR measurements are usually performed. For thisreason, in many cases, the spin Hamiltonian param-eters are now determined by fitting the experimen-tal magnetic field values of the EPR transitions withthe corresponding values obtained from a numericaldiagonalization of the spin Hamiltonian (14).
In several particular cases accurate values of thespin Hamiltonian parameters have been obtainedby fitting the transition fields with analytical so-lutions corresponding to the diagonalization of thespin Hamiltonian (14) in various approximations. Inall cases the energy levels are mainly determined bythe first two terms, which are the largest.
The nuclear quadrupole interaction term hasbeen considered only in a very few cases. It van-ishes for / < 1/2. In other cases it is either toosmall, or it is difficult to determine, being a secondorder phenomena.
The superhyperfine (shf) interaction with thenuclei of the neighboring ligands has been takeninto consideration only in those cases when the cor-responding structure in the EPR spectrum is re-solved. Its theoretical treatment will be discussedseparately.
In the high symmetry crystal-lattice hosts, suchas alkali halides, the EPR spectra, of the n51-centersare isotropic, or there is a small anisotropy (~ 1%)in g and A, which is neglected. The EPR spectraare then described by the simple spin Hamiltonian
H = -S + AS-I- I (16)
The eigenvalues of (16) are given by the Breit-Rabiformula
E(F,mF) = —— -
±-AW1 +
Am p21 + 1
1/2(17)
where F — S + I,mF = m ± ^,x =gfiB)H/AW = gTfiBH/AW, AW = (A/2)(2I + 1).
In the zero magnetic field there are only two lev-els with energies (A/2)I and -(A/2)(I + 1), sep-arated by AW. Two types of transitions are ob-served, corresponding to the selection rules in theextreme cases:
> A: AF = ±1, AmF = ±1(AM = ±l,Am = 0)
< A: AF = 0, AmF = ±1(18)
(19)
In the strong magnetic field approximation [for-mula (18)] the intensity of the transitions are ~jg2HBH2, where Hi is the microwave magnetic fieldcomponent. For such transitions the spin Hamilto-nian parameters can be determined with the aid ofthe following general formulae:
21+1
-A(2mgTfiBH) - (hu +-(gTiiBH)2 = 0
9T \ A )V
V Ahv + (20)
where v is the microwave frequency of the ESR tran-sitions. In the g^BH S> A case, a perturbation solu-tion of the spin Hamiltonian (16) in the third orderof approximation gives the following formula for themagnetic field at resonance [40]:
hv A I A Agfj,B
1-m 2 gp,B hv
I A A2
Ag/j,B(hv)\
H 7A
A Ag\xB
(21)
In the case of a weak magnetic field the spinHamiltonian parameters can be determined from thefollowing formula:
1 / r, ,, U \ 2
— | IA2
+(hv ± gNiiNH)2 + = 0 (22)For some of the ns1-centers, such as Pb3+ or Tl2+,two transitions corresponding to the selection rules(19) are observed at the magnetic fields H\ and H2.The spin Hamiltonian parameters are then obtainedin a good approximation with the simple formulae:
2hv(hv + A) 2hv(hv - A)9 = (2hu (2hv - (23)
Vol. 16, No. 3/4 199
A =and
(24)
Additional transitions, corresponding to the selec-tion rules AM +_ 2, Am = 0, ±1, normally forbid-den in the high field limit, can be observed in inter-mediate cases with intensities lower by a factor of(A/g^sH)2 compared to the normally allowed ones.
In many crystal lattices with lower symmetry theEPR spectrum of the nsx-centers exhibits a clearanisotropy, which was attributed [41] to the presenceof an odd crystal field component which mixes theexcited 2 P state into the ground 2S state.
The exact solutions of the anisotropic spinHamiltonian (14), from which the last two termswere neglected, have been reported earlier [42, 43,44] for the case of the magnetic field along one ofthe principal axes, when 5 = 7 = 1/2. In the caseof H || z they are:
= ^ ± \ \{AX -(25)
\(AX + Ay)2(26)
The solutions for H \\ x and H \\ y are obtainedby cyclic permutations of gi and Ax. Similar expres-sions have been reported for the 5 = 1/2, I = 5/2system [45, 32].
Approximate solutions to the secular equation,for moderately anisotropic spectra were obtained[46] by considering the anisotropy as a perturbationadded to (16). The starting point is the expressionof the magnetic field transition for the isotropic casewritten as,
/ \ 2
where/ _
Hm = H'm (for gNfiN = 0)Formula (27) is valid for all positive solutions and,in particular, for all values of/ u / » (A/2) (21+1).
The corrections to the EPR transitions, at fixedm, in the first order of perturbation associated withthe anisotropy in the spin Hamiltonian are given by
coszm + i ]
m+-J coszm+± (28)1/2
1/2
sin 2.
where
andPm = m
(29)
(30)1 + 1/2
In a different approach [47] the spin Hamiltonian(14) has been expressed in a reference frame asso-ciated to the magnetic field. Afterwards, only thefollowing part of the rotated Hamiltonian has beendiagonalized:
ASZIZ1 (AzAxy + AxAy
Axy
(S+I- + S-I+) + [{QX COS2 ip + Qy sin2
sin2 6 + Qz cos2 6] II - gNpNHIz (31)
Here g and A have the usual [1] angular dependenceof the polar angles 0 and ip of the magnetic field, inthe frame associated to the principal axes of the g, Aand Q tensors, considered coaxial. Assuming smallanisotropies, the rest of the terms were neglected.Analytical expressions for the energy levels, wavefunctions and transition probabilities were obtainedfor I > 1/2, S = 1/2.
Solutions for the first two terms of the spinHamiltonian (14) with rhombic symmetry, for S =
200 Bulletin of Magnetic Resonance
I = 1/2, have been obtained [48] by rewriting it ina coordinate system associated with the magneticfield (H || C):
HoHiH2
H3
— Ho + Hi + H2 + H3
= gPHSt + KStl?= KiS+I?+KtS-I?— A20+J4- + A 2 O- i -
— 1\3J + 1— + JX-iO — l^-
(32)(33)(34)(35)(36)
where K{ are polynomial expressions of g,, A, andorientation angles of H. The relative contributionof Hj's to 7is differs from center to center, but Hiis considered to be the smallest, at least for centerswith large hf coupling.
B. The superhyperflne interaction
The interaction of the s-electron with the mag-netic momenta of the neighboring ligands is consid-ered as a perturbation, producing the shf splittingof the EPR lines. However, for the majority of thens -centers its contribution consists only in an inho-mogeneous broadening of the EPR lines. Neglectingthe shf interaction in determining the spin Hamilto-nian parameters might result in significant errors ifa low field transition with energy comparable to theshf splitting is considered.
Due to the usually isotropic character of the ns1-type EPR spectra the shf structure represents themain source of information concerning the structureof the involved center.
The number and the intensity of the various com-ponents of the shf structure are obtained by the bi-nomial rules [2, 40]. The shift of each componentfrom the center of the EPR line is given by
[{A\f cos26 + {A\)2sin2d\^ (37)
where 9 is the angle between the direction of themagnetic field and the bond direction, and mn rep-resents the nuclear magnetic moment of the n-th lig-and. Formula (37) can be rewritten by introducingthe isotropic (AJ) and anisotropic (A") componentsof the shf tensor An;
= Ans (38)
The isotropic part (As) is considered to be mainlydue to a Fermi-type interaction of the s-electron
with the ligand nucleus. The anisotropic part (Aa)is a sum of two contributions: the anisotropic inter-action of the p-orbitals (Ap) and the dipole-dipolemagnetic interaction {Ap) between the paramag-netic electron and the ligand nucleus:
A — A AD (39)
The quantitative analysis of the shf parametersis usually performed [2, 49] by admixing the n's andn'p orbitals from the neighboring ligands into thecentral ns orbital. By considering covalency effectsit is possible to explain the large positive Ag shiftand the decrease of the hf constant A, compared tothe free ion value Af. The same molecular orbital(MO) model in a covalency calculation offers a con-sistent interpretation of the optical absorption spec-tra of the ns2- and ns centers in crystals [50, 51].
