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Electrical resistivity, thermal conductivity and thermopower of nonmagnetic REAL2 compounds
Journal
of the Less-Common
Metals,
111
(1985)
369
- 3’i3
369
ELECTRICAL RESISTIVITY, THERMAL CONDUCTIVITY AND THERMOPOWER OF NONMAGNETIC REAl> COMPOUNDS* E. BAUER, Institut
E. GRATZ,
H. KIRCHMAYR
fiir Experimentalphysik,
and N. PILLMAYR
TU, A-1040
Vienna
(Austria)
TU, A-l 040
Vienna
(Austria)
H. NOWOTNY Institut
fiir Theoretische
(Received
December
Physik,
10, 1984)
Summary
The temperature dependence of the electrical and the thermal resistivity, as well as the thermopower of the three nonmagnetic REA& compounds, are compared (RE = Y, La, Lu). As with other physical properties, LaAl, shows a different behaviour in transport phenomena compared with the Lu and Y compounds. From the analysis of p(T) and h(T) data we show that the anomalous behaviour of LaAl* can be understood by assuming that in this case the electron-phonon coupling is about twice as strong. The temperature dependence of the thermopower of LaAl, also shows its exceptional position. This fact, however, cannot be simply referred to the enhanced electron-phonon coupling, because the thermopower depends much more on electronic-state properties at the Fermi energy than do the electrical and thermal resistivities. Introduction
Of the REAl, compounds, YAl,, LaAl, and LuAl, show no magnetic order even at the lowest temperatures. Although these compounds crystallize in the same structure (cubic MgCu* type) and the rare earth ions in all cases are in the 3+ state, experimental investigations performed on them reveal an exceptional position for LaAl*. Specific-heat measurements show that the y-value for LaAlz is double that of YAl,? and LuAlz [l]. LaAlz undergoes a superconducting transition at 3.3 K whereas the Y and the Lu compounds do not show superconductivity down to 0.34 K [2]. Calorimetric measurements [l] and investigations of the elastic constants [3] have shown that the Debye temperature of LaAl, is considerably lower than those of YA12 and LuAl*. Measurements of the phonon dispersion curves indicate a softening of the phonon spectrum of LaAl*, *Paper presented at the International land, March 4 - 8, 1985.
Rare Earth Conference,
0022-5088/85/$3.30
0 Elsevier Sequoia/Printed
ETH Zurich,
Switzer-
in The Netherlands
370
giving rise to a gap in the phonon density of states [ 41. From recent band structure calculations [ 51 it has been found that the f-band of LaAl, lies about 3 eV above the Fermi energy, E,, and the f-components in the electron states near EF are less than 10%. Below EF the band structures of LaA& and YAl,! are very similar. The aim of the present study of the transport phenomena (electrical and thermal resistivities as well as thermopower) was twofold. On the one hand we wanted to determine whether LaAI, also shows exceptional behaviour with respect to the transport phenomena. On the other hand, it was of interest to know how much of the anomalous transport behaviour of LaAl, could be explained by the application of known theoretical models.
Exper~ental
details
The samples were prepared by high-frequency melting in a watercooled copper boat under a protective argon atmosphere. Annealing procedures at different temperatures were subsequently applied to the samples in order to study the influence of heat treatment on the transport phenomena, which will be discussed later. The phase purity was checked by Debye-Scherrer photographs. Whereas in YAl;, and LaAl, no foreign phases were detectable, in all the LuA12 samples which we prepared small traces of a second phase were observed. Similar problems have been reported by Hungsberg and Gschneidner [ 11. It seems to us that the preparation of REAI, compounds becomes more difficult for elements at the end of the rare earths series in the Periodic Table.
