MAGNETOCHEMICAL INVESTIGATIONS
ON FE (III) IN SOME TERNARY COMPOUNDS
I \
C10044
84281
MAGNETOCHEMICAL INVESTIGATIONS
ON FE (III) IN SOME TERNARY COMPOUNDS
PROEFSCHRIFT
ter verkrijging van de graad van doctor in de technische
wetenschappen aan de Technische Hogeschool Delft,
op gezag van de rector magnificus Prof. Dr. Ir. F.J. Kievits,
voor een commissie aangewezen door het college van dekanen
te verdedigen op woensdag 10 oktober te 16.00 uur
door
Gerrit Anton Korteweg
scheikundig doctorandus
geboren te Wageningen
, : 1376
r ^ 452 I
j - -U Delft C 448428Dit proefschrift is goedgekeurd door de promotor
Prof. Dr. Ir. L.L. van Reijen
Ka;, aUTOo car {v irpo Travioiv Kai, xa TiavTa ev auiu auveoxriKEV
I.
en Hij is vóór alles
en alle dingen hebben hun bestaan in Hem
(Col. 1:17)
Hierbij wil ik graag allen die hebben bijgedragen aan de totstandkoming van dit proefschrift hartelijk bedanken. In het bijzonder dank ik dr.ir. G. van Veen, die mij bij de inleiding in dit onderwerp met raad en daad terzijde heeft gestaan en mij voorzien heeft van zeer bruikbare computerprogramma's. De heer Y. Timmerman bedank ik hartelijk voor de bereiding van de AgMO -verbindingen. Mijn collega's dr.ir. G. Hakvoort, drs. P.J.J.M, van der Put en ir. J.J.M. Potters ben ik erkentelijk voor een aantal nuttige adviezen. Voor de Mössbauer-spectroscopie ben ik veel dank verschuldigd aan dr.ir. A.M. van der Kraan en de heer E. Gerkema van het IRl (Interuniversitair Reactor Instituut).
De heer P. Bode (IRI) dank ik voor de neutronenactiveringsanalyses en mej. L.A. Schouten voor enkele chemische analyses. Verder heb ik deskundige steun gehad van de diensten binnen het Gebouw voor Scheikunde, met name van de glasblazerij.
Verder wil ik de heren J. van Willigen en J.C. Ruis en de reprografische dienst van het Gebouw voor Scheikunde hartelijk bedanken voor het verzorgen van de figuren in dit proefschrift. Voor het typewerk en de lay-out van het proefschrift ben ik tenslotte veel dank verschuldigd aan mej. M.J.A. Wijnen.
C O N T E N T S
I GENERAL INTRODUCTION 1
II PREPARATION AND CHARACTERIZATION 4 1. Structure and some properties of chalcopyrites 4
2. Preparation of chalcopyrites 8 3. Crystal growth of chalcopyrites 9 4. Structure and some properties of 3-AgMO compounds 11
5. Preparation of 3-AgM0„ compounds 13
III MAGNETIC PROPERTIES 16 1. Introduction 16 2. Cluster statistics 19 3. Magnetic susceptibility measurements 21
5.1. Experimental procedure 21
3.2. CuGa, Fe S^ 22
1-x X 2
3.S. CuAl, Fe S. and Culn, Fe S„ 26
1-x X 2 1-x X 2 3.4. AgM^ Fe n systems 30 1 —X X ^ 4. Mössbauer spectroscopy 34 IV EPR SPECTROSCOPY 38 1. Introduction 38 2. Single crystal spectra 41
3. Powder spectra of single ions 46
3.1. CuGa^ Fe S„ 46
1-x X 2
3.2. Other systems 47
4. Powder spectra of clusters 49 5. Interpretation of AgMO : Fe powder spectra 52
V QUANTITATIVE EVALUATION OF EPR SPECTRA 56 1. Determination of relative EPR intensities 56
2. Determination of absolute spin concentration 59 3. Determination of spin concentrations from fine 61
VI THEORETICAL CONSIDERATIONS ON EPR SPECTRA OF CLUSTERS 66
1. Introduction 66 2. Zero field splitting constants for pairs of para- 67
magnetic ions
3. Zero field splitting constants for clusters of 3, 71 4 or 5 paramagnetic ions
4. Spectra of clusters 78 5. Calculation of second and fourth moments 81
6. Lineshape and linewidths 84
VII DISCUSSION AND CONCLUSIONS 88
List of symbols 95
References 97
Summary 101
CHAPTER I
GENERAL INTRODUCTION
During the last decades extensive studies have been made on the magnetic properties of transition metal compounds. These studies started with well-known minerals, e.g. the iron oxides and sulphides.
Later on many new materials were made and their magnetic properties were investigated. Among these the ferrites play an important role, because several of them have applications in electronics [1].
For many compounds, the interpretation of the kind and the strength of the magnetism is not an easy task. One can observe macroscopic quantities (magnetization, susceptibility, transition temperatures, etc.), but these give little information about the magnetic interactions between the transi-tion metal ions. This is caused by the fact that in most cases more than one type of magnetic interaction is needed to describe the kind and strength of the magnetic structure.
This problem can often be solved by dilution, i.e. making a solid solution of the transition metal compound in a diamagnetic compound which has the same structure. If the transition metal ions are distributed homogeneously, one can get much information from the magnetic susceptibili-ties of these diluted compounds [2, 3 ] .
Moreover, the application of magnetic resonance and optical techniques can give useful information.
Using the EPR technique one observes only single ion spectra at very low concentrations of paramagnetic ions. As the concentration increases, spectra from pairs of paramagnetic ions arise. From the study of the temperature dependence of these pair spectra one can get accurate data on the magnetic interactions [4].
This thesis contains a study of some systems having Fe(III) as the paramagnetic ion by means of magnetic susceptibility measurements and EPR.
Our first class of systems has been derived from CuFeS„ (chalcopyrite), which is a well-known mineral. Its structure which is given in Fig. I.l,
represents a sujVerstructure of the sphalerite (cubic ZnS) structure [5] . Other compounds having the chalcopyrite structure can be used as diamagnetic host lattices for Fe(III). The systems which were studied are CuH Fe S
b.
n - Na Fe O2
with M = Al, Ga or In.
The second class of systems under investigation has been derived from B-AgFeO„. This has the same structure as (3-NaFeO , which has been shown in Fig. I.l; it represents a superstructure of the wurtzite (hexagonal ZnS) structure [6]. The systems which were studied are AgM Fe 0„ with M = Al or Ga.
CuFeS and 3-AgFe0_ have some common features:
a. Both structures are tetrahedral i.e. each cation is surrounded by a (distorted) tetrahedron of anions and each anion by a tetrahedron of cations (2 Fe ions and 2 Ag or Cu ions). Therefore the kinds and numbers of the various interaction paths are similar in both compounds. This is demonstrated by the cluster statistics in Chapter III-2. b. Both compounds have strong magnetic interactions. The T of CuFeS- has
N i
been found to be 550 C [7]. For S-AgFeO_ T could not be determined; o T is higher than room temperature and probably higher than 460 C [6J. Thus the aim of this work is the investigation of the magnetic inter-actions between Fe ions in the chalcopyrite and B-AgMO structures.
Chapter II gives information about these structures and the preparation of the various compounds. The results of magnetic susceptibility measure-ments and some Mössbauer spectroscopy have been described in Chapter III.
In Chapter IV the results of the various EPR spectra are interpreted and discussed.
Chapter V describes the determination of relative intensities and spin concentrations from EPR spectra. Chapter VI contains a theoretical analysis of the origin of EPR spectra at higher concentrations of paramagnetic ions. Finally, in Chapter VII the main results from the foregoing Chapters are discussed.
CHAPTER II
PREPARATION AND CHARACTERIZATION
II.1 STRUCTURE AND SOME PROPERTIES OF CHALCOPYRITES
The chalcopyrite structure which has been shown in Fig. I.la is described as follows:
Table II.1. Description of the chalcopyrite structure. Chemical formula: 12
ABX_. Space group: D^^ - I42d.
2. 2d Atom A B X Number 4 4 8 Symmetry 4 - S^ 4 - S^
2 - s
Position (0, 0, 0) (J, \ , \) +(0,0,0) (0,-1-,J)
(0,0,i) (0,è,^)
(u,i,|) (ü,f,i)(J,u,^) (è,n,|)
c /a ~ 2 u ; J 0 oIt is a superstructure of the sphalerite structure [1, 2 ] . The unit cell of chalcopyrite has been doubled with respect to the sphalerite unit cell; so ideally c would be equal to 2a . In most chalcopyrite compounds some tetragonal compression is found, i.e. c /a < 2.