According to the MO model, initially appliedto octahedral [52] coordination (MX6 clusters) andtetrahedral [53] coordination (MX4 clusters) of lig-ands, the wave function of the paramagnetic elec-tron is written as:
(40)
(41)where
^ s is the ns orbital of the central ion. Xs and Xthe linear combinations of atomic orbitals (LCAO)of the neighboring ligands with the same symmetryproperties i.e., the a\g and a\ representations of theOh and Td symmetry groups, respectively [49, 54].
Neglecting the overlap of the atomic orbitals, thehf constant is given in both cases by:
A = N2Af (42)
where Aj is the free nsMon (atom) hf constant.The shf constants are given by:
A, = HNX.fA",
AD =
(43)
where / is 1/6 and 1/4 for the MX6 and MX4 clus-ters, respectively. A® and A® represent the free lig-and ion hyperfme parameters,
25*
~-3\/n'p (44)
Vol. 16, No. 3/4 201
The Ag shift is given by the following formula,valid for both coordinations [53]:
= ~N2[\l + XaXsmR{3px \x\3s)
xAE(p- s)Ti~ lAE(45)
where m is the electronic mass, R is the distanceto the ligand, AE(p — s) is the energy separationbetween the n'p and n's orbitals, ((r) is the spin-orbit interaction constant of the n'p electron andAE is the energy separation between the groundantibonding a\g orbital and the nonbonding t\g or-bital, which can be determined from optical spectra.Formula (45) explains the large Ag shift observedfor the ns1-centers in crystals with strong covalentbonding and offers the possibility of connecting theEPR and optical spectra.
The relevant free-atom values in the above for-mulae were calculated [30] for elements from thal-lium to bismuth, using Hartree-Fock-Slater atomicorbitals [55]. Formula (42) shows a decrease of thehf-constant with an increase of the covalency. Theconsistency of the MO model has been checked forvarious ns1-centers by fitting the covalency param-eters As and \a to the measured shf constants andafterwards calculating the hf constant A, accordingto formulae (44). The calculation usually results ina smaller hf-constant. Better results were obtainedby considering [56] the overlap of the orbitals. Thetheory of Watanabe has been further refined [57],by choosing the wave functions which diagonalizethe spin-orbit interaction as the basis wave func-tions. Such an approach takes a better account ofthe larger spin-orbit interaction in the progressionof ligands from S, Se to Te.
IV. EPR Results
A. Trapped electron ns^centers
Trapped electron ns -centers are easily producedby irradiating with ionizing radiation crystals dopedwith IB or IIB cation impurities, as well as by subse-quent optical bleaching and/or pulse anneal at vari-ous temperatures. The corresponding trapped elec-tron ns1-centers have been mainly observed in alkalihalide crystals.
1. The IB-group (Cu°, Ag°, Au°)
With very few exceptions, the ns^centers associ-ated with the IB-group impurity cations have beenreported in copper and silver doped alkali halides.Gold centers were less studied, mostly due to thedifficulties in doping (Tables 3-5). It is worth-while mentioning that the IB-group cations, withd10 outer electron configuration, can also trap holesresulting in paramagnetic d? transition ions.
The alkali halide crystals employed in these stud-ies were grown from melt, with about 0.1 to 0.2mol% of the impurity halide added. Both copperand silver halides being stable at high temperatures,large amounts of the corresponding Cu+ or Ag+ im-purity ions are found in the crystals grown from melt(about 10% of the initial concentration). Due tothe thermal instability of the gold halides, the dop-ing with gold was done by adding the metal to themelt, under a chlorine atmosphere.
The trapping of electrons by the Ag+ and Cu+
ions in alkali halides has been earlier suggested[25, 58] to explain the new optical absorption bandsobserved after X-ray irradiation.
The first EPR spectrum of a ns1—center(Ag°)has been observed [9] in a KCl:Ag crystal afterelectron-irradiation at 77K. It consisted of two tran-sitions attributed to the superposition of the hf com-ponents from the two silver isotopes with 7 = 1 / 2(Table 2). The interpretation of the well resolvedshf structure confirmed the substitutional localiza-tion in a regular six-fold octahedral coordination,which suggests that the center is produced accord-ing to the reaction (1). The substitutional model ofthe Ag° centers in KC1 and NaCl, has been latterconfirmed by ENDOR measurements [71, 72].
Cu° centers in alkali chlorides [31, 61] and Au°centers [59] in NaCl and KC1, have been also ob-served after X-ray irradiation at 77K. Their EPRspectra exhibit a more or less resolved shf structureand were interpreted with the spin Hamiltonian (16)to which the shf interaction was added.
Due to the presence of two isotopes with I =3/2 (Table 2), the X-band EPR spectra of the Cu°centers consist of a pair of lines for each isotope,attributed to the (F = l,mF = -1) <—> (F =2,mF = -2) and {F = 2,mF = -2) <—> (F =2, mp = — 1) transitions (A > g(5H approximation).
Gold has only one natural isotope with nuclearspin / = 3/2 and hf splitting A ~ g(5H (Table 2).
202 Bulletin of Magnetic Resonance
Table 3: The EPR parameters of the Cu°—type centers at 77K. The hf parameter A and the shf parametersAs and Ap for the NN anion ligands are given in MHz.
CenterCu^ in LiClCu° in NaClCu° in KClCu° in KClCu° in RbClCu£ in NaClCu°, in KClCu°(I") in KClCu°(I) in quartza
a Measured at 120K. Shf interaction with one 29Si ligand.
Three EPR transitions were observed [59] in the X-band.
It has been mentioned [59] that before X-ray ir-radiation the alkali chlorides doped with copper orgold had to be annealed at high temperatures andquenched to 77K. This observation suggests that acertain amount of the two impurities enters the lat-tice in a higher valency state (+2, +3), resulting inimpurity-cation vacancy aggregates which have tobe thermally dispersed.
From the analysis of the isotropic shf constant Asof the Cu° and Ag° centers in alkali chlorides andin KBr, it has been found [66] a significant outwardrelaxation (between 14% and 27%) of the nearest lig-ands. This effect has been explained as an accom-modation effect of the larger Cu° and Ag° atoms,compared to the host lattice cations.
A strong temperature dependence of both hf con-stant A and isotropic shf constant As, has been ob-served at low temperatures, for the Ag° and Cu°centers in LiCl, NaCl and KCl [67], and for the Cu°centers in RbCl [61]. With the exception of the Cu°in KCl and RbCl, for all other centers both param-eters decrease by increasing the temperature. No
quantitative interpretation of the above results hasbeen given yet.
The quantitative evaluation [70] of the isotropicshf constant As for the Cu° and Ag° centers andof the hf constant A for the Ag° center in alkalichlorides, in the frame of the Adrian theory [68],resulted in a good fitting with the experimental dataonly for the Ag° centers in KCl and RbCl.
