ACTAUNIVERSITATIS
UPSALIENSISUPPSALA
2014
Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1197
Structure-Magnetic Relationshipsin the Fe-Mn-P-Si System forEnergy Applications
VIKTOR HÖGLIN
ISSN 1651-6214ISBN 978-91-554-9091-1urn:nbn:se:uu:diva-234516
Dissertation presented at Uppsala University to be publicly examined in Polhemsalen,Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 12 December 2014 at 09:15 forthe degree of Doctor of Philosophy. The examination will be conducted in English. Facultyexaminer: Dr Mogens Christensen (Aarhus University, Denmark).
AbstractHöglin, V. 2014. Structure-Magnetic Relationships in the Fe-Mn-P-Si System for EnergyApplications. Digital Comprehensive Summaries of Uppsala Dissertations from theFaculty of Science and Technology 1197. 74 pp. Uppsala: Acta Universitatis Upsaliensis.ISBN 978-91-554-9091-1.
Demands for new, energy-efficient appliances have greatly increased in response to ourgrowing need for a more environmentally friendly society. Magnetic refrigeration is atechnique that utilizes the magnetocaloric effect, with possible energy savings of up to 30%compared to commercial gas compression refrigerators. A material appropriate for commercialmagnetocaloric devices should be both cheap and non-toxic; it should also exhibit a first-order magnetic transitions close to room temperature. The magnetic properties of Fe2P-relatedmaterials can be relevant in this context, since their magnetic properties can be finely tunedthrough the substitution of Fe by Mn and P by Si, As, Ge or B to meet the general requirementsfor a magnetocaloric device.
An in-depth study has therefore here been made of the structural and magnetic properties ofthe (Fe,Mn)2(P,Si)-system. The phase diagram of the FeMnP1-xSix-system has been carefully re-examined. It is found to contain two single-phase regions: an orthorhombic Co2P-type structure(x < 0.15) and a hexagonal Fe2P-type structure (0.24 ≤ x < 0.50). Selected compounds within theFe2P-type region of the phase diagram have been shown to exhibit potential for use in magneticrefrigeration applications.
Neutron powder diffraction has here been used to determine the magnetic structures ofselected crystalline compositions within the FeMnP1-xSix-system to gain a better understandingof its magnetic properties. The Fe2P-type region is mainly ferromagnetic, but an incommensurateantiferromagnetic structure has also been identified close to the Co2P/Fe2P-type phase borderfor x ≈ 0.25.
The so-called ''virgin effect'' in the Fe2P-type region of the FeMn(P,Si) phase diagram is foundto be accompanied by an irreversible structural phase transition induced by magnetostriction.This new phase is found to be preserved during successive cooling-heating cycles. Furthermore,the magnetic properties of the substituted Fe2P-type structure changes significantly formetal:non-metal ratios away from 2:1. Such deviations could well explain the apparentlyconflicting structure-property relationships described in earlier literature for the FeMnP1-xSix-system.
Keywords: Magnetocaloric, X-ray powder diffraction, Neutron powder diffraction,Magnetization measurements, Phase diagram, Crystal structure, Magnetic structure,Incommensurate structure, Ferromagnetic, Antiferromagnetic, Fe2P, Fe-Mn-P-Si.
Viktor Höglin, Department of Chemistry - Ångström, Inorganic Chemistry, Box 538, UppsalaUniversity, SE-751 21 Uppsala, Sweden.
© Viktor Höglin 2014
ISSN 1651-6214ISBN 978-91-554-9091-1urn:nbn:se:uu:diva-234516 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-234516)
”Tittar man noga efter så ska man finna små, små skillnadersom faktiskt gör varje gump till ett unikum.”
Tage Danielsson
Till Johanna och August
List of Papers
This thesis is based on the following papers, which are referred to in the textby their Roman numerals.
I The crystal and magnetic structure of the magnetocaloriccompound FeMnP0.5Si0.5V. Höglin, M. Hudl, M. Sahlberg, P. Nordblad, P. Beran, Y. Andersson.Journal of Solid State Chemistry, 184, 2434-2438 (2011).
II Strongly enhanced magnetic moments in ferromagneticFeMnP0.5Si0.5M. Hudl, L. Häggström, E. K. Delczeg-Czirjak, V. Höglin, M.Sahlberg, L. Vitos, O. Eriksson, P. Nordblad, Y. Andersson.Applied Physics Letters, 99, 152502 (2011).
III Detailed study of the magnetic ordering in FeMnP0.75Si0.25V. Höglin, M. Hudl, L. Caron, P. Beran, M. H. Sørby, P. Nordblad, Y.Andersson, M. Sahlberg.Journal of Solid State Chemistry, 221, 240-246 (2015).
IV Irreversible structure change of the as prepared FeMnP1−xSix-structure on the initial cooling through the Curie TemperatureV. Höglin, J. Cedervall, M. S. Andersson, T. Sarkar, P. Nordblad, M.Sahlberg.Journal of Magnetism and Magnetic Materials, 374, 455-458 (2015).
V Phase diagram, structures and magnetism of the FeMnP1−xSix-systemV. Höglin, J. Cedervall, M. S. Andersson, T. Sarkar, M. Hudl, P.Nordblad, Y. Andersson, M. Sahlberg.Submitted.
Reprints were made with permission from the publishers.
My contributions
Paper I. I have planned the study, synthesized the samples and performed allstructural characterizations. I wrote the main part of the manuscript and wasinvolved in all discussions.
Paper II. I have synthesized the samples and taken part in the planning,discussion and writing of the manuscript.
Paper III. I have planned the study, synthesized the samples and performedall structural characterizations except the representational analysis. I wrotethe main part of the manuscript and was involved in all discussions.
Paper IV. I have planned the study, synthesized the samples and taken part inthe structural characterizations, discussion and writing of the manuscript.
Paper V. I have planned the study, synthesized a majority of the samplesand performed all structural characterizations. I wrote the main part of themanuscript and was involved in all discussions.
Other publications to which the author has contributed.
Magnetocrystalline anisotropy and the magnetocaloric effect in Fe2PL. Caron, M. Hudl, V. Höglin, N. H. Dung, C. P. Gomez, M. Sahlberg, E.Brück, Y. Andersson, P. Nordblad.Physical Review B, 88, 094440, (2013).
Thermodynamics around the first-order ferromagnetic phase transitionof Fe2P single crystalsM. Hudl, D. Campanini, L. Caron, V. Höglin, M. Sahlberg, P. Nordblad, A.Rydh.Physical Review B, 90, 144432, (2014).
Contents
1 Introduction 131.1 The magnetocaloric effect . . . . . . . . . . . . . . . . . . . . 141.2 Material systems . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.1 The mother compound Fe2P . . . . . . . . . . . . . . 161.2.2 Substituted Fe2P-type compounds . . . . . . . . . . . 171.2.3 Fe2P-type compounds in magnetocaloric applications . 18
2 Methods 192.1 Material synthesis . . . . . . . . . . . . . . . . . . . . . . . . 192.2 X-ray diffraction techniques . . . . . . . . . . . . . . . . . . 19
2.2.1 X-ray powder diffraction . . . . . . . . . . . . . . . . 202.2.2 Synchrotron radiation X-ray powder diffraction . . . . 21
2.3 Neutron powder diffraction . . . . . . . . . . . . . . . . . . . 222.4 Determination of crystal and magnetic structures . . . . . . . 24
2.4.1 The Rietveld method . . . . . . . . . . . . . . . . . . 252.4.2 Representational analysis . . . . . . . . . . . . . . . . 25
2.5 Magnetic characterization . . . . . . . . . . . . . . . . . . . . 252.6 Other experimental methods . . . . . . . . . . . . . . . . . . 26
2.6.1 Differential thermal analysis and thermogravimetry . . 262.6.2 Mössbauer spectroscopy . . . . . . . . . . . . . . . . 262.6.3 Theoretical methods . . . . . . . . . . . . . . . . . . 27
3 Results and discussion 293.1 The phase diagram of FeMnP1−xSix . . . . . . . . . . . . . . 293.2 Compounds of Fe2P-type . . . . . . . . . . . . . . . . . . . . 35
3.2.1 FeMnP0.50Si0.50 . . . . . . . . . . . . . . . . . . . . . 353.2.2 FeMnP0.75Si0.25 . . . . . . . . . . . . . . . . . . . . . 39
3.3 The virgin effect . . . . . . . . . . . . . . . . . . . . . . . . . 493.4 Phosphorus deficient samples . . . . . . . . . . . . . . . . . . 533.5 In field XRD experiments . . . . . . . . . . . . . . . . . . . . 56
4 Summary and concluding remarks 59
5 Sammanfattning på svenska 61
6 Acknowledgments 65
References 67
Abbreviations
CPA Coherent potential approximationDFT Density functional theoryDTA Differential thermal analysisEMTO Exact muffin-tin orbital methodEPMA Electron probe micro analysisEDS Energy-dispersive X-ray spectroscopyf.u. Formula unitFOMT First order magneto-structural phase transitionµB Bohr magnetonM MagnetizationMsat Saturated magnetizationMCE Magnetocaloric effectMPMS Magnetic property measurements systemNPD Neutron powder diffractionPPMS Physical property measurements systemRA Representational analysisRT Room temperatureSQUID Superconducting quantum interference deviceSR-XRD Synchrotron radiation X-Ray powder diffractionXRD X-ray powder diffraction
11
1. Introduction
Alloying of metals is a craft with historical heritage back to around 2000 B.C.when humans learned to melt copper and tin to prepare bronze [1]. The aspira-tion to find new and to improve existing materials is still present today whenresearchers of the world continuously strive to develope new materials withextreme properties.
The phase diagram of silver and copper reported by W. Chandler Robertsin 1875 [2] is believed to be the first ”temperature-composition”-diagram [3].The first compilation of binary phase diagrams was published by Max Hansenin German in 1936 and was translated, expanded and published in Englishin 1958 [4]. The amount of phase related data grew rapidly during the sec-ond half of the 1900s and in 1970 the CALPHAD (CALculation of PHAseDiagrams) method to predict phase equilibrium in not yet experimentally in-vestigated system was described by Kaufman and Bernstein [5]. Calculationsare fast and economical compared to experimental phase determination andconsequently computational simulation has grown to become the dominantmethod in present time [3].
The work to study alloy systems and to construct phase diagrams is verytime consuming and is today rarely performed experimentally, since the ma-jority of the binary compounds already have been studied and the ternary andquaternary phase diagrams take unreasonably large efforts to produce exper-imentally. Nevertheless, it is possible to construct parts of ternary or quater-nary phase diagrams to put focus on certain areas to be studied. Because if onepossesses knowledge of the structural characteristics of a certain alloy systemthis can be used to understand and predict other qualities such as the magneticproperties.
The primary objective of this thesis has been to explore materials whichhave potential to be used in magnetocaloric applications, e.g. magnetic re-frigeration. The work has been made from a crystallographic point of viewand detailed studies of the structures of the investigated materials have beenperformed using a broad spectrum of characterization techniques with focuson diffraction methods. All materials in this thesis are of (Fe,Mn)2(P,Si)-typeand efforts have been made to derive phase diagrams of the structural andmagnetic orderings of FeMnP1−xSix. This work has been part of an interdisci-plinary project on magnetocalorics where the focus of this thesis has been onsample preparation and complete determination of the structural and magneticproperties of the FeMnP1−xSix-system.