There are two classes of chalcopyrite compounds [1]: a. Chalcogenides, having the general formula:
A(I) B(III) X(VI)^ with A(I) = Cu, Ag
B(III) = Fe, Al, Ga, In, Tl X(VI) = S, Se, Te.
b. Pnictides, having the general formula:
A(II) B(IV) X(V)2 with A(II) = Mg, Zn, Cd B(IV) = Si, Ge, Sn X(V) = P, As, Sb.
In the scope of this thesis, only the chalcogenides are relevant. Some structural parameters are given in Table II.2.
The anions (X) are displaced with respect to their ideal positions. This displacement can be considered as a rotation of the anions in the ab plane around the cations, so that the BX distances decrease and the AX distances increase.
In this way the coordination of the B ions is kept nearly tetrahedral. In CuFeS the Fe ions are found to be surrounded by a perfect tetrahedron of S ions [3] , which is confirmed by the absence of a quadrupole splitting in the Mössbauer spectrum [4].
In this case there is the following relation between the parameters u and c /a :
o o
u = ^ - ^ V2(c /a ) ^ - 4
2 8 o o
which is perfectly correct for CuFeS„ and nearly correct for CuAlS , CuGaS , CuInS and most of the pnictides [1, 5 ] .
This points to a strong covalency of the BX bonds in nearly all chalcopyrites. The distortion of the AX^ tetrahedron is generally much higher than the distortion of the BX tetrahedron.
From Mössbauer- and EPR-spectroscopy some data have become available about the local distortion around Fe in chalcopyrite host lattices (CuAlS , CuGaS and AgGaS ) .
The presence of a quadrupole splitting in Mössbauer spectra of CuGa, Fe S„ points to a distortion of FeS. tetrahedra in this matrix
1-x X 2 *^ 4 (Section III.4) .
EPR spectroscopy allows to determine the rotation of S ions around Fe ions [2, 6]. The angle of this rotation x(Fe) is much larger than the rotation angle x of the host lattice, as determined from u. In:
CuAlS^ : X(Fe) = 5.1° (1), T = 2.1° (4) CuGaS^ : T(Fe) = 5.1° (1), X = 2.6° (6) AgGaSg : x(Fe) = 10.9° (2), T = 6.9° (6).
Now it can be assumed that the displacements of S ions around Fe would have the same directions as the displacements from their ideal positions in
Table IX.2. Structural parameters of some chalcopyrites (ABS ) . Compound CuAlS^ CuGaS CuInS^ AgGaS^ CuFeS Ref. 6 6 5 6 5 5 3
a
(X)
o 5.336 5.351 5.3474 5.523 5.5228 5.754 5.7572 5.289c^ (X)
10.444 10.480 10.4743 11.12 11.1330 10.295 10.3036 10.423 c /a o' o 1.958 1.958 1.9588 2.013 2.0158 1.789 1.7897 1.971 u 0.268 0.272 0.2538 0.214 0.2295 0.304 0.2908 0.2574 S-B-S 108.7° 108.2° 109.1° 112.9° 111.2° 109.7° 111.1° 109.5° S-B-S* 109.9° 110.1° 110.2° 107.7° 108.6° 109.3° 108.7° 109.5° B-S (S) 2.239 2.235 2.288 2.517 2.464 2.235 2.276 2.257the host lattice, i.e. there would be a local change of the u parameter at the positions of Fe ions. Then from the T(Fe)-values the following values of the S-Fe-S angles and Fe-S distances could be obtained. In:
CuAlS^ CuGaS^ AgGaS^ 106 106 106 2 ,
2°,
9°,
111.1 , 111.1°, 110.7°, 2 2 2 174 181 161A
S
S
According to this model, in these matrices FeS, tetrahedra would be far from perfect and the Fe-S distances would be lower than the Fe-S distance in CuFeS„ (2.257 A ) .
Thus it is probable that the displacements of S ions around Fe ions in these host lattices are not simply described by a local change of the u parameter.
The tetrahedral coordination of Cu in CuFeS is also far from perfect. 2+ + This rather high distortion is more likely for Cu than for Cu . So from
+ 3-H 2+ 2+ the structural data an ionic configuration between Cu Fe S„ and Cu Fe S„ has been postulated [3].
By neutron diffraction however, the magnetic moments of Cu and Fe have been established to be 0.02 3 and 3.85 3 respectively [7]. This points to a
-^ 2+ 2+
2-1-configuration much closer to Cu Fe S than to Cu Fe S .
Recently, from XPS measurements it has been shown that Cu has the (3d) electron configuration, i.e. Cu is monovalent [4]. Moreover the temperature dependence and pressure dependence of Mössbauer parameters point
3-H r -,
to Fe in the high spin state [4J. This is confirmed by the small isomer shift of the Mössbauer spectrum [8].
The diamagnetic sulphides and also some selenides are semiconductors, as their binary analogs (ZnS, ZnSe, CdSe, etc.). In contrast to the binary compounds some chalcopyrite compounds can have both n-type and p-type conduction; this is dependent on the preparation atmosphere.
Much investigation has been done on their electrical, optical and electro-optical properties [1, 9, 22]. Some of these compounds are promising for applications in electronic industry. The optical band gaps range from 3.5 eV (CuAlS ) to 0.8 eV (CuInSe ) ; these values are lower than in the corresponding binary analogs.
d levels of Ag or Cu into the valence band, which consists mainly of the S (or Se) 3p levels. Presumably the conduction band consists mainly of the highest s levels of the cations.
When the trivalent element is substituted by Fe, the lattice constants show small changes.
In CuGa, Fe S„ the a axis decreases linearly as x increases. On the 1-x X 2
other hand the c axis as a function of x shows a maximum at x ~ 0.25 (Fig. II.1, [12]). This maximum can be related to different cation-cation linkage in the a- and c-directions.
Such a maximum has also been observed in the Cu Ag GaS systems and similar systems [13], so this effect is not caused by magnetic interactions only.
Fiq. II.1 Lattice constants a^ and a^ as a function of x in CuGa^ Fe S^,
0 0 1 X X Ó
from Ref. [12].
II.2 PREPARATION OF CHALCOPYRITES
The chalcopyrite compounds CuM Fe S (M = Al, Ga, In) have been made as described in the thesis of Van Veen [2].
This method starts from the elements; stoichiometric amounts with a small excess of sulphur are put together into a silica ampoule, which is
-5
In order to prepare CuAl Fe S the silica wall of the ampoule has to be protected from adhesion and attack by Al. This was done by coating the wall with a carbon film obtained by pyrolysis of acetone.
After evacuation the ampoule was closed, slowly heated up to about o
850 C and held at this temperature for a few days. In the case of CuAl, Fe S_ the ampoule was rotated during the heating.
1-x X 2 "^ " "
After a rapid cooling, the product was mixed by means of an agate ball mill and heated again. As the excess of sulphur had been distilled off at low temperatures, a small amount (about 100 mg) of sulphur was added before this second heating step.
This is very important, for only at an excess of sulphur all iron is trivalent, as has been shown in CuGa, Fe S_ [141 and CuAl, Fe S„ [2, 151.
1-x X 2 '^ -' 1-x x 2 '- '
The mixture was reheated at 850°C for a few days and slowly cooled o
down at a rate of about 15 C/h.
This slow cooling appears to be necessary in order to prevent the ferromagnetic contribution to the magnetic susceptibility as found in quenched samples of CuGa Fe S [2]. The origin of this ferromagnetism having its T at about 140 K could not be traced down to any possible contamination. Moreover, no impurity could be found from X-ray diffraction.
X-ray diffraction patterns of all the samples were made in order to check their purity and homogeneity. Sometimes inhomogeneities could be seen from a broadening or even a splitting of lines, i.e. from small differences between lattice constants. The CuGa, Fe S„ samples had to be heated for a
1-x X 2
third time in order to get good homogeneous samples.
From X-ray diffraction it could be concluded that the lattice constants of CuAlSo, CuGaS and CuInS agree with those reported in the literature
[5, 6].
II.3 CRYSTAL GROWTH OF CHALCOPYRITES
The growth of a series of single crystals having different Fe con-centrations is important for EPR spectroscopy, as much more information could be obtained from single crystal spectra than from powder spectra.
Single crystals of CuGa, Fe S. have been grown by means of the
1-x X 2 o J
chemical vapour-phase transport (CVT) technique from a powder of the same material.
this way have well-developed facets, so that they can easily be oriented with respect to the magnetic field in EPR spectroscopy [2].
