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Low-temperature elastic constants of polycrystalline La2CuO4 and La1.85Sr0.15CuO4
Physica C 162-164 (1989) 460-461 North-Holland
LOW-TEMPERATURE
ELASTIC CONSTANTS OF POLYCRYSTALLINE
La2CuO 4 AND Lal.85Sr0.1sCuO 4
Hassel LEDBETTER I, S.A. KIM I, C.E. VIOLET 2, and J.D. THOMPSON s INational Institute for Standards and Technology, Boulder, CO 80303, USA ~Lawrence Livermore National Laboratory, Livermore, CA 94550, USA SLos Alamos National Laboratory, Los Alamos, NM 87545, USA
Using ultrasonic methods, we measured the 295-4-K elastic constants of superconductive La,.85Sr0.15CuO 4 and nonsuperconductive La2CuO 4. These materials show two elastic-constant similarities: nearly the same ambient-temperature elastic constants and an elastic-stiffness minimum in the 20-40-K region. Their principal difference is that La2CuO 4 softens 3% during cooling, while Lax.ssSro.,sCuO 4 softens 30%. This reversible wlde-temperature-range softening resembles a magnetic phase transition. Perhaps it relates to the large drop in spin-excitation intensity found by Shirane and coworkers using inelastic neutron scattering. Low-temperature sound velocities and elastic constants of oxide superconductors provide interest for several reasons: they represent long-wavelength acoustic phonons, which may enter the basic superconductivity mechanism*; they provide sensitive probes of various phase transitions2; they connect directly with the electron-phonon parameter, As; they lead to the elastic Debye temperature, 8D, which equals the zero-temperature specific-heat Debye temperature4; they relate to other basic physical properties such as specific heat, thermal expansivity, atomic volume, and the thermodynamic Gr~neisen parameterS; they relate to engineering properties such as fracture toughnessS; they provide checks of proposed interatomic potentials ? . We prepared specimens by usual ceramic procedures that we shall describe elsewhere. We used a MHZ-frequency pulse-echo-overlap method to determine the sound velocities, which in turn give the elastic constants 8. By x-ray diffraction, we found theoretical mass densities. Combined with Archimedes-method macroscopic densities, these led to void volume fractions. The dc-squid magnetic susceptibility showed, for the La-Sr-Cu-O, a single well-defined normal-super-conducting transition at 39 K. (See Fig. i.) Table I shows the ambient-temperature results. In this table, p denotes mass density (from x-ray diffraction), v 2 longitudinal sound velocity, v t transverse sound velocity, v m mean sound velocity, C$ longitudinal modulus, G shear modulus, B bulk modulus, E Young modulus, v Poisson ratio, Va, average atomic volume, c void volume fraction, O D elastic Debye temperature. We calculated 6 D from the zero-temperature v m and
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
V a using a standard relationship ° . Table I Void-free-state sound velocities and elastic constants of La-Cu-O and La-Sr-Cu-O La2CuO4 p(g/cm s) v$(cm/#s) vt(cm/~s) Vm(Cm/~s) C2(GPa) G(GPa) B(GPa) E(GPa) Va(k3) c 8D(K)
7.062 0.5400 0.2985 0.3326 205.9 62.92 122.0 161.1 0.280 13.61 0.0259 414.7 --
Lal.ssSr0.15CuO4 7.023 0.5693 0.3105 0.3463 227.6 67.69 137.4 174.4 0.288 13.43 0.0643 433.7 0.92
For La-Cu-O, our elastic-constant results agree well with the Voigt-Reuss-Hill average of monocrystal C lj --I° For example, the two bulk moduli are 122 and 114 GPa. Similarly, our results agree well with theoretical Cij 11. The bulk-modulus comparison is 122 versus 108 GPa. •
Table I also shows the electron-phonon parameter ~ calculated using Kresin's approximation of the Eliashberg equations s,12. In their elastic-constant behavior, La-Cu-O and La-Sr-Cu-O show two similarities. First, the ambient-temperature elastic constants are quite similar; La-Sr-Cu-O is roughly ten percent stiffer. They show nearly identical Poisson ratios, which indicates similar interatomic bonding. At low temperatures, -20 K for La-Cu--O, -40 K for La-Sr-Cu-O, they show an elastic-
H. Ledbetter et al. I Polycrystalline LaeCuO4 and Lal.85Sro. 15Cu04
stiffness minimum. This minimum may correspond to thermal-expansion anomalies 12,*s, where in La-Cu-O the transition is structural while in La-Sr-Cu-O the transition is normalsuperconductive. 5
The largest difference in the two materials appears in their temperature dependence. Upon cooling, La-Cu-O softens about three percent. La-Sr-Cu-O softens about thirty percent. Both softenings suggest irregular behavior during cooling, as found in previous studies Is-~°.
6 7.
8.
The La-Sr-Cu-O reversible, nearly hysteresisfree softening transition over a wide temperature interval suggests a second-order magnetic transition. The recent inelastic-neutronscattering study by Shirane and coworkers ~I supports this view. They found that spinexcitation intensity is "approximately constant between 300 and 150 K, drops precipitously for temperatures down to about 50 K, and is then approximately constant down to 5 K." REFERENCES i. 2.
