Measurement of single-crystal elastic constants by neutron diffraction from polycrystals

Elastic behaviour of orientation-correlated grains in multiphase aggregates

Diffraction elastic constants (DEC) describe the elastic response of a sub-set of orientation correlated grains which share a common lattice vector. DEC reflect the elastic behaviour of the single crystal constituents through their dependence on grain orientation. DEC furthermore depend on the behaviour of the polycrystal aggregate both through the dependence on preferred orientation and through the average elastic interaction of the grains in the sub-set with their surroundings. The latter is also known as grain-matrix interaction which is grain shape dependent. Both dependencies can make the DEC uniquely sensitive to the elastic effects of the grain shape, texture, and phase composition. Several micro-mechanical models are explored with respect for use both in calculating diffraction elastic constants and overall elastic constants. Furthermore, it is shown how discrete data from electron backscatter diffraction on grain shape, grain orientations, and neighbouring grains can be used for DEC calculations. Lastly, the inverse problem of calculating single crystal elastic constants from DEC is discussed in detail. All calculations discussed in this work can be verified using the freely available computer program IsoDEC.

Elastic Moduli: a Tool for Understanding Chemical Bonding and Thermal Transport in Thermoelectric Materials

The elastic behavior of a material can be a powerful tool to decipher thermal transport. In thermoelectrics, measuring the elastic moduli-directly tied to sound velocity-is critical to understand trends in lattice thermal conductivity, as well as study bond anharmonicity and phase transitions, given the sensitivity of elastic moduli to the chemical bonding. In this review, we introduce the basics of elasticity and explain the origin of high-temperature lattice softening from a bonding perspective. We then review elasticity data throughout classes of thermoelectrics, and explore trends in sound velocity, anharmonicity, and thermal conductivity. We reveal how experimental sound velocities can improve the accuracy of common thermal conductivity models and present a critical discussion of Grüneisen parameter estimates from elastic moduli. Readers will be equipped with tools to leverage elasticity measurements or calculations to accurately interpret thermal transport trends.

DISEMM: a tool for the investigation of elasto-plastic behaviour on polycrystalline samples using X-ray and neutron diffraction

DISEMM is a software tool to analyse neutron or X-ray diffraction data on polycrystalline samples collected under mechanical load, combining the determination of single-crystal elastic constants and the methods of elasto-plastic self-consistent modelling in one package.

The software DISEMM is designed to analyse diffraction data from in situ loading experiments on polycrystalline samples for the determination of single-crystal elastic constants (SECs) and elasto-plastic self-consistent (EPSC) modelling of lattice strains. The SECs can be obtained from powder-diffraction elastic constants using a variety of grain-to-grain interaction models, namely Voigt, Reuss, Hill, Kröner, de Wit and Matthies approaches. The texture of the polycrystalline sample can be taken into account using the orientation distribution function of the grains. For the analysis of two-phase materials, an approach was implemented to calculate the stress transfer between the phases and its impact on the apparent elastic properties. The calculated SECs can then be used as input into the EPSC model, which allows the user to predict the elasto-plastic behaviour for comparison with experimental lattice strain data and to investigate the activation of individual slip systems. For this purpose, critical resolved shear stresses and hardening parameters are adapted iteratively.

Diffraction-based determination of single-crystal elastic constants of polycrystalline titanium alloys

The single-crystal elastic constants of polycrystalline titanium alloys have been determined using neutron and synchrotron powder diffraction.

Single-crystal elastic constants have been derived by lattice strain measurements using neutron diffraction on polycrystalline Ti-6Al-4V, Ti-6Al-2Sn-4Zr-6Mo and Ti-3Al-8V-6Cr-4Zr-4Mo alloy samples. A variety of model approximations for the grain-to-grain interactions, namely approaches by Voigt, Reuss, Hill, Kroener, de Wit and Matthies, including texture weightings, have been applied and compared. A load-transfer approach for multiphase alloys was also implemented and the results are compared with single-phase data. For the materials under investigation, the results for multiphase alloys agree well with the results for single-phase materials in the corresponding phases. In this respect, all eight elastic constants in the dual-phase Ti-6Al-2Sn-4Zr-6Mo alloy have been derived for the first time.

Quantitative neutron diffraction texture measurement applied to α-phase alumina and Ti3AlC2

Orientation distribution functions, essential for making a quantitative connection between single-crystal and polycrystal properties, have been determined for extruded α-phase alumina, hot-pressed Ti3AlC2and cold isostatically pressed Ti3AlC2using experimental pole figures recorded on the fixed-wavelength neutron diffractometer KOWARI. Some practical improvements to the calculation of the pole-figure density from the raw area-detector data, and for constructing pole figures on ann×n° hemispherical grid, are presented. The textures give some insight into particle flow during manufacture. Directly measured material textures were compared with one-dimensional pole density functions, such as the March and Rietveld functions commonly used for the correction of preferred orientation in Rietveld refinements, as a means of assessing the utility of the latter for the computation of diffraction elastic constants and other polycrystal properties from a given set of single-crystal properties.

Nonhydrostatic compression of gold powder to 60 GPa in a diamond anvil cell: estimation of compressive strength from x-ray diffraction data

Two gold powder samples, one with average crystallite size of ≈30 nm (n-Au) and another with ≈120 nm (c-Au), were compressed under nonhydrostatic conditions in a diamond anvil cell to different pressures up to ≈60 GPa and the x-ray diffraction patterns recorded. The difference between the axial and radial stress components (a measure of the compressive strength) was estimated from the shifts of the diffraction lines. The maximum micro-stress in the crystallites (another measure of the compressive strength) and grain size (crystallite size) were obtained from analysis of the line-width data. The strengths obtained by the two methods agreed well and increased with increasing pressure. Over the entire pressure range, the strength of n-Au was found to be significantly higher than that of c-Au. The grain sizes of both n-Au and c-Au decreased under pressure. This decrease was much larger than expected from the compressibility effect and was found to be reversible. An equation derived from the dislocation theory that predicts the dependence of strength on the grain size and the shear modulus was used to interpret the strength data. The strength derived from the published grain size versus hardness data agreed well with the present results.

X-ray diffraction evaluation of stress in high pressure deformation experiments

This paper explores the applicability of x-ray diffraction measurements of stress to high pressure deformation experiments. We model measurements of elastic lattice strains in various geometries for both axial and rotational deformation apparatus. We then show that, for most cases, stresses can be inverted from the diffraction data. A comparison between the results of our models and actual experimental data also indicates that plastic deformation can have an influence that is not addressed properly in the elastic models of lattice strains and should therefore be treated with caution.