The technique proceeds as follows: Some powder of the compound or a mixture of the elements is put into one end of an evacuated silica ampoule. By heating evaporation takes place, which can be stimulated by the addition of a transport agent; together with the original material this forms volatile compounds.
So a chemical equilibrium is established in which the original solid material is involved. At the other end of the tube which is a little colder, this equilibrium is shifted back a little to the original material. Thus this material is transported from the hot end to the cold end, where it is deposited very slowly so that crystals can grow.
For CuGa Fe S_, about 1 g of the powder was put into a silica ampoule having a diameter of 1 cm and a length of 15 cm; 70 mg of I had been added which gives a concentration of 7 mg/ml.
The transport took place during 1 week from 800 C to 780 C. Nearly all the material was transported, even at this small temperature gradient.
The shape of the crystals obtained is bar-like; the length of the greater crystals amounts to 10 mm and the diameter to 1 mm.
A cross-section of a typical sample crystal is shown in Fig. II.2. The longitudinal axis is [111] and the faces parallel to this axis are: (112) , (101) and (Oil), as is known from literature [1].
m
(IOi)\
(II2K
Fig. II. 2 Shape of chat.'cpyrite crystals perpendicular to the longitudinal
axis.
The c r y s t a l s were analysed by means of n e u t r o n a c t i v a t i o n a n a l y s i s (Table I I . 3 ) .
The concentration of Fe in the crystals appeared to be approximately the same as the original concentration (x) in the powders.
Table 11.3. Analysis results of CuGa Fe S single crystals.
r
x(%) 0.5 1.0 2.0 3.0 4.0 6.0 Fe/Cu molar ratio (%) 0.561 + 0.046 0.956 + 0.082 2.25 + 0.15 2.87 -H 0.19 3.92 + 0.21 8.88 + 0.49 I (weight %) 0.17 0.76 0.16 0.22 0.20 0.13Except for one sample, the iodine content is <^ 0.22% of the total weight. If all this iodine would have been incorporated into the crystals, the iodine contamination would amount to less than 0.4% molar.
However, it is not likely that iodine is incorporated as its atomic and ionic radii are much larger than the structure of CuGaS would permit. Presumably, during the cooling down the adsorption of iodine and/or iodides on the crystal surface could not be totally prevented.
II.4 STRUCTURE AND SOME PROPERTIES OF g-AgMO^ COMPOUNDS
The AgMO- (M = Al, Ga, Fe) compounds occur in two modifications: a, having octahedral coordinations and 3, having tetrahedral coordinations. In this thesis only the 3-modifications are studied.
These compounds can be easily synthesized from the corresponding 3-NaMO compounds, which have the same structure [16].
In Fig. I.lb a model of this structure has been given for 3-NaFeO„. The structure can be considered as a superstructure of wurtzite (hexagonal ZnS); it is a hexagonal close packing of anions with half of the tetrahedral sites occupied by cations.
Because of the presence of two types of cations, the unit cell has been changed from,hexagonal to orthorhombic. Its ideal lattice constants have
Table II.4. Description of the 3-AgMO structure Chemical formula: AgMO or NaMO„
Space group Eq. positions
9 C„ -Pna
2v
(xyz), (x,y,z-^J), (.i-x ,y+i ,z + i) , (x+è,è-y,z), Coordinates of NaFeO-Atom Na Fe 0 (1) 0 (2) X 0.40 0.075 0.05 0.38 y 0.135 0.128 0.10 0.125 z 0.50 0.00 0.33 -0.10
Table II.5. Structural parameters of some (from Ref. [16]).
-NaMO„ and 3-AgHO compounds
Compound NaFeO^ • ^ ^ 0 . 8 % • ^ ^ 0 . 5 % ''^0.2^^0 AgFeO^ NaAlOg •^^0.5^^0 AgAlOg NaGaO AgGaOg ZnO* 2^^02 5^^02 8^^°2
..^^°2
Ideal wurtzitea(S)
5.664 5.662 5.659 5.670 5.635 5.375 5.410 5.428 5.519 5.563 5.628 structure:hd)
7.139 7.143 7.138 7.145 7.105 7.048 6.96P 6.990 7.201 7.149 6.499cd)
5.381 5.382 5.382 5.393 5.547 5.202 5.323 5.377 5.301 5.471 5.207 a/b 0.793 0.793 0.793 0.794 0.793 0.763 0.776 0.777 0.766 0.778 0.866 0.866 c/b 0.754 0.753 0.754 0.755 0.781 0.738 0.764 0.769 0.736 0.765 0.801 0.816V ( S ^
54.38 54.42 54.35 54.62 55.50 49.28 50.18 51.00 52.68 54.40 47.61been transformed in t h e following way:
a = \ / ^ a ' ; b = 2 a ' a n d c = c ' =— V ? a'
in which a' and c' represent the lattice constants of the hexagonal wurtzite unit cell.
In Table II.4 the symmetry has been described and the coordinates of NaFeO- have been given [17]. Although no coordinates of the other NaM0„ or AgMO compounds are known, these have similar structures as NaFeO .
Particularly the coordinates of AgFeO are expected to be close to
+ +
those of NaFeO , as the ionic radii of Ag and Na are nearly the same: 1.02 A and 0.99 X respectively [18].
From Table II.5 it appears that ZnO has a nearly ideal wurtzite structure; in the AgMO- compounds the main deviations from this ideal structure are encountered in the b-values.
The molecular volume of Na ^Ag A10„ is approximately the same as 0.5 0.5 2
the average of the molecular volumes of AgAlO- and NaA10„.
In the series Na, Ag FeO„ however, the molecular volume remains near-1-x X 2
ly the same as in NaFeO„, up to x = 0.8.
The relatively sudden increase from x = 0.8 to x = 1.0 has been
related by Hakvoort to the magnetism of the substances. At room temperature samples from x = 0 . 0 t o x = 0 . 8 appeared to be ferromagnetic; only AgFeO is antiferromagnetic at room temperature [16].
On the other hand, the lattice constants in the system NaAl, Fe 0„ •' 1-x X 2 show a l i n e a r dependence on x [ 1 9 ] .
.0 n-f f5_A(T'P^f_,
Presumably the Neel temperature of 3-AgFe0„ is higher than 460 C, as o
no transition could be detected between room temperature and 460 C from DTA. Certainly T is higher than room temperature, so AgFeO- is rather strongly antiferromagnetic.
11. 5 PREPARATION OF 3-AgMO COMPOUNDS
Generally it is possible to make a AgMO- compound by precipitation from a alkaline solution or by heating in air of the constituent metals or their oxides.
In this way however, always a-modifications are obtained instead of 3-modifications, as the latter are metastable at lower temperatures and
normal pressures. For NaMO compounds however, the 3-modifications are stable at lower temperature [16, 19].
Therefore the logical way to make the 3-AgMO compounds would be to start from the corresponding 3-NaMO compounds and let them react with molten AgNO_. This route appeared to be successful [16, 20]. Thus the synthesis proceeds by two steps:
a. Synthesis of NaMO-; b. Transformation into AgMO_.
a. Synthesis of NaMO„
M O (a-Al 0 , 3-Ga 0 or Fe 0_) is made by precipitating the ^ o ^ o ^ o ^ o
corresponding hydroxide from a nitrate solution and heating it during one o
hour up to 800 C. In this way a fine powder of the oxide M„0_ is obtained. Its water content appears to be negligible as nearly no weight is lost by heating up to 1200 C.
The oxide (or a mixture of two oxides) is mix<;d with a stoichiometric amount of sodium carbonate. At elevated temperatures NaMO- is formed from this mixture:
Na^COg (s, 1) -1- M^Og (s) ^ 2NaM02 (s) + CO^ (g) .
In order to carry this reaction to completion, the temperature is raised to 650°C, 750°C, 850°C, 1000°C and 1050°C successively with intervals of one day.
The X-ray diffraction patterns of the products are equal to those of the 3-NaMO compounds which had been made by Hakvoort [16] and did not show significant amounts of impurities.
b. Transformation into AgMO
The NaHO compounds obtained are transformed into AgHO„ compounds in the following way:
280 C
A large excess amount of silver nitrate is molten by heating to 280 C in a dry nitrogen atmosphere. After the addition of NaMO the mixture is stirred thoroughly and held at the same temperature during one day. The reaction flask is protected from light in order to prevent the decomposi-tion of AgNO_.
