On the Orientation Dependent Grain Boundary Migration in an Fe-6at. %Si Alloy

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1 On the Orientation Dependent Grain Boundary Migration in an Fe-6at. %Si Alloy P. Lejcek, J. Adámek To cite this version: P. Lejcek, J. Adámek. On the Orientation Dependent Grain Boundary Migration in an Fe-6at. %Si Alloy. J. Phys. IV, 1995, 05 (C3), pp.c3-107-c < /jp4: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1995 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE IV Colloque C3, supplément au Journal de Physique III, Volume 5, avril 1995 C3-107 On the Orientation Dependent Grain Boundary Migration in an Fe-6at.%Si Alloy P. Lej ek and J. Adamek Institute of Physics, Academy of Sciences, Na Slovance 2, CZ Prague 8, Czech Republic Résumé: Les joints de flexion symétriques autour de [001] présent l'anisotropie de l'enthalpie d'activation de migration. Les valeurs de l'enthalpie sont élevés pour les joints spéciaux en comparison avec les joints généraux. Ce résultat inattendu est expliqué par le modèle de Gottstein et Shvindlerman modifié. On propose trois contributions principaux a l'enthalpie de migration: l'enthalpie intrinsèque, l'enthalpie de migration donné par la ségrégation dans les joints de grains et l'enthalpie de migration donné par la mixture d'alliage. Il est démonstré que la différence dans l'enthalpie de migration entre les joints spéciaux et généraux dans un alliage concentré peut-être expliqué par la migration intrinsèque qui domine aux effects de ségrégation. Abstract: The [100] symmetrical tilt grain boundaries in an Fe-6at.%Si alloy were found to exhibit a pronounced anisotropy of activation enthalpy of migration characterized by its high values for special boundaries as compared to general ones. This rather surprising result is explained on the basis of extended model of Gottstein and Shvindlerman supposing three main contributions to the migration enthalpy: intrinsic migration enthalpy, migration enthalpy resulting from grain boundary segregation, and migration enthalpy resulting from alloy mixing. It is shown that the differences in migration enthalpy of special and general grain boundaries in a concentrated alloy reflect the prevailing character of the intrinsic migration enthalpy over the weakened segregation effects. 1. INTRODUCTION The motion of grain boundaries represents one of the basic mechanisms in developing structures of polycrystalline solids [1], Since a close connection exists between the structure and properties of polycrystals, the knowledge of parameters of grain boundary migration can be used in controlling the structure - and thus, the properties - of such materials, e.g., by producing a desired grain boundary character distribution suitable for grain boundary design [2]. Therefore, a great attention of investigators is still attracted to the research on these dynamic properties of grain boundaries (e.g. [1]). Grain boundary migration is a complex phenomenon which depends on many variables as e.g., temperature, concentration of soluble impurities, size and dispersion of second-phase particles, sample Article published online by EDP Sciences and available at

3 C3-108 JOURNAL DE PHYSIQUE IV thickness [3], and grain boundary structure [4]. Whereas the former effects on grain boundary migration have been well described by suitable theories [3], there is still a lack of both the experimental data and the relevant models to elucidate the structural dependence of grain boundary migration. Although many features of interfacial mobility were revealed by studying collective (i.e. average) behavior of boundaries in polycrystals, the quantitative determination of its anisotropy can only be made from measurements of single grain boundary migration in well-characterized bicrystals [5]. Rutter and Aust [6] observed high migration ability of a few, so called special high-density grain boundaries in pure and tin doped lead as compared to the rest general ones. The migration rate of both types of grain boundaries decreased with increasing content of Sn, however, this decrease was much more pronounced in the case of general boundaries. In addition, an anisotropy of activation enthalpy of migration of [loo] tilt grain boundaries was found, characterized by its low values for special grain boundaries as compared to those of general interfaces. Qualitatively similar orientation dependence of activation enthalpy of migration of [loo] tilt grain boundaries in high purity aluminum (5N2) was reported by Fridman et al. [7]. However, no anisotropy was observed either in ultra-high purity A1 (6N5) or in low purity material (3N8). In the former case, all grain boundaries possess the same low value of migration enthalpy as special bounda,ries in high purity material whereas much higher migration enthalpy was measured for all grain boundaries in the latter case. Recently Gottstein and Shvindlerman [8] explained these results on the basis of specific segregation effect on migration of particular grain boundaries. They distinguish four regimes of purity level which reflect different orientation dependences of migration enthalpy for high angle grain boundaries (fig. 1). In a completely pure material, general grain boundaries move more easily than special ones since the lower energy of special boundaries provides an enhanced resistance to a temporary modification of the structure, as necessary for grain boundary motion. This is represented by higher migration enthalpy for the special boundaries (line 4). In the other materials an impurity segregation also occurs, however, its effect is limited to a small interval of total impurity Fig. 1. Schematic dependence of enthalpy of grain boundary migration, AHM, for differently pure material: 1 - low purity, 2 - high purity, 3 - ultra-high purity, 4 - completely pure material. According to Gottstein and Shvindlerman [8].

