Methodology to estimate single crystal elastic constants from polycrystalline materials – A case study with an entropy stabilized transition metal oxide
Single crystal Elastic Constants (SECs) are fundamental to the understanding of the deformation behaviour of materials. SECs define the elastic resistance of single crystals to external forces. Estimation of SECs is particularly important as single crystals find applications in semiconductors, sensors and turbine blades. Also, SECs directly relate to the bonding between the atoms and are most often used for the validation of interatomic potentials. SECs are also essential for micromechanical modelling of various properties, for residual stress measurements using diffraction techniques and for interpretation of seismic data in the field of geological sciences. Though the necessity for estimating SECs is well established, standard methodologies for the estimation are limited and accompanied by complexities. The most common techniques used to measure SECs are resonant acoustic spectroscopy (RUS) and the Brillouin scattering and in both these techniques sufficiently large single crystals are required. But for many of the inorganic compounds and engineering alloys, it is difficult to grow a single crystal of sufficiently large length and also of the same composition as a polycrystalline counterpart. This led to the use of computational techniques and in particular first principle Density Functional Theory (DFT) simulations. Though DFT simulations are successful in estimating SECs for several inorganic compounds, the method fails for several new engineering alloys and also the SECs estimated using computational techniques require experimental validation. One alternate approach to estimate SECs is by in situ loading of polycrystalline samples in a diffractometer. Such experiments are usually carried out in synchrotron and neutron diffraction facilities. However, it takes a while before beamtime is allotted in such facilities.
Therefore in this thesis, we intend to develop an elegant and easy to access methodology wherein SECs could be determined from the polycrystalline samples using a commercial laboratory X-ray diffractometer. For this purpose, a universal miniature multiaxial loading fixture was custom-built that is capable of performing in-situ experiments by integrating it with a commercial laboratory X-ray diffractometer. Proof-of-concept experiments were carried out using the optimized miniaturized sample geometries in the custom-built loading fixture. The results obtained from miniature sample geometries were validated using the data obtained from ASTM standards in a standard testing machine. After which,in situ uniaxial compression loading of phase pure nickel samples was carried out using the custom-built fixture and X-ray diffractometer. Using a robust micromechanical model and optimization subroutine along with the Diffraction Elastic Constants (DECs) calculated from the in situexperiments and elastic constants measured using ultrasonic resonant frequency testing, SECs were determined. The aforementioned methodology was validated for phase pure nickel, and it was found that the experimentally obtained SECs matched well with the literature reported values. Similar experiments were carried out for an entropy stabilized oxide of composition [(MgNiCoCuZn)O]. This particular entropy stabilized oxide is of specific interest because of the immense potential exemplified by this material system. Therefore, it is of practical significance to estimate the SECs for [(MgNiCoCuZn)O], as it could be of use to experimentalists and computational material scientists. However, there was a difference in the experimentally estimated values and literature reported SECs for this material. The difference in results was rationalized using comprehensive heat-treatment coupled with characterization and molecular dynamics simulations.