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GRAIN BOUNDARY STRUCTURE AND PHASE TRANSFORMATIONS : A CRITICAL REVIEW OF
COMPUTER SIMULATION STUDIES AND COMPARISON WITH EXPERIMENTS
V. Pontikis
To cite this version:
V. Pontikis. GRAIN BOUNDARY STRUCTURE AND PHASE TRANSFORMATIONS : A CRITICAL REVIEW OF COMPUTER SIMULATION STUDIES AND COMPARISON WITH EXPERIMENTS. Journal de Physique Colloques, 1988, 49 (C5), pp.C5-327-C5-336.
�10.1051/jphyscol:1988539�. �jpa-00228036�
JOURNAL DE PHYSIQUE
Colloque C5, supplément au n°10, Tome 49, octobre 1988 C5-327
GRAIN BOUNDARY STRUCTURE AND PHASE TRANSFORMATIONS : A CRITICAL REVIEW OF COMPUTER SIMULATION STUDIES AND COMPARISON WITH EXPERIMENTS
V. PONTIKIS
Section de Recherches de Métallurgie Physique, Centre d'Etudes Nucléaires de Saclay, F-91191 Gif-sur-Yvette Cedex, France
Résumé. - Nous présentons une revue critique des résultats de simulations concernant la structure des joints des grains à des températures T >. 0.4 Tfusion. En s'appuyant sur des approches phénoménologiques de la transition solide cristallin-liquide et, par analogie, sur des résultats expérimentaux obtenus dans le cas des surfaces nous discutons de l'existence possible de phénomènes précurseurs de la fusion aux joints de grains. Contrairement aux résultats de certains calculs, que nous examinons en détail, les expériences indiquent que les joints de grains ne pourraient se transformer à du liquide d'épaisseur macroscopique qu'à proximité du point de fusion.
La simulation de systèmes de grande taille, des expériences plus précises et l'investigation théorique des transformations de phase aux interfaces sont nécessaires pour clarifier cette question.
Abstract. - We present a review of available computer simulation results on the structure and thermodynamical properties of grain boundaries at temperatures T > 0.4 Tmeltin . We discuss the possible existence of premelting effects in internal interfaces by comparing the results with the predictions of phenomenological theories of melting and, by analogy, with recent experimental results on surface melting. Experiments on possible premelting effects in grain boundaries indicate that melting of internal interfaces, in the sense of the formation of a macroscopic thick liquid layer inside the boundary, should occur in pure systems only near to the bulk melting point. These computer simulation studies which leaded to a different conclusion are examined in detail. Large scale computer simulations, additional theoretical work and more precise experiments are needed to clarify this point.
1. Introduction
Although the structure of grain boundaries is the determining factor for many material properties -e.g. mass transport, segregation, mechanical behavior, interfacial oxidation and corrosion phenomena - our knowledge of the atomic arrangement in grain boundaries is still far from being complete. The crystallinity of grain boundaries at low temperatures is now well established thanks to experiments which showed the intergranular diffusion coefficient to be anisotropic [1], transmission electron microscopy (TEM) observations of secondary grain boundary dislocations [2]
and, more recently, observations of the atomic columns in tilt boundaries using high resolution electron microscopy [3]. At intermediate and high temperatures (T>0.4Tm) however, many experimental results obtained from decohesion tests, TEM observations at triple junctions, measurements of grain boundary migration and/or sliding have been interpreted in favor of the existence of a grain boundary structural transition at a temperature lower than the bulk melting point [4,5]. The possibility that these results are related to a grain boundary melting (GBM) cannot be excluded. Shewmon [6] first discussed the theoretical aspects of GBM and concluded that for equilibrium grain boundaries such a transformation is inconsistent with Thermodynamics.
