Combined Analysis

Chapter 5

Quantitative Microstructure Analysis

5.1. Introduction

Important information on the microstructure may also be extracted from the width of the diffraction peaks. A diffraction peak can be considered as the convolution product of several effects: the small size of the coherently diffracting domains (named Coherent Size Domain or CSD, or crystallite sizes), elastic microdistorsions (microstrains) due to linear and point defects, stacking faults, strain heterogenities, dislocations, etc. Voigt functions are convolutions of Cauchy and Gaussian contributions. Regarding the peak profile, this is expressed by equation [1.14] in the direct space, or in the reciprocal space:

[5.1] 

Here we introduce the h indice to take into account the eventual anisotropy (h planes dependency) of the peak broadening. Equation [5.1] is rewritten:

[5.2] 

with ∆h being the variation in inter-reticular spacing due to microstrains and finite sizes. The contribution of microstrains ɛ_h produced by any stresses (mechanical, thermal, compositional, etc.) are seen as relative variations of the d_hkℓ spacings:

[5.3] 

But diffraction only probes the mean values <ε_h> of ε_h (average over all the irradiated volume ...