4 content (high purity material, line 2) in which special grain boundaries are less segregated and move faster than general boundaries which are dragged by a large impurity atmosphere. Therefore, the observed orientation dependence of migration enthalpy reflects rather the contribution of grain boundary segregation than the true migration anisotropy. Outside this concentration interval the mobility of high angle grain boundaries apparently does not depend on misorientation (low purity material, line 1, and ultra-high purity material, line 3) [8]. The branches 1-3 in fig. 1 schematically depict the results of Fridman et al. [7] while the line 4 has been remaining rather speculative till now due to the absence of experimental results on completely pure materials [8]. In the present paper we report the results of our measurements of migration of various wellcharacterized [loo] tilt grain boundaries in bicrystals of an Fe-Gat.%Si alloy. Observed anisotropy of grain boundary migration is interpreted on the basis of the "segregation" approach of Gottstein and Shvindlerman, and offers an extension of this model to "concentrated" alloys. 2. EXPERIMENTAL Bicrystals of an Fe-Gat.%Si alloy containing phosphorus (550 PP~), carbon, nitrogen and oxygen (each of the order of 10' ppm) as the impurities, with the diameter of 13 mm and the length of 50 mm were grown by the floating zone technique [9]. All bicrystals used in this study were characterized by a tilt rotation along the [loo] axis which was simultaneously the rod axis. The symmetrical grain boundaries were always planar and parallel to this [loo] axis. Grain boundary migration was studied using a modified reversed-capillary technique [lo] on small samples cut off from the bulk bicrystals so that the angles between the planar boundary (perpendicular to the (100) sample surface) and both side surfaces were 45". Individual samples were repeatedly annealed at a chosen temperature between 1223 K and 1373 K for a defined time period. After each annealing cycle the position of migrated boundary was visualized by chemical etching. All details concerning the experimental technique and conditions are given and thoroughly discussed elsewhere [l RESULTS In the reversed-capillary techniques, grain boundary is driven to reduce its energy by reducing its total area. In our arrangement, both ends of the originally planar grain boundary are curving in the course of annealing so that the right angles are ultimately established between the boundary and the side surfaces. The curved segments then move to their centres of curvature. The displacement distance a was found to be a square-root function of the annealing time t a=c& (1) where the parameter C is temperature and orientation dependent. The driving force F is given by F = 7f la (2) where y is the boundary energy per unit area, and f is the geometrical factor. The migrating velocity v was found to be proportional to F, where M is the grain boundary mobility which is temperature dependent as M = MO~X~(-AH~/RT)

5 C3-110 JOURNAL DE PHYSIQUE IV Here Mo is the preexponential factor and AHM is the activation enthalpy of grain boundary migration. Thus, the product My can be determined by and from its temperature dependence the activation enthalpy of migration AHM for individual grain boundaries can be obtained according to eq. (4) assuming a negligible temperature dependence of y. The orientation dependence of migration enthalpy is displayed in fig. 2. Fig. 2. Orientation dependence of migration enthalpy AHM for [loo] tilt grain boundaries in an Fe-Gat.%% alloy. Intervals of AHM for special (S) and general (G) grain boundaries are distinguished 4. DISCUSSION As is apparent from fig. 2, a pronounced anisotropy of grain boundary migration enthalpy exists in the [100] tilt bicrystals of an Fe-Gat.%Si alloy: The grain boundaries characterized by low values of reciprocal density of coincident sites C possess high values of AHM. Accepting the value of C to be a rough indication of grain boundary specialty we can conclude from our measurement that the special grain boundaries are characterized by the high values of AHM. This rather surprising conclusion seems to contradict to the model of Gottstein and Shvindlerman [8] (cf. fig. 1): An anisotropy of migration enthalpy was found in a concentrated alloy in which no differences between special and general grain boundaries should be expected. Moreover, the character of this anisotropy is qualitatively similar to that which is (speculatively) expected for a completely pure material. To explain these apparent discrepancies we will now analyze possible contributions to AHM and compare then its orientation dependences for special and general grain boundaries. According to Gottstein and Shvindlerman, in completely pure material AHM will reflect the intrinsic tendency of a grain boundary to migrate whereas the presence of an impurity will introduce the segregation effect [8]. We can express the former contribution by the intrinsic grain boundary