Shewmon's arguments were questioned by Li [7], which argued that a grain boundary is a highly strained crystal region and should therefore melt before the bulk melting point. As a consequence, the liquid wetting the interface is not in equilibrium with the strain-free grains. GBM should occur if the relation y > 2y. holds, where y and y, are the free energies per unit area for the grain boundary and the crystal-liquid interface respectively. This is the condition for wetting of the interface by the liquid phase prior to Tm. Owing to the fact that the energy of grain boundaries increases with increasing misorientation, GBM is more likely to occur in high-angle general
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988539
C5-328 JOURNAL DE PHYSIQUE
boundaries to which correspond elevated values of the free energy.
From the available experimental values of interfacial energies Miller and Chadwick [8]
concluded that :
i) GBM should occur at undercoolings within 0.02 T, giving rise to a liquidlike boundary of about 20
A
in thickness.ii) Owing to the thinness of the "melted" boundary, surface tension and viscosity are expected to achieve high intergranular cohesion and therefore GBM is not synonymous with grain boundary fracture.
Bolling [9] obtained similar results for various materials by means 0f.a phenomenological model accounting for interactions between the two solid-liquid interfaces. Experimental results and theoretical models published before 1972 (see in ref. [4] for a review) were not able to prove unambiguously the existence of GBM.
A general argument in favor of GBM, which is also invoked for surface melting, is the well known absence of overheating effects for many materials and particularly for metals. According to it, metastability for the solid is supressed at T, because the liquid phase is nucleated at surfaces or grain boundaries before the melting point. Theoretical predictions, conclude in favor of surface melting at temperatures close to the melting point as they do for grain boundaries
.
Rutheford backscattering, helium beam diffraction and grazing incidence X-ray diffraction experiments were able to prove that a progressive disorder appears on surfaces by increasing the temperature due to the occurence of a roughening transition. However, the existence of surface melting has not yet been proved despite the fact that experiments are easier to perform on atomically clean surfaces than in grain boundaries.Thus for free surfaces a temporary conclusion is that surface melting should occur but only very close to the melting point and therefore experiments are not able to prove clearly its existence [lo].
From a speculative point of view it may be possible that grain boundaries, like surfaces, become rough at a certain temperature but they melt only at the bulk melting point. The lack of information at the atomic scale and the experimental difficulties one encounters in studying grain boundaries preclude from drawing any valid conclusion on grain boundary roughening and/or melting.Thus one can easily understand why computer modelling is especially important and has been extensively used for studying grain boundaries. In the first investigation of the temperature effects on the structure of grain boundaries Kikuchi and Cahn [12] used a two-dimensional lattice-gas model with short range interactions. These authors founded that high-angle grain boundaries become disordered starting from roughly half the melting point temperature. This disorder results from a gradual transition which leads to a preferential melting at the grain boundary when the bulk melting point is reached. These two transitions, disorder and preferential melting, appear to be related and therefore Kikuchi and Cahn called the gradual disorder a melting transition though the structure at the transition temperature is still far from that obtained at the bulk melting point. Because the boundary used in this study was unidimensional, the behavior of a two-dimensional realistic grain b~xndary may be different though qualitatively similar.
In section 2 the results of Molecular Dynamics simulations (MD) for the study of the temperature dependence of grain boundary structure are reviewed. We also comment on some technical aspects of MD methods currently in use which can lead to erroneous interpretations of the computational results. Few recent experimental results are presented in section 3 and compared with those obtained by MD. In section 4 the possibility of a roughening transition occuring in grain boundaries is briefly discussed. Section 5 is devoted to some concluding remarks.
2. Moleculalr Dynamics
Molecular dynamics simulations are a powerfull tool for testing theoretical speculations on the high temperature structure of grain boundaries. MD techniques consist in sampling the phase space of an atomic system by numerical integration of the newtonian equations of motion provided that the forces law is given [l 11. Thermodynamic quantities can be calculated on a local basis and thus this approach is well suited for the study of nonuniform systems such as bicrystals. Unlike lattice dynamics methods, MD allows for an easy investigation of anharmonicity effects which are naturally present in the model under study. Moreover, the knowledge of the atomic trajectories in the real space leads to an atomic scale view of the structure, mechanisms of diffusion and of structural transformations which cannot be reached by experiments. Depending on the kind of potentials used in MD computations these are either of the generic type -one draws conclusions which are believed
to be of general validity (Lennard-Jones potential)- or more specifically adapted to a real material (first principles or empirical potentials). Results from available MD computations of GBM are summarized in Table I.