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1.1 The magnetocaloric effectThe magnetocaloric effect (MCE) is a phenomena experimentally discoveredby Weiss and Piccard in 1918 [6]. Warburg and his observations from 1881[7] have by tradition been cited as the discovery of the MCE but in a review ofliterature by Smith [8], Weiss and Piccard are proposed as the real discoverersof the MCE when they found a reversible heating close to the Curie temper-ature (TC) of nickel when a magnetic field was applied (a temperature rise of0.7 K in a field of 1.5 T). Thus, in contrast to Warburg, they identified the twomain features of the magnetocaloric effect: it is reversible and it is largest attemperatures close to the TC.
The MCE is quantified by two parameters, the entropy change per mass unit∆S (for an isothermal field change) and the temperature change ∆Tad (for anadiabatic field change). ∆Tad is defined as the temperature difference when asample is initially exposed to a magnetic field Hi which is changed to the finalfield H f (Hi < H f ) under adiabatic conditions. Similarly, ∆S is defined as theentropy change when a sample is exposed to an magnetic field change Hi toH f under isothermal conditions, see figure 1.1.
Temperature
Tota
l en
tro
py
Hi
Hf
∆Tad
(T;Hi,H
f)
∆S(T;Hi ,H
f)
TC
Figure 1.1: The isotropic entropy and adiabatic temperature in the initial (Hi) and final(H f ) magnetic fields at the Curie temperature, TC.
The isothermal entropy change can be calculated as a function of field andtemperature from magnetization (M) measurements using the Maxwell rela-tion
(
∂S
∂H
)
T
= µ0
(
∂M
∂T
)
H
(1.1)
as starting point (where µ0 is the vacuum permeability = 4π·10−7
V·s·A−1m−1). The entropy change can be calculated according to
14
∆S = µ0
H f∫
Hi
(
∂M
∂T
)
H
dH (1.2)
and the adiabatic temperature change can be estimated from magnetizationand heat capacity (C) experiments using
∆Tad =−µ0
H f∫
Hi
T
CH
(
∂M
∂T
)
H
dH. (1.3)
The derivation and numerical methods to calculate ∆S and ∆Tad are describedby Thishin and Spichkin [9]. Experimental methods for direct measurementsof ∆S and ∆Tad are continuously being developed [10–17].
∆S and ∆Tad are quantitative quality measures of the efficiency of a mag-netocaloric material. However, the two quantities are directly coupled and hasto be optimized simultaneously [18]. The actual performance of a material isbetter appreciated if also the refrigerant capacity (RC) is derived:
RC =
Thigh∫
Tcold
∆S dT (1.4)
as it gives a measure of how much energy a given amount of material cantransfer betweeen the desired low temperature (Tcold) and ambient temperature(Thigh) [19; 20]
Figure 1.2 schematically illustrates the refrigeration cycle of amagnetocaloric system. The magnetic moments of the magnetocaloricmaterial are initially randomly oriented (1), then a magnetic field is appliedand the magnetic moments align along the field reducing the magneticentropy, which results in heating of the working material (2). The heat isremoved from the material using heat transfer (with a transfer medium suchas water, air or helium) (3) and a subsequent removal of the magnetic fieldwill cool the material below the initial temperature (4). This final step is usedto extract heat from the system to be cooled by using heat transfer.
The efficiency of the magnetocaloric refrigeration cycle promises possi-ble energy savings of up to 30% if compared with gas compression refrig-erators [21]. The discovery of the giant MCE in Gd5(Ge,Si)4 compounds byPecharsky and Gschneidner [22] boosted the interest in magnetic refrigera-tion. A large number of material systems such as La(Fe,Si)13, MnAs, Heusler-alloys and related compounds have been studied in order to find an optimal
15
Figure 1.2: Scheme of the magnetic refrigeration cycle.
material for use in magnetocaloric applications [23–25]. An optimal materialmust show large ∆S and ∆Tad and the first materials showing giant MCE wererare earth compounds. But in order to go commercial, an ideal material mustshow advantageous magnetocaloric characteristic, be economically favorableand be synthesized from non toxic elements.
A commercialization of magnetic refrigeration has not yet been achievedeven if there are ongoing efforts to start large scale material synthesis of mag-netocaloric materials.
1.2 Material systems1.2.1 The mother compound Fe2PIn 1929 Hägg [26] performed the first examinations of Fe2P using X-ray pow-der diffraction (XRD). He determined the lattice parameters and proposeda hexagonal structure. A complete structure was not determined until 1959when Rundqvist and Jellinek [27] stated that Fe2P has the symmetry of theP62m space group. The structure of Fe2P (from now called the Fe2P-typestructure in the text) has two iron sites, one on the crystallographic 3f site sur-rounded by four phosphorus atoms in a tetrahedral ordering. The second ironsite is situated on the 3g position surrounded by five phosphorus atoms in apyramidal arrangement. The two phosphorus sites (2c and 1b) are surroundedby trigonal prisms of iron atoms. Layer arrangements are formed by the 3f
iron and 2c phosphorus and the 3g iron and 1b phosphorus respectively, seetable 1.1 and figure 1.3.
16
Table 1.1: Atomic parameters of the Fe2P-type structure, space group P62m. Numer-ical data are from ref. [28]
Atom Site x y z
Fe I 3g 0.2568(1) 0 12
Fe II 3f 0.5946(1) 0 0
P I 2c 13
23 0
P II 1b 0 0 12
a b
c
Fe I (3f)
Fe II (3g)
P I (2c)
P II (1b)
a b
Figure 1.3: Unit cell of the hexagonal Fe2P-type structure, space group P62m
A first order magneto-structural phase transition (FOMT) is observed forFe2P at TC = 216 K. Sample series of Fe2−xP have shown that the latticeparameters and, consequently, the magnetic properties are very sensitive todeviations in sample composition [28–30]. This makes Fe2P a very delicatematerial system to study since small changes in the sample composition mayalter the characteristics heavily.
1.2.2 Substituted Fe2P-type compoundsElemental substitutions in Fe2P manipulate the magnetic properties. For ex-ample, TC is very sensitive to substitution of phosphorus and is increased to∼350 K [31], ∼450 K [32] and ∼350 K [33] for 10% substitution of silicon,boron and arsenic respectively retaining Fe2P-type structure. On the metalsites substitution of iron with manganese ((Fe1−xMnx)2P) will retain pure fer-romagnetic ordering for x ≤ 0.015 while for 0.0015 < x ≤ 0.03 there is fer-
17
romagnetism for low temperatures (<100K) and an incommensurate screw-antiferromagnetism at high temperatures (>150K). Pure antiferromagnetic or-dering is found for x > 0.03 [34]. The hexagonal Fe2P-type structure is pre-served until x > 0.26 where a phase transition to the orthorhombic Co2P-typestructure takes place [35; 36]. The magnetic moments on the metal sites areincreased by manganese substitution and the manganese atom at the pyrami-dal 3g site of FeMnP possesses a magnetic moment of 2.6 µB [37] comparedto 1.78 µB for the iron atom on the 3g site in Fe2P [38].
The increased magnetic moment on the metal atoms can be combined with atunable TC by creating a quaternary system of (Fe,Mn)2(P,A)-type (A = Si, Asand/or Ge). During the 1990s, comprehensive studies of the FeMnP1−xAsx-system were performed regarding structural and magnetic properties as wellas magnetic structures [39–43]. This material system paved the way for nu-merous new compounds to be studied or re-investigated for magnetocaloricapplications during the 2000s.
1.2.3 Fe2P-type compounds in magnetocaloric applicationsThe (Fe,Mn)2P1−xAsx-system was found to be very promising for usein magnetic refrigeration [44–46] due to its giant MCE and transitiontemperature tunable close to room temperature. Further studies to improve(Fe,Mn)2P1−xAsx-type materials were made by adding a fifth alloy element(germanium) in order to enhance the MCE, increase TC and reduce thethermal hysteresis for selected compounds [47–49]. However, the use ofarsenic-rich compounds in products meant for commercial use is alwaysreceived with aversion. It was therefore crucial to substitute arsenic witha more environmentally friendly element while keeping the advantageousmagnetocaloric properties found in this material system. Arsenic was foundto be satisfactory replaced by silicon or a Si/Ge combination [50–53].
The latest approach of magnetocaloric materials based on the Fe2P-typestructure are samples with metal deficiencies of (Fe,Mn)1.95(P,Si)-type [54–57]. These samples have exhibit less thermal hysteresis which is a knownproblem for many compounds of Fe2P-type.
18
2. Methods
2.1 Material synthesisThe materials studied in this thesis are from the (Fe,Mn)2P1−xSix-system andsamples were prepared for 0.05-steps of x except at selected phase borderswere smaller steps of x were used. Since manganese and phosphorus arehighly volatile elements the drop synthesis technique [28] was used to en-sure low losses of the raw materials due to evaporation during sample synthe-sis. The equipment used for the drop synthesis technique is shown in figure2.1. Proper amounts of iron and silicon were put in crucibles of alumina andmelted using induction heating. The temperature of the melt was measured us-ing a pyrometer. After a stable melt of iron and silicon was formed, pieces ofmanganese and phosphorus were dropped into the melt causing an immediatereaction with the iron-silicon melt. Successful experiments produce samplesof 10-30 g with losses < 0.5 wt%. This technique for phosphide synthesisis well described in the literature and only minor changes have been madecompared to the techniques described by Haughton [58] and Hägg [26].
Selected compositions (FeMnP, FeMnP0.25Si0.75, FeMnP0.50Si0.50,FeMnP0.25Si0.75, FeMnSi, FeMnP0.40Si0.50 and (Fe0.375Mn0.625)2P0.50Si0.50.)were prepared using the drop synthesis method while the intermediatecompositions were prepared from mixtures of the larger batches (mostcharacterization techniques used in this thesis only need orders of mg towork satisfyingly, except for neutron powder diffraction where the amount ofsample preferably should be > 1 cm3). All samples were grounded and heattreated in evacuated silica ampules and finally either slowly cooled to roomtemperature or quenched in water.
2.2 X-ray diffraction techniquesX-ray diffraction is undoubtedly one of the most important methods for char-acterizing crystal structures. Diffraction occurs when X-rays are scattered co-herently by atomic planes in a crystal. The scattering strength of the X-raysdepends on the atomic number and falls of with increased diffraction angle.
19
(1)
(2) (3) (4)
(5)
(6)
(7)
(8)
(9)
(10)
b)a)
Figure 2.1: The experimental set-up for the drop synthesis method. Photo of the fur-nace in (a) and schematic view in (b). (1) viewing window, (2) volatile elements (suchas phosphorus and manganese), (3) soft magnetic pusher, (4) Pyrex glass tube, (5)silica funnel, (6) silica tube, (7) alumina crucibles, (8) RF work coil, (9) starting ma-terials (such as iron and silicon), (10) vacuum connection.
2.2.1 X-ray powder diffractionAn ideal powder is defined as a polycrystalline sample with randomized crys-tals arranged in every possible orientation. By varying the incident angle θ ofthe X-ray beam, a sufficiently large number of randomly oriented crystals inthe studied polycrystalline material will be oriented in such way that some ofthe hkl planes in the crystals will be oriented in the Bragg angle. A sweep overa selected θ -range will produce a so called powder pattern. Every crystallinephase has an unique powder pattern which can be used for identification.
