Grain Boundary and Interface Structures in Ceramics

S110 Special Review "Launching into The Great New Millennium"

Journal of the Ceramic Society of Japan 109 [7] S110-S120 (2001)

Grain Boundary and Interface Structures in Ceramics Yuichi IKUHARA EngineeringResearch Institute, The University of Tokyo(PRESTO, JST), 2-11-16,Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan

セラミックスの粒界及び界面の構造

幾原雄- 東京大学工学部総合試験所 (科学技術振興事業団), 113-8656 東京都文京区弥生 2-11-16

This paper reviews grain boundary and interface structures in ceramics. Firstly, geometrical treatments are briefly described for both grain boundary and hetero-interface. For the grain boundary, grain boundary character, small angle grain boundary, coincidence site lattice (CSL) theory, structure unit, segregation and amorphous grain boundary are reviewed to show a couple of examples observed in ceramics. For the het ero-interface, O-lattice theory, lattheory,latry,latace,theory,latry, latttticecoherency O-lattice and interfacial dislocation are discussed and the results ob tained for metal/ceramics interfaces are introduced. Transmission electron microscopy (TEM) enables us to characterize the very narrow regions less than 1nm, and therefore is powerful technique for investigating grain boundary and interface structures. In this paper, recent experimental TEM studies are presented to demonstrate grain boundary and interface characterization at high spatial resolution. [Received November 27, 2000]

Key-words: Grain boundary, Hetero-interface, Transmission electron microscopy, Analytical electron microscopy, Grain boundary character, Small angle grain boundary, Coincidence site lattice (CSL), Structure unit, Segregation, Amorphous, O-lattice, Lattice continuity, Interfacial dislocation, Lattice mismatch, Alumina, Silicon carbide, Siliconn nitride, Vanadi um, Magnesia

1. Introduction puritu-doped alumina which has high creep resistance.12) HE mechanical and electronic properties of ceramics are Covalent bonded ceramics such as Si3N4 and SiC are known strongly influenced by the atomic structure of grain as hard sintering materials, so sintering additives are usual boundaries.1)-3) On the other hand, grain boundary and in ly used for the sintering. In this case, amorphous film with terface structure itself are sensitive to the grain boundary the thickness of about 1 nm is frequently formed along the character. Therefore, it is important that we investigate the grain boundaries. The chemical composition and bonding relationship between grain boundary structure and its state in the film are considered to determine the high-tem character so that we can understand how grain boundary perature mechanical properties of such ceramics.13) Amor structure affects the intrinsic properties of ceramics. In this phous grain boundary is also briefly discussed in this paper. review paper, the importance of grain boundary character is Hetero-interfaces are always formed in ceramic compo briefly described, and typical examples are introduced for a sites and thin films. The hetero-interface structure is of wide small angle grain boundary4) and a coincidence site lattice interest not only from a fundamental point of view but also (CSL) grain boundary5) as in the case. Like the grain boun because of its importance in many modern materials which daries of metals, the grain boundaries of ceramics can be are composites consisting of two or more phases. The sig described as dislocation boundary or CSL boundary. nificance of the interface lies in the fact that many of the However, the atomic structures in ceramics are a little bit properties of structural or electronic composites depend complicated, compared with simple metals. Ceramics gener sensitively on it. The O-lattice theory can treat geometric ally consist of more than two kinds of elements , and often matching at hetero-interface.6),7) But, this involves the use have a hexagonal structure . Examples of such ceramics are of several complicated transformations between two lat Al2O3, Si3N4 and SiC. In these ceramics, there is little simple tices, and the theory can not predict the most stable orienta geometrical matching at grain boundaries except for the ro tion relationship (OR). Recently, the concept of the coinci tation around the special axis. CSL theory , therefore, can dence of reciprocal lattice points (CRLP) has been not fully describe grain boundaries in ceramics . For this proposed, and applied to predict stable ORs for many kinds purpose, O-lattice theory6),7) or an evaluation of lattice of hetero-interfaces.8),9) The contents of these theories are continuity8),9) is needed as shown in Section 3. The struc explained in detail in this paper. The adhesion between two ture of interfacial dislocation at boundaries is also influenced materials is basically made by atomic interactions across the by the intrinsic structure of ceramics because more than two interface and its strength is ultimately determined by the elements interact at grain boundaries. Several examples of strength of interfacial bonds between the atoms of two con this are shown for the grain boundary in Al2O3.10) stituent materials.2) Hence, the adhesion between two Sutton and Vitek11) proposed the idea of structure unit to materials is inherently related to the structure of, and describe grain boundary atomic structure. The concept is defects in, the interface between them. The strength and that a grain boundary generally consists of some structure fracture properties of a structural composite are in turn units, and it has been successfully applied for a couple of related to adhesion. Besides its practical importance, the ceramics. It therefore will be briefly covered in this paper. structure of a hetero-interfaces is important from a fun Doping impurities into ceramics is a useful way to control damental viewpoint because of the desire to understand how grain boundary properties. The impurities often segregate nature accommodates the mismatches across the contact along the grain boundary, changing intrinsic properties. A plane of two translationally periodic structures.1) Interfacial typical example of this is shown for a small amount of im dislocations play an important role here, and are described Special Review "Launching into The Great New Millennium" S111

