An X-Ray Method of Determining Rates of Diffusion in the Solid State

Abstract

data to within 0.5 percent in nine cases, and to within 1.0 percent in all cases. While the data are not sufficient to show definitely that the method of calculating densities developed in this paper is applicable to these other types of oils, there seems to be good indication that it is.Two thermodynamic quantities of interest, the isothermal compressibility and the thermal expansivity, can be calculated from the data of this paper. The compressibility can be obtained by differentiation of the density equation at the temperature corresponding to the constants a and h, and, if computed at two pressures, shows the normal decrease with increase of pressure. On the other hand, if the compressibility is calculated at two temperatures, it will be found to increase with temperature. The thermal expansivity can be calculated by applying the density equation at two temperatures at constant pressure. If computations are made at two pressures it will be found that the expansivity decreases also with increase of pressure. In regard to these derived quantities it should be noted that they cannot be calculated to an accuracy claimed for the basic density data. However, this lack of accuracy becomes important only at the lowest pressures where possible inaccuracy in measuring pressure by means of the manganin coil is recognized. An X-Ray Method of Determining Rates of Diffusion in the Solid StateJESSE DuMOND AND J. PAUL YOUTZ California Institute of Technology, Pasadena, California (Received November 7, 1939) Gold and copper were simultaneously deposited in·.,. action of diffusion alone, rapidly and automatically lose vacuum by vaporization on a plate of glass, the copper the higher Fourier harmonics of its periodic density dis· being deposited at a uniform rate while the gold was tribution function and retain the fundamental in such a deposited in one hundred stratified layers in the copper way as to render the determination of the diffusion coefby alternately raising and lowering the temperature of ficient quite accurate. The observed behavior of the dif· the molybdenum vaporizing trough containing the boiling fracted maxima seem to support these expectations as does gold. The translucent deposit so formed had a total also the absence of any intensity in higher orders than the thickness of about 1O,OOOA and hence an average interfirst. This purification by diffusion probably takes place planar distance of 100A. In an especially constructed x-ray principally during the depositing process itself while the spectrograph selective diffraction of Mo K radiation from temperatures are still quite high. Formulae are derived these stratified films was observed corresponding to the relating the observed rate of decay of the diffracted inartificially imposed periodicity of the stratification and the tensity, the artificial "grating constant" of the strata, and intensity of this diffracted image relative to the direct the diffusion coefficient. The method seems especially beam was found to fall off with time so as to indicate a prom...

Preferred orientation and interdiffusion in zinc oxide/copper oxide multilayered films

“…It was Dumond and Youtz [6] who proposed a method of obtaining a very low value of interdiffusivity,/)a, from the decay rate of the first order (n = 1) satellite X-ray intensity, I(t), in multilayered films…”

Strain Energy Effects in the Spinodal Decomposition of Cu-Ni(Fe) Nanolaminate Coatings

“…A review is presented of the formulations [1][2][3][4][5][6][7][8][9][10] for spinodal decomposition that relate to use of the X-ray diffraction method for experimental measurement [21][22][23][24][25][26][27][28][29][30][31][32][33][34] of the time-temperature dependent changes in the composition wave. In particular, reference to formulations and the equations are shown which comprise the basis to compute the higher-order gradient energy coefficients, the diffusion coefficients, and the strain energy variation with nanolaminate spacing.…”

“…The macroscopic diffusion coefficient Ď for the alloy system corresponds with an infinite composition wavelength. The relative decay in satellite intensity I ± (t) for the composition fluctuation is normalized to the Bragg peak intensity, and this value is used to determine [22][23][24][25][26]33] the amplification factor R as…”

“…The linear theory of diffusion for spinodal decomposition [1][2][3][4][5]8,[21][22][23][24] provides for the accommodation of energy associated with new evolving surfaces and interface strain for the composition fluctuations. The wavenumber dependent interdiffusivity ĎB is linearly proportional to the square of the wavenumber β 2 where the amplification factor R of growth to the composition wave equals −β 2 ·ĎB.…”

X-ray diffraction study of laser-driven solid-state diffusional mixing and new phase formation in Ni-Pt multilayers

“…Furthermore, when integrated with simple thermal excitation, the kinetics of compositional changes can be directly revealed 7 . For example, as early as 1940, it was shown that XRD methods can be used to study diffusional mixing in solids 8 . These studies, however, have primarily been limited to the quasi-static regime, i.e.…”