XRD intensities were collected on a Bruker D8 diffractometer equippedwith a Våntec position sensitive detector (PSD) with 4◦ opening using CuKα1radiation (λ = 1.540598 Å). Measurements were performed in temperaturesfrom 16 K to 403 K and in a 2θ -range of 20-90◦. Measurements above RTwere performed using an Anton Paar XRK 900 reaction chamber and mea-surements below RT were performed using an Oxford Phenix cryostat.
20
2.2.2 Synchrotron radiation X-ray powder diffractionSynchrotron radiation X-Ray powder diffraction (SR-XRD) is a technique us-ing accelerated electrons to produce high intensity X-rays. The high intensitymakes it possible to perform ”one shot” experiments and collect X-ray inten-sities over the whole 2θ -range within seconds. The ability of this method tocollect complete data sets makes SR-XRD an excellent technique for structureinvestigations vs. temperature.
SR-XRD experiments were performed on the I711 beamline at the MAXIV Laboratory in Lund, Sweden [59]. Wavelength and sample to detector dis-tances were determined using a LaB6 standard and collected data were han-dled in the FIT2D software [60].
Pulverized samples were carefully loaded in a thin quartz capillary andplaced in a single crystal sapphire tube which was attached to the sample cell.The sample cell [61] was heated using resistive heating (tungsten or kanthalwire) and the temperature was measured using a thermocouple placed insidethe sapphire tube. A custom built add-on to the sample cell featuring a strongpermanent magnet of NdFeB-type, see figure 2.2, made it possible to performXRD experiments in a magnetic field of 0.35 T.
(1)
(2)
Figure 2.2: Sample cell for SR-XRD experiments in field. A permanent magnet ofNdFeB-type is placed inside the aluminum box (1). Samples placed in the gap (2) areexposed for a magnetic field of 0.35 T.
21
2.3 Neutron powder diffractionNeutron powder diffraction (NPD) is an elastic scattering technique with sim-ilarities to XRD but complementary information can be determined since theinteraction with matter is different. The neutrons interact with the nucleus ofthe atom in contrast to XRD where the X-rays are scattered by the electronssurrounding the nucleus. Therefore, while the scattering length of the X-rayshas a linear dependence on the atomic number the scattering amplitude ofthe neutrons depends on two factors. Firstly, the contribution called ”poten-tial scattering” which depends on the size of the nucleus. Secondly there maybe ”resonance scattering” which depend on the detailed structure of the nu-cleus which can vary greatly from element to element and even from isotopeto isotope [62]. The summarized neutron scattering amplitude has an irregulardependence on the atomic number, see figure 2.3. This makes it possible toseparate iron from manganese which has been of importance for the work inthis thesis.
20 40 60 80 100
-1
0
1
2
3
4
5
6
Neutrons
62Ni
58Ni56Fe
MnTi
ScCl
7Li
X-rays(sin )/ = 0.5 Å-1
Sca
tterin
g am
plitu
de (1
0-12 c
m)
Atomic weight
X-rays = 0°
1H
Figure 2.3: The irregular variation of the neutron scattering amplitude as a functionof atom weight. The regular increase for X-rays is shown for comparison.
The neutron is an uncharged particle, but it carries a magetic moment andtherefore interacts with the unpaired electrons which arises in the electroncloud around the nucleus in a magnetic material. This makes it possible todetermine the microscopic magnetic structure of a material. In a simple casewith a ferromagnetic structure where all magnetic moments, within a domain,align in the same direction, the magnetic diffraction peaks will occur at thesame angular positions as the nuclear peaks. Thus, the magnetic scattering ina ferromagnetic material (see figure 2.4a) will merely increase the intensity ofthe nuclear peaks (as seen in figure 2.5a). In a case with a simple antiferro-magnetic structure (see figure 2.4b) the magnetic moments point alternately
22
up and down in the structure making the magnetic unit cell twice as large asthe chemical cell along the b-axis. This type of antiferromagnetic material willgive diffraction peaks of purely magnetic origin, see figure 2.5b. An importantfeature of the magnetic scattering is that it decreases with increased scatteringangle in contrast to the nuclear scattering. Consequently, high intensity peaksfrom magnetic scattering occurs at low 2θ angles.
ba
b
c
a) b)
Figure 2.4: Unit cells of a ferromagnetic (a) and an antiferromagnetic (b) structure.The dashed lines in the ferromagnetic case indicate a second unit cell. The directionsof the arrows indicate the directions of the magnetic moments.
A
B
C
2θ
2θ
Inte
nsi
ty
a)
b)
Figure 2.5: Neutron diffraction intensities from a ferromagnetic (a) and antiferromag-netic (b) ordered sample. The additional magnetic scattering (shaded) contributes tothe nuclear peaks for a ferromagnetic material and appears as new peaks A, B and Cfor an antiferromagnetic material.
23
The iteration of the a magnetic structure can (simplified) be described be thepropagation vector k = (qx qy qz). The simple ferromagnetic structure abovecan be described by the vector k = 0 since the chemical and magnetic unitcells are the same. The propagation vector in the antiferromagnetic case is k= (0 1/2 0) since the magnetic cell propagates in the b-direction and there istwo crystallographic unit cells needed to describe the magnetic unit cell.
In more complicated cases when the terms of the propagation vector cannot be described by rational numbers the structure is incommensurate. Thesetypes of magnetic structures are infinite and can be e.g. helical or sinusoidal,see figure 2.6.
a)
b)
Figure 2.6: Models of a sinusoidal (a) and a helical (b) magnetic structure.
The NPD experiments presented in paper I and III were performed usingthermal neutrons at the Nuclear Physics Institute in Rez, Czech Republic. In-tensities were collected using the MEREDIT diffractometer and the neutronbeam was monochromatized by a copper mosaic monochromator (reflection220) providing a wavelength of λ = 1.46 Å. A 2θ -range of 4-144 (and 148)◦
was used at 16 K, 298 K and 450 K. Intensities in paper III were also collectedusing thermal neutrons on the PUS diffractometer at the Institute for EnergyTechnology in Kjeller, Norway. The neutron beam was monochromated by agermanium mosaic monochromator (reflection 511) giving a wavelength of λ= 1.556 Å. A 2θ -range of 10-105◦ was used at 8 K and 298 K.
2.4 Determination of crystal and magnetic structuresThere is a long list of parameters that can be derived from powder diffrac-tion data. Most essential are the lattice parameters which were determinedfrom Bragg peak positions of XRD intensities using a non-linear least squaremethod implemented in the software UNITCELL [63]. Methods for in depthstudies of the powder diffraction intensities are described below.
24
2.4.1 The Rietveld methodThe method to perform structural analysis using the the whole pattern frompowder diffraction experiments was developed by Hugo M. Rietveld [64] dur-ing the 1960s. The structural model and the instrument parameters are refinedin a least-square procedure where the function
M = ∑i
Wi
{
yi(obs)−1c
yi(calc)
}2
(2.1)
is minimized over the whole profile. Wi is a weighting factor, yi(obs) andyi(calc) are the observed and calculated intensities respectively and c is a scalefactor. This procedure is carried out by varying selected parameters until asatisfactory fit is obtained. The fit is numerically calculated and the parametersRp, Rwp, RBragg, Rexp, RF and χ2 are used as guides for the progress of therefinement [65; 66]. Nevertheless, the user must still evaluate all parametersmanually and determine if they are reasonable.
All refinements to resolve crystallographic and magnetic structures wereperformed according to the Rietveld method using the software FULLPROF
[67; 68] on intensities generated from XRD and NPD measurements.
2.4.2 Representational analysisThe determination of a magnetic structure can be very time consuming andfrustrating if using a trial and error method. The number of possible structurescan be reduced by only investigating structures that are allowed by symmetry.A method to perform this selection is representational analysis (RA) and thisapproach to study magnetic structures rests on a mathematical idea first usedby Dzyaloshinskii [69; 70]. RA is based on the Landau thermodynamic theoryof second-order phase transitions [71] and the method implements a system-atic decomposition of the magnetic representation Γ of the little group Gk intoirreducible representations (IR). The number of symmetry allowed magneticstructures for the system will be equal to the number of non-zero IR in thefinal decomposition of Γ.
In this thesis, the symmetry analysis of the incommensurate antiferromag-netic structure in paper III was performed using simulated annealing and rep-resentational analysis (SARAh) [72].
2.5 Magnetic characterizationThe magnetic properties of a material can be characterized by several tech-niques. In this thesis, the magnetization has been studied as a function of tem-perature and applied magnetic field. A superconducting quantum interference
25
device (SQUID) magnetometer was used to measure the magnetic moment ofthe samples. A SQUID uses the quantization of magnetic flux in a closed loopof a superconducting material containing one or two Josephson junctions inorder to measure the magnetic fields.
Magnetization experiments in paper II, III, IV and V were performed us-ing a Quantum Design MPMS SQUID magnetometer and a Quantum DesignPPMS with the VSM option.
The MCE was determined from magnetization measurements by calcula-tion of the magnetic entropy change, ∆S, using equation 1.2.
2.6 Other experimental methods2.6.1 Differential thermal analysis and thermogravimetryDifferential thermal analysis (DTA) and thermogravimetry (TG) aretechniques for studying thermal effects in a material such as polymorphictransitions and mass changes. The studied sample and a reference arearranged with identical thermocouples which are connected back-to-back.When heated, the sample and reference will be at the same temperature andresult in a ∆T = 0 output. When a thermal effect occurs in the sample, ∆Twill deviate from 0 and the output shows if the thermal event was exo- orendothermic.
DTA and TG measurements were performed using a Netzsch STA 409 PCLuxx TG-DTA/DSC instrument. All samples were measured under a flowingAr atmosphere and Ar was also used as purge gas. Measurements were per-formed with an increased temperature from 303 to 1373 K using a heating rateof 10 K/min. The temperature was cycled three times for all samples.
2.6.2 Mössbauer spectroscopyMössbauer spectroscopy is a method to study chemical bonding, magneticproperties and oxidation states for isotopes with sufficiently large mass andexcitation energies lower than ∼100 keV. A unique Mössbauer nucleus isthe isotope 57Fe. The technique is based on the resonant emission and ab-sorption of γ-rays in solid matter. To perform such experiments, the γ-sourcemust match the studied material, e.g., the 57Fe isotope is studied using a 57Cosource and Mössbauer spectroscopy is an element specific technique. The in-teractions between the nucleus and the surrounding electrons are indicated byhyperfine interactions which is described by the hyperfine field. Quantifica-tion of the magnetic moments can be achieved within an order of magnitudeaccuracy.
26
Mössbauer absorption spectra in paper II were recorded in the constantacceleration mode at temperatures between 5 K and 440 K using a 57CoRhsource.
2.6.3 Theoretical methodsThe foundation of Density Functional Theory (DFT) is that the total energyof a system can be described solely by the electron density [73]. Over time,this theory has been developed to reproduce physical parameters of realisticmaterials [74]. A majority of the DFT based theoretical methods are basedon solving the Kohn-Sham equation [75] and there are several methods tofind a solution depending on the set up. In the exact muffin-tin orbital method(EMTO) [76; 77] the potentials are built using overlapping spherical potentialsand the Kohn-Sham equation is solved exactly for these potentials. The EMTOmethod can be combined with the coherent potential approximation (CPA)[78; 79] to allow for chemical disorder. The real atomic potential is replacedby the coherent potential built from the atomic potentials from the componentsof the studied material.