Yuichi IKUHARA Journal of the Ceramic Society or Japan 109 [7] 2001 in detail for the case of metal/ceramics interface in this paper. Transmission electron microscopy (TEM), in particular, high-resolution electron microscopy (HREM) is one of the most useful techniques for studying the atomic structure of grain boundaries and has in recent years been used to inves tigate various kinds of grain boundaries in many kinds of ceramics.2),14) Analytical electron microscopy (AEM) ena bles us to evaluate an element distribution and a chemical bonding state with nanometer-order spatial resolution,6) and recent improvements in the field emission gun have made it possible to employ energy-dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS) with spatial resolution better than 1nm.14),15)This paper includes many HREM and AEM results of the grain boundary and in terface structures in ceramics.

2. Grain boundary 2.1 Grain boundary character Grain boundary character can be described in terms of the relative orientation relationship between two crystals and the orientation of the boundary plane. Geometrically speak ing, there are nine degrees of freedom that we must con sider to exactly describe the grain boundary character.1) Consider a grain boundary with the plane normal to the vec tor P, in which one crystal is rotated by ƒÆ around the rotation axis n with respect to the other crystal. In this case, there are totally five macroscopic parameters because two degrees of freedom are, respectively, given for n and P. The remaining four are microscopic parameters, and are in troduced from atomic structure relaxation at grain bounda ry. That is to say, they are three degrees of freedom of rigid body displacement on grain boundary plane and one degree of freedom of displacement perpendicular to the boundary. A grain boundary can be classified into a small angle boundary or a large angle boundary depending on the degree of rotation angle ƒÆ. Although it varies a little by materials, the angle of a small angle grain boundary is generally limited 10-15•‹ which is close to the overlapping of Fig. 1. High resolution electron micrographs of (a) 10•‹ small an dislocation cores.16) On the other hand, among the angles of gle tilt grain boundary in Al2O3 and (b) Burgers circuit around the large angle grain boundaries, there are some specific angles dislocation in (a). at which two adjacent grains well-match geometrically. A grain boundary having such an angle is called a coincidence site lattice (CSL) grain boundary,5) and generally the energy is low and its structure is considered to be stable. boundary as indicated by the arrows. Figure 1(b) is a Burg CSL grain boundary is expected to be mechanically strong, ers circuit around the dislocation shown in (a). From this and therefore has been used to design grain boundary con circuit, the Burgers vector of the dislocation can be identi trolled materials.17)-19) fied as 1/3[110n] since the circuit is just a projected circuit

We often use the terms tilt boundary and twist boundary along [0001] direction. As candidate Burgers vectors, b1= to describe grain boundary character. A tilt boundary has 1/3[1102], b2=1/3[1101] and b3=1/3[1100] can be consi the plane parallel to the rotation axis n, while a twist boun dered, in which b1 and b2 are perfect dislocations and b3 is a dary has the plane perpendicular to n. A grain boundary that partial dislocation. The sizes of these Burgers vectors are falls in between these two is called a mixed grain boundary, |b1|=0.908, |b2|=0.512 and |b3|=0.274nm, respectively, which comprises both tilt and twist components. Whether a and thus b3 has the smallest vector among them. If bl and b2 grain boundary becomes a tilt or twist grain boundary de dislocations are formed along the grain boundary, a large pends on the location of the grain boundary plane even if the twist component is introduced at the boundary. Consequent orientation of two crystals is exactly the same. ly, b3 dislocation should be formed periodically at an interval 2.2 Small angle grain boundary spacing of about 2nm to compensate the misorientation an

