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STRUCTURAL TRANSFORMATION AND SUPERIONIC BEHAVIOR OF A HIGH ANGLE
GRAIN BOUNDARY IN CaF2 : A COMPUTER SIMULATION STUDY
C. Maunier, V. Pontikis
To cite this version:
C. Maunier, V. Pontikis. STRUCTURAL TRANSFORMATION AND SUPERIONIC BEHAVIOR OF A HIGH ANGLE GRAIN BOUNDARY IN CaF2 : A COMPUTER SIMULATION STUDY.
Journal de Physique Colloques, 1990, 51 (C1), pp.C1-245-C1-250. �10.1051/jphyscol:1990138�. �jpa- 00230296�
STRUCTURAL TRANSFORMATION AND S U P E R I O N I C BEHAVIOR O F A H I G H ANGLE G R A I N BOUNDARY I N CaF, : A COMPUTER S I M U L A T I O N STUDY
C. MAUNIER and V . P O N T I K I S
Section de Recherches d e Metallurgie Physique, Centre d'Etudes Nucleaires de Saclay, F-91191 Gif sur Yvette Cedex, France
Resume - Nous prtsentons les rtsultats d'une ttude par simulation, de !a diffusion intergranulaire pour le joint de flexion X=5 [OOl] (210) dans CaF2, B l'aide de la technique de dynamique molCculaire
B
temperature constante. Les interactions entre ions derivent d'un potentiel de type ions rigides. Nous avons trouve par minimisation, que le joint de coincidence correspond au minimum d'tnergie interne B T=O K. Cette structure reste stable jusqu'h Tz0.2 Tfusion, temperature B partir de laquelle des mouvements cooptratifs des atomes du joint conduisent brutalement B une nouvelle structure. Pour des tempCratures -0.44 Tmsion, le coefficient de diffusion des anions dans le joint atteint des valeurs ClevCes, pouvant etre calculies par simulation. Ce comportement pourrait etre lie au changement de structure observk. La temperature--
critique de comportement superionique h proximite du joint, ~ y 1 7 5 0 K, s'avere 6tre significativement plus faible que celle du mattriau massif, T,=1400 K. De plus, I'analyse detaillie des trajectoires atomiques des anions, montre l'existence de nombreux mCcanismes coopCratifs, responsables de la superconductivite ionique intergranulaire prkcoce.
Abstract - We present the results of a molecular dynamics study of diffusion in a E 5 [001] (210) tilt grain boundary in CaF2 using a rigid-ion potential. We found by minimization that the coincidence position corresponds to the lowest energy structure of the boundary. This structure remains stable up to Tz0.2 TmeItin , a temperature above which a local structural transition occurs. For temperaturesb0.44 Tmehing, enhanced anionic diffusion is observed possibly related to this transformation. The critical temperature for superionic conduction in the grain boundary, ~ y S ' 7 5 0 K, is substantially lower than in the bulk, T,=1400 K. The analysis of the atomic trajectories reveals the existence of a variety of cooperative diffusion mechanisms originating this premature intergranular superionic behavior.
1- INTRODUCTION
Materials with the fluorite structure are of great practical interest since most of them, e.g. halide fluorites, become superionic conductors above a critical temperature, Tc, and are therefore used as solid electrolytes for various applications /1,2/. On the other hand, the oxide fluorites such as U02, are widely employed in nuclear technology. Although the superionic behavior of the latter is not demonstrated, due to the high values expected for Tc, they are strongly suspected to behave similarly /3,4/. Unlike other superionic materials, e.g. AgI, the superionic conductivity in fluorites is not associated with a structural phase transition despite the anomaly observed in the excess specific heat near Tc /5/. The origin and the mechanism underlaying the superionic behavior of fluorites have motivated numerous theoretical and numerical simulation studies 121.
However, only experimental investigations /6,7/ of grain boundaries (GB) in these materials are available despite the fact that fluorites used for applications are polycrystalline /1,2/. More specifically, no simulation work exists, at least to our knowledge.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990138
Cl-246 COLLOQUE DE PHYSIQUE
The present paper is devoted to a molecular dynamics (MD) study of a high angle, tilt grain boundary E 5 [OOl] (210) in CaF2. Our results show that the lowest energy structure at T=O K corresponds to the coincidence position. This structure becomes unstable for 720.2 T, (T,:
melting point temperature), temperature above which a local structural transition occurs in the grain boundary. Moreover, enhanced intergranular anionic mass transport is observed for D 7 5 0 K. However, we cannot clearly establish that this behavior is a consequence of the above mentioned grain boundary structural transition due to the space-time limitations of the MD technique. Indeed, these do not allow to evaluate diffusion coefficients smaller than 10-7 cm2s-1 whereas anionic intergranular diffusion coefficients lower than this limit are expected at the transition temperature.
