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Elastic properties and thermal expansion of the UNi5−xCux system
Physica B 163 (1990) 389-390 North-Holland
ELASTIC A.M.
PROPERTIES
VENTER”,
AND THERMAL
P. DE V. DU PLESSISh
EXPANSION
OF THE UNi,_,Cu,
SYSTEM
and P. SMITb
“Atomic Energy Corporation of S. A. (Ltd.), Pelindaba, Pretoria, South Africa bDepartrnent of Physics, Rand Afrikaans Universiq, PO Box 524, Johannesburg
2000, South Africa
Measured values of longitudinal and transverse ultrasonic velocities are given between of UN&&, after correction for thermal expansion.
10 and 300 K for polycrystalline
samples
Resistivity and specific heat measurements by Van Daal et al. [l] indicated large changes in these properties for the system UNi,_XCu, for 4 G x G 5. It was also observed for the cubic crystal that its lattice parameter a, which increases linearly for 0 G x s 3.5, undergoes an additional increase for x > 3.5. Furthermore, the electronic specific heat coefficient y was observed to increase rapidly for x > 4 and a value of y = 200 mJ/mol K’ is obtained for UC+. Van Daal et al. suggested that these results should be attributed to a mixed-valency state for the Cu-rich compounds and also remarked on the Kondo-like behaviour of the observed resistivity. In retrospect one recognises that this early observation places UCu, in the category of a group of uranium compounds that exhibit heavy fermion behaviour [2], and which in the present case also orders antiferromagnetic with T, = 15 K [3]. Recent resistivity and specific heat measurements indicate the existence of a new phase below 1 K, the nature of which is as yet unresolved [4]. Interesting elastic constant anomalies are predicted [5,6] for intermediate valence and heavy fermion compounds and have been observed most notably on single crystal specimens [5,7]. Since single crystals have not been available for this study, our ultrasonic measurements between 10 and 300 K were performed on polycrystalline samples of representative members of the UNi 5mXCu, system in order to investigate any trends in the elastic behaviour as one progresses towards the Cu-rich heavy fermion end of the series. Furthermore, thermal expansion measurements have been performed and used to effect (small) corrections of the measured velocities. Both longitudinal and transverse velocities, uL and uT respectively, have been measured at 10 MHz by a pulse-echo overlap technique using Matec equipment. Depicted in fig. 1 are the observed values of PUN = B + 4 G, where p is the density, B is the bulk modulus 0921-4526/90/$03.50 0 Elsevier Science Publishers B.V. (North-Holland)
UCu,Ni,
ucu,
180-
100 200 TEMPERATURE
300 (K)
Fig. 1. Ultrasonic measurements of put (= B + 3 G) vs. temperature for the UNi,_,Cu, system. B denotes the bulk modulus and G is the shear modulus
and G is the shear modulus. In fig. 2 values of pu: = G are plotted. Values of density ranging from 11.28 gem-’ for UNi, to 10.54gcm-’ for UCu, as calculated from the lattice parameters at room temperature [l], were used. Thermal expansion measurements were performed using the strain gauge technique and with tungsten as reference material [8]. The results shown in fig. 3 were used to correct the entities pu2 for the temperature dependence of density and pathlength before plotting it in figs. 1 and 2. The correction to the pu* values amounts to not more than 0.3% at the lowest temperature and has changed (increased) the temperature dependence by -8% for pu’, and -5% for pu:. Propagation of transverse waves suffered appreciable attenuation and we were unable to obtain data for samples with x = 1, 2 and 3. For this reason the temperature dependence of the bulk modulus is not presented for the series, but one
A.M.
390
Venter et al.
4.50+-
200 TEMPERATURE(K)
I Ultrasonic
velocities
of UNi,
1CM>
elastic moduli (B + 4 G) varies in a smooth way across the UNi 5_ ,Cu, series without noticeable renormalization effects in the Cu-rich region. It would seem as if the shear modulus undergoes a more rapid decrease in the Cu-rich region, but the lack of data for specimens with x = 1, 2 and 3 preclude establishing the complete trend. For UCu, a slight change in slope below 50 K and a dip at T, amounting to 0.025 x IO’” Nm-’ were observed for put. This is a relative small effect compared with renormalizations of up to several percent observed due to magnetoelastic and quadrupolar interactions in many f-electron systems [9,10] or for some intermediate valence and heavy fermion compounds [S, 71. In view of the considerable interest in the heavy fermion properties of UCu,, we are attempting growth of suitable single crystals of this material in order to perform a detailed study of the elastic behaviour. Such a study will give more information on this intermediate valent heavy fermion material by observing the effects of the interaction between valence fluctuations and lattice vibrations [6, 111.
