Quantitative description of atomic architecture in solid solutions: A generalized theory for multicomponent short-range order

This Brief Report introduces a short-range order parameter, called the generalized multicomponent short-range order (GM-SRO) parameter. The application to Monte Carlo simulations is described for higher order solid solutions. The results show the ability to create atomic-scale systems with a particular subset of the GM-SRO parameters and the power of the GM-SRO expressions in determining the relationship between two sets of atomic species.

Figure 1

(Color online) PM-SRO and GM-SRO calculation for the first shell, for a quaternary system. The matrix atoms are in small and blue while the three solute atom types are labeled A–G. The first four shells are highlighted around solute atom E. The PM-SRO probabilities are first determined through collecting the probabilities for each atom, in this case in the first shell $\left(m=1\right)$. Based on the PM-SRO probabilities, the GM-SRO probability is calculated, which is then used to generate the GM-SRO parameters.

Figure 2

(Color online) Clusters identified using the 3-dimensional Markov field (3DMF) algorithm of synthetic quaternary data (Al-1.75Cu-1.75Mg-0.05Si) with a volume of $20\times 20\times 80{\text{nm}}^3$. Atom map for clusters containing five atoms or more in (a) random $\text{PM-SRO}=0$ data set and (b) with the PM-SRO in Table . (c) Cluster size distribution comparison between simulated and random.

Figure 3

(Color online) GM-SRO significance of the parameter compared to $\text{GM-SRO}=0$. The red shades indicate a GM-SRO that is greater than random and blue shades indicate a negative difference between simulated and random.