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Mixed valence state of Sm1−xGdxS studied by lattice parameter, LIII edge and extended X-ray absorption fine structure measurements
Journal
of the Less-Common Metals,
94 (1983) 177-186
MIXED VALENCE STATE OF Sm,_@d,S PARAMETER, L,,, EDGE AND EXTENDED FINE STRUCTURE MEASUREMENTS*
STUDIED BY LATTICE X-RAY ABSORPTION
C. GODARTand J. C. ACHARD Laboratoire de Chimie Metallurgique des Terres Rares, Equipe de Recherche du CNRS 209, I place A. Briand, F92190 Meudon (France) G. KRILL and M. F. RAVET-KRILL Laboratoire de Magnktisme et de Structure Electronique des Solides, Universite’ L. Pasteur, 4 rue B. Pascal, F67070Strasbourg(France)and Laboratoirepour l’lltilisation du Rayonnement Electromagne’tique, Universite de Paris Sud, F91&5 Orsay (France) (Received March 3,1983)
Summary Studies of the transition from black semiconductor (B) to gold metal (M) in Sm, _,Gd,S (x = 0.14, 0.18) were performed on both sides of the critical concentration (5, z 0.16). Measurements of the lattice parameter uersus the temperature (12-300 K) for Sm,.,, Gd,,,,S showed that the limits of the temperature region in which the M and B phases coexisted depended on the direction of the temperature cycles but not on the number of cycles (up to three). L,,, absorption edge measurements were used to determine the valence state of samarium at temperatures in the range 20300 K. The extended X-ray absorption fine structure (EXAFS) spectra are very different for the two compounds. The EXAFS data for the first nearest-neighbour sulphur atoms of each samarium ion can be fitted to one mean distance and an [Sm2+]/[Sm3’] ratio which corresponds to the valence deduced from the L,,, edge and two energy thresholds. This distance changes as the lattice collapses at the B -+ M transition, To fit the data for the sample with x = 0.14 some disorder effects must be added in the high temperature phase.
1. Introduction It is well known that SmS undergoes a transition from a black semiconducting state (B) to a gold metallic state (M) at 300 K and a pressure of 6.5 kbar. This transition can be induced at 300K without applying external
* Paper presented at the Sixteenth Rare Earth Research Conference, Tallahassee, FL, U.S.A., April M-21,1983.
0022~5088/83/$3.00
The Florida State University,
Q Elsevier Sequoia/Printed
in The Netherlands
178
pressure by using the chemical pressure produced in the lattice when trivalent rare earth ions of a smaller size are substituted for samarium. When gadolini~ is used as the substituent the critical concentration x, is about 0.16. The correlation between the ionic radius of a rare earth (RE) ion and the average occupation of the 4f level has often been used to determine the valence [l J. However, many assumptions are included in this determination, so we have used lattice parameter measurements to define the temperature range in which two phases (of the same crystallographic stru~t~e) coexist when 1: is slightly higher than xc. The L,,, edge of the X-ray absorption spectra of RE compounds shows a peak at threshold. This “white line” in RE compounds of configuration (4f)” is shifted towards higher energy by about 8eV relative to that of RE compounds of configuration (4f)“+‘. For intermediate valence compounds the valence can be derived by fitting the double-hop structure of the experimental peak with a weighted superposition of the two white lines. This was done to determine the valence change uersus temperature and hence the atomic ratio [Sm2+]/[Sm3+]. In mixed valence RE compounds the rate of the valence fluctuation depends on the f-d hybridization energy which is generally believed to be small {about lo-l3 s). As extended X-ray absorption fine structure (EXAFS) measurements can detect changes taking place in about lo- l6 s, this technique enables the instantaneous atomic configuration surrounding an RE ion to be studied. The EXAFS spectra measured between 20 and 300 K on Sm, _,Gd,S with x = 0.14 and x = 0.18 are different, indicating that the distribution of atoms neighbouring each samarium ion changes when the gadolinium concentration is increased slightly above the critical concentration.