After cooling down, AgNO and NaNO are washed out by means of water. The remaining solid substance is dried at 200 C in a dry nitrogen
atmosphere. In this way the following powders were obtained:
3-AgAl, Fe 0„: x values from 0.005 to 0.40 1-x X 2
S-AgGa^_^Fe^02:
a-AgFeO-It is rather surprising that the a-modification of AgFeO was obtained instead of the 3-modification. This appeared from X-ray analysis [21] and from its magnetism which is described in Chapter III of this thesis. As mentioned before, the NaFeO was in the B-modification.
Apparently the conditions during the reaction with AgNO were also favourable for the transformation of 3-AgFeO„ into a-AgFeO . Also some a-AgFeO has been observed in our AgGa Fe 0 samples at x = 0.3 and X = 0.4.
As appeared from X-ray diffraction all the samples contained a con-siderable amount of metallic silver. This can be attributed to some de-compositon of AgNO .
For each sample the amount of metallic silver has been determined by means of atomic absorption analysis. Its mean value appeared to be 25 weight percent. This contamination was taken into account in the magnetic susceptibility measurements and the relative EPR intensity measurements.
CHAPTER III
MAGNETIC PROPERTIES
III.l INTRODUCTION
When a small fraction of paramagnetic ions, e.g. Fe(III), is in-corporated randomly into a diamagnetic host lattice, the magnetic suscept-ibility becomes paramagnetic.
The magnetization per mole of paramagnetic ions can be described by a Brillouin-like function [1]:
M^ = jNg 3 {(2S + 1) coth
[Sm^-Lll]
- coth [ f g p (1)
At higher temperatures and lower magnetic fields i.e. if g3H << kT -this magnetization is proportional to the magnetic field and inversely proportional to the temperature. In this case the product of the magnetic susceptibility (x ) and the temperature has a constant value:
M T 2 2
^s-^ = - i r =
^ ^ ^ ^ - ^ ^ ~~
I g^S(S . 1) emu.mor\K (2)
For Fe(III), S = 5/2 and g == 2.0, so y .T = 4.4 emu.mol" .K.
Even at quite low Fe concentration (x > 0.005), the magnetic suscept-ibility of the Fe(III) ions is influenced by magnetic interactions.
When the magnetic interaction between two paramagnetic ions is strong with respect to g3H, the Hamiltonian of such a pair consists mainly of the
isotropic interaction term:
H = J.S .S = iJ (S^ - sf - S ^ (3)
p 1 2 1 2
where J = exchange energy, S , S = spin operators of the two individual ions and S = S, + S .
1 2
The eigenvalues of this Hamiltonian are given by:
For a pair of Fe(III) ions S = S„ 1 ^
5/2, so the possible values of S are: S = 0, 1, 2, 3, 4 and 5. As only energy differences will be considered, the terms with S. and S in Eq. (4) can be omitted.
Taking into account a Boltzmann distribution over the various energy levels, the susceptibility per mole Fe(III) pairs (x ) can be written as follows: Xp-T _ Ng 2„2 3k I (2S -K 1) S (S -H 1) e S=0 •Eg/kT 5 I (2S -H 1 ) e S=0 -Eg/kT (5)
If all Fe ions would be present in Fe(III) pairs, the susceptibility per mole of Fe(III) ions would be equal to X
Fe % •
X_ .T has been p l o t t e d v e r s u s | k T / J | in F i g . I I I . l for a n t i f e r r o -magnetic p a i r s (AF, J > 0) and for f e r r o m a g n e t i c p a i r s (F, J < 0 ) .
Fig. III.l Susceptibilities of ferromagnetic and antiferromagnetic Fe pairs as a function of \ kT/J \ .
For both types of pairs x^. -^ approaches the single ion value x -T if kT >> | j | . On the other hand, if kT << | j | , the magnetic susceptibility falls down to zero for AF pairs and it increases to the value 12/7.X for F pairs.
If the Fe(III) concentration is not too large, the total magnetic susceptibility consists of contributions from single Fe(III) ions and from various kinds of pairs. The ratios between these contributions can be determined by statistical considerations, which will be described in Section III.2.
If all interactions are antiferromagnetic (or ferromagnetic) the equivalent neighbour model can be applied [7]. The basic assumption of this model is that the possible interactions of a particular ion with its
neighbours can be divided into a certain number (q) of equivalent ones -i.e. having equal J's- and all other interactions being neglected (J = 0 ) .
The model states that this number q is about inversely proportional to the critical concentration x , i.e. the concentration x at which the mean
c cluster-size becomes infinite.
When X < X , a three-dimensional network is not yet present, so addition of paramagnetic ions should enhance the magnetization (per mole of compound). As soon as this network is formed (at x ^ x ) , addition of para-magnetic ions should contribute to compensation of the para-magnetic sublattices,
so the magnetization would decrease.
So a (temperature dependent) value of x can be determined experiment-ally from the maximum of the magnetization plotted vs. x at constant
temperature [1]. This x measures only those interactions, which significant-ly influence the magnetization M, i.e. the interactions having J >_ kT.
Application of the equivalent neighbour model then gives the number of neighbours q for which J ^ kT.
At higher Fe concentrations (x > x ) and lower temperatures (T < T ) long range order is present. At T » T the susceptibility generally can be
N d e s c r i b e d by a Curie-Weiss function:
From the Curie constant C the effective magnetic moment U „„ is
^ eff calculated by means of the following relation:
^ = 1^ • 4f (^>
Now the effective moment is given by:y^^j = g 3 Vs(S + 1)' (8)
Free Fe(III) has g = 2.0023 and S = 5/2, so the spin-only value of the magnetic moment of Fe is 5.92 3. For CuFeS the effective magnetic moment of Fe has been found to be 3.85 3, from neutron diffraction [8].
II I.2 CLUSTER STATISTICS
In order to determine the number of single Fe(III) ions at a given fractional Fe concentration (x), x should be multiplied by the probability that a certain Fe ion is isolated from other Fe ions [1, 2 ] .
V
This probability is P = (1 - x) , where v is the number of neighbour-ing sites, occupation of which would destroy the isolation of the original Fe ion; v depends on the range of the magnetic interactions.
Similarly, the probability for a certain Fe ion to occur in a specific type of Fe pair is:
w. P . = c .x(l - x)
p , l 1
where c. is the number of pairs of type i, which can be formed from a certain Fe ion, so Z c. - v; w. is the number of neighbouring sites, occupa-tion of which would destroy the isolaoccupa-tion of the Fe pair.
In CuFeS each Fe ion is surrounded by 4 nearest neighbour Fe ions, assigned as nn or In - P; each nn interaction path involves one intermediate S ion.
There are 24 next-nearest neighbour (nnn) Fe ions; each nnn interaction path involves two intermediate S ions and one intermediate cation. The nnn pairs can be divided into three types [3]:
4 pairs having 4 interaction paths (2n - P)
16 pairs having 2 interaction paths (3n - P) 4 " " 1 " " (4n - P)
The probabilities of the single Fe ions and the various Fe pairs in a CuM, Fe S„ system have been given in Table III.l.
1-x X 2
Table III.l. Statistics of single Fe ions and Fe pairs in CuM, Fe S„
'^ 1-x X 2 compounds
s
In-P 2n-P 3n-P 4n-P d^> aVl/2' a aV3/2 'a V ^
P (x)2> (l-x)^« 37 4x(l-x) 4x(l-x)'*° 16x(l-x) 47 4x(l-x) P (0.01) P (0.02) 0.7547 0.5680 0.0276 0.0379 0.0268 0.0357 0.1018 0.1289 0.0249 0.0310 Total 0.9358 0.8015 1 ) 2)d is the Fe-Fe distance assuming that c 2a.
P is the probability that a Fe ion is a single ion or a part of a certain type of pair.
The main features of the AgM, Fe 0„ structure are the same as in the 1-x x 2
chalcopyrite structure: 4 nn sites and 24 nnn sites.
However, there are 2 different kinds of nn pairs and 9 different kinds of nnn pairs.
If only the nn pairs and one kind of nnn pairs (2n - P) are taken into account, one gets the same statistics as would be obtained for only In- and 2n-interactions in CuM, Fe S„.
1-x X 2
T a b l e I I I . 2 . S t a t i s t i c s of s i n g l e Fe ions and Fe p a i r s in AgM, Fe 0„ compounds. S
m^P
ln''-P 2n -Pcl(X)^>
3.32 (3 3.36 (3 4.89 (4 33) 43) 88) P (X) (1-x)® 2x(l-x)-^^ ^ 2x(l-x)"^^ 13 4x(l-x) Total P (0.01) 0.9227 0.0355 0.0351 0.9933 P (0.02) 0.8508 0.0628 0.0615 0.9751 1)d is the Fe-Fe distance in NaFeO (real coordinates); the values between parentheses are from AgFeO (ideal coordinates).