The electronic structure and total energy calculations in this thesis wereperformed using the EMTO method combined with CPA. Ab initio calcu-lations were performed for three different phases of FeMnP0.50Si0.50. Twophases were set as ordered: one with manganese atoms occupying the pyra-midal 3g site and one with the manganese atoms occupying the tetrahedral 3f
site. A third disordered phase was also considered where the iron and man-ganese atoms were randomly distributed on the two metal sites in the Fe2P-type structure. Internal positions and lattice parameter were taken from NPDdata in Paper I and all numerical details of the calculations are similar to theones reported in Ref. [80]
27
3. Results and discussion
The results have been divided into five parts. In part one overall characteris-tics of the FeMnP1−xSix phase diagram will be presented. In part two the fo-cus is put on the compounds FeMnP0.50Si0.50 and FeMnP0.75Si0.25 which arefound on the borders of the single phase Fe2P-type region in the FeMnP1−xSixphase diagram. The virgin effect observed in (Fe,Mn)2(P,Si)-type compoundsis discussed in part three. The properties of phosphorus deficient samples of(Fe,Mn)2(P,Si)-type are presented in part four. Finally, the results from XRDmeasurements in a magnetic field are discussed in part five.
3.1 The phase diagram of FeMnP1−xSixCareful phase analysis has been performed in order to study the phase diagramof the FeMnP1−xSix-system. The FeMnP1−xSix phase diagram exhibits fiveregions out of which two are single phase, see figure 3.1. The single phasesare one orthorhombic of Co2P-type (Pnma) for x < 0.15 and one hexagonalof Fe2P-type (P62m) for 0.24 ≤ x < 0.50. A two phase region of the Co2P-and Fe2P-type structures was found for 0.15 ≤ x < 0.24. For 0.50 ≤ x < 1.00,a three phase region, which consists of the Fe2P-type, hexagonal Mn5Si3-type(P63/mcm) and cubic Fe3Si-type (Fm3m) structures, was found. Finally, x =1.00 was shown to result in the Mn5Si3- and Fe3Si-type structures. The phasefraction of x ≥ 0.50 is shown in figure 3.2 and the amount of the Fe2P-typephase linearly decreases with increased silicon concentration (x).
As seen in figure 3.1, the phase border at x = 0.50 is temperature dependentand thus the composition obtained at room temperature is related to the heattreatment and cooling rate. Single phase samples of Fe2P-type close to thisphase border were prepared by quenching in cold water after the heat treat-ments. Quenched and slowly cooled samples of FeMnP0.52Si0.48 are comparedin figure 3.3 and reflexions confirmed to belong to the Mn5Si3- and Fe3Si-typestructures were observed in the slowly cooled sample. This indicates that thethree phase region seen in figure 3.1 for 0.50 ≤ x < 1.00 is present for lowtemperatures at x = 0.48 and that quenched samples are needed to reach asingle phase of Fe2P-type.
DTA-data collected from x = 0.50 are seen in figure 3.4 where a kink is ob-served at about 950 K on heating at the first temperature cycle. The subsequentcycles do not show any thermal activities indicating an oxidation or decom-
29
0,0 0,2 0,4 0,6 0,8 1,0
Fe3Si + Mn5Si3
Fe2Phex.
Fe2Phex.
Tem
pera
ture
(K)
Si conc. (x)
Co 2P
- or
th.
1473 K
Figure 3.1: Phase diagram of the FeMnP1−xSix-system. White regions represent sin-gle phases while regions with multiple phases are grey. Detailed phase analysis of thequenched and slowly cooled samples with compositions close to x = 0.50 indicates atemperature dependence of the phase boundary of the three-phase region for 0.50 ≤ x
< 1.00 to extend slightly below x = 0.50 at lower temperatures.
Figure 3.2: Phase fractions of the Fe2P-, Mn5Si3- and Fe3Si-type structures in thecomposition range 0.50 ≤ x ≤ 1.00 for FeMnP1−xSix
position of the samples. XRD experiments before and after the DTA-analysisconfirm these observations with several oxide phases and a decomposed Fe2Pstructure likely due to losses of phosphorus. Similar observations were seenfor the samples of composition x = 0.40, 0.48 and 0.65. It is shown that se-lected samples of Fe2P-type are stable at temperatures up to ∼950 K.
The unit cell parameters (measured at 298 K) and magnetic properties forthe two single phase regions of Co2P- and Fe2P-type are summarized in table3.1 and are visualized in figures 3.5 and 3.6. The unit cell distortion observed
30
39 40 41 42 43 44 45 46 47
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Quenched Slowly cooled Mn5Si3-type Fe3Si-type
Figure 3.3: XRD intensities of quenched and slowly cooled samples ofFeMnP0.52Si0.48. Peaks of the Mn5Si3- and Fe3Si-type structures are observed in theslowly cooled sample. Data were collected at 298 K.
300 600 900 1200 1500
d(T)
/dT
(arb
. uni
ts)
Temperature (K)
1st cycle 2nd cycle 3rd cycle
Figure 3.4: The derivated DTA-signal of FeMnP0.50Si0.50 vs. temperature. A kink(indicated by a vertical arrow) is observed on heating at about 950 K on the firstheating/cooling cycle indicating a thermal activity.
at x = 0.35 originates from magnetostriction effects which occur when themagnetic state changes from para- to ferromagnetic at room temperature (TC
reaches values above RT), table 3.1: TC for x = 0.30 is 275 K and 308 K for x
= 0.35.The magnetic ordering in the Co2P-type region is mainly antiferromag-
netic with TN in a range from 260 K to 285 K. The magnetic transitions ofFeMnP agree with previous work [34; 36; 81]. An orthorhombic (Co2P-type)to hexagonal (Fe2P-type) phase transition has been reported to occur at 1473
31
0,0 0,1 0,2 0,3 0,4 0,55,9
6,0
6,1
6,2
6,6
6,7
6,8
Si conc. (x)
cell
para
met
er le
ngth
(Å)
3,2
3,3
3,4
3,5
3,6
TC at 308 K
a
cell
para
met
er le
ngth
(Å)
c
b
a
c
298 K
TC at 275 K
Figure 3.5: Unit cell parameters of the orthorhombic (0.00 ≤ x < 0.15) and hexagonal(0.24 ≤ x < 0.50) region of FeMnP1−xSix. A unit cell distortion is observed for x
= 0.35 due to magnetostriction. Shadowed regions contain two phases. Data werecollected at 298 K.
0,0 0,2 0,4 0,6 0,8 1,0
80
160
240
320
400
3-ph
ase
regi
on
Fe2P
(hex
.)
Co 2P
(orth
.) TN
T* T
C
M (Am
2/kg)
Tran
sitio
n te
mpe
ratu
re (K
)
Si conc. (x)
2-ph
ase
regi
on
40
80
120
160
MT = 20 K; µ0H = 1 T
Figure 3.6: Magnetic phase diagram for the FeMnP1−xSix-system. Transition temper-atures of all samples and saturation magnetization of the ferromagnetic samples at T= 20 K and µ0H = 1 T are indicated
K in FeMnP [82]. This occurrence is indicated in the phase diagram in figure3.1. The magnetic transition temperatures are shown vs. silicon concentrationin figure 3.6 where T∗ indicates the temperature of a minimum in the M vs. Tcurves (measured in a field of 1 T). A linear dependency is seen for TC vs sili-
32
Table 3.1: Structural and magnetic properties of FeMnP1−xSix crystallizing in theCo2P-type structure (0.00 ≤ x < 0.15) and the Fe2P-type structure (0.24 ≤ x < 0.50).Unit cell parameters are determined at 298 K and TC is measured at heating.
x a (Å) b (Å) c (Å) V (Å3) TC/TN (K) ∆Thys (K)
0.00 5.9603(3) 3.5722(2) 6.7415(2) 143.53(1) 261∗ 7
0.05 5.9611(2) 3.5786(2) 6.7519(2) 144.03(2) 255∗ 8
0.10 5.9574(2) 3.5826(2) 6.7548(2) 144.17(1) 284∗ 9
0.15 5.9582(2) 3.5982(2) 6.7653(2) 144.77(1) 281∗ 9
0.20 5.9584(2) 3.5927(2) 6.7672(2) 144.86(1)
0.20 5.9816(2) 3.4936(2) 108.25(1)
0.24 5.9823(2) 3.4914(2) 108.21(1) 215 96
0.25† 5.9879(2) 3.4937(2) 108.48(1) 150∗
0.25 5.9907(2) 3.4996(3) 108.77(1) 250 90
0.30 6.0025(1) 3.4922(1) 108.96(1) 275 74
0.35‡ 6.0118(3) 3.4833(4) 109.03(2) 308 57
” 6.1731(5) 3.3102(4) 109.24(2) ” ”
0.40 6.1801(2) 3.3088(2) 109.44(2) 350 42
0.45 6.1921(2) 3.2995(2) 109.56(1) 370 27
0.48 6.2016(2) 3.2931(1) 109.68(2) 392 24
0.50 6.2075(2) 3.2906(2) 109.81(2) 395 18∗Néel temperature†Antiferromagnetic phase of FeMnP0.75Si0.25‡Two different unit cells are observed at x = 0.35 because of a
unit cell distortion due to magnetostriction effects.
con concentration in the Fe2P-type region. In the same region a plateau is ob-served for the saturated magnetization (Msat) which decreases abruptly closeto the phase border at lower concentration of silicon (x ∼ 0.25). In the threephase region for x ≥ 0.50, Msat decreases linearly with increased amount ofsilicon and TC abruptly decreases close to x = 1.00 where the Fe2P-type phasedisappears. Hence, the presence of the Fe2P-type structure strongly influencesthe magnetic properties in this composition range and Msat correlates with theamounts of the Fe2P-type phase in the material (cf. figure 3.2).
The sample of nominal composition FeMnSi contains two phases in equi-librium: one with the cubic Fe3Si-type structure (Fm3m, a = 5.6687(2) Å) andthe other with hexagonal Mn5Si3-type structure (P63/mcm, a = 6.8499(1) Å,c = 4.7564(1) Å). The unit cell parameters are similar to the compositions
33
∼(Fe0.4Mn0.6)3Si [83] and ∼(Fe0.5Mn0.5)5Si3 [84; 85]. This indicates that theFe/Mn ratio in the FeMnSi samples is close to one. Two magnetic transitiontemperatures are observed for FeMnSi with TN ∼ 60 K (for (Fe,Mn)3Si) andTC = 169 K (for (Fe,Mn)5Si3), these transition temperatures agree with thevalues reported in earlier studies of (Fe,Mn)3Si [86] and (Fe,Mn)5Si3 [85].
34
3.2 Compounds of Fe2P-typeThe main work in this thesis has been to study compounds of Fe2P-type inthe FeMnP1−xSix-system. Therefore this section will go more deeply into themagnetic and crystallographic properties of this part of the system.