An unusual behavior of the shf structure of theCu° center in KCl at very low temperatures (T <20K) has been reported [60]. By lowering the tem-perature, the observed shf structure, characteristicfor an interaction with six equivalent chlorine nu-clei, becomes unresolved at T < 40K. Below 20Kthe shf structure is again resolved, but its interpre-tation shows that the Cu° atom is now displaced toan off-center position, along a (111) direction. Atheoretical analysis of the shf parameters tempera-ture dependence shows [69] that in the 30-40K rangethe interaction constant of the Cu° atom increases2.8 times for the nearest ligand lying in the directionof the off-center displacement and decreases for theother NN ligands.
It has been suggested [61] that the similar tem-
Vol. 16, No. 3/4 203
Table 4: The EPR parameters of the Ag°—type of centers at 77K. The hf parameter A and the shf parametersAs and Ap for the NN anion ligands are given in MHz.
CenterAg" in LiClAg° in NaClAg° in NaCl a
Ag° in KClAg° in KCl a
Ag° in RbClAg° in KBrAg° in KIAg£, in LiClAg^ in NaClAg£ in KClAg£ in RbClAg°(I") in KClAg^(Br-) in KClAg° in SrCl2Ag° in KClAg° in L1KSO4Ag° in (NH4)2SO4
ENDOR measurements.Measured at 290K.X-ray irradiated at 77K.X-ray irradiated at 300K.Measured at 120K. Shf interaction with one 29Si ligand.
perature dependence of the hf constant A observedfor the Cu° center in KCl and RbCl must be due tothe same off-center displacement of the Cu° atom.
Another type of ns1-centers, called PSp centers,have been observed [75, 15] in silver doped alkalichlorides after X-ray irradiation at RT followed byoptical bleaching in the F-band. Such centers havebeen latter obtained [63, 62] in copper doped NaCland KCl, directly by X-ray irradiation at RT. Their
concentration could be further increased by bleach-ing in the F-band. k°F centers have been directlyobserved [74] in silver doped thin films of alkali chlo-rides. A°F centers have not yet been reported in golddoped crystals. The corresponding spin Hamilto-nian parameters are given in Tables 3 and 4. No shfstructure has been observed in the EPR spectra ofthe A1^ centers.
It has been suggested [75] that the A°p center
204 Bulletin of Magnetic Resonance
Table 5: The EPR parameters of the Au°—type centers at 77K. The hf parameter A and the shf parametersAs and Ap for the NN anion ligands are given in MHz.
CenterAu^ in NaClAu° in KC1Au£ in NaClAuS in KC1Au£ in RbClAu°, in NaClAu°, in KC1Au°, in RbCl
g2.0012.0042.002.0202.0242.0122.0102.020
| i 9 7A|2,8402,5302,3502,1701,9802,7802,4102,160
As
46.236
Ap
56References[59][59][59][59][59][59][59][59]
consists of a ns1-atom (A = Cu°, Ag°) next to ananion vacancy. Because the unpaired electron is ex-pected to be partly localized at the anion vacancy,it is possible to consider the A°F center as being anF-center next to the cation impurity.
In the absence of a clear anisotropy of the EPRspectra, or of a resolved shf structure, the structuralmodel of the AF centers had to be supported byindirect arguments. The proposed structural modelhas been initially based on the similar production ofthe A^ centers with the F^ centers [17].
Additional arguments favoring the A°F centermodel, were based on the analysis of the hf con-stant shift 8A and of the linewidth of the variousnsx-centers [75].
According to formulae (15) and (42) the quantity
A -AjA~ = 8A•f (46)
which is the relative shift of the hf constant A to thefree atom/ion hf constant Af, represents the degreeof the delocalization of the paramagnetic electronat the neighboring ligands. Due to the F-characterof the unpaired electron wave function at the an-ion vacancy site, the A°F structural model with aneighboring anion vacancy involves a large 8A shift.By examining the hf constant of the correspond-ing M° and A°F center (Tables 3,4), it was foundthat in each particular case 8A(A°F) > 6A(M®).For example, in the case of the Ag° centers in KC18A{A%) = 34% > 6A(Ag°) = 4.4%. This type of
argument has been latter employed to identify newA°F centers.
Considering the linewidth of the ns1-centers asbeing mainly determined by the isotropic shf con-stant As, in the case of the AF centers one has toconsider the shf interaction with five anions nextto the ns1 atom and the shf interaction with fivecations next to the anion vacancy. It is then ex-pected that crystals grown with various isotopicpure cations will exhibit different linewidths of theA°F centers. Using single crystals of alkali chlo-rides grown from the isotopic pure cations 39K, 41K,85Rb and 87Rb, a variation in the linewidth of theAg^ centers from 4.5 mT in 39KC1 to 16 mT in87RbCl was determined [82], which could be ac-counted for by the anion vacancy model. Newns^centers, called Cu°(X~~) and Ag°(X~), whereX~ =I~ and Br~, have been observed [64, 77, 83]in mixed crystals of KCl(KI) and KCl(KBr). Thestructural model, inferred from the analysis of theshf structure is based on a M° model (M = Cu, Ag)with one of the six neighboring ligands replaced byan impurity anion. The larger isotropic shf constantAs (X~) due to the shf interaction with the NN im-purity anion, compared to the shf constant with theNN host anions, suggests a local deformation of thecrystal lattice.
The trapping of an anion vacancy next to acationic substitutional neutral impurity atom is nowsupported by the direct observation [10, 18] of sucha process in the EPR spectra of the anisotropic
Vol. 16, No. 3/4 205
np1-M°(l) centers (M=Ga,In,Tl). An analysis ofthe production properties of the A°F centers [15, 75]shows that reactions (9) and (11) are involved in theformation of both M°(l) and A^ centers.
Alkali chloride crystals doped with gold exhibitafter X-ray irradiation at 77K, besides the cubic Au°centers, a second type of ns^centers, called Au° cen-ters [59]. The Au° centers are converted to new Au°centers by annealing above 140K. The Au° centersexhibit the largest 6A shift and an isotropic splittingof the EPR lines in 7 equidistant components, with amaximum along a (100) direction. They are consid-ered [59] to consist of an Au° atom at a cationic site,with a Vfc center in the NN anion site, along a (100)direction. The Au°, centers, with a 6A shift slightlylarger compared to the Au° centers and with simi-lar linewidths, are considered [59] to be Au° centerswith a perturbing defect in a NNN position.
The X-ray irradiation at RT of the silver dopedalkali chlorides results in the formation of Ag°, Ag2+
and F-centers, with their characteristic EPR spec-tra, as well as of negative Ag~ ions, supposed tobe localized at anion sites and identified by theiroptical absorption B-band [19, 20].
The Ag° center, observed [15, 75] after opticalbleaching at 300K, in the B-band of the KCl-Agcrystals, is considered to be a silver atom at an un-perturbed anion site, produced according to reac-tion (12). In the absence of a resolved shf structurethe anion localization of the silver atom is suggestedby the smaller linewidth; 2.1 mT for the Ag° centersin KC1, compared to 4.1 mT for the Ag^ centers,both at 300K. Because they are produced at temper-atures where the vacancies are mobile, the presenceof vacancies in the neighborhood of the Ag~ or Ag°centers cannot be however completely excluded.
The observed linewidth and hf constant increasewith temperature of the Ag^ centers, for T < 100K,has been explained [79] by an off-center displace-ment in a (111) direction, by analogy with the Cu°centers in RbCL
The production of a dimer-type of trapped elec-tron center has been reported [84] in KCl:Ag crys-tals, after long X-ray irradiation at RT. The result-ing Agj" center exhibits an isotropic EPR spectrumwith ^=1.986, suggesting the unpaired electron tobe localized in a s-type orbital. A well resolved shfstructure could be observed in samples doped withsilver enriched in the 109Ag isotope. It has been sug-
gested that the Ag j" center consists of two Ag+ ionsin a cation site, which have trapped an electron.