Results and discussion The experimental results for the different transport properties shown below have been obtained from the same sample. Figure 1 shows the temperature dependence of the electrical resistivity of YA12, LaAlz and LuAl,. The inset to this Figure shows the superconducting transition on an expanded scale. From this measurement the superconducting transition temperature is found to be 3.30 rt 0.02 K. This value is in good agreement with the transition temperature of 3.29 K obtained from specific-heat measurements [l]. A comparison of the p uersus T curves of these three compounds shows that the curve is considerably steeper for LaAl, . It is also interesting to note that samples of different p4.2 values, as obtained by different annealing procedures, show the same deviations for LaAl,. The residual resistivity range of values for LaAl, was 0.3 - 5.2 $-‘J cm and for YAl, it was 2.8 - 18.5 ps2 cm. The simplest model to describe the electron-phonon-scattering contribution to the electrical resistivity is given by the well known BlochGriineisen formula [6] which was used to fit the experimental data. The Debye temperature, on, was used as a single fit parameter. The mean 0n value
371
Fig. 1. The (p - ~4.2) us. T curves of YAl 2, LaA12 and LuA12 (p4 2: 18.5, 3.5, 25.5 /JR cm for YA12, LaA12 and LuA12, respectively; p4.* denotes the resistkity at 4.2 K). The inset shows details of the superconducting transition for LaA12.
obtained from different annealed samples, related to the mass M of YA12 by (~REA1,/~x41,)“2~ is 320 K for YAl,, 230 K for LaAl, and 310 K for LuAl* . We observed that a decrease of the residual resistivity causes a slight increase of the Debye temperature. Since band-structure calculations reveal nearly the same density of electronic states for all these compounds [ 71, the steeper gradient of the p versus T curve for LaAlz must be attributed to a higher electron-phonon coupling. The relative strength of the electron-phonon interaction can be estimated from [ ~(0,) - p4.J/0,. The values obtained are 0.1 for YAl,! and LuA12 and 0.2 for LaAl*. It is interesting to note also that the enhancement factor in the specific heat is twice as large in LaAl* as in YA12and LuAl* (LaA12: 1.5 - 2.7; YAl*: 0.3 - 0.8; LuAl,: 0.4 - 1.2 [?I). The temperature dependence of the thermal conductivity h is given in Fig. 2. Again, a remarkably different behaviour is found for LaAl,. The X uersus T curve of LaAl, is characterized by a pronounced maximum around 18 K whereas, for higher temperatures, the increase of h(T) is smaller compared with YAl,! or LuAl*. A comparison of X(T) measurements of different heat-treated samples shows a strong dependence of the shape of the h versus T curve upon the annealing procedure, especially in the low-temperature region. Usually the electron-phonon-scattering contribution to the thermal resistivity is given by Wilson’s formula [ 81. This formula has been used to fit the experimental data. The Debye temperatures obtained from such a fit are, in general, 10 - 20% higher than the values deduced from the p data. Again, the value for LaAl* is remarkably lower than those for YAl, and LuAl,. The mean 8, values from the X data are 360 K for YA12, 260 K for LaAl, and 370 K for LuAl,. For this fit, the scattering processes contribution due to static imperfections has been assumed to be proportional to l/T over the whole temperature range; the lattice thermal conductivity was neglected [9]. This is possibly the reason for the higher values of the Debye tempera-
312
h imW/cmKJ
0
So
m
Fig. 2. The temperature LuAl*,
Eo
200
dependence
250
300
of the thermal
conductivity,
h, for
YA12,
LaAl2 and
tures obtained from the h data. For high temperatures the theoretical formula yields a constant value for X. This value is proportional to the inverse of the strength of the electron-phonon interaction. An estimate of these values of h(T + 00) from the fit yields 150 mW cm-’ K-’ for LaAlz (see Fig. 2), 320 mW cm-’ K-’ for YAlz and 380 mW cm-’ K-’ for LuAlz. Again, this roughly shows that the strength of the electron-phonon interaction is about twice as large in LaA12. Recently we have studied the influence of annealing conditions on thermopower in the case of YAl, [lo]. It has been found that scattering processes of the conduction electrons on static imperfections considerably influence the shape of the S uersus T curve. For this reason we have shown in Fig. 3 the S uersus T data of two different LaAlz and YAl,! samples. Although
Fig. 3. The temperature dependence of the thermopower for YA12, LaAl2 and LuAlz. Experimental results obtained from different heat-treated samples are given by closed and open symbols.
