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On generating Special Quasirandom Structures: Optimization for the DFT computational efficiency

Andrzej P. Kądzielawa

TL;DR

The paper tackles the computational bottleneck of modeling configurational disorder in alloys using DFT by generating Special Quasirandom Structures (SQS) optimized for solver efficiency. It introduces an extinction-based evolutionary algorithm that filters high-symmetry candidates, leveraging symmetry as a proxy for non-randomness to produce small supercells with maximal local environmental distinctness. On the W70Cr30 alloy, the method achieves near-equivalent disorder representation to established tools while reducing the number of unique displacements required for phonon calculations by about a factor of five, e.g., comparing $E=2.01\times 10^{-4}$ for ATAT and $E=2.92\times 10^{-4}$ for the extinction-based approach. This approach enables scalable and efficient ab initio exploration of composition–enthalpy spaces, enabling faster thermal-property predictions and robust stability assessments through convex-hull analyses.

Abstract

We present our novel evolutionary algorithm for generating Special Quasirandom Structures (SQS) designed to optimize the computational efficiency of Density Functional Theory (DFT) computations. Operating on the premise that symmetry proxies non-randomness, we rigorously filter out 1.P1 candidate structures prior to evaluating correlation functions. Our extinction-based workflow includes the seeding, filtration, evaluation, extinction, and repopulation phases to produce efficient supercells with maximal local environmental distinctness. We compare our results against those generated by established software packages, on the example of the W\textsubscript{70}Cr\textsubscript{30} alloy. Although standard tools achieve (marginally) lower correlation errors, our best-performing structures require approximately five times fewer unique displacements for phonon calculations. This approach sacrifices negligible quantitative disorder accuracy to significantly reduce the computational cost of modeling thermal properties.

On generating Special Quasirandom Structures: Optimization for the DFT computational efficiency

TL;DR

The paper tackles the computational bottleneck of modeling configurational disorder in alloys using DFT by generating Special Quasirandom Structures (SQS) optimized for solver efficiency. It introduces an extinction-based evolutionary algorithm that filters high-symmetry candidates, leveraging symmetry as a proxy for non-randomness to produce small supercells with maximal local environmental distinctness. On the W70Cr30 alloy, the method achieves near-equivalent disorder representation to established tools while reducing the number of unique displacements required for phonon calculations by about a factor of five, e.g., comparing for ATAT and for the extinction-based approach. This approach enables scalable and efficient ab initio exploration of composition–enthalpy spaces, enabling faster thermal-property predictions and robust stability assessments through convex-hull analyses.

Abstract

We present our novel evolutionary algorithm for generating Special Quasirandom Structures (SQS) designed to optimize the computational efficiency of Density Functional Theory (DFT) computations. Operating on the premise that symmetry proxies non-randomness, we rigorously filter out 1.P1 candidate structures prior to evaluating correlation functions. Our extinction-based workflow includes the seeding, filtration, evaluation, extinction, and repopulation phases to produce efficient supercells with maximal local environmental distinctness. We compare our results against those generated by established software packages, on the example of the W\textsubscript{70}Cr\textsubscript{30} alloy. Although standard tools achieve (marginally) lower correlation errors, our best-performing structures require approximately five times fewer unique displacements for phonon calculations. This approach sacrifices negligible quantitative disorder accuracy to significantly reduce the computational cost of modeling thermal properties.
Paper Structure (7 sections, 2 equations, 1 figure, 2 algorithms)

This paper contains 7 sections, 2 equations, 1 figure, 2 algorithms.

Table of Contents

  1. Introduction
  2. Theoretical Foundations of Configurational Disorder
  3. The Cluster Expansion Formalism
  4. Extinction-Based Generation Method (Pseudocode)
  5. Comparative Analysis
  6. Conclusions
  7. Acknowledgments

Figures (1)

  • Figure 1: Correlation (a) and error (b) functions for different $4\times 4\times 4$ bcc Special Quasirandom W70Cr30 Structures (exactly W90Cr38 supercell). Histograms on the right sum up the corresponding populations. We used two sqsgeneratorsqsgen generated 1.P1-symmetry cells with 109 (1.P1_sqsgen1) and 109 (1.P1_sqsgen2) iterations, and three ATATATAT 109 (1.P1_ATAT1 and 1.P1_ATAT2), and 102 (1.P1_ATAT3) iterations. We included our own cells from 5.C2 and 38.Amm2 symmetry groups, while the result for purely random 1.P1 cell is given as a reference point. Note that, while 1.P1_ATAT1 (brown hexagons) is the best (error-wise with $\mathfrak{E} = 2.01 \,\cdot 10^{-4}$), our 5.C3_03 ($\mathfrak{E} = 2.92 \,\cdot 10^{-4}$, red pentagons) has $\sim 5$ times fewer displacements for phononic calculations.