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Determination de la cinetique de carburation par thermogravimetrie dans le domaine de temperatures 1173-1373 K, en utilisant les systemes Fe-20 Cr et Ni-30 Cr et les melanges gazeux H 2 -CH 4

Etude de la cinetique de croissance pour plusieurs systemes avec des etats fondamentaux fortement degeneres trempes a partir d'une temperature elevee jusqu'a une temperature basse. La taille moyenne des domaines augmente algebriquement avec le temps. On observe un croisement distinct d'une classe d'universalite a l'autre quand l'interaction de spin varie

The Frenkel-Kontorova (FK) model is generalized to two spatial dimensions and studied by finite temperature molecular dynamics simulations. The model allows dislocations of arbitrary orientation and Burgers vector, including edge and screw dislocations. Straight dislocations, dislocation loops and mechanisms for dislocation generation are studied. Two new mechanisms for dislocation generation have been identified: (1) the heterogeneous nucleation of dislocations on pre-existing dislocations and (2) the generation of dislocation loops in the wake of a moving dislocation. These mechanisms may be important in materials subjected to high strain rates.

A Monte Carlo computer simulation technique has been developed which models grain growth for the case in which the grain boundary energy is anisotropic. The grain growth kinetics, as represented by the growth exponent n ( R = Ct n ), is found to decrease continuously from 0.42 ± 0.02 to 0.25 ± 0.02 as the anisotropy is increased, where 0.42 is the growth exponent in the isotropic case. The grain size distribution functions become broader as the anisotropy is increased. For large anisotropy, the microstructure is described as consisting of large grains with extended regions of small grains. The small grains tend to have low angle grain boundaries. Anisotropic grain boundary energies can result in preferred crystallographic orientation, however the orientational correlations are limited to a few times the mean grain radius when potentials yielding reasonable microstructures are utilized.

We present a generalized theory for the growth of columnar microstructure in vapor‐deposited thin films under the joint influence of a constant uniform deposition flux coming down with an arbitrarily chosen incidence angle, and surface diffusion. The dependences of the zone I to zone II transition temperature, and the characteristic length scales associated with the unstable modes on the deposition angle are predicted. The surface morphology is obtained as a function of vapor incidence angle. For a specific deposition angle, there is a one‐parameter family of steady‐state surface profiles that corresponds to a range of possible columnar orientation angles, among which only one angle is associated with the tangent rule. These results agree with experimental observations.

The microstructures produced by the grain growth simulation technique described in the previous paper are analyzed. The grain size distribution function is found to be time invariant when the grain size, R, is scaled by the mean grain size, R , and is shown to fit the experimental data better than either the log-normal function or the grain size distribution function suggested by Hillert. The grain size distribution peaks at approximately R and has a maximum at ~2.1 R . The topological class distribution (number of edges per grain) is monitored and found to reproduce the existing experimental data. Similarly, the experimentally observed linear relationship between edge class number and the means of the individual edge class distributions is reproduced. The mean curvature per grain is also measured. Finally, the temporal evolution of the sizes of individual grains is monitored to provide a link between the observed grain size distribution function and the macroscopic grain growth kinetics.

We present a detailed analysis of the relative motion of a pair of edge dislocations with parallel line directions due to their mutual interactions in the overdamped limit. In particular, we derive analytic expressions for the trajectories in the three cases of parallel, antiparallel, and perpendicular Burgers vectors for both zero climb and finite climb. In each of these cases, we find attracting (stable) or repelling (unstable) equilibria, and this allows a simple characterization of the motion. For all other orientations, no such equilibria exist, and the two dislocations either come together or escape to infinity. In addition, we give the equations of motion for the trajectories in the presence of an external stress.

The possibility of defining structural defects in amorphous solids in terms of parameters such as atomic-level internal stresses and local symmetry coefficients was proposed in a previous paper (Egami, Maeda and Vitek 1980). Using a model amorphous structure generated by a computer, these parameters are statistically analysed in the present paper. It is shown that the stress and the symmetry coefficients are closely correlated and that spatial correlations of various kinds exist. The structural defects are then defined as regions in which the corresponding characterizing parameter deviates significantly from its average value. Two distinct classes of defects were found; (i) positive (p-type defects) and negative (n-type defects) local density fluctuations; and (ii) regions of large shear stresses and large deviations from spherical symmetry. Defects consisting of pairs of p-type and n-type defects separated by regions of large shear stresses are also common. The effect of annihilation of p- and n...

