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THE BEHAVIOUR OF LATTICE PARAMETERS IN Bi-Sn-Zn M. Helena Braga , J. Ferreira, L. F. Malheiros

THE BEHAVIOUR OF LATTICE PARAMETERS IN Bi-Sn-Zn M. Helena Braga , J. Ferreira, L. F. Malheiros DEF – FEUP, INETI, DEMM – FEUP. (Sn). The βSn (A5) Structure. bct_A5. Covalent radius: 1.46 Å 1.405 Å (Sn-Sn). Tetragonal, space group #141 I 4 1 /a m d. (4a) (0, 3/4, 1/8). (Bi).

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THE BEHAVIOUR OF LATTICE PARAMETERS IN Bi-Sn-Zn M. Helena Braga , J. Ferreira, L. F. Malheiros

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  1. THE BEHAVIOUR OF LATTICE PARAMETERS IN Bi-Sn-Zn M. Helena Braga, J. Ferreira, L. F. Malheiros DEF – FEUP, INETI, DEMM – FEUP

  2. (Sn) The βSn (A5) Structure bct_A5 Covalent radius: 1.46 Å 1.405 Å (Sn-Sn) Tetragonal, space group #141 I 41/a m d (4a) (0, 3/4, 1/8)

  3. (Bi) The αAs (A7) Structure rhombo_A7 Covalent radius: 1.54 Å 1.545 Å (Bi-Bi) Rhombohedral (trigonal) space group #166 R-3m (6c) (0, 0, z) (hexagonal axis)

  4. (Zn) The HCP (A3) Structure hcp_A3 Covalent radius: 1.45 Å 1.333 Å (Zn-Zn) Hexagonal, space group #194 P 63/m m c (2c) (1/3, 2/3, 1/4)

  5. THE BEHAVIOUR OF LATTICE PARAMETERS IN Bi-Sn-Zn Room temperature

  6. Bi-Sn Bi-Zn

  7. (Zn) (Bi) (Sn) 20 ºC

  8. (101) (200) w(Bi) = 25.6%, w(Sn) = 38.2%, w(Zn) = 36.2% • observed – points, and calculated - continuous line; • Bragg positions for (Sn), (Zn), and (Bi) respectively; • difference between observed and calculated patterns. (1) (2) (3)

  9. w(Bi) = 21.0%, w(Sn) = 8.6%, w(Zn) = 70.4% • observed – points, and calculated - continuous line; • Bragg positions for (Sn), (Zn), and (Bi) respectively; • difference between observed and calculated patterns. (1) (2) (3)

  10. After Rietveld refinement Data from CRC Handbook

  11. After Rietveld refinement Data from CRC Handbook

  12. After Rietveld refinement Data from CRC Handbook

  13. After Rietveld refinement Data from CRC Handbook

  14. After Rietveld refinement Data from CRC Handbook

  15. After Rietveld refinement Data from CFC book

  16. Conclusions (room temperature: different compositions) ●As expected from the phase diagram at room temperature, the only phases that show the possibility of having higher crystallineparameters(lattice parameters) than the pure element, are (Sn) (especially for a = b) and (Bi) (especially for c), when comparing our Rietveld refinements data with the CRC handbook for Sn and Bi pure elements. Nevertheless, a closer look to the available information shows that Bi has the highest covalent radius compared with that from Sn and Zn. The latter makes us conclude that it is not expected that the substitution of Bi by these atoms will make the lattice parameters increase. Hence, the discrepancy found for (Bi)’ c parameter is due to the presence of Sn and Zn atoms in interstitial spaces or due to experimental inaccuracies. ● As expected from the phase diagram at room temperature, all samples have similar lattice parameters for (Sn), (Bi) and (Zn).

  17. THE BEHAVIOUR OF LATTICE PARAMETERS IN Bi-Sn-Zn High temperature

  18. (002)

  19. After Rietveld refinement

  20. [002] [002] The (002) plan for Zn The (002) plan for Zn

  21. ● The Zinc phase (Zn) has different expansion coefficients for different crystallographic directions a = b and c: Conclusions (different temperatures) ●If a crystalline solid is isometric (has the same structural configuration throughout), the expansion will be uniform in all dimensions of the crystal. If it is not isometric, there may be different expansion coefficients for different crystallographic directions, and the crystal will change shape as the temperature changes. ● The Bismuth phase (Bi) has similar expansion coefficients for different crystallographic directions a = b and c.

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