2.1 GENERAL REQUIREMENTS FOR RELIABLE MD COMPUTATIONS
In studying by MD nonuniform systems like bicrystals and their possible phase transitions (GBM) one has to take care of the following :
a ) Phase diagram : MD systems are usually small (N = 103-104particles) due to available computer performances and memory limitations. Thus by introducing a non-equilibrium defect such as a grain boundary the phase diagram of the perfect system can be seriously modified. One should verify that the size of the specimen is big enough so that far from the defect a perfect, solidlike region can be preserved. The right choice of the system size results in a phase diagram practically identical to that of the perfect infinite solid. In small systems, for which the "surface" to volume energy ratio per particle is important, bulk driven premelting effects at surfaces are observed [10,13] and may also occur in the case of grain boundaries.
b) Borundary conditions : Periodic boundary conditions (PBC) are currently employed in order to avoid border effects. For MD computations of internal interfaces their use results in the presence of two opposite misorientation grain boundaries in the simulation box. When increasing the temperature these may migrate towards one another and mutually annihilate [14]. The behavior of grain boundaries near the melting point cannot be studied unless this undesirable effect is avoided by increasing the thickness of the system along the direction normal to the boundaries. This is of course an expensive solution and therefore fixed border conditions (FBC) are sometimes used [15-171 : PBC are applied parallel to the boundary plane but along the direction perpendicular to it the system is embedded in a static crystal. If the size of the system is large enough, the resulting phase diagram is very similar to that obtained for a system with PBC since the influence of the static-dynamic crystal interfaces goes like 1/N. FBC can be a good solution in the low temperature range if a local measure of the stress tensor gives zero-values for its shear components. At higher temperatures the grain boundary can oscillate between different structures [18,19] resulting one from another through local migration and/or sliding [19]. Thus shear stresses will appear, when FBC are used, which may seriously affect the structure of the boundary and possibly the melting point of the region around it.
A problem of lesser importance related to FBC is related to the pressure evaluation method.
Commonly pressure is calculated using the virial theorem which is no more valid, in its standard form, when FBC are used. An additional term appears in the internal virial expression whose strength depends on the system size and the extent of the dynamic-static interface [ZO]. When
"constant pressure" calculations consist in adjusting the density of the system at each temperature studied, the evaluation of the pressure by using only the virial expression may introduce errors as much important as high is the value of the corrective term compared to the internal virial.
Another problem, related with PBC, arises from the use of a constant stress MD technique [21]. Roughly speaking this technique consists in adjusting homothetically the linear dimensions of the considered system, at each timestep, in order to maintain the stress tensor at a constant value.
Owing to the small size of MD simulation systems when a grain boundary is introduced the pressure increases with respect to the perfect system at the same density. For a [001] (310) C=5 boundary in a Lennard-Jones (LJ) system the pressure increase is about 230% with respect to the perfect crystal pressure (see Table I in ref. [14]). In a constant stress MD simulation of a bicrystal a uniform but direction-dependent scaling of the box dimensions will occur affecting both regions, close and far from the grain boundary. Thus when using this simulation technique the determination of the stress tensor and the phase diagram should be made on a local basis for a correct evaluation of the melting point far and close from the boundary. Moreover if, for reference purposes, MD results for the perfect soIid are needed the external pressure should be fixed at the local value measured far from the boundary in the "bulk" region of the bicrystal.