3.2.1 FeMnP0.50Si0.50
The compound FeMnP0.50Si0.50 was found to be at the upper border of thephase region of Fe2P-type in the FeMnP1−xSix phase diagram. Traces of theMn5Si3- and Fe3Si-type structures can be observed even for quenched sampleswhich indicate that the limit concentration of silicon in the single phase regionis reached. The unit cell parameters are determined to a = 6.2090(3) Å and c
= 3.2880(2) Å at 296 K in paper I. High temperature XRD experiments showan iso-structural phase transition at approx. 385 K as shown in figure 3.7. Thistransition originates from magnetostrictive effects when the magnetic state ischanged. Magnetization measurements of FeMnP0.50Si0.50 are seen in figure3.8a and indicate a first order para- to ferromagnetic transition with TC = 395K (measured on heating). In figure 3.8b, the magnetization at 5 T and 295 Kis 156 Am2/kg which corresponds to 3.9 µB/f.u. The saturated moment at 5K is determined to be 4.4 µB/f.u. which is higher than previous experimentalstudies (3.8 µB/f.u.) [52] and slightly higher than previous calculations (4.2µB/f.u.) [87] have reported. The ∆S of FeMnP0.50Si0.50 was estimated frommagnetization data and a magnetic entropy change of 8 J/kgK was obtainedfor a magnetic field change of 1.8 T.
The magnetic structure of FeMnP0.50Si0.50 was determined using NPD andit was found that the iron atoms occupy the tetrahedral 3f site while the man-ganese atoms preferably occupy the pyramidal 3g site. The magnetic momentsare aligned along the hexagonal a/b-axis and the direction of the moments haschanged from the c-axis to the basal plane if compared to the mother com-pound Fe2P [29; 30], see figure 3.9. The size of the magnetic moments ofFeMnP0.50Si0.50 was found to be 1.9(1) µB on the iron site and 2.5(1) µB onthe manganese site giving a total magnetic moment of 4.4(2) µB/f.u. whichis significantly higher than Fe2P having a total magnetic moment of 2.9(1)µB/f.u. [38; 88–91]. The size of the magnetic moments determined from NPDintensities agree with magnetization experiments and the theoretical calcula-tions shown in figure 3.10. The total calculated energies are presented as afunction of the lattice parameter a for a fixed c/a = 0.5296 for three differentphases (described in section 2.6.3). As seen in figure 3.10, the case with man-ganese occupying the pyramidal 3g site has the lowest energy for all volumes(lattice parameters) and this concords with the NPD experiments. However,the Mn-pyramidal case has a energy minimum for a lattice constant a around6.16 Å while the experimental value is 6.2090(3) Å in paper I and 6.2075(2)Å in paper V.
35
40 50 60
403 K111201
210 300 211/002
393 K
Inte
nsity
(arb
. uni
ts)
388 K
383 K
373 K
300
2-theta (deg.)
303 K111201
210 300 211 002
Figure 3.7: XRD intensities of FeMnP0.50Si0.50 from 303 to 401 K. A structural tran-sition due to magnetostriction is seen to occur at approx. 385 K. λ = 1.540598 Å.
320 360 400 4400
30
60
90
120
150
-4 -2 0 2 4-200
-150
-100
-50
0
50
100
150
200
Temperature (K)
µ0H = 1 T
b)a)
Mag
netiz
atio
n (A
m2 /k
g)
µ0H (T)
295 K
Figure 3.8: Field cooled cooling and heating magnetization experiments ofFeMnP0.50Si0.50. (a): magnetization vs. temperature measured at 1 T. (b): magneti-zation vs. magnetic field measured at 295 K.
The occupancies of the iron and manganese atoms were also confirmedby Mössbauer spectroscopy experiments. The Mössbauer spectra forFeMnP0.50Si0.50 are shown in figure 3.11. The upper panel shows a broadsingle line centered at 0.17 mm/s. This together with an average electricquadrupole splitting of 0.32 mm/s show that the iron atoms in the samplesonly occupy the tetrahedral 3f site. A marked shoulder should have been
36
a b
c
Fe I (3f)
Fe II (3g)
P I (2c)
P II (1b)
a b
c
Fe (3f)
Mn (3g)
P/Si I (2c)
P/Si II (1b)
a)
b)
Figure 3.9: The magnetic structure of (a) FeMnP0.50Si0.50 and (b) Fe2P. The length ofthe arrows correspond to the magnitude of the magnetic moments.
6.0 6.1 6.2 6.3 6.4
a-axis (Å)
1.0
1.5
2.0
2.5
3.0
3.5
ma
gn
etic
mo
me
nt (µ
B/s
ite)
Mn pyramidal
Mn tetrahedral
Fe tetrahedral
Fe pyramidal
-20
-15
-10
-5
0
5
E (
mR
y/si
te)
Mn pyramidalDisordered
Fe pyramidal
Figure 3.10: Theoretical results for FeMnP0.50Si0.50. Total energy per site (up-per panel) and site-projected magnetic moments (lower panel) of the Mn- and Fe-pyramidal and Mn- and Fe-tetrahedral ordered phases as a function of the unit cellparameter a and for fixed c/a = 0.5296. The dashed line indicates the experimentalunit cell parameter.
present on the resonance line if there had been any iron on the pyramidal 3g
site [42; 92]. The spectrum collected in the ferromagnetic regime at 298 K(see lower panel in figure 3.11) shows a six-line pattern along with a broadcentral line. Two sextets were needed to fit the spectrum due to differences inthe line intensities in the outer lines, an electric quadrupole split doublet wasused to fit the broad central line and the amount of the doublet was ∼5% at
37
295 K and it had disappeared at 77 K and below. The observed co-existenceof para- and ferromagnetic ordering in FeMnP0.50Si0.50 may indicate localnon-stoichiometry [38].
(a)
(b)
PM
T = 440 K
FM
T = 295 K
Figure 3.11: Mössbauer spectra for FeMnP0.50Si0.50 measured at (a) 440 K and (b)295 K. Inset: magnetic hyperfine field distribution measured at 295 K.
The compound FeMnP0.50Si0.50 has been investigated by several techniquesin order to study its structural and magnetic properties. Evaluations of theexperiments show that FeMnP0.50Si0.50 exhibits a rather large magnetocaloriceffect in combination with the smallest thermal hysteresis of the samples in theFe2P-type region (see table 3.1). This makes FeMnP0.50Si0.50 one of the mostpromising compounds in the FeMnP1−xSix-system for use in magnetocaloricapplications.
38
3.2.2 FeMnP0.75Si0.25
The compound FeMnP0.75Si0.25 is close to the lower silicon limit in the Fe2P-region of the FeMnP1−xSix phase diagram. Samples of FeMnP0.75Si0.25 werefirst synthesized and properly analyzed. Then followed another heat treat-ment of the analyzed samples and a second round of characterizations. Theflowchart of the work with FeMnP0.75Si0.25 is shown in figure 3.12. It shouldbe emphasized that the sample labeled ”sample II” is a re-heat-treated batchof the sample labeled ”sample I”.
Drop synthesis
technique
Heat treatment 1
(Sample I)Sintering at 1373 K (2h)
Annealing at 1273 K (10d)
Slow cooling (36h)
X-ray diffrac"on
Magne"za"on
Neutron diffrac"on
Heat treatment 2
(Sample II)
Annealing at 1273 K (25d)
Slow cooling (24h)
X-ray diffrac"on
Magne"za"on
Neutron diffrac"on
Fab
rica
"o
nC
ha
ract
eri
za"
on
Figure 3.12: Flowchart showing the order of sample preparation and experimentalwork for the samples I and II of FeMnP0.75Si0.25.
Table 3.2: Unit cell parameters of FeMnP0.75Si0.25 at (a) 298 K and (b) 16 K forsample I (phase A, the majority phase in sample I) and sample II (phase B, the majorityphase in sample II), as determined from X-ray powder diffraction data. λ = 1.540598Å.
Sample T (K) a (Å) c (Å) V ( Å3)
I 298 5.9907(2) 3.4996(3) 108.77(1)
I 16 6.1630(2) 3.3035(2) 108.66(1)
II 298 5.9879(1) 3.4937(2) 108.48(1)
II 16 5.9756(3) 3.4878(2) 107.86(1)
Collected XRD intensities at 298 K and 16 K of sample I and II are shownin figure 3.13 and 3.14. Careful analysis of the intensity profiles detects over-lapping reflexions over the whole 2θ range. Two phases of Fe2P-type (labeled
39
20 30 40 50 60 70 80 90
20 30 40 50 60 70 80 90
50 51 52 53 54 55 56
50 51 52 53 54 55 56
B
b) 16 K
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
a) 298 K
A
BA
B
A
B
A
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Figure 3.13: X-ray powder diffraction intensities of sample I at (a) 298 K and (b) 16K. Red dots and black lines correspond to observed and calculated data respectively.Blue lines show the difference between the observed and calculated data. Tick marksindicate the position of Bragg reflections of the two phases of Fe2P-type (phase A andB). The low angle intensities of the 16 K data have been excluded because of highbackground from the cryostat. Insets: Zoom showing phase A and B in detail. λ =1.540598 Å.
40
20 30 40 50 60 70 80 90
20 30 40 50 60 70 80 90
50 51 52 53 54 55 56
50 51 52 53 54 55 56
B
b) 16 K
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
a) 298 K
A
BA
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
BA
B
A
Figure 3.14: X-ray powder diffraction intensities of sample II at (a) 298 K and (b) 16K. Red dots and black lines correspond to observed and calculated data respectively.Blue lines show the difference between the observed and calculated data. Tick marksindicate the position of Bragg reflections of the two phases of Fe2P-type (phase A andB) and the phase of (Fe,Mn)3Si-type. The low angle intensities of the 16 K data havebeen excluded because of high background from the cryostat. Insets: Zoom showingphase A and B in detail. λ = 1.540598 Å.
41
A and B) with only narrowly different lattice parameters are found with theratio A/B ∼70/30 in sample I and ∼10/90 in sample II. The unit cell param-eters of the majority phases in sample I and II are shown in table 3.2 and thelarge changes of the unit cell dimensions of sample I at 16 K indicates a lowtemperature ferromagnetic ordering as observed in FeMnP0.50Si0.50 and pureFe2P [30].
0 50 100 150 200 250 3000
20
40
60
80
100
120
140
0 50 100 150 200 250 300
1
2
3
4
5
6
7
125 150 175 200
1,4
1,5
1,6
1,7
Virgin cycle Second cycle
Mag
netiz
atio
n (A
m2 /k
g)
Temperature (K)
µ0H = 2 T
Mag
netiz
atio
n (A
m2 /k
g)
Temperature (K)
ZFCFC
µ0H = 1 T
a)
b)
Figure 3.15: Magnetization vs. temperature data. (a): Magnetization data of sampleI measured in a magnetic field of 2 T. Black squares correspond to the first cooling-heating event and the red circles to the second. (b): Magnetization data of sampleII measured in a magnetic field of 1 T. The antiferromagnetic ordering temperatureTN ∼ 150 K is evident from the weak bump in both the ZFC and FC magnetizationcurves. Inset: blow-up of the temperature range near TN of the FC curve.
