Compositional stability analysis based on dual decomposition

We propose a compositional stability analysis framework for verifying properties of systems that are interconnections of multiple subsystems. The proposed method assembles stability certificates for the interconnected system based on the certificates for the input-output properties of the subsystems. The decomposition in the analysis is achieved by utilizing dual decomposition ideas from optimization. Decoupled subproblems establish subsystem level input-output properties whereas the "master" problem imposes and updates the conditions on the subproblems toward ensuring interconnected system level stability properties. Both global stability analysis and region-of-attraction analysis are discussed

A phase-field study of elastic stress effects on phase separation in ternary alloys

Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. To elucidate the key effects of elastic stress on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to study phase separation in ternary alloy system. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model incorporates coherency strain interactions between the phases using Khachaturyan's microelasticity theory. We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation kinetics. We also vary the ratio of interfacial energies between the phases to understand the interplay between elastic and interfacial energies on morphological evolution. The sign and degree of misfit affect strain partitioning between the phases during spinodal decomposition, thereby affecting their compositional history and morphology. Moreover, strain partitioning affects solute partitioning and alters the kinetics of coarsening of the phases. The phases associated with higher misfit strain appear coarser and exhibit wider size distribution compared to those having lower misfit. When the interfacial energies satisfy complete wetting condition, phase separation leads to development of stable core-shell morphology depending on the misfit between the core (wetted) and the shell (wetting) phases

Tuning phase-stability and short-range order through Al-doping in (CoCrFeMn)100-xAlx high entropy alloys

For (CoCrFeMn)$_{100-x}$Al$_{x}$ high-entropy alloys, we investigate the phase evolution with increasing Al-content (0 $\le$ x $\le$ 20 at.%). From first-principles theory, the Al-doping drives the alloy structurally from FCC to BCC separated by a narrow two-phase region (FCC+BCC), which is well supported by our experiments. We highlight the effect of Al-doping on the formation enthalpy and electronic structure of (CoCrFeMn)$_{100-x}$Al$_{x}$ alloys. As chemical short-range order (SRO) in multicomponent alloys indicates the nascent local order (and entropy changes), as well as expected low-temperature ordering behavior, we use thermodynamic linear-response within density-functional theory to predict SRO and ordering transformation and temperatures inherent in (CoCrFeMn)$_{100-x}$Al$_{x}$. The predictions agree with our present experimental findings, and other reported ones.Comment: 27 pages, 9 figures, 1 tabl

Growth and thermal stability of TiN/ZrAlN: Effect of internal interfaces

Wear resistant hard films comprised of cubic transition metal nitride (c-TMN) and metastable c-AlN with coherent interfaces have a confined operating envelope governed by the limited thermal stability of metastable phases. However, equilibrium phases (c-TMN and wurtzite(w)-AlN) forming semicoherent interfaces during film growth offer higher thermal stability. We demonstrate this concept for a model multilayer system with TiN and ZrAlN layers where the latter is a nanocomposite of ZrN- and AlN- rich domains. The interfaces between the domains are tuned by changing the AlN crystal structure by varying the multilayer architecture and growth temperature. The interface energy minimization at higher growth temperature leads to formation of semicoherent interfaces between w-AlN and c-TMN during growth of 15 nm thin layers. Ab initio calculations predict higher thermodynamic stability of semicoherent interfaces between c-TMN and w-AlN than isostructural coherent interfaces between c-TMN and c-AlN. The combination of a stable interface structure and confinement of w-AlN to nm-sized domains by its low solubility in c-TMN in a multilayer, results in films with a stable hardness of 34 GPa even after annealing at 1150 °C.Peer ReviewedPostprint (author's final draft

Enhanced thermal stability and fracture toughness of TiAlN coatings by Cr, Nb and V-alloying

The effect of metal alloying on mechanical properties including hardness and fracture toughness were investigated in three alloys, Ti~0.33Al0.50(Me)~0.17N (Me¿=¿Cr, Nb and V), and compared to Ti0.50Al0.50N, in the as-deposited state and after annealing. All studied alloys display similar as-deposited hardness while the hardness evolution during annealing is found to be connected to phase transformations, related to the alloy's thermal stability. The most pronounced hardening was observed in Ti0.50Al0.50N, while all the coatings with additional metal elements sustain their hardness better and they are harder than Ti0.50Al0.50N after annealing at 1100¿°C. Fracture toughness properties were extracted from scratch tests. In all tested conditions, as-deposited and annealed at 900 and 1100¿°C, Ti0.33Al0.50Nb0.17N show the least surface and sub-surface damage when scratched despite the differences in decomposition behavior and h-AlN formation. Theoretically estimated ductility of phases existing in the coatings correlates well with their crack resistance. In summary, Ti0.33Al0.50Nb0.17N is the toughest alloy in both as-deposited and post-annealed states.Peer ReviewedPostprint (author's final draft

Domain Decomposition for Stochastic Optimal Control

This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high polynomial degree to capture local phenomena. To improve the scalability of the method to problems of interest, a domain decomposition scheme is presented. By using local approximations, lower degree polynomials become sufficient, and both local and global properties of the value function are captured. The domain of the problem is split into a non-overlapping partition, with added constraints ensuring $C^1$ continuity. The Alternating Direction Method of Multipliers (ADMM) is used to optimize over each domain in parallel and ensure convergence on the boundaries of the partitions. This results in improved conditioning of the problem and allows for much larger and more complex problems to be addressed with improved performance.Comment: 8 pages. Accepted to CDC 201