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Role of phonon dynamics in the thermopower of niobium hydrides
Solid State Communications, Vol. 28, pp. 1009—1011. Pergamon Press Ltd. 1978. Printed in Great Britain. ROLE OF PHONON DYNAMICS IN THE THERMOPOWER OF NIOBIUM HYDRIDES Z. Henkie, OJ. ~oga1and B. Stalthski Institute for Low Temperature and Structure Research, Polish Academy of Sciences, Wroclaw, Poland (Received 25 September 1978 by A.R. Miedema) The thermopower of NbH~alloys for x varying from 0.607 to 0.883 has been examined at temperatures ranging from 100 to 430 K. It was found that the transition from orthorhombic j3 to cubic a’ phase is accompanied by a strong change of thermopower. It is concluded that differences in phonon spectra of these two phases are responsible for the observed differences in the transport properties. The sensitivity of the thermopower to any other phase transitions in this system has been observed as well. SEVERAL NMR STUDIES [1—3] have been devoted to the Nb—H system with the purpose to obtain information on how the conduction electron band character of Nb metal is altered by the addition of hydrogen. The phase diagram of the system shows the existence of several phases [4]. Recently [3], it has been found that no significant changes in band structure details are involved in the transition from the high temperature cubic phase a’ to the orthorhombic 13 phase existing in the intermediate temperature range. Once we can neglect the changes in the band structure we have an interesting possibility to determine the role of phonon dynamics in the transport properties ofhydrides. We report data on the thermopower 5(7’) of NbHX with x = 0.607, 0.709, 0.784 and 0.883, determined in the temperature range 100—430 K and relate them to the S(7) data of Nb used in the preparation of these hydrides, The powdered samples of NbHX were prepared from powdered niobium as described in [5]. The rectangular shape samples needed in the experiment of dimensions 15 x4 x 2mm3, both ofNb and its hydrides,were obtained by pressing their powders at 3000 psi. The absolute thermopower 5(1) has been measured as described earlier [6] in argon atmosphere with 15 K gradient on the sample. The results are presented in Figs. 1(a, b). The inset in Fig. 1(b) shows a fragment of the Nb—H diagram drawn according to [4]. The vertical dashed lines show the compositions of the samples examined and the upper boundary of the examined ternperature range. The numbers refer to the S(T) curves. For transition metals the 5(7’) data of different authors usually differ by a few pV/K (e.g. for Ta by 3 pV/K at room temperature) [7] This is partly due by the difference both in the reference material used and the source of literature data of its absolute thermopower (in our case the Pt and Cusack’s data, respectively see [6]). Vedernikov [7], after reviewing literature data on .
—
the thermopower of transition metals, found the shape of S(7) curve to be the best reproducible thermopower characteristic of transition metal. Our S(7) data for a niobium pressed powder sample result in a curve [curve 1 in Fig. 1(a)] of the same shape as the literature data for a solid sample (see [7]) but shifted to more negative values by about 2 pV/K. So we expect that our S(7) data for the pressed powder samples of hydrides are reliable when we consider the temperature dependence or relate them to the 5(7’) data of our Nb sample. The measurements above room temperature were done both in a heating and a cooling cycle and are presented in Fig. 1 for the hydrogen richest sample (curve 5). There is some difference between them, presumably due to some chemical changes, but there is no doubt that the observed increase at about 400K is a physical effect. For the other samples, although they were examined to higher temperatures, these differences are about 3 times smaller so they were neglected and the results determined at heating cycle are presented only. Generally the thermopower of hydrides is more negative than that of niobium. Moreover, it shows marked anomalies in contrast to the slowly varying monotonic temperature dependence of S for Nb. Each curve reveals one anomaly below room temperature at T 1 and one above it (T2). In Table 1 we give the temperatures at which extrema of the first temperature derivative of S(T) are observed. The temperature 7’2 increases with the increase of hydrogen concentration and is approximately equal to the temperature of transition from a’ to 13-phase. Apparently, the distinct change in the value of S at 7’2 is a consequence of this phase transition. It is reasonable to assume that above room temperature the electron diffusion thermopower dominates the measured S(7) value. Then we have [8]:
1009
—
1010
THERMOPOWER OF NIOBIUM HYDRIDES
200 -15
400
T (K)
Table 1. Temperatures of extrema of the first temperature derivative of 5(T)
‘i’
~-w
15
~
~
b
2
0
0 200
400
300
TIK) Fig. 1. The temperature dependence of the absolute thermoelectric power (5) for: Nb 1, NbHO~OI 2, NbHo,o~ 3, NbH~~ —4, NbH 0~ 5. The inset shows a part of Nb—H phase diagram, drawn according to [4], with the upper examined temperature range and the composition of the examined samples marked by vertical dotted lines, —
;:::tboul
~5±6
NbHO7M
206±7 234±’4
362±8 383 ±3 386±10
NbH0~
118
>400
NbH0~
5
1
Vol. 28, No. 12
—
±4
result of a change of composition. Therefore, if we accept the conclusion of Hwang et al. [3] , we do not expect the second terms of equation (1) to be different for the two phases, but rather the first ones. This means that the energy dependence of the mean-free-path in the two phases is different. It seems reasonable to account for the changes in terms of phonon dynamics a change in the self-diffusion process of hydrogen atoms. NMR studies [1, 11, 12] showed that the proton self-
—
—
5(7)
=
KT[d ln L(ff)/dE + d in AQI’)/dEJE = EF
1
The first term between the brackets is due to the energy dependence of the mean-free-path L, and the second one is due to the energy dependence of the Fermi surface area A. K is a constant. In the last decade it was recognised both theoretically [9] and experimentally [10], that for the 1st group periodic table of elements, in contrast to previous opinions, the phonon dynamics can yield high positive or negative values for the first term, and this is the situation we probably meet in the Nb—H system. Hwang et a!. Knight [3] found the isotropic component 93Nb shiftthat tensor has the same value in of thethe a’ as in the 13 phase at fixed values ofx, where 0.73 ‘~x~ 0.88, indicating that no significant changes in band structure occur. Inspecting the phase diagram [inset in Fig. 1(b)] one can see that in the case of sample No. 4 when increasing the temperature we pass from the 13-phase to the a’-phase, keeping the same composition in both phases. So, it is evident that the observed large difference in the S values for the two phases is not a
diffusion rate is much higher in a’ phase than in the j3 phase. This is the case for other examined samples too, however the picture is complicated because of changes .