Magnetization vs. temperature curves of sample I are shown in figure 3.15aand a para- to ferromagnetic transition is indicated at 250 K (measured onheating). When measured on cooling and re-heating, the magnetic transitiontemperature shows a strong thermal hysteresis of the order of 100 K and thecooling cycles exhibit a considerable virgin effect on the magnetic transition
42
0 1 2
0
20
40
60
80
100
120
140
M (A
m2 /k
g)
µ0H (T)
sample I sample II
T = 5 K
Figure 3.16: Magnetization vs. magnetic field data of sample I and II measured at 5K.
between the first|second (and subsequent) cooling cycles. The saturation mag-netization of sample I at 5 K is about 125 Am2/kg (measured at 1 T), see figure3.16.
Similar magnetization measurements on sample II show a strongly alteredbehavior. As seen in figure 3.15b, the ferromagnetic amplitude is substantiallylower and an indication of an antiferromagnetic transition is observed at 150K noticed as a weak bump on both cooling and heating. The large thermalhysteresis of the ferromagnetic transition temperature, which was observed insample I, is preserved.
The decreased ferromagnetic component is unexpected (the only differencebetween sample I and II is an additional heat treatment) but clearly illustratedin the low temperature magnetization vs. temperature curves in figure 3.16where the magnetization of sample II only reaches 5 Am2/kg at 1 T. Thisis about 25 times smaller compared to the corresponding magnetization ofsample I.
The NPD data collected on sample I agrees with results from XRD andmagnetization measurements. Observed and calculated NPD profiles of sam-ple I are shown in figure 3.17 and the two phases A and B of the Fe2P-type(determined from XRD intensities) are observed in the paramagnetic regionmeasured at 298 K. In accordance with FeMnP0.50Si0.50 and other Fe2P-typecompounds [56; 57], the iron atoms in phase A preferably occupy the tetrahe-dral 3f site while the manganese atoms mainly are occupying the pyramidal3g site. In the 8 K profiles, magnetic intensities from a ferromagnetic structurewere observed for phase A. There were also small amounts of phase B togetherwith a few extra peaks that could not be indexed by any of the crystal struc-tures known to occur in the FeMnP1−xSix-system. The magnetic moments ofthe ferromagnetic phase were determined to be aligned in the hexagonal basal
43
20 40 60 80 100
20 40 60 80 100
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Yobs
Ycalc
Yobs-Ycalc
Bragg position
101
101
001
110
111
001
110
111
211
211a) 298 K
b) 8 K
BA
B
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Yobs
Ycalc
Yobs-Ycalc
Bragg position
A
Figure 3.17: Neutron powder diffraction intensities of sample I at 298 K and 8 K.Red dots and black lines correspond to observed and calculated data respectively.Blue lines show the difference between the observed and calculated data. Tick marksindicate the position of Bragg reflections of the two structural phases of Fe2P-type(phase A and B) at 298 K in (a) and the majority phase of Fe2P-type (phase A), theferromagnetic part of the majority phase, the minority phase of Fe2P-type (phase B)and the antiferromagnetic low T phase derived from the minority phase in (b). λ =1.556 Å.
44
20 40 60 80 100
20 40 60 80 100
110
211
001
A
b) 16 K
Yobs
Ycalc
Yobs-Ycalc
Bragg position
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
a) 298 K
B
211
110001
010
+ k
110
+ k
100
- k
B
Yobs
Ycalc
Yobs-Ycalc
Bragg position
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
A
000
± k
010
- k11
0 - k
Figure 3.18: Neutron powder diffraction intensities of sample II at 298 K and 16 K.Red dots and black lines correspond to observed and calculated data respectively.Blue lines show the difference between the observed and calculated data. Tick marksindicate the position of Bragg reflections of the two structural phases of Fe2P-type(phase A and B) and the structural phase of (Fe,Mn)3Si-type at 298 K in (a) and theminority phase of Fe2P-type (phase A), the ferromagnetic part of the minority phase,the majority phase of Fe2P-type (phase B), the antiferromagnetic part of the majorityphase and the structural phase of (Fe,Mn)3Si-type in (b). λ = 1.46 Å.
45
plane (as for FeMnP0.50Si0.50) with a moment of 2.1(1) µB on the iron site and2.8(2) µB on the manganese site giving a total moment of 4.9(2) µB/f.u.
In sample II, the observed and calculated NPD profiles (shown in figure3.18) showed similar sample characteristics at 298 K as for sample I, exceptthe altered phase ratio. At 16 K, phase B was observed together with smallamounts of the ferromagnetically ordered phase A and several peaks that couldbe indexed as an incommensurate antiferromagnetic ordering of phase B. Thepropagation vector of the incommensurate antiferromagnetic structure was de-termined to qx = 0.363(1) and the amplitude of the magnetic moments werefound to propagate sinusoidally along the a-axis. The magnetic moments onthe iron sites are aligned along the b-axis and the magnetic moments on themanganese site align along the a-axis, see figure 3.19. The maximum ampli-tude of the magnetic moments were 2.2(2) µB and 2.0(2) µB on the iron andmanganese sites respectively. Sinusoidal arrangements of the magnetic mo-ments can be very hard (if not impossible) to separate from a helical orderingwhen the magnetic structure is determined from NPD intensities [93]. Butseveral magnetic structures were evaluated (including helical arrangements)using representational analysis (RA) and the present antiferromagnetic struc-ture was found to be the most reasonable ordering.
a
bFe (3f)Mn (3g)P/Si (2c/1b)
Figure 3.19: The antiferromagnetic and incommensurate (qx = 0.363(1)) low tem-perature structure of sample II. The magnetic moments of the iron and manganeseatoms are aligned in the basal plane along the the a- and b-axis respectively and theamplitude of the moments propagate sinusoidally along the the a-axis.
This is the first time this type of antiferromagnetic structure has beenreported in the (Fe,Mn)2(P,Si)-system. However, a similar structure has beenreported in the analogous FeMnP1−xAsx-system for x = 0.15-0.22 [40], butthe corresponding arsenic compound (x = 0.25) is strictly antiferromagneticand there are no reports on any order-disorder behavior as seen forFeMnP0.75Si0.25. Co-existing ferromagnetic and incommensurate ordering isunusual but is still observed occasionally, a related example is for pure Fe2Pwhere a simultaneous order-disorder behavior has been observed in a narrowtemperature range below TC [89]. A similar dramatic change in the magneticordering has been observed for Fe2P caused by narrow differences of thecomposition where just a few percent substitution of manganese in Fe2Pswitch the magnetic ordering from ferromagnetic to antiferromagnetic [34].
The strength and direction of the magnetic interactions in Fe2P-type struc-tures have been reported from experiments [31; 36] and calculations [94] andare found to critically depend on changes of the Me-Me distances. As seen in
46
table 3.3, the Fe-Fe and Mn-Mn distances in sample I and II are significantlydifferent in the paramagnetic state. Since the magnetic low temperature order-ing of sample I and II are different, the Me-Me distances of the two samplesare considerably different due to the magnetoelastic effect in the ferromag-netic sample I.
The observations of the two samples with compositions close toFeMnP0.75Si0.25 present a new magnetic ordering not observed beforein the (Fe,Mn)2(P,Si)-system. Even if the antiferromagnetic orderingmakes this compound a weak candidate for magnetocaloric applications;the findings are not less important for the fundamental understanding ofthe (Fe,Mn)2(P,Si)-system which has been found more complicated thanexpected.
47
Ta
ble
3.3
:In
tera
tom
icdi
stan
ces
ofth
em
ajor
ityph
ases
insa
mpl
eI
(at
298
K(p
aram
agne
ticst
ate,
P)an
d8
K(f
erro
mag
netic
stat
e,F)
)an
dsa
mpl
eII
(at
298
K(p
aram
agne
ticst
ate,
P)an
d16
K(a
ntif
erro
mag
netic
stat
e,A
F))
inÅ
.M
ean
dist
ance
sin
side
<>
.D
eriv
edfr
omne
utro
npo
wde
rdi
ffra
ctio
nda
ta.
Sam
ple
T(K
)St
ate
Fe-P
/Si
Mn-
P/Si
Fe-F
eM
n-M
nFe
-Mn
I29
8P
2.26
4(1)
x2
2.45
1(5)
x1
2.66
2(2)
x2
3.14
3(1)
x4
2.66
2(2)
x2
2.32
8(1)
x2
2.52
0(1)
x4
2.76
8(1)
x4
<2.
296(
1)>
<2.
506(
2)>
<2.
733(
2)>
8F
2.29
1(1)
x2
2.49
1(4)
x1
2.75
3(2)
x2
3.24
1(1)
x4
2.65
2(3)
x2
2.31
9(1)
x2
2.49
5(1)
x4
2.73
7(1)
x4
<2.
305(
1)>
<2.
494(
2)>
<2.
709(
2)>
II29
8P
2.27
1(1)
x2
2.47
4(5)
x1
2.63
8(2)
x2
3.12
8(2)
x4
2.65
0(4)
x2
2.31
7(1)
x2
2.51
2(1)
x4
2.77
9(1)
x4
<2.
294(
1)>
<2.
504(
2)>
<2.
736(
3)>
16A
F2.
264(
1)x
22.
456(
3)x
12.
634(
2)x
23.
126(
2)x
42.
652(
5)x
2
2.31
3(1)
x2
2.51
0(1)
x4
2.76
6(1)
x4
<2.
288(
1)>
<2.
499(
1)>
<2.
728(
4)>
48
3.3 The virgin effectFurther studies of the first order magnetic transitions of polycrystalline sam-ples of Fe2P-type from the FeMnP1−xSix-system were performed in Paper IVto gain understanding of the magnetic phenomenon called the virgin effect.In figure 3.20, magnetization vs. temperature cycles in field cooled cooling(FCC) and field cooled heating (FCH) protocols of FeMnP0.75Si0.25 in a mag-netic field of 1 T are shown. On the first cooling, TC is found to occur at alower temperature than on subsequent cycles, while the transition temperatureon heating remains unaffected through subsequent cycles.
0 100 200 300 4000
40
80
120
160 FCC (I) FCH (I) FCC (II) FCH (II) FCC (III) FCH (III) FCC (IV) FCH (IV)
µ0H = 1 T
Mag
netiz
atio
n (A
m2 /k
g)
Temperature (K)
Figure 3.20: Magnetization vs. temperature curves for FeMnP0.75Si0.25 under a mag-netic field of 1 T. The labels FCC (I) and FCH (I) refer to the initial cooling andheating events; FCC (II, III and IV) and FCH (II, III and IV) to the second, third andfourth cooling and heating events, respectively.
The ferromagnetic transition is followed by structural changes dueto magnetostrictive effects. The room temperature XRD intensities ofFeMnP0.75Si0.25 are seen in figure 3.21 and the inset shows intensitiescollected on cooling the samples through TC. A magnetostrictive transition isobserved as abrupt changes of the peak intensities occur with the appearanceof extra peaks. The first cooling through TC introduces an irreversiblechange of the as prepared structure. When the sample is re-heated to theparamagnetic regime this minute structural change persists which is decisiveon the magnetic properties.
This permanent structure change is demonstrated in figure 3.22 where theXRD intensities collected before and after the first cooling/heating cycle areshown. The inset shows observed peak splits at high diffraction angles whichoccur after the virgin cooling. This split is an indication that the sample de-composes into two very similar phases with slightly different lattice parame-
49
20 40 60 80
40 45 50
***
*
*
Inte
nsity
(arb
. uni
ts)
2-theta ( )
*
298 K
*
2 theta (deg.)