2. Experimental
details
2.1. SampEes Single crystals of Sm, -,Gd,S were grown as described in ref. 2 and were manipulated in an argon filled glove-box. The samples were crushed and sifted through a 32 pm screen. They were not annealed. 2.2. Lattice parameter measurements The lattice parameter of the powdered sample was measured as a function of temperature using a Siemens goniometer. The temperature stability was 0.1 K in the range 10300 K. Cr Kcr, radiation was used together with a diamond powder internal standard. To ensure good accuracy for the lattice parameter measurements we performed them at large Bragg angles: the (400) and (331) reflections were used for the M phase and the (331) reflection was used for the B phase. This yielded an accuracy of better than 5 0.001 A. 2.3. LIII edge and extended X-ray absorption fine structure measurements The powdered samples were spread on Scotch tape and supported on a window of dimensions 40 mm x 5 mm cut in an aluminium plate. The average
179
mass of the sample in this configuration was approximately constant (about 5 mg cm -2 which corresponded to a mean thickness of 6 urn per layer). The sample thickness was varied by stacking layers of this type. The absorption experiments were carried out on the DC1 storage ring at Orsay (Laboratoire pour 1’Utilisation du Rayonnement Electromagnetique). We measured the logarithm of the ratio I,/Iof the intensity of the incident beam to the intensity of the transmitted beam. log(l,,/l) was measured as a function of energy over an interval of 100 eV on each side of the energy of the L,,, edge of the samarium ion. The curves were normalized by setting the difference between the values of log&/l) about 30eV before and 70eV after the L,,, discontinuity (which occurs at about 6710eV) equal to unity. Accurate correction of the variation in the background with energy was neglected because this variation, which is about 8eV between the two peaks, is very small relative to the difference in the heights of the two peaks. In the cases studied the error in the estimated valence was less than 1%. The EXAFS spectra were measured in the energy range 6400-7050 eV. They showed some discontinuity at about 350 eV above the threshold of the samarium ion which prevented investigation of the Fourier transform at higher energies. This discontinuity may be due to an imperfection in the Si(220) channel-cut crystal used. Therefore only information about the first-nearest neighbours (sulphur shell) of each samarium ion was obtained. 3. Results 3.1. Lattice parameter measurements At 300 K the lattice parameters of Sm, _,Gd,S with x = 0.14 and x = 0.18 are 5.87 A and 5.68 A respectively, from which we deduced values of 2.1, and 2.7, for the valence of samarium assuming that the system Sm,_.Gd,S obeys Vegard’s law and that the ionic radius of the samarium ion varies linearly with the occupation number of the 4f level. These lattice parameter values are in good agreement with these reported by Jayaraman et al. [S]. The M + B transition at low temperature only occurs when the gadolinium concentration is slightly higher than x, [S], so we measured the dependence of the lattice parameter on temperature for the 3c= 0.18 sample only. The results of these measurements for three cycles 300 K-12 K-300 K are shown in Fig. 1. As the temperature decreases the lattice parameter of the M phase slowly decreases to 5.67 A and then increases. At 140 K the B phase, which has the same rock salt structure, appears with a lattice parameter of 5.82 A corresponding to an estimated valence of 2.2 for the samarium ion. The two phases coexist down to 60 K. At lower temperatures only the B phase is present with a constant value of the lattice parameter. As the temperature of the B phase is increased the M phase appears at 110 K. The two phases coexist from 110to 250K, and then only the M phase is present. The temperatures of the transitions and the values of the lattice parameters were reproducible throughout three temperature cycles. The results of Jayaraman et al. [S]for 3c= 0.17 (above x,) are also shown in l&g. 1. Their results are similar to those reported here. With decreasing
180
temperature there is a weak decrease in the lattice parameter below 300K followed by an increase. The limits of the domain in which M and B phases coexist are about the same and the change Aa in the lattice parameter at the B c) M transition is about 0.12 A compared with Aa z 0.15 A in our sample. 3.2. L,,, spectra L,,, edge measurements were performed for samples with x = 0.14 and 3c= 0.18 for decreasing and increasing temperatures in the range 20-300 K. The spectra of the sample with x = 0.14 at 220 K and the sample with x = 0.18 at 160 and 77 K are plotted in Fig. 2. Calculations were performed (Fig. 2, dotted curve)
64
: .
i
.“’ ,
5.85.
,.. :. ‘,,
... .. ... ,~,:.:;....
,,,.,..............-
r ........
‘?
-
.
5.80-
2
04
5
5.15.
5.70 -
100
200
~
300
6680
Fig. 1. Lattice parameter ofSm,,s, Gd,,,sS us. temperature: A, increasing temperature (this work); 0,17x Gd [a].
E(eV)
0780
I, decreasing temperature (this work);
Fig. 2. L,,, absorption edge of (a) Sm,,,, Gd,,,,S (220 K; u z 2.32), (b) Sm,.,,Gd,,,,S (160 K; u x 2.56) and(c) SmO,szGdO.,sS (77 K; LJz 2.32) energy: 0, 0, A, experimental data; ..., calculated data.
