We describe a technique for constraining macroscopic fluctuations in thermodynamic variables well-suited for Monte Carlo (MC) simulations of multiphase equilibria. In particular for multicomponent systems this amounts to a statistical ensemble that implements constraints on both the average composition as well as its fluctuations. The variance-constrained semi-grandcanonical (VC-SGC) ensemble allows for MC simulations, in which single-phase systems can be reversibly switched into multiphase equilibria allowing the calculation of excess free energies of precipitates of complex shapes by thermodynamic integration. The basic features as well as the scaling and convergence properties of this technique are demonstrated by application to an Ising model. Finally, the VC-SGC MC simulation technique is used to calculate alpha/alpha' interface free energies in Fe-Cr alloys as a function of orientation and temperature taking into account configurational, vibrational, and structural degrees of freedom.
A novel phase field model has been developed to study the effect of coherent precipitate on the Zener pinning of matrix grain boundaries. The model accounts for misfit strain between precipitate and matrix as well as the elastic inhomogeneity and anisotropy between them. The results show that increase in elastic misfit, elastic inhomogeneity, and elastic anisotropy increases the coarsening rate of the precipitates. Increased coarsening of precipitates in turn decreases the pinning of grain boundaries. Therefore, increase in misfit strain, elastic inhomogeneity and anisotropy negatively affect …
We investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the interaction of composition and stress [R. Spatschek and A. Karma, Phys. Rev. B {\bf 81}, 214201 (2010)] and free-energies corresponding to two-dimensional hexagonal and three-dimensional BCC crystal structures that exhibit isotropic and anisotropic elastic properties, respectively. We consider two experimentally motivated geometries where (i) a lamellar pre…
Modern engineering alloys have bespoke microstructures, where features such as precipitates are used to control properties. In many Ni-based alloys, carbo-nitride precipitates are introduced to strengthen and improve performance. These precipitates can be distributed throughout the microstructure and niobium rich carbides are often found at grain boundaries. In this work, we used combined energy dispersive X-ray spectroscopy (EDS) and electron backscatter diffraction (EBSD) to characterise the population of these precipitates. Processing of the EDS signal is used to label the Mo/Nb-rich precip…
The tensile creep performance of a polycrystalline Co/Ni-base superalloy with a multimodal gamma prime distribution has been examined at 800C and 300MPa. The rupture life of the alloy is comparable to that of RR1000 tested under similar conditions. Microstructural examination of the alloy after testing revealed the presence of continuous gamma prime precipitates and M23C6 carbides along the grain boundaries. Intragranularly, coarsening of the secondary gamma prime precipitates occurred at the expense of the fine tertiary gamma prime. Long planar deformation bands, free of gamma prime, were als…
An Al-11.3Li-0.11Sc (at. %) alloy was double-aged to induce first alpha'-Al3Sc and then delta'-Al3Li precipitates. Atom-probe tomography revealed both single-phase delta'-precipitates and core-shell alpha'/delta'-precipitates (with respective average radii of 16 and 27 nm, and respective volume fractions of 12 and 9%) conferring a high strength to the alloy. Although the delta'-shells contain little Sc (~0.027 at. %), the alpha'-cores have a high Li content, with an average composition of Al0.72(Sc0.17 Li0.11). The Li concentrations within the delta'-phase and the Li interfacial excess at the …
Precipitation hardening, which relies on a high density of intermetallic precipitates, is a commonly utilized technique for strengthening structural alloys. Structural alloys are commonly strengthened through a high density of small size intermetallic precipitates. At high temperatures, however, the precipitates coarsen to reduce the excess energy of the interface, resulting in a significant reduction in the strengthening provided by the precipitates. In certain ternary alloys, the secondary solute segregates to the interface and results in the formation of a high density of nanosize precipita…