V.Z. Kresin and S.A. Wolf, Physica C 158 (1989) 76. B. LOthi and W. Rehwald, in Structural Phase Transitions I, eds. K.A. M~ller and H. Thomas (Springer, Berlin, 1981) pp. 131-184. 1.03
9. i0. 11.
12. 13. 14. 15. 16. 17 18 19 20 21
461
Hassel Ledbetter et al., Phase Transitions, forthcoming. M. Blaekman, in Handbueh der Physik, Vol. VII, Part 1 (Springer, Berlin, 1955) pp. 323-382. Hassel Ledbetter, Physica C 159 (1989) forthcoming. R.F. Cook et al., Appl. Phys. Lett. 51 (1987) 454. R. Baetzold, Phys. Rev. B 38 (1988) 11304. H.M. Ledbetter, in Materials at Low Temperatures (Amer. Soc. Met., Metals Park, 1983) pp. 1-45. Ref. 4., p. 341, Eq. (9.11). A. Migliori et al., LANL preprint (1989). N.L. Allan and W.C. Maekrodt, Philos. Mag. A 58 (1988) 555. For the orthorhombic case, except for CII and C12, divide by 2. V. Kresin, Phys. Lett. A 122 (1987) 434. S. Bhattacharya et al., Phys. Rev. B 37 (1988) 5901. D.J. Bishop et al., Ibid. 35 (1987) 8788. L.C. Bourne et al., Ibid. 35 (1987) 8785. P. Esquinazi et al., Ibld. 36 (1987) 2316. K. Fossheim et al., Solid State Commun. 63 (1987) 531. Y. Horie et al., Ibid. 63 (1987) 653. B. L~thi et al., Jap. J. Appl. Phys. 26-3 (1987) 1127. R. Yoshizaki et al., Ibid. 26-3 (1987) 1129. G. Shirane et al., BNL preprint (1989). 1.2
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(LaSr) 2 CuO4
La2 CuO4 0.0
100
200
TEMPERATURE (K)
300
. . . . . . . . . .
0
! . . . . . . . . .
100
i . . . . . . . . .
200
300
TEMPERATURE (K)
Fig. i. Temperature dependence of elastic constants of La2CuO 4 and Lax.ssSr0.,sCuO 4. scale difference. For the superconductors, we show de magnetic suseeptibiliEy, X.
Note
LOW-TEMPERATURE
ELASTIC CONSTANTS OF POLYCRYSTALLINE
La2CuO 4 AND Lal.85Sr0.1sCuO 4
Hassel LEDBETTER I, S.A. KIM I, C.E. VIOLET 2, and J.D. THOMPSON s INational Institute for Standards and Technology, Boulder, CO 80303, USA ~Lawrence Livermore National Laboratory, Livermore, CA 94550, USA SLos Alamos National Laboratory, Los Alamos, NM 87545, USA
Using ultrasonic methods, we measured the 295-4-K elastic constants of superconductive La,.85Sr0.15CuO 4 and nonsuperconductive La2CuO 4. These materials show two elastic-constant similarities: nearly the same ambient-temperature elastic constants and an elastic-stiffness minimum in the 20-40-K region. Their principal difference is that La2CuO 4 softens 3% during cooling, while Lax.ssSro.,sCuO 4 softens 30%. This reversible wlde-temperature-range softening resembles a magnetic phase transition. Perhaps it relates to the large drop in spin-excitation intensity found by Shirane and coworkers using inelastic neutron scattering. Low-temperature sound velocities and elastic constants of oxide superconductors provide interest for several reasons: they represent long-wavelength acoustic phonons, which may enter the basic superconductivity mechanism*; they provide sensitive probes of various phase transitions2; they connect directly with the electron-phonon parameter, As; they lead to the elastic Debye temperature, 8D, which equals the zero-temperature specific-heat Debye temperature4; they relate to other basic physical properties such as specific heat, thermal expansivity, atomic volume, and the thermodynamic Gr~neisen parameterS; they relate to engineering properties such as fracture toughnessS; they provide checks of proposed interatomic potentials ? . We prepared specimens by usual ceramic procedures that we shall describe elsewhere. We used a MHZ-frequency pulse-echo-overlap method to determine the sound velocities, which in turn give the elastic constants 8. By x-ray diffraction, we found theoretical mass densities. Combined with Archimedes-method macroscopic densities, these led to void volume fractions. The dc-squid magnetic susceptibility showed, for the La-Sr-Cu-O, a single well-defined normal-super-conducting transition at 39 K. (See Fig. i.) Table I shows the ambient-temperature results. In this table, p denotes mass density (from x-ray diffraction), v 2 longitudinal sound velocity, v t transverse sound velocity, v m mean sound velocity, C$ longitudinal modulus, G shear modulus, B bulk modulus, E Young modulus, v Poisson ratio, Va, average atomic volume, c void volume fraction, O D elastic Debye temperature. We calculated 6 D from the zero-temperature v m and