300
Fig. 2. Ultrasonic mesurements of pus = G vs. temperature for the UNi ,_,CU~ system. G is the shear modulus.
The Foundation for Research Development, the Rand Afrikaans University and Atomic Energy Corporation of S.A. (Ltd.) are thanked for financial support.
References
/ 0
-’
0
I
I
200
300
1
100 TEMPERATURE
Fig. 3. Thermal measured above
expansion 75 K.
for
IKI
the
UNi,_,Cu,
system
as
notes that it takes values of B = 12.18 x 10’” Nrn-~’ for UCu, and B = 17.22 x 10’” Nm-* for UNi, at 293 K. It is concluded from fig. 1 that the combination of
[l] H.J. van Daal, K.H.J. Buschow, P.B. van Aken and M.H. van Maaren, Phys. Rev. Lett. 34 (1975) 1457. [2] H.R. Ott and 2. Fisk, in: Handbook on the Physics and Chemistry of the Actinides, A.J. Freeman and G.H. Lander, eds. (North-Holland, Amsterdam, 1987). p. 85. [3] A. Murasik, S. Ligenza and A. Zygmunt, Phys. Stat. Sol. (a) 23 (1974) K163. E. Felder, Z. Fisk and B. I41 H.R.‘ Ott, ‘H. Rudigier, Batlogg, Phys. Rev. Lett. 55 (1985) 1595. [51 B. Liithi, J. Magn. Magn. Mat. 52 (1985) 70. [61P. Thalmeier, J. Magn. Magn. Mat. 76 & 77 (1988) 299. and A. [71 T. Goto, T. Suzuki, Y. Ohe, T. Fujimura Tamaki, J. Magn. Magn. Mat. 76 & 77 (1988) 305. PI G.K. White and R.B. Roberts, High TemperaturesHigh Pressures 15 (1983) 321. Properties of Solids, G.H. (91 B. Liithi, in: Dynamical Horton and A.A. Maradudin, eds. (North-Holland, Amsterdam, 1980) p. 245. IlO1 P. Morin and D. Schmitt, J. de Phys. 49 (1988) C8-321. Phys. Rev. B 23 Vll Y. Kuroda and K.H. Bennemann, (1981) 4114.
ELASTIC A.M.
PROPERTIES
VENTER”,
AND THERMAL
P. DE V. DU PLESSISh
EXPANSION
OF THE UNi,_,Cu,
SYSTEM
and P. SMITb
“Atomic Energy Corporation of S. A. (Ltd.), Pelindaba, Pretoria, South Africa bDepartrnent of Physics, Rand Afrikaans Universiq, PO Box 524, Johannesburg
2000, South Africa
Measured values of longitudinal and transverse ultrasonic velocities are given between of UN&&, after correction for thermal expansion.
10 and 300 K for polycrystalline
samples
Resistivity and specific heat measurements by Van Daal et al. [l] indicated large changes in these properties for the system UNi,_XCu, for 4 G x G 5. It was also observed for the cubic crystal that its lattice parameter a, which increases linearly for 0 G x s 3.5, undergoes an additional increase for x > 3.5. Furthermore, the electronic specific heat coefficient y was observed to increase rapidly for x > 4 and a value of y = 200 mJ/mol K’ is obtained for UC+. Van Daal et al. suggested that these results should be attributed to a mixed-valency state for the Cu-rich compounds and also remarked on the Kondo-like behaviour of the observed resistivity. In retrospect one recognises that this early observation places UCu, in the category of a group of uranium compounds that exhibit heavy fermion behaviour [2], and which in the present case also orders antiferromagnetic with T, = 15 K [3]. Recent resistivity and specific heat measurements indicate the existence of a new phase below 1 K, the nature of which is as yet unresolved [4]. Interesting elastic constant anomalies are predicted [5,6] for intermediate valence and heavy fermion compounds and have been observed most notably on single crystal specimens [5,7]. Since single crystals have not been available for this study, our ultrasonic measurements between 10 and 300 K were performed on polycrystalline samples of representative members of the UNi 5mXCu, system in order to investigate any trends in the elastic behaviour as one progresses towards the Cu-rich heavy fermion end of the series. Furthermore, thermal expansion measurements have been performed and used to effect (small) corrections of the measured velocities. Both longitudinal and transverse velocities, uL and uT respectively, have been measured at 10 MHz by a pulse-echo overlap technique using Matec equipment. Depicted in fig. 1 are the observed values of PUN = B + 4 G, where p is the density, B is the bulk modulus 0921-4526/90/$03.50 0 Elsevier Science Publishers B.V. (North-Holland)
UCu,Ni,
ucu,
180-
100 200 TEMPERATURE
300 (K)
Fig. 1. Ultrasonic measurements of put (= B + 3 G) vs. temperature for the UNi,_,Cu, system. B denotes the bulk modulus and G is the shear modulus
and G is the shear modulus. In fig. 2 values of pu: = G are plotted. Values of density ranging from 11.28 gem-’ for UNi, to 10.54gcm-’ for UCu, as calculated from the lattice parameters at room temperature [l], were used. Thermal expansion measurements were performed using the strain gauge technique and with tungsten as reference material [8]. The results shown in fig. 3 were used to correct the entities pu2 for the temperature dependence of density and pathlength before plotting it in figs. 1 and 2. The correction to the pu* values amounts to not more than 0.3% at the lowest temperature and has changed (increased) the temperature dependence by -8% for pu’, and -5% for pu:. Propagation of transverse waves suffered appreciable attenuation and we were unable to obtain data for samples with x = 1, 2 and 3. For this reason the temperature dependence of the bulk modulus is not presented for the series, but one
A.M.
