In Fig.1 are shown the crystal structures of the β , α , and ω phases of the equiatomic alloy TiZr used in the calculation. It is seen that the β phase was represented by a structure of the CsCl type with Ti atoms at the cube sites and a Zr atom at the center. The α phase had a hexagonal close-packed lattice in which one atom was Zr, the other Ti. Finally, to describe the ω phase we used a hexagonal lattice with 6 atoms per cell (an ω structure doubled along the z axis). The atomic arrangement and species in this case were chosen as follows: (0 , 0 , 0) - Zr, ( 1 $_{3}$, 2 $_{3}$, 1 $_{4}$) - Ti, ( 2 $_{3}$, 1 $_{3}$, 1 $_{4}$) - Zr, (0 , 0 , 1 $_{2}$) - Ti, ( 1 $_{3}$, 2 $_{3}$, 3 $_{4}$) - Zr, ( 2 $_{3}$, 1 $_{3}$, 3 $_{4}$) - Ti. Thus, the β and α phases were represented by layers of Ti and Zr alternating along the z axis, and in the ω phase layers of Ti and Zr were separated by a mixed Ti-Zr layer. In the hexagonal structures the ratio c/a was optimized for the experimental volume values. In the following, when calculating the volume dependence of the total en- ergy, the c/a ratio was considered to be constant. In Table I are listed the calculated and experimental equi- librium values of the TiZr lattice parameters. It is seen from the table that the lattice parameters a and c/a obtained in our calculation agree well with the experimental data. The greatest discrepancy is observed for the lattice constant of the ω phase. It should be noted that in Ref. 1 the lattice parameters were calculated for a metastable ω structure at atmospheric pressure, and in Ref. 3 for pressure-strained samples. The total energy of each structure was calculated for 7 values of the cell volume V . The data obtained were then interpolated using the technique proposed by Moruzzi $^{8}$. Such an interpolation scheme, together with the Debye- Gr¨ uneisen model, makes it possible to include implicitly The phase diagram of TiZr based on the analysis of Gibbs potentials for different structures is presented in Fig.4. The results of calculation are shown by the solid line. The dotted line denotes the experimental equilib- rium boundaries for the α , β and ω phases of TiZr ob- tained in Ref. $^{1}$. The experimental values of the α − ω Figure 3 presents the volume dependence of the free energy at different temperatures. The free energy of the TiZr alloy was calculated in the Debye-Gr¨ uneisen model with allowance made for the contributions from the elec- tron entropy. The technique of calculating this latter has been described in detail in Ref. $^{9}$. As seen from the figure, the relationship between the energies of different struc- tures changes with temperature. So, at 300 K and zero pressure the energy minimum falls, as in the ground state, on the ω phase which remains energetically preferable up to T = 600 K. In the temperature range 600 K<T< 900 K it is the α phase of TiZr alloy which becomes stable, while above 900 K it is the β phase. As seen from the figure, the energy minimum in the ground state falls on the ω phase. And only at the relative volume change V/V 0 = 0 . 75 the β phase be- comes energetically preferable. A similar situation was observed in pure Ti and Zr as well. However the dif- ference in energy between the α and ω phases in TiZr amounts to Δ E$_{α}$ − ω = 6 mRy, while in pure Ti and Zr it is 0 . 8 mRy and 1 mRy, respectively. Hence it follows that in the equiatomic alloy TiZr the stability region of the ω phase should be much larger in temperature than in pure metals Ti,Zr. The equilibrium values of the volume are V$_{eq}$ = 20 . 47 ˚ A $^{3}$, 20 . 52 ˚ A $^{3}$, and 19 . 97 ˚ A 3 for the α , ω and β phases, respectively. anharmonic effects. The curves obtained for the volume dependence of the electron subsystem total energy are shown in Fig. 2. The energy zero in figure corresponds to -8906.0 Ry. FIG. 1: Crystal structure of the β , α and ω phases of equiatomicTiZr. The Zr atoms are grey, the Ti atoms are dark. FIG. 2: Volume dependence of the total energy of equiatomic TiZr alloy for the β , α and ω phases II. PHASE DIAGRAM a calc. ( c/a )$_{calc.}$ a exp. [1] ( c/a ) exp. [1] a exp. [3] ( c/a ) exp. [3] β 6.457 1 - 1 - - α 5.860 1.583 5.866 1.583 - - ω 9.122 0.617 9.152 0.617 9.131 0.616 TABLE I: Equilibrium values of the TiZr lattice parameters in atomic units  0.06  0.07  0.08  0.09  0.10  0.11  0.12  0.13  16  18  20  22  24 Energy (Ry) Volume (Å $^{3}$) TiZr 2 and 2 . 26 a.u. for Ti.