While previous analyses of dislocation-inclusion interactions during the creep of dispersion strengthened systems have generally concluded that the dislocation climbs over the inclusion, detailed consideration of the associated elastic and diffusive problems, analyzed here, indicate that climb by-pass of the inclusion is not possible. In order to keep the elastic problem tractable, we consider a straight edge dislocation interacting with a cylindrical inclusion of infinite extent. Additionally, since we are concerned with interactions at elevated temperatures, we allow the matrix-inclusion interface to slip. We find that along approximately 1 2 of the glide planes intersecting the inclusion, the dislocation is attracted toward the inclusion. Dislocations originally lying on those glide planes, where the dislocation-inclusion interaction is repulsive, respond by either climbing on to a glide plane where the interaction is attractive or by diffusionally relaxing the repulsion. Therefore, a dislocation that is gliding on my plane that intersects the inclusion will end its trajectory at the inclusion-matrix interface. When the dislocation-inclusion separation is of order a dislocation core diameter, the dislocation core relaxes into the inclusion-matrix interface, thereby pinning the dislocation. Unpinning the dislocation requires a stress of order the Orowan stress, which is believed to give rise to the observed threshold stress for creep in dispersion strengthened systems.

Results from simulations of Ni, Al, Ni/sub 3/Al, and NiAl show long-range, oscillatory surface relaxations that decay exponentially into the bulk. Pure fcc Ni and Al have oscillation periods that are close to the nearest-neighbor distance, independent of crystal face. This is shown to be due to surface smoothing and steric effects. In Ni/sub 3/Al and NiAl, the surface planes are rippled, with the Ni-Ni and Al-Al interlayer spacings oscillating 180/sup 0/ out of phase. Very good agreement between our results and experimentally measured atomic relaxations is obtained.

A stability theory is presented which describes the conditions under which thin films rupture. It is found that holes in the film will either grow or shrink, depending on whether their initial radius is larger or smaller than a critical value. If the holes grow large enough, they impinge to form islands; the size of which are determined by the surface energies. The formation of grooves where the grain boundary meets the free surface is a potential source of holes which can lead to film rupture. Equilibrium grain boundary groove depths are calculated for finite grain sizes. Comparison of groove depth and film thickness yields microstructural conditions for film rupture. In addition, pits which form at grain boundary vertices, where three grains meet, are another source of film instability.

Intermetallic compounds have long been of interest for their superior strength and stability at elevated temperatures. However, the low symmetry crystal structures common to these materials generally lead to a very low level of ductility. While compounds which form in the Ll/sub 2/ (Cu/sub 3/Au) crystal structure do not suffer from a restricted number of available slip systems, many have been found to be prone to intergranular brittleness. One such compound which has received considerable attention is Ni/sub 3/Al. It has been previously demonstrated that polycrystalline Ni/sub 3/Al is inherently susceptible to intergranular failure. Subsequently, another study found that small additions of B could eliminate grain boundary failure and restore ductility to levels found in single crystals. An enormous literature treating ductile versus brittle behavior in Ni/sub 3/Al, and Ll/sub 2/ compounds in general, has evolved in recent years. The action of B in increasing the cohesive strength in grain boundaries in Ni/sub 3/Al and other Ll/sub 2/ compounds is well accepted. However, the regimes in B concentration, temperature, and alloying additions over which the B enhanced grain boundary strength is observed are not well correlated. The purpose of this note is to rationalize the existing experimental literature with amore » simple model based on the competitive nature of the fracture process.« less

Monte Carlo computer simulation techniques have been utilized to investigate abnormal grain growth in a two dimensional matrix. The growth of abnormally large grains is modelled under two conditions: 1. (a) where the driving force is provided solely by curvature and 2. (b) where the driving force is provided by the difference in the gas-metal surface energy between grains of different crystallographic orientation. For curvature driven growth three cases are considered: 1. (a) the growth of abnormally large grains in microstructures without grain growth restraints, 2. (b) the growth of abnormally large grains in microstructures with particle dispersions, and 3. (c) grain growth in a particle pinned microstructure in which a sudden decrease in the number of particles occurs. In all these cases, the initiation of abnormal grain growth/secondary recrystallization is not found to occur. In systems free from grain growth restraints the normal grain size distribution is very robust and strongly resistant to perturbations. For systems which contain particle dispersions strong pinning of the grain boundaries is always observed. However, when a preferred surface energy orientation is introduced, abnormal grain growth/secondary recrystallization does take place. The microstructural evolution observed during secondary recrystallization is in good correspondence with experiment. The area fraction of secondary grains exhibits sigmoidal behavior as a function of time, and is characterized by an Avrami exponent of 1.8 ± 0.3 when fit to a modified Avrami equation.