c) The potential : GBM depends strongly on interatomic forces. For van der Waals long range forces wetting does not occur [22]. The behavior for short ranged potentials constitutes an open question but the results obtained for small 2D bicrystals (see below 52.2) provides evidence for wetting possibly related to the short cutoff radius r, used. Some attention must also be paid to the fact that when using small r, values the corresponding potential value at the cutoff can be far from negligible. Due to the important density variations enhanced thermal vibrations may cause nearest
Table I. Summary of MD simulation results on grain boundary melting. (N,V,E) and (N,C,Hs) indicate simulations in the microcanonical and the constant stress ensembles [12,21] where N,V,E,C,H,, represent respectively the number of particles, the volume, the internal energy, the stress tensor, and the generalized enthalpy. The mention constantpressure means that the dimension of the simulation box has been adjusted in order to obtain the desired pressure value. For the cutoff radius we indicate above which neighbor the potential is set to zero. Reference Ensemble Potential Cutoff N Boundary Conditions GB-Type Melting Remarks LJ(12-6) Morse A1 LJ(12-6) 1, Morse A1 400 Fixed 5611 12 PBC 1 101220 PBC 11211 10 PBC 696 PBC 900 Fixed 648 PBC 1920 PBC 1848 It 1440 84013360 Fixed General [Ill] C=7 38.21' Yes [Ill] C=13 27.8' Yes x=7lz=13 Yes [001] C=5 36.86' No [OOl] C=5 36.86' Yes [lll] C=7 38.21' Yes [001] C=5 36.86" Yes [Ol 11 C=ll20.05' No 14431 C=123 14.65' No [001] C=5 36.86' Yes
2 2D-Free energy Calc.
$
'0 3D-Constant pressurex,
4 3D-SlidingK! 4
3D-Constant pressureB
9, --(9
In the original publication [14], it is erroneously indicated that contributions to forces were considered up to the sixth neighbor.neighbors to leave the interaction sphere more frequently near the grain boundary than far from it.
This results in an artificial loss of cohesion in the grain boundary region and possibly leads to a artificial GBM.
Finally one should keep in mind that MD simulations are not "more realistic" when using empirical instead of LJ potentials since for these potentials the comparison with experiments is not reliable. Such a conclusion is justified by the fact that empirical, pair potentials i) obey to the Cauchy relation, not fulfilled by metals, ii) give different melting points for the model and the simulated material and iii) over- or underestimate the pair interactions contribution to the total cohesion energy.
2.2 TWO-DIMENSIONAL SYSTEMS
The feasibility of MD studies of grain boundaries has been firstly demonstrated by Cotterill et al. [IS], in the case of a 2D general grain boundary in a bicrystal grown from the melt. Additional MD studies of high-angle grain boundaries have been performed more recently in 2D LJ systems using the constant stress MD technique and excess free energy calculations [23-251. The reported results converge to the conclusion that GBM occurs for all the grain boundaries studied at about 80%
of the bulk melting point. Independently of possible problems related to PBC (82.lb) the short range of interactions (Table I, see 52.1~) and the dimensionality of the system may be responsible for GBM in these systems. One interesting fact is the behavior of the [ I l l ] C=13 27.8' grain boundary reported in [24a]. For this boundary a spontaneous reorientation occurs, towards a =44O misorientation, which has not been observed for other boundaries. This result constitutes the best illustration of the importance of border conditions on the structure of the simulated boundaries (52.lb). If FBC were used in this case the resulting structure would be very different from that presently observed. Namely one would obtain the structure which is compatible with the imposed border conditions but not necessarily a realistic one. The importance of the border conditions is also reflected by the result obtained by GuillopC [19] for a 3D model of the [001](210) C=5 tilt boundary using PBC. For this boundary an allotropic transformation occurs characterized by the transition between the ground state configuration and the intermediate temperature structure generated by short distance spontaneous sliding and migration.
