Influence of Si, Mn, Cr, and C doping impurities on grain boundary segregation of phosphorus in α–iron

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Abstract

This paper first uses ab initio calculations for a systematic study of an influence of Cr, Mn, Si, C, and P alloying elements on a grain boundary segregation of phosphorus in ferromagnetic α-Fe and its dependence on the nature of grain boundaries. Segregation energies of each element and site are fully calculated for two special grain boundaries of the types Σ3(111) and Σ5(310). We study the effect of grain boundary type on the segregation process of alloying elements. The estimate of effective segregation energy for each model of grain boundaries from the obtained segregation energies and analysis of the alloying element distribution at various boundary points are carried out. The paper shows that the Voronoi volume of a Fe site at the segregation point determines the segregation energy of the elements under study. The segregation energies of various pairs of impurities on the boundary are calculated. The effect of substitutional impurities on the change in the segregation energy of phosphorus atoms at the interstitial and substitutional sites and the effect of the phosphorus atom on the change in the impurity segregation energy at various boundary points are studied. The results obtained in this study correspond closely to the available experimental data and provide important base data for the design of high strength steel materials, and are useful for understanding the effect of alloying elements on bcc Fe.

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About the authors

A. V. Verkhovykh

South Ural State University (National Research University)

Email: diuriaginans@susu.ru
Russian Federation, Chelyabinsk, 454080

A. A. Mirzoev

South Ural State University (National Research University)

Email: diuriaginans@susu.ru
Russian Federation, Chelyabinsk, 454080

N. S. Dyuryagina

South Ural State University (National Research University)

Author for correspondence.
Email: diuriaginans@susu.ru
Russian Federation, Chelyabinsk, 454080

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Supplementary files

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2. Fig. 1. Schematic representation of the grain boundary of bcc iron and the position of impurity atoms (P, Cr, Si, Mn, C): (a) Σ5(310); (b) Σ3(111) (1–3 positions for impurity atoms; ο – 0 interstitial position for phosphorus and carbon atoms, zero position; □ – position of carbon atom during joint segregation of P and C in interstitial positions; 2ʹ and 3ʹ – positions for impurity atoms during joint segregation).

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3. Fig. 2. Dependence of the volume of the Voronoi polyhedron for an impurity atom on the position number. The dotted line shows the volume of the Voronoi polyhedrons for iron atoms near the grain boundary in pure bcc-Fe.

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4. Fig. 3. Dependence of the magnetic moment on the impurity atom X and the dissolution energy of impurity X (X=P, Mn, Cr, Si) on the position number for the Σ5(310) GB.

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5. Fig. 4. Dependence of the magnetic moment on the impurity atom X and the dissolution energy of impurity X (X=P, Mn, Cr, Si) on the position number for the Σ3(111) GB. The dotted line shows the data from [30].

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6. Fig. 5. Dependence of the distance between the phosphorus atom (in position 2 (a) and in position 0 (b)) and the impurity on the impurity position number.

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7. Fig. 6. Dependence of the relative energy (En–E0) of the grain boundary Σ5(310) containing a phosphorus atom (in position 2 (a) and 0 (b)) and impurities Mn, Cr, Si, P, on the impurity position number.

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8. Fig. 7. Change in co-segregation energy depending on the position number of X atoms (X=Mn, Cr, Si, P) at the Σ5(310) grain boundary: (a); (b). The phosphorus atom is in position 2.

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9. Fig. 8. Change in co-segregation energy depending on the position number of X atoms (X=Mn, Cr, Si, P) at the Σ5(310) grain boundary: (a); (b). The phosphorus atom is in position 0.

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10. Fig. 9. Cosegregation energies of phosphorus with carbon and depending on the phosphorus position number (a). Carbon occupies the interstitial position (0). Dependence of the relative energy (En–E0) of the grain boundary with the carbon atom (0) and phosphorus on the P position number (b).

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11. Fig. 10. Dependence on the position number of impurity X at the grain boundary Σ3(111): (a) the distance between the phosphorus atom (in position 2) and impurity X; (b) the relative energy ( ) of the grain boundary containing the phosphorus atom (in position 2) and impurity X in different positions.

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12. Fig. 11. Cosegregation energies of P–X atoms (X=Mn, Cr, Si, P) depending on the position number at the grain boundary Σ3(111) (a); (b). The phosphorus atom was in position 2.

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13. Fig. 12. Cosegregation energies of phosphorus with carbon and depending on the phosphorus position number at the grain boundary Σ3(111) (a). Carbon occupies the interstitial position (0). Dependence of the relative energy of the grain boundary with the carbon atom (0) and phosphorus on the position number P (b).

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