Anharmonicity of the Debye-Waller factor in copper, silver, and lead using Moessbauer gamma-ray diffraction

John Thomas Day, Purdue University

Abstract

Using high intensity ($\sim$70 Ci) $\sp{183}$Ta Mossbauer sources, we have measured the elastic scattering fraction values, $\cal F$, and the relative integrated scattering intensities for the (200), (400), (600), and (220) Bragg planes of copper and silver single crystals; and for the (200), (400), and (600) reflections of a lead single crystal. The experiments were done as a function of temperature from 82K to a high temperature of 1086K, 1211K, and 507K for Cu, Ag, and Pb, respectively. The $\cal F$ values were found by Mossbauer line shape studies (1), and were used to correct the measured integrated intensities for thermal-diffuse scattering, so that accurate Debye-Waller factors (DWF's) could be evaluated. The measured DWF's for Cu, Ag, and Pb each have a significant anharmonic contribution at about 50% of the melting temperature ($T\sb{m}$). Contrary of what Martin & O'Connor (2) have reported for copper, we observed no $Q\sp4$ contribution to the DWF. The anharmonic contributions to the DWF have been calculated from perturbation theory by a twelve-nearest-neighbor-central-force model, which used a three-parameter Morse potential and a modified potential by Jaswal & Girifalco (JG) (3). The DWF for Cu and Ag deviates significantly from the Morse model at about 40% and 60% of $T\sb{m}$, respectively; at about 70% of $T\sb{m}$ for Pb using the quasi-harmonic model; and about 50% of $T\sb{m}$ for Cu using the JG model. At about 50% of $T\sb{m}$, the volume dependence of the two-body potential is significant for Cu, Ag, and Pb. For Ag and Pb, the argument of the exponent of the DWF exhibits a $T\sp3$ dependence, which is most likely due to the nonlinear nature of the thermal lattice expansion at high temperatures, and corroborates the temperature dependence of the Grunisen constant measured from specific heat data by A. J. Leadbetter (4).

Degree

Ph.D.

Advisors

Mullen, Purdue University.

Subject Area

Condensation

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