Ag° centers have been reported in X-ray irradi-ated SrCl2 and LiKSC-4 crystals doped with silver[78]. A partly resolved shf structure has been ob-served for the SrCl2 crystals, suggesting a cationiclocalization of the Ag° atom, but no detailed anal-ysis has been reported. Atomic Ag° centers havebeen also observed [85, 81] after X-ray irradiationat RT of silver doped (NH4)2SO4 and K2SO4 crys-tals, both exhibiting low symmetry crystal latticeand structural phase (SP) transitions.
2. The IIB-group (Zn+, Cd+, Hg+)
The elements of the IIB-group are expected toenter the crystal lattice in their +2 valency state. Inthe case of the alkali halides, in which the resultingns1-centers were mainly reported, several effects areto be expected:
• The segregation coefficient during the growth ofsuch doped crystals is larger than in the case of thedoping with monovalent impurities. Consequentlya smaller concentrations of IIB-group impurities isfound in the resulting crystals. For example, theconcentration of cadmium in the KBr crystals wasfound to be 200 times smaller than in the melt [86].
• The IIB-group impurities enter the lattice ac-companied by an equal number of charge compen-sating cation vacancies, usually at NN lattice sites.
• The impurity-charge compensating vacancypairs have the tendency to aggregate, even at RT.Consequently, before producing ns^centers by irra-diation the samples have to be annealed at tempera-tures close to the melting point and quenched at RTor even at lower temperatures, in order to achievetheir dispersion.
The presence of trapped electron ns1-centers incrystals doped with IIB impurities has been initiallysuggested [87] from optical studies on additively col-ored KChCd crystals.
Cubic Cd,f centers have been observed by EPR inalkali chlorides [88, 89] after X-ray irradiation at RT,or after X-ray irradiation at 77K followed by warm-ing up to temperatures close to RT, where the ini-tially bound cation vacancy could move away. Cubic
206 Bulletin of Magnetic Resonance
Zn+ centers in NaCl and cubic rlg^ centers in LiCl,NaCl and KC1 were obtained by similar productionprocedures [90]. They all exhibit well resolved shfstructures, characteristic for a substitutional Me+
(Me = Zn, Cd, Hg) ion in a regular octahedral co-ordination of chlorine ligands.
The EPR spectra of the Zn+ centers in NaClexhibit only one transition at g ~ 2, due to the evenisotopes. The hf transitions from the 67Zn isotope,with 7 = 5/2 and natural abundance of 4.16%, couldbe observed [90] only in crystals doped with 88%enriched 67Zn isotope.
Natural cadmium contains six isotopes, of whichfour are even isotopes (7 = 0) and only two exhibitnuclear moments jv > 0 (Table 2). The X-bandspectrum of the Cd+ centers consists of a line atg ~ 2, from the even isotopes and two pairs of linesdue to the hf transitions of the odd isotopes,
(F = l ,m F = 1) <—> (F = 0,mF = 0)
and
(F=l,mF = = l,mF =
Natural mercury contains, besides the even iso-topes with 7 = 0, two isotopes with 7 = 1/2 and3/2 and nuclear momenta of opposite sign (Table2). Consequently, the X-band EPR spectra exhibit,besides the g ~ 2 line, two lines from the hf transi-tions,
and
(F = l,mF = -1 ) <—> (F = l,mF = 0)
(F = 1, mF = 0) *—> (F = 1, mF = 1)
of the 199Hg isotope and one line from the hf tran-sition,
(F = 2, mF = 1) <—y (F = 2, mF = 2)
of the 201Hg isotope.The EPR spectra of the IIB-group n^-centers
have been described by the spin Hamiltonian (16).including the shf interaction term, if necessary. Theresulting EPR parameters are given in Tables 6-8.
A decrease of the hf constant A with increasingtemperature was found [92] for the Cd+ centers inKC1. The temperature dependence, described byformula:
A = Ao(l - CT) (47)
where C = 1.5 xlO 4K 1 in the investigated tem-perature range (100-300K), has been quantitativelyaccounted for [92] with a Simanek-Orbach typemechanism [97]. According to this interpretationthe thermal vibrations of the crystal lattice inducea noncubic crystal field at the Cd+ ion, which mixesthe 5p excited states into the ground 5s electronicstate. The normalization of the new, mixed elec-tron wave function results in a reduction of the 5selectron density at the Cd nucleus, and accordingto formula (15), of the hf constant A. Neglectingthe contribution from the dipolar interaction term,the temperature dependence of the hf constant A isdescribed by formula:
1 - l.— coth2kT
(48)where 7? = 3.1 xlO-10m, E5p - E5s = 4eV and(5s|x|5p) = 1.6 x 10~10m. In the investigated tem-perature range formula (48) can be approximated by(47). The resulting value of a; = 1.4xl013s~x is closeto the phonon frequency UQ = 1 x 1013s-1 obtainedfrom the analysis of phonon-induced optical transi-tions of Ag+ in KC1. It seems highly probable thatthe same mechanism, involving the decrease of theFermi-type hf interaction by the electron-lattice cou-pling of the excited p-like states, describes the sim-ilar temperature dependence of other ns1-centers,such as Ag° in KC1.
Three types of paramagnetic centers, exhibitingbroad lines, without shf structure, have been ob-served [91] in cadmium doped NaCl and KC1 crys-tals, after X-ray irradiation at 77K. The centers,called CdJ (I), (II) and (III), are considered to bethe precursors of the Cd+ centers, i.e., Cd+ — vcpairs with the cation vacancy vc situated at varioussites next to the Cd+ ion. By warming up the sam-ples the cation vacancy is freed, which results in theformation of the cubic Cd+ centers (reaction 7).
EPR spectra attributed to Cd£ centers havebeen observed [91] after X-ray irradiation at RT ofcadmium doped LiCl, NaCl and KC1. The proposedstructural model is based on the observation thattheir linewidth is smaller than for the Cd^ centersand changes as a function of the lattice host in asimilar way as the linewidth of the F centers.
Cd+" centers have been observed [93] in all alkaliearth fluorides doped with cadmium after x-ray irra-diation at 77K or, in the case of the BaF2, even after
Vol. 16, No. 3/4 207
Table 6: The EPR parameters of the Zn + - type centers at 77K. The hf parameter A and the shf parametersAs and Ap for the NN anion ligands are given in MHz.
RT irradiation. The resolved shf structure has beeninterpreted with a substitutional model in which theCd+ ion is surrounded by a regular cube of eight F~ligands.
EPR spectra attributed to Cd+ centers havebeen reported in Cd2+ doped f3—K2SO4 crystals[94] and Cd2+ doped (NH4)2SO4 crystals [95, 96] af-ter X-ray irradiation at RT. The two rhombic EPRspectra (Table 7) have been attributed to Cd+ ionsat the two inequivalent cation sites with Cs symme-try, which are distinguished by their different coor-dination. It has been reported [94] that the Cd+
centers are not produced in the /3—K2SO4 crystalsby X-ray irradiation at 77K. No shf structure hasbeen reported for these centers.
