Modeling the final sintering stage of doped ceramics: mutual interaction between grain growth and densification

Applying the thermodynamic extremal principle, a model for grain growth and densification in the final stage of sintering of doped ceramics was derived, with segregation-dependent interfacial energies and mobilities (or diffusivities). The model demonstrated an interdependence between the driving forces of grain growth and densification during sintering evolution, observed because the surface energy contributes positively to the driving force of grain growth while the GB energy negatively to the driving force of densification. The model was tested in alumina as a host system, and calculations demonstrate that dopants with more negative GB (or surface) segregation enthalpy or which cause lower GB diffusion coefficient can induce higher relative densities at a given grain size. Comparatively studying yttria- and lanthana-doped alumina, the lanthana doping showed significantly enhanced sintering attributed to the larger La³⁺ radius causing a more negative GB segregation energy. This present model is expected to help dopant designing to improve control over sintering.     

Grain boundary sliding and migration in copper: the effect of vacancies

The atomic structure and mechanism of the interface sliding of the Σ = 5(2 1 0)[0 0 1] symmetric tilt grain boundary (GB) in copper and its interaction with vacancies at an elevated temperature has been studied using a computationally efficient potential based on the Embedding Atom Method in connection with the finite temperature Monte Carlo technique. Grain boundary sliding is performed for pure copper as well as copper containing a vacancy at a selected position. The discontinuous changes of the GB energy at certain sliding distances are associated with GB migrations. Elevated temperature reduces the grain boundary sliding/migration energy by a factor of about 2 but does not increase the rate of migration. Migration of the GB is mediated by the flow of atoms along the interface in coordination with the atoms in bulk. The sliding and migration properties partially depend on the position of the vacancy in the GB core. We found that the grain boundary sliding energy profile in the presence of a vacancy placed at the interface increased the GB energy, but reduces the sliding energy. The sliding process invokes the interface migration in such a way that the vacancy effectively migrates to a more convenient position and reduces the GB energy.     

Local migration of grain boundaries in polycrystalline materials under plastic deformation conditions

We propose a theoretical model describing the local migration of grain boundaries (GBs) near triple junctions according to the new mechanism stimulated by the GB slip. Within the framework of this model, a driving force for the local migration is due to the interaction between sliding and structural GB dislocations responsible for the GB slip and misorientation, respectively.     

Modeling of non-equilibrium solute diffusion upon rapid solidification: effective mobility versus kinetic energy

Abstract

The effective mobility approach is compared with the kinetic energy approach in terms of sharp interface modeling and phase-field modelling of non-equilibrium solute diffusion upon rapid solidification of binary alloys. The two approaches are equivalent for modelling of long range solute diffusion in bulk phases, but only the effective mobility approach can introduce the non-equilibrium solute diffusion effect to short range solute diffusion at a sharp interface or within a diffuse interface. Addition of the kinetic energy terms results in an unreasonable non-bilinear expression of the flux and thermodynamic driving force in the free energy production of interface migration or phase field propagation, whereas the effective mobility approach allows the thermodynamic extremal principle workable.     

A strategy for designing stable nanocrystalline alloys by thermo-kinetic synergy

Aiming to design stable nanocrystalline(NC) materials, so far, it has been proposed to construct nanostructure stability maps in terms of thermodynamic parameters, while kinetic stabilization has seldom been considered, despite the synergy of thermodynamics and kinetics. Consequently, the thermodynamically stabilized NC materials may be easily subjected to grain growth at high temperatures due to the weakly kinetic stabilization. Starting from the thermo-kinetic synergy, a stabilization criterion is proposed as a function of intrinsic solute parameters(e.g. the activation energy for bulk diffusion and the segregation enthalpy), intrinsic solvent parameters(e.g. the intrinsic activation energy for GB migration and the GB energy) and processing parameters(e.g. the grain size, the temperature and the solute concentration). Using first-principles calculations for a series of combinations between fifty-one substitutional alloying atoms as solute atoms and Fe atom as fixed solvent atom, it is shown that the thermal stability neither simply increases with increasing the segregation enthalpy as expected by thermodynamic stabilization, nor monotonically increases with increasing the activation energy for bulk diffusion as described by kinetic stabilization. By combination of thermodynamic and kinetic contributions, the current stabilization criterion evaluates quantitatively the thermal stability, thus permitting convenient comparisons among NC materials involved by various combinations of the solute atoms, the solvent atoms, or the processing conditions. Validity of this thermo-kinetic stabilization criterion has been tested by current experiment results of Fe-Y alloy and previously published data of Fe-Ni, Fe-Cr, Fe-Zr and Fe-Ag alloys,etc., which opens a new window for designing NC materials with sufficiently high thermal stability and sufficiently small grain size.     