181
to estimate the valence from the best visual fits of the two humps using In(+)
= v[Axexp{
-(EP~~‘)2)+arctan(E~~~1)]+ (E--Ecl.2)2
r
} + arctan( “;:,‘)1
where u is the fractional part of the valence, A is the amplitude of the white line relative to the normalized discontinuity of the edge and E,,, and E,,, are the energies of the two peaks such that AE = E,,, -E,,, = 7.3 kO.1 eV. The inverse tangent term corresponds to the discontinuity of the L,,, edge [4] with the density of final states assumed to be constant and the exponential term corresponds to the lorentzian width of the white line. There is a significant difference in the shapes of the L,,, edges for the two samples at 300 K which corresponds to a valence change from 2.32 for x = 0.14 to 2.58 for x = 0.18. The valence of the sample with x = 0.14 does not change between 25 and 300 K. The valence of the sample with x = 0.18 is unchanged between 300 and 150 K (or changes by -0.02); at 85 K it decreases to 2.41 and at 77 K it is 2.32. It then remains constant down to 25 K. This knowledge of the dependence of valence on temperature is useful in determining the number of Sm2 + or Sm3 + ions which is required for the EXAFS calculations. 3.3. Extended X-ray absorption fine structure measurements EXAFS measurements were performed on the x = 0.14 sample at 25 and 300 K and on the x = 0.18 sample at 300,160,77 and 25 K. The EXAFS spectra of the 3t = 0.14 sample at 25 K (B phase) and of the x = 0.18 sample at 77 K (B phase) and 160 K (M phase) are shown in Fig. 3. The two spectra in the B phase are qualitatively identical. Some frequencies in the Kronig oscillations (at about 6740 and 6780 eV) in the spectra of the M phase disappear. The Fourier-filtered EXAFS spectrum associated with the first sulphur shell (each samarium ion is surrounded by six sulphur atoms) is approximately reproduced using the EXAFS formula [5]
X(k) = k-1C~lf,(n,k),eXp(-oik2)eXp I
X
r-$$I
X
Sin[BkRi +262(12) + arg(fi(x, lz))]
atoms where K = h-‘{2m(EE,J)-‘, Ni is the number of nearest-neighbour located at a radial distance Ri from the ion, exp( - olz’) is an attenuation factor analogous to the DebyeWaller factor, exp{ -2R@(k)} accounts for the inelastic losses, a,@) is the phase shift of the central atom, fi and arg{fi(7c, k)} are the backscattering amplitude and the back-scattered phase shift respectively, and E, is the threshold energy.
182
(a)
(b)
Fig. 3. EXAFS spectra of (a) Sm,,,,Gd,,,,S (160 K) us. energy in the M and B phases.
(25 K), (b) Sm,,s,Gd,,,,S
(77 K) and (c) Sm,,,,Gd,.,,S
The partial EXAFS spectrum in the low temperature range obtained by back transforming the first peak of the Fourier transform of K3a in iz space are shown in Fig. 4. The data for the high temperature range are shown in Fig. 5. Four different hypotheses were tested for the results at 25 K. In the first case two different distances d1 and dz, which were chosen to be d1 w ~(uSm2+S) and d 2 * th,,~+s), an d one threshold were assumed. In the second hypothesis the same two distances were used with two thresholds (one for Sm2 ‘S denoted 6 = 0 eV and one for Sm3 +S denoted S = 7.5 eV). It was not possible to fit the data using two distances and small changes in d, and dz did not improve the fit. In the third run we used one distance d =: a/Z and one threshold. Figure 4(a) shows that the fit is roughly correct for the sample with x = 0.14. In the fourth hypothesis we used one distance d x a/2 and two thresholds, and Fig. 4(b) shows that the best fit for the x = 0.14 sample is obtained if the ratio of the number of atoms at each threshold corresponding to a valence of 2.33 is used. The same procedure (one distance and two thresholds) gave a slightly better fit to the EXAFS data of the two samples at various temperatures than that obtained using one distance and one threshold. The mean Sm-S distances of 2.95 A for the x = 0.14 sample and 2.88 A for the x = 0.18 sample (Fig. 4(c)) are in agreement (with an accuracy to +0.03 A) with
_. 1 : .
j
t
d
184
0.60&01
-E.S0E-a1
64
-%.SBE-81
0.80
I
SE.00
I
180.08
ON
I
158.00
I
280.08
I
250.00
I 300.88
356.80
ECN> e.25c-0%
-e.zsz-a1
(4
X(E)
B B5
1
58.88
t 1k3a.00
I 168.88
/
286.08
, 258.80
I 300.80
350.0%
ECN>
Fig. 5. EXAFS data for the sulphur atoms neighbouring the samarium ions in the high temperature range: (a) Sm,,s,GdO.lsS (160K; R = 2.83A; 2.4 atoms at 6 = OeV and 3.6 atoms at 7.5 eV); (b) Sm,,,,Gd,.,,S (3OOK; R = 2.83A; two atoms at 6 = OeV and four atoms at 6 = 7.5eV); (c) Sm,,,,Gd,,,,S (300 K; R = 2.94 A; four atoms at 6 = 0 eV and two atoms at d = 7.5 eV; u = 0.19).