III.3 MAGNETIC SUSCEPTIBILITY MEASUREMENTS
III. 3.1 Experimental procedure
The apparatus used for magnetic susceptibility measurements is a vibrating sample magnetometer (Princeton Applied Research Model 155). Liquid He was used as cooling agent for temperatures between 4.2 K and 100 K, liquid N was used from 80 K to 250 K.
The magnetization is calibrated accurately (error less than 1%) by means of a nickel sample which has a well-known magnetic moment.
The cryogenic temperature controller (PAR Model 152) is calibrated by means of a potassium chromium alum (KCr(S0,)-.12H 0) SEunple. This sample is
also used for the calibration of the magnetic field at 4.2 K. For both these calibrations, the Brillouin-type behaviour of the magnetization has to be taken into account.
Temperature errors range from 1% (at 4.2 K) to about 5% (at room temperature), while the magnetic field is accurate to 1%.
In order to correct properly for diamagnetic contributions, the susceptibilities of the empty sample holders and of some samples of the diamagnetic substance CuGaS- were measured at room temperature.
—fi
The diamagnetic susceptibility of CuGaS appeared to be -80(jf 5).10
-1 -6 -1 emu.mol . This value is close to the estimated value -96.10 emu.mol ,
obtained by addition of the estimated ionic diamagnetic contributions [4,5]. The error induced by the difference between these values can be at most 10%, i.e. at room temperature and x = 0.005.
—fi
For CuInS- the experimental diamagnetic susceptibility is -96.10
-1 -6 -1 emu.mol [15], whereas the estimated value amounts to -107.10 emu.mol For the other substances, the diamagnetic correction was calculated from the ionic diamagnetic contributions. In the AgM Fe 0 substances also the diamagnetic correction for metallic silver impurity was taken into account.
III. 3.2 CuGa, Fe S„
1-x X 2
In Fig. III.2 Xp 'T has been plotted versus T for some smaller values of X. The curve for x = 0.005 is close to the calculated curve for single ions, as expected. o E D E C u G a , _ ^ F e x S 2 X =0.005 x = 0.01 o — o — o o — o x =0.02 x=0.0A 50 100 150 200 - ^ T(K) 250
Fig. III. 2 Magnetic susceptibility per mole Fe vs. temperature for
different values of x; the broken line indicates the calculated single ion
susceptibility.
However, at higher Fe c o n c e n t r a t i o n s , the susceptibility is c o n s i d e r ably lower. This decrease can be attributed to the formation of a n t i f e r r o -magnetic (AF) p a i r s .
The susceptibility of single ions is calculated from Eq. (1) by taking g = 2.02 (this value is obtained from EPR [ 3 ] ) . At 4.2 K the product of the temperature and the susceptibility p e r mole of isolated Fe ions is x -T =
-1 ^ 3.87 emu.mol .K.
Using the values of the probabilities for single ions from Table III.l the following values are calculated for T = 4.2 K:
x = 0.08
- ^ T ( K )
Fig. III.3 Inverse magnetic susceptibility per mole Fe vs. temperature for
different values of x; the lines indicate the Curie-Weiss behaviour at
higher temperatures.
a t X = 0 . 0 1 : X -T = 0 . 7 5 4 7 X -T = 2 . 9 2 emu.mol .K
^Fe '^s _^
at X = 0.02 : X -T = 0.5680 X -T = 2.20 emu.mol .K.
^Fe ^s
The experimental values are 2.45 and 1.76 emu.mol .K respectively. So even if all nn and nnn pairs would be strongly antiferromagnetic, i.e. their contributions to the susceptibilities would be negligible, a total suscept-ibility is measured which is lower than expected.
From this it can be concluded that the relevant magnetic interactions are not confined to nn and nnn sites.
The inverse susceptibility is linearly dependent on temperature for X <_ 0.20, as can be seen from Fig. III.3 and Fig. III.4.
At higher x-values, the susceptibility tends to nearly temperature-in-dependent behaviour which has been found in bulk CuFeS- [4, 6 ] . For x <^ 0.20 the susceptibility can be described rather well by Eq. (6) with 6 ~ -X.700K.
The linear dependence of 9 on x has also been observed in other systems, e.g. Mg^_^Mn^S [1]. 1.0 3 E <» 0.5 CuFeSj -CuGa^.^Fex S2 • X = 0.2 o X = 0.3 D X = 0.5 ^ X = 0.6 50 100 150 200 - ^ T(K) 250
Fig. III.4 Inverse magnetic susceptibility per mole CuGa^_ Fe S„ vs. temperature for some higher values of x. The broken line represents the inverse susceptibility of CuFeS^ [5].
The maximum of the susceptibilities at 4.2 K is found at x = 0.005 (Fig. 111.5). Following the equivalent neighbour model, for x = 0.06 the
c number of relevant neighbour sites amounts to q = 42.
This number contains only the interactions which have an exchange -23
energy in the order of magnitude of kT : 5.8 x 10 Joule or higher. As has already been indicated, the number of relevant interactions at 4.2 K exceeds the number of nn -H nnn sites (v = 28) .
At 86 K the maximum of the susceptibilities is found at x = 0.30, which corresponds to q = 6. This refers only to those interactions which
-21
have exchange energies higher than or equal to 1.21 x 10 Joule. It can be concluded that the exchange energy of the 4 nn interactions has this order of magnitude, i.e. J.,/k » 100 K.
C u G a . , _ ^ F e , S 2
0.8
- 2
— — X1.0
- > XFig. 111.5 Magnetic sus'óeptibility vs. x for some different temperatures; points marked by x indicate values at 77 K from Ref. [4].
III. 3. 3 CuAl, Fe 5„ and Cuin, Fe 5„
1-x X 2 1-x x 2
The susceptibilities in the CuAl Fe S system contain a ferromagnetic contribution at lower temperatures (Fig. III.6). At higher temperatures these susceptibilities are nearly the same as in the CuGa, Fe S„ system.
^ •' 1-x X 2 ^
At 4.2 K the susceptibilities of Cuin, Fe S_ are similar to those of
1-X X 2 CuGa, Fe S„: 1-x X 2 at X = 0.01 : X .T = 2.32 emu.mol .K ^Fe at X = 0.02 : x .T = 1.61 emu.mol .K •^Fe il 2 — — CuIn,.^FexS2 CuAli.xFexS2 - - x = a o 2 — x = 0.0A 50 100 150 200 - ^ T ( K ) 250
Fig. III.6 Magnetic susceptibility per mole Fe vs. temperature in CuAl, Fe 5- and CuIn, Fe S„.
^ X
Fig. III. 7 Magnetic susceptibility of CuAl ^^^^2 '^"^ '^^^^ 1-x^^x^2 "^' ^
for liquid Helium temperature and room temperature.
At higher temperatures the CuIn Fe S system has susceptibilities which are a little higher than the corresponding susceptibilities in
CuAl, Fe S. and CuGa, Fe S„. The critical concentrations (from Fig. III.7)
1-x X 2 1-x X 2 V & /
X ~ 0.06 in CuIn, Fe S„ c 1-x X 2 X = 0.08 in CuAl, Fe S„ c 1-x X 2
These values are about the same as in CuGa, Fe S„. At higher 1-X X 2
temperatures the susceptibilities of all these systems can be described by Eq. (6) with 6 =•• -x.700 K.
The effective magnetic moment y „„ decreases as x increases, in contrast eff
to the system Mg '''"x^ where V^ff is independent on x.
(P)
A -^ s p i n - only m o m e n t of Fe(in)(=5.92 j3) • j CuGa^_xFexS2 ( • f r o m ref.[A]) mo ment of Fe in Cu Fe S2 (= 3.8 5 P) 0.05 0.10 0.15 0.20Fig. III.8 Effective moment of Fe (in Bohr magnetons) in CuM^_ Fe
5-systems as a function of x.
As appears from the experimental values, given in Fig. III.8, the value of CuFeS- (3.85 3) is reached at x ~ 0.2; all values lie between 6.0 3 and 3.85 3.
For CuGa, Fe S_ our values show a good agreement with the |j ^^-values
1-x X z eff
obtained by Digiuseppe et al. [4] from measurements up to 650 K.
Their 6 values agree reasonably well with the calculated values (from Eq. (6), between parentheses):
X = 0.025 : e = - 46 K (- 18 K) X = 0.10 : 9 = - 70 K (- /O K) X = 0.20 : 9 = -129 K (-140 K ) .