373
the heat treatment and the purity make a large difference in thermopower, this cannot be the reason for the different behaviour found for LaAl, on the one hand and YAl, and LuAl, on the other. From the theory of the generation of thermopower it is known that S(T) depends on the energy derivatives of quantities averaged over surfaces of constant electron energy. In the simplest approximation the logarithmic derivative of the density-of-states function appears in the expression for the thermopower. Therefore it seems that in the La and the Y compound this derivative may be different in sign. Because of the lack of a meaningful formula for S(T) with a small set of physically relevant parameters, it was not possible to analyse the S(T) data in more detail as was done for p(T) and X(T).
Acknowledgment We thank the “Hochschuljubilaumsstiftung support.
der Stadt Wien” for financial
References 1 R. E. Hungsberg and K. A. Gschneidner, Jr., J. Phys. Chem. Solids, 33 (1972) 401. 2 B. W. Roberts, J. Phys. Chem. Ref. Data, 5 (1976) 581. 3 R. J. Schiltz, Jr. and J. F. Smith, J. Appl. Phys., 45 (1974) 4681. 4 C. T. Yeh, W. Reichardt, B. Renker, N. Niicker and M. Loewenhaupt, J. Phys. (Paris), 42 (1981) C6-371. 5 A. Hasegawa and A. Yanase, J. Phys. F, 10 (1980) 847. 6 F. J. Blatt, Physics of Electronic Conduction in Solids, McGraw-Hill, New York, 1968, p. 190. 7 A. C. Switendick, in C. J. Kevane and T. Moeller (eds.), Proc. Tenth Rare Earth Research Conf., Carefree, AZ, United States Atomic Energy Commission Technical Information Center, Oak Ridge, TN, 1973, p. 235. 8 J. M. Ziman, Electrons and Phonons, Clarendon Press, Oxford, 1972, p. 391. 9 E. Bauer, E. Gratz and G. Adam, Physica B, 130 (1985) 81. 10 E. Gratz and H. Nowotny, Physica B, 130 (1985) 75.
of the Less-Common
Metals,
111
(1985)
369
- 3’i3
369
ELECTRICAL RESISTIVITY, THERMAL CONDUCTIVITY AND THERMOPOWER OF NONMAGNETIC REAl> COMPOUNDS* E. BAUER, Institut
E. GRATZ,
H. KIRCHMAYR
fiir Experimentalphysik,
and N. PILLMAYR
TU, A-1040
Vienna
(Austria)
TU, A-l 040
Vienna
(Austria)
H. NOWOTNY Institut
fiir Theoretische
(Received
December
Physik,
10, 1984)
Summary
The temperature dependence of the electrical and the thermal resistivity, as well as the thermopower of the three nonmagnetic REA& compounds, are compared (RE = Y, La, Lu). As with other physical properties, LaAl, shows a different behaviour in transport phenomena compared with the Lu and Y compounds. From the analysis of p(T) and h(T) data we show that the anomalous behaviour of LaAl* can be understood by assuming that in this case the electron-phonon coupling is about twice as strong. The temperature dependence of the thermopower of LaAl, also shows its exceptional position. This fact, however, cannot be simply referred to the enhanced electron-phonon coupling, because the thermopower depends much more on electronic-state properties at the Fermi energy than do the electrical and thermal resistivities. Introduction
Of the REAl, compounds, YAl,, LaAl, and LuAl, show no magnetic order even at the lowest temperatures. Although these compounds crystallize in the same structure (cubic MgCu* type) and the rare earth ions in all cases are in the 3+ state, experimental investigations performed on them reveal an exceptional position for LaAl*. Specific-heat measurements show that the y-value for LaAlz is double that of YAl,? and LuAlz [l]. LaAlz undergoes a superconducting transition at 3.3 K whereas the Y and the Lu compounds do not show superconductivity down to 0.34 K [2]. Calorimetric measurements [l] and investigations of the elastic constants [3] have shown that the Debye temperature of LaAl, is considerably lower than those of YA12 and LuAl*. Measurements of the phonon dispersion curves indicate a softening of the phonon spectrum of LaAl*, *Paper presented at the International land, March 4 - 8, 1985.
