When given High Entropy Alloy with known ratio of two phases, known elements, two lattices - one HCP and second BCC, how should one calculate theoretical density of such an alloy?
The density of a two-phase high entropy alloy (HEA) can be calculated using the following formula:
Density = (mass of solid phase 1 + mass of solid phase 2) / (volume of solid phase 1 + volume of solid phase 2)
In order to calculate the density, the mass and volume of both solid phases need to be determined. The mass can be determined by weighing a known volume of the alloy and the volume can be determined by using a method like X-ray diffraction (XRD) or electron microscopy to measure the lattice parameters of the solid phases. Once the mass and volume of both solid phases are known, the density can be calculated using the above formula.
Alternatively, the density of the solid phases can be measured by Archimedes principle. The samples are submerged in a liquid of known density and the buoyancy force is measured. The volume of the sample can be determined by the buoyancy force and density of the liquid.
It's important to note that, generally, when the two-phase HEA is formed by solidification, the density of the solid alloy is not the same as the density of each of the single phase from which the alloy is composed. The density of an alloy is affected by the size and shape of the grains, the microstructure, and the presence of any porosity or internal defects, which can affect its density
First know composition of the two phases- elements present there and their ratio.
If you know individual Lattice parameter of HCP and BCC metals, you can find metallic radii of individual atoms. 'Average' atom's metalic radius would be weighed sum of constituent metallic radii, so would be average atomic mass of a lattice point. Now once you know 'average' atom's mass, radius and crystal structure, you can easilly calculate theoretical density of BCC and HCP phases, and then you can reach density of whole of the HEA.
The density of a two-phase high entropy alloy can be calculated using the rule of mixtures. This involves taking the volume fraction of each phase and multiplying it by the density of each phase, then summing the products to get the total density. Additionally, the density can also be calculated by weighing the sample and finding its volume, then dividing the weight by the volume.
Density = (Volume fraction of phase 1 x Density of phase 1) + (Volume fraction of phase 2 x Density of phase 2)
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