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Elastic properties of polycrystalline rare earth-cobalt laves compounds
Journal of Magnetism and Magnetic Materials 7 (1978) 361-364 0 North-Holland Publishing Company
ELASTIC PROPERTIES OF POLYCRYSTALLINE
RARE EARTH-COBALT
LAVES COMPOUNDS
H. KLIMKER and M. ROSEN Nuclear Research Center-Negev and Department Beersheva. Israel
of Materials Engineering,
Ben-Gurion
University of the Negev,
The elastic moduli of the RCo2 compounds have been measured in the temperature range between 4.2 to 300 K. A magneto-elastic lattice softening was observed in the magnetically ordered state. This effect is particularly large in NdCo2, SmCo2, and TbCo2. In addition NdCo2 and HoCo2 exhibit spin reorientations at 12 and 42 K, respectively, which appear as a narrow dip in the elastic moduli. At the Curie temperature of these compounds a prominent anomaly in the adiabatic compressibility is observed. The shape of the anomalies in the elastic moduli of these compounds is indicative of a first order transition observed in DyCo2, HoCo2, and ErCo2. The Curie temperature deduced from the elastic moduli is in satisfactory agreement with the temperature determined previously. The anomalous behavior of the elastic constants in the paramagnetic temperature range is attributed to crystal field effects of a similar character to that observed in RAl2 compounds.
The rare earth-transition Laves phase compounds of the MgCa2 structure exhibit pronounced anisotropy and magnetoelastic effects in their magnetic behavior [l-3]. The complex variety of the magnetic properties of the rare earth-cobalt compounds, RCo2, is governed by the interaction between the 4f localized shells of the rare earths and the crystal fields. The present study is concerned with the behavior of the elastic moduli and magnetoelasticity of RCo2 com-
pounds, where R = Y, Pr, Nd, Sm, Cd, Tb, Dy, Ho, Er, Tm and Lu. An ultrasonic pulse-echo technique was employed to determine the variation of the sound velocities over a wide temperature range [2]. Samples were prepared from high-purity metals in an arc furnace under an inert atmosphere. X-ray, metallographic and microprobe examinations revealed single-phased, stoichiometric structures. Table 1 summarizes the values of the elastic moduli
Table 1 Values of Young and shear moduli, adiabatic compressibility, and Debye temperatures of RCo2 Laves compounds at 4.2 and 300 K E (10” dyn/cm)2 4.2 K YCo2 Prcoz NdCo2 SmCo2 GdCo2 Tbcoz DyCo2 HoCo2 ErCo2 TmCo2 LuCo2
9.326 5.915 6.575 4.887 7.186 7.814 9.056 8.661 9.615 8.186 12.648
E = Young’s modulus; G = shear modulus;
G (10”
300 K 9.118 6.199 6.740 6.021 7.227 8.177 8.578 8.969 9.629 9.872 11.676
4.2 K
dyn/cm)’ 300 K
3.531 2.127 2.376 1.719 2.617 2.856 3.359 3.192 3.581 2.980 4.787
3.461 2.236 2.448 2.155 2.643 3.001 3.160 3.296 3.560 3.65 1 4.380
K, = adiabatic compressibility;
f?D= Debye temperature. 361
KS (10-13cm2/dyn)
4.2 K
300 K
11.55 11.13 10.62 9.67 10.59 10.13 10.06 9.94 9.820 9.26 8.49
12.04 11.00 10.98 10.30 11.01 10.10 9.99 9.34 9.19 8.99 8.59
8D (K) 4.2 K 293 208 216 182 220 229 245 238 251 229 283
300 K 290
213 219 203 221 234 238 242 250 252 272
H. Klimker, M. Rosen /Elastic
362
moduli of RCo2 compounds
3.2 1
2.9
2.8 8.0
I 0
TEMPERATURE
Fig. 1. The temperature
dependence
of the Young
300
200
100
(
(E), shear (G) moduli,
(I$ G) compressibilities (K,), and Debye temperatures (0,) of the eleven compounds investigated between 4.2 and 300 K. With the exception of SmCo, values of the elastic moduli increase with the lanthanide contraction. The temperature dependence of the elastic properties of these compounds, except for YCoa and LuCoa, shows a variety of magnetic transitions. A typical behavior is displayed in figs. 1 and 2, for DyCoa and TbCoz, respectively. Table 2 shows the Curie temperatures (T,) of the magnetically ordering compounds, and the magnitude of the elasticity anomalies in the vicinity of the transition points. The Curie point is characterized by a peak in the adiabatic compressibility, K,, and by a dip in the elastic moduli, E and G, indicating elastic softening effects. With the exception of HoCoz, which displays a spin reorientation at 12 K, the softening of the other compounds recovers with decreasing temperature. The compounds (table 2) can roughly be divided into two groups, according to the magnitude of the elastic softening effect. A rather small lattice softening, less than
K
t and adiabatic
compressibility
(K,) of DyCo2.