We present new simulations of the domain-growth kinetics for the Q-state Potts model in two and three dimensions. The time dependence of the average grain radius R\ifmmode\bar\else\textasciimacron\fi{} can be described by R\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\simeq}${\mathrm{Bt}}^{n}$, where B is a temperature-dependent constant. In two dimensions, we find n=0.49\ifmmode\pm\else\textpm\fi{}0.02 for a range of Q values from 2 to 48. This value of n is obtained from very long simulations on lattices up to size ${1000}^{2}$ and is in contrast to our earlier estimates for n which were less than (1/2 (n\ensuremath{\simeq}0.41\ifmmode\pm\else\textpm\fi{}0.01) for large Q. In three dimensions on lattices of size ${100}^{3}$, we find that n=0.48\ifmmode\pm\else\textpm\fi{}0.04 if early-time data are excluded from the fit to the kinetic data but smaller if the entire data set is used. The grain-size distribution for several values of Q in both two and three dimensions is also determined and compared with our results for grain growth in real polycrystalline materials.

The development of order in the clock (${\mathbf{Z}}_{N}$) model is studied following a quench from high temperature ($T\ensuremath{\gg}{T}_{c}$) to very low temperatures, where the system has a ferromagnetic ground state. We find that the mean domain size $R$ and energy $E$ do not increase algebraically with time, in contrast to the behavior observed for the $Q$-state Potts model. Instead, we find that quenched-in vortices, present even at low temperature, play an important role in the domain growth, ultimately pinning the growth for long times.

A theory for the growth of columnar microstructures in thin films is presented. The zone-I to zone-II transition temperature is predicted. The surface morphology and the columnar grain structure are obtained both analytically and numerically, and the scaling behavior of the columnar grain size with film thickness is derived. Monte Carlo simulations are used to follow the evolution of the three-dimensional zone-II microsctuctures and to account for the formation of film texture. These results agree with experimental observations.

Resultats de simulations sur ordinateur de la cinetique d'un modele de Potts a etat Q ferromagnetique

A dense random packing model of amorphous iron was analysed in terms of the Voronoi polyhedral statistics and the recently proposed local structure parameters, in particular stresses and site symmetry coefficients (Egami et al., 1980). The purpose of this study is to clarify the relationship between these two types of methods of describing the local structure of amorphous solids. It has been shown that the topology of the local structure represented by the Voronoi polyhedra is related to the local stresses and symmetry only through the coordination number. On the other hand, the degree of distortion of the environment, which is of primary importance to many physical properties and is well characterised by the local parameters, is practically independent of the polyhedral topology. It is concluded, therefore, that the topological description based upon the polyhedral statistics does not provide an unambiguous microscopic basis for relating the local structure of the dense random packing model to its physical properties and could even be misleading.

This paper presents a specialized microstructural lattice model, MCFET (Monte Carlo finite element technique), which simulates microstructural evolution in materials in which strain energy has an important role in determining morphology. The model is capable of accounting for externally applied stress, surface tension, misfit, elastic inhomogeneity, elastic anisotropy, and arbitrary temperatures. The MCFET analysis was found to compare well with the results of analytical calculations of the equilibrium morphologies of isolated particles in an infinite matrix.

Computer simulation results are presented for various types of planar defect occurring on the (111) plane of the intermetallic compound Ni3 A1. The relaxed defect structures produce oscillations in the static displacements, both perpendicular and parallel to the boundary plane. This type of relaxation behaviour is related to the fact that the ordered lattice contains more than one atom per lattice site. Therefore, two different types of static distortion mode are found which, by analogy with lattice vibration modes, are called acoustic and optical. For the planar defects studied here, these two types of distortion mode were separated and it was found that the optical distortion mode is of similar nature in all of them. The acoustic mode is similar to that found in pure Ni and A1.

