A Novel Computational Thermodynamics Framework with Intrinsic Chemical Short-Range Order

Exploiting chemical short-range order (SRO) is a promising new avenue for manipulating the properties of alloys. However, existing computational thermodynamic modeling frameworks do not account for the possibility of chemical SRO in multicomponent ($\geq 3$) alloys. CALPHAD is a leading method for modeling and calculating phase equilibria in materials. Still, the prevailing solution model used in CALPHAD, the sublattice model, is an empirical mean-field model based on Bragg-Williams (ideal entropy of mixing) approximation. This makes CALPHAD inadequate for properly describing order-disorder transformations or chemical SRO in alloys. First-principles calculations of phase diagrams, using the cluster variation method(CVM), or cluster expansion method(CEM), can describe SRO but are generally limited to binary or ternary systems due to the large number of configuration variables.
Here, we propose to develop a hybrid framework by marrying the unique advantages of CVM and CALPHAD by incorporating chemical SRO into CALPHAD using a cluster-based solution model. The most crucial technique is the Fowler-Yang-Li transform which can decompose the cumbersome cluster probabilities in CVM into fewer site/point probabilities of the basis cluster, thereby considerably reducing the number of variables that must be minimized for multicomponent ($\geq 3$) systems. Modern, efficient algorithms are employed to minimize the non-linear cluster-based free energy functions. Prototype phase diagrams of the fcc AB binary system have been calculated as benchmark tests for different models. The phase diagram calculated from FYL-CVM possesses the same topology as that obtained from CVM and has a good balance of accuracy and efficiency. We also included free energy contributions from vibrational, elastic, and electronic contributions using reduced-order models. We observed that all the physical contributions clearly influence the order-disorder phase boundaries.
We have also implemented our current method in the Cu-Au, a typical fcc ordering system, to test its effectiveness in real materials. We created a workflow to determine the cluster energies for the Cu-Au system. The result is a new set of parameters that are regularized for the CVM-CALPHAD modeling. The calculated phase diagram agrees well with experimental phase boundary data. The importance of including non-configurational contributions to free energy (vibrational, elastic, and electronic contributions) is revealed and satisfies the physics of the real system. The SRO parameters in the Cu-Au system based on the tetrahedron cluster probability are visualized in the composition-temperature space. Similarly, we have generalized the algorithms of SRO parameters to any multicomponent($\geq 3$) alloys in the disordered phase and present the demonstrated results for the Cu-Au-Ag system. In summary, our proposed CVM-CALPHAD modeling framework enables the chemical SRO to be exploited for systems exhibiting order-disorder transformations of the solid solution using a novel cluster-based model, which balances both accuracy and efficiency and incorporates more physics into CALPHAD.