185
the expected value for the x = 0.14 sample and the measured value for the x = 0.18 sample. The same values were measured for the x = 0.18 sample at 77 K (Fig. 4(d)) as were used at 25 K. The mean Sm-S distance for the x = 0.18 sample at 160 K is 2.83 A which corresponds to the lattice parameter of the M phase and a good fit is obtained (Fig. 5(a)) using two thresholds. The number of Sm2+ and Sm3+ ions used corresponds to a valence of 2.60 which is very close to the value of 2.56 deduced from the L,,, measurements. The same distance gives a relatively good fit for the x = 0.18 sample at 300 K (Fig. 5(b)) provided that an integral number of atoms is used (in this case the valence is 2.66 compared with the measured value of 2.58). The fit is improved if a non-integral number of atoms is used such that the valence is closer to 2.58. A relatively good fit is obtained for the x = 0.14 sample at 300 K (Fig. 5(c)) if a disorder effect is taken into account by including a disorder parameter rr = 0.19 (in the preceding cases G = 0).
4. Conclusion We studied two samples from the Sm,_,Gd,S system with gadolinium concentrations near the critical value. Lattice parameter measurements on the x = 0.18 sample showed the existence of either one or two phases depending on the temperature range, in agreement with the results reported in ref. 3. Our results revealed that the proportions of the two phases present differ depending on whether the temperature was increased or decreased. This appeared to be an intrinsic property of the powdered sample since it did not change with temperature cycling. L,,i absorption edge measurements showed that the valence of the x = 0.14 sample had the same value (2.32) throughout the temperature range 25-300 K. The valence of the x = 0.18 sample decreased from 2.58 at 150 K to 2.3, at 7’7 K. In pure phases (temperatures above 150 K or below 77 K) the valence remained constant. The experimental values of the lattice parameter can be used to fit the EXAFS data for the contribution of the first-nearest-neighbour shell (six sulphur atoms) with only one Sm-S distance. Similar results have been reported previously for Sm, _,Y,S [6] and SmS, _,O, [7]_ However, in contrast with these two systems, we obtain the best fit to our EXAFS data in the pure phase range using two different thresholds corresponding to the two valence states (and not one as in refs. 6 and 7). The number of atoms attributed to each threshold are defined from the value of the valence deduced from the I;,,, edge measurements. The interpretation of these results is not easy: in particular, why does the change in the ionic radius of the RE ion not affect the EXAFS of the first shell? Additional EXAFS measurements in insulating samples are necessary to study the appearance of the disorder effect from 25 to 300 K in the B’ -+ B phase transition and in the x = 0.18 sample to study the range of admixture temperatures and the effect of transitions between a homogeneous and an inhomogeneous intermediate valence state on EXAFS spectra.
186
References 1 F. Holtzberg, Proc. Conf. on Magnetism and Magnetic Materials, Boston, 1973, in AIP Conf. Proc., 18(1973) 478. A. Jayaraman, E. Bucher, P. D. Dernier andL. D. Longinotti, Phys. Reu. Lett., 31(1973) 700. T. Penney and F. Holtzberg, Phys. Rev. Lett., 34 (1975) 322. 2 D. Ravot, C. Godart, J. C. Achard and P. Lagarde, in L. H. Falicov, W. Hanke and M. B. Maple (eds.), Valence Fluctuations in Solids, North-Holland, Amsterdam, 1981,p. 423. 3 A. Jayaraman, P. D. Dernier and L. D. Longinotti, Phys. Rev. B, Ii (1975) 2783. 4 F. R. Richtmyer, S. W. Barnes and E. Ramberg, Phys. Reu., 46(1934) 843. 5 D. Raoux, Rev. A&. Phys., i5(1980) 1079. 6 J. B. Boyce, R. M. Martin, J. W. Allen and F. Holtzberg, in L. H. Falieov, W. Hanke and M. B. Maple (eds.), Valence Fluctuations in Solids, North-Holland, Amsterdam, 1981, p. 427. 7 G. Krill, J. P. Kappler, J. Rohler, M. F. Ravet, J. M. Leger and F. Gautier, in P. Wachter and H. Boppart (eds.), VaZence Instabilities, North-Holland, Amsterdam, 1982,p. 155.
