Ising-like description of structurally relaxed ordered and disordered alloys

First-principles study of order-disorder transitions in multicomponent solid-solution alloys

In this review, we will focus on the recent development of the order-disorder transition in metallic materials. The past decades have witnessed fast development in the first-principles methodologies and their applications to ordering transitions in multi-component alloys, particularly the high-entropy alloys. The driving force for the proceedings comes from (i) the advance of algorithms and increasingly cheaper hardware, and also (ii) the great passion to model alloys with increasing number of components. The review starts with a brief introduction of the history for the ordering transitions. More detailed scientific proceedings prior to the 1970s had been well summarized in Krivoglaz and Smirnov (1965 The Theory of Order-Disorder in Alloys (New York: Elsevier)) and Stoloff and Davies (1968 Prog. Mater. Sci. 13 1-84). In the second part, the methods to study the ordering transitions, primarily on the theoretic methods are introduced. These will include (i) KKR-CPA method and supercell methods for energetic calculations; and (ii) thermodynamic and statistical methods to compute the transition temperatures. The third part will focus on representative applications in alloys, including our own work and many others. This part supplies the primary information of this review to the readers. The fourth part will summarize the connections between ordering transitions and broader physical properties (e.g. the mechanical properties). In the last part, some concluding remarks and perspectives will be given.

Interplay between subsurface ordering, surface segregation, and adsorption on Pt-Ti(111) near-surface alloys

Using the first-principles cluster expansion (CE) method, we studied the subsurface ordering of Pt/Pt-Ti(111) surface alloys and the effect of this ordering on segregation and adsorption behavior. The clusters included in the CE are optimized by a genetic algorithm to better describe the interactions between Pt and Ti atoms in the subsurface layer. Similar to bulk Pt-Ti alloys, Pt-Ti(111) subsurface alloys show a strong ordering tendency. A series of stable ordered Pt-Ti subsurface structures are identified from the two-dimensional (2D) CE. As an indication of the connection between the 2D and the bulk ordering, the CE predicts a ground-state Pt(8)Ti structure in the (111) subsurface layer, which is the same ordering as the close-packed plane of the bulk Pt(8)Ti compound. We carried out Monte Carlo simulations (MC) using the CE Hamiltonian to study the finite temperature stability of the Pt-Ti subsurface structures. The MC results show that subsurface structures in the Pt-rich range have higher order-disorder transition temperatures than their Ti-rich subsurface counterparts. We calculate the binding energy of different adsorbates (O, S, H, and NO) on Pt-terminated and Ti-segregated surfaces of ordered PtTi and Pt(8)Ti subsurface alloys. The binding of these adsorbates is generally stronger on Ti-segregated surfaces than Pt-terminated surfaces. The adsorption-induced Ti surface segregation is determined by two factors: (i) the unfavorable energy penalty for the Ti atom to segregate to the clean surface and (ii) the favorable energy decrease from stronger adsorbate binding on the Ti-segregated surface. The two factors introduce similar magnitude in energy change for the S and NO adsorption on Ti-segregated surfaces of PtTi subsurface alloys. We predict an adsorption-induced Ti surface segregation that is dependent on the atomic configurations of the Ti-segregated surfaces resulting from the competition of the two factors.

Thermodynamic theory of epitaxial alloys: first-principles mixed-basis cluster expansion of (In, Ga)N alloy film

Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)(2)/(GaN)(2) (at x = 0.50) and (InN)(4)/(GaN)(1) (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.