In a small angle grain boundary, the misorientation angle gle of 10•‹. This can be reasonably explained by the Eq. (1). between two adjacent crystals is relatively small, and the Grain boundary energy for a dislocation boundary can be misorientation is compensated by introducing a periodic dis calculated by the next equation.20) location array. In the case of a pure tilt boundary with mis orientation angle ƒÆ, dislocation separation h and Burgers γgb=Gbθ/4 π(1-v)(ln(b/2πr0θ)+1) (2) vector b, the following equation can be obtained.4) where G, v and r0 are shear modulus, Poisson's ratio and the ƒÆ =tan-1b/h=b/h (1) core radius, respectively. In the case of small angle grain Figure 1 shows (a) a high-resolution electron micrograph boundary in Al2O3 in Fig. 1, the grain boundary is consisted of the 10•‹ small angle grain boundary in Al2O3.10) Disloca of partial dislocations with Burgers vector of 1/3[1100] and tion contrast can be observed periodically along the grain the stacking faultson the(1100)planes. Since the perfect S112 Special Review "Launching into The Great New Millennium"

Grain Boundary and Interface Structures in Ceramics

dislocation with Burgers vector of [1100] is dissociated to cell, the particular orientations at which low values of E three partial dislocations with Burgers vector of 1/3[1100], occur can be deduced from simple geometrical the stacking faults are formed on the 2/3 area of the whole considerations;22) thus ‡”=3, 9, 11, 17 when one lattice is ro grain boundary plane. Grain boundary energy of small angle tated around the <110> axis of the other lattice through an grain boundary can be, therefore, expressed as the following gles 70.53•‹, 38.94•‹, 50.48•‹, and 86.63•‹, respectively (see equation.21) Fig. 11 in Section 3.2). A particular grain boundary can be obtained by passing a γgb=Gbpθ/4 π(1-v)(ln(bp/2πr0θ)+1)+2/3γsf (3) plane (hkl) through the interpenetrating composite. The grain boundary is then termed ‡” (hkl), Relaxation of atoms where bp is a Burgers vector of a partial dislocation and ƒÁsf at the two sides of the boundary, or slight rigid body transla stacking fault energy. The results calculated from this equa tions of one grain with respect to the other (which destroys tion agree well with the experimentally measured values.21) the CSL!), can lower the energy of the system. Numerous 2.3 Coincidence site lattice (CSL) boundary calculations have shown that the higher the density of the In the case of a single-phase polycrystal, a concept that coincident sites is, i.e., the lower the E, and also the more has often been used to predict the orientation relationship closely packed the plane (hkl) is, the lower the energy of

(OR) between two adjacent grains is the "coincidence site the grain boundary becomes.23) lattice" (CSL).5) The concept of CSL is based on the fact Figure 3 shows the relationship between grain boundary that certain rotations about an axis bring a lattice into partial energy and misorientation angle in [0001] symmetric tilt self-coincidence (for rotational symmetry operations the grain boundaries in Al2O3.10) This profile was experimental self-coincidence is of course complete). The common lattice ly obtained by a thermal grooving technique. There are two sites (c.l.s.) then form a larger lattice known as a coincident large energy cusps at the angles corresponding to ‡”7 and site lattice (CSL). The CSL can also be considered a lattice ‡” 3. The energy of these two CSL grain boundaries is ex of coincidence sites in the composite lattice obtained by in tremely low less than 0.05J/m2. From the misorientation terpenetration of two single lattices. Figure 2 shows inter angles of 0•‹ to 32•‹, the grain boundary energy increases with penetration of two simple cubic lattices by means of rotation increasing misorientation angle, although ‡”21 and ‡”13 CSL the <001> axis.6) The points of overlap correspond to CSL boundaries exist in this region. The highest grain boundary