Rare Earth Conference,
0022-5088/85/$3.30
0 Elsevier Sequoia/Printed
ETH Zurich,
Switzer-
in The Netherlands
370
giving rise to a gap in the phonon density of states [ 41. From recent band structure calculations [ 51 it has been found that the f-band of LaAl, lies about 3 eV above the Fermi energy, E,, and the f-components in the electron states near EF are less than 10%. Below EF the band structures of LaA& and YAl,! are very similar. The aim of the present study of the transport phenomena (electrical and thermal resistivities as well as thermopower) was twofold. On the one hand we wanted to determine whether LaAI, also shows exceptional behaviour with respect to the transport phenomena. On the other hand, it was of interest to know how much of the anomalous transport behaviour of LaAl, could be explained by the application of known theoretical models.
Exper~ental
details
The samples were prepared by high-frequency melting in a watercooled copper boat under a protective argon atmosphere. Annealing procedures at different temperatures were subsequently applied to the samples in order to study the influence of heat treatment on the transport phenomena, which will be discussed later. The phase purity was checked by Debye-Scherrer photographs. Whereas in YAl;, and LaAl, no foreign phases were detectable, in all the LuA12 samples which we prepared small traces of a second phase were observed. Similar problems have been reported by Hungsberg and Gschneidner [ 11. It seems to us that the preparation of REAI, compounds becomes more difficult for elements at the end of the rare earths series in the Periodic Table.
Results and discussion The experimental results for the different transport properties shown below have been obtained from the same sample. Figure 1 shows the temperature dependence of the electrical resistivity of YA12, LaAlz and LuAl,. The inset to this Figure shows the superconducting transition on an expanded scale. From this measurement the superconducting transition temperature is found to be 3.30 rt 0.02 K. This value is in good agreement with the transition temperature of 3.29 K obtained from specific-heat measurements [l]. A comparison of the p uersus T curves of these three compounds shows that the curve is considerably steeper for LaAl, . It is also interesting to note that samples of different p4.2 values, as obtained by different annealing procedures, show the same deviations for LaAl,. The residual resistivity range of values for LaAl, was 0.3 - 5.2 $-‘J cm and for YAl, it was 2.8 - 18.5 ps2 cm. The simplest model to describe the electron-phonon-scattering contribution to the electrical resistivity is given by the well known BlochGriineisen formula [6] which was used to fit the experimental data. The Debye temperature, on, was used as a single fit parameter. The mean 0n value
371
Fig. 1. The (p - ~4.2) us. T curves of YAl 2, LaA12 and LuA12 (p4 2: 18.5, 3.5, 25.5 /JR cm for YA12, LaA12 and LuA12, respectively; p4.* denotes the resistkity at 4.2 K). The inset shows details of the superconducting transition for LaA12.