.
.
in composition of the phases with mcreasmg temperature in the two phase range. K the onlythephase in samplesdepends Nos. 2, strongly 3 and 4 is theAta 420 phase. Then thermopower .
and nonmonotonically on x. However, since the contribution reflecting the energy dependence of the meanfree-path is important, the results are not very informative as concerns the electronic structure of examined hydrides. Besides the anomaly in S(7) above room temperature there is another anomaly at T1 below room ternperature. For sample No. 5 it may be connected with the transition from the j3 to the ‘y phase, which for NbH08.78 starts at about 160 K [13]. According to literature data [141, the other samples phase transitions can for be expected. The low different temperature anomaly of S(7) can be ascribed to these phase transitions. Since, around T 1 we measure a value of S resulting from two phases, we can not expect an accurate correlation between T1 and temperature of phase transition. Nevertheless, it is fully clear that the thermopower is a sensitive parameter to indicate the presence of phase transitions in the Nb—H system.
Vol. 28, No.12
THERMOPOWER OF NIOBIUM HYDRIDES REFERENCES
1.
LOTGEMEIER H., ARONS R,R. & BOHN H.G., J. Magn. Resonance 8,74(1972).
2. 3.
ZAMIRD.,Phys.Rev. 140,A27l (1965). HWANG Y.S., TORGESON D.R. & BARNES R.G., Solid State Commun. 24,773(1977).
4.
WALTER R.J. & CHANDLER W.T., Trans. AIME 233,762(1965).
5.
STALINSKI B. & ~OGALO.J., Bull. Acad. Polon. S.cL, Sdr. Sci. Chim. 13, 397 (1965).
6.
HENKIE Z. & TRZEBIATOWSKI W., Phys. Status Solidi 35,827(1969).
7. 8.
VEDERNIKOV M.V., Adv. Phya 18, 337 (1969). HUEBENER R.P., Solid State Phys. 27,63 (1972).
9.
ROBINSON J.E.,Phys. Rev. 161,815 (1968).
10.
BARN~RD.,J.Phys. C2,2114(1969).
11. 13.
ZAMIR D. & COTTS R.M.,Phys. Rev. 134, A666 (1964). ~OGAL O.J. & COTFS R.M.,Phys. Rev. Bli, 2443 (1975). PICK MA., International Meeting on Hydrogen in Metals, JUl-Conf. 6,90 (1972).
14.
SCHOBER T., ScriptaMetallurgica 7, 1119(1973).
12.
