Structural stability of the ternary compound Ti 6 Si 2 B in the Ti-Si-B system

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1 Structural stability of the ternary compound Ti 6 Si 2 B in the Ti-Si-B system Catherine Colinet a, Jean-Claude Tedenac b a Science et Ingénierie des Matériaux et Procédés, UMR 5266, CNRS INP Grenoble - UJF, BP 75, 3842 Saint Martin d Hères Cedex b Institut de Chimie Moléculaire et des Matériaux I.C.G., UMR-CNRS 5253, Université Montpellier II, Place E. Bataillon, 3495 Montpellier Cedex 5, France

2 Outline Ternary compounds T 6 X 2 X with T : early transition metal, X and X : p elements, and Fe 2 P (C22) type structure Ab initio calculations (VASP) Formation enthalpies and lattice parameters Comparaison with experimental values Conclusions

3 Ternarycompounds T 6 X 2 X with Fe 2 P-type structure T: early transition metal, X and X p elements V X << V X Ternary Fe 2 P-type structure prototype: K 2 UF 6, ternary variant: Zr 6 CoGa 2, Ti 6 Si 2 B isotypic with Ni 6 Si 2 B Experimental results Ti 6 Si 2 B (Ramos et al. 23, 24) Ti 6 Ge 2 B (Borisov et al., 27)

4 Experimentalphase diagrams Ti 6 Si 2 B Ti 6 Ge 2 B Ramos et al. 23, 24 Borisov et al. 27

5 Fe 2 P type structure hp9, C22, P(-6)2m, N 189 Binary Ternary Elements Wyckoff positions x y z Elements Wyckoff positions x y z T 3f x 1 T 3g x 2 1/2 X 1b 1/2 X 2c 1/3 2/3 T 3f x 1 T 3g x 2 1/2 X 1b 1/2 X 2c 1/3 2/3 V X << V X

6 Binaryand ternaryfe 2 P type structure Si 1b Si 1b Si 1b Si 1b Binary Ti 2 Si B 1b B 1b Ternary Ti 6 Si 2 B B 1b B 1b

7 TernaryFe 2 P type structure

8 Ab initio calculations Density functional theory (DFT) Vienna ab-initio simulation package (VASP) Projected augmented waves technique (PAW) Generalized gradient approximation (GGA) Electronic configurations: with p semi-core electrons of Ti Cutoff 32eV

9 Calculatedenthalpies of formation f H (kj/mol of atoms) f H(kJ/mol of atoms) A3-Ti C16 C22 D8m D88 D81 D5a Bg B27 B33 prot B4Ta x B Ti-B C32 D8 i D8h prot B 4 Th prot B 4 W hr12-b A3-Ti A4-Si prot Ni3P prot PTi3 A15 D 19 C4 C54 C49 B82 C16 D8 1 C22 Si 4 Ti 5 hp18 B33 D8m B27 D8 8 Si D5 4 Ti 5 prot Ge 4 Sm 5 a Si 4 Ti 5 prot Si 4 Zr xsi Ti-Si f H (kj/mol of atoms) Ti-Si-B Ti 6 Si 3 Ti 6 B 3 C22-Ti 6 Si 3 C22-Ti 6 SiB 2 C22-Ti 6 Si 2 B C22-Ti 6 B 3 Equilibrium between A3-Ti and B27-TiB xb/(xb+xsi)

10 Calculated lattice parameters a (A ) 6.6 V (A 3 ) xb/(xb+xsi) xb/(xb+xsi) c (A ) c/a xb/(xb+xsi) xb/(xb+xsi) Experimental values: Ramos et al. 24

11 Vertical prismsformedby and by atoms B 2.88 Å Å B 2.74 Å Si Si Å Si Si 2.64 Å B Å B

12 C22-Fe 2 P prototype Electronicdensities 2 Ti6B3 EF of states 1 BSi 2-8 Ti Ti6Si B2 1 n(e) (states/ev/fu) Ti6Si2B Ti6Si E(eV)

