Modeling Short-Range Ordering in Binary BCC Ti-X (X = Nb, V, Zr) Alloys using CE-CVM

Experimental evidence for short-range order (SRO) has been discovered for many alloys, and it affects several physical and mechanical properties of the alloys. Hence, treatment of SRO in the thermodynamic modeling of the phases is required for reliable description of alloy systems. In addition, the availability of first-principles-based thermochemical data has created the possibility for further improving existing thermodynamic descriptions. The present work uses the cluster expansion and cluster variation methods (CE-CVM) for the bcc solid phase to address these issues. Three binary Ti-X (X = Nb, V, Zr) alloys were thermodynamically accessed using existing experimental and calculated first-principles-based thermochemical data. Density functional theory (DFT), along with techniques, such as CE and special quasirandom structures (SQS), were used to calculate thermochemical data. Thermodynamic descriptions of binary Ti-X systems were obtained by optimizing all the available experimental, first-principles-based thermochemical, and phase diagram data. The phase diagram and thermodynamic properties calculated using model parameters agree well with the experimental data. The SRO of the bcc solid phase at various compositions and temperatures were determined using optimized model parameters. While the experimental determination of SRO remains a challenge, a CE-CVM based modeling approach offers a viable option for determining the SRO states of the alloys.