Anisotropic EPR spectra attributed to Zn+ typecenters have been reported in irradiated CaCO3(calcite) [32] and K2SO4 crystals [45]. The EPRspectrum, observed after 7-ray irradiation at RT ofnatural calcite crystals containing 0.05% zinc, ex-hibits axial symmetry, characteristic for a Zn+ ion ata Ca2+ site. The strong intensity of the EPR spec-trum made possible the observation of the hf struc-ture of the 67Zn isotope. The observed six hf com-ponents were attributed to the AF — 1, Amp = 0transitions. The spectral parameters (Table 6) weredetermined by using the following analytical expres-sions of the resonance fields for the axial case [32]:
hv
a + ^a2\ ' hv (49)
5/?3,4 = T ^
where
16a I hv
= 9\\, A=z:A\\
a = 2 142]
for H || (111), and
9 = 9±,
a = 4 [{hvf - I^i]
for HI (111).The number of the Zn+ centers observed in
K2SO4 crystals after irradiation at RT depends onthe nature of radiation [45]. Eight centers have beenobserved after X-ray irradiation and four centers af-ter 7-ray irradiation. No EPR spectra attributed toZn+ centers could be observed after irradiation at77K. Two of the Zn+ centers, called I and II, andconsidered to be situated substitutionally at the twoK+ sites, were found to be the most stable, theirconcentration increasing by subsequent warm-up to400K, an effect also reported in alkali chloride crys-tals [91]. EPR spectra were recorded in both X and
208 Bulletin of Magnetic Resonance
Table 7: The EPR parameters of the Cd+—type centers at 77K. The hf parameter A and the shf parametersAs and Ap for the NN anion ligands are given in MHz.
CenterCd+ in LiClCd+ in NaClCd+ in KClCd+ in LiClCd+(I) in NaClCdJ(II) in NaClCd+(III) in NaClCd+(I) in KClCd+(II) in KClCd£ in LiClCd+ in NaClCd+ in KClCd+ in CaF2
Cd+ in SrF2Cd+ in BaF2
Cd+(I) in /3-K2SO4Cd+(II) in /3-K2SO4
Cd+ in (NH4)2SO4 a
site I
Cd+ in (NH4)2SO4 a
site II
g 1 r AI1.9981.9961.9961.9981.9951.9982.0001.9981.9981.9931.9902.001.99841.99651.98961.9990X=1.9965y=1.998c/2=2.000gx=l.9975gy=1.99725z=2.0002<?x=1.9975$,,=1.9972ff2=2.0002
Q bands on samples doped with zinc enriched 67Znisotope. The spin Hamiltonian parameters (Table6), have been determined with generalized versionsof formulae (25,26).
In the absence of any resolved shf structure itis difficult to suggest accurate models for the Zn+
centers in CaCC>3 and K2SO4. The large 6A shiftin both cases suggest the presence of neighboringvacancies, although that would result in a loweringof the local crystal field symmetry.
Anisotropic EPR spectra attributed to Hg+ cen-ters at low symmetry lattice sites have been reported
[95, 36] in (NH4)2SO4, KH2PO4 and NH4H2PO4crystals X-ray irradiated at RT. The two Hg+ cen-ters observed in (NH4)2SO4 were attributed [95]to substitutional Hg+ ions at the two inequiva-lent sites with Cs symmetry. No shf structurehas been observed at the measuring temperature(290K). The Hg+ centers exhibit in both KH2PO4and NH4H2PO4 lattice hosts an axial symmetry(Table 8), suggesting a substitutional K+ or NH4"site. A shf structure consisting of a 1:4:6:4:1 quin-tet has been observed for H || c in both crystals,at 300K, in the paraelectric phase. By lowering thetemperature the quintet changes to a 1:2:1 triplet at
Vol. 16, No. 3/4 209
Table 8: The EPR parameters of the Hg+—type of centers. The hf parameter A and the shf parameters Asand Ap for the NN ligand are given in MHz.
CenterHg+ in LiClHg+ in NaClHg+ in KClHg+ in (NH4)2SO4site I
148K, the phase transition temperature to the fer-roelectric phase of NH4H2PO4. The shf structurehas been attributed to the interaction with protons(7=1/2).
B. Trapped hole ns^centers
The trapped hole n^-centers are easily pro-duced by irradiating with ionizing radiation crystalsdoped with IIIA or IVA cation impurities. However,in studying their production properties one shouldtake into consideration that such cations can alsoact as electron traps, resulting in paramagnetic np1-type centers [98]. The trapped hole ns1-centers havebeen observed not only in alkali halides but also inmany other ionic and semiconducting crystals.
1. The IIIA-group (Ga 2 + , In2 + , Tl2 +)
The IIIA-group cations enter the alkali halides lat-tice mainly as monovalent ions. Consequently, it ispossible to grow doped crystals containing relativelylarge concentrations of such impurities, especiallythallium. It seems that in gallium or indium dopedalkali halide crystals a certain amount of impuritiesare in a higher valency state (+3). This could ex-plain the increased concentration of the ns1-centers
obtained in samples annealed at high temperaturesbefore irradiation, as well as the presence of newns1-centers with cation vacancies in their structureafter low temperature irradiation [99, 100].
Cubic ns^M24" (M = Ga, In, Tl) centers havebeen obtained in alkali chloride crystals after X-rayirradiation at various temperatures. The highestconcentration was obtained [52, 56, 99, 100] by ir-radiating at 77K and pulse-annealing at tempera-tures where the holes are mobile (> 170K in KCl).The resulting Ga2+, In2+ and Tl2,"1" centers exhibita well resolved shf structure for the magnetic fieldalong the main crystal axes. The analysis of the shfstructure confirms [52, 56] the regular octahedralsymmetry of the surrounding ligands.
Additional isotropic EPR spectra, without shfstructure, attributed to noncubic n^-centers havebeen observed [99, 100] in gallium and indium dopedKCl crystals after X-ray irradiation at 77K. The one(Ga2 +) ' and the two (In2 +) ' and (In2 +)" centers ob-served in KCl have been considered to consist of aGa2+ and In2 + substitutional ion, respectively, nextto a cation vacancy. The presence of two noncubicIn2 + centers has been attributed [100] to the exis-tence of two ns1 ion-cation vacancy configurations.It is considered [100] that in the (In;?+)" centers,
210 Bulletin of Magnetic Resonance
which are produced at higher temperatures thanthe (In2+)' centers and exhibit a partly resolved shfstructure, the vacancy is farther away from the In2+
ion, resulting in a smaller perturbing effect.High concentrations of cubic Tl2+ centers were
produced by X-ray irradiation at 77K of doubledoped KCl:Tl:Pb and NaCl:Tl:Pb crystals [100].This effect has been explained by the strong electrontrapping properties of the Pb2+ ions [101, 102]. Bywarming up such crystals, at temperatures corre-sponding to the onset of motion of cation vacanciesreleased by the Pb+ centers, it has been than pos-sible to obtain Tl2+vc centers according to reaction(6). The presence of such centers was reflected inthe splitting of the Tl2+ hf structure in two compo-nents with less resolved shf structure.
The EPR spectra of the M2+ (M = Ga, In, Tl)centers were described by the spin Hamiltonian (16),with or without the shf interaction term.
The EPR lines of the Ga2+ centers, observed inthe X-band, were attributed to the transitions (F =2,mF = -2) <—> (F = 2,mF = -1) and (F =\,mF — —1) *—* (F = 2, mF = —2) from the twonatural isotopes 69Ga and 71Ga, both with nuclearspin / = 3/2 (Table 2).
Indium has two natural isotopes, 113In and 115In,both with / = 9/2 (Table 2). The X-band EPR spec-trum consists of one line, due to the transition (F =5,mF = —5) <—> (F = 5,mF = —4), which can beseen at high magnetic fields (~ 1.5T). Another tran-sition (F = -5,mF = -5) <—> (F = 4,mF = -4)has been observed in the Q-band.
