The three elastic constants of tantalum, tungsten, and molybdenum have been measured in the temperature range between 4.2 and 300'K. The directly measured quantities Cr. and -, '(CI& -C») for molybdenum and the computed bulk moduli of all three elements show an anomalous temperature dependence. These data along with published results for other metals generally show a dif7erence in temperature dependence of the bulk modulus between 3d and 4d -5d metals. Overlap contributions to the elastic constants are found to favor an antiferromagnetic ordering. The Debye characteristic temperatures calculated from elastic constants are found to be in substantial agreement with results obtained from calorimetry.
INTRODUCTIOÑ~~~~~~~~S
Quick soundvelocity measurements by an improved pulsesuperposition methodThe "elastic constants" of a crystal are referred to a Cartesian coordinate system which has a definite relation to the crystal axes. In determining these constants from sound-velocity mea~urements at least as many measurements must be made as there are constants to be determined a?~ in general m~re than o.ne propagation direction will be used. Thus, in order to relate the m:asu:ed velocIties t.o the :lastlc properties of the crystal one needs to solve the equation of motion for the directIOn under ~onsl~erat~on, and to k?ow the transformation equations that relate the elastic properties along the propagatIOn directIOn to the desired elastic constants. In this paper a perturbation solution to the equation of motion is presented as w.ell a~ the transformation equations for triclinic and all higher symmetry crystal classes. Also pre~ented ~re slm~hfica tions that will be of use in designing experiments and reducing the data. Several mistakes III prevIOusly published work are corrected. 4
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