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The substitutional solute atom induced local lattice distortion (LLD) in dilute metal solid solution was believed to be uniform that may even be modeled by using soap bubble raft. Contrary to this conventional picture, we report in this manuscript that the Mo induced LLD in dilute Ti-Mo solid solution is highly non-uniform as evidenced by our first principles calculations. The non-uniform LLD is ascribed to the Jahn-Teller splitting of the degenerated d states of Mo atom. We propose that the substitutional solid solutions with non-uniform LLD should satisfy two conditions. With which, the solid-solutions suffering from non-uniform LLD are predicted. The non-uniform LLD is expected to result in non-spherical stress field around the solute atom, and, therefore, challenges the application of classical solid solution hardening model to this kind of solid solutions., Comment: 8 pages and 4 figures

The ductile-to-brittle transition is commonly observed in metastable β-titanium (Ti) alloys containing ω-precipitates, while the fundamental understanding on ω-embrittlement hitherto remains elusive. In this work, the prototypical Ti-20 wt% Mo metastable β-Ti alloy has been systematically investigated by coupling experiments and first-principles calculation to eliminate this puzzle. It is shown that the structural evolution of ω-phase controls the deformation mechanism transition of twinning-to-slip in Ti Mo alloy, being the origin of ductile-to-brittle transition of this alloy. The initial trigonal ω-structure continuously collapses to hexagonal ω-structure (structural collapse) whilst Mo-atoms are rejected out concurrently (stoichiometric varieties), both leading to hardening of ω-precipitates. This self-hardening of ω-precipitates was further rationalized in terms of the enhanced propensity for a covalent character of the atomic bond demonstrated by the electronic density of states (DOS) from first-principles calculation. Specifically, the self-hardening behavior of ω-precipitates promotes dislocation slip on isolated planes in lieu of correlative slip on successive planes inside ω1-variant, while dislocations are completely blocked ahead ω2/ω3/ω4-variants. This in turn renders the transition from deformation twinning that contributes to great macro-plasticity to ordinary dislocation slip that contributes to localized deformation bands in the present Ti Mo alloy.

An intricate understanding of the fundamental β→α phase transformation upon the presence of metastable ω phase is vital for tailoring the multiphase microstructures of titanium and titanium alloys for various specific applications. To approach this, the structures and energetics of heterophase interfaces among α, β, and ω in titanium were thoroughly investigated, using the combination of high-resolution transmission electron microscopy and first-principles density functional theory calculations. The results strongly suggest that metastable ω does not necessarily act as the precursor of α but can reduce the energy barrier for α nucleation in β. The ω/β interfaces acts as favorable nucleation sites for α which, once forms, tends to grow favorably into the β matrix. These findings validate the ω-assisted α nucleation mechanism, and adequately rationalize many TEM observations on titanium alloys.

Breakdown of Schmid's law is a long-standing problem for exploring the orientation-dependent deformation mechanism in intermetallics. The lack of atomic-level understanding of the selection rules f ...

Using density-functional theory, we determine the generalized stacking fault energy (GSFE) for the { 1 1 ¯ 2 } 〈 1 ¯ 11 〉 twinning system in ferromagnetic (FM) body-centered cubic Fe and Fe-Cr alloys with molar fraction of Cr ≤ 0.5 . We adopt both reflection and isosceles twinning pathways and reveal the magnetic ordering effects on the GSFE by contrasting the FM results to those obtained for the magnetically disordered paramagnetic (PM) state. The results show that the isosceles twin boundary configuration is energetically preferred in this binary. The loss of long-range magnetic order lowers the GSFE amplitude but increases the twin boundary migration (TBM) energy regardless of the Cr content. The twin boundary formation (TBF) energy and the TBM energy show non-linear dependences on Cr content in the FM and PM states, and the effect of Cr on these properties critically depends on the magnetic state. We discuss our results in regard to the stable twin boundary structure and deformation twinning experimentally observed in homogeneous Fe-50 wt.% Cr alloy up to temperatures slightly above the magnetic ordering temperature.

First-principles calculations have been performed to study the effect of C on the stacking fault energy (SFE) of paramagnetic γ -Fe and Fe Cr Ni austenitic steel. In these systems, the local magnetic structure is very sensitive to the volume in both fcc and hcp structures, which emphasizes the importance of the magnetovolume coupling effect on the SFE. The presence of C atom suppresses the local magnetic moments of Fe atoms in the first coordination shell of C. Compared to the hypothetical nonmagnetic case, paramagnetism significantly reduces the effect of C on the SFE. In the scenario of C being depleted from the stacking fault structure or twin boundaries, e.g. , due to elevated temperature, where the chemical effect of C is dissipated, we calculate the C-induced volume expansion effect on the SFE. The volume induced change in the SFE corresponds to more than ∼ 50% of the total C effect on the SFE obtained assuming uniform C distribution.

Unlike the general belief that either dislocations cut or by-pass the ω -precipitates contributes to the high strength of Ti alloys, here we uncovered a new strengthening mechanism of lattice disordering of ω -precipitates by investigating the deformation behavior of body-centered-cubic (bcc) single crystalline Ti-10V-2Fe-3Al (Ti1023) alloy micropillars. This unique ω -precipitate disordering strengthening mechanism emerges in-between the precipitate cutting and by-passing mechanisms, because the dislocations pile-up stress reaches the ideal strength of ω -phase. The ω -precipitates with four variants manifest the strong deformation anisotropies, as verified by both the crystallographic orientation analysis and energy landscapes from the first principle calculations. The combination of precipitates cutting of ω 1-variant and precipitates disordering of ω 2/ ω 3/ ω 4-variants leads to the formation of precipitate-free channel in bcc (146) β -oriented Ti1023 alloy micropillars. Due to the presence of ω -precipitates, the bcc Ti1023 alloy micropillars exhibit stable plastic flow, associated with weak-size dependent superior strength. These findings provide fundamental understanding of the deformation characteristic of precipitate-hardening alloys, and have important implications for the design of small-scale materials.