lo%, is observed in DyCoa, HoCo2 and ErCo2. However, these compounds display large anomalies in the adiabatic compressibility, table 2 and figs. 1 and 2. The shape and magnitude of the compressibility anomalies indicate a first order transition. This is in satisfactory agreement with lattice parameter measurements [4,51. TbCoa (fig. 2) exhibits a very large elastic softening below T,, extending over a wide temperature interval. The A-type behavior of the adiabatic compressibility is indicative of a second order magnetic transition. A similar softening effect is observed in SmCo2 and NdCo2. The large lattice softening in the group of compounds represented by TbCoz and SmCo, is due to magnetoelastic origin. An analogous behavior was observed in TbFea and SmFes which display particularly high magnetostriction and AI? effects [2,6]. In these compounds the anisotropy and magnetoelastic behavior, and consequently the elastic softening, is dependent on the interaction between the 4f localized shells and the crystal fields.
363
H. Klimker, M. Rosen /Elastic mod& of RCo2 compounds
-12.5
9.0
-12.0
-11.5
“E :
i %
g 2.8 = = u 2.6
-11.0 -?I
-10.5
r"
-10.0
2.4 9.5
6.5 0
100 TEMPERATURE
200 ( K
1
Fig. 2. The temperature dependence of Young (E), shear (C) moduli, and adiabatic compressibility
dependence of the elastic moduli of NdCoa, GdCoa, and HoCoa show additional spin reorientation effects at 42,220 and 12 K, respectively. The temperature
Table 2 Curie temperatures and elasticity anomalies of RCoz Laves compounds
Prcoz NdCo2 SmCo2 Gdcoz Tbco2 DyCo2 HoCo2 E&o2 TmCo2
Tc (K)
Gp - Ef)/Ep (%I
(Kf - K,/K, (%)
34 98 204 398 230 135 89 30 4
16.5 23.1 21.8 15.9 20.2 5.2 4.5 7.5 20.9
7.5 11.9 5.0 12.7 21.9 44.9 49.3 24.0 7.2
T, = Curie temperature. (Ep - Ef)/Ep = elastic softening during the paramagnetic to ferromagnetic transition. (Kf - Kp)/Kp = adiabatic compressibility peak during the magnetic transition.
(K,) of TbCoz.
These results are in satisfactory agreement with Mossbauer effect measurements [7]. The elasticity anomaly observed in GdCo2 is relatively small and extends over a wide transition temperature interval of about 150 K, centered around 220 K. Such behavior is typical of compounds in which the magnetocrystalline-anisotropy energy is rather small. The behavior of the elastic moduli in the paramagnetic state of SmCo2, DyCo2, TbCoa, HoCo2 and TmCo2 is almost temperature independent. In PrCo2 and NdCo2, between r, and room temperature, an anomalous positive slope of the elastic moduli was observed. This behavior was attributed to crystal field effects [8].
References (11 A.E. Clark and H.S. Belson, Phys. Rev. B6 (1972) 3642. [2] H. Klimker, M. Rosen, M.P. Dariel and U. Atzmony, Phys. Rev. BlO (1974) 2968. [ 31 D. Gignoux, F. Givord and R. Lemaire, Phys. Rev. B12 (1975) 3878.
364
H. Klimker, M. Rosen / Elastic moduli of RCo2 compounds
[4] R. Minakata, M. Shiga and N. Nakamura, .I. Phys. Sot. Jap. 41 (1976) 1435. ]5] D. Bloch, D.M. Edwards, M. Shimizu and J. Voiron, J. Phys. F: Metal Phys. 5 (1975) 1217. [6] M. Rosen, H. Klimker, U. Atzmony and M.P. Dariel, Phys.
Rev. B9 (1974) 254. [7] U. Atzmony, M.P. Dariel and G. Dublon, Phys. Rev. B14 (1976) 3713. [8] M. Godet and H.G. Purwins, Helv. Phys. Acta 49 (1976) 821.