The low value of 9 at x = 0.025 as found by Digiuseppe could be due to an overestimation of the diamagnetic correction.
The y „„ values of CuAl, Fe S„ are nearly the same as those of eff 1-x X 2
CuGa Fe S-, whereas the values of CuIn Fe S- are significantly higher. -L~X X ^ J."~X X ^
The temperature at which y ^. is obtained (150-250 K) are much higher than
the Neel temperatures in these diluted systems (Section III.4).
A decrease of y „^ with increasing x is also observed by Teranishi et eff
al. for CuAl. Fe S„ [14]. However, their values of y „„ are larger, as the
1-x x 2 '^ ^ eff
susceptibilities were measured up to higher temperatures (700 K ) . Although Curie-Weiss behaviour is postulated at these temperatures, no 9 values are mentioned.
If no strong interactions (with respect to kT) would be present, y should remain about 5.9 3 throughout the whole series, as in Mg Mn S.
However, Fig. III.5 indicates that J../k is in the same order of magnitude as the temperatures of the measurements.
So in first approximation the differences between the y values in Fig. 111.8 and the y value of free Fe(III) may be attributed to the strong nn interactions.
If only these interactions are taken into account, the probability of 4
single ions would be P = (1 - x) . Then y would be reduced by a factor 2
( 1 - x ) ; this gives the -.-.-.- line in Fig. 111.8.
This model can describe the effective moment in CuIn, Fe S„ adequate-1-x X 2
ly, but it is too simple for CuGa, Fe S_ and CuAl, Fe S„. 1-x X 2 1-x X 2
III.3.4 AgM^_ Fe^O^ systems
The magnetic susceptibilities of the system AgAl Fe O are given in Fig. III.9.
As x increases, X shows a decrease which at higher temperatures is similar to the decrease in the CuM, Fe S„ systems.
1-x X 2 •'
At lower temperatures the decrease of x is less than in the CuM Fe S
1-x X 2
systems. At 4.2 K the experimental values are close to the values calculated from nn + nnn interactions (between parentheses) :
X = 0 . 0 0 5 X = 0 . 0 1 4 X = 0 . 0 2 0 X .T = 3 . 1 3 ( 3 . 3 6 ) emu.mol .K Xp^.T = 2 . 5 2 ( 2 . 6 1 ) Xpg.T = 2 . 2 4 ( 2 . 2 0 ) o E
i 3
A g A l , j^ F e ^ O -x=0.005 0.020 x = a 0 59 0.098 . x = ai97 _ ^ _ ^ . _ + — I - x = 0.395 50 100 150 200 - ^ TCK) 2 5 0Fig. III.9 Magnetic susceptibility per mole Fe vs. temperature in
^S^h-x''x°2-So the range of weaker interactions is a little smaller than in CuM, Fe S„. This can be related to the fact that in oxides the
delocaliza-1-x X 2
tion of magnetic moments is less than in sulfides.
As appears from Fig. 111.10 the magnetic susceptibilities of AgAl, Fe 0„ at 4.2 K show a maximum at x K 0.20.
1-x X 2 c According to the equivalent neighbour model this would give a number of relevant neighbouring sites: q = 12 [7].
-> X
Fig. III.10 Magnetic susceptibilities of AgM^_ Fe 0„
different temperatures.
•Jstems vs. x for
This value distinctly differs from the number of nn + nnn interactions, V = 28, giving a good description of the susceptibilities for low x values at 4.2 K.
This discrepancy could be caused by the presence of some bulk a-AgFeO-at higher x values, which would enhance the susceptibility and also x .
In the AgGa Fe 0 system this contamination was observed by X-ray diffraction at x = 0.3 and x = 0.4. It could explain the absence of any susceptibility maximum in AgGa Fe 0 (x <^ 0.4) at 4.2 K.
The susceptibilities of AgAl, Fe 0„ at higher temperatures can be 1-x X 2
described well by assuming a Curie-Weiss behaviour having 9 = - 240.x and an effective magnetic moment of Fe which decreases as x increases.
At lower x values, this decrease is almost the same as in the CuM Fe S systems (Fig. III. 11); at higher x values the decrease of y
X — X X ^ Gil
is smaller than in the CuGa, Fe S„ system. 1 - x X 2
CuGa^_^FexS2 s p i n - o n l y mo nn e n t of Fe(in)(=5.92 P)
Fig. III.11 Comparison of the effective moment of Fe as a function of x in AqAl, Fe 0- and CuGa, Fe S„.
As mentioned Ijefore, a-AgFeO was obtained from 3-NaFeO . Some suscept-ibility values of a-AgFeO are given by Hakvoort [9].
The short range ordering temperature of a-AgFeO„ appears to be T = 18 -H 1 K (Fig. III.12). The high temperature data show a Curie-Weiss behaviour having: 109 (-1- 4) K and C = 3.88 {+ 0.06) emu.mol .K, from which y = 5.57 (+ 0.04) 3-eff — 2.5 2.0 1.5 1.0 0.5 X X
'f\
-\ p
1 a - A g F e 0 2 (x f r o m Ref .[9] )"
x
^
^
^
^
^
^
^
^
^
^
50
100
- >
T(K)
150
200
250
Fig. III. 12 Magnetic susceptibility of a.-AgFeO as a function of temperature.
III.4 MÖSSBAUER SPECTROSCOPY
It was impossible to determine the Neel temperatures of our systems from the magnetic susceptibility measurements. Only for CuFeS T has been
£> N
determined from susceptibility measurements on single crystals [6]. An alternative way to determine T is Mössbauer spectroscopy, which has been applied by Digiuseppe et al. [4] on the system CuGa Fe S for 0 . 5 < x £ 1 . 0 .
In order to make a complete T vs. x plot of this system, we have performed Mössbauer measurements for lower x values. The results are given in Fig. III.13, together with the literature data.
T N ( K ) A 8 0 0
600
AOO-200
C u G a ^ _ x F e ^ S 2 X/
/
/
/
/
/
— -V L T 0.2 Xf- = 0.06O.A
0.6 — > X0.8
1.0
Fig. III.13 neel temperature vs. x in CuGa^_ Fe S^: x from Ref. [4], and from Ref. [6].
As X increases, T„ shows a drastic increase at x = 0.4. A similar increase N
of T from x = 0 . 4 t o x = 0 . 5 i s also reported for Mg, Mn S [1] and
N 1-x X '^ '
(Mg Fe ) SiO [10], though the effect in these systems is much less than in our system.
From Fig. III.14 it appears that T is below 4.2 K for x = 0.3. The spectrum shows a small electric quadrupole splitting 2e = 0.21 (jf 0.05) mm/ sec, in accordance with the 2e value for Fe(III) in samples having very low Fe concentrations [ll]. Comparison with the spectra of these very diluted
.o
<
0 *i, +8
^ Velocity ( m m / s e c ) • 12
Fig. III. 14 Mössbauer spectra of CuGa^_ Fe S^ at 4.2 K: x = 0.1 (a), x-0.2 (b), X = 0.3 (c) and x = 0.4 (d).
Table 111.3. Mössbauer parameters of CuGa, Fe S„ at some different 1-x X 2 temperatures. X 0.002 0.10 0.20 0.30 0.40 0.5 to 1.0 1.0 1.0 T (K) 295 77 4.2 77 4.2 77 4.2 77 4.2 77 4.2 295 295 77 295
(
^
(mm/sec) 0.60** 0.67** 0.66** 0.63 0.64 0.69 0.61 0.65 0.64 0.59 0.64 0.44 0.49 0.63 0.50** 2£ (mm/sec) 0.25 0.23 0.26 0.25 0.21 0.19 0.13 <0.11—
-0.02 -0.03 0.00 H (kOe)—
270—
310—
345 370* 356 368 353 Ref. [11] this work this work this work this work[4]
[12] [13]H v a l u e , obtained from a large number of temperature-dependent M ö s s b a u e r m e a s u r e m e n t s .
57
*Corrected v a l u e s . As source w e used Co-Rh; all isomer shifts are given here w i t h respect to N a Fe(CN) N0.2H 0 (N.B.S. Standard Reference Material No.,. 725) . T h e errors of isomer shifts (6) and quadrupole splittings ( 2 E ) amount to 0.05 mm/sec or less. T h e errors of the hyperfine fields (H) are less than 5 k O e .
samples shows that our samples do not contain a detectable amount of di-valent iron.