The large zero-field splitting and the close nu-clear momenta of the two thallium isotopes 203Tland 203Tl, both with / = 1/2 (Table 2), yields anEPR spectrum consisting of two lines. They rep-resent the superposition of the transitions (F =l,mF = 0) <—> (F = l,mF = -1) and (F =l,mF = 1) <—> (F = l,mF = 0) from the twoisotopes. The spin Hamiltonian parameters can bedetermined with the formulae (23,24).
The isotropic EPR spectrum, without shf struc-ture, observed [103] in SrCl2:Tl crystals after X-rayirradiation at 77K, has been attributed to Tl2+ ionswith a neighboring charge compensating vacancy.By pulse annealing above 130K the vacancy movesaway resulting in a partly resolved shf structure.
Isotropic Ga2+ centers [104, 105, 106], In2+ cen-ters [107, 105] and T12+ centers [105] have been ob-
served in ZnS crystals by photostimulation. All cen-ters exhibit large 5A shifts, compared to the corre-sponding cubic centers in alkali chlorides (see Tables8-10). Such large 6A values can be explained by thestronger covalent character of the bondings in ZnS(formula 42).
Slightly anisotropic ns1-type EPR spectra, at-tributed to Ga2+ in silicon [109], In2+ in ZnO[110], Tl2+ in hexagonal ZnS [105] and in K2SO4[111, 112], have been also reported. The anisotropyof the EPR spectra of the Tl2+ centers in the or-thorhombic /3-K2SO4 has been quantitatively ex-plained [111] by the effect of the odd crystal fieldcomponent at the cation sites (C5-local symmetry).By using a cluster model in deriving the effectivecrystal field operator, a good agreement between thecalculated and the experimental spin Hamiltonianparameters has been obtained [111].
The spin-lattice relaxation time T\ of the Tl2+
centers in K2SO4 has been measured in the 1.5 to25K temperature range by observing the spin-echosignal [113]. It exhibits a temperature dependenceof the form:
Tf1 = LOT x 3.3 x l(T5T/(0/T) (50)
where T is the temperature, #=120K is the Debyetemperature and f(0/T) is a factor describing thedeviation from a pure Raman process, attributed[113] to the large hf splitting.
Tl2+ centers produced by X-ray irradiationhave been used as paramagnetic probes in stud-ies concerning structural phase transitions, such asthe paraelectric/ferroelectric transition in KD2PO4,Rb2H2PO4 and (NH4)2SO4 crystals [41, 114, 115,116, 117] and the paraelectric/antiferroelectric tran-sition in NH4H2PO4 crystals [118]. The measuredspin Hamiltonian parameters (Table 11) are slightlybut clearly anisotropic, reflecting the local symme-try of the paramagnetic center and the changes inthe local symmetry, such as the lowering of the sym-metry by going from the paraelectric phase to a fer-roelectric or antiferroelectric one.
The spontaneous symmetry breaking and the lo-cal freeze-out during the transition from the para-electric to the ferroelectric phase has been studied[117] in the KH2ASO4 crystals using both Tl2+ andAsO4~ paramagnetic centers, simultaneously pro-duced by X-ray irradiation at 77K. The spectra ofboth centers exhibit axial symmetry in the high
Vol. 16, No. 3/4 211
Table 9: The EPR parameters of the Ga2+—type centers. The hf parameter A and the shf parameters Asand Ap with the NN ligands are given in MHz.
CenterGa^+ in NaClGa2+ in KClGa2,+ in KClGa2+ in ZnS(cub)Ga2+ in ZnS(hex)Ga2+ in ZnS a
a ODMR measurements. The hf constants correspond to three different sites.
temperature, paraelectric phase, and orthorhombicsymmetry with additional splittings due to the pres-ence of four inequivalent lattice sites, in the low tem-perature, ferroelectric phase. It has been observedthat the temperature dependence around the tran-sition temperature Tc of the additional line splittingdue to the presence of domains of opposite polar-ization is different for the two paramagnetic cen-ters. The corresponding spontaneous dynamic sym-
metry breaking, seen above Tc in the EPR spectraof AsO^", but not of Tl2 + , has been explained bythe different coupling of the two defects to the sur-rounding pseudospins.
2. The IVA-group (Ge3+, Sn3+, Pb3+)
The impurities of the IVA group of elements en-ter the ionic crystals mainly as divalent ions: Ge2 +,Sn2+ and Pb 2 + . Consequently, monovalent lattice
212 Bulletin of Magnetic Resonance
Table 11: The EPR parameters of the Tl2+—type centers. The hf parameter A and the shf parameters As
and Ap for the NN ligands are given in MHz.
CenterTl^+ in NaClTl2 + in KClTl2 + in RbClTl2 + in KBrTl2 + in SrCl2T12+ in ZnS(cub)Tl2 + in ZnS(hex)
a Slightly different values of the hf constant are reported in Reference [121].6 As reported in Reference [16].
hosts, such as alkali halides, can be doped only withrelatively low concentrations (~ 102ppm) of suchimpurities. The doping with germanium is evenmore difficult due to the low boiling point and ther-mal instability of germanium halides. The presenceof the charge compensating cation vacancies is ex-pected to have the same consequences as in the case
of doping with IIB impurities.
Ge3 + centers have not yet been reported in al-kali halides. However, germanium doped NaCl andKCl crystals have been obtained and the electrontrapped Ge+ centers could be observed after X-rayirradiation [122].
A Ge3+ center, exhibiting the largest reported hf
Vol. 16, No. 3/4 213
Table 12: The EPR parameters of the Ge3+—type centers. The hf parameter A and the shf parameters Asand Ap for the NN ligands are given in MHz.
CenterGed + in BaGeF6Ge3 + in ZnS(cub)Ge3 + in ZnSeGe3 + in ZnTe
Ge3 + in CdS
Ge3 + in CdTeGe3 + in quartz;A(GeLi) center
Ge3 + in quartz;C(GeLi) center
Ge3 + in quartz;(Ge(I)e~)~ center
Ge3 + in quartz;(Ge(II)e~)~ center
Ge3 + in quartz;(Ge(A)e-/Li+)°,or A, or AM+ centerGe3 + in quartz;(Ge(A)e-/Na+)°centerGe3 + in quartz;(Ge(C)e-/Li+),or C, or Cji/+ centerGe3 + in quartz;(Ge(C)e-/Na+)center
Ai(7Li)=1.15A2(7Li)=2.94A3(7Li)=1.29yli(23Na)=1.71A2(23Na)=2.74yl3(23Na)=1.71Ai(7Li)=2.3A2(7Li)=-0.2A3(7Li)=-0.9Ai(23Na)=1.9^ 2 (23 N a ) = 2 .5A3(23Na)=2.97
Ap
98.1204192
170
References[123][124][125][126, 124][108][127]
[126]
[128, 129, 121, 46]
[128, 129, 121, 46]
[121]
[121]
[128, 121]
[129, 121]
[128, 121]
[121]
a A value of 864MHz is reported in Reference [130].
constant, has been observed [123] in 7-ray irradiatedpowders of BaGeFg. The center, which seems to bea self-trapped hole, exhibits a shf structure from aregular octahedron of six NN F " ligands.