Comparison of the intergranular segregation for eight dilute binary metallic systems in the Σ 11′ {332} tilt grain boundary

Intergranular segregation is studied in the limit of infinitely diluted solution for eight dilute metallic systems made of four face centred cubic metals, one transition metal, nickel, and three noble metals, copper, silver and gold. The grain boundary (GB) chosen is the symmetrical tilt Σ = 11′ {332} 〈110〉 GB with its characteristic “zigzag” structural pattern as numerically calculated and experimentally observed by high resolution transmission electronic microscopy in nickel. The metallic interactions are modelled with Finnis-Sinclair like potentials. The atomic sites are characterised by a geometrical parameter defined with their exact Voronoï’ volumes and the tensor of the stresses locally exerted. The {332} GB presents the most diversity of sites in these respects. The segregation energies are computed and analysed versus the only two ‘driving forces’ which can play a role in metallic intergranular segregation, viz. the elastic size effect and the excess cohesion energy effect. The elastic size effect calculated by the method of virtual impurity represents the main segregation driving force in most cases of the considered systems. It is worth noting however that the excess cohesion energy effect is important for non hydrostatic or compressive sites. It can even be predominant, as in the case of Ni(Cu).     

The thermodynamic driving force for bone growth and remodelling: a hypothesis

The Eshelby stress (static energy momentum) tensor is derived for bone modelled as an inhomogeneous piezoelectric and piezomagnetic Cosserat (micropolar) medium. The divergence of this tensor is the configurational force felt by material gradients and defects in the medium. Just as in inhomogeneous elastic media, this force is identified with the thermodynamic force for phase transformations, in bone it is the thermodynamic cause of structural transformations, i.e. remodelling and growth. The thermodynamic approach shows that some terms of driving force are proportional to the stress, and some acting on material inhomogeneities are quadratic in the stress-the latter outweigh by far the former. Since inertial forces due to acceleration enter the energy-momentum tensor, it follows that the rate of loading matters and that both tension and compression stimulate growth, which is favoured at heterogeneities.     

The spectrum of atomic excess free volume in grain boundaries

The grain boundary (GB) excess volume is an important structural factor that is strongly correlated with various thermodynamic and kinetic properties of GBs such as GB energy, GB mobility, GB diffusivity, and GB segregation energy, etc. However, the excess volume is usually reported as an average value of the entire GB. Such simplification does not consider the spectral nature of the excess volume in a GB, which cannot be used to describe the atomic mechanisms of some kinetic process, such as GB migration, that involves only a few atoms at a time. Here, we explore the spectrum of atomic excess volume in representative nanocrystalline Ni and Al samples as well as 388 Ni bicrystals based on the Olmsted dataset by using atomistic simulations. It is found that the nanocrystalline Ni and Al models show a skew-normal distribution in the spectrum of both the atomic excess volume and the atomic excess energy in the GBs, which show a weak inverse correlation between them. This is in stark contrast to the widely reported positive correlation between GB energy and excess volume based on the average value. We further show based on the statistical analysis that the correlation between the atomic excess volume and excess energy strongly depends on the GB type and a universal trend between them does not exist. While low ∑ Ni GBs generally shows a strong inverse linear correlation between these two properties, such correlation is weak for high ∑ Ni GBs. Moreover, we find that the spectrum of the excess volume shows characteristics distribution in some special Ni GBs. For example, twist GBs generally show a symmetrical unimodal distribution while most surveyed ∑3 Ni GBs with anti-thermal behavior show an apparent bimodal distribution. Nevertheless, a strong correlation is found between the atomic excess volume and the segregation energy based on the nanocrystalline Al model with Mg impurity, which implies a possible universal trend between the two properties. The current study thus shows that the excess volume provides useful insights in revealing the elemental structure–property correlations in GBs, which may be used as a structural variable in future thermodynamic modeling of GBs.

