Influence of crystallography on aspects of solid-solid nucleation theory

Expressions for the major variables in the general rate equation for solid-solid nucleation were developed on the basis of various models of the critical nucleus shape during homogeneous and heterogeneous nucleation. These models are based upon spheres, but in some a facet was incorporated at one boundary orientation to represent the presence of a partially or fully coherent structure. Gibbs’ relationship for the critical radius is applicable to all of the models. The other variables in the nucleation rate equation are affected by the model and by faceting. Reduction of AG* by faceting is concluded to be the primary cause for the presence of reproducible lattice orientation relationships and for the existence of transition phases during precipitation from solid solutions.     

优质GH738合金热变形过程中的再结晶机制

结合MTS压缩实验,分析了不同变形温度、应变速率、变形量及变形后保温时间对优质GH738合金再结晶的影响规律;进而,利用光学金相显微镜(OM)、透射电子显微镜(TEM)和电子背散射衍射(EBSD)分析,系统研究了该合金热变形前后的合金的晶粒组织、晶内亚结构、晶粒取向差异和弯曲晶界.结果表明:在实验参数范围内,优质GH7...     

Evolution of bivariate particle size distributions

A simple and general procedure is presented for the calculation of bivariate particle growth paths (and, hence, local particle growth rates) from the experimentally measured series of bi- variate size distributions during an evolutionary process. For modeling of microstructural evo- lution, a mathematical relationship is derived to relate the bivariate particle size distribution function to the nucleation rate and growth rate. A deterministic nucleation and growth process is assumed, and hence, the results are applicable only to the "mean field" models of nucleation and growth. A generalized continuity equation is derived for evolving bivariate and multivariate distributions.     

Observations of the formation and kinetics of surface steps during evaporation and condensation

Surface step patterns produced by crystal growth or evaporation can be observed, e.g., on NaCl, AgBr, Ag, and Si, by means of the electron microscopic method of decoration. These observations give insight into the mechanisms (random two-dimensional (2-D) nucleation, formation of hills or pits by spirals or repeated preferential 2-D nucleation, kinematic step interaction, orientation dependence of step motion, light-influenced evaporation, and stage of coalescence of thin films) and molecular processes (surface and edge diffusion) of crystal and thin film growth. Combining the decoration and platinum-carbon replica techniques enables an interesting insight into the step kinetics during the process of faceting. The pinning of moving steps at impurities and their piling up are decisive particulars. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Modeling of recrystallization after inhomogeneous deformation

Recrystallization in an inhomogeneously predeformed material (a cold-drawn cylindrical rod) is described by an analytical model and simulated with the Monte-Carlo technique. For this purpose, an equation for the nucleation rate during recrystallization as a function of local deformation has been derived. The analytical model considering the derived nucleation equation is capable of predicting the progress of the recrystallization front as observed in experiments with Titanium Grade 2. The Monte-Carlo model has been developed on the basis of the analytical model. Different functions for the local deformation were introduced, and recrystallization and subsequent grain growth were simulated. With the aid of simulation, the formation of both a grain size gradient and large elongated grains in the region of critical deformation can be understood. The graded microstructure is a consequence of the combined effect of inhomogeneous nucleation and anisotropic growth of the recrystallizing grains. Experimental grain size gradients were reproduced quantitatively by the present simulations. Agreement was also found for the grain elongation that forms during the recrystallization and grain growth stages.     

Theory of nucleation with cluster loss and injection: Application to plastic deformation and irradiation

Conventional nucleation theory considers the growth and decay of clusters only by thermally activated single atom addition or subtraction. Many environments of interest, including plastic deformation and energetic particle irradiation, induce numerous dynamic processes to create a host of defects which may produce a new nucleation regime. Creation and movement of dislocations and point defects and passage of thermal and stress waves could readily destroy or remove atoms from subcritical clusters, which typically contain at most only a few tens of atoms. Displacement cascades could destroy subcritical precipitates or vacancy clusters. It is also possible that clusters are injected into the system, as with vacancy-rich displacement cascades which may act as precursors for dislocation loop or void nuclei. This article modifies the nucleation equation to account for such cluster loss and injection and solves the resulting equation analytically for the steady state. The effects of cluster loss are described by several dimensionless groupings of kinetic and thermodynamic parameters. Cluster loss is found significant only if the probability of destruction is comparable to or greater than the probability of growth by single atom capture. The effects of cluster loss are predicted to be greatest for phases which form with large critical nuclei or complex unit cells. Athermal single atom loss, as by radiation resolution in ion mixing, appreciably reduces the nucleation rate only when the rate of loss approaches or exceeds the rate of solute atom capture. This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,” organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3–5, 1994, in Rosemont, Illinois.     