6 migration enthalpy, AHft,, which is constant for a chosen grain boundary in the whole composition range. The latter contribution can be characterized as the migration enthalpy resulting from grain boundary segregation, AHE, which reflects the dragging effect of atmosphere of segregated impurities (or solutes) on the motion of the interface, i.e., a difference between chemical composition of grain boundary and bulk material. Besides these two terms, however, changed matrix composition in an alloy affects migration tendency also in the case if no segregation effects would be observed. This contribution can be represented by the migration enthalpy resulting from mixing in the matrix, AH$,. Thus, the migration enthalpy can be written as To model the concentration dependence of AHM for both special and general grain boundaries in a binary system A-B, the segregation and mixing terms can be expressed by and AH^, = X(l- X)WAB respectively, where X is the bulk atomic concentration of the solute, X6 is its grain boundary concentration, AH,,, is the segregation enthalpy of the solute in the matrix, and WAB is the term reflecting differences in bonding energies ~ ij between the nearest neighbours in the matrix, WAB M 2EAB - - EBB. The value of AH$, is the same for all grain boundaries in a chosen alloy whereas the values of AHZg differ for special and general grain boundaries due to different values of AH,,, and thus the segregation levels X4. Of course, the values of AHEtT also differ for these two types of interface. Model concentration dependences of individual enthalpy terms in a binary alloy are schematically depicted in fig. 3 for both special (S) and general (G) grain boundaries. In this modelling, following values of the parameters were used: WAB = 50 kj/mol, = -40 kj/mol, AH,,,,s = -20 kj/mol, AHEt,,G = 10 kj/mol and AHftTTS = 20 kj/mol, assuming complete solid solubility and equilibrium segregation of the minority element. A summary concentration dependence of AHM for these two groups of grain boundaries is shown in fig. 4. It is seen in fig. 4 that both AHY and AH: increase with increasing solute concentration. Due to the higher value of as compared to AHtzr,G, AHY > AH: establishes for very low concentrations of solute. The increase of AHY with increasing concentration is smaller than that of AH2 reflecting the lower ability of special grain boundaries to solute segregation. Therefore, at a concentration XI all grain boundaries will possess the same value of AHM. At higher concentrations, larger differences in segregation levels of these two groups of grain boundaries occur so that AHY < AH:. However, during a further increase of solute concentration in the region of "concentrated" alloys the segregation effects are lowered because the difference between the boundary and bulk composition decreases (cf. fig. 3). As a result, the difference between migration enthalpies of special and general grain boundaries are reduced to such an extent that at a concentration X3 they are equal and in more concentrated alloys ANY > AHF is again valid. In this region (i.e., X4 > X3), the effect of intrinsic enthalpy prevails the segregation one similarly to the completely pure material (0 < X < XI), however, due to the contribution of mixing enthalpy, AHZ,, the absolute values of AHy(i = S, G) are much higher than corresponding LIHE~,~. The relationship between the migration enthalpies of special and general grain boundaries at different concentrations is more apparent from the concentration dependence of the difference AHY- AH2 which is also plotted in fig. 4. Let us construct now a model orientation dependence of AHM (fig. 5). In a completely pure material (X = 0), this dependence is characterized by higher values of AHY for special boundaries as compared to AH$' for general ones. With increasing concentration, the difference is reduced so

7 JOURNAL DE PHYSIQUE IV Fig. 3. Concentration dependences of individual Fig. 4. Concentration dependence of migration enthalpy terms contributing to the migration en- enthalpy for special (S) and general (G) grain thalpy: AH,!& (upper graph), AH& (central boundaries (up) and difference AHY - AHg graph), and (bottom graph). Concen- (bottom). tration axis is non-linear with enlarged low concentration range.