The spectra for x = 0.2, x = 0.3 and x = 0.4 show a six-line hyperfine spectrum caused by the antiferromagnetic ordering. The linewidths are much larger than those of the hyperfine spectrum in CuFeS„. This is expected, as for these diluted compounds the spectrum is a superposition of spectra arising from many different clusters.
In these samples T., >> 4.2 K, so at 4.2 K the internal magnetic field N
(H) is about equal to its saturation value (H ^ ) . H increases as x in -sat
creases; even at x = 0.4 H is lower than in CuFeS-.
From the data in Table III.3 it appears that the isomer shift is only slightly temperature dependent and not dependent on x.
The data on the electric quadrupole splitting show a gradual decrease as X increases. Apparently, as the iron content increases, the small distor-tion of the FeS tetrahedron in CuGaS : Fe decreases gradually to zero.
CHAPTER IV
EPR SPECTROSCOPY
IV.1 INTRODUCTION
Electron paramagnetic resonance (EPR) can give useful information about the electronic groundstate of paramagnetic ions. In this work EPR
spectroscopy is applied on the study of magnetic interactions between Fe(III) ions.
If a magnetic field (H) is applied on a paramagnetic ion with total electron spin S, the degeneracy of the 2S -(- 1 energy levels is removed. Their (Zeeman) energies are g3m H, where m ranges from -S to +S with unit intervals.
Transitions between the successive energy levels takes place if the magnetic field fulfils the condition: g3H = hv, where V is the radiation frequency (in the microwave range).
Generally transitions are observed at different magnetic fields by the presence of spin-orbit interactions, crystal fields and interactions with nuclear spins.
The energy levels of the ground manifold of a Fe(III) ion in an orthor-hombic crystal field can be described by the following spin Hamiltonian:
ff=3.H.i.S-.A°0°.A^\^.A°0°^A^0j.A>J (1)
where the first term is the general Zeeman term. The other terms are zero-field splitting terms, arising from the crystal zero-field, spin-orbit inter-actions and spin-spin interinter-actions in a complex way.
0
The spin operators 0', which are functions of the spin operator S, have been tabulated elsewhere [l, 2 ] . The values of the coefficients A depend on the surroundings of the paramagnetic ion.
Instead of the spin operators 0', irreducible spherical tensor operators T can be used [3]. The terms A^O^ in Eq. (1) are replaced by the following terms:
B^ [T^ + T^ ^. a q ^ 0,
B*" T'' if q = O.
1 q
k q The coefficients B are simply converted to A^" from the transformation
equa-q , k tions of O** [1, 2] and T [3].
k <J
If the crystal field is tetragonal, Eq. (1) is reduced to the following expression:
- - - 2 2 4 4 4 4 4
H = 3.H.g.S -H B T + B T ^- B F T , -^ T 1 (2)
^ o o o o 4'-4 -4-' This can also be written in the alternative form:
H = 3.H.i.S + DS^ -I- (a/6)[s'* -H S -f s"*] -H (7/36) F[s'*-(95/14)S^] (3)
z x y z z z where: D = V^.B^ o a = 48 B^ (4) F = 1801/2/35' B - 72 B o 4
The eigenvalues of the Hamiltonian can be calculated as functions of the magnetic field and from these eigenvalues the resonance fields are calculated.
As the direction of the magnetic field is changed with respect to the crystallographic axes, the resonance fields shift. A plot of the different resonance fields vs. the orientation angle can be obtained from EPR spectra of single crystals at many different orientations.
In a powder, all orientations contribute to the EPR spectrum. So a summation of many EPR spectra has to be performed in order to get a good simulation of the experimental EPR powder spectrum. A satisfactory simula-tion method is provided by Van Veen [3, 4 ] .
When a small fraction of Fe(III) is incorporated into a diamagnetic host lattice, only a spectrum from single Fe ions is observed.
At higher Fe concentrations (x > 0.005) spectra from small Fe clusters become important.
Spectra from Fe pairs are observed in single crystals of CuAlS :Fe and CuGaS- : Fe [3]. At even higher Fe concentrations (x > 0.05) both single ion and pair spectra are replaced by an isotropic spectrum situated near g = 2 which is caused by higher Fe clusters.
The concentration dependences of the various EPR spectra give useful information about the range of the magnetic interactions.
The relative intensity should be proportional to the concentration of the species (single ion, pair or higher cluster).
Assuming random distribution of Fe(III) ions the intensity is propor-tional to X and the corresponding probability P given in Section II 1.2:
I '\' x.P = x(l - x)™ -> I /x = a(l - x ) " (5) s s s
2 n 2 n
I % x.P % X (1 - X) ->• I /x = b(l - X) (6)
P P P
where I is the intensity of a single ion transition, I is the intensity
s p of a pair transition and a, b are proportionality constants.
The exponents m and n have a meaning which is different from their analogues v and w in section III.2.
m refers to all interactions which would spoil the single ion spectrum, -24
i.e. the interactions having J > hv = 6.0 x 10 Joule. On the other hand, -23
at 4.2 K V refers to the interactions having J > 5.8 x 10 Joule (i.e. kT). So it can be expected that m > v and - in the same way - n > w.
Let z be the number of intermediate anions just allowing an interaction of the appropriate magnitude. Then in the ideal chalcopyrite structure
(c /a = 2) m represents the number of trivalent cation sites within a sphere having the radius r = z.a / / 2 :
3 3 3
m :; (4/3).7T.r .2/a = (27r /2/3) z (7) In the same way n is approximately the number of trivalent cation sites
within two interpenetrating spheres:
3 2 3
n X (4/3.TT.r [1 -^ (r /4r)(3 - (r /2r) )] 2/a (8)
o o o
where r is the distance between the two Fe ions. From Eq. (7) and (8) and the condition: 0 < r < r, it can be derived that:
1.00 < n/m < 1.69 (9)
This will be compared with the experimental n/m-value obtained from EPR intensities in CuGa_ Fe S single crystals (next Section). Sections IV.3 and IV.4 describe results from EPR in polycrystalline samples. Finally, Section IV.5 concerns the interpretation of single Fe ion spectra in powders of AgAlO : Fe and AgGaO : Fe.
IV.2 SINGLE CRYSTAL SPECTRA
A series of CuGa, Fe S„ single crystals was made as described in 1-x X 2
Section II.3.
At lower x-values (x < 0.02) the EPR spectrum consists mainly of the single Fe(III) ion spectrum, as described by Van Veen [3].
The angular dependence of this spectrum is presented in Fig. IV.1. This 9 vs. H plot is obtained by mounting a single crystal on a quartz tube so that it can be rotated arounds its [llO] axis.
As the magnetic field direction is perpendicular to the rotation axis, it can move from [001] to [110].
2 4 4
The EPR parameters (g , gi, B , B and B ) obtained from these spectra show good agreement with those reported earlier [3, 5 ] .
Some single crystal spectra having H// [110] are presented in Fig. IV.2. Strong single ion absorptions are observed at 0.45, 1.25 and 3.0 kGauss.
[OOl] 0
A 5 6 7 - magnetic field (l< Gauss)
Fig. IV. 1 Angular dependence .pf the X-band EPR spectrum of isolated Fe ions in CuGaS2.
2 3 - ^ magnetic field Ck Gauss)
Fig. IV.2 EPR spectra of some CuGa^_ Fe S„ single crystals: a) x = 0.005, b) X = 0.01, o) X = 0.02. The magnetic field is parallel to [110]. The range between 1.4 and 2.8 kGauss was amplified lOx with respect to the other parts of the spectrum.
The weak absorptions in the range between 1.4 and 2.8 kGauss were attributed tentatively to Fe pairs by Van Veen [3]. The angular dependence of these resonances is similar in shape to that of the Fe pair spectrum in CuAlS : Fe; the magnitude is larger in CuGaS- : Fe, in accordance with the larger single ion zero field splitting in CuGaS„ : Fe.
The intensity ratios between the weak lines and the single ion lines -1 -2
have an order of magnitude (10 to 10 ) which can be expected if the weak lines are attributed to pairs.
The relative intensities of the different lines can be calculated from their linewidths and heights (see Section V.1).
In Fig. IV.3 I /x and I /x are plotted versus log (1-x). According to s p
Eq. (5) and (6) these plots should be linear. The deviation from linearity at higher x values (x > 0.08) is also observed in powders (Section IV.3).
According to Eq. (5) and (6) and the relation b = 4a which holds for In and 2n pairs, the following relation would be obtained at x = 0:
log (10 I /x ) - log (I /x) = log 10 + log 4 = 1.60. p s
The experimental value is 2.3.