points indicated by white circles. Like any other lattice, a energy among the examined specimens is about 0.8J/m2 for CSL can be defined in terms of a unit cell, the volume of the 42•‹ high angle grain boundary. Noteworthy here is that which is proportional to the density of lattice sites; the the grain boundary energy strongly depends on the grain higher the c.l.s. density is, the smaller the volume of the boundary characters even in ceramics, and partially agree CSL unit cell becomes. Conventionally, the volume of the with the CSL concept. CSL unit cell is normalized with respect to the volume of the Interestingly, Schober and Balluffi24) found experimental lattice unit cell and the result, which is necessarily an in evidence that a number of near-coincident grain boundaries teger, n, is denoted by ‡”=n. Each ‡” defines a particular (those that are inclined to each other at angles close to, but orientation relationship between the two lattices; thus, for not exactly in, a coincidence condition) consist of a combi two lattices in parallel orientation, ‡”=1 and the c.l.s. densi nation of a CSL boundary and a network of grain boundary ty is a maximum. The angle ƒÆ, which forms CSL by rotating dislocations. In analogy to small-angle grain boundaries, the around the [hkl] axis, can be obtained by the next equation. separation of the dislocations in the network depended on ƒÆ =2tan-1(Ry/x) (4) the deviation from the coincidence condition. According to Bolhnann,6) the Burgers vectors of these grain boundary where R2=h2+k2+l2, x and y are integers. In this case, ‡” dislocations are not necessarily lattice vectors, but rather can be expressed as ‡”=x2+Ry2. In the case of a cubic unit they belong to the DSC (Displacement Shift Complete) lat tice, i.e; they translate the coincident lattice from one set of lattice sites to an adjacent one. 2.4 Structure unit CSL model is just deduced from the geometry of two adja cent crystals. It is, however, a periodic atomic configuration

Fig. 2. CSL plot of ‡”5 grain boundary in the simple cubic lattice , Fig. 3. Relationship between grain boundary energy ƒÁgb and mis in which one lattice is rotated around the <001> axis by 36.52•‹ with orientation angle 2ƒÆ, indicating that there are two energy cusps at respect to the other lattice. the angles of ‡”3 and ‡”7. Special Review "Launching into The Great New Millennium" S113

Yuichi IKUHARA Journal of the Ceramic Society of Japan 109 [7] 2001

must be directly related to the grain boundary energy. As ceramics.12),29) The origin of this improvement is considered the model for treating this, we have the structure unit model to be the segregation of cation ions along grain boundaries. proposed by Sutton and Vitek,11) which is widely accepted Figure 5 shows a high resolution electron micrograph of a in this field at present.1) This idea is that grain boundary can grain boundary in 0.05mol% Lu2O3 doped alumina. As can be constructed by the combination of some kinds of struc been seen in the micrograph, no secondary phase is formed ture units. In the case of a CSL boundary, the boundary con at the boundary and two adjacent grains are directly joined sists of a couple of stable structure units, and the strain of across the boundary. This is generally also observed in each structure unit is small, so the grain boundary energy is ZrO2-doped, MgO-doped and and lanthanoid (Sm, Tm, Eu, low. On the other hand, a large angle grain boundary, which Y, Lu) oxide-doped alumina ceramics.12),29) The addition of is composed of distorted structure units, shows high grain Lu2O3 is the most effective in retarding creep stain rate boundary energy. Recent HREM studies and first principles among the specimens. Figure 6 shows (a) STEM image and grain boundary calculations have confirmed that the struc (b) Lu Kƒ¿ image obtained by STEM (Scanning Transmis ture unit model is appropriate. Figure 4 shows a high resolu sion Electron Microscopy) -EDS method for the grain boun tion electron micrograph of ‡”9 CSL grain boundary in SiC dary in the 0.05mol% Lu2O3 doped Al2O3.30) It is clear that with the incident beam parallel to <011>.25) It is obvious that a continuous segregation layer is formed along the grain this boundary is consisted of the structure units of five and boundary. Figure 7 (a) shows the energy loss near edge seven member rings. structure (ELNES) of Al L1-edge measured with the probe 2.5 Grain boundary segregation less than 1nm from the grain boundary and grain interior in The explanation above is for the grain boundaries at Lu2O3-doped Al2O3. The peak obtained from the grain boun which two pure crystals are directly joined without any im dary is always slightly broader than that from the grain in purities and secondary phase. However, in the case of poly terior, as typically seen in the energy level of about 95eV, crystals, impurities often segregate at grain boundaries, and in that over 100eV. The ELNES contains a fine struc which affects the properties of materials. For example, ture around the unoccupied density of states in the conduc phosphorus is well known to segregate in iron along the tion band (DOS), and thus can be evaluated by first princi grain boundaries, where it makes the chemical bonding ples molecular orbital calculations. The model clusters used state at the boundaries brittle.26) Generally, the amount of in the calculation are shown in Fig. 7 (b), where clusters segregation is small in low energy boundaries, and large in (Al5O21)-27 and (Al2Lu3O21)-27 represent grain interior high energy boundaries. McLean considered grain boundary and grain boundary models, respectively. The DOS ob segregation on the basis of thermodynamics, and proposed tained by the molecular orbital calculations are shown in the following equation.27) Fig. 7 (a). The peak of DOS calculated from the grain boun dary model is a little bit broader than that calculated from Xb the grain interior model at the energy level of about 95eV (Xb0-Xb)Xc(1-Xc)expQRT (5) and over 100eV, which is in accordance with the ex perimental spectra. This is evidence that the chemical bond where Xc, Xb, and Xb0 are the solute concentration in a ing state is changed at the grain boundary by the segrega- grain, solute concentration in a grain boundary, and saturat ed solute concentration in a grain boundary. Q represents the difference in strain energy that arises when solute atoms exist in a grain and a grain boundary. Grain boundary segregation is closely related to the properties of ceramics,28) and a typical example of cation doped alumina ceramics is introduced here.12),29) The addi tion of a small amount of cation oxide is known to be very effective in improving the creep resistance of pure alumina