     

Size and microstructure effects on the mechanical behavior of FCC bicrystals by quasicontinuum method

The effects of structure and size on the deformation of <110> tilt bicrystals in copper are investigated by concurrent multiscale simulations at zero temperature. In the simulation of eleven grain boundary (GB) structures, a direct relation is shown between structural units and sliding at GBs. We find that GB sliding operates by atom shuffling events localized on one particular type of structural units, which are present in the GB period. When this type of unit is absent, the GB deformation process occurs by migration, or GB-mediated nucleation of partial dislocations with no sliding, depending on the initial GB configuration. The elastic limit causing sliding is found to vary slightly at zero temperature, but no correlation was obtained with the GB energy at equilibrium. Additionally, both modulus of rigidity, and elastic limit remain constant as the bicrystal size varies from 1 nm up to 25 nm. However, differences in the stress relaxation after sliding are observed with respect to the size.     

Atomistic simulation of grain boundary sliding and migration

Interatomic potentials using Embedded Atom Method (EAM) are used in conjunction with molecular statics and dynamics calculations to study the sliding and migration of [1 1 0] symmetric tilt grain boundaries (STGB) in aluminum, under both applied displacement and force conditions. For equilibrium grain boundaries (without applied displacements and forces), three low energy configurations (corresponding to three twin structures) are found in the [1 1 0] STGB structures when grain boundary energies at 0 K are computed as a function of grain misorientation angle. Pure grain boundary sliding (GBS) without migration is simulated by applying external displacement. When forces are applied, the energy barriers are reduced consequent to the fact that grain boundary sliding of STGB is always coupled with migration. The propensity for pure GBS is evaluated by computing the energy associated with incremental equilibrium configurations during the sliding process and compared to the case when sliding is accompanied by migration. The magnitude of the energy barriers is found to be much higher in pure GBS than when migration accompanies sliding. Relations between the applied force, internal stress field, and displacement field are established and the role of grain boundary structure on the deformation process are examined. It is found that the GBS displacement is proportional to applied force, GB energy, and time.     

Grain boundary motion and grain growth in zinc in a high magnetic field

The motion of grain boundaries in zinc bicrystals (99.995 %) driven by the “magnetic” driving force was measured. An in situ technique for observations and continuous recording the boundary migration was applied. Planar symmetrical and asymmetrical $ \left\langle {10\overline{1} 0} \right\rangle $ tilt grain boundaries with rotation angles in the range between 60° and 90° were studied. The boundary migration was measured in the temperature regime between 330 and 415 °C. The mobility of $ \left\langle {10\overline{1} 0} \right\rangle $ tilt boundaries in zinc and its temperature dependence were found to depend on the misorientation angle and the inclination of the boundary plane. An application of a magnetic field during the annealing of cold rolled (90 %) zinc–1.1 % aluminum alloy sheet specimens substantially affected the texture and microstructure evolution. This effect is attributed to the additional magnetic driving force for grain growth arising due to the magnetic anisotropy of zinc.     

Improved mechanical properties of V-microalloyed dual phase steel by enhancing martensite deformability

A good combination of ultimate tensile strength(UTS)up to 1365 MPa and total strain to failure(StF)to 15.5％has been achieved due to deformable martensite in the invented vanadium-microalloyed dual-phase(DP)steel,which was manufactured by two-stage annealing of cold rolled steel strip.The employed extensive characterizations revealed that the ductile martensitic phase in this DP steel differ-entiated from ordinarily low-carbon martensitic lath in both morphology and lattice structure.Complex coherent orientation relationships between ferrite,reverse austenite,martensitic phase and vanadium carbide(VC)do exist,leading to a new martensitic transformation mechanism and resultant dual-phase microstructure.Besides,a detailed characterization including essential phase transformation analysis in combination with in situ TEM observation,shows that,all the essential processing including recrystal-lization,reverse austenitic and martensitic transformation,in debt to the particular effects of VC,can be recognized as phase transformations with higher thermodynamic driving force and higher kinetic energy barrier as compared to previously common processing,which actually changes the microstructure and,indirectly leads to higher strength and higher ductility.This synergy of thermodynamics and kinetics can be generalized to improve mechanical properties of present steels.     

Interface Migration between Martensite and Austenite during Quenching and Partitioning （Q＆P） Process

An Fe-0.2C-1.5Si-1.67Mn steel was subjected to quenching and partitioning （Q＆P） process, and the interface migration between martensite and austenite at an elevated partitioning temperature was observed. The interface migration is excluded in constrained paraequilibrium （CPE） model. Based on ＂endpoint＂ predicted by CPE model the thermodynamic condition of interface migration is analyzed, that is, the difference in the chemical potential of iron in both ferrite （martenisite） and austenite produces the driving force of the iron atoms to migrate from one phase to the other phase. In addition, the interface migration can change the austenite fraction; as a result, the austenite fraction at partitioning temperature may be higher than that at quenching temperature through the interface migration, but this phenomenon cannot be explained by CPE model.     