2.3 THREE-DIMENSIONAL SYSTEMS
The first MD study o f the structure of a high-angle grain boundary in a three-dimensional system was performed by Ciccotti et al. [14,26]. These authors investigated the temperature dependence of a fcc (310)[001] C=5 boundary using standard MD in the microcanonical ensemble (N,V,E), where N,V,E are the number of particles, the volume of the system and the internal energy respecnvely. Their calculations have been performed at fixed density using LJ (12-6) pair-interaction potential with a cutoff radius in between the ninth and tenth neighbcr distances. The temperature dependence of the local thermodynamic properties in a small region around the grain boundary indicates the onset of a gradual disordering transition starting at To=0.5Tm. The thickness of the disordered region grows with increasing temperature and finally causes the direct interaction, migration coupled to sliding and annihilation, of the two grain boundaries of opposite misorientation present in the system, due to the use of PBC. After the mutual annihilation of the boundaries the system falls into the solid-liquid coexistence region thus producing a solid-liquid interface. This occured at Tz0.9 T, and precluded from investigation of the grain boundary structure near T,. The Bragg peak intensity decreases slowly to about 40% at the highest temperature reached. This last result and evidence for a solidlike intergranular diffusion [26] over the temperature range investigated in this study, indicate that GBM does not occur before T,. This is in agreement with theoretical arguments according which long range van der Waals forces prevent from wetting [22]
and agrees with the results obtained by Kikuchi and Cahn in their 2D lattice gas model [12]. These results have been criticized by Ho and al. [16] which draw just the opposite conclusion from their calculations on the same boundary in "Aluminum". They argue that possible metastability effects hiddened the GBM in [14] and that constant density MD will increase T, by increasing the pressure in the system. The latter objection is not justified because Ciccotti et al. monitored the system behavior by using the calculated LJ phase diagram and the adequate T,,, value resulting from the isochore curve they explored. On the other hand the observed spontaneous migration and sliding of
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the two bountiaries contained in their system is a guarantee against metastability effects especially near the melting point. Thus metastability cannot be invoked to explain why these authors do not observe GBMI.
Deymier and Kalonji [25] studied for a 3D LJ bicrystal the influence of sliding, induced by a shear stress, on the structure of a [ I l l ] C=7 38.21' tilt boundary. GBM is observed to occur at approximately 50% of the bulk melting point, a lower temperature than for the equivalent 2D case due to the applied shear stress. The cutoff radius used in this study has not been reported in [25] but if a short cutoff was used, the similarity between 2D and 3D results for this boundary can be easily understood. Iri addition, due to the sliding the system will dissipate energy and possibly never reach a stationary state. As stated by Parrinello and Rahman the constant stress MD technique is valid to calculate thermodynamical quantities in equilibrium states but leads to highly unphysical transient states. Therefore these results are of doubtful meaning as far as GBM is concerned.
A new approach has been followed by Broughton and Gilmer [27], who have investigated GBM for three different boundaries (Table I) both through MD excess free energy calculations and comparisons with the results of an harmonic analysis of the ground-state configurations. Their results clearly show the existence of GBM for the [OOl] (310) E=5 boundary whereas the two other boundaries they studied remain stable up to T,. These authors stress that i) GBM is not a low order phase transition that can be identified at a given temperature and ii) that the quasiliquid layer limited by the two adjacent grains retains some solidliie character.
MD sim~dations were also performed by using both, a Morse potential with parameters chosen to fit the vacancy formation energy in aluminum, and a pseudopotential derived from first principles adapted to this metal [16,17]. In these studies the [001](310) C=5 tilt boundary properties were investigated up to the presumed melting point of the system. At about 50% of the melting point an increasing disorder appears near the grain boundary which leads, unlike the LJ systems, to GBM at Tz0.8 T,. The authors verified that the system size has no influence on the results and tested, to a lesser extent, for a possible influence on them of the short cutoff radius they used (see Table I). Due to recent experimental results on aluminum, which showed that GBM does not occur up to the melting point (see below $3) and to the MD results of Ciccotti et al. in qualitative agreement with that conclusion, it appears to be of importance to identify the reasons for the discrepancies between simulation results concerning the same grain boundary. We list below s o z e possible explanations based on the work reported by Ho et al. and Nguyen et al. [16,17] :
i) The identification of the melting point for the perfect solid (reference system) is highly empirical and certainly overestimated. T, has been estimated using the internal energy versus temperature plot instead of the thermodynamical definition which requires the equality of the free energies of the solid and liquid phases at the melting point. The value of the melting point temperature depends also on the potential cl~ltoff radius and the boundary conditions one uses. Thus, even for the pseudopotential used in these studies, bulk solid T, values from litterature cannot be used.
