An X-ray study of lattice-distortion in rhodium

Measurements of the intensities of X-ray reflections from filed and chemically prepared specimens of rhodium powder are made relatively to each other and are then converted to absolute units by comparison with suitable aluminium reflections. The scattering factors, fT, obtained experimentally for both types of powder agree satisfactorily for the higher order reflections, with a theoretically estimated scattering factor, but for the lower order reflections the experimental values are markedly low, which suggests the existence of appreciable primary extinction. Detailed calculation shows that the variation of [fT(filed)/fT(chem.)] with (sin θ)/λ can be accounted for almost entirely in terms of primary extinction, and that there is very little residual effect due to lattice-distortion of the kind found in similar experiments with copper and nickel. Measurements of the widths of the reflections are made for both types of powder; for the filed powder a total of 23 reflections for five radiations are measured. The results are discussed in relation to various theories of the nature of lattice distortion produced in metals by cold-work. The results are shown to be incompatible with the view that the broadening is due to smallness of crystal-size since the observed widths when plotted against theta fall on or near a mean curve, whereas with small crystal broadening there should be a separation according to wave-length. The difficulties attendant on any explanation in terms of periodic or semiperiodic lattice-distortion which have been discussed by Boas are briefly outlined. It is shown that the observed results may be explained in terms of a variation of the lattice spacing about the normal mean value due to the stresses caused by the filing process. Assuming a Gaussian distribution for the variation (δa/a), the spread of the distribution is calculated. In this calculation there is only one adjustable parameter and this fixes the spread of the distribution. From this distribution a calculation is made of the internal energy of the worked metal.