To investigate excess-hydrolysis of titanium alkoxides, TiO2 powders were fabricated from titanium-tetra-isopropoxide using 6:1 and 100:1 H2O:Ti (r) ratios. Powders were dried and fired at a range of temperatures ( up to 800 C). Hydroxylation and organic content in powders were characterised using ATR-FTIR, laser Raman microspectroscopy, and elemental microanalysis; surface area and pore size distribution were evaluated using N2 gas adsorption; phase composition was analysed using XRD and laser Raman microspectroscopy; and crystallite size was evaluated by XRD, TEM and SEM. Results showed near…
We have found a remarkably large response of the transition temperature of CaFe2As2 single crystals grown out of excess FeAs to annealing / quenching temperature. Whereas crystals that are annealed at 400 C exhibit a first order phase transition from a high temperature tetragonal to a low temperature orthorhombic and antiferromagnetic state near 170 K, crystals that have been quenched from 960 C exhibit a transition from a high temperature tetragonal phase to a low temperature, non-magnetic, collapsed tetragonal phase below 100 K. By use of temperature dependent electrical resistivity, magneti…
Grain boundary diffusion in severely deformed Al-based AA5024 alloy is investigated. Different states are prepared by combination of equal channel angular processing and heat treatments, with the radioisotope $^{57}$Co being employed as a sensitive probe of a given grain boundary state. Its diffusion rates near room temperature (320~K) are utilized to quantify the effects of severe plastic deformation and a presumed formation of a previously reported deformation-modified state of grain boundaries, solute segregation at the interfaces, increased dislocation content after deformation and of the …
Intermetallic precipitates formed in heat-treated and aged Mg-Zn and Mg-Zn-Y alloys have been investigated via electron microscopy. Coarse spheroidal precipitates formed on deformation twin boundaries contained domains belonging to either the MgZn2 hexagonal Laves phase or the monoclinic Mg4Zn7 phase. Both phases are structurally related to the quasi-crystalline phase formed in Mg-Zn-Y alloys, containing icosahedrally coordinated zinc atoms arranged as a series of broad rhombohedral units. This rhombohedral arrangement was also visible in intragranular precipitates where local regions with the…
The Ni-base superalloy 718 is the most widely used material for turbomachinery in the aerospace industry and land-based turbines. Although the relationship between processing and the resulting properties is well known, an understanding of the specific deformation mechanisms activated across its application temperature range is required to create more mechanistically accurate property models. Direct atomic-scale imaging observations with high angle annular dark-field scanning transmission electron microscopy, complemented by phase-field modeling informed by generalized stacking fault surface ca…
The excess volume associated with grain boundaries represents a key structural parameter for the characterization of grain boundaries. It plays a critical role in segregation of impurity and alloy elements to grain boundaries, and influences significantly the mechanical and functional properties of materials. We have carried out first-principles density functional calculations on the atomic structure of the (10-12) coherent twin boundary in hexagonal close packed (hcp) Ti and Zr and the basal-prismatic boundary in Zn, Cd, and Zr. We find the calculated excess volume has a vanishing magnitude a…
We describe a simple method to determine, from ab initio calculations, the complete orientation-dependence of interfacial free energies in solid-state crystalline systems. We illustrate the method with an application to precipitates in the Al-Ti alloy system. The method combines the cluster expansion formalism in its most general form (to model the system's energetics) with the inversion of the well-known Wulff construction (to recover interfacial energies from equilibrium precipitate shapes). Although the inverse Wulff construction only provides the relative magnitude of the various interfaci…
Formation of large volume fractions of Mn-Ni-Si precipitates (MNSPs) causes excess irradiation embrittlement of reactor pressure vessel (RPV) steels at high, extended-life fluences. Thus, a new and unique, semi-empirical cluster dynamics model was developed to study the evolution of MNSPs in low- Cu RPV steels. The model is based on CALPHAD thermodynamics and radiation enhanced diffusion ki- netics. The thermodynamics dictates the compositional and temperature dependence of the free energy reductions that drive precipitation. The model treats both homogeneous and heterogeneous nucleation, wher…