The EPR spectra of the Ge3+ centers consist of
an intense line at 5 ~ 2 from the even isotopes anda weak hf structure of 10 lines from the 73Ge iso-tope with / = 9/2 (Table 2). Due to the smallzero-field splitting, the hf structure is due to theAM = ± l , A m = 0 transitions, described by for-
214 Bulletin of Magnetic Resonance
Table 13: The EPR parameters of the Sn3+—type centers. The hf parameter A and the shf parameters As
and Ap for the NN ligands are given in MHz.
CenterSn3+ in NaCl(Sn3 +) ' in NaCl(Sn3 +)" in NaClSn3+ in KCl(Sn3 +) ' in KCl(Sn3 +)" in KCl(Sn3 +)/ in KCl(Sn3 +)/ / in KClSn3+ in SnCl2
Sn3+ in Snl2Sn3+ in SnSO4
Sn3+ in K2SnF6Sn3+ in CdS
Sn3+ in CdSe
Sn3+ in CdTeSn3+ in ZnS(cub)Sn3+ in ZnS(hex)Sn3+ in ZnSe
mulae (20). The spin Hamiltonian parameters ofthe various Ge3 + centers are presented in Table 12.
Although the 73Ge isotope has a small abun-dance, the corresponding hf structure has been re-ported in irradiated SiO2 (quartz) [43, 46, 128, 129].
Ge3 + centers have been also observed in as grownII-VI semiconductors doped with germanium by dif-fusion. The concentration of the Ge3+ centers couldbe drastically altered by photoexcitation with lightof energy close to the band gap. The shf structureobserved in ZnSe [125], ZnTe [126, 124] and CdTe[126], has been attributed to the interaction of the4s electron with the nuclei of the tetrahedrally co-ordinated ligands 77Se (/ = 1/2, 7.58% abundant),123Te (/ = 1/2, 0.9% abundant) and 125Te (/ = 1/2,7% abundant), respectively.
The natural tin contains, besides the even iso-topes, three isotopes with nuclear spin / = 1/2, butdifferent nuclear momenta and abundances (Table2). For this reason it is difficult to study the hf in-teraction of the Sn3+ centers in crystals doped withnatural tin. Various Sn3+ centers were reported inNaCl and KCl doped with SnCl2 containing 87.8%117Sn [26, 131], as well as in KCl doped with tinenriched in the 119Sn isotope [132].
Besides the g ~ 2 line from the even isotopesthe X-band EPR spectra of the Sn3 + exhibit athigh magnetic fields two hf lines due to the AF =0, Amp = ±1 transitions. The hf constant A canbe determined with the aid of formulae (23,24). Thespin Hamiltonian parameters of the Sn3+ centers re-ported in the literature are presented in Table 13.
Vol. 16, No. 3/4 215
Sn3+ centers with isotropic lines and well re-solved shf structure were obtained [26] in KC1 andNaCl in a maximum concentration, by X-ray irradi-ation at 77K and pulse-annealing around 160K.
Two Sn3+ centers, called (Sn3+)' and (Sn3+)",exhibiting anisotropic high field hf transitions wereobserved [131] in both NaCl and KC1 after X-rayirradiation at 77K. The (Sn3+)" center exhibits aC2 symmetry axis, attributed to the presence of aNN cation vacancy, along a (111) direction.
Other two Sn3+ centers, called (Sn3+)/ and(Sn3+)//, with resolved shf structure at 35K, havebeen also reported in KC1, after X-ray irradiationat 77K and warming up at various temperatures[132]. The (Sn3+)/ center reaches its maximum con-centration after pulse annealing at 230K. The shfstructure, due to the interaction with six neighbor-ing ligands, exhibits a (111) symmetry attributed tothe presence of an interstitial Cl~ ion. The (Sn3+)//center reaches its maximum concentration by pulse-annealing at 280K. The suggested structural modelconsists of a Sn3+ ion with two neighboring cationvacancies.
Sn3+ centers, which seems to represent self-trapped holes at cationic sites, were reported inSnCl2, Snl2 and SnSO4 crystals [133] after X-rayirradiation at 77K and in K2SnFg powder after7-irradiation [123]. The Sn3+ center observed inK2SnFg exhibits the largest reported hf constant ina crystal lattice, characteristic for a strongly ioniccompound.
Sn3+ centers have been also observed in variousII-VI semiconductors. With the exception of CdSand CdSe, where they exhibit axial symmetry, in allother crystals the Sn3+ centers are isotropic.
Pb3+ centers have been reported in alkali chlo-rides, in alkali earth fluorides, in various oxides andin II-VI semiconductors (Table 14).
Natural lead contains only one odd isotope(207Pb) with / = 1/2 (Table 2). Due to the largezero-field splitting, the EPR spectra of the Pb3+
centers consist of a line at g — 2 due to the evenisotopes and two lines at higher magnetic fields dueto the two AF — 0,Amj? = ±1 transitions. Thespin Hamiltonian parameters for the isotropic caseare determined by formulae (23,24).
Two types of Pb3+ centers have been observedin KCl:Pb crystals [138] after X-ray irradiation at77K and subsequent warm-up. The first one, al-
ready produced after irradiation, reaches its maxi-mum concentration by pulse-annealing at 220K. Itswell resolved shf structure has been described in agood approximation by the interaction with a regu-lar octahedron of six chlorine ligands. It has been as-sumed that an accompanying charge compensatingcation vacancy may be present in a (2,0,0) site, orfurther away. The second Pb3+ center was producedby pulse-annealing above 220K. It had the same gand A values, but a less resolved shf structure, at-tributed to the presence of a second cation vacancy.The source of the cation vacancies seems to be thePb+ centers, also produced by X-ray irradiation[29, 101]. Similar Pb3+ centers have been observedin other alkali chlorides [26, 131, 136]. Two types ofPb3+ centers have been reported [131] in KC1 andNaCl, after X-ray irradiation at 77K, and attributedto different configurations of Pb3+-vc pairs.
Pb3+ centers have been reported [85, 139] in leaddoped CaF2 and BaF2 crystals, after X-ray irradia-tion at 77K or RT and in SrF2 after X-ray irradia-tion at 77K. The well resolved shf structure corre-sponds to a substitutional Pb3+ ion surrounded bya cube of eight F~ ligands. Due to the large shfinteraction the forbidden (Am/ = ±1) transitionsare partly allowed. A second type of Pb3+ centersexhibiting different shf structure has been observed[139] at T<100K. The EPR spectra are described bythe same spin Hamiltonian as the Pb3+ centers towhich a supplementary term due to the interactionwith a ninth fluorine ligand situated in an intersti-tial site is added. Only the Ay9 shf component hasbeen reported, with values of 952 MHz for CaF2,812MHz for SrF2 and 615MHz for BaF2.
Cubic Pb3+ centers, representing the self-trapped hole at a cationic site, have been reportedin PbF2 crystals after 7—ray or neutron irradiationat low temperatures [140]. Due to the complexity ofthe shf structure only the shf parameters from thefirst shell of eight F~ ligands could be determined.
Pb3+ centers, which seem to represent self-trapped holes at cation sites, have been also re-ported in PbCO3 crystals [133] and BaPbF6 crystals[123].
Cubic Pb3+ centers have been reported [141, 143]in ThO2 and CeO2 crystals with the fluorite struc-ture, grown from lead based fluxes, after e~ or 7-ray irradiation at 77K or RT. An additional Pb3 +
center, exhibiting anisotropic spectra with trigonal
216 Bulletin of Magnetic Resonance
symmetry around the < 111 > axes and shf struc-ture due to the interaction with one 19F ligandnucleus, has been observed only in TI1O2 crystalsgrown from a PbF2 based flux. The center is con-sidered to consist of a substitutional Pb3+ ion, withone of the eight nearest O2~ ligands substituted byan F~ ion. The presence of both Pb3+ and Pb3+
centers was also reported [142] in as grown ThO2crystals prepared from a PbF2 based flux. In thiscase it has been found that their concentration isgreatly enhanced by illumination with 400 nm light.
