Automating first-principles phase diagram calculations

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented

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

First-principles computation of the vibrational entropy of ordered and disordered Pd3V

Experimental as well as theoretical work indicates that the relative stability of the ordered and the disordered states of a compound may be significantly affected by their difference in vibrational entropy. The origin of this difference is usually attributed to the fact that disordering reduces the number of stiff bonds between different atomic species in favor of soft bonds between identical atomic species. The results of previous theoretical investigations, however, suggest that this simple mechanism is significantly modified as a result of local atomic relaxations. To gain further insight regarding the importance of relaxations, we employ first-principles calculations to investigate the magnitude of the vibrational entropy difference between the ordered and the disordered state of Pd3V. Our investigation reveals that bond stiffness changes due to relaxation entirely mask the large configurational dependence of vibrational entropy provided by bond stiffness differences. Our analysis also suggests a simple technique to estimate vibrational entropy based on the relationship between bond length and bond stiffness

First-Principles Thermodynamics of Coherent Interfaces in Samarium-Doped Ceria Nanoscale Superlattices

Nanoscale superlattices of samarium-doped ceria layers with varying doping levels have been recently proposed as a novel fuel cell electrolyte. We calculate the equilibrium composition profile across the coherent {100} interfaces present in this system using lattice-gas Monte Carlo simulations with long-range interactions determined from electrostatics and short-range interactions obtained from ab initio calculations. These simulations reveal the formation of a diffuse, nonmonotonic, and surprisingly wide (11 nm at 400 K) interface composition profile, despite the absence of space charge regions

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

Structure, energetics, and mechanical stability of Fe-Cu bcc alloys from first-principles calculations

Atomic volumes, magnetic moments, mixing energies, and the elastic properties of bcc Fe1–xCux solid solutions are studied by ab initio calculations based on the cluster expansion framework. For the calculation of concentration-dependent elastic moduli in disordered solid solutions, we introduce a generalization of the cluster expansion technique that is designed to handle tensorial quantities in high-symmetry phases. Calculated mixing energies, atomic volumes, and magnetic moments are found to be in good agreement with available measurements for metastable alloys prepared through nonequilibrium processing techniques. Additionally, the predicted variations of the bulk modulus and shear moduli C44 and C[prime] with respect to copper concentration are calculated for the disordered bcc phase. While the bulk modulus and C44 are positive for all concentrations, C[prime] is predicted to be positive only for Cu concentration less than 50 atomic %, and negative otherwise. Our results thus indicate that the mechanical instability of bcc Cu persists over a wide range of compositions. The implications of the present results are discussed in relation to the observed metastability of bcc Fe-Cu alloys, and the strengthening mechanism of nanoscale bcc precipitates in an alpha-Fe matrix

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

First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

First principles phase diagram calculations were performed for the wurtzite-structure quasibinary systems AlN–GaN, GaN–InN, and AlN–InN. Cluster expansion Hamiltonians that excluded, and included, excess vibrational contributions to the free energy, Fvib, were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, (XC,TC), for AlN–GaN, GaN–InN, and AlN–InN equal to (0.50, 305 K), (0.50, 1850 K), and (0.50, 2830 K) without Fvib, and (0.40, 247 K), (0.50, 1620 K), and (0.50, 2600 K) with Fvib, respectively. In spite of the very different ionic radii of Al, Ga, and In, the GaN–InN and AlN–GaN diagrams are predicted to be approximately symmetric