8 that at the concentration XI no anisotropy is observed. However, at higher solute concentrations the differences between special and general grain boundaries occur again. The character of the orientation dependence is quite opposite to that for pure material. At a concentration X3 all AH^ possess again the same value. A common feature of this dependence is an increase of the value AHM for both types of grain boundaries. Supposing that concentrations X = 0, Xl,X2, and X3 correspond to completely pure material, ultra-high purity material, high purity material and low purity material, respectively, as used by Gottstein and Shvindlerman [8], the trend of these dependences in fig. 5 is qualitatively identical to that in fig. 1. According to our considerations, however, a further increase of solute concentration to Xq evokes again differences in migration enthalpies so that another kind of anisotropy is observed having a qualitatively similar character to that in a completely pure material. The absolute values of AHM in such an alloy are indeed much higher than those in the pure material. A comparison of the modelled (Xq in fig. 5) and the experimental (fig. 2) dependences reveal a good qualitative agreement. This suggests that segregation effects do not play a decisive role in the migration of grain boundaries in bicrystals of an Fe-6at.%Si alloy. The migration enthalpy in the case of such a concentrated alloy arises mainly from a superposition of intrinsic migration enthalpy and enthalpy term reflecting the alloy mixing effects. Fig. 5. Model orientation dependence of migration enthalpy AHM for concentrations corresponding to individual regions according to fig. 4. Si and Gi are representatives of special and general grain boundaries, respectively. 5. CONCLUSIONS 1. A pronounced anisotropy of migration enthalpy of [loo] symmetrical tilt grain boundaries was measured using a modified reversed-capillary bicrystal technique in a concentrated Fe-6at.%Si alloy. This anisotropy is characterized by higher values of migration enthalpy for special boundaries as compared to general ones. 2. Considering activation enthalpy of migration to be composed from intrinsic migration enthalpy,

9 C3-114 JOURNAL DE PHYSIQUE IV migration enthalpy resulting from grain boundary segregation, and migration enthalpy resulting from alloy mixing, the model of Gottstein and Shvindlerman was rationalized and extended to cover migration behavior of concentrated alloys. 3. The differences in migration enthalpy of special and general grain boundaries in a concentrated alloy reflect the prevailing character of the intrinsic migration enthalpy over the weakened segregation effects. Absolute value of migration enthalpy in the case of such a concentrated alloy arises mainly from a superposition of intrinsic migration enthalpy and enthalpy term reflecting the alloy mixing effects. Acknowledgement This work was partially supported by the Grant Agency of the Czech Republic (contract no. 202/94/1177) and the Grant Agency of the Academy of Sciences of the Czech Republic (contracts nos and ). References [I] Chandra, T., Ed., Recrystallization '90 (TMS, Warrendale, PA, 1990). [2] Watanabe, T., Mater. Sci. Eng. A 166 (1993) [3] Cotterill, P. and Mould, P.R., Recrystallization and Grain Growth in Metals (Surrey University Press, London, 1976). [4] Gottstein, G. and Schwarzer, F., Mater. Sci. Forum (1992) [5] Masteler, M.S. and Bauer, C.L. "Experimental techniques", Recrystallization of Metallic Materials (Dr. Riederer Vrlg., Stuttgart, 1978), pp [6] Rutter, J.W. and Aust, K.T., Acta Metall. 13 (1965) [7] Fridman, E.M., Kopezky, Ch.V. and Shvindlerman, L.S., 2. MetaZlk.de 9 (1975) [8] Gottstein, G. and Shvindlerman, L.S., Scripta Metall. Mater. 27 (1992) [9] KadeEkovi, S., Toula, P. and Adimek, J., J. Crystal Growth 83 (1987) [lo] LejEek, P., KadeEkovi, S. and Paidar, V., "Grain boundary migration in Fe-3%Si bicrystals", Annealing Processes - Recovery, Recrystallization and Grain Growth, Risg, September 8-12, 1986 (Ris~ National Laboratory, 1986) pp [ll] LejEek, P., Paidar, V., Adimek, J. and KadeEkovi, S., Interface Sci., 1 (1993)