ii) Under FBC migration or sliding is impossible for the grain boundary which may then oscillate at high temperature 118,191 between different configurations. Such a constraint results in shear stress values which may be very high and leads to a decrease of the melting point in the grain boundary region. In references [16,17] the method used to evaluate the pressure is not mentioned. The comments made above (92.lb) on this subject may be of interest in this case.
iii) The cutoff radius of the potential is another parameter which may affect seriously the results. The larger part of the computations by Ho et al. and Nguyen et al. has been realized using a cutoff radius rc between the second and third neighbor distances (18 first neighbors). Moreover the Morse potential used is short ranged. As mentioned in 5 2 . 1 ~ short ranged potentials can lead to GBM whereas van der Waals long range forces do not. The fact that increasing rc up to the fifth neighbor distance does not alter the results [17] is somewhat spurious since such an increase will in general increase the system stability (and T,). However this may indicate that fixed boundary conditions and an overestimatiion of T, value are the main reasons for obtaining systematically GBM.
A last point concerning these studies is the "realistic" aspect of the interaction potential. In addition to remarks in $ 2 . 1 ~ it is interesting to note that the potential used here, fitted to the vacancy formation energy in aluminum, leads to a cohesion energy of 0.75 eV (deduced from figure 3 in ref.
[16]) which should be compared with the experimental value of ~ 3 . 5 8 eV ! This may result in a lower melting point temperature for the model as compared to aluminum.
3. Experiments
A review of the earlier experimental investigations on GBM has been made by Gleiter and Chalmers [4] according which at that time (1972) there was no experimental observation providing unambiguous evidence for the existence of GBM. The situation has not been considerably modified in the last years due to the difficulty in performing direct experiments on grain boundaries near T,.
The sliding and migration experiments on A1 [28], Cu [29] and Zn [30] bicrystals, have shown that the activation energy associated to the sliding rate decreases near T, for high-angle grain boundaries.
This change does not occur for suboundaries and an increase ofimpurities content increases the temperature at which this change occurs. Such a behavior was attributed [30] to a change in the structure of the boundary but no evidence exists for a GBM.
The rotating crystallite method has been used by Erb and Gleiter [31] which showed that many boundaries in copper remain crystalline up to 0.97 T,. More recently Chan et al. [32] investigated by TEM near C=5 [001] twist and (310) tilt boundaries up to T=0.9Tm. These boundaries contained localized secondary grain boundary dislocations (SGBD's) which remained observable up to the melting point. Ordered grain boundary structures being necessary to maintain localized arrays of SGBD's Chan et al. results indicate the absence of GBM.
Observations of fcc 4 ~ e thin films in contact with the liquid phase have shown partial melting of the polygonization structure and the almost complete wetting of grain boundaries by the liquid phase, revealed by the low values of the dihedral angle at the interface between the two solids and the liquid [33]. The low content of impurities in that'system make this experiment more convincing than previous dihedral angle measurements in Bi [5]. However the possibility that non-equilibrium segregation of impurities occured, thus inducing GBM, cannot be excluded.
4. A roughening transition ?
The possibility of disorder-induced structural transitions in grain boundaries has been invoked by Hart [34] zscording whom a possible microscopic mechanism could be the production of vacancies at grain boundaries, enhanced by cooperative effects due to their hig.1 concentration. Such a mechanism is similar to that suggested by Burton et al. [35] for roughening of surfaces.
Moreover, the elevated concentration of vacancies (c2109) observed by MD computations in high-angle grain boundaries [14,36], are compatible with such a transition. Possible roughening of low angle grain boundaries has been recently investigated by Rottman [37]. Thermal fluctuations of the boundary position are showed to decrease the excess free energy of the boundary which appears to be smooth for misorientations sufficiently small. In the case of a Cu low angle grain boundary, roughening is predicted for misorientations 6 such as 21' 6 I firnax, where
emax
corresponds to the misorientation above which the dislocation theory for low angle grain boundaries is no more valid.Unfortunately at present time no experimental evidence is available in favor of a roughening transition either in suboundaries or high-angle grain boundaries.