of the Less-Common Metals,
94 (1983) 177-186
MIXED VALENCE STATE OF Sm,_@d,S PARAMETER, L,,, EDGE AND EXTENDED FINE STRUCTURE MEASUREMENTS*
STUDIED BY LATTICE X-RAY ABSORPTION
C. GODARTand J. C. ACHARD Laboratoire de Chimie Metallurgique des Terres Rares, Equipe de Recherche du CNRS 209, I place A. Briand, F92190 Meudon (France) G. KRILL and M. F. RAVET-KRILL Laboratoire de Magnktisme et de Structure Electronique des Solides, Universite’ L. Pasteur, 4 rue B. Pascal, F67070Strasbourg(France)and Laboratoirepour l’lltilisation du Rayonnement Electromagne’tique, Universite de Paris Sud, F91&5 Orsay (France) (Received March 3,1983)
Summary Studies of the transition from black semiconductor (B) to gold metal (M) in Sm, _,Gd,S (x = 0.14, 0.18) were performed on both sides of the critical concentration (5, z 0.16). Measurements of the lattice parameter uersus the temperature (12-300 K) for Sm,.,, Gd,,,,S showed that the limits of the temperature region in which the M and B phases coexisted depended on the direction of the temperature cycles but not on the number of cycles (up to three). L,,, absorption edge measurements were used to determine the valence state of samarium at temperatures in the range 20300 K. The extended X-ray absorption fine structure (EXAFS) spectra are very different for the two compounds. The EXAFS data for the first nearest-neighbour sulphur atoms of each samarium ion can be fitted to one mean distance and an [Sm2+]/[Sm3’] ratio which corresponds to the valence deduced from the L,,, edge and two energy thresholds. This distance changes as the lattice collapses at the B -+ M transition, To fit the data for the sample with x = 0.14 some disorder effects must be added in the high temperature phase.
1. Introduction It is well known that SmS undergoes a transition from a black semiconducting state (B) to a gold metallic state (M) at 300 K and a pressure of 6.5 kbar. This transition can be induced at 300K without applying external
* Paper presented at the Sixteenth Rare Earth Research Conference, Tallahassee, FL, U.S.A., April M-21,1983.
0022~5088/83/$3.00
The Florida State University,
Q Elsevier Sequoia/Printed
in The Netherlands
178
pressure by using the chemical pressure produced in the lattice when trivalent rare earth ions of a smaller size are substituted for samarium. When gadolini~ is used as the substituent the critical concentration x, is about 0.16. The correlation between the ionic radius of a rare earth (RE) ion and the average occupation of the 4f level has often been used to determine the valence [l J. However, many assumptions are included in this determination, so we have used lattice parameter measurements to define the temperature range in which two phases (of the same crystallographic stru~t~e) coexist when 1: is slightly higher than xc. The L,,, edge of the X-ray absorption spectra of RE compounds shows a peak at threshold. This “white line” in RE compounds of configuration (4f)” is shifted towards higher energy by about 8eV relative to that of RE compounds of configuration (4f)“+‘. For intermediate valence compounds the valence can be derived by fitting the double-hop structure of the experimental peak with a weighted superposition of the two white lines. This was done to determine the valence change uersus temperature and hence the atomic ratio [Sm2+]/[Sm3+]. In mixed valence RE compounds the rate of the valence fluctuation depends on the f-d hybridization energy which is generally believed to be small {about lo-l3 s). As extended X-ray absorption fine structure (EXAFS) measurements can detect changes taking place in about lo- l6 s, this technique enables the instantaneous atomic configuration surrounding an RE ion to be studied. The EXAFS spectra measured between 20 and 300 K on Sm, _,Gd,S with x = 0.14 and x = 0.18 are different, indicating that the distribution of atoms neighbouring each samarium ion changes when the gadolinium concentration is increased slightly above the critical concentration.
