First-principles prediction of phase-segregating alloy phase diagrams and a rapid design estimate of their transition temperatures

Abstract

We calculate the transition temperature versus concentration ͑T c vs c͒ phase diagrams of several phasesegregating alloys ͓fcc Ca-Sr, Au-Pt, and Rh-͑Pd,Cu,Ag,Au͔͒ using a multiscale method combining firstprinciples calculations and Monte Carlo via the cluster expansion ͑CE͒. We study Pd-Rh, with its well-known high-T miscibility gap, to verify the method's reliability. We predict that Ca-Sr segregates at low temperatures. We then show that a rapid estimate of T c is obtained from enthalpies analytically derived from a CE, and, using thermodynamic integration, we determine under what circumstances this mean-field estimate is accurate compared to Monte Carlo results. Also, we discuss how an electronegativity difference of the alloying elements quickly assess when vibrational entropy effects should be included in the estimate of T c .

Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

“…recovering both cases in (2 Nc configurations, is evaluated instead. Therefore, only state variables, such as m i and G ij , whose site indices are in the cluster are configurationally averaged.…”

“…Cluster mean-field theories (cMFTs) are formulated and applied extensively in the study of materials phase transitions for classical Hamiltonians, i.e., the Ising model and cluster expansions. [1][2][3][4][5] Only for a few cases can the Ising model be solved exactly. 6 Generally, the partition function (Z[A], with source fields A), and quantities such as site magnetization (m i ) and pair correlations (G ij ), which dictate thermodynamic behavior, have to be approximated.…”

Configurational thermodynamics of Fe–Ni alloys at Earth's core conditions

“…It has been shown (Zarkevich et al, 2007) that for phase segregating alloys 129 where the difference in electronegativity between the constituents is small and 130 the mixing enthalpy is symmetric with respect to the equiatomic composition, 131 a quick estimate of the temperature of transition from segregation to mixing,…”

Nanoalloy composition-temperature phase diagram for catalyst design: Case study of Ag-Au

“…Here we use the cluster expansion 18 (CE) method with DFT calculations, an approach that has proved to be very successful for bulk alloys [19][20][21][22][23][24][25][26][27][28] , to study the configurational thermodynamics of a 55-atom truncated cuboctahedral (TC) NP with face-centered cubic (fcc) stacking. We study the specific site occupations as functions of both composition (c) and temperature (T).…”