ELASTIC PROPERTIES OF POLYCRYSTALLINE
RARE EARTH-COBALT
LAVES COMPOUNDS
H. KLIMKER and M. ROSEN Nuclear Research Center-Negev and Department Beersheva. Israel
of Materials Engineering,
Ben-Gurion
University of the Negev,
The elastic moduli of the RCo2 compounds have been measured in the temperature range between 4.2 to 300 K. A magneto-elastic lattice softening was observed in the magnetically ordered state. This effect is particularly large in NdCo2, SmCo2, and TbCo2. In addition NdCo2 and HoCo2 exhibit spin reorientations at 12 and 42 K, respectively, which appear as a narrow dip in the elastic moduli. At the Curie temperature of these compounds a prominent anomaly in the adiabatic compressibility is observed. The shape of the anomalies in the elastic moduli of these compounds is indicative of a first order transition observed in DyCo2, HoCo2, and ErCo2. The Curie temperature deduced from the elastic moduli is in satisfactory agreement with the temperature determined previously. The anomalous behavior of the elastic constants in the paramagnetic temperature range is attributed to crystal field effects of a similar character to that observed in RAl2 compounds.
The rare earth-transition Laves phase compounds of the MgCa2 structure exhibit pronounced anisotropy and magnetoelastic effects in their magnetic behavior [l-3]. The complex variety of the magnetic properties of the rare earth-cobalt compounds, RCo2, is governed by the interaction between the 4f localized shells of the rare earths and the crystal fields. The present study is concerned with the behavior of the elastic moduli and magnetoelasticity of RCo2 com-
pounds, where R = Y, Pr, Nd, Sm, Cd, Tb, Dy, Ho, Er, Tm and Lu. An ultrasonic pulse-echo technique was employed to determine the variation of the sound velocities over a wide temperature range [2]. Samples were prepared from high-purity metals in an arc furnace under an inert atmosphere. X-ray, metallographic and microprobe examinations revealed single-phased, stoichiometric structures. Table 1 summarizes the values of the elastic moduli
Table 1 Values of Young and shear moduli, adiabatic compressibility, and Debye temperatures of RCo2 Laves compounds at 4.2 and 300 K E (10” dyn/cm)2 4.2 K YCo2 Prcoz NdCo2 SmCo2 GdCo2 Tbcoz DyCo2 HoCo2 ErCo2 TmCo2 LuCo2
9.326 5.915 6.575 4.887 7.186 7.814 9.056 8.661 9.615 8.186 12.648
E = Young’s modulus; G = shear modulus;
G (10”
300 K 9.118 6.199 6.740 6.021 7.227 8.177 8.578 8.969 9.629 9.872 11.676
4.2 K
dyn/cm)’ 300 K
3.531 2.127 2.376 1.719 2.617 2.856 3.359 3.192 3.581 2.980 4.787
3.461 2.236 2.448 2.155 2.643 3.001 3.160 3.296 3.560 3.65 1 4.380
K, = adiabatic compressibility;
f?D= Debye temperature. 361
KS (10-13cm2/dyn)
4.2 K
300 K
11.55 11.13 10.62 9.67 10.59 10.13 10.06 9.94 9.820 9.26 8.49
12.04 11.00 10.98 10.30 11.01 10.10 9.99 9.34 9.19 8.99 8.59
8D (K) 4.2 K 293 208 216 182 220 229 245 238 251 229 283
300 K 290
213 219 203 221 234 238 242 250 252 272
H. Klimker, M. Rosen /Elastic
362
moduli of RCo2 compounds
3.2 1
2.9
2.8 8.0
I 0
TEMPERATURE
Fig. 1. The temperature
dependence
of the Young
300
200
100
(
(E), shear (G) moduli,
(I$ G) compressibilities (K,), and Debye temperatures (0,) of the eleven compounds investigated between 4.2 and 300 K. With the exception of SmCo, values of the elastic moduli increase with the lanthanide contraction. The temperature dependence of the elastic properties of these compounds, except for YCoa and LuCoa, shows a variety of magnetic transitions. A typical behavior is displayed in figs. 1 and 2, for DyCoa and TbCoz, respectively. Table 2 shows the Curie temperatures (T,) of the magnetically ordering compounds, and the magnitude of the elasticity anomalies in the vicinity of the transition points. The Curie point is characterized by a peak in the adiabatic compressibility, K,, and by a dip in the elastic moduli, E and G, indicating elastic softening effects. With the exception of HoCoz, which displays a spin reorientation at 12 K, the softening of the other compounds recovers with decreasing temperature. The compounds (table 2) can roughly be divided into two groups, according to the magnitude of the elastic softening effect. A rather small lattice softening, less than
K
t and adiabatic
compressibility
(K,) of DyCo2.