Precipitate phase selection and grain boundary morphology in Cu-Ni-Si-Mn alloys: A machine-learning interatomic potential study
Korea Electrotechnology Research Institute (KERI)（韩国电工技术研究所）；Korea Institute of Materials Science (KIMS)（韩国材料科学研究所）；Seoul National University（首尔大学）；University of Science and Technology (UST)（科学技术联合大学院大学）；Korea Institute for Advanced Study（韩国高等研究院）
Isothermal ageing of plastically deformed Mg-Zn-Y alloys resulted in precipitation along {10-12} twin boundaries. The bulky precipitates formed had structures similar to those recently reported for the rod-like β' precipitates, but afforded a more detailed study by high resolution TEM due to their larger size. The core of the precipitates often had the structure of monoclinic Mg4Zn7 phase, and had the orientation [0001]_Mg//[010]; {10-10}_Mg // (201) with either the matrix or the twin. On this Mg4Zn7 phase, hexagonal MgZn2 phase grew in two orientations, both with [010]_Mg4Zn7 // [11-20]_MgZn2…
Microalloying elements tend to segregate to the matrix-precipitate phase boundaries to reduce the interfacial energy. The segregation mechanism is emerging as a novel design strategy for developing precipitation-hardened alloys with significantly improved coarsening resistance for high temperature applications. In this paper, we report a nanoscopic diffuse-interface thermodynamic model that describes multicomponent segregation behavior in two-phase substitutional alloys. Following classical approaches for grain boundaries, we employ the regular solution thermodynamics to establish segregation …
To assess long-term structural integrity under operational conditions in nuclear reactors, SS 316LN with varying nitrogen content is subjected to thermal aging for 20000 hours at 650°C. While the annealing twins and heterogeneous grain evolution by bimodal division are independent of chemical composition, the type, size and morphology of evolving secondary phases are characteristic for nitrogen concentration. Colour contrast in bright field optical microscopy combined with transmission electron microscopy reveals the presence of three major precipitate phases; M23(C, N)6, Fe2Mo intermetallics …
Dislocation and grain boundary melting are studied in three dimensions using the Phase Field Crystal method. Isolated dislocations are found to melt radially outward from their core, as the localized excess elastic energy drives a power law divergence in the melt radius. Dislocations within low-to-mid angle grain boundaries melt similarly until an angle-dependent first order wetting transition occurs when neighboring melted regions coalesce. High angle boundaries are treated within a screening approximation, and issues related to ensembles, metastability, and grain size are discussed.
Grain boundaries often exhibit ordered atomic structures. Increasing amounts of evidence have been provided by transmission electron microscopy and atomistic computer simulations that different stable and metastable grain boundary structures can occur. Meanwhile, theories to treat them thermodynamically as grain boundary phases have been developed. Whereas atomic structures were identified at particular grain boundaries for particular materials, it remains an open question if these structures and their thermodynamic excess properties are material specific or generalizable to, e.g., all fcc met…
Grain boundary tracer diffusion of Ni, Fe and Cr was studied in a Ni-base 602CA coarse-grained alloy. A co-existence of several short-circuit contributions was distinguished at higher temperatures in Harrison's B-type regime (773-873 K), which were related to different families of high-angle grain boundaries with distinct coverages by precipitates and segregation levels as revealed by HAADF-STEM combined with EDX measurements. Annealing at 873 K for 18 hours resulted in Cr23C6-type carbides coexisting with an α-Cr-Mn-enriched phase in addition to sequential segregation layers of Al, Fe and Ni …
Grain boundaries are thermodynamically unstable. Hence, their properties should be path-dependent: grain boundaries in nanocrystals prepared using different methods might exhibit different properties. Using molecular dynamics simulations, we investigated grain boundaries of nanocrystals formed by quenching,solidification with pre-induced nucleation sites, and Voronoi tessellation. Some properties were found to be path depend: the quenched model has lower boundary energy per atom, smaller boundary excess free volume per atom, and slower grain growth than the Voronoi model. We surmise that these…