13 Electronicdensities of states 1 5 B 1b Total C22-Ti 6 Si 2 B Ti s Ti p Ti d n(e) states/ev/f.u. 1 Ti s Ti p Ti d B s 6 8 B p B d Si s Si p Si d E (ev)

14 Calculated enthalpies of formation f H (kj/mol of atoms) f H (kj/mol of atoms) A3-Ti prot Ni3P B82,C16 C49 C54 A4-Ge B33 C22 B27-6 prot Si 4 Zr 5 prot Ge 5 Ti 6 D88 prot -7 Ge4Sm x Ge -1 A3-Ti C16 C22 D8m D88 D81 D5a B27 Bg B33 prot B4Ta3 C32 D8i D8h hr12-b prot B4Th prot B4W f H (kj/mol of atoms) Ti2Ge ev C22-Ti 2 Ge Ti-Ge-B C22-Ti6BGe2 C22-Ti6B2Ge Ti2B C22-Ti 2 B ground state line in binary Ti-B xb / (xb+xsi)..2.4 x B

15 Calculated lattice parameters Ti-Ge-B Experimental values Abinitiocalculatedvalues Ti 67.5 Ge 21.5 B 11 Ti Ge B a Å Å c Å Å Borisov et al. 27

16 Calculated enthalpies of formation Ti-Sn-B Ti-Sn-Si Ti 2 Sn Ti 2 B Ti2Sn Ti2Si f H (kj/mol of atoms) C22-Ti 2 Sn B8 2 -Ti 2 Sn C22-Ti 6 Sn 2 B C22-Ti 6 SnB 2 C22-Ti 2 B Equilibrium between A3-Ti and B27-TiB atoms) f H (kj/mol of C22-Ti6Sn3 B82-Ti2Sn C22-Ti6Sn2Si C22-Ti6SnSi2 C22-Ti6Si xb/(xb+xsn) x Si /(x Si +x Sn ) However not stable in the ternary Ti-Sn-Si

17 Calculated enthalpies of formation Hf-Si-B Zr-Si-B Hf 2 Si Hf 2 B Zr 2 Si Zr 2 B f H (kj/mol of atoms) C22-Hf 2 Si C22-Hf 6 SiB 2 C22-Hf 2 B C22-Hf 6 Si 2 B Equilibrium between A3-Hf and C32-HfB 2 f H (kj/mol of ato oms) C22-Zr 2 Si C22-Zr 6 Si 2 B C22-Zr 6 SiB 2 C22-Zr 2 B Equilibrium between A3-Zr and C32-TiB 2-7 C16-Hf 2 Si -7 C16-Zr 2 Si xb/(xb+xsi) x B /(x B +x Si ) Agreement with Ramos et al. (24)

18 Conclusions The ab initio calculations confirm the results of the experimental determinations allow to obtain the value of the enthalpy of formation of the ternary phase give lattice parameters in good agreement with the experimental values allow to predict the systems in which ternary this phase is stable or not

19 Interatomic distances in C22 phases Ti 6 Si 3 Ti 6 Si 2 B Ti 6 SiB 2 Ti 6 B 3 Si 1b B 1b Si 1b B 1b B 2c B 2c Si 1b B 1b Si 1b B 1b B 2c B 2c B 2c B 2c Si 1b B 1b Si 1b B 1b

20 2.53 Å 2.99 Å 2.87 Å Zr 3f Zr 3g 2.84 Å B 1b

21 Nextnearestneighboursof B and Si atoms 2.31 Å B 1b CN= 9 CN= 9 Very short distance between B (1b) and Ti (3f) in the Ti 6 Si 2 B compound

22 Nextnearestneighboursof and atoms B 1b B 1b 2.31 Å B 1b B 1b CN= 12 CN= 11 Very short distance between B (1b) and Ti (3f) in the Ti 6 Si 2 B compound

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