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
V a using a standard relationship ° . Table I Void-free-state sound velocities and elastic constants of La-Cu-O and La-Sr-Cu-O La2CuO4 p(g/cm s) v$(cm/#s) vt(cm/~s) Vm(Cm/~s) C2(GPa) G(GPa) B(GPa) E(GPa) Va(k3) c 8D(K)
7.062 0.5400 0.2985 0.3326 205.9 62.92 122.0 161.1 0.280 13.61 0.0259 414.7 --
Lal.ssSr0.15CuO4 7.023 0.5693 0.3105 0.3463 227.6 67.69 137.4 174.4 0.288 13.43 0.0643 433.7 0.92
For La-Cu-O, our elastic-constant results agree well with the Voigt-Reuss-Hill average of monocrystal C lj --I° For example, the two bulk moduli are 122 and 114 GPa. Similarly, our results agree well with theoretical Cij 11. The bulk-modulus comparison is 122 versus 108 GPa. •
Table I also shows the electron-phonon parameter ~ calculated using Kresin's approximation of the Eliashberg equations s,12. In their elastic-constant behavior, La-Cu-O and La-Sr-Cu-O show two similarities. First, the ambient-temperature elastic constants are quite similar; La-Sr-Cu-O is roughly ten percent stiffer. They show nearly identical Poisson ratios, which indicates similar interatomic bonding. At low temperatures, -20 K for La-Cu--O, -40 K for La-Sr-Cu-O, they show an elastic-
H. Ledbetter et al. I Polycrystalline LaeCuO4 and Lal.85Sro. 15Cu04
stiffness minimum. This minimum may correspond to thermal-expansion anomalies 12,*s, where in La-Cu-O the transition is structural while in La-Sr-Cu-O the transition is normalsuperconductive. 5
The largest difference in the two materials appears in their temperature dependence. Upon cooling, La-Cu-O softens about three percent. La-Sr-Cu-O softens about thirty percent. Both softenings suggest irregular behavior during cooling, as found in previous studies Is-~°.
6 7.
8.
The La-Sr-Cu-O reversible, nearly hysteresisfree softening transition over a wide temperature interval suggests a second-order magnetic transition. The recent inelastic-neutronscattering study by Shirane and coworkers ~I supports this view. They found that spinexcitation intensity is "approximately constant between 300 and 150 K, drops precipitously for temperatures down to about 50 K, and is then approximately constant down to 5 K." REFERENCES i. 2.
V.Z. Kresin and S.A. Wolf, Physica C 158 (1989) 76. B. LOthi and W. Rehwald, in Structural Phase Transitions I, eds. K.A. M~ller and H. Thomas (Springer, Berlin, 1981) pp. 131-184. 1.03
9. i0. 11.
12. 13. 14. 15. 16. 17 18 19 20 21
461
Hassel Ledbetter et al., Phase Transitions, forthcoming. M. Blaekman, in Handbueh der Physik, Vol. VII, Part 1 (Springer, Berlin, 1955) pp. 323-382. Hassel Ledbetter, Physica C 159 (1989) forthcoming. R.F. Cook et al., Appl. Phys. Lett. 51 (1987) 454. R. Baetzold, Phys. Rev. B 38 (1988) 11304. H.M. Ledbetter, in Materials at Low Temperatures (Amer. Soc. Met., Metals Park, 1983) pp. 1-45. Ref. 4., p. 341, Eq. (9.11). A. Migliori et al., LANL preprint (1989). N.L. Allan and W.C. Maekrodt, Philos. Mag. A 58 (1988) 555. For the orthorhombic case, except for CII and C12, divide by 2. V. Kresin, Phys. Lett. A 122 (1987) 434. S. Bhattacharya et al., Phys. Rev. B 37 (1988) 5901. D.J. Bishop et al., Ibid. 35 (1987) 8788. L.C. Bourne et al., Ibid. 35 (1987) 8785. P. Esquinazi et al., Ibld. 36 (1987) 2316. K. Fossheim et al., Solid State Commun. 63 (1987) 531. Y. Horie et al., Ibid. 63 (1987) 653. B. L~thi et al., Jap. J. Appl. Phys. 26-3 (1987) 1127. R. Yoshizaki et al., Ibid. 26-3 (1987) 1129. G. Shirane et al., BNL preprint (1989). 1.2
"N
........
1.02
x'
.........
4mb • • ~'•
° ° °4"•
' ......... • ••
• °"
• •'1' • • •
•I!
1.1
1.01
.t
°
B~
o +~
1.0
% a .
: oo ~"
."
1.00
AI--
~"
•
•"
=,
%
0.9
t--
o
0
0.99
t
0.8
÷A
0.7
0.98
"G
o.976
(LaSr) 2 CuO4
La2 CuO4 0.0
100
200
TEMPERATURE (K)
300
. . . . . . . . . .
0
! . . . . . . . . .
100
i . . . . . . . . .
200
300
TEMPERATURE (K)
Fig. i. Temperature dependence of elastic constants of La2CuO 4 and Lax.ssSr0.,sCuO 4. scale difference. For the superconductors, we show de magnetic suseeptibiliEy, X.
Note