The following sections 2 and 3 are respectively devoted to the description of the model, the study of its reliability and the presentation of our results. Section 4 contains some concluding remarks.
2- MODEL
AND
COMPUTATIONAL DETAILS 2.1- Geometrical modelsThe model we used is a fluorite bicrystal of N=4320 particles (1440 cations and 2880 anions) constructed by the following procedure :
(a) Two crystals with faces respectively parallel to the (210), (130) and (001) crystallographic planes are joined together at a distance equal to the (210) interplanar spacing. Periodic boundary conditions are imposed along the [210], [l201 and [OOl] crystallographic directions and thus, two infinitely extended [OOl] (210) 0=36.9" tilt GB's exist in the system. The perturbation of the atomic positions in the bulk, related to the presence of a GB, is known to propagate at a distance roughly equal to the boundary periodicity. Therefore the size of the bicrystal is chosen equal to 6[210]~3[1~0]x4[001] identity periods in order to preserve a bulk region between the two GB's.
(b) Different translations of the two crystals with respect to the coincidence condition produced the initial configurations for the subsequent investigation of the lowest energy structure by minimization.
Moreover, it is necessary to investigate the stability of the bicrystal with respect to intergranular decohesion by comparing the GB excess internal energy at T=O K, with twice the excess internal energy of a (210) surface. This is performed using a model which consists in an isolated lamina of 720 particles (240 cations and 480 anions) having a square base of side length
~ = 2 ~ 6 x a (a: lattice parameter) and periodic boundary conditions acting along the [001] and
[l201
directions parallel to the system surfaces.2.2
-
PotentialThe particles interact through a rigid ion potential 181 which provides a qualitatively faithful representation of the real crystal properties such as diffusivity, conductivity, specific heat, elastic constants.. ./8-101:
m(rij) =
Q
Ai+ exp - I?L-
-Yrij
(
Pii) '6 r..1J
4 -,
Where rij =
-
rjl and Q, Qj are respectively the mutual distance and charges of ions i and j, A++=C++=C+ -=O, A- -=l808 eV, p--=0.293A,
C- -=109.1 e~hA6, A+ -=674 eV, p+ -=0.336A.
The Ewald summation is used for the calculation of the coulombic contribution to the potential energy and forces with a convergence parameter a=5.865/2rc, where rc=1.7a is the cutoff radius for the real space Ewald summation and the non-coulombic interaction terms 11 l/ and, a,
by Heyes et al. 1131.
2.3 - Computational details
The simulations were performed at constant temperature using the Nose MD technique 1141 with a pseudomass Q=10-36 ergs2 at various temperatures ranging from T=250 to 1500 K (T","*=1691 K 11 50. At each temperature the lattice parameter leading to a zero pressure value has been chosen. The equations of motion are integrated using a fifth order predictor corrector algorithm I161 with a timestep 6t = 2.10-l5 S.
To obtain equilibrium at a given temperature, the system is allowed to evolve during 5000 time steps which were excluded from the calculation of thermodynamical averages.
The structure factor components for anions, S,(k), and cations, S,(k), were calculated on a local basis, layer by layer, each layer corresponding to a (210) atomic plane parallel to the GB plane 1171. The shortest wave vector, l?=(0,0,2nla), common to the two sublattices has been chosen in order to minimize Debye-Waller effects. Average values, of the partial structure factors are computed from equilibrium trajectories which lasted 2000 6t and are normalized by dividing them by the squared mean number of atoms in each layer.
The GB self-diffusion coefficient has been calculated in a slab containing the GB, delimited by two (210) planes chosen arbitrarily to fit the region of high mobility at T=750 K.
2.4 - Model reliability
The atomic structure of lowest energy for the GB has been obtained by minimization using a quasidynamic procedure which consists in a MD calculation modified to include a damping force 1181. The same final structure, corresponding to the coincidence position, is obtained systematically whatever the translations of the different initial configurations with respect to this position are.
The interfacial energy and the energy of the (210) relaxed surface, are found equal to 1.2 J-m-2 and 1.3 J.m-2 respectively. Since the interfacial' energy is lower than that of the corresponding two free surfaces by 1.4 J.m-2, we conclude that the bicrystal is stable against decohesion.
0 10
20 30
4050
60layers
Fig. l - Partial anionic structure factors computed locally and averaged over 2000 timesteps.
Cl-248 COLLOQUE DE PHYSIQUE
We also compared the internal energies of the bicrystal and of a bulk system with the same number of particles for the different temperatures we studied. These are nearly identical thus indicating that the excess internal energy per molecule, due to the presence of the GB, remains small and thereby that the phase diagram of our system is close to that of the perfect one. This is futher confirmed by the fact that in the bulk regions the partial structure factors and the mean square displacements are very close to those of the perfect crystal even near T, (Maunier C., in preparation).