We analyze the dislocation content of grain boundary (GB) phase junctions, i.e., line defects separating two different GB phases coexisting on the same GB plane. While regular GB disconnections have been characterized for a variety of interfaces, GB phase junctions formed by GBs with different structures and different numbers of excess atoms have not been previously studied. We apply a general Burgers circuit analysis to calculate the Burgers vectors b of junctions in two Σ5 Cu boundaries previously simulated with molecular dynamics. The Burgers vectors of these junctions cannot be described b…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using chemical potentials and diffusion potentials, respectively. All interface excess quantities are derived using Cahns (1979) generalized excess method without resorting to geometric dividing surfaces. We present expressions for the interface free energy as an excess quantity and derive a generalized adsorption equation and an interface Gibbs-Helmholtz equation that d…
We present the results of first-principles calculations of selected structural and thermodynamic properties of a set of grain boundaries (GBs) in zirconium, spanning a range of misorientation angles and boundary planes. We performed plane-wave density functional theory calculations on low-sigma grain boundaries - five symmetric tilt GBs (STGBs) and three twist GBs; all with misorientation axes about [0001] and in optimised microscopic configurations - to gain insight into the associated atomistic structures. From studying the interface energetics, we found that higher GB excess volumes tended …
Grain boundaries (GBs) and interfaces in polycrystalline materials are significant research subjects in the field of materials science. Despite a more than 50-year history of their study, there are still many open questions. The main challenge in studying interfacial structures is the extreme complexity of their experimental and theoretical observation and description. The presence of phase-like states at grain boundaries called complexions requires even more effort in their study. Here, we demonstrate the effect of grain boundaries on the properties of polycrystalline minerals on the example …
We report a novel multi-scale simulation methodology to quantitatively predict the thermodynamic behaviour of polymer mixtures, that exhibit phases with broken orientational symmetry. Our system consists of a binary mixture of oligomers and rod-like mesogens. Using coarse-grained molecular dynamics (CGMD) simulations we infer the topology of the temperature-dependent free energy landscape from the probability distributions of excess volume fraction of the components. The mixture exhibits nematic and smectic phases as a function of two temperature scales, the nematic-isotropic temperature $T_{N…
The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy
A number of experimental and theoretical findings in age hardening alloys suggest that specific solute elements preferentially segregate to and reduce the energy of the interphase boundary (IB). This segregation mechanism can stabilize the precipitation microstructure against coarsening, allowing higher operating temperatures in structural applications. Herein, we present a phase field model of solute segregation to IBs that separate matrix and precipitate phases in binary alloys. The proposed modeling framework is capable of capturing bulk thermodynamics and interfacial free energies, while a…
Co-based superalloys in the Co-Al-W system exhibit coherent L12 Co3(Al,W) γ' precipitates in an fcc Co γmatrix, analogous to Ni3Al in Ni-based systems. Unlike Ni3Al however, experimental observations of Co3(Al,W) suggest that it is not a stable phase at 1173K. Here, we perform an extensive series of density functional theory (DFT) calculations of the γ' Co3(Al,W) phase stability, including point defect energetics and finite-temperature contributions. We first confirm and extend previous DFT calculations of the metastability of L12 Co3(Al0.5W0.5) γ' at 0K with respect to HCP Co, B2 CoAl, and D0…
The surface orientation can have profound effects on the atomic-scale processes of crystal growth, and is essential to such technologies as GaN-based light-emitting diodes and high-power electronics. We investigate the dependence of homoepitaxial growth mechanisms on the surface orientation of a hexagonal crystal using kinetic Monte Carlo simulations. To model GaN metal-organic vapor phase epitaxy, in which N species are supplied in excess, only Ga atoms on a hexagonal close-packed (HCP) lattice are considered. The results are thus potentially applicable to any HCP material. Growth behaviors o…
