Determination of Twin Fault Probabilities from the Diffraction Patterns of fcc Metals and Alloys

Twin faults may be detected from diffraction patterns of fcc metals and alloys by two existing methods: (1) from the sine coefficients of a one‐dimensional Fourier series representing the peak, and (2) from the excess intensity between two peaks which are asymmetric in opposite directions, such as the 111 and 200. However, the contribution of twin faults to the particle size measured by Fourier analysis appears too large when the fault probabilities are determined by these methods. A third technique has been developed based on the displacement of the center of gravity of a peak from the peak maximum, ΔC.G. The displacements for the 111 and 200 peaks are related to the twin fault probability β: $$\begin{array}{c}\Delta \mathrm{C.G.}{\mathrm{\hspace{0.17em}(}}^{\circ }{\text{2θ)}}_{111}\text{=+11β\hspace{0.17em}}\tan {\theta }_{111}\\ \Delta \mathrm{C.G.}{\mathrm{\hspace{0.17em}(}}^{\circ }{\text{2θ)}}_{200}\text{=−14.6β\hspace{0.17em}}\tan {\theta }_{200}.\end{array}$$ By using two peaks, such as the 111 and 200, the difficult choice of background and instrumental effects can be minimized. A comparison of the three techniques is presented. As a consequence of the new method, it is clear that the probability of deformation stacking faults (α) should be measured from the displacements of peak maxima from those of an annealed specimen; if the C.G. is used and twin faults are present, a large error is possible.