A compound unit method for incorporating ordered compounds into lattice models of alloys

Abstract

a b s t r a c tLattice models can be a basic tool for alloy design, due to their ability to capture the most important thermodynamic and kinetic phenomena of a wide-range of alloys at a low computational cost. However, in order to correctly treat ordered precipitates at off-stoichiometric compositions requires multi-body potentials, and these can be challenging to calibrate to known alloy behaviors. Here we introduce a simple means of capturing the multi-body terms needed to treat ordered compounds in a lattice model based on defining ''compound units". This approach is particularly designed for, and easily calibrated in, cases where the structure and formation energy of equilibrium compounds are already known. This is accomplished by defining a compound unit that derives its energy from the formation energy of the compound as an a priori input. The method is illustrated for a binary alloy with D0 3 and B2 stable compounds.

Higher Temperatures Yield Smaller Grains in a Thermally Stable Phase-Transforming Nanocrystalline Alloy

“…To demonstrate this behavior we begin our alloy design process with the regular nanocrystalline solution model [20] and subsequent improvements of it [21][22][23]. The output of this model is a "stability map", which is divided into three distinct zones [22].…”

Stability criteria for nanocrystalline alloys

“…However, the pairwise potential does not correctly produce bulk ordered phases in a lattice model, and multi-body terms are generally required. A complicated interatomic potential can be avoided by using the compound unit approach, which can incorporate compounds with known structure and formation energy into a lattice model [47]. This introduces an additional energy, which can conveniently be represented as an effective pairwise bond energy, A x B c .…”

“…Atom and grain swaps, as proposed by Chookajorn and Schuh[41], were used to explore the configuration space until 4x109 Monte Carlo swaps were attempted, starting from a temperature of 10,000°C and reducing the temperature towards a final temperature of 500°C at a rate of 0.1% every Monte Carlo step (equivalent to 4x10 4 swap attempts). Using the compound unit approach[47], a D03 compound (25 at.% stoichiometry) with an enthalpy of formation of -20 kJ/mol was incorporated into the configuration space of the model. Simulations were conducted varying the ∆ mix and ∆ seg as shown by the circles in the stability map inFig.…”

Phase transitions in stable nanocrystalline alloys

“…While we chose a positive enthalpy of mixing system in this study, this approach can be generalized to include negative enthalpy of mixing systems with stable intermetallics and ordered compounds by using the compound unit approach. 35 The ability to construct phase diagrams of this type should improve the selection of alloying candidates for stabilizing grain size, as not only can systems be designed to have stable nanocrystalline states at low temperature but also selected based on their ability to retain a fine grain size up to higher temperatures. In addition, the similarities and differences between the order-disorder transition of the nanocrystalline state and that of a standard two-phase alloy allow us to better understand the thermodynamic implications of having a nanocrystalline ground state.…”