Heat transfer-solidification kinetics modeling of solidification of castings

A close examination of the recent developments in the field of computer simulation of solidification process reveals that a combination of both macroscopic and microscopic models is necessary in order to accurately describe the solidification of castings. Currently available macroscopic models include models that describe heat transfer from metal to mold, fluid flow of liquid metal during mold filling, and stress field in the casting. At the microscopic level, the models should include more intricate issues such as solidification kinetics and fluid flow in the mushy zone. Although significant progress has been accomplished over the years in each field, the task of including all of these models into a comprehensive package is far from being complete. This paper describes the state of the art on coupling the macroscopic heat transfer (HT) and microscopic solidification kinetics (SK) models and introduces thelatent heat method as a more accurate method for solving the heat source term in the heat conduction equation. A new method for calculation of fraction of solid evolved during solidification based on computer-aided cooling curve analysis (CA-CCA), as well as a method based on nucleation and growth kinetics laws, is discussed. A new nucleation model based on the concept of instantaneous nucleation, which is used to describe equiaxed eutectic solidification of commercial alloys, has been introduced. It is demonstrated that the instantaneous nucleation model agrees well with the experimental results in terms of cooling curves and of evolution of the fraction of solid during solidification. Validation results are also shown for SK models that are based on CA-CCA coupled with HT models for eutectic Al-Si and gray cast iron alloys.     

Electron microscopic investigation of the microstructure of rolled and annealed Ni-single crystals

Ni single crystals of near cube orientation were rolled 90%. The deformed microstructure and the nucleation of recrystallization were investigated in the EM correlating the microstructure with the orientation relations measured. Main results are: The majority component of the deformed crystals is a rotated cube orientation. In addition the texture contains components which are approximately in twin orientation to the initial orientation or which were formed by microbands resp, shearing. At the boundaries of these inhomogeneities nucleation takes place during annealing in a three step mechanism.     

The initial stages of the cellular reaction

Both the nucleation process per se and the organization of nearby nuclei or precipitates formed at a given disordered grain boundary into a viable cell structure are considered. When the critical nucleus is modeled in simple fashion, based upon a rectangular parallelepiped, the rate of nucleation by the “conventional” mechanism, in which the grain boundary is essentially immobile during the nucleation process, far exceeds that by the Tu-Turnbull “pucker” mechanism, in which the grain boundary is deflected so that its plane is parallel to the habit plane of the nucleus. A more rigorous model of the critical nucleus, based upon the somewhat specialized assumption that an energy cusp facet forms at only one boundary orientation but developed without a preconceived view of the nucleus morphology, leads to this result only when the facet energy is greater than one-half the energy of a disordered grain boundary. In the reverse energetic situation, the nucleus morphology is effectively that supposed by the pucker mechanism. The initial stage of cellular growth is examined in the framework of the question: why do allotriomorphs form at disordered grain boundaries under some conditions of alloy composition and temperature and cells develop under other conditions? The conditions for the two reaction paths are established on the basis of two key ideas: the direction in which the torque term associated with a facet deflects a grain boundary meeting the edge of the facet (deduced from the considerations of Hoffman and Cahn), and the existence of a driving force for the breakaway of a grain boundary from such a junction resulting from the requirement of continuity of path to another junction located nearby.     

高磁感取向硅钢中A1N的析出研究

通过热力学和动力学计算相结合的方法,系统地分析了高磁感取向硅钢中A1N在均热过程中的析出机 制。计算结果表明,在高磁感取向硅钢的均热温度下AIN处在α+γ 两相区,同时具备热力学析出条件。在均匀形核、晶界形核和位错形核3种机制下,A1N的临界形核尺寸处在同一数量级且随温度降低而减小。相同温度下, A1N晶界形核的临界形核功最小,相对形核率最大,即较易发生晶界形核。A1N在α相和γ相中均匀形核、晶界形 核和位错形核的最快析出温度分别为1203 K、1303 K、1243 K和1213 K、1305 K、1233 K。 AIN在均热温度下以晶界形核为主。     

