Energy calibration and full-pattern refinement for strain analysis using energy-dispersive and monochromatic X-ray diffraction

Abstract

Precise channel-to-energy conversion is very important in full-pattern refinement in energy-dispersive X-ray diffraction. Careful examination shows that the channel-to-energy conversion is not entirely linear, which presents an obstacle to obtaining accurate quantitative data for lattice strains by pattern refinement. In order to establish an accurate quadratic channel-to-energy conversion function, a Matlab program was written to find the best quadratic coefficient and hence the whole energy conversion function. Then this energy conversion function was used to perform a whole-pattern fitting of the energy-dispersive X-ray diffraction pattern of a Ti64 sample. The strain across the Ti64 bar calculated from the fitting results has been compared with values obtained by single-wavelength X-ray diffraction utilizing a Laue monochromator.

Variational eigenstrain analysis of synchrotron diffraction measurements of residual elastic strain in a bent titanium alloy bar

“…The accuracy of determination of individual peak position and shape resolution in the white-beam mode is usually related to the resolution of the energy-dispersive detector, but can in fact be several orders of magnitude better. The accuracy of interpretation in terms of lattice parameters and hence strain can be significantly improved by using multiple peak analysis or whole pattern fitting [Liu et al 2005].…”

“…Eigenstrain modelling is a powerful analytical technique for the representation of residual stress states in solids [Mura 1987]. A practical approach to the use of eigenstrain in residual stress modelling can be developed based on the following fundamental postulates [Korsunsky 1997;2005]: (a) In the absence of eigenstrain (stored inelastic strain), any elastic solid is completely free from residual stress.…”

“…In practice, residual stresses are only ever measured indirectly via observing relaxation or their effect on some other physical quantity, for example, bond vibration frequency as in Raman spectroscopy. Experimental techniques for stress evaluation can be classified into relaxation methods, physical correlation methods and diffraction techniques [Withers and Bhadeshia 2001].…”

High energy white beam x-ray diffraction studies of residual strains in engineering components

“…Recent experimental studies [1][2][3][4][5][6][7][8] have demonstrated that the use of high energy X-rays (up to and exceeding 100keV) allows diffraction experiments to be carried out in transmission through thick sections (exceeding several millimeters, and up to several millimeters) of important structural engineering alloys based on magnesium, aluminium, titanium, iron and nickel. Since these materials find extensive use in various parts of aerospace and automotive engine and body assemblies, reliable knowledge of residual stress states in manufactured components is essential for developing reliable and suitably precise predictions of thermo-mechanical fatigue resistance and durability under complex service loading conditions.…”

“…Furthermore, simultaneous collection of information about scattered intensity across a wide range of energies results in a diffraction pattern (that can be converted to intensity vs lattice spacing pattern using appropriate calibration, [8][9][10][11]) allows subsequent data interpretation that involves the refinement of a crystal lattice and scattering model (Rietveld refinement) through non-linear least squares fitting to the entire pattern containing multiple diffraction peaks. This allows the determination of average lattice parameters (e.g.…”