Doctoral Dissertations

Date of Award

3-1970

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Metallurgical Engineering

Major Professor

Charlie R. Brooks

Abstract

This dissertation deals with an analysis of contributions to the high temperature specific heat capacity of solid gold, lead, and zinc. The specific heat capacities have been measured with high accuracy from 300°K to 1200°K for gold, and into the liquid region for lead and zinc. These data then have been used as a basis for estimating the contribution of anharmonic lattice vibrations to the specific heat capacity. The specific heat capacity at constant pressure Cp was converted to the constant volume condition by applying the dilation correction, Then the specific heat capacity at constant volume Cv was assumed to be formed by four independent contributions: (C1v)v (c2v)v, related to the formation of equilibrium monvacancies and divacancies, respectively, in lattice; (CL)V, related to the harmonic vibrations of the atoms in the lattice, CE)v, related to changes in the energy distribution of the conduction electrons; and (Ca)v, related to the anharmonic vibrations of the lattice. An analysis and summary of the expressions given in the literature for each of these independent contributions is presented. The results of the of rather extensive and careful measurements of the specific heat capacity of high purity (greater than 99.9 weight percent pure) gold, lead and zinc are presented and compared to other data from the literature, The measurements made in this research have a reproducibility of ± 1.0 per cent; and the absolute error is believed to lie within this range, The Cp results for gold are around four per cent higher than those obtained in other investigations. For solid lead and zinc the Cp results are within ± 1.0 percent of those of other investigations. The data of the present investigation has been treated statistically in order to represent Cp for each metal by a polynomial, Cv was obtained by applying the dilation correction to the experimental Cp from this investigation. The dilation correction requires the coefficient of thermal expansion, the molar volume, and the isothermal compressibility, all as a function of temperature. A critical analysis was made of value of these quantities from the literature, and the data available were treated statistically and fitted by polynomials. Where sufficient data. do not exist, extrapolations of existing data were used. From the uncertainties in the quantities in the dilation correction and in the experimental Cp, an estimate of the uncertainty in the Cv was obtained. (Cl)v was calculated by using the Debye model of a harmonic lattice characterized by a single Debye temperature, obtained from the literature. (Ce)v was calculated from the Sommerfeld theory, assuming the contribution to be proportional to the absolute temperature; the proportionality constant was taken as the conventional electronic specific heat capacity coefficient, obtained from the literature. The contribution from the formation of equilibrium monovacancies and divacancies was calculated from the temperature derivative of the energy of formation of each defect. Values of the molar energy and entropy of formation of each type of defect, which are required for the calculations, were obtained from the literature. The variation in the values of the quantities needed to calculate each of the contributions (CL)v, (CE)v and [

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