Thesis (M.Sc. (Physics)) --University of Limpopo, 2005 / Self-consistent electronic structure calculations have been performed on ordered cubic-based magnesium-lithium (Mgx-Li1−x) alloys spanning the concentration range 0 ≤ x ≤ 1, using an ab initio plane wave pseudopotential (PWP) method. The first principle pseudopotential planewave approach is used within the local density approximation (LDA) and generalized-gradient approximation (GGA)of the density functional theory (DFT) framework. We have calculated the binding energy curves and the systematic trends in various cohesive and elastic properties at zero temperature, as a function of Li concentration. The calculated equilibrium lattice parameters show a large deviation from Vegard’s rule in the Li-rich region whilst the bulk moduli decrease monotonically with increase in Li concentration. The heats of formation for different ground state superstructures predict that the DO3, B2 and DO22 structures would be the most stable at absolute zero amongst various phases having the Mg3Li, MgLi and MgLi3 compositions, respectively. This stability is reflected in the electronic density of states (DOS). Because of the special significance of the isotropic bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio for technological and engineering applications, we have also calculated these quantities from the elastic constants. The elastic constants indicate the softness of the material as more Li is added with the bcc-based phases becoming mechanically less stable for Li concentration less than 50%. Our results show good agreement within the estimated uncertainty with both experimental and previous theoretical results. / The National Research Foundation (NRF), South Africa-Royal Society (RS), Great Britain collaboration and Council for the Scientific and Industrial Research (CSIR)

Mg alloys have spurred a renewed academic and industrial interest because of their ultra-light-weight and high specific strength properties. Hexagonal close packed Mg has low deformability and a high plastic anisotropy between basal and non-basal slip systems at room temperature. Alloying with Li and other elements is believed to counter this deficiency by activating non-basal slip by reducing their nucleation stress. In this work I study how Li addition affects deformation mechanisms in Mg using atomistic simulations. In the first part, I create a reliable and transferable concentration dependent embedded atom method (CD-EAM) potential for my molecular dynamics study of deformation. This potential describes the Mg-Li phase diagram, which accurately describes the phase stability as a function of Li concentration and temperature. Also, it reproduces the heat of mixing, lattice parameters, and bulk moduli of the alloy as a function of Li concentration. Most importantly, our CD-EAM potential reproduces the variation of stacking fault energy for basal, prismatic, and pyramidal slip systems that influences the deformation mechanisms as a function of Li concentration. This success of CD-EAM Mg-Li potential in reproducing different properties, as compared to literature data, shows its reliability and transferability. Next, I use this newly created potential to study the effect of Li addition on deformation mechanisms in Mg-Li nanocrystalline (NC) alloys. Mg-Li NC alloys show basal slip, pyramidal type-I slip, tension twinning, and two-compression twinning deformation modes. Li addition reduces the plastic anisotropy between basal and non-basal slip systems by modifying the energetics of Mg-Li alloys. This causes the solid solution softening. The inverse relationship between strength and ductility therefore suggests a concomitant increase in alloy ductility. A comparison of the NC results with single crystal deformation results helps to understand the qualitative and quantitative effect of Li addition in Mg on nucleation stress and fault energies of each deformation mode. The nucleation stress and fault energies of basal dislocations and compression twins in single crystal Mg-Li alloy increase while those for pyramidal dislocations and tension twinning decrease. This variation in respective values explains the reduction in plastic anisotropy and increase in ductility for Mg-Li alloys.