5. Discussion and concluding remarks
MD modeling though powerful for studying materials behavior at the atomic scale cannot be reliable without the same rigour in the definition of the computer "experiment" as the one required by real experiments. The choice of a cutoff radius for the potential, whose importance has been sometimes underestimated in computations devoted to GBM, is crucial
.
In the simulator's community one is familiar with this question which has been widely discussed in relation with stacking fault energy calculations [38]. Concerning the problem of GBM the main difference between available MD simulations is precisely the range of interatomic forces they use (Table I) : GBM is not observed when van der Waals forces and high values of the cutoff radius are used. The use of border conditions adequate for grain boundary studies is required in order to evaluate the right value of the melting point and the nature of possible structural transformations.Following Li's arguments [7], the possible existence of GBM is related to the strain generated by the grain boundary. MD simulation [26] confirmed St Venant's principle according which the perturbation extends over a distance comparable with the periodicity of the grain boundary.
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High-angle grain boundaries have a short distance period thus the perturbation propagates into the grains only over small distances and increases smoothly when the temperature increases (see figure 5 in [14]). Therefore if GBM occurs in these boundaries in the early stage the thickness of the quasiliquid region will be small and thus it must retain a pronounced solidlike character whenever a macroscopic thickness has not been reached [27]. This assertion is supported by MD studies of the LJ solid-liquid interface which have shown this interface to be diffuse over more than ten layers [39]. Boiling's [9] phenomenological model based on experimental interfacial energy data shows that for many metals GBM, in the sense of the formation of a thick "liquid layer, may occur only at the close vicinity of the melting point. Such a conclusion is also compatible with available experimental data since the only good explanation of why experiments cannot clearly decide upon the existence of GBM is that the transition temperature is located very close to the melting point. It is worth noting that an eauivalent situation exists for surface melting. both, for simulations and
experiments-il0].
-
The possibility of wetting a grain boundary by a compound of crystalline phases of different misorientation has been also suggested [40]. The possible existence of this kind of wetting and the reorientation phenomena reported by Kalonji et al. [24] suggest that for boundaries which may undergo GB141 (yc? 2yc, ""
".
) reorientation through sliding/migration of the boundary prevents from such a transition to occur. In this case recrystallization replaces GBM and grain boundaries appear to be less metastable than free surfaces.The gradual disorder transition put in evidence by some computations [12,14,16-17,23-261, may be related to the possible roughening of grain boundaries. A compilation of diffusion data in grain boundaries showed an upward curvature of the intergranular diffusion coefficient [41]. This behavior is compatible with the activation of new diffusion mechanisms and/or the existence of a high concentration of defects at high temperatures which are known to occur in association with the roughening transition. Similar results exist for surfaces [lo] for which the existence of the roughening transition has been experimentally established. More precise X-rays scattering experiments on bicrystals and diffracted intensity measures as a function of temperature may contribute to a better understanding of the high temperature structure of grain boundaries. On the other hand MD calculations on large models will be of interest in order to compare the temperature dependence ctf Bragg peak intensities calculated for grain boundaries with experimental values.
Acknowledgement : The author would like to thank Prof. G. Ciccotti for enjoyable discussions during the preparation of this paper and for the careful reading of the manuscript.
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N.W. Ashcroft Can you describe i n a l i t t l e more detail what is meant by a wquasi-liquid88. Is it a state that is s t r a t i f i e d (in the one-particle density) perpendicular t o the boundary but is uniform parallel t o the boundary (with liquid-like diffusion) ?
V. Pontikis The term uliquid-like88 is used here for the highly disordered region inside the boundary. In the high tenperatwe range only small deviations are obtained for the density with respect w i t h the t o t a l average value. Diffusion values are high (liquid l i k e ) , but the activation energy associated with in-ular diffusion is definitely higher than the value obtained for a supercooled liquid i n the same t a p r a t m e range. Thus, in spite of thermal disorder, the Imwky region exhibits solid like diffusion.
