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

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

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

4. The HCP (A3) Structure hcp_A3 Hexagonal, space group #194 P 6 3 /m m c (Zn) (2c) (1/3, 2/3, 1/4) Covalent radius: 1.45 Å 1.333 Å (Zn-Zn)

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

6. Bi-ZnBi-Sn

7. (Bi) (Zn) (Sn) 20 ºC

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

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

10. Data from CRC Handbook After Rietveld refinement

11. Data from CRC Handbook After Rietveld refinement

12. Data from CRC Handbook After Rietveld refinement

13. Data from CRC Handbook After Rietveld refinement

14. Data from CRC Handbook After Rietveld refinement

15. Data from CFC book After Rietveld refinement

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 crystalline parameters (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

19. (002)

20. After Rietveld refinement

23. [002] The (002) plan for Zn

24. 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 Zinc phase (Zn) has different expansion coefficients for different crystallographic directions a = b and c: ● The Bismuth phase (Bi) has similar expansion coefficients for different crystallographic directions a = b and c.