01,
og (1-x)
Fig. IV. 3 Relative EPR intensities of isolated Fe ions (I^) and Fe pairs (I ) in CuGa,_ Fe 5„ si
p 1 X X <^
arise from errors in x.
(I^) in CuGa, Fe S^ single crystals as a function of x; indicated errors
The difference between these values can be due to the difference between the transition probabilities and the difference between the thermal populations.
From m = 290 and Eq. (7) it can be derived that the relevant inter-actions extend over at most 5 intermediate S ions.
The experimental ratio n/m K 410/290 = 1.41 lies within the range pre-dicted by Eq. (9).
At X = 0.02 (Fig. IV.2c) a broad absorption near g = 2 (H = 3.2 kGauss) can clearly be observed. Its intensity increases about linearly as a function of X, as shown in Fig. IV.4.
From this concentration dependence of the intensity it can be concluded that this g = 2 band arises from higher Fe clusters.
At X = 0.06 its intensity is already much stronger than the single ion transitions. The strong intensity and large linewidth cause the pair lines
rel. int.
0.02 OM
->x
0.06
Fig. IV.4 Relative EPR intensity of the g = 2 band in CuGa, Fe S„ sinale
1-x X 2
2.10
2.08
2.06
2.0A
-2.02
g
Fig. IV. è Angular dependence of the linewidth (W) and g value of the g = 2 band in a single crystal of CuGa^ qa^^n nR^P'
to be obscured at x >^ 0.04.
Under rotation of the magnetic field from [001] to [110], the intensity of the broad resonance remains constant within the experimental error (about 10%) .
The linewidth W and the g value however show a considerable angular dependence, as shown in Fig. IV.5. The linewidth at H// [001] is 1.63 kGauss, which is nearly the double of the linewidth at H// [110], 0.86 kGauss.
This reminds to the fact that the total spectrum-width of a para-magnetic ion with a small zero-field splitting shows the same behaviour.
So presumably some zero-field splitting is still present in the g = 2 band. This problem will be discussed theoretically in Chapter VI.
IV.3 POWDER SPECTRA OF SINGLE IONS
IV. 3.1. CuGa, Fe 5„
1-x X 2
At low Fe concentrations (x < 0.01) the EPR spectrum of a CuGa, Fe S„ — 1-x X 2 powder consists mainly of the powder spectrum of isolated Fe ions.
This spectrum can be calculated from the single crystal EPR parameters by means of a computer program, written by Van Veen [3, 4 ] . The calculated spectrum agrees fairly well with the experimental spectrum (Fig. V.2).
Fig. IV.6 shows the low-field part of this spectrum at several x-values. As in the single crystals, the single ion spectrum intensity decreases rapidly as x increases. A g = 2 band dominates the spectrum at x ^ 0.02.
-> magnetic field (kGauss)
Fig. IV. 6 EPR powder spectra of CuGa, Fe S„ at different values of x.
The relative intensities of two single ion transitions were calculated from their heights and half-amplitude linewidths. In Fig, IV.7 the relative intensities have been plotted in the same way as in Fig. IV.3.
From this plot m ~- 140; this value is much lower than in single crystals: m ^ 290. The corresponding maximum numbers of intermediate anions are z = 3.6 and z = 4.6, respectively. The reason of this difference is not clear.
CuGa^.^Fe^Sj
>-10-' logd-x)
Fig. IV.7 Relative EPR intensity from isolated Fe ions (I ) in CuGa, Fe S„
" S 1—X X ci
powders as a function of x. Line 1 and 2 refer to the transitions-shovM.in Fig. IV. 6.
The crystallite size of powders is larger than 500 A - from X-ray dif-fraction linewidths - while m = 290 would correspond to a maximum distance of 35 A. So the limited crystallite size cannot cause the difference between the m values in single crystals and powders.
IV. 3.2. Other systems
In the same way as for the system CuGa, Fe S„, the relative EPR
•' 1-x X 2 '
intensities of isolated Fe ions in the other systems under investigation were measured. The results are given in Fig. IV.8.
logcVx)
A \ . ° ^ Z n ( A l i _ , C r , ) 2 0 ^\
""es.
:25 ^ " l - x C o x R f i 2 ° 4 ^ V " ^ ^ • ^ ^\
1 _m=lA5 Zn(Ga^_x Crx)2 0^ A g G a i _ ^ F e x 0 2 ^Ag^Al,_,Fe^02 """ - o CuAl,_xFexS2 0.02 QO^ 0.06 008 010 - l o g { l - x ) > 0.12Fig. IV.8 Relative EPR intensity of isolated Fe ions (I ) as a function of X in powders of Culn,_ Fe S^, CuAl, Fe S„, AgAl^_ Fe 0^, AgGa, Fe 0„ (this work), Zn^_^Co^Rh^O^ [6], Zn(Al^_^Cr^)^0^ [7] and Zn(Ga^_^Cr^)^0^ [8].
Some recent results in literature for oxyspinel systems, in which Co(II) or Cr(III) is the paramagnetic component [6, 7, 8 ] , have been analysed in the same way. It turns out, that in these spinel systems, m is about 50, both for tetrahedral Co(II) and octahedral Cr(III).
In the AgM, Fe 0_ systems the m values also are rather low. In 1-x X 2 •'
CuIn, Fe S„ however, m ~ 145 which is about the same as in CuGa, Fe S„. 1-x X 2 1-x X 2 The low m value of CuAl, Fe S„ is not very reliable, due to the
consider-1-x X 2
able deviation from linearity in Fig. IV.8 at x >^ 0.04.
This deviation at higher concentrations of paramagnetic ions seems to be a general phenomenon (see also Fig. IV.3 and Fig. IV.7), which could be caused by non-random clustering.
IV.4 POWDER SPECTRA OF CLUSTERS
As in the CuGa Fe S single crystals a g = 2 band is observed in
1—X X ^
powders of CuM, Fe S and AgM Fe 0 .
i—X X ^ 1~X X ^
It is also observed in many other oxide systems, e.g.: Zn Co Rh 0 [6], Zn(Al^_^Cr^)20, [7], Zn(Ga^_^Cr^)204 [8], Y-(Al,_^Fe^)203 [9],
Mg Mn 0 [10] and 3-NaAl Fe 0 [11].
l^X X 1—X X ^
In all these systems the g = 2 band is attributed to small clusters of paramagnetic ions.
In this Section the system CuGa, Fe S„ is studied more in detail. 1-x X 2
Table IV. 1 gives the relative intensities, g-values and linewidths of this system at room temperature.
The g value is nearly independent of x. Particularly in X-band spectra the linewidth shows some variation as x increases, which could be due to dipolar broadening and exchange narrowing effects. The origin of the line-width will be discussed theoretically in Chapter VI.
As in the single crystals, the intensity increases about linearly as a function of x at lower x values. A plot of the intensity vs. x for some systems (Fig. IV.9) shows that this linearity holds up to x = 0.2 or 0.3. At higher x values the intensity falls down rapidly.
In CuGa, Fe S„ T„ ~ 300 K at x ~ 0.45 (from Fig. III. 13). So in this 1-x X 2 N ^ B / system the g = 2 signal intensity falls down as soon as the Fe clusters become nearly infinite. In an ordered system, hardly any g = 2 signal can be seen.
Additional information about the character of the g = 2 band can be 4 9
obtained from its temperature dependence (Fig. IV.10). The intensity I as a function of temperature shows a paramagnetic behaviour - i.e. I.T is temperature-independent - at T > 150 K. As the temperature decreases below 150 K some decrease of I.T can be observed. These experimental results will be discussed in Chapters VI and VII.
Fig. IV.9 Relative EPR intensity of the g = 2 band as a function of x in some systems: CuAl, Fe S„, CuGa, Fe S„ and AgGa,_ Fe 0 .
Fig. IV.10 Relative intensity (I) and linewidth (W, in kGauss) of the EPR g = 2 band in a CuGa„ n^Sn -r^p powder sample as a function of temperature.
I.T
100
150 200
> T(K)
250
Table IV.1. Relative intensity I, linewidth W (in Gauss) and g value of the EPR g = 2 band in the system CuGa Fe S .
X 0.010 0.020 0.040 0.060 0.080 0.100 0.197 0.299 0.396 0.498 g (Q-band) 2.031 2.036 2.041 2.040 2.038 2.036 2.033 2.031 2.031 2.033 I (X-band) 13 69 270 306 550 600 860 1200 710 45 W (X-band) 620 880 920 840 820 700 565 495 540 600 (Q-band) 525 600 660 680 700 625 525 490 540 650 51