2. Experimental
details
2.1. SampEes Single crystals of Sm, -,Gd,S were grown as described in ref. 2 and were manipulated in an argon filled glove-box. The samples were crushed and sifted through a 32 pm screen. They were not annealed. 2.2. Lattice parameter measurements The lattice parameter of the powdered sample was measured as a function of temperature using a Siemens goniometer. The temperature stability was 0.1 K in the range 10300 K. Cr Kcr, radiation was used together with a diamond powder internal standard. To ensure good accuracy for the lattice parameter measurements we performed them at large Bragg angles: the (400) and (331) reflections were used for the M phase and the (331) reflection was used for the B phase. This yielded an accuracy of better than 5 0.001 A. 2.3. LIII edge and extended X-ray absorption fine structure measurements The powdered samples were spread on Scotch tape and supported on a window of dimensions 40 mm x 5 mm cut in an aluminium plate. The average
179
mass of the sample in this configuration was approximately constant (about 5 mg cm -2 which corresponded to a mean thickness of 6 urn per layer). The sample thickness was varied by stacking layers of this type. The absorption experiments were carried out on the DC1 storage ring at Orsay (Laboratoire pour 1’Utilisation du Rayonnement Electromagnetique). We measured the logarithm of the ratio I,/Iof the intensity of the incident beam to the intensity of the transmitted beam. log(l,,/l) was measured as a function of energy over an interval of 100 eV on each side of the energy of the L,,, edge of the samarium ion. The curves were normalized by setting the difference between the values of log&/l) about 30eV before and 70eV after the L,,, discontinuity (which occurs at about 6710eV) equal to unity. Accurate correction of the variation in the background with energy was neglected because this variation, which is about 8eV between the two peaks, is very small relative to the difference in the heights of the two peaks. In the cases studied the error in the estimated valence was less than 1%. The EXAFS spectra were measured in the energy range 6400-7050 eV. They showed some discontinuity at about 350 eV above the threshold of the samarium ion which prevented investigation of the Fourier transform at higher energies. This discontinuity may be due to an imperfection in the Si(220) channel-cut crystal used. Therefore only information about the first-nearest neighbours (sulphur shell) of each samarium ion was obtained. 3. Results 3.1. Lattice parameter measurements At 300 K the lattice parameters of Sm, _,Gd,S with x = 0.14 and x = 0.18 are 5.87 A and 5.68 A respectively, from which we deduced values of 2.1, and 2.7, for the valence of samarium assuming that the system Sm,_.Gd,S obeys Vegard’s law and that the ionic radius of the samarium ion varies linearly with the occupation number of the 4f level. These lattice parameter values are in good agreement with these reported by Jayaraman et al. [S]. The M + B transition at low temperature only occurs when the gadolinium concentration is slightly higher than x, [S], so we measured the dependence of the lattice parameter on temperature for the 3c= 0.18 sample only. The results of these measurements for three cycles 300 K-12 K-300 K are shown in Fig. 1. As the temperature decreases the lattice parameter of the M phase slowly decreases to 5.67 A and then increases. At 140 K the B phase, which has the same rock salt structure, appears with a lattice parameter of 5.82 A corresponding to an estimated valence of 2.2 for the samarium ion. The two phases coexist down to 60 K. At lower temperatures only the B phase is present with a constant value of the lattice parameter. As the temperature of the B phase is increased the M phase appears at 110 K. The two phases coexist from 110to 250K, and then only the M phase is present. The temperatures of the transitions and the values of the lattice parameters were reproducible throughout three temperature cycles. The results of Jayaraman et al. [S]for 3c= 0.17 (above x,) are also shown in l&g. 1. Their results are similar to those reported here. With decreasing
180
temperature there is a weak decrease in the lattice parameter below 300K followed by an increase. The limits of the domain in which M and B phases coexist are about the same and the change Aa in the lattice parameter at the B c) M transition is about 0.12 A compared with Aa z 0.15 A in our sample. 3.2. L,,, spectra L,,, edge measurements were performed for samples with x = 0.14 and 3c= 0.18 for decreasing and increasing temperatures in the range 20-300 K. The spectra of the sample with x = 0.14 at 220 K and the sample with x = 0.18 at 160 and 77 K are plotted in Fig. 2. Calculations were performed (Fig. 2, dotted curve)
64
: .
i
.“’ ,
5.85.
,.. :. ‘,,
... .. ... ,~,:.:;....
,,,.,..............-
r ........
‘?
-
.
5.80-
2
04
5
5.15.
5.70 -
100
200
~
300
6680
Fig. 1. Lattice parameter ofSm,,s, Gd,,,sS us. temperature: A, increasing temperature (this work); 0,17x Gd [a].
E(eV)
0780
I, decreasing temperature (this work);
Fig. 2. L,,, absorption edge of (a) Sm,,,, Gd,,,,S (220 K; u z 2.32), (b) Sm,.,,Gd,,,,S (160 K; u x 2.56) and(c) SmO,szGdO.,sS (77 K; LJz 2.32) energy: 0, 0, A, experimental data; ..., calculated data.
