Monocrystal elastic constants of orthotropic Y 1 Ba 2 Cu 3 O 7 : An estimate
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Monocrystal elastic constants of orthotropic An estimate Hassel Ledbetter and Ming Lei Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Boulder, Colorado 80303 (Received 19 February 1991; accepted 18 June 1991)
For Y!Ba2Cu3O7, using only reported monocrystal measurements and some analysistheory, we estimated the complete nine-component orthotropic-symmetry elastic-stiffness matrix, the Voigt C^ matrix. Comparison with very-high-frequency tetragonal-symmetry phonon-dispersion results shows good agreement (9% on average), except for Ci 2 .
A crystal's elastic-stiffness constants C^ represent basic cohesive properties related to many other solidstate physical properties. For YiBa2Cu 3 O 7 , these constants remain uncertain because existing crystals are too small for usual measurement methods. The usual necessary size, a few mm, is nonavailable by present crystal-growth methods. Since Y!Ba2Cu3O7 possesses orthotropic symmetry (Pmmm, D\h, oP13, no. 47), it exhibits nine independent C^. Although YxBaaCusO? received enormous study, only one report,exists of the complete C^. Reichardt and coworkers1 derived them from phonondispeision curves obtained by inelastic neutron scattering. However useful, the Reichardt-coworker results (see Table I) present some problems. First, their C^ represent tetragonal symmetry, thus only six of the nine Cij. Second, their C^ fail to yield by Voigt-Reuss-Hill 2 averaging the correct bulk modulus: B = 115 GPa reported by Aleksandrov and coworkers.3 Third, by usual calculations,4 their C^ give a slightly low Debye characteristic temperature: QD (Reichardt) = 423 K versus the specific-heat value5 ®D — 440 K. Fourth, their C 44 differs from a reported ultrasonic (megahertz-
frequency) value by a 2 factor. This raises a perennial question: do the Cij determined at lattice-vibration frequencies correspond to the usual low-frequency longwavelength values? Fifth, elastic constants from phonondispersion-slopes du/dk usually have larger errors than values measured ultrasonically. Here, we report our view of the YiBa 2 Cu 3 07 elastic constants (see Table I), a view based mainly on measurements on monocrystals combined with some analysis-theory. We used no polycrystal measurement results. Especially, we avoided all high-pressure measurements made on polycrystals, a problem we described elsewhere.6 First, we adopted two gigahertz-frequency measurements of Cii and C 3 3 reported by Golding and coworkers.7 To get C22, we adopted a ratio calculated by Baetzold8 by an empirical two-body-potential method: C 2 2 /Cii = 1.091. To get C12, C13, C 23 , we used the three principal monocrystal linear compressibilities found by Aleksandrov and coworkers3 (see Table I). To solve this problem, we found it convenient to focus on the strain
TABLE! I. Measured and estimated elastic constants of monocrystalline
Source Aleksandrov et al? Baumgart et al.16'17 Golding et al.1 Reichardt et al.1 Saint-Paul et al.l3~15 Present aAdjusted
C
C2
C33
C4
211 223 a 230
35
230
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