Fig. 4. High resolution electron micrographs of ‡”9 grain bounda ry in SiC, indicating that the grain boundary is consisted of periodic Fig. 5. High resolution electron micrograph of a grain boundary in structure units of five and seven member rings (by Drs. K. Tanaka LU2O3 doped Al2O3, indicating that no amorphous phase is formed and M. Kohyama). at the grain boundary. S114 Special Review "Launching into The Great New Millennium"

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Fig. 6. (a) STEM image and (b) Lu Kƒ¿ image of grain bounda ries in Lu2O3 doped Al2O3, showing that Lu ions segregate along the boundaries.

tion of Lu ions. It is supposed that the grain boundary diffu Fig. 7. (a) ELNES of the Al-L1 edge experimentally taken from a sion of Al and O ions is restricted by the segregation, and grain boundary and grain interior, and the unoccupied density of that creep resistance is improved when the creep deforma states (DOS) calculated from the model clusters of (b) (Al5O21)-27 tion is controlled by grain boundary diffusion. Recent theo and (Al2Lu3O9)-27, which represent grain interior and grain boun retical calculations also suggest that the creep resistance in dary, respectively. A1203 is affected by a change in the ionic bonding state be tween Al and O atoms in grain boundaries caused by the segregation of Lu3+ ions.12),29) 2.6 Amorphous grain boundary In the case of ceramics sintered with sintering additives, an amorphous film is frequently formed along grain bounda ries. For example, Si3N4 is usually sintered with metal oxides, and the added oxides form an amorphous film along grain boundaries. High-temperature properties of Si3N4 are actually influenced by the composition and chemical bond ing state of the amorphous film.13),31)-34)Figure 8 shows a HREM image of a grain boundary in Y2O3-Al2O3 added Si3N4 sintered body.35) It is obvious that an amorphous film with the thickness of about 1nm is formed along the grain boundary. Clarke theorized that the equilibrium thickness of the amorphous layer is determined by balancing the van der Waals force between two adjacent grains and the steric force of the amorphous layer.13) According to his theory, van der Waals force is related to dielectric property of the grain and amorphous layer, and the steric force is dependent on the chemical composition of the thin amorphous film. As Fig. 8. High resolution electron micrograph of a grain boundary in the result, the equilibrium thickness h can be expressed as Y2O3-Al2O3 doped Si3N4, indicating that amorphous phase with the the following equation. thickness of about 1nm is formed at the grain boundary.

