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360 TEMPERATURE agreement anomalous behavior atom attenuation b.c.c. matrix Bragg angle calculated cent alloy cent Nb alloys composition crystallographic directions curve decrease difference diffraction displacement vector dynes/cm dynes/cm Elastic Constant Data elastic constant measurements elastic energy density elastic waves electron equation error evaluate extra reflections force constants fraction of omega function give group velocity heat treatment Hewlett-Packard increase in intensity independent elastic constants lattice parameter linear longitudinal displacement longitudinal mode longitudinal wave low temperature maximum megahertz Mg temperature mode of propagation Nb as quenched Nb content Nb crystal Nb-Zr as quenched Niobium omega particles omega phase phase velocity present study quartz transducer quenched alloy resonance frequency shear constant shown in Fig signal single crystals sound velocity specimen holder stants stress tensors TABLE Temperature dependence TEMPERATURE K Figure tion transverse modes TRANSVERSE WAVE unit cell values variation volume fraction wavelength X-ray measurements X-ray traces zero Zr-Nb system