Fundamental study of immiscible Ti-Mg system : ball milling experiments and ab initio modelling

Abstract

A combination of ball milling experiments and ab initio calculations in this study successfully yielded results that shed light into understanding the fundamental basis for immiscibility and the concept of mechanical alloying in Ti-Mg system. In addition, the conditions for achieving extended solid solubility in elements that usually do not dissolve in each other under thermodynamic equilibrium conditions have been predicted using ultrasoft (US) and norm-conserving (NC) pseudopotentials. Hydostatic pressures required to stabilize ordered phases were determined. Our new systematic representation of martensitic transformation (MT) paths as a result of dislocation necessary to induce α→FCC, α→BCC and α→ω phase transitions led to, for the first time, a direct determination of CRSS and tensile strength for Ti and Mg HCP metals. Furthermore, a new ω phase which is less stable than α phase at 0 GPa is proposed. Based on this phase, α→ω deformation path which yielded the onset of uniaxial transition pressure of 4.167 GPa is reported. Attempts of synthesizing Ti-Mg solid solutions by means of Simoloyer high energy ball mill were not successful; however, nanocrystalline Mg-TiH2-x composites were instead formed. These results were attributed to quick formation of metastable Ti hydrides or cold welding at early stages of BM prior to alloying, thus serving as possible obstacles to forming such solid solutions. The deformed Ti crystals adsorbed H+ from the stearic acid leading to formation of metastable orthorhombic TiH2-x phase which later transformed to a tetragonal TiH2-x or even cubic TiH2 when stoichiometric amount of H2 had been adsorbed. Although the yield was significantly lower, the product of milling a mixture of coarse Mg and fine Ti particles was comprised of Ti particles adhering around ductile Mg particles in a core shell manner. The adhesion of the fine hard titanium particles on the surface of the large ductile magnesium particles impeded the further plastic deformation of the titanium particles, thus suppressing the formation of the faults necessary for mechanical alloying. Nanocrystalline Ti powder of about 40 nm was produced by 30h ball milling. During BM of Ti powder, solid-state transformation from HCP to FCC occurred in the presence of PCA with lattice parameters of 4.242 and 4.240 Å after 24 and 30 h, respectively, v due to protonation. When Ti powder was milled in the absence of PCA, no phase transformation was observed for both uninterrupted and interrupted milling cycles. In addition, nanocrystalline Mg powder with crystallite size varying between 60 and below 40 nm was produced by ball milling. However, no solid-state transformation took place even if the powder was milled for 90 h. Therefore, we evidently report for the first time that the interstitial H+ is the driving force for α → FCC phase transformation in ball milled Ti powder. Our theoretical results predicted the ω phase to be the ground-state structure of Ti at 0K and P=0 GPa, in support of other previously reported calculations. We noticed that the stability of the α phase was surpassed by that of the FCC lattice at ~ 100 GPa, corresponding with sudden sharp rise in c/a ratio, hence attributed to α → FCC phase transition. Similar results were obtained for Mg at 50 GPa, although in this case the crossing of lattice energies coincided with minimum c/a. However, using our proposed HCP→BCC MT path mechanism for Mg, it is evident that the minimum c/a at 50 GPa corresponds to a change in the preferred deformation slip from basal (below 10 GPa) to prismatic rather than phase transition. Nonetheless, the proposed MT model predicts that both elemental Ti and Mg prefer to deform via prismatic slip as indicated by lower shear stress as well as CRSS values compared to those calculated for basal slip. Theoretical findings from ab initio calculations on hypothetical ordered Ti-Mg phases indicated absence of intermetallic phases at equilibrium conditions, in agreement with experimental data. However, the formation becomes possible at 80 GPa and above with respect to c/a ratio but requires at least 200 GPa with respect to stable lattices. Using calculated heats of formation, elasticity and DOS, it has been possible to show that L12 TiMg3 could not form even at high pressure as 250 GPa. Nonetheless, both approaches indicate that forming an intermetallic compound between Ti and Mg requires a crystal structure change, α→FCC for Ti and HCP→BCC for Mg. Proposed DFT-based solid solution model for predicting phase stability and elastic properties of binary random alloys, with Mg-Li system serving as a test case, successfully yielded reliable results comparable to experimental data. This method was successfully applied to study an immiscible Ti-Mg system and the solubility limit vi was for the first time theoretically established. Based on formation energy of Ti-Mg solid solutions, our calculations predicted for the first time that the solubility of up to 60 and 100 at.% Mg into Ti with the use of USP and NCP, respectively, to be thermodynamically favourable with necessary lattice kinetics being the main challenge. Nonetheless, NCP proved to be reliable in predicting structural and elastic properties of disordered alloys.