obtained from different annealed samples, related to the mass M of YA12 by (~REA1,/~x41,)“2~ is 320 K for YAl,, 230 K for LaAl, and 310 K for LuAl* . We observed that a decrease of the residual resistivity causes a slight increase of the Debye temperature. Since band-structure calculations reveal nearly the same density of electronic states for all these compounds [ 71, the steeper gradient of the p versus T curve for LaAlz must be attributed to a higher electron-phonon coupling. The relative strength of the electron-phonon interaction can be estimated from [ ~(0,) - p4.J/0,. The values obtained are 0.1 for YAl,! and LuA12 and 0.2 for LaAl*. It is interesting to note also that the enhancement factor in the specific heat is twice as large in LaAl* as in YA12and LuAl* (LaA12: 1.5 - 2.7; YAl*: 0.3 - 0.8; LuAl,: 0.4 - 1.2 [?I). The temperature dependence of the thermal conductivity h is given in Fig. 2. Again, a remarkably different behaviour is found for LaAl,. The X uersus T curve of LaAl, is characterized by a pronounced maximum around 18 K whereas, for higher temperatures, the increase of h(T) is smaller compared with YAl,! or LuAl*. A comparison of X(T) measurements of different heat-treated samples shows a strong dependence of the shape of the h versus T curve upon the annealing procedure, especially in the low-temperature region. Usually the electron-phonon-scattering contribution to the thermal resistivity is given by Wilson’s formula [ 81. This formula has been used to fit the experimental data. The Debye temperatures obtained from such a fit are, in general, 10 - 20% higher than the values deduced from the p data. Again, the value for LaAl* is remarkably lower than those for YAl, and LuAl,. The mean 8, values from the X data are 360 K for YA12, 260 K for LaAl, and 370 K for LuAl,. For this fit, the scattering processes contribution due to static imperfections has been assumed to be proportional to l/T over the whole temperature range; the lattice thermal conductivity was neglected [9]. This is possibly the reason for the higher values of the Debye tempera-
312
h imW/cmKJ
0
So
m
Fig. 2. The temperature LuAl*,
Eo
200
dependence
250
300
of the thermal
conductivity,
h, for
YA12,
LaAl2 and
tures obtained from the h data. For high temperatures the theoretical formula yields a constant value for X. This value is proportional to the inverse of the strength of the electron-phonon interaction. An estimate of these values of h(T + 00) from the fit yields 150 mW cm-’ K-’ for LaAlz (see Fig. 2), 320 mW cm-’ K-’ for YAlz and 380 mW cm-’ K-’ for LuAlz. Again, this roughly shows that the strength of the electron-phonon interaction is about twice as large in LaA12. Recently we have studied the influence of annealing conditions on thermopower in the case of YAl, [lo]. It has been found that scattering processes of the conduction electrons on static imperfections considerably influence the shape of the S uersus T curve. For this reason we have shown in Fig. 3 the S uersus T data of two different LaAlz and YAl,! samples. Although
Fig. 3. The temperature dependence of the thermopower for YA12, LaAl2 and LuAlz. Experimental results obtained from different heat-treated samples are given by closed and open symbols.
373
the heat treatment and the purity make a large difference in thermopower, this cannot be the reason for the different behaviour found for LaAl, on the one hand and YAl, and LuAl, on the other. From the theory of the generation of thermopower it is known that S(T) depends on the energy derivatives of quantities averaged over surfaces of constant electron energy. In the simplest approximation the logarithmic derivative of the density-of-states function appears in the expression for the thermopower. Therefore it seems that in the La and the Y compound this derivative may be different in sign. Because of the lack of a meaningful formula for S(T) with a small set of physically relevant parameters, it was not possible to analyse the S(T) data in more detail as was done for p(T) and X(T).
Acknowledgment We thank the “Hochschuljubilaumsstiftung support.
der Stadt Wien” for financial
References 1 R. E. Hungsberg and K. A. Gschneidner, Jr., J. Phys. Chem. Solids, 33 (1972) 401. 2 B. W. Roberts, J. Phys. Chem. Ref. Data, 5 (1976) 581. 3 R. J. Schiltz, Jr. and J. F. Smith, J. Appl. Phys., 45 (1974) 4681. 4 C. T. Yeh, W. Reichardt, B. Renker, N. Niicker and M. Loewenhaupt, J. Phys. (Paris), 42 (1981) C6-371. 5 A. Hasegawa and A. Yanase, J. Phys. F, 10 (1980) 847. 6 F. J. Blatt, Physics of Electronic Conduction in Solids, McGraw-Hill, New York, 1968, p. 190. 7 A. C. Switendick, in C. J. Kevane and T. Moeller (eds.), Proc. Tenth Rare Earth Research Conf., Carefree, AZ, United States Atomic Energy Commission Technical Information Center, Oak Ridge, TN, 1973, p. 235. 8 J. M. Ziman, Electrons and Phonons, Clarendon Press, Oxford, 1972, p. 391. 9 E. Bauer, E. Gratz and G. Adam, Physica B, 130 (1985) 81. 10 E. Gratz and H. Nowotny, Physica B, 130 (1985) 75.