Extending the Williamson-Hall method: a qualitative approach for microstructural analysis under non-ideal conditions

Abstract As a first approximation, the Williamson Hall plot method can be applied for obtaining a quantitative assessment of particle size and strain by analysing the integral breadth of the diffraction lines as a function of the reciprocal interplanar spacing. For this purpose, it is necessary to use a reference sample with negligible structural imperfections. Not infrequently, the relative variation of one of these parameters as a function of some experimental variable is of greater interest than the estimate of their absolute value. The proposed differential Williamson-Hall method qualitatively evaluates the strain/size difference between a sample and a non-standard reference material (in which a sizeable size and/or strain contribution to the diffraction broadening is not negligible) as they are subjected to an intensive parameter (temperature, pressure, composition, defectivity). The method can be applied to compare the microstructural properties of related specimens or in the case the use of a standard sample is prevented by the experimental set-up; it thus provides a convenient visualization of microstructural trends among related samples. The results obtained using this differential method are shown to be in excellent qualitative agreement with those derived from an ideal standard sample.