390
Venter et al.
4.50+-
200 TEMPERATURE(K)
I Ultrasonic
velocities
of UNi,
1CM>
elastic moduli (B + 4 G) varies in a smooth way across the UNi 5_ ,Cu, series without noticeable renormalization effects in the Cu-rich region. It would seem as if the shear modulus undergoes a more rapid decrease in the Cu-rich region, but the lack of data for specimens with x = 1, 2 and 3 preclude establishing the complete trend. For UCu, a slight change in slope below 50 K and a dip at T, amounting to 0.025 x IO’” Nm-’ were observed for put. This is a relative small effect compared with renormalizations of up to several percent observed due to magnetoelastic and quadrupolar interactions in many f-electron systems [9,10] or for some intermediate valence and heavy fermion compounds [S, 71. In view of the considerable interest in the heavy fermion properties of UCu,, we are attempting growth of suitable single crystals of this material in order to perform a detailed study of the elastic behaviour. Such a study will give more information on this intermediate valent heavy fermion material by observing the effects of the interaction between valence fluctuations and lattice vibrations [6, 111.
300
Fig. 2. Ultrasonic mesurements of pus = G vs. temperature for the UNi ,_,CU~ system. G is the shear modulus.
The Foundation for Research Development, the Rand Afrikaans University and Atomic Energy Corporation of S.A. (Ltd.) are thanked for financial support.
References
/ 0
-’
0
I
I
200
300
1
100 TEMPERATURE
Fig. 3. Thermal measured above
expansion 75 K.
for
IKI
the
UNi,_,Cu,
system
as
notes that it takes values of B = 12.18 x 10’” Nrn-~’ for UCu, and B = 17.22 x 10’” Nm-* for UNi, at 293 K. It is concluded from fig. 1 that the combination of
[l] H.J. van Daal, K.H.J. Buschow, P.B. van Aken and M.H. van Maaren, Phys. Rev. Lett. 34 (1975) 1457. [2] H.R. Ott and 2. Fisk, in: Handbook on the Physics and Chemistry of the Actinides, A.J. Freeman and G.H. Lander, eds. (North-Holland, Amsterdam, 1987). p. 85. [3] A. Murasik, S. Ligenza and A. Zygmunt, Phys. Stat. Sol. (a) 23 (1974) K163. E. Felder, Z. Fisk and B. I41 H.R.‘ Ott, ‘H. Rudigier, Batlogg, Phys. Rev. Lett. 55 (1985) 1595. [51 B. Liithi, J. Magn. Magn. Mat. 52 (1985) 70. [61P. Thalmeier, J. Magn. Magn. Mat. 76 & 77 (1988) 299. and A. [71 T. Goto, T. Suzuki, Y. Ohe, T. Fujimura Tamaki, J. Magn. Magn. Mat. 76 & 77 (1988) 305. PI G.K. White and R.B. Roberts, High TemperaturesHigh Pressures 15 (1983) 321. Properties of Solids, G.H. (91 B. Liithi, in: Dynamical Horton and A.A. Maradudin, eds. (North-Holland, Amsterdam, 1980) p. 245. IlO1 P. Morin and D. Schmitt, J. de Phys. 49 (1988) C8-321. Phys. Rev. B 23 Vll Y. Kuroda and K.H. Bennemann, (1981) 4114.