Atomistic simulations of free surfaces and [001] symmetric tilt grain boundaries in pure Ni and Al and the intermetallic, Ni3Al, are presented. In the vicinity of the grain boundary, we show the existence of a rapidly decaying oscillatory strain which is similar to that observed at free surfaces. The total expansion or excess volume associated with the grain boundary is shown to be proportional to the grain boundary energy. The atomistic structures of the simulated grain boundaries have been analyzed in terms of the structural unit model, which is found to be of limited utility in the case of the intermetallic. Preliminary results show that boron segregates more strongly to grain boundaries than to free surfaces. Boron segregation strengthens the grain boundary but has little effect on grain boundary structure other than a small local expansion.

The properties of domains generated following a quench from very high temperatures ($T\ensuremath{\gg}{T}_{c}$) to low temperatures are studied for an Ising model evolving under conserved or nonconserved dynamics. Before the quench the clusters satisfy percolation statistics, since $T$ is too large for the interactions to be relevant. However, after the quench to low temperatures, we observe that the largest clusters are still percolationlike for large distances in that they are described by the same Hausdorff dimension as percolation clusters. For short distances the clusters are compact. At intermediate distances, the large clusters appear to be more fractal than percolation clusters. We interpret this intermediate regime as a crossover between a constant density at short distances and percolationlike low-density regime for large distances, not as a new type of fractal.

The computer simulation of a shear deformation of a model monoatomic amorphous metal has been performed. The strain was applied incrementally, relaxing the structure at each step. The complete stress-strain curve was thus obtained. A large number of microscopic deformation events have been observed and analyzed using the description of the local atomic structure by the atomic level stresses. Although no temperature effects have been included in the present study the calculated stress-strain curve is in very good agreement with the stress-strain curves measured experimentally at or above room temperature. The common feature of these experiments and present calculations is, however, the homogeneity of the deformation. Hence, it is argued that fundamental microscopic deformation mechanisms are the same at low and high temperatures and the macroscopic differences arise owing to the strain localization in the former case. The regions of inhomogeneous atomic movement which results in plastic deformation, have not been found to be correlated with local density fluctuations in contrast with assumptions of the models based on free volume theory. They are, however, correlated with regions of high shear stresses, called τ-defects. These defects are formed during the deformation, are sustained by the applied stress and appear to act as stress concentrators in the vicinity of which a localized viscous flow develops.

We analyze a simple model of elastic failure in randomly inhomogeneous materials such as minerals and ceramics. We study a two-dimensional triangular lattice with nearest-neighbor harmonic springs. The springs are present with probability p. The springs can only withstand a small strain before they fail completely and irreversibly. The applied breakdown stress in a large, but finite, sample tends to zero as the fraction of springs in the material approaches the rigidity percolation threshold. The average initial breakdown stress, ${\ensuremath{\sigma}}_{b}$, behaves as ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{b}}^{\mathrm{\ensuremath{\mu}}}$\ensuremath{\approxeq}[A(p)+B(p)ln(L)${]}^{\mathrm{\ensuremath{-}}1}$, where L is the linear dimension of the system and the exponent \ensuremath{\mu} is between 1 and 2. The coefficient B(p) diverges as p approaches the rigidity percolation threshold. The breakdown-stress distribution function ${F}_{L}$(\ensuremath{\sigma}) has the form ${\mathit{F}}_{\mathit{L}}$(\ensuremath{\sigma})\ensuremath{\approxeq}1-exp[-${\mathit{cL}}^{2}$exp(-k/${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{\mu}}}$)]. The parameters c and k are constants characteristic of the microscopic properties of the system. The parameter k tends to zero at the rigidity percolation threshold. These predictions are verified by computer simulations of random lattices. The breakdown process can continue until a macroscopic elastic failure occurs in the system. The failure occurs in two steps. First, a number of springs fail at approximately the strain which causes the initial failure. This results in a system which has zero elastic modulus. Finally, at a considerably larger strain a macroscopic crack forms across the entire sample.

The transmission electron micrographs of submicrometer-thick specimens of incommensurate barium sodium niobate obtained by Xiao-qing et al. exhibit textures with lines of disclinations ending in vertices of Friedel index m=+1. These are similar to those observed in nematic-liquid-crystal films with continuously degenerate boundary conditions. The nature of the vertices at which these lines meet permits us to examine the physical and topological basis for the equivalence of the two systems. A four-state clock model, in two dimensions, is shown to predict the observed structure.

