Is Y 1 Ba 2 Cu 3 O 7 stiff or soft?
- PDF / 367,444 Bytes
- 4 Pages / 593.28 x 841.68 pts Page_size
- 27 Downloads / 247 Views
Is YiBa 2 Cu 3 O 7 stiff or soft? Hassel Ledbetter and Ming Lei Institute of Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Boulder, Colorado 80303 (Received 6 September 1989; accepted 16 October 1989) Using several measured and calculated physical properties, we argue that the high-Tc metal-oxide superconductor YiBa 2 Cu 3 O 7 is elastically soft compared with BaTiO3 or SrTiO3. We conclude that the bulk modulus equals approximately 107 GPa, despite several high-pressure x-ray diffraction studies that report values up to approximately 200 GPa. Part of the argument uses an ionic-crystal-model calculation of the bulk modulus. Along with volume and cohesive energy, the bulk modulus (reciprocal compressibility) represents one of a solid's three basic cohesive properties, which link lattice dynamics with electronic structure. The bulk modulus, B, relates directly to, and provides a good test of, interatomic potentials: B = V(d2U/dV2) = (ro2/9Vo)(d2U/dr2). (1) Here, U denotes internal energy; V, volume; r, effective atomic radius; and subscript zero, equilibrium value. The bulk modulus relates to various thermodynamic properties. For example, y = BfiV/C. (2) Here, y denotes Griineisen parameter (the most useful single parameter for characterizing anharmonic properties), /3 denotes volume thermal expansivity, and C, heat capacity. Actually, as shown by Eq. (1), B represents a harmonic property and this shows also in the EinsteinMadelung-Sutherland relationship for what we now call the Einstein temperature: © £ = KVall6M-1/2B112. (3) Here, Va denotes atomic volume; M, atomic mass; and K, a dimensionless material-independent parameter. Using a simple lattice-dynamics model,1 we can show that @£ = (3/4) ®£>, the Debye characteristic temperature. The Debye temperature enters explicitly into the Bardeen-Cooper-Schrieffer2 relationship for the superconducting critical temperature [their Eq. (3.29)]: Tc = 1.14 &D exp(-A- 1 ). (4) Here, A denotes the electron-phonon coupling parameter, which also depends on ®D, varying as ®D~2. Subsequent stronger-coupling models by McMillan3 and by Allen and Dynes 4 retain a dependence on ®D. Indeed, after the emergence of high-71,; metal-oxide superconductors, Ginsburg5 estimated the maximum expected Tc as &D/5. From the Eliashberg equation, Kresin6 derived a relationship applicable to the full range of A: Tc = 1.14 ®n (e2/A - l)~m.
(5)
Unlike the BCS and McMillan relationships, Kresin's relationship predicts that, for the same A, elastic softening (lower B) always increases Tc. Thus, for many reasons given above, and for many others omitted for brevity, we see the need to know the bulk-modulus value. And, we need to know it within an inaccuracy commensurate with its companion thermodynamic properties, say a few percent. At least five7"11 high-pressure x-ray diffraction studies on YiBa 2 Cu 3 O 7 report that B ranges between 100 and 196 GPa. Other authors used the higher values to estimate other thermodynamic properties, for example the Griineise
Data Loading...