45 60 75 105 120 135 150 175 298
Figure 3.21: X-ray powder diffraction intensities of FeMnP0.75Si0.25 at 298 K. Theinset shows a sequence of diffractograms, at temperatures according to the color code,on cooling the samples through TC. Silicon (*) was used as an internal standard.
ters. It is possible that the origin of this phase decomposition is the magneticdomain formation at low temperature which alters the local strain distributionto a more stable formation than in the high temperature situation of the asprepared sample. The irreversible change is further illustrated in figure 3.23where diffractograms recorded at 150 K on the virgin and second cooling cy-cles are shown. For the second cycle, the peaks of the magnetically orderedphase to have higher intensities than in the virgin cycle since a larger fractionof the sample has ordered at 150 K in the second cycle.
In a further view of the virgin effect in the FeMnP1−xSix-system, it is shownthat the observed virgin effect is strongly dependent of the magnitude of TC.As seen in figure 3.25, samples with TC close to or above room temperatureshow minor or zero virgin effect while samples with TC below room tempera-ture show an increased virgin effect along with a decreased TC. The tempera-ture dependence of the virgin effect is further illustrated in figure 3.24 where asample of composition FeMnP0.52Si0.48 exhibits a partial virgin effect. On thefirst cooling, a high temperature reversible part is observed above RT and anirreversible part showing the virgin effect is seen below RT. This shows thatthe virgin effect is driven by temperature and take place when the as preparedsample is first cooled through the first order magnetic transition.
50
40 50 60 70 80 90
84 86 88 90
**
*
*
*
298K
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Virgin After
*
2-theta (deg.)
Figure 3.22: Room temperature X-ray powder diffraction intensities ofFeMnP0.75Si0.25 recorded before and after the virgin cooling cycle. The insetshows the minute changes of the high angle peaks. Silicon (∗) was used as internalcalibration standard.
40 45 50
After Virgin
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Si
150 K
Figure 3.23: X-ray powder diffraction intensities during the transition at the virgincooling cycle and the 2nd cycle measured at 150 K. The contribution from the mag-netically ordered phase (arrows) is higher for the 2nd cycle than for the virgin cycle,confirming that a larger fraction of the sample has ordered in the second cycle. Thedata was normalized against ”unaltered” diffraction peaks so that the contribution ofthe magnetically ordered phase could be extracted. Silicon was used as an internalcalibration standard of the peak positions.
51
0 100 200 300 4000
40
80
120
160
Mag
netiz
atio
n (A
m2 /k
g)
H = 1 T
FCC (I) FCH (I) FCC (II) FCH (II)
Temperature (K)
Figure 3.24: Magnetization vs. temperature curves for FeMnP0.52Si0.48 under a mag-netic field of 1 T. The vertical line is a reference line showing T = 300 K. Nomencla-ture as in figure 3.20.
0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
0
10
20
30
40
50
Si conc. (x)
virg
in e
ffect
(K)
50
100
150
200
250
300
350
400
TC in first cooling cycle
Figure 3.25: Virgin effect and TC in the first cooling cycle vs. temperature for ferro-magnetic samples of the FeMnP1−xSix-system.
52
3.4 Phosphorus deficient samplesThere are two major studies of the FeMnP1−xSix-system, one by Cam Thanhet al. [52] and another by Katagiri et al. [53]. The reported results in refs. [52]and [53] are coherent but do not agree with the observations found in paperV. These three studies are here compared in detail and a central differenceis the techniques used for sample preparation. In Paper V, the drop synthesismethod has been utilized while ball milling was used in refs. [52] and [53].Comparing the phase analysis of the three investigations show that relativelylarge amounts of a secondary phase of the Fe3Si-type structure was present inthe samples of refs. [52] and [53]. In the thesis by Cam Thanh [95], selectedsamples of Fe2P-type in the FeMnP1−xSix-system were reported to contain asmuch as 18% of the phase of Fe3Si-type.
20 30 40 50 60 70 80 90
Inte
nsity
(arb
. uni
ts)
2-theta (deg.)
Yobs
Ycalc
Difference Bragg position
298 K
Figure 3.26: X-ray powder diffraction intensities of FeMnP0.40Si0.50 at 298 K. Reddots and black lines correspond to observed and calculated intensities respectively.Blue lines show the difference between the observed and calculated data. Tick marksindicate the position of Bragg reflections of two phases of Fe2P-type (RBragg =8.67/11.41%) and a phase of Fe3Si-type (RBragg = 4.87%). λ = 1.540598 Å. Rp =1.02%, Rwp = 1.34%, χ2 = 1.53
It has been suggested that losses of phosphorus could explain the divergentresults in-between the different investigations. The drop synthesis techniqueprevents major losses of the volatile elements phosphorus and manganese.Therefore a sample with composition FeMnP0.40Si0.50 was prepared in orderto study how deficiency of phosphorus influences the structural and magneticproperties. Observed and calculated XRD intensities of FeMnP0.40Si0.50 areshown in figure 3.26. The sample was found to contain three phases, two sim-ilar phases of Fe2P-type and one phase of Fe3Si-type. The phase ratio of the
53
two Fe2P-type structures and the Fe3Si-type structure were ∼ 70/30. This in-dicates that the solid solubility of silicon has been exceeded and a two phaseregion of Fe2P-type and a minority phase of Fe3Si-type is formed. The mag-netization vs. temperature curves of FeMnP0.40Si0.50 and FeMnP0.50Si0.50 infigure 3.27 shows that the first order transition temperature of FeMnP0.40Si0.50is reduced to 271 K. The saturation magnetization at T = 20 K was reduced aswell.
0
50
100
150
FeMnP0.40Si0.50
TC = 271 K
b)
M
agne
tizat
ion
(Am
2 /kg)
Temperature (K)
a)
FeMnP0.50Si0.50
TC = 395 K
0 100 200 300 400 5000
50
100
Figure 3.27: Magnetization vs. temperature curves recorded under a magnetic fieldof 1 T for (a) FeMnP0.50Si0.50 and (b) FeMnP0.40Si0.50. The red and black arrowsindicate that the data was recorded on heating and cooling respectively.
Unit cell parameters from Refs. [52] and [53] are compared with theFeMnP0.40Si0.50 compound in figure 3.28. It was found that the unit cellparameters of FeMnP0.40Si0.50 are similar to those with compositionFeMnP0.50Si0.50 by Katagiri et al. [53] and FeMnP0.52Si0.48 by Cam Thanhet al. [52]. The magnetic parameters of FeMnP0.40Si0.50 and FeMnP0.52Si0.48[52] are also found to closely agree. The TC of FeMnP0.40Si0.50 is 271 K andis reported to be 268 K for FeMnP0.52Si0.48 [52]. The thermal hysteresis forFeMnP0.40Si0.50 was 23 K and reported as 21 K for FeMnP0.52Si0.48 in ref.[52]. This comparison has given further insight on how the structural andmagnetic properties are correlated in the FeMnP1−xSix-system and a possibleexplanation to why nominally similar samples exhibit vastly differentstructural and magnetic properties in different studies.
54
0,3 0,4 0,5 0,6
3,3
3,4
3,5
6,0
6,1
6,2
6,3
c-axis
This work Cam Thanh et al. (2008) Katagiri et al. (2013)
FeMnP0.40Si0.50
cell
para
met
er le
ngth
(Å)
Si conc. (x)
a-axis
Figure 3.28: Unit cell parameters of the hexagonal Fe2P-type structurein the FeMnP1−xSix-system determined in this thesis (FeMnP0.50Si0.50 andFeMnP0.40Si0.50) compared with previous reported values of Cam Thanh et al. [52]and Katagiri et al. [53].
55
3.5 In field XRD experimentsThe concept to perform XRD measurements in an applied field of 0.35 Tusing synchrotron radiation was tested on a compound with composition(Fe0.45Mn0.55)2P0.50Si0.50. The integrated 2D diffractograms vs. temperatureare seen in figure 3.29 where the intensities were collected in a field of 0.35T. A structural transition due to magnetostriction is observed at approx 352K on heating. The experiment is further illustrated in figure 3.30 wherethe relative changes of the unit cell parameters are plotted vs. temperatureon heating and subsequently cooling. A thermal hysteresis was observedin the in-field measurements and was also observed in magnetization vs.temperature measurements in the same applied field, 0.35 T, see figure 3.31.The transition temperature from the in-field XRD experiments correlateswith the transition temperature observed in the magnetization experiments.
25
30
35
40310 320 330 340 350 360 370
Temperature (K)
2-th
eta
(deg
.) µoH = 0.35 T
Figure 3.29: Diffraction intensities vs. temperature for (Fe0.45Mn0.55)2P0.50Si0.50measured on heating. Intensities were collected in a field of 0.35 T.
300 320 340 360 380
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
a
µ0H = 0.35 T
Temperature (K)
a
cc
Figure 3.30: The relative changes of the unit cell parameters of(Fe0.45Mn0.55)2P0.50Si0.50 measured in a field of 0.35 T.
56
300 320 340 360
0,00
0,01
0,02
0,03
Lo
ng
mo
me
nt
(em
u)
Temperature (K)
FCC FCH
µ0H = 0.35 T
Figure 3.31: Magnetization vs. temperature data of (Fe0.45Mn0.55)2P0.50Si0.50 mea-sured in a magnetic field of 0.35 T.
57
4. Summary and concluding remarks
The work presented in this thesis shows how the crystallographic and mag-netic properties of the compound Fe2P can be tuned by substitution of man-ganese and silicon to form compounds of (Fe,Mn)2(P,Si)-type. The character-istics of compounds with equal amount iron and manganese and varied con-centration of phosphorus and silicon (FeMnP1−xSix) have been studied usingtechniques such as X-ray powder diffraction, neutron powder diffraction, syn-chrotron radiation X-ray powder diffraction, SQUID-magnetometry, differen-tial thermal analysis, Mössbauer spectroscopy and electronic and total energycalculations. Samples have been synthesized using the drop synthesis methodin order to prevent losses of the volatile elements manganese and phosphorus.
The phase diagram of the FeMnP1−xSix-system consists of five regions outof which two are single phase: one with the orthorhombic Co2P-type struc-ture (x < 0.15) and one with the hexagonal Fe2P-type structure (0.24 ≤ x <0.50). The FeMn(P,Si)-phase of Fe2P-type is ferromagnetic with the magneticmoments on the two metal sites aligned in the basal plane along the hexag-onal a/b-axis. Increased silicon content of the Fe2P-type increases the Curietemperature from 215 to 395 K and decreases the thermal hysteresis from96 K to 18 K. The growing hysteresis co-exists with an increased so calledvirgin effect which, in the Fe2P-type structure within this material system, isaccompanied by an irreversible structure change, induced by magnetostrictioneffects, that persists on succeeding cooling-heating cycles.
For x = 0.25, a low temperature incommensurate antiferromagnetic orderedstructure is shown to co-exist along with the ferromagnetic structure. Themagnetic structures arise from two phases of Fe2P-type with narrow differ-ences regarding structural properties in the paramagnetic regime.