181
to estimate the valence from the best visual fits of the two humps using In(+)
= v[Axexp{
-(EP~~‘)2)+arctan(E~~~1)]+ (E--Ecl.2)2
r
} + arctan( “;:,‘)1
where u is the fractional part of the valence, A is the amplitude of the white line relative to the normalized discontinuity of the edge and E,,, and E,,, are the energies of the two peaks such that AE = E,,, -E,,, = 7.3 kO.1 eV. The inverse tangent term corresponds to the discontinuity of the L,,, edge [4] with the density of final states assumed to be constant and the exponential term corresponds to the lorentzian width of the white line. There is a significant difference in the shapes of the L,,, edges for the two samples at 300 K which corresponds to a valence change from 2.32 for x = 0.14 to 2.58 for x = 0.18. The valence of the sample with x = 0.14 does not change between 25 and 300 K. The valence of the sample with x = 0.18 is unchanged between 300 and 150 K (or changes by -0.02); at 85 K it decreases to 2.41 and at 77 K it is 2.32. It then remains constant down to 25 K. This knowledge of the dependence of valence on temperature is useful in determining the number of Sm2 + or Sm3 + ions which is required for the EXAFS calculations. 3.3. Extended X-ray absorption fine structure measurements EXAFS measurements were performed on the x = 0.14 sample at 25 and 300 K and on the x = 0.18 sample at 300,160,77 and 25 K. The EXAFS spectra of the 3t = 0.14 sample at 25 K (B phase) and of the x = 0.18 sample at 77 K (B phase) and 160 K (M phase) are shown in Fig. 3. The two spectra in the B phase are qualitatively identical. Some frequencies in the Kronig oscillations (at about 6740 and 6780 eV) in the spectra of the M phase disappear. The Fourier-filtered EXAFS spectrum associated with the first sulphur shell (each samarium ion is surrounded by six sulphur atoms) is approximately reproduced using the EXAFS formula [5]
X(k) = k-1C~lf,(n,k),eXp(-oik2)eXp I
X
r-$$I
X
Sin[BkRi +262(12) + arg(fi(x, lz))]
atoms where K = h-‘{2m(EE,J)-‘, Ni is the number of nearest-neighbour located at a radial distance Ri from the ion, exp( - olz’) is an attenuation factor analogous to the DebyeWaller factor, exp{ -2R@(k)} accounts for the inelastic losses, a,@) is the phase shift of the central atom, fi and arg{fi(7c, k)} are the backscattering amplitude and the back-scattered phase shift respectively, and E, is the threshold energy.
182
(a)
(b)
Fig. 3. EXAFS spectra of (a) Sm,,,,Gd,,,,S (160 K) us. energy in the M and B phases.
(25 K), (b) Sm,,s,Gd,,,,S
(77 K) and (c) Sm,,,,Gd,.,,S
The partial EXAFS spectrum in the low temperature range obtained by back transforming the first peak of the Fourier transform of K3a in iz space are shown in Fig. 4. The data for the high temperature range are shown in Fig. 5. Four different hypotheses were tested for the results at 25 K. In the first case two different distances d1 and dz, which were chosen to be d1 w ~(uSm2+S) and d 2 * th,,~+s), an d one threshold were assumed. In the second hypothesis the same two distances were used with two thresholds (one for Sm2 ‘S denoted 6 = 0 eV and one for Sm3 +S denoted S = 7.5 eV). It was not possible to fit the data using two distances and small changes in d, and dz did not improve the fit. In the third run we used one distance d =: a/Z and one threshold. Figure 4(a) shows that the fit is roughly correct for the sample with x = 0.14. In the fourth hypothesis we used one distance d x a/2 and two thresholds, and Fig. 4(b) shows that the best fit for the x = 0.14 sample is obtained if the ratio of the number of atoms at each threshold corresponding to a valence of 2.33 is used. The same procedure (one distance and two thresholds) gave a slightly better fit to the EXAFS data of the two samples at various temperatures than that obtained using one distance and one threshold. The mean Sm-S distances of 2.95 A for the x = 0.14 sample and 2.88 A for the x = 0.18 sample (Fig. 4(c)) are in agreement (with an accuracy to +0.03 A) with
_. 1 : .
j
t
d
184
0.60&01
-E.S0E-a1
64
-%.SBE-81
0.80
I
SE.00
I
180.08
ON
I
158.00
I
280.08
I
250.00
I 300.88
356.80
ECN> e.25c-0%
-e.zsz-a1
(4
X(E)
B B5
1
58.88
t 1k3a.00
I 168.88
/
286.08
, 258.80
I 300.80
350.0%
ECN>
Fig. 5. EXAFS data for the sulphur atoms neighbouring the samarium ions in the high temperature range: (a) Sm,,s,GdO.lsS (160K; R = 2.83A; 2.4 atoms at 6 = OeV and 3.6 atoms at 7.5 eV); (b) Sm,,,,Gd,.,,S (3OOK; R = 2.83A; two atoms at 6 = OeV and four atoms at 6 = 7.5eV); (c) Sm,,,,Gd,,,,S (300 K; R = 2.94 A; four atoms at 6 = 0 eV and two atoms at d = 7.5 eV; u = 0.19).