lo%, is observed in DyCoa, HoCo2 and ErCo2. However, these compounds display large anomalies in the adiabatic compressibility, table 2 and figs. 1 and 2. The shape and magnitude of the compressibility anomalies indicate a first order transition. This is in satisfactory agreement with lattice parameter measurements [4,51. TbCoa (fig. 2) exhibits a very large elastic softening below T,, extending over a wide temperature interval. The A-type behavior of the adiabatic compressibility is indicative of a second order magnetic transition. A similar softening effect is observed in SmCo2 and NdCo2. The large lattice softening in the group of compounds represented by TbCoz and SmCo, is due to magnetoelastic origin. An analogous behavior was observed in TbFea and SmFes which display particularly high magnetostriction and AI? effects [2,6]. In these compounds the anisotropy and magnetoelastic behavior, and consequently the elastic softening, is dependent on the interaction between the 4f localized shells and the crystal fields.
363
H. Klimker, M. Rosen /Elastic mod& of RCo2 compounds
-12.5
9.0
-12.0
-11.5
“E :
i %
g 2.8 = = u 2.6
-11.0 -?I
-10.5
r"
-10.0
2.4 9.5
6.5 0
100 TEMPERATURE
200 ( K
1
Fig. 2. The temperature dependence of Young (E), shear (C) moduli, and adiabatic compressibility
dependence of the elastic moduli of NdCoa, GdCoa, and HoCoa show additional spin reorientation effects at 42,220 and 12 K, respectively. The temperature
Table 2 Curie temperatures and elasticity anomalies of RCoz Laves compounds
Prcoz NdCo2 SmCo2 Gdcoz Tbco2 DyCo2 HoCo2 E&o2 TmCo2
Tc (K)
Gp - Ef)/Ep (%I
(Kf - K,/K, (%)
34 98 204 398 230 135 89 30 4
16.5 23.1 21.8 15.9 20.2 5.2 4.5 7.5 20.9
7.5 11.9 5.0 12.7 21.9 44.9 49.3 24.0 7.2
T, = Curie temperature. (Ep - Ef)/Ep = elastic softening during the paramagnetic to ferromagnetic transition. (Kf - Kp)/Kp = adiabatic compressibility peak during the magnetic transition.
(K,) of TbCoz.
These results are in satisfactory agreement with Mossbauer effect measurements [7]. The elasticity anomaly observed in GdCo2 is relatively small and extends over a wide transition temperature interval of about 150 K, centered around 220 K. Such behavior is typical of compounds in which the magnetocrystalline-anisotropy energy is rather small. The behavior of the elastic moduli in the paramagnetic state of SmCo2, DyCo2, TbCoa, HoCo2 and TmCo2 is almost temperature independent. In PrCo2 and NdCo2, between r, and room temperature, an anomalous positive slope of the elastic moduli was observed. This behavior was attributed to crystal field effects [8].
References (11 A.E. Clark and H.S. Belson, Phys. Rev. B6 (1972) 3642. [2] H. Klimker, M. Rosen, M.P. Dariel and U. Atzmony, Phys. Rev. BlO (1974) 2968. [ 31 D. Gignoux, F. Givord and R. Lemaire, Phys. Rev. B12 (1975) 3878.
364
H. Klimker, M. Rosen / Elastic moduli of RCo2 compounds
[4] R. Minakata, M. Shiga and N. Nakamura, .I. Phys. Sot. Jap. 41 (1976) 1435. ]5] D. Bloch, D.M. Edwards, M. Shimizu and J. Voiron, J. Phys. F: Metal Phys. 5 (1975) 1217. [6] M. Rosen, H. Klimker, U. Atzmony and M.P. Dariel, Phys.
Rev. B9 (1974) 254. [7] U. Atzmony, M.P. Dariel and G. Dublon, Phys. Rev. B14 (1976) 3713. [8] M. Godet and H.G. Purwins, Helv. Phys. Acta 49 (1976) 821.