We propose an ω-lattice mechanism that is irrelevant to dislocation behaviors for a popular twinning ({1 1 2}〈1 1 1〉-type) system in body-centered-cubic (bcc) metals and alloys. The twinning process is dependent on the reverse transformation of ω (hexagonal) → bcc. The driving force of the twinning is attributed to the instability of a high density of nanoscale metastable ω precursors, and the mechanism has been experimentally and theoretically confirmed in bcc-Ti alloys with the {1 1 2}〈1 1 1〉-type twin formed under conditions free of external stress and internal strain. The ω-lattice mechanism involves bcc lattice shuffling only, thus can be applied to all bcc metals and alloys.

Stacking fault energy (SFE) plays an important role in the plastic deformation of metals. As compared to those of face-centered cubic metals, the SFEs of hexagonal close-packed (hcp) metals are less reported in literature. In this paper, we derive the expressions of four types ( I 1 , I 2 , E and T 2 ) of basal plane SFEs of hcp metals in terms of the interlayer interaction energies within the framework of the Ising model. The SFEs of 14 kinds of hcp metals are then evaluated with the interlayer interaction energies extracted from the total energies of four prototypes calculated by using the first-principles full-potential augmented plane-wave method. We show that the hcp metals can be divided into three types according to their interlayer interaction energies. For all the hcp metals involved in this study, I 1 has the lowest SFE, whereas E has the highest. The metals (Mg, Co, Zn and Cd) with principal slip system (0 0 0 1) [ 1 1 2 ¯ 0 ] generally have low basal plane SFEs. The I 1 and T 2 SFEs increase linearly with the energy difference between double hexagonal close-packed and hcp structures, whereas the I 2 and E SFEs increase linearly with the energy difference between the short-period twin and hcp structures, indicating a trivial contribution of the interaction energy between atomic layers over third nearest neighbors to the SFEs. The SFEs also correlate with the cohesive energy density (cohesive energy of unit volume) with the exception of Be, Co, Tc and Re.

In this paper, the five-layer modulated (5M) martensitic structures of Ni(2)Mn(Al(x)Ga(1-x)), with x = 0, 0.1 and 0.2, are investigated by the use of the exact muffin-tin orbital method in combination with the coherent potential approximation. The 5M martensite is modeled by varying c/a (shear) and wave-like displacements of the atoms on (1 1 0) plane (shuffle) scaled by eta according to Martynov and Kokorin (J. Phys. III 2, 739 (1992)). For Ni(2)MnGa, we obtain 5M martensite with equilibrium c/a of 0.92 and eta of 0.08, in reasonable agreement with the experiment results (0.94 and 0.06, respectively). c/a and eta are linearly coupled to each other. Al-doping increases c/a and decreases eta, but the linear c/a similar to eta coupling remains. Comparing the total energies of the 5M martensite and L2(1) austenite, we find that the martensite is more stable than the austenite. Al-doping increases the relative stability of the austenite and finally becomes energetically degenerated with the 5M martensite at an Al atomic fraction (x) of about 0.26. The relative phase stability is analyzed based on the calculated density of states. The calculated total magnetic moments mu(0) as a function of c/a exhibit a maximum around the equilibrium c/a. Al-doping reduces mu(0) (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The composition-dependent elastic properties and electronic structure of off-stoichionietric TiNi with a B2 structure are investigated by using the first-principles exact muffin-tin orbitals method in combination with coherent potential approximation and first-principles plane-wave pseudopotential method (for computing bonding charge densities). The Zener anisotropy, c(44)/c', increases with increasing Ni contents, but is quite small, indicating a strong correlation between the softening Of c(44) and c' with decreasing temperature during martensitic transformation (NIT). For the Ni-rich TiNi, c(44) increasing Ni content whereas c' decreases. On the Ti-rich side, both c(44)and c' are insensitive to the composition. It was observed that larger c(44) corresponds to higher MT temperature, and the composition dependence of elastic modulus is discussed on the basis of the bonding charge densities and electronic density of states. We propose that the strong composition dependence of the elastic modulus of the Ni-rich TiNi can be attributed to the Coulomb static electronic repulsion between the antisite Ni atorns and their surroundings. The insensitivity of the elastic modulus of the Ti-rich TiNi to the composition is due to the absence of such repulsion between the Ti antisites and their nearest neighbors. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A recently developed mean-field model has been combined with first principles calculations of binding energy to investigate the site occupancies of micro-alloying elements and vacancies in NiAl as well as the stability of the micro-alloyed B2 phase with respect to disordering and second-phase formation. The theoretical results suggest that the transition metal elements in the same row of the periodic table increasingly tend to the Ni sublattice with increasing atomic number. Micro-alloying addition tends to decrease the vacancy concentration of NiAl alloys. Alloying with X that substitutes for Ni is predicted to have the sides of its solubility lobe parallel to the Ni-X side of the isotherm, but parallel to the Al-X side if X substitutes for Al. Micro-alloying was shown to raise the ordering temperature of the B2 phase over the corresponding binary alloy, in contrast with the effect of vacancies. Alloying effects on ordering temperature and the formation of point defects appear independent of the site substitution behaviour, and are less significant for 3d than for 4d and 5d transition metal elements. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.