The corrosion of metallic components is a significant problem in many high temperature processes. In studying such corrosion phenomena, the scientist must identify simpler laboratory environments which can reproduce the corrosion product composition and morphology found in the more complex service environments. The present work was undertaken to develop a graphical method to aid in accomplishing the above objective. A predominantly oxidizing-sulfidizing environment which also contains some carbon was selected as an example. Such an environment is characteristic of processes such as coal gasification and can be produced by mixing CO2, H2, and H2S in appropriate quantities. Starting from selected initial compositions of such gas mixtures, an approach based upon free energy minimization was used to determine which condensed corrosion product phases will be stable for selected metals, temperatures, and total pressure. Graphs with initial CO2/H2 and H2S/H2 ratios as axes were then constructed; in these graphs, areas represent single condensed phases, lines represent two condensed phases in equilibrium, and triple points represent three condensed phases in equilibrium. The graph indicates at a glance the product phases which are possible for a given initial gas composition. When dealing with alloys, diagrams for the component pure metals must be combined.

The authors analyze a simple model of failure in an elastic material with randomly distributed defects. The model that they employ is a two-dimensional triangular lattice of springs. These springs are linearly elastic up to some small strain and irreversibly break at larger strain. Defects are introduced into the model by breaking a certain fraction of the springs before straining. During the simulation, a uniaxial strain is applied, the equilibrium configuration of the lattice is determined, and then the strain is incremented again. The failure stress is found to decrease as the fraction of springs removed is increased and decreases logarithmically with linear dimension of the sample L. The cumulative failure stress distribution is well fitted by the form F(sigma) = 1 - exp(cL/sup -2/ exp(-k/sigma/sup ..mu../)), where sigma is the failure stress, ..mu.. is a constant between 1 and 2, and c and k are constants which are characteristic of the microscopic properties of the system.

The equilibrium shape of the pit where a dislocation intersects a free surface is calculated in a variational formalism. The constant dislocation line tension approximation, made by previous workers, is shown to be clearly inadequate for all realistic cases. Employment of a variable dislocation line tension model for the case of finite dislocation density shows the existence of two regimes of behaviour. In the first, pits formed at dislocation-surface intersections have a well defined shape and are of finite depth. However, a second regime exists, in which the pit depth is infinite and the dislocation core size exceeds the bulk value. This may result in the formation of open-core dislocations, as discussed by Frank.

Abnormal grain growth has been studied by means of a computer-based Monte Carlo model. This model has previously been shown to reproduce many of the essential features of normal grain growth. The simulations presented in this work are based on a modified model in which two distinct types of grains are present. These two grain types might correspond to two components of different crystallographic orientation, for example. This results in three classes of grain boundaries: (a) between unlike types, (b) between grains of the tirst type and (c) between grains of the second type, to which different grain boundary energies or different mobilities can be assigned. Most simulations started with a single grain of the first type embedded in a matrix of grains of the second type. Anisotropic grain boundary energies were modeled by assigning a higher energy to boundaries between like type than to boundaries between grains of unlike type. For this case, abnormal grain growth only occurred for an energy ratio greater than 2 and then wetting of the matrix by the abnormal grain occurred. Anisotropic grain boundary mobilities were modeled by assigning a lower mobility to boundaries between grains of like type than to boundaries between unlike type. For this case the extent of abnormal grain growth varied with the ratio of mobilities and it is tentatively concluded that there is a limiting ratio of size of the abnormal grain relative to the matrix, A simple treatment of anisotropic grain boundary mobility was developed by modifying Hillert's grain growth model (Acta meralf. 13,227 (1965)I. This theoretical treatment also produced a limiting ratio of relative size that is a simple function of the mobility ratio. RhsumP-La croissance anormale des grains a ete u (b) entre grains du premier type; (c) entre grains due second type, auxquels peuvent @tre assignees differentes energies intergranulaires ou differentes mobilitts. La plupart des simulations concernent un seul grain du premier type entoure par une matrice de grains du second type. On a tenu compte des energies intergranulaires anisotropes en assignment aux joints separant des grains du mm entsprechend konnen diese Korngrenzarten unterschiedliche Energien und Beweglichkeiten aufweisen. Die meisten der Simulationen begannen mit einem einzigen Kom des ersten Typs, welches in einer Matrix von Kornem des zweiten Typs eingebettet war. Anisotrope Komgrenzenergien wurden im Model1 beschrieben, indem den Komgrenzen zwischen gleichen Komem eine hohere Energie als zwischen ungleichen Kiimern zugeschrieben wurde. In diesem Fall ergab sich anormales Kornwachstum nur, wenn das Verhaltnis der Energien griil3er als 2 war und dann das anormale Kom die Matrix benetzte. Anisotrope Korngrenzbeweglichkeiten wurden im Model1 beschrieben, indem Komgrenzen zwischen Kdrnem des gleichen Typs mit einer geringeren Beweglichkeit als zwischen ungleichen Kiimern versehen wurden. In diesem Fall hing der Grad des anomalen Wachstums von dem Verhaltnis der Beweglichkeiten ab; daraus kann gefolgert werden, daB es eine Grenze

