Thermodynamic properties of binary hcp solution phases from special quasirandom structures

Abstract

Three different special quasirandom structures ͑SQS's͒ of the substitutional hcp A 1−x B x binary random solutions ͑x = 0.25, 0.5, and 0.75͒ are presented. These structures are able to mimic the most important pair and multi-site correlation functions corresponding to perfectly random hcp solutions at those compositions. Due to the relatively small size of the generated structures, they can be used to calculate the properties of random hcp alloys via first-principles methods. The structures are relaxed in order to find their lowest energy configurations at each composition. In some cases, it was found that full relaxation resulted in complete loss of their parental symmetry as hcp so geometry optimizations in which no local relaxations are allowed were also performed. In general, the first-principles results for the seven binary systems ͑Cd-Mg, Mg-Zr, Al-Mg, Mo-Ru, Hf-Ti, Hf-Zr, and Ti-Zr͒ show good agreement with both formation enthalpy and lattice parameters measurements from experiments. It is concluded that the SQS's presented in this work can be widely used to study the behavior of random hcp solutions.

First-Principles Calculations and CALPHAD Modeling of Thermodynamics

“…For simplicity, the ideal c/a ratio was used to generate SQS supercells with 8 and 16 atoms. [128] It should be mentioned that the order of a given figure may be Fig. 6 Predicted heat capacity for second-order magnetic transition of Ce as a function of temperature at 2.25 GPa pressure, slightly above the critical pressure [151] Basic and Applied Research: Section I altered with the variation of c/a ratio, e.g., changing from second nearest neighbor to third nearest neighbor, but it will not cause changes in the values of the correlation functions.…”

“…Based on the SQS supercells for binary fcc solutions, [70] we developed the SQS supercells for binary bcc, [127] binary hcp, [128] and ternary fcc solutions. [129] The SQS for ternary bcc and hcp solutions are also developed and will be published shortly.…”

Linking length scales via materials informatics

“…10 Each method has its own limitations in representing random solutions, and it seems that the SQS provide an optimal combination in terms of computational efficiency and accuracy. 11 The SQS mimic a random solution phase by creating a small (4-48 atoms) periodic structure that best satisfi es the pair and multisite correlation functions corresponding to a random solid solution, up to a certain coordination shell. In terms of computa- …”

“…Using the ATAT code, 6 the SQS are now available for bodycentered cubic, 12 B2, 13 Laves phases, 14 halite, 15 hexagonal-close packed, 16 and L1 2 structures. 17 Additionally, fi rst-principles calculations of a wide range of materials properties such as interfacial energy, 18,19 antiphase boundary energy, 20 diffusivity, 21,22 and elastic constants, 23 are also possible.…”

The development of phase-based property data using the CALPHAD method and infrastructure needs

“…Even though the Additional information discrepancies on lattice stability between the classic CALPHAD modeling and DFTbased first-principles calculations still exist [123] progresses have been made to narrow the differences such as bcc Ti [124] and fcc W [125], even for liquid solution phases [44]. The efficient special quasirandom structures (SQS) approach [126][127][128] is particularly useful in predicting the enthalpy and entropy of mixing in solid solution phases using phonon or Debye models [129,130]. Consequently, the thermodynamic model parameters of all individual phases can be evaluated solely from DFT-based first-principles calculations.…”