Kinetics of growth of the Ti-Co

The growth behavior of the disordered and ordered intermetallic compounds in the Ti-Co system from undercooled melts during rapid solidification has been studied in detail. It was found that cooling rates of the order of 10¹⁰ to 10¹² K s^-1 were insufficient to suppress the nucleation and growth of the intermetallic compounds. The compound isomorphous to Ti₂Co does not exhibit faceting, indicating a nonsingular crystal/liquid interface morphology at high growth velocities. While a TiCo-like compound was found to have a ordered bcc structure, the formation of even the disordered TiCo₃ was completely suppressed by the high isothermal velocities, leading to glass formation. The growth velocity of compounds formed in the composition range 23.3 to 59.7 at. pct Co was found to be diffusion limited with nucleation times smaller than the total melt lifetimė in the process. The overall glass formation range was found to be very small, although the equilibrium phase diagram shows the presence of a variety of intermetallic compounds.     

Crack and cavity nucleation at interfaces during creep

Athermal nucleation of microcracks and thermal nucleation of cavities during creep deformation are reviewed with an emphasis on effects of solute segregation to grain boundaries and cavity surfaces. The magnitude and the duration of stress concentration at a triple grain junction or at a grain boundary inclusion are estimated for transient Coble creep and steady state power-law creep conditions. Stable configurations of wedge-type microcracks are predicted by a Griffith-like crack model. The rate for thermal nucleation of cavities is obtained by the Fokker-Planck equation for vacancy clusters. Cracks and cavities are interdependent, and cavity nucleation occurs continuously throughout the three creep stages. The local stress concentration enhances microcrack and cavity nucleation. The cavity nucleation rate is generally increased as a result of solute segregation to the surfaces and interfaces and/or gas precipitation into cavity volume. This enhanced nucleation is more effective in a system with mobile solutes than with immobile solutes. Immobile solute or trace elements may affect the nucleation rate also by changing the grain boundary diffusivity. Experimental techniques for quantitative analyses of cavity nucleation processes are discussed. This paper is based on a presentation made at the symposium “The Role of Trace Elements and Interfaces in Creep Failure” held at the annual meeting of The Metallurgical Society of AIME, Dallas, Texas, February 14-18, 1982, under the sponsorship of The Mechanical Metallurgy Committee of TMS-AIME.     

苄叉丙酮对锌—氨—氯化铵溶液电沉积锌的影响

用线性极化曲线、循环伏安法和计时电流法等考察了添加剂苄叉丙酮对锌—氨—氯化铵体系锌电沉积过程、电锌形貌和结构的影响。结果表明,苄叉丙酮抑制锌离子的还原过程,当其浓度为0.08g/L时,锌的析出电位较未加入添加剂时负向移动了132mV,交换电流密度由3.47×10-4 A/m2变为0.51×10-4 A/m2。苄叉丙酮没有改变锌电沉积的形核方式,仍为3D瞬时成核,但减小了晶体的生长速率。锌的形貌主要以层状为主,苄叉丙酮不仅使锌晶面生长具有择优取向,同时还能细化晶粒。     

A Fatigue Life Model for Predicting Crack Nucleation at Inclusions in Ni-Based Superalloys

Engineering alloys such as Ni-based alloys, Al-alloys, and steels often contain non-metallic inclusions in their microstructures. These inclusions, which include oxide particles, carbides, and intermetallic particles, are introduced during component manufacturing processes such as casting, powder-metallurgy, or additive manufacturing methods. The presence of inclusions in the microstructure can promote fatigue crack nucleation by competing against slipband nucleation and reduce fatigue life performance of an engineering component. While it has been reported in many occasions, the competition between fatigue crack nucleation at inclusions and slipbands is still not well understood. In this article, the conditions for the concurrent occurrence of fatigue crack nucleation at inclusions and slipbands are analyzed theoretically. The analysis indicates that there exists a critical inclusion size (diameter) below which there is no fatigue life debit due to crack initiation at inclusions and above which a transition from slip-induced to inclusion-induced crack nucleation occurs. The low-cycle fatigue life model is applied to Ni-based superalloys and the model predictions are compared against experimental data from the literature to assess the dependence of the critical inclusion size on the slip morphology, grain size of the matrix, and the shear modulus of the inclusion.     

The effect of undercooling on the cellular precipitation reaction in Cu-3 Pct Ti

The effect of undercooling on the morphology of the cellular precipitation reaction in Cu-3 Pct Ti is examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and serial sectioning experiments. The reaction front formed at small undercooling, which exhibits strong faceting of the precipitate growth interfaces, gradually changes with increasing undercooling to a smoothly curved reaction front with concave precipitate growth interfaces and convex grain boundary segments. This concealment of the faceted reaction front appears to be due to the rapid accumulation of growth ledges with increasing undercooling. This study also indicates that the cellular precipitation reaction, at small undercooling, is initiated by Widmanstätten precipitation. At larger undercoolings, a second mechanism is responsible for cellular genesis. Finally, contrary to accepted models of colony development, serial sectioning experiments show that nucleation of additional lamellae may occur at the faces of existing lamellae, from where they extend laterally to achieve the characteristic interlamellar spacing for that temperature.     