Certain compounds with high silicon content in the Fe2P-type phase regionhave been found promising for use in magnetocaloric applications. The TC istunable and close to room temperature for x = 0.35 and the magnetic entropychange 8 J/kgK is obtained for a magnetic field change of 1.8 T for x = 0.50.
A study of a phosphorus deficient sample (FeMnP0.40Si0.50) has broughtmore knowledge to the conflicting properties of the FeMnP1−xSix-system re-ported in literature. It is indicated that the disagreements are due to slightdifferences in composition of the investigated compounds of Fe2P-type. Atwo-phase region with the Fe2P- and Fe3Si-type structures is reached evenfor small losses of phosphorus during preparation. This knowledge is im-
59
portant for future investigations in order to find the optimum compounds of(Fe,Mn)2(P,Si)-type in magnetic cooling applications.
A concept to perform experiments in an applied field of 0.35 T has beentested for use in synchrotron radiation X-ray powder diffraction. The qualityof the collected intensities was satisfactory and crystal structural propertiescan be obtained in a magnetic field.
60
5. Sammanfattning på svenska
Dagens energisamhälle ställer hela tiden högre krav på att teknik och elektro-nisk utrustning ska vara mer energisnål. Något av det mest energiförbrukandesom finns i våra hem idag är kylanläggningar som till exempel luftkonditione-ring och kylskåp. En ny teknik kallad magnetisk kylning är under utvecklingför att på lång sikt kunna ersätta dagens kommersiella kylskåp. Tekniken ut-nyttjar den magnetokaloriska effekten och kan vara upp till 30% mer effektivän den teknik som används idag.
Den magnetokaloriska effekten bygger på att de atomära magnetiskamomenten i ett ferromagnetiskt material linjeras upp av ett momentantpålagt magnetiskt fält, vilket innebär att materialets magnetiska entropi(oordning) minskar. Samtidigt kräver termodynamikens lagar att materialetstotala entropi inte ändras, vilket betyder att atomernas vibrationsrörelse(temperatur) ökar, det vill säga materialets temperatur stiger. På motsvarandesätt: när ett pålagt magnetiskt fält tas bort från materialet minskarupplinjeringen av de magnetiska momenten och oordningen i det magnetiskasystemet ökar. Detta betyder att atomernas vibrationsrörelse måste minska,det vill säga materialet kyls. Den magnetokaloriska effekten är störst näramaterialets ferromagnetiska fasövergångstemperatur (Curie temperaturen).Detta kan utnyttjas i den magnetokaloriska cykeln (se figur 1) där ett oordnatmagnetiskt material (1) placeras i ett magnetiskt fält vilket leder till attmaterialet blir varmare (2). Det varmare materialet kyls sedan ner genomatt värmen leds bort (3) och har nu ungefär samma temperatur som viddet inledande steget. När materialet sedan förs ut ur det magnetiska fältetkommer temperaturen i materialet att vara lägre än ursprungstemperaturen(4). Det ”kalla” materialet kan nu användas för att leda bort värme frånt.ex. ett kylskåp vilket gör att materialet får samma temperatur som vid detinledande steget och cykeln sluts och kan börja om igen.
Ett lämpligt material för magnetisk kylning bör vara billigt, fritt från gifti-ga ämnen samt ha egenskapen att gå från magnetiskt oordnat till magnetisktordnat nära rumstemperatur. Genom att byta ut järn och fosfor mot andra grun-dämnen i järnfosfiden Fe2P kan dess egenskaper skräddarsys till att vara lämp-ligt för magnetiskt kylning. Material av typen (Fe,Mn)2(P,Si) (där järn delvishar ersatts av mangan och fosfor delvis har ersatts av kisel) har visat sig varasärskilt intressant för magnetokaloriska tillämpningar. Den här avhandlingenhandlar om hur den atomära strukturen hos material av typen (Fe,Mn)2(P,Si)påverkar de magnetiska egenskaperna.
61
Materialet förs in
i ett magnetiskt fält
Materialet förs ut
ur det magnetiska fältet
Värme
leds bortVärme
leds bort Kylskåp
Figur 5.1: Illustration av den magnetokaloriska cykeln.
Eftersom fosfor och mangan förångas vid relativt låga temperaturer har ensärskild metod använts för att tillverka prover där dessa grundämnen ingårtillsammans med järn (och i detta fall kisel). Korrekta mängder av järn ochkisel hettas upp tills provet smälter. Detta sker vid temperaturer över 1400◦C.Sedan har små bitar av fosfor och mangan ”knuffats ner” i smältan. Reak-tionen mellan de nedknuffade bitarna och smältan sker så fort att fosfor ochmangan inte hinner förångas. När allt fosfor och mangan reagerat i smältansänks temperaturen och det önskade materialet har bildats.
Proverna har studerats med en mängd olika analystekniker men medstörst fokus på röntgen- och neutronpulverdiffraktion och magnetiserings-experiment. Ett fasdiagram av FeMnP1−xSix (för 0.00 ≤ x ≤ 1.00) harsammanställts och det kunde visas att det består av två enfasiga områden; ettområde med ortorombisk struktur av Co2P-typ (för x < 0.15) och ett områdemed hexagonal struktur Fe2P-typ (för 0.24 ≤ x < 0.50). Det kunde ocksåvisas att utvalda prover i området av Fe2P-typ är lämpliga för användninginom magnetisk kylning. För sammansättningen x = 0.35 är exempelvis denmagnetiska övergångstemperaturen nära rumstemperatur.
I material som är magnetiska får varje magnetisk atom en riktning. Dessaatomer kan peka åt olika håll och sammantaget bilda en magnetisk struktur.Den magnetiska ordningen eller magnetiska strukturen bestäms genom att be-stråla materialet med neutroner med tekniken neutronpulverdiffraktion. Utval-da prover av Fe2P-typ har studerats med denna teknik och sammansättningenför x = 0.50 har visats vara ferromagnetisk, det vill säga att alla magnetiskaatomer är riktade åt samma håll. Detta gäller för nästan alla sammansättningarav Fe2P-typ i FeMn(P,Si)-fasdiagrammet. Dock, provet med sammansättningx = 0.25 skiljer sig ur mängden. Detta prov bestod av två faser av Fe2P-typ där
62
den ena var ferromagnetisk och den andra var antiferromagnetisk, vilket bety-der att riktningarna på de magnetiska atomerna är motriktade och sammanta-get tar ut varandra. Det visade sig också att ordning i den antiferromagnetiskstrukturen uppvisar en komplex magnetisk struktur som varierar likt en våggenom kristallen, se figur 5.2.
a
b
järn
mangan
fosfor
kisel
Figur 5.2: Den antiferromagnetiska strukturen för FeMnP0.75Si0.25.
Studier av prover av Fe2P-typ visade också att temperaturen där materia-let ordnade sig magnetiskt förändrades sig mellan den första och andra kyl-ningscykeln, för att sedan vara densamma för alla påföljande cykler. På svens-ka kan denna temperaturberoende effekt översättas från engelskans ”virgin ef-fect” med jungfrueffekt. Röntgendiffraktionexperiment visade att även struk-turen i materialet påverkas av temperaturcyklingen. Efter den första cykelnsyns en förändring i strukturen som inte går tillbaka efter att temperaturcy-keln är genomförd. Denna förändring av strukturen kan vara en bidragandeorsak till att den magnetiska övergångstemperaturen förändras efter den förs-ta temperaturcykeln.
En studie av Fe2P-typ med otillräcklig mängd fosfor (FeMnP0.40Si0.50) ge-nomfördes för att studera hur brist på fosfor påverkar strukturen och de mag-netiska egenskaperna. Det visades att brist på fosfor skapar stora förändringarhos såväl strukturen som hos de magnetiska egenskaperna och detta kan indi-kera varför det har förekommit avvikelser mellan olika studier av material av(Fe,Mn)2(P,Si)-typ.
Sammantaget är (Fe,Mn)2(P,Si) ett materialsystem där utvalda sammansätt-ningar kan vara konkurrenskraftiga inom magnetisk kylning. Den här avhand-lingen har också visat att materialsystemet är komplicerat med olika typer avmagnetisk ordning och att små variationer i sammansättning av de olika grun-dämnena kraftigt påverkar de önskade magnetiska egenskaperna.
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6. Acknowledgments
Till att börja med vill jag tacka mina handledare för allt jobb ni har lagt ner föratt hjälpa mig fram till mitt slutmål. Tack Yvonne för alla diskussioner och föratt du har lärt mig allt från hur man tacklar bångstyriga parametrar i fullproftill den engelska stavningen av fosfor (phosphou... phosphorou... phospho-rus?). Tack Per för din expertis och all assistans med ”politiska” dokument,det har verkligen varit till stor hjälp. Ett särskilt tack till Martin för att dutidigt hoppade på tåget och för allt stöd du har gett mig både i arbetet och pådet personliga planet. Ni har alla tre varit ett stort stöd och har gjort att jagkunnat nå högre mål än vad jag någonsin trodde var möjligt. Tack!
Thank you Matthias, Mikael A, Tapati and Luana for all your help andsupport with the magnetic measurements (you have been great!); Johan forhelping me with various work in the basement and in the X-ray lab; Premekand Magnus for all your hard work and assistance with the neutron diffractionexperiments; Erna, Olle and Levente for all your work with the computationalcalculations; Girma for your efforts to help me with the single crystal measure-ments; Lennart, Tore, Rolf, Sergey, Torbjörn and Josh for support, suggestionsand helpful discussions.
Tack Mattis för att du alltid har varit en så trevlig kontorskamrat. Tack Jonas”back seat refiner” Å för all hjälp vid 711:an (R.I.P.) och för att vi har blivitså pass goda kamrater under åren som gott. Tack Rickard för alla trevliga (ochfåniga) stunder.
Även de tyngsta av dagar har blivit lättsamma efter en vistelse i lunchrum-met. Tack Fredde, David, Adam, Tomas, Linus, Daniel m.fl. för alla diskus-sioner som faktiskt har haft hyfsad höjd vid några få enstaka tillfällen.
Tack Eva och Tatti för all hjälp med allt som rör administration. Förlåt Evaoch Tatti för att jag alltid kommit till er med allt som rör all administration.
Tack Pedro och Janne för all teknisk hjälp, stort som smått. Ett särskilt tacktill Anders och Mikael O för all den support ni har gett mig och för att ni harhaft tålamod med alla mina ständiga små problem.
I also want to thank all my colleagues at the department. I am grateful that Ihad the opportunity to make my PhD at a place where I always have felt goodspirit and joy. It is all of you that have made it possible!
Tack också till min familj och mina svärföräldrar, tack för att ni finns.Men, framför allt vill jag tacka min underbara fru Johanna för allt stöd och
all glädje du ger mig. Du och August är det viktigaste jag har och jag älskarer verkligen över allt annat.
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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1197
Editor: The Dean of the Faculty of Science and Technology
A doctoral dissertation from the Faculty of Science andTechnology, Uppsala University, is usually a summary of anumber of papers. A few copies of the complete dissertationare kept at major Swedish research libraries, while thesummary alone is distributed internationally throughthe series Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology.(Prior to January, 2005, the series was published under thetitle “Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology”.)
Distribution: publications.uu.seurn:nbn:se:uu:diva-234516
ACTAUNIVERSITATIS
UPSALIENSISUPPSALA
2014