4 - RESULTS
4.1
-
Stuctural and thermodynamical propertiesThe coincidence subsists for all temperatures we studied. A local phase transition occurs in the GB above T=250 K, identified by the abrupt change of the structure factor (Fig. 1).
The resulting changes of the atomic positions in the GB are illustrated by figures 2a-2b for the anions.
Fig. 2 - Trajectories of the anions pertaining to the four grain boundary planes affected by the structural transition. These are recorded during 5000 timesteps and are projected on the (001) (x,y) plane: (a) T=250 K, (b) T=500 K. Only a small section of the system is displayed.
On increasing the temperature, the local structure factors increase, the thermal disorder driving the GB atoms back to their low temperature average positions. This feature of the transition we observed is similar to what happens during surface reconstruction phenomena. At T=1500 K (T=0.88 T,), the lowest value of the normalized local structure factor of cations, is larger than 0.6 thus indicating that the GB remains well crystalline.
4.2 - Diffusion
Despite the considerably larger mean square displacements of cations in the GB with respect to the bulk no measurable diffusion of calcium has been detected over the investigated temperature range. On the contrary, detectable anionic diffusion in the GB's occurs for temperatures as low as T=750 K, the number of diffusive anionic layers increasing when the temperature increases.
It is worthnoting that for a bulk system, a much higher critical temperature for superionic conduction is observed, experimentally I151 and by MD simulations /8,9/, T=1400 K. Owing to
transition temperature for superionic conduction in the GB,
F<
750 K.Our results are in qualitative agreement with those of a recent experiment which showed that polycrystalline CaF, exhibits larger conductivity values than single crystalline samples in the extrinsic region (T < 700 K) /6/. Unfortunately, the grain size of samples used in this study (50 pm) did not allowed to detect a significant contribution of GB's to the conductivity at higher temperatures.
Fig. 3 - Trajectories of anions involved in: (a) a direct ring-exchange mechanism and, (b) a substitution chain sequence in the grain boundary.
The analysis of the ionic trajectories at T=750 K allowed us to detect two types of ring exchange diffusion mechanisms in the (001) plane and a substitution chain mechanism along the [OOl]
direction. The first ring sequence is induced by the jump of a fluorine atom in an unstable position and is very similar to that discovered by Doan and Adda 1191 in a perfect CaF2 crystal.
Ring exchanges of four anions jumping quasi-simultaneously are also observed (Fig. 3a).
Finally more complicated cooperative mechanisms operate parallel to the tilt axis illustrated by the substitution chain sequence displayed on figure 3b.
At T=1500 K (T >Tc) the anions diffuse everywhere in the system the GB's remaining always more diffusive than the bulk
.
The intergranular anionic diffusion coefficient is practically isotropic as indicated by the value R=Dll/D~=l of the anisotropy ratio computed in the GB region for all the temperatures we studied.
The Arrhenius plot of the isotropic intergranular diffusion coefficient leads to an apparent activation energy
E:~=o.s
eV. As expected this value is smaller than those determined experimentally for bulk diffusion (E,=2 eV in the intrinsic conductivity region /20/).Finally, the analysis of local quantities such as diffusion, mean square displacements and structure factors, shows that the boundary width is of the order of one nanometer (i.e. =l0 (210) atomic planes) (Maunier C., in preparation), in good agreement with experimental results in ionic crystals /21/.
Cl-250 COLLOQUE DE PHYSIQUE
5
-
DISCUSSION AND CONCLUSIVE REMARKSUsing molecular dynamics at constant temperature we have shown that the C=5 [OOl] (210) 8=36.g0 tilt GB we studied in CaF2 undergoes a structural phase transition above T=0.2 T,.
Premature superionic behavior with respect to the bulk is observed in the grain boundary at temperatures as low as
f
B =0.44 T,. By analogy, we can speculate on the existence of a similar behavior of other fluorites and namely of U02, for which ~ : ~ = 1 1 0 0 OC. In polycrystalline UO2, plastic deformation at low strain rates around this temperature shows the occurence of a softening which is often referenced to as the brittle to ductile transition 1221. It will be of great interest to identify the possible connexion between the premature superionic behavior near grain boundaries in fluorites and the mechanical behavior of such polycrystalline materials.A final remark concerns the diffusion of anions in the bicrystal above Tc, the critical temperature for superionic conduction in the bulk : above this temperature intergranular and bulk diffusion of the anions both reach values measurable by MD indicating that the grain boundary and the bulk can reach the thermodynamical equilibrium simultaneously. This is an exceptional situation for MD simulations since in models adapted to metals the melting point temperature is reached before bulk diffusion becomes detectable. Fluorites can therefore be used as models to study the interactions of point defects created in a grain boundary with the bulk and to obtain information on the role of internal interfaces as sources and sinks of point defects.
ACKNOWLEDGMENT
We are deeply indebted to G. Evangelakis for fruitfuldiscussions and constructive comments.
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