185
the expected value for the x = 0.14 sample and the measured value for the x = 0.18 sample. The same values were measured for the x = 0.18 sample at 77 K (Fig. 4(d)) as were used at 25 K. The mean Sm-S distance for the x = 0.18 sample at 160 K is 2.83 A which corresponds to the lattice parameter of the M phase and a good fit is obtained (Fig. 5(a)) using two thresholds. The number of Sm2+ and Sm3+ ions used corresponds to a valence of 2.60 which is very close to the value of 2.56 deduced from the L,,, measurements. The same distance gives a relatively good fit for the x = 0.18 sample at 300 K (Fig. 5(b)) provided that an integral number of atoms is used (in this case the valence is 2.66 compared with the measured value of 2.58). The fit is improved if a non-integral number of atoms is used such that the valence is closer to 2.58. A relatively good fit is obtained for the x = 0.14 sample at 300 K (Fig. 5(c)) if a disorder effect is taken into account by including a disorder parameter rr = 0.19 (in the preceding cases G = 0).
4. Conclusion We studied two samples from the Sm,_,Gd,S system with gadolinium concentrations near the critical value. Lattice parameter measurements on the x = 0.18 sample showed the existence of either one or two phases depending on the temperature range, in agreement with the results reported in ref. 3. Our results revealed that the proportions of the two phases present differ depending on whether the temperature was increased or decreased. This appeared to be an intrinsic property of the powdered sample since it did not change with temperature cycling. L,,i absorption edge measurements showed that the valence of the x = 0.14 sample had the same value (2.32) throughout the temperature range 25-300 K. The valence of the x = 0.18 sample decreased from 2.58 at 150 K to 2.3, at 7’7 K. In pure phases (temperatures above 150 K or below 77 K) the valence remained constant. The experimental values of the lattice parameter can be used to fit the EXAFS data for the contribution of the first-nearest-neighbour shell (six sulphur atoms) with only one Sm-S distance. Similar results have been reported previously for Sm, _,Y,S [6] and SmS, _,O, [7]_ However, in contrast with these two systems, we obtain the best fit to our EXAFS data in the pure phase range using two different thresholds corresponding to the two valence states (and not one as in refs. 6 and 7). The number of atoms attributed to each threshold are defined from the value of the valence deduced from the I;,,, edge measurements. The interpretation of these results is not easy: in particular, why does the change in the ionic radius of the RE ion not affect the EXAFS of the first shell? Additional EXAFS measurements in insulating samples are necessary to study the appearance of the disorder effect from 25 to 300 K in the B’ -+ B phase transition and in the x = 0.18 sample to study the range of admixture temperatures and the effect of transitions between a homogeneous and an inhomogeneous intermediate valence state on EXAFS spectra.
186
References 1 F. Holtzberg, Proc. Conf. on Magnetism and Magnetic Materials, Boston, 1973, in AIP Conf. Proc., 18(1973) 478. A. Jayaraman, E. Bucher, P. D. Dernier andL. D. Longinotti, Phys. Reu. Lett., 31(1973) 700. T. Penney and F. Holtzberg, Phys. Rev. Lett., 34 (1975) 322. 2 D. Ravot, C. Godart, J. C. Achard and P. Lagarde, in L. H. Falicov, W. Hanke and M. B. Maple (eds.), Valence Fluctuations in Solids, North-Holland, Amsterdam, 1981,p. 423. 3 A. Jayaraman, P. D. Dernier and L. D. Longinotti, Phys. Rev. B, Ii (1975) 2783. 4 F. R. Richtmyer, S. W. Barnes and E. Ramberg, Phys. Reu., 46(1934) 843. 5 D. Raoux, Rev. A&. Phys., i5(1980) 1079. 6 J. B. Boyce, R. M. Martin, J. W. Allen and F. Holtzberg, in L. H. Falieov, W. Hanke and M. B. Maple (eds.), Valence Fluctuations in Solids, North-Holland, Amsterdam, 1981, p. 427. 7 G. Krill, J. P. Kappler, J. Rohler, M. F. Ravet, J. M. Leger and F. Gautier, in P. Wachter and H. Boppart (eds.), VaZence Instabilities, North-Holland, Amsterdam, 1982,p. 155.