Calculation of the P-T phase diagram and tendency toward decomposition in equiatomic TiZr alloy V.Yu. Trubitsin, E.B. Dolgusheva ∗ Physical-Technical Institute, Ural Branch of Russian Academy of Sciences, 132 Kirov Str.,426001 Izhevsk, Russia (Dated: November 3, 2018) Electronic, structural and thermodynamic properties of the equiatomic alloy TiZr are calculated within the electron density functional theory and the Debye-Gr¨ uneisen model. The calculated values of the lattice parameters a and c/a agree well with the experimental data for the α , ω and β phases. The ω phase is shown to be stable at atmospheric pressure and low temperatures; it remains energetically preferable up to T = 600 K. The α phase of the TiZr alloy becomes stable in the range 600 K < T < 900 K, and the β phase at temperatures above 900 K. The constructed phase diagram qualitatively agrees with the experimental data available. The tendency toward decomposition in the equiatomic alloy ω − TiZr is studied. It is shown that in the ground state the ω phase of the ordered equiatomic alloy TiZr has a tendency toward ordering, rather than decomposition. PACS numbers: 63.20.Ry, 05.10.Gg, 63.20.Kr, 71.15.Nc Keywords: Phase diagram, decomposition, alloy, zirconium, titanium It has been experimentally found that the TiZr sys- tem is characterized by full solubility of its constituents. As in pure titanium and zirconium, three phases ( α , β and ω ) are observed in the TiZr alloy $^{1–3}$. The structural α → β transformations of the equiatomic alloy were ex- tensively studied in Ref. 1 by the differential thermal anal- ysis (DTA) at temperatures up to 1023 K, and pressures up to 7 GPa. It was found that the β → α transition tem- perature, being equal to 852 K at atmospheric pressure, decreases with pressure down to the triple equilibrium point of the α , β and ω phases ( P$_{tr}$ = 4 . 9 ± 0 . 3 GPa, T$_{tr}$ = 733 ± 30 K). At pressures above the triple point the β phase transforms immediately to the ω phase with a light positive slope of the equilibrium line. If a sample is cooled to room temperature at a pressure of 6 GPa, and then unloaded, one can obtain at atmospheric pres- sure a metastable ω phase which on heating transforms into an α phase in the temperature interval from 698 K to 743 K. Cooling of the β phase in the pressure range 2 . 8 - 4 . 8 GPa results in the formation of a two-phase mixture of a stable α and a metastable ω phase. The structural α → ω transformations in the TiZr alloy were studied in detail in Ref. $^{3}$. Investigating TiZr samples under shear- strain conditions at pressures up to 9 GPa at tempera- tures 300 and 77 K, the authors arrived at the conclusion that in equiatomic TiZr the equilibrium α → ω boundary is situated on the P-T diagram at 6 . 6 GPa. In the same paper the phase diagram of TiZr was constructed in the regular-solution approximation, and the triple point pa- rameters were calculated ( P = 8 . 5 GPa, T = 693 K). As may be seen, these values differ substantially from those of Ref. $^{1}$. Detailed studies performed in Ref. 4 have shown that in the region of high pressures and temperatures there exist two ω phases ( ω and ω 1 ) that differ in atomic vol- ume by about 14 %. The authors suggested the existence of a isostructural phase transition ω − ω 1 connected with changes in the electron structure of the alloy. They sup- posed that the large difference in the atomic volume be- tween the two phases points to the existence of an s-d electronic transition in ω − TiZr. Later, phase separation of a hexagonal TiZr ω phase was experimentally detected in Ref. $^{5}$. The ω → ω 1 + ω 2 decomposition was revealed after a prolonged heat treatment at P = 5 . 5 ± 0 . 6 GPa and T = 440 ± 30 0 C. It was supposed that in a wide concentration range at pressures above the triple equilib- rium point, the ω phase may exist in the T i$_{x}$Zr 1 − x alloy only as a metastable one that persists due to low diffu- sive mobility of its constituents. The decomposition of the ω − TiZr solid solution into two ω phases of different structure was used as an alternative explanation for the experimental results obtained in Ref. $^{4}$. Up to now the electron structure and structural trans- formations of the equiatomic alloy TiZr have never been calculated. Below we present the results of our theoret- ical calculations of electronic, structural and thermody- namic properties of the equiatomic alloy TiZr performed within the framework of the electron density functional theory and the Debye-Gr¨ uneisen model. The tendency of the ordered equiatomic alloy ω − TiZr to decompose is also investigated. The electron structure and total energy were calcu- lated by the scalar relativistic full-potential linearized augmented-plane-wave (FPLAPW) method, using the WIEN2K package $^{7}$. To ensure the desired accuracy of the total energy calculation, the number of plane waves was defined by the condition RK$_{max}$ = 7 , the total num- ber of k -points in the Brillouin zone was equal to 3000, 3000, 600 for the β , α and ω phase, respectively. The total and partial densities of states were obtained by a modified tetrahedron method $^{6}$. The atomic radii were the same for all phases and pressures: 2 . 42 a.u. for Zr, I. CALCULATION TECHNIQUE Introduction arXiv:1001.1700v1 [cond-mat.mtrl-sci] 11 Jan 2010