/6πh3=aη021/sinh2(h/2ζ) (6) is the correlation length in the amorphous film. The details Where H is related to the Hamaker constant, aƒÅ0 is a fac to derive this equation is reported elsewhere,13) but, this tor derived from the free energy difference between the equation actually well explains some experimental results amorphous film with and without structural ordering, and ƒÌ obtained for Si3N4 ceramics.33),34) However, there is still Special Review "Launching into The Great New Millennium" S115

Yuichi IKUHARA Journal of the Ceramic Society of Japan 109 [7] 2001

some questions as to whether van der Waals force effective ly works between two grains 1nm apart. On the other hand, an amorphous-like film is often observed even in ceramics sintered without sintering additives, particulary in ceramics having covalent bonds, such as SiC.31).36),37) If the surface of the starting powders is oxidized, the oxide layer can form an amorphous film during sintering even without additives. The amorphous film in HIPed Si3N4 without sintering addi tives is in this category,32)-34) but the amorphous-like layer in well-defined, high-purity materials is very much different.31),37) This layer is not composed of impurities, and the layer has been confirmed to consist of the same elements as the grain interior by nano-probe EDS.37) It is, therefore, believed that the amorphous-like structure is considered to appear to relax the atomic configuration to reduce high energy at the grain boundary. In other words, high energy grain boundary is extended to form a relaxed structure with some thickness to reduce its high energy. We previously proposed the concept of "the extended grain bounday",31),36) Fig. 9. Schematic of O lattice described so that one simple cubic and the amorphous-like grain boundary in high-purity ce lattice is rotated around the <001) axis by 31.53•‹ with respect to the ramics is likely such a boundary. The extention width of the other simple cubic lattice. Orthogonal sets of bold line represent the layer is considered to depend on the grain boundary charac Wigner-Seitz cells, in which O lattice exists at the center points. ter. The presence of the extended grain boundary is also reasonably predicted by first principles calculations.25)

3. Hetero interface

3.1 O-lattice theory points in which the internal coordinates of lattices ƒ¿ and ƒÀ Applying CSL theory to the interface geometry between are equal. According to linear algebra, the area of the O-lat

two dissimilar crystals is difficult, as mentioned in the Sec tice cell is inversely proportional to det |I-A-1|. Therefore, tion 2.3. In addition, CSL theory can not quantitatively treat the interface that minimizes det |I-A-1| can be considered ORs other than those for a CSL. When the geometrical to be a highly coherent interface. In fact, the O-lattice cell matching is considered at the hetero-interfaces in thin films, forms a Wigner-Seitz cell, as shown by the bold line in Fig.

precipitates, and composite materials, solving these 9, and interfacial dislocations are introduced along the cell problems requires a more general geometrical theory. It is to accommodate the lattice mismatch at the interface. When O-lattice theory, which was firstly developed by det |I-A-1|=0, an O-plane or O-line is formed, and their Bollmann,6),7) that can overcome these probems. The CSL coherency is higher than the case of a cell formed. The de model describes the geometrical matching at the grain boun tails of this argument are described elsewhere.13),14)

dary by the coincidence site lattice when two crystal lattices 3.2 Lattice continuity (Three dimensional orientation are superimposed at special ORs, but the 0-lattice model relationship)

generally describes the pattern in which two crystal lattices As mentioned above, generally there is no coincidence of ƒ¿ and ƒÀ are overlapped. Therefore, CSL is included as a spe lattice points when two dissimilar lattices interpenetrate,

cial case of O-lattice theory. When the geometry of hetero and it is safe to say that no general method exists that is interfaces is considered, O-lattice theory is useful because capable of predicting the OR between two adjoining dissimi the geometry can be treated even if the two crystal lattices lar crystals. A frequently used assumption in such cases is are different.38) In O-lattice theory, we need to obtain combi that the interface between the two crystals plays a dominant nation of the nearest neighbor lattice points in the two over role in determining the OR between them. Thus, orienta

lapping crystal lattices, and find the origins to choose the tions where two crystals in contact match at their interfacial

combination. The origins form the superlattice of the O lat plane are thought to be favored, and the two lattices are con tice. That is to say, an O lattice is one consisting of of all pos tinuous across the interface.38) This implies that the OR is

sible origin groups that enable transformation of the given determined by an interfacial plane on which the atomic con lattice ƒ¿