A first principles study of the phase stabilities in Ti-Transition-Metal compounds and the shape memory effect in TiNi

Zhang, Jinming (1997) A first principles study of the phase stabilities in Ti-Transition-Metal compounds and the shape memory effect in TiNi. University of Southampton, Doctoral Thesis.

Abstract

I have ab initio studied the lattice stabilities and phase transformations in the 12 TiM compounds (M = Fe, Co, Ni, Cu; Ru, Rh, Pd, Ag; Os, Ir, Pt, Au) and calculated their physical properties. In my ab initio studies, the FLAPW method and, to a less extent, the LMTO-ASA method have been used to carry out the first-principles electronic structure studies and to perform ab initio total energy calculations. In the aspect of electronic structure studies, all of the detailed information about the electronic structures for the 12 TiM has been obtained and analysed in conjunction with the observed experimental facts. There are clear signs of the band filling effect which is measured by the averaged number of valence electrons per atom, Ñ. The decreased stability with the increase of Ñ could be accordingly attributed to the gradual occupation of the antibonding states and the results of B2-TiCu, B2-TiAg, and B2-TiAu indicate that the singularity in their antibonding peak is responsible for the observed B2 phase instability. The electronic structures of the low temperature phases have also been studied intensively which indicate that the thermodynamic driving mechanism of the band Jahn-Teller effect nature may work in the TiM systems. The re-population of the electrons among the orbitals alters the valence charge densities (VCD). The VCD changes, mainly along the Bain path, have been plotted and analysed to give a good view of the bonding situation and to show how the bonding system responds to the gradually tetragonallized potential. Moreover the generalized susceptibility χ₀(q̅;) has been derived for the 12 TiM to detect the anomalies in their electronic structures. The quantity has indeed effectively shown the phase instability in B2-TiCu, B2-TiAg, and B2-TiAu. The sequence of the B2 phase instabilities and the cubic → orthorhombic (or monoclinic) → orthorhombic (or monoclinic) → tetragonal tendency in the three TiM series have been discussed in terms of the Ñ. In the ab initio total energy calculations, I have evaluated the energy changes for the tetragonal Bain distortions in the 12 TiM, the P_m3m → P_4/mmm → C_mmm symmetry distortions in TiRh, TiPd, and TiAg and also the k⃗; = π/a[101] B2 → β19 distortion mechanism for TiNi, TiPd, TiRh, and TiAg. Through the calculations, a reliable picture of the driving mechanism for the phase transformations in the TiM series have been obtained and the important phase transformation-related properties and thermodynamical functions, such as lattice parameters, energy barrier heights, total energy changes, and the entropy have been derived simultaneously. Thermodynamic qualities, such as phase transformation temperatures T₀, have also been ab initio evaluated for some of the TiM.

My calculated results show that transformation-related physical properties can be obtained with great preciseness from the first principles total energy calulations based on the local density function scheme. For example, quantitatively precise total energy differences and the energy barrier height have been obtained fr the 6-TiM (TiCo, TiNi, TiCu, TiRh, TiPd, and TiAg) and the calculated transformation temperatures T₀ for the TiRh and TiNi have been found in very good agreement with experiments. Many long-time-believed points, such as anharmonic term would be very important for TiNi thermodynamocs and Ti-d electrons drive the phase instabilities in the TiM series, have been challenged based on the present calculations.

I found that the B2 structure of shape memory alloy, TiNi unlike that of the other TiM compounds, is stable against both Bain and orthorhombic distortions, and that TiNi has some flat energy areas around local minimum points. Based on these findings, I have presented a microscopic theory of the shape memory effect (SME) and describe some thermodynamic models in which some features of the SME are displayed. My electronic structures analyses reveal the importance of the Ni metallic bonding to the B2 phase stability and to the detwinning mechanism.

I concluded that the study of the electronic states at the parent (austenite)-martensite (P-M) interface and their role in martensitic transformations (MAT) may hold the key to the problems facing MAT studies. In this thesis, I have presented a very simple model case to simulate the electron transition at the interface. The method use is the Green's function technique. Both sides are described by s-type tight-binding Hamiltonians from which the the analytical results for the interface Green's function can be derived. These results have shown how the lectronic transition occurs (from the band states of parent phase, to the localized interface states and finally to the band states of martensitic phase.) to bring about crystal transformation. This is a new machanism for MAT of heterogeneous nature. However, it is only a more or less crude model case in which a good idea has been presented and advanced techniques are needed to explore some real P-M interface cases.

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