First-Principles Investigation of Perfect and Diffuse Anti-Phase Boundaries in HCP-Based Ti-Al Alloys

First-principles thermodynamic models based on the cluster expansion formalism, monte-carlo simulations and quantum-mechanical total energy calculations are employed to compute short-range-order parameters and diffuse-antiphase-boundary energies in hcp-based $\alpha$-Ti-Al alloys. Our calculations unambiguously reveal a substantial amount of SRO is present in $\alpha$-Ti-6 Al and that, at typical processing temperatures concentrations, the DAPB energies associated with a single dislocation slip can reach 25 mJ/m$^{2}$. We find very little anisotropy between the energies of DAPBs lying in the basal and prism planes. Perfect antiphase boundaries in DO$_{19}$ ordered Ti$_3$Al are also investigated and their interfacial energies, interfacial stresses and local displacements are calculated from first principles through direct supercell calculations. Our results are discussed in light of mechanical property measurements and deformation microstructure strudies in $\alpha$ Ti-Al alloys

Surface energetics and structure of the Ge wetting layer on Si(100)

Ge deposited on Si(100) initially forms heteroepitaxial layers, which grow to a critical thickness of ~3 MLs before the appearance of three-dimensional strain relieving structures. Experimental observations reveal that the surface structure of this Ge wetting layer is a dimer vacancy line (DVL) superstructure of the unstrained Ge(100) dimer reconstruction. In the following, the results of first-principles calculations of the thickness dependence of the wetting layer surface excess energy for the c(4×2) and 4×6 DVL surface reconstructions are reported. These results predict a wetting layer critical thickness of ~3 MLs, which is largely unaffected by the presence of dimer vacancy lines. The 4×6 DVL reconstruction is found to be thermodynamically stable with respect to the c(4×2) structure for wetting layers at least 2 ML thick. A strong correlation between the fraction of total surface induced deformation present in the substrate and the thickness dependence of wetting layer surface energy is also shown

Modeling carbon black reinforcement in rubber compounds

One of the advocated reinforcement mechanisms is the formation by the filler of a network interpenetrating the polymer network. The deformation and reformation of the filler network allows the explanation of low strain dynamic physical properties of the composite. The present model relies on a statistical study of a collection of elementary mechanical systems, This leads to a mathematical approach of the complex modulus G* = G' + iG". The storage and loss modulus (G' and G", respectively), are expressed in the form of two integrals capable of modeling their Variation with respect to strain

Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic

Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the desired quantities. To address this problem, we have devised a variety of high-level algorithms that serve as an interface between the user and a traditional MC code. The user specifies the goals sought in a high-level form that our algorithms convert into elementary tasks to be performed by a standard MC code. For instance, our algorithms permit the determination of the free energy of an alloy phase over its entire region of stability within a specified accuracy, without requiring any user intervention during the calculations. Our algorithms also enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system

First-principles calculation of phase equilibrium of V-Nb, V-Ta, and Nb-Ta alloys

In this paper, we report the calculated phase diagrams of V-Nb, V-Ta, and Nb-Ta alloys computed by combining the total energies of 40–50 configurations for each system (obtained using density functional theory) with the cluster expansion and Monte Carlo techniques. For V-Nb alloys, the phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature T_c=1250 K. Including the constituent strain to the cluster expansion Hamiltonian does not alter the consolute temperature significantly, although it appears to influence the solubility of V- and Nb-rich alloys. The phonon contribution to the free energy lowers T_c to 950 K (about 25%). Our calculations thus predicts an appreciable miscibility gap for V-Nb alloys. For bcc V-Ta alloy, this calculation predicts a miscibility gap with T_c=1100 K. For this alloy, both the constituent strain and phonon contributions are found to be significant. The constituent strain increases the miscibility gap while the phonon entropy counteracts the effect of the constituent strain. In V-Ta alloys, an ordering transition occurs at 1583 K from bcc solid solution phase to the V_(2)Ta Laves phase due to the dominant chemical interaction associated with the relatively large electronegativity difference. Since the current cluster expansion ignores the V_(2)Ta phase, the associated chemical interaction appears to manifest in making the solid solution phase remain stable down to 1100 K. For the size-matched Nb-Ta alloys, our calculation predicts complete miscibility in agreement with experiment

Pourbaix-like phase diagram for lithium manganese spinels in acid

Calculations are performed on the free energies for proton-promoted reactions of the lithium-ion-battery electrode material LiMn_(2)O_4 spinel in acid, as a function of lithium excess and lithium deficiency relative to stoichiometry. In particular, we consider the dissolution reaction proposed by Hunter (J. Solid State Chem., 1981, 39, 142), in which protons react with lithium manganate spinel to form λ-MnO2, Li^+, and Mn^(2+) products. The calculations employ a hybrid method developed in previous work in which first principles total energy calculations are applied for the solid phases and free atom energies, and tabulated ionization and hydration energies for the aqueous species. A correction to the atomic energies, derived from analysis of binary oxide dissolution reactions, improves the accuracy of the results. A Pourbaix-like dissolution/stability phase diagram is constructed from the resultant reaction free energies

The Alloy Theoretic Automated Toolkit: A User Guide

Although the formalism that allows the calculation of alloy thermodynamic properties from first-principles has been known for decades, its practical implementation has so far remained a tedious process. The Alloy Theoretic Automated Toolkit (ATAT) drastically simplifies this procedure by implementing decision rules based on formal statistical analysis that frees the researchers from a constant monitoring during the calculation process and automatically "glues" together the input and the output of various codes, in order to provide a high-level interface to the calculation of alloy thermodynamic properties from first-principles. ATAT implements the Structure Inversion Method (SIM), also known as the Connolly-Williams method, in combination with semi-grand-canonical Monte Carlo simulations. In order to make this powerful toolkit available to the wide community of researchers who could benefit from it, this article present a concise user guide outlining the steps required to obtain thermodynamic information from ab initio calculations.Comment: 15 pages, 4 figure