A method of interpreting radial distribution functions (RDF) of amorphous metals is proposed in which the role of the local atomic structure is emphasized. It is found that the width and height of the peaks of the RDF are related to the second moment of the atomic-level hydrostatic stress distribution $〈{p}^{2}〉$. The results of this analysis are then used to explain the details of the changes that occur in the RDF when structural relaxation takes place. The theoretical ▵RDF is found to be in excellent agreement with the results of a computer study and previous experimental results. It is further proposed that changes in $〈{p}^{2}〉$ may be most easily accounted for in terms of changes in the density of the structural defects defined in terms of the local fluctuations in the hydrostatic stress. In this way the changes that occur in the structure of amorphous metal during structural relaxation, as represented by the RDF, may be explained in terms of the motion and annihilation of these structural defects. It is concluded that the number density of defects which could account for the observed changes in the experimental RDF is 10%. It is also found that while the hydrostatic stress distribution may be significantly changed during structural relaxation, the distribution of the atomic-level shear stresses remains unaltered.

The development of order for the Q-state Potts model for 2lQ\ensuremath{\le}48 in the presence of static, random impurities is studied following a quench from high temperature (T\ensuremath{\gg}${T}_{c}$) to very low temperatures. We find that the domain growth becomes pinned for quenches to T=0 and the average pinned domain area ${A}_{f}$ varies inversely with the concentration c of impurities. This value of the proportionality factor between ${A}_{f}$ and ${c}^{\mathrm{\ensuremath{-}}1}$ can be understood in terms of a simple topological analysis for large Q.

We have used “local volume” (embedded atom) type potentials to study the surfaces and grain boundaries of Ni, Al, and Ni3Al. The simulations show that with appropriately fit potentials, the surface and grain boundary structure can be realistically calculated. The surface rippling and relaxation show good agreement with experiments. The energies of most surfaces and grain boundaries also agree with existing data. The structural unit model for grain boundaries in Ni3Al shows the same generic units as in pure metals, but with large variations due to distortions and multiplicity. The utility of the structural unit model is thus more limited for alloys. The grain boundary energies were found to be the highest for Al-rich Ni3Al grain boundaries, and depend significantly on the local composition of the grain boundary. The cusps in the grain boundary energy as a function of misorientation angle are different for different grain boundary stoichiometries. The Ni3Al grain boundaries have approximately the same grain boundary energy and cohesive energy as that of Ni.

Description de la methode de simulation permettant l'analyse de l'interaction entre les particules et les joints de grains,et de la relation entre la grosseur des grains et la fraction volumique des particules.

A new criterion is proposed for quasi-brittle fracture based on the recognition that quasi-static fracture toughness measurements are merely a limiting case of dynamic fracture. It is found that a unique relationship exists between the energy stored ahead of a loaded crack or blunt notch and the velocity of a crack injected into the material by the failure of a microstructural element lying in the zone of elevated stress. The criterion establishes a minimum velocity required for the continued propagation of the injected crack as a function of the crack tip opening displacement at the instant of crack nucleation. Comparison of the predictions of the model with existing data on various steels and an aluminum alloy show excellent correlation. The implications of the model for phenomena such as the ductile-to-brittle transition, microstructural effects on the resistance to unstable crack propagation and grain boundary embrittlement/strengthening by solute segregation are also explored.

A statistical model of microstructural evolution is developed for the evolution of grain structure during deposition. In cases where the atomic mobility on the surface greatly exceeds that in the bulk of the film, the bulk microstructure may be viewed as static while all of the evolution is controlled by the free surface. This leads naturally to a two‐dimensional model of microstructural evolution. Since the surface is advancing at a constant rate during deposition there is a linear relationship between time in the two‐dimensional model and depth in the film. A Monte Carlo computer simulation technique is described which models the evolution of microstructure in this way. Various driving forces are included. Simulated microstructures in the plane of the film and in the plane perpendicular to the free surface are shown.

