Elastic constants of polycrystalline Y 1 Ba 2 Cu 3 O x
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Elastic constants of polycrystalline Hassel Ledbetter Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Boulder, Colorado 80303 (Received 15 July 1991; accepted 23 July 1992)
We measured the elastic constants of polycrystalline Y1Ba2Cu3O;c with eleven oxygen contents varying from 6.2 to 6.9. Reported properties include sound velocities; bulk, shear, Young's moduli; Poisson ratio; Debye temperature. After correction to the void-free state, the measurements fail to show a systematic dependence on oxygen content. Focusing on the bulk modulus, all measurements fall below an ionic-crystal model prediction, by 5-50%. We attribute this macroscopic softness to either microcracks or weak grain-boundary mechanical linkages. For the case x = 6.9, we suggest a set of intrinsic elastic constants. Both our understanding of the high-!Tc oxide superconductors and their engineering applications require knowing their elastic constants. Despite enormous study, these constants remain uncertain. The present study focused on eleven polycrystalline YiBaaCusOj materials, where x ranged from 6.2 to 6.9. Specimens with roughly similar geometries were measured under similar conditions with one apparatus. This apparatus, by a megahertz-frequency pulse-echooverlap method, measures group velocity v, which combines with mass density p to give an elastic stiffness C = pv2. Details of equipment and methods appear elsewhere.1'2 Specimens were obtained from various laboratories. All were prepared by the usual sintering methods. Magnetic-susceptibility measurements suggested that, except for one with low oxygen content, all were superconductors. We examined all specimens optically and with x-ray diffraction. We discarded all specimens containing more than 5% impurity phase(s). For example, we found that an x =* 6.0 specimen contained about 10% Y 2 BaCu0 5 . Specimen 1 (x = 6.2) contained some anomalous, nonidentified diffraction peaks. Specimens near x = 6.9 tended to show BaCuO 2 , Y 2 BaCu0 5 , Y2O3, and perhaps BaCu2O2 and YCuO 2 . Table I shows the measured ambient-temperature elastic constants. The void content c was estimated from macroscopic and microscopic mass densities. Oxygen content x was determined by either iodine titration, x-ray diffraction, or both. Because specimen 2 showed a magnetic Tc, its oxygen content must be higher than 6.21. Perhaps impurity phases obscured the x-ray-diffraction results. Tc was estimated from the midpoint of the x(T) curve. Macroscopic mass density was determined by Archimedes' method. Microscopic density (shown in Table I) was determined by x-ray diffraction. Ultra-
sonic velocities vi and vt resulted from propagating waves with longitudinal and transverse polarizations. For most cases, these represent averages over direction to eliminate texture effects, which never exceeded a few percent. From the sound velocities, using standard formulas, we derived the elastic stiffnesses B = bulk modulus, E = Young's modulus, G = shear modulus, and v = the Poisson ratio. Th
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