Direct alloying of immiscible molybdenum-silver system and its thermodynamic mechanism

Direct alloying is difficult to be realized in an immiscible Mo-Ag system with a positive formation heat due to the absence of thermodynamic driving force at equilibrium.In this work,a direct alloying method is developed to realize the direct alloying between Mo and Ag and construct Mo-Ag interface.The direct alloying method was mainly carried out through a direct diffusion bonding for Mo and Ag rods at a temperature close to the melting point of Ag(Tm Ag).Then the microstructure and phase constitution of the as-constructed Mo-Ag interface are characterized.The results show that Mo-Ag metallurgical bonding interface has been constructed successfully,indicating that a direct alloying in the immiscible Mo-Ag system has been realized.Additionally,mechanical tests are carried out for the Mo-Ag joints prepared through the direct alloying method.The test results show that the average maximum tensile strength of the joints is about 107 MPa.The effect of alloying parameters on the tensile strength is also discussed,which shows that there is an effective temperature range for the direct alloying between Mo and Ag.Lastly,an improved thermodynamic model that considers the formation of Mo-Ag crystalline and amorphous phase is presented to reveal the thermodynamic mechanism of the direct alloying.Combining the calculation and differential scanning calorimetry(DSC)tests results,the Gibbs energy diagram for the direct alloying is obtained.It is confirmed that the co-release of storage energy and surface energy can serve as the thermodynamic driving force to overcome the effect of positive formation heat and lead to direct alloying for Mo-Ag systems.     

A new solution for 3D crack extension based on linear elastic stress fields

A solution to the 3D stress field based on the maximum tangential stress (MTS) criterion is presented in this paper. The solution allows for the estimation of the critical crack plane, the direction of growth in terms of both twist and tilt angles and the equivalent crack driving force for a given mixed-mode loading condition. It also shows the graphical relationship between the three different stress intensities for a given driving force. Initial results have shown good correlation with experimental data obtained from literature.     

Characterization and thermodynamic study of nanostructured Cu-26Zn-4Al (wt.%) shape memory alloy through mechanical alloying

In the current study, nanostructured Cu−Zn−Al ternary alloy was synthesized via mechanical alloying. The structural evolutions were also measured using x-ray diffraction and scanning electron microscope. The results showed an increase in lattice strain while the crystallite size decreased. Afterwards, thermodynamic analysis was carried out on Cu−Zn, Cu−Al and Zn−Al binary systems through Miedema's semi-empirical model. It was found that in all binary systems, there is a driving force for solid solution formation over all compositions due to its negative Gibbs free energy changes in those compositions, whilst, this value is positive for the formation of amorphous phase over some compositions which can be attributed to the absence of driving force. Finally, the extended version of Miedema's semi-empirical model was used and discussed in detail to determine the thermodynamic desirability of solid solution and amorphous phase formation for Cu−Zn−Al ternary system. It was concluded that in this ternary system, the minimum thermodynamic driving force for solid solution formation occurred for those compositions which were located in the corners of ternary diagram.     

Effect of Interstitial Hydrogen on Cohesive Strength of Al Grain Boundary with Mg Segregation

The effect of interstitial hydrogen on the cohesion of the Al ∑ =11（113） grain boundary （GB） is investigated based on the thermodynamic model of Rice-Wang using the first-principles density tunction calculation. I he results indicate that interstitial H behaves as an embrittler from ＂strengthening energy＂ analysis. The reduced GB cohesion due to the presence of H at the GB is attributed to the low affinity between H and Al, and the weakened bonding of Al atomic pairs perpendicular to GB plane.     

Properties of tilt grain boundaries in ordered alloys

Computer simulation of symmetric tilt grain boundaries (GB) Σ = 5 [100](012) in ordered alloys Ni₃Al and NiAl was carried out. The energy of GB ws calculated by a method construction of γ-surface construction using Morse's empirical centralforce potentials. Results show GB having several steady states: (i) one is stable; or (ii) metastable. These states differ by energy and atomic structure of GB. Transition of GB from one state to the other is investigated and Burgers vector of GB dislocations are determined. It is shown that a direction fo GB slip in both alloys is [100].