The local parameters are introduced to describe the local atomic structure of amorphous metals. They define the structural defects which facilitate the explanation of various properties, including the volume change by annealing.

The purpose of this paper is to offer an analytical model that accounts for the different variation of the limiting grain radius with volume fraction of particles found in previous computer simulations as compared to the classic Zener predictions. The effect of particles, seen both in the simulations and in the predictions, is to cause grain growth to cease at some limiting grain size. The source of the discrepancy arises from Zener's assumption of random particle/grain boundary intersections. The computer simulation, on the other hand, shows a high correlation between boundaries and particles.

The classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation (F = 1 - exp( - kt)") for nucleation and growth transformations works very well for most solid state transformations but fails regularly when applied to recrystallization of plastically deformed metals. Under conditions of near constant growth rate, a high exponent (n 2 3) is predicted but low exponents (n < 2) are typically measured. Another common observation is that the slope of a JMAK plot, from which the exponent is inferred, decreases as recrystalli~tion proceeds. Analysis of the published data suggested the h~thesis that the failure of the JMAK theory as applied to recrystallization is because of the lack of uniformity of the stored energy of plastic deformation on the grain size scale. This hypothesis was tested by use of Monte Carlo simulations of the type previously used successfully to model grain growth and re- crystallization. The earlier simulations of recrystallization used uniform stored energies whereas the simulations presented here varied the stored energy from grain to grain. The kinetics were plotted on JMAK plots which exhibited low and varying exponents closely resembling experimental data. Specific simulations were performed to test the basic JMAK assumption that makes a correction for the effect of impingement under conditions of random nucleation, namely dF/dF, = (1 - F), where F is the actual volume fraction and F, is the extended volume fraction-that which would obtain in the absence of impingement and overlap between new grains. It was found the assumption is accurate under conditions of uniform stored energy. With non-uniform stored energy, however, the correction underestimated the effect of impingement by a factor that rapidly increased (to over two orders of magnitude) during recrystallization. R~um~~~quation classique de Johnson, Mehl, Avrami et Kolmogorov (JMAK), (F = 1 - exp( -kt )")

A quantitative analysis of oxide growth stresses is carried out for the model advanced by Rhines and Wolf in which new oxide forms along preexisting oxide grain boundaries. The mean oxide stress developed within the oxide is calculated using standard techniques from continuum dislocation theory. This analysis shows that the mean growth stress is compressive and is directed parallel to the oxide/ matrix interface. The growth stress is found to be independent of the oxide scale thickness, provided that the scale is thicker than the oxide grain size. However, in thin scales, the growth stress is very sensitive to oxide scale thickness. The compressive growth stress increases in direct proportion to the width of the new grain boundary oxide layer formed. The oxide scale is expected to either fail by buckling, or the growth mode will change to one in which additional compressive stresses are not generated.

A Monte Carlo computer simulation technique has been developed which models grain growth in the presence of a particle dispersion. The simulation allows for the monitoring of an evolving microstructure as a function of time. The model predicts normal grain growth, i.e. R = Ct n , where R is the average grain size and n is the grain growth exponent, followed by an abrupt transition to a pinned state. Both the exponent n and the grain size distribution are found to be in close agreement with that observed for grain growth in the absence of particles. The grain size distribution and kinetics are independent of particle concentration. The final average grain area and the time required for the microstructure to pin are both approximately proportional to the inverse of the particle concentration. The results are quantitatively accounted for in terms of a simple topological theory.

We consider the instabilities of a solid film perturbed by a single hole which exposes the substrate. We predict growth for holes larger than a critical size, proportional to ρc, the ratio of the film thickness and the equilibrium contact angle. The asymptotic velocity of the hole decays to zero with time t as t¾[log3 (t/ρc4)]. The growth of these holes eventually ruptures the film, creating a set of disconnected islands.

Surface coatings (e.g. oxides and deposited coatings) are susceptible to failure in compression during quenches, due to differences in coefficients of thermal expansion between the base metal and the surface coating. In addition, the compressive stresses generated during the growth of some oxide films can also lead to failure. The development of hillocks before extensive delamination suggests that buckling plays an important role in the failure of coatings in compression. Therefore, elastic buckling theory was modified to account for coating/metal adhesion and applied to the failure of coatings in compression. It is found that buckling cannot occur without an interfacial defect where coating/metal adhesion has been lost. Buckling is shown to be a pre-requisite for extensive coating failure, which occurs by the unstable growth of the buckled region. Simple criteria are derived for the onset of buckling, as well as for extensive coating failure.

