displacement occurs without strain. The displacements shown in Fig.7(a) correspond to those characteristic of the ω → β transition. The volume value V ≈ 15 ˚ A 3 at which begins a sharp decrease in Δ E , agrees well with the results of the total energy calculation for the ω and β phases of TiZr plotted in Fig.2. Based on the data presented, we can draw an important conclusion that the pressure value at which occurs the ω → β transi- tion depends substantially on the ordering type in the equiatomic TiZr alloy. This also indirectly confirms our statement that the disagreement with the experiment concerning the ω − β equilibrium boundary position on the phase diagram calculated in the Debye model (Fig.4) is caused by the presence of inhomogeneities in actual TiZr alloys used in experiments in Refs. $^{1–3}$. The volume dependence of the total energy for the re- laxed structures of type I and II is plotted in Fig.8(a). As may be seen, in the whole range of volume change the energy is minimum for the structure of type I corre- sponding to the most uniform distribution of Ti and Zr atoms. Recall that in variant I the lattice is represented by pure monolayers of titanium and zirconium separated by a mixed Ti-Zr layer, and in variant II by a system of two Ti layers alternating with two Zr layers (with no intermediate layer). Thus, as decomposition grows, the system energy increases. This tendency persists on fur- ther decomposition, which may be seen in Fig.8(b), where the total energy is plotted versus volume for the struc- tures of type II, III and IV. In the structure of type IV five Ti layers are separated from five Zr layers by a mixed intermediate layer, while in structure III there are six lay- ers of each metal without intermediate layer. It is seen from the figure that as the thickness of pure metal layers increases (from one to five layers), the system energy sig- nificantly rises. As could be expected, the presence of an intermediate layer reduces the total energy of the system. This may be seen from a comparison of the energy values at V ≈ 18 . 5 ˚ A 3 for the calculation variants III and IV (structure III is presented in the figure by a single point). To summarize, the calculations performed show that in the ground state the ω phase of TiZr exhibi ts a ten- dency toward ordering and not toward decompos ition, as was suggested in Ref. $^{5}$. The analysis of the tot al energy curves shows that the allowance for temperatur e effects in the Debye-Gr¨ uneisen model will not chang e the en- ergy relation between different calculation varia nts, and cannot explain the experimentally observed form ation of two ω structures. Besides, we have not found any pe- culiarities connected with the s-d electron tran sition in the total-energy curves. Thus, also the sugge stion ad- vanced in Ref. 4 that there exists an isostructur al transi- tion ω → ω 1 due to the pressure-induced chang es in the electron structure, is not confirmed by the calcula tion. In our opinion, the high-temperature decompositio n in the ω phase of equiatomic TiZr alloy is connected not with the change in electron structure under pressure, but with peculiarities of the lattice dynamics, in particul ar, with the presence of strongly anharmonic vibrationa l modes which are of crucial importance in stabilization of the ω lattice of pure titanium and zirconium $^{12}$. The authors acknowledge the partial support f rom the RFBR Grants No. 07-02-00973 and No. 07-02-9 6018. Acknowledgments  15  20  25  30  35  40  45  50  55  60 15  16  17  18  19  20  21  22  23 Energy (mRy) Volume (Å $^{3}$) −TiZr (a)  I  II   15  20  25  30  35  40  45  50  55  60  15  16  17  18  19  20  21  22  23 Energy (mRy) Volume (Å $^{3}$) −TiZr (b) I III IV FIG. 8: Total energy of ω − TiZr for different types of decom- position ( I - IV) designated in accordance with Fig. 5. FIG. 7: The direction of atomic displacements upon lattice relaxation for calculation variants I (a) and II (b) 5