Gamma Profile Analysis for Stress, Texture and Grain Size

Bob B He

doi:10.4028/www.scientific.net/amr.996.209

Abstract

Two-dimensional X-ray diffraction pattern can be described by the diffraction intensity distribution in both 2θ and γ directions. The 2D pattern can be reduced to two kinds of profiles: 2θ-profile and γ-profile. The 2θ-profile can be evaluated for phase identification, crystal structure refinement and many applications with many existing algorithms and software. The γ-profile contains information on texture, stress, and crystal grain size. This article introduces the concept and fundamental algorithms for stress, texture and crystal size analysis by γ-profile analysis.

Highlights

The diffracted x-rays from a polycrystalline sample form a series diffraction cone in 3D space since large numbers of crystals oriented randomly in the space are covered by the incident xray beam
Based on the effective diffraction volume and the crystallographic nature of the sample, in reflection mode diffraction, the crystal size is given by: d phkl b2 arcsin[cos θsin(∆γ where d is the average diameter of the crystallite, phkl is the multiplicity of the diffracting planes, b is the size of the incident beam, μ is the linear absorption coefficient and N s is the number of diffraction spots within the measured range ∆γ of the diffraction ring
Two-dimensional X-ray diffraction pattern can be described by the diffraction intensity distribution in both 2θ and γ directions

Summary

Introduction

The diffracted x-rays from a polycrystalline (powder) sample form a series diffraction cone in 3D space since large numbers of crystals oriented randomly in the space are covered by the incident xray beam. Two-dimensional x-ray diffraction (abbreviated as XRD2) pattern from a polycrystalline solid or powder sample can be considered as a cross section of the detecting plane and the diffraction cones [1]. In order to evaluate the materials structure associated with the intensity distribution along γ angle, either the 2D diffraction pattern should be directly analyzed or the γ-profile generated by 2θ-integration should be used. The diffraction vector H and its unit vector hL in the laboratory coordinates are given by Advanced Materials Research Vol 996

H H hx hy

Conclusions