1011
—
the thermopower of transition metals, found the shape of S(7) curve to be the best reproducible thermopower characteristic of transition metal. Our S(7) data for a niobium pressed powder sample result in a curve [curve 1 in Fig. 1(a)] of the same shape as the literature data for a solid sample (see [7]) but shifted to more negative values by about 2 pV/K. So we expect that our S(7) data for the pressed powder samples of hydrides are reliable when we consider the temperature dependence or relate them to the 5(7’) data of our Nb sample. The measurements above room temperature were done both in a heating and a cooling cycle and are presented in Fig. 1 for the hydrogen richest sample (curve 5). There is some difference between them, presumably due to some chemical changes, but there is no doubt that the observed increase at about 400K is a physical effect. For the other samples, although they were examined to higher temperatures, these differences are about 3 times smaller so they were neglected and the results determined at heating cycle are presented only. Generally the thermopower of hydrides is more negative than that of niobium. Moreover, it shows marked anomalies in contrast to the slowly varying monotonic temperature dependence of S for Nb. Each curve reveals one anomaly below room temperature at T 1 and one above it (T2). In Table 1 we give the temperatures at which extrema of the first temperature derivative of S(T) are observed. The temperature 7’2 increases with the increase of hydrogen concentration and is approximately equal to the temperature of transition from a’ to 13-phase. Apparently, the distinct change in the value of S at 7’2 is a consequence of this phase transition. It is reasonable to assume that above room temperature the electron diffusion thermopower dominates the measured S(7) value. Then we have [8]:
1009
—
1010
THERMOPOWER OF NIOBIUM HYDRIDES
200 -15
400
T (K)
Table 1. Temperatures of extrema of the first temperature derivative of 5(T)
‘i’
~-w
15
~
~
b
2
0
0 200
400
300
TIK) Fig. 1. The temperature dependence of the absolute thermoelectric power (5) for: Nb 1, NbHO~OI 2, NbHo,o~ 3, NbH~~ —4, NbH 0~ 5. The inset shows a part of Nb—H phase diagram, drawn according to [4], with the upper examined temperature range and the composition of the examined samples marked by vertical dotted lines, —
;:::tboul
~5±6
NbHO7M
206±7 234±’4
362±8 383 ±3 386±10
NbH0~
118
>400
NbH0~
5
1
Vol. 28, No. 12
—
±4
result of a change of composition. Therefore, if we accept the conclusion of Hwang et al. [3] , we do not expect the second terms of equation (1) to be different for the two phases, but rather the first ones. This means that the energy dependence of the mean-free-path in the two phases is different. It seems reasonable to account for the changes in terms of phonon dynamics a change in the self-diffusion process of hydrogen atoms. NMR studies [1, 11, 12] showed that the proton self-
—
—
5(7)
=
KT[d ln L(ff)/dE + d in AQI’)/dEJE = EF
1
The first term between the brackets is due to the energy dependence of the mean-free-path L, and the second one is due to the energy dependence of the Fermi surface area A. K is a constant. In the last decade it was recognised both theoretically [9] and experimentally [10], that for the 1st group periodic table of elements, in contrast to previous opinions, the phonon dynamics can yield high positive or negative values for the first term, and this is the situation we probably meet in the Nb—H system. Hwang et a!. Knight [3] found the isotropic component 93Nb shiftthat tensor has the same value in of thethe a’ as in the 13 phase at fixed values ofx, where 0.73 ‘~x~ 0.88, indicating that no significant changes in band structure occur. Inspecting the phase diagram [inset in Fig. 1(b)] one can see that in the case of sample No. 4 when increasing the temperature we pass from the 13-phase to the a’-phase, keeping the same composition in both phases. So, it is evident that the observed large difference in the S values for the two phases is not a
diffusion rate is much higher in a’ phase than in the j3 phase. This is the case for other examined samples too, however the picture is complicated because of changes .
.
.
in composition of the phases with mcreasmg temperature in the two phase range. K the onlythephase in samplesdepends Nos. 2, strongly 3 and 4 is theAta 420 phase. Then thermopower .
and nonmonotonically on x. However, since the contribution reflecting the energy dependence of the meanfree-path is important, the results are not very informative as concerns the electronic structure of examined hydrides. Besides the anomaly in S(7) above room temperature there is another anomaly at T1 below room ternperature. For sample No. 5 it may be connected with the transition from the j3 to the ‘y phase, which for NbH08.78 starts at about 160 K [13]. According to literature data [141, the other samples phase transitions can for be expected. The low different temperature anomaly of S(7) can be ascribed to these phase transitions. Since, around T 1 we measure a value of S resulting from two phases, we can not expect an accurate correlation between T1 and temperature of phase transition. Nevertheless, it is fully clear that the thermopower is a sensitive parameter to indicate the presence of phase transitions in the Nb—H system.
Vol. 28, No.12
THERMOPOWER OF NIOBIUM HYDRIDES REFERENCES
1.
LOTGEMEIER H., ARONS R,R. & BOHN H.G., J. Magn. Resonance 8,74(1972).
2. 3.
ZAMIRD.,Phys.Rev. 140,A27l (1965). HWANG Y.S., TORGESON D.R. & BARNES R.G., Solid State Commun. 24,773(1977).
4.
WALTER R.J. & CHANDLER W.T., Trans. AIME 233,762(1965).
5.
STALINSKI B. & ~OGALO.J., Bull. Acad. Polon. S.cL, Sdr. Sci. Chim. 13, 397 (1965).
6.
HENKIE Z. & TRZEBIATOWSKI W., Phys. Status Solidi 35,827(1969).
7. 8.
VEDERNIKOV M.V., Adv. Phya 18, 337 (1969). HUEBENER R.P., Solid State Phys. 27,63 (1972).
9.
ROBINSON J.E.,Phys. Rev. 161,815 (1968).
10.
BARN~RD.,J.Phys. C2,2114(1969).
11. 13.
ZAMIR D. & COTTS R.M.,Phys. Rev. 134, A666 (1964). ~OGAL O.J. & COTFS R.M.,Phys. Rev. Bli, 2443 (1975). PICK MA., International Meeting on Hydrogen in Metals, JUl-Conf. 6,90 (1972).
14.
SCHOBER T., ScriptaMetallurgica 7, 1119(1973).
12.
1011