First-principles calculation of elastic moduli of early-late transition metal alloys

Motivated by interest in the elastic properties of high-strength amorphous metals, we examine the elastic properties of select crystalline phases. Using first-principles methods, we calculate elastic moduli in various chemical systems containing transition metals, specifically early (Ta,W) and late (Co,Ni). Theoretically predicted alloy elastic properties are verified for Ni-Ta by comparison with experimental measurements using resonant ultrasound spectroscopy. Comparison of our computed elastic moduli with effective medium theories shows that alloying leads to enhancement of bulk moduli relative to averages of the pure elements and considerable deviation of predicted and computed shear moduli. Specifically, we find an enhancement of bulk modulus relative to effective medium theory and propose a candidate system for high-strength, ductile amorphous alloys. Trends in the elastic properties of chemical systems are analyzed using force constants, electronic densities of state, and crystal overlap Hamilton populations. We interpret our findings in terms of the electronic structure of the alloys.

Figure 1

Frank-Kasper Voronoi polyhedra, listing coordination numbers and polyhedron codes.

Figure 2

XRD verification of single phases of Ni${}_8$Ta, Ni${}_3$Ta, Ni${}_2$Ta, and NiTa.

Figure 3

Stacked bar chart of Honeycutt-Andersen common neighbor statistics [39, 40].

Figure 4

Enthalpies of formation for (Co,Ni)-(Ta,W) alloys. Values for Ta shown in black, for W shown in green. Plotting symbols explained in text.

Figure 5

Elastic moduli for (Co,Ni)-(Ta,W) compounds. Lines show CPA estimates. Data points are our DFT calculations. Asterisks are experimental values from our experiments on Ni-Ta alloys and from the literature for pure elements.

Figure 6

Calculated Poisson ratios. Dashed line at $\nu =0.32$ is putative threshold for ductility.

Figure 7

Electronic densities of states for hR13 structures. Line segments indicate the mean and standard deviations of the element projected $d$ bands.