Mg-alloys, despite being the lightest structural metallic materials, find limited applications due to their poor workability, which is due to the hcp structure that does not provide sufficient number of independent slip systems for compatible deformation. Workability improves with the increase in the deformation temperature, when non-basal slip starts playing a larger role in deformation. Efforts were made to improve the workability through control of texture, grain refinement and alloying. Alloying activates non-basal slip by decreasing the critical resolved shear stress (CRSS) on non-basal planes or by promoting cross slip through an increase in the stacking fault energy (SFE) on basal planes. In this thesis, the effect of Li addition to the most widely used wrought Mg-alloy AZ31 on its workability is examined. Plastic deformation behaviour of a series of AZ31-Li alloys with temperature, T, and strain rates, ε , as variables was studied, so as to identify the optimum Li content that results in highly workable alloy. The T and ε combinations that are best suited for hot deformation of these alloys were also identified through processing maps and microstructural analysis. First, deformation behaviour of the base AZ31 is examined in detail. Compression tests were carried out, with T ranging between 150 and 400 °C and at ranging from 10-3 to 102 s-1, covering entire hot working range of the alloy. The results suggest that the deformation behaviour of AZ31 could be partitioned into three temperature regimes. In low T regime, twinning played an important role. It changes the orientation and increases hardening rate, θ (given by dσ/dε where σ and ε are true stress and strain respectively); material exhibits macroscopic flow localization and cracking along twin boundaries. The onset of twinning was examined in detail by examining the local maxima before ϵpeak strain in plot between d2σ/dε2 vs. ε. Twinning was found to occur at all the deformation conditions. Dynamic recrystallization (DRX) was observed at temperatures above 250 °C whereas deformation at low T (< 250 °C) led to extensive twinning at all . ε . At intermediate T of 250-300 °C, plastic strains tend to localize near grain/twin boundaries, confining DRX only to these regions. Increase in T promotes non-basal slip, which, in turn, leads to uniform deformation; DRX too becomes uniform. The dependence of critical stress (σc) for the onset of DRX and peak flow stress (σp) on Zener-Hollomon parameter (Z) indicates that these stresses increase with Z. Activation energy (Q) for the deformation of AZ31 was estimated at peak stress and steady state conditions. High values of Q (150-200 kJ/mol) indicate cross slip as the rate controlling mechanism, at the peak, in the stress-strain responses. For steady state, Q corresponds to lattice/grain boundary diffusion (90-150 kJ/mol). Next, the effect of Li on deformation behaviour of AZ31 was examined. In addition to AZ31 without any Li (0Li), three alloys 1 (1Li), 3 (3Li) and 5 (5Li) wt% Li were prepared with the aid of a specially designed set-up for melting and casting of Li containing alloys. Experimental results on homogenized alloys show that 1Li alloy’s overall response is similar to that of 0Li alloy, but 3Li and 5Li alloys exhibit distinctly different deformation behaviour. Li addition facilitates cross slip by increasing SFE on basal planes, thus leading to change in the deformation mechanism of the alloy. Increased softening due to cross slip decreases θ and also the twin density at low ϵ (<10-2 s-1). During deformation at low ϵ and low T, high Li alloys reveal cavities along the grain boundaries in contrast to cracking along twin boundaries that was observed in AZ31. In the intermediate T range, high Li alloys reveal the presence of a small mantle, which can be attributed to the increased cross slip with increasing Li. In fact, Li addition was found to restrict DRX and promote dynamic recovery (DRY). As ϵ increases in this T regime deformation becomes more homogeneous and twinning occurs extensively in high Li alloys. This results in remarkable increase in dσ/dε (θ) in these alloys and DRX was predominantly seen at twinned regions. At high ϵ -T regime, where non-basal slip and twinning occur uniformly, DRX is observed throughout the samples. On the basis of d2σ/dε2 – ε plots, it was found that twinning occurs at almost all -T combinations examined in present study for 0Li and 1Li alloys. In high Li alloys, twinning activity was found to be insignificant at low ε , resulting in low twin density than low Li alloys. Twinning occurs at very early stages of deformation. In the low T and high ε regime, extensive twinning in high Li alloys is noted. In high T regime, presence of twins was not prominent due to the preferential occurrence of DRX at twin boundaries. Estimated values of Q in high Li alloys were found to be very low and correspond to lattice/grain boundary diffusion of Li in Mg, indicating that cross slip is no longer the rate controlling mechanism. Instead, unpinning of kinks from Li atoms appears to control the deformation. Cross slip is promoted by Li through increase in SFE at basal planes. Onset of the DRX was predicted and it was observed that high Li alloys posses lower σc at low ε , but at high ε , σc was either comparable to or higher than low Li alloys. Processing maps were generated for all the alloys using Prasad's as well as Murty's models. Instability predictions of Prasad’s and Murty’s models are similar, except that isoefficiency contours in the latter are slightly shifted to higher ε . These maps indicate to an increase in the workability with the addition of Li to AZ31. Instability predicted by processing maps in the low ε regime in high Li alloys is attributed to underestimation of stress values due to spline interpolation. High sensitivity observed for high Li alloy at intermediate ε (10-1 – 100 s-1) is attributed to the change in the deformation mode i.e. from slip to twinning. Deformation at high T leads to dissolution of Li containing precipitates, which in turn increases the solid solution strengthening in the alloy. Hence, increase in flow stress is observed with increase in T in high Li alloys. This structural change too causes instability predictions in the high -T regime. The 0 Li alloy exhibits peak efficiency of 45% in T = 250-400 °C and ε = 10-1.25 - 100.25 s-1 regime. DRX is observed in this regime and optimum conditions for deformation predicted for this alloys are T = 350 °C and ε = 10-1 s-1. These alloys can be worked at low ε regime too (T = 250-400 °C and ε = 10-2.5 – 10-1 s-1) where the softening mechanism is DRY. Accordingly, it is concluded that the intrinsic workability of AZ31Mg-alloy increases with the addition of 3% and 5% Li.