Research ArticleENGINEERING

Prediction of interface structures and energies via virtual screening

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Science Advances  25 Nov 2016:
Vol. 2, no. 11, e1600746
DOI: 10.1126/sciadv.1600746
  • Fig. 1 Comparison of all-candidate calculation method and virtual screening method.

    Schematic illustration of the method to determine the grain boundary (GB) structure and energy using the all-candidate calculation method (A) and the virtual screening method (B). Optimized configuration (Opti. config.) is obtained from the corresponding initial configuration (Ini. config.) via structure and energy calculations, using the first-principles method and the static lattice method.

  • Fig. 2 Schematic illustration of symmetric tilt CSL grain boundary and the Σ values and misorientation angles (θ) of grain boundaries.
  • Fig. 3 The most stable structures in the training data.

    The most stable structures in the training data obtained by the all-candidate calculations: (from top to bottom) Σ5[001]/(210), Σ5[001]/(310), Σ17[001]/(350), and Σ17[001]/(410). Previously reported structures are overlaid with silver circles (16, 26).

  • Fig. 4 Result of regression analysis and calculated stable structures.

    Predicted grain boundary energies and accurate grain boundary energies for the training data (A) and the test data (B). (C) The most stable structure of Σ13[001]/(230) obtained by the all-candidate calculations and (D) the structure predicted by the virtual screening method. Yellow lines represent the position of the grain boundary.

  • Fig. 5 Predicted 13 grain boundary energies and a stable structure of Σ37[001]/(750).

    (A) Grain boundary energies as a function of the misorientation angle. Red and purple circles are obtained by the present method and all-candidate calculations, respectively, and open and filled black circles are obtained from previous studies. (B) Predicted stable structures for Σ37[001]/(750) in this study (orange circles) and in a previous report (silver circles) (26).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/11/e1600746/DC1

    section S1. The most straightforward method to determine the structure and energy of single grain boundary.

    section S2. Descriptors used for the regression analysis in this study.

    section S3. The results obtained through the linear regression method.

    section S4. Predictions for 12 grain boundary structures using the virtual screening method.

    section S5. Effect of the training data selection.

    section S6. Effect of the parameters for the regression analysis.

    fig. S1. Plot of the calculated grain boundary energies by the all-candidate calculation method.

    fig. S2. Descriptors for the SVR analysis.

    fig. S3. Predicted grain boundary energies through linear regression method.

    fig. S4. Predictions for 12 grain boundary structures using the virtual screening method.

    fig. S5. Predicted grain boundary energies with two of four kinds of grain boundary as the training data.

    fig. S6. Predicted grain boundary energies under over-fitting.

  • Supplementary Materials

    This PDF file includes:

    • section S1. The most straightforward method to determine the structure and energy of single grain boundary.
    • section S2. Descriptors used for the regression analysis in this study.
    • section S3. The results obtained through the linear regression method.
    • section S4. Predictions for 12 grain boundary structures using the virtual screening method.
    • section S5. Effect of the training data selection.
    • section S6. Effect of the parameters for the regression analysis.
    • fig. S1. Plot of the calculated grain boundary energies by the all-candidate calculation method.
    • fig. S2. Descriptors for the SVR analysis.
    • fig. S3. Predicted grain boundary energies through linear regression method.
    • fig. S4. Predictions for 12 grain boundary structures using the virtual screening method.
    • fig. S5. Predicted grain boundary energies with two of four kinds of grain boundary as the training data.
    • fig. S6. Predicted grain boundary energies under over-fitting.

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