Pb3+ centers with isotropic EPR spectra, at-tributed to substitutional Pb3+ ions at cubic siteshave been reported in the as grown crystals ofZnO and CaO [144], Lu3Ga50i2, Y3A15O12 andLu3Al5012 [42].
Axial Pb3 + centers, at substitutional cationicsites, in CaW04 crystals [146, 147] and CaCO3 (cal-cite) crystals [44, 143, 145], have been observed af-ter X or 7-ray irradiation. The EPR spectra of thePb3+ centers in CaW04 exhibit a partly resolvedshf structure, attributed to the interaction with the183W nuclei (I = 1/2, 14.4% abundance). The hfconstant of the Pb3+ centers in CaCO3 exhibits [44]the same temperature dependence as the one previ-ously observed for the Cd+ centers in KC1 (formula47). The temperature dependence of the hf constantand the large Lorentzian linewidth of the varioustransitions have been quantitatively explained [152]in terms of a Raman spin-lattice relaxation corre-sponding to a Kramers spin system with large hfinteraction.
Pb3+ centers with axial symmetry were reportedin as grown YPO4 and LUPO4 orthophosphates pre-pared from lead based fluxes [148]. In an unexpectedway, the shf interaction parameters with the 31P nu-clei of the second shell of ligands has been found tobe larger than for the first shell.
Photosensitive Pb3+ centers have been also ob-served in the II-VI semiconductors, ZnSe [150],ZnTe [27, 125, 126, 124] and CdS [133, 127] as wellas in CaSe [151].
The spin Hamiltonian parameters of the IVA-group of ns1 —centers in cubic II-VI semiconduc-tors (Tables 12-14) exhibit specific features: largeand positive Ag = g - ge shifts and large hf shifts6A. The above characteristics have been explained
[53, 57] in a satisfactory manner with the hole-trapped MO model. The model, briefly presentedin paragraph 1.3.2., describes the wave function ofthe paramagnetic electron as a linear combinationof the central ns wave function and the s-p orbitalsof the ligands (formulae 40,41). Quantitative anal-ysis of the experimental spin Hamiltonian parame-ters have been initially performed for the n51-centersin zinc chalcogenides [150, 153] using Watanabe'smodel [53]. Further analysis, have been performedfor the ns^centers in zinc chalcogenides [57], for theGe3+ and Pb3+ centers in zinc chalcogenides andCdTe [149], and for the Ge3+, Sn3+ and Pb3 + cen-ters in CdTe and ZnTe [126]. The analysis showthat the increased spin-orbit coupling in the S, Se,Te sequence of ligands is responsible for the posi-tive, increasing Ag shift, observed along the zinc orcadmium chalcogenides sequence. In the same man-ner the hf shift 6A decreases with the ionicity of theligand bonds.
V. Concluding Remarks
The present survey shows that among the var-ious inorganic crystal-hosts of the n51-centers theinterest was mainly concentrated on the cubic alkalihalides. However, even inside this group of com-pounds there is a strong discrepancy between alkalichlorides and bromides, in which many ns^centershave been observed, the alkali iodides in which a fewsuch centers have been observed and the alkali flu-orides and cesium halides in which ns1-centers havenot been reported yet. In this connection the studyof the ns^centers in the latter crystal-hosts wouldbe of interest regarding the validity of their produc-tion and recombination mechanisms under irradia-tion.
Although a relatively large number of ns1-centershave been reported in other cubic and non-cubiccrystal-lattices, only a few reports are concernedwith the identification of their structural modeli.e., their position in the lattice and the pres-ence/absence of neighboring lattice defects. This isnot at all surprising considering that in the absenceof a resolved shf structure the structure determina-tion is extremely difficult.
Several papers have been devoted, especially inthe last years, to the study of the ns1-centers pro-duced in crystals with low symmetry lattice exhibit-
Vol. 16, No. 3/4 217
Table 14: The EPR parameters of the Pb3+—type of centers. The hf parameter A and the shf parameters Asand Ap for the NN ligands are given in MHz.
CenterPb^+ in LiClPb 3 + in NaCl(Pb3 +) ' in NaCl(Pb3 +)" in NaClPb 3 + v c in KClPb3 +2vc in KCl(Pb3 +) ' in KCl(Pb3 +)" in KClP b 3 + in RbClPb 3 + in CaF2
P b 3 + in SrF2
Pb 3 + in BaF2
Pb 3 + in PbCO3Pb 3 + in BaPbF6Pb 3 + in PbF2Pb 3 + in ThO2
CenterPb 3 + in CdTePb 3 + in ZnSePb 3 + in ZnTePb 3 + in CaSe
T(K)207777
g2.20542.07212.1672.173
\'M7A\14,64220,65415,68020,480
As416.5215130
Ap
18611070.3
References[126, 149][150][27, 125, 126, 124][151]
a The shf parameters are referring to the 19F ligandb The shf parameters are referring to the 3 1P ligand.
Table 15: The EPR parameters attributed to the VA group of ns1 centers. The hf parameter A for the 75As,121Sb and 209Bi isotopes and the shf parameters As and Ap are given in MHz.
Center j T(K)As4 + in CsAsF6Sb4 + in CsSbF6Bi4+ in CsAsF6
3030
g2.00302.00152.0134
\A\9,403a
21,3906
36,020c
As
693697414
Av
160153163
6A0.360.390.55
References[154][154][155]
a A/(75As)=14,660 MHz.6 A/(121Sb)=35,100 MHz.c A/(209Bi)=77,530 MHz.
ing structural phase transitions (SPT). Besides pro-ducing and describing their EPR properties, the re-sulting ns1-centers have been employed in certaincases as paramagnetic probes in investigating themechanism of the SPT. Considering the wide tem-perature range in which some of the n^-centers canbe observed by EPR, it is expected that their use asmicroscopic probes in the study of the SPT will beextended.
It should be also mentioned that other impurityions, besides those presented in Table 1. are able inprinciple to produce new ns^centers. It is the caseof the VA-group of elements (As4+, Sb4 +, Bi4+), aswell as Al2+ and Si3+.
In this respect one should mention the reportedobservation of new EPR spectra in 7-irradiatedpolycrystalline samples of CsAsF6, CsSbF6 [154]and CsAsF6 doped with BiF^r [155]. Although theresulting paramagnetic species were assigned to freeradicals of the type MeF|~ (Me = As. Sb, Bi), re-
spectively, the parameters (Table 15) correspondingto the spin Hamiltonian (16) describing the observedspectra, strongly suggest the presence of Me4+(ns1)centers. The large hf shift 8 A and shf coupling pa-rameters As and Ap of the observed centers resultfrom a strong delocalization of the central ns1 elec-tron to the neighboring ligands, which may explaintheir assignment to free radicals.
Acknowledgments
One of the authors (I.U.) would like to expresshis gratitude to Professor Abdus Salam for the kindinvitation to work at the ICTP-Trieste, as well asfor continuous support, encouragement, advice andcriticism. Financial support from the Belgian Min-istry of Science Policy (DPWB) and from the Uni-versity of Antwerp (U.I.A.), for one of the authors(SVN) and from the International Center for The-
Vol. 16, No. 3/4 219
oretical Physics (ICTP), Trieste for another author(IU) is gratefully acknowledged.
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