Intragranular ferrite nucleation in medium-carbon vanadium steels

In this study, the mechanism of intragranular ferrite nucleation is investigated. It is found that “intragranular ferrite idiomorphs” nucleate at vanadium nitrides which precipitate at manganese sulfide particles during cooling in the austenite region. It is observed that intragranular ferrite has the Baker-Nutting orientation relationship with vanadium nitride which precipitated at manganese sulfide. According to classical nucleation theory, the proeutectoid ferrite nucleation rate depends on the following factors: (1) the driving free energy for ferrite nucleation, (2) the diffusivity of carbon atoms in austenite, and (3) the increase in the interfacial energy associated with ferrite nucleation. In the Baker-Nutting orientation relationship, the lattice mismatch across the habit planes is likely to be very small. Depleted zones of solute atoms such as vanadium are assumed to be formed in the austenite matrix around precipitates. The effect of the depleted zones on factors (1) and (2) is estimated thermodynamically and it is proved that those effects are negligibly small. Thus, we conclude that the most important factor in nucleation kinetics of intragranular ferrite is the formation of precipitates which can develop coherent, low energy interfaces with ferrite.     

Critical Driving Forces for Formation of Bainite

An empirical equation for predicting bainite start temperatures of steels was recently derived by starting from binary Fe-C alloys and continuing with ternary Fe-C-M alloys. This result is now illustrated with a family of B_S lines in a T,C diagram for a series of constant Mn contents. The critical driving force for the formation of ferrite is calculated for diffusionless or diffusional processes, and these quantities are used as dependent variables with carbon content or temperature as independent variables. Negative critical driving forces are predicted for a diffusionless process in binary Fe-C alloys, showing that this process cannot apply to the formation of bainite. The critical driving force for a diffusional process increases strongly with decreasing temperature and increasing carbon content. Mn and Ni, contrary to Cr, Mo and Si, have remarkably small effects on this critical driving force. The results are discussed by imagining that the magnitude of the critical driving force is governed by the height of an energy barrier that must be surmounted during growth. It is modeled as completely determined by the alloy composition. It is represented with an equation evaluated by fitting to the recent empirical equation and describing the carbon dependence of the barrier.     

The kinetics of martensite formation in small particles

The kinetics of martensite nucleation in “atomized” particles of Fe-24.2 Ni-3.6 Mn and Fe-22 Ni-0.49 C have been investigated as a function of particle size (10 to 140 μ) and reaction temperature. The dependence of particle fraction transformed on particle size indicates that martensite nucleates at surface or near-surface sites for the Fe?Ni?C powder and throughout the bulk for the Fe?Ni?Mn powder. It is shown that, in contrast to kinetic measurements on bulk samples where autocatalysis predominates, the present technique measures reaction rate due solely to the sites present initially. The measurements show that there is no detectable incubation time for nucleation and that the nucleation sites have a specific distribution of activation energies. A method for extracting the distribution from experimental measurements is given and the result is used to develop a revised equation for describing isothermal martensite formation. The isothermal kinetics of martensite formation in Fe-22 Ni-0.49 C are investigated despite the fact that such measurements are not possible in bulk samples because the alloy transforms by “bursting”. It is found that the apparent activation entropy for martensite nucleation is significantly higher for this alloy than for Fe-24.2 Ni-3.6 Mn. This suggests that the dislocation-dislocation interactions at the critical nucleation step are longer-range in the Fe?Ni?C alloy than in the Fe?Ni?Mn alloy.     

取向硅钢中AlN析出的动力学

利用理论计算方法系统地计算和分析了取向硅钢中AlN在不同的形核机制下的析出动力学特征,如临界形核半径、临界形核功、相对形核率以及时间-温度-析出(TTP)曲线。计算结果显示,AlN在均匀形核、晶界形核或位错形核时临界形核尺寸不变。晶界形核时,AlN的临界形核功最小,相对形核率最大,AlN沉淀析出TTP曲线鼻子点温度为1 020℃,AlN沉淀析出的形核机制主要为晶界形核。