While previous analyses of the elastic interaction between dislocations and inclusions predict repulsion when the shear modulus of the inclusion exceeds that of the matrix, experimental observations in oxide-dispersion-strengthened alloys show that dislocations are able to reach the surface of the stiffer oxide particles. We attempt to rectify this apparent contradiction by analysing the effects of diffusion, in the vicinity of the inclusion, on the elastic interactions. The problem is divided into two parts, depending on whether the dislocation loads the inclusion predominantly in shear or hydrostatically. We show that in each case the dislocation-particle separation decays exponentially with time, the time constant being proportional to the ratio of the inclusion volume and the inclusion-matrix interfacial diffusivity for shear loading, and proportional to the ratio of the square of the inclusion radius and the bulk diffusivity for hydrostatic loading. A comparison of the time required for diff...

We consider the kinetic evolution of perturbations to thin films. Since all small (nonsubstrate intersecting) perturbations to the film surface decay, we consider the evolution of large perturbations, in the form of a single hole which exposes the substrate. For large holes, the hole radius increases at a constant rate under the assumption of evaporation/condensation kinetics. When the dominant transport mode is surface diffusion, large holes grow with a rate proportional to t−3/4[log3(t/ ρ4c) ]. Small holes with a radii less than ρc shrink, where ρc is the film thickness divided by the tangent of the equilibrium wetting angle. The growth of these holes eventually leads to hole impingement which ruptures the film, creating a set of disconnected islands. The relaxation time for these islands to go to their equilibrium shape and size ( ρeq) scales as ρ2eq or ρ4eq for evaporation/condensation or surface diffusion kinetics, respectively.

A novel Monte Carlo procedure is applied to the study of the kinetics of grain growth in two dimensions. The model employed maps the microstructure onto a discrete lattice. Each lattice site is assigned a number, between 1 and Q, which indicates the local crystallographic orientation. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest neighbor pairs of unlike crystallographic orientation. The temporal evolution of the microstructure is monitored to yield the time dependence of the size and shapes of the grains. The microstructures produced are in good correspondence with experimental observations of soap bubbles, foams and cross-sections of isotropic metallurgical specimens. Examination of the temperature and lattice dependence of the kinetics shows the existence of a number of universal features. The model properly reproduces the kinetics of the Ising model in the limit that Q approaches 2. For large Q, power law kinetics [Rm(t) − Rm(0) = Bt] are observed with the growth exponent, m, is found to be independent of Q with a value of approximately 2.4. The deviation of the growth exponent from the mean field value of 2 is discussed in terms of the role of vertices.

Monte Carlo simulations of ordering in the two-dimensional axial next-nearest-neighbor Ising model following a quench were performed using nonconserved dynamics for a wide range of frustration parameters, kappa, and temperatures. It was found that in quenches from T>>T/sub c/ to T phase (i.e., striped phase). Quenches to higher temperatures show the presence of a finite glass-transition temperature. Discontinuous changes in the value of the frustration parameter from the ferromagnetic to the -phase region of the phase diagram at low temperature yields a phase change which occurs via classical nucleation and growth. A simple energetic or growth model is proposed which accounts for all of the temperatures at which the ordering kinetics undergoes transitions

Grain growth is the term used to describe the increase in average grain size R which occurs upon annealing a polycrystalline aggregate after primary recrystallization is complete. In the long time limit, R increases with time t raised to a value n which is the growth exponent. Most existing grain growth theories implicitly assume that grains can be described as spherical and that growth occurs in an average environment. This, however, ignores the fact that adjacent grains share common boundaries, resulting in a microstructure that is topologically connected. These theories predict long term growth kinetics of the order n=1/2. Since experimental studies of grain growth yield an exponent less than 1/2, the discrepancy may be a consequence of neglecting topological constraints and the detailed environment. To examine this possibility a lattice model for 2-dimensional grain growth was developed in which topology and local environment are included. While this 2-dimensional model accurately simulates grain growth in thin encapsulated films, the validity of its predictions for 3-dimensional grain growth remains to be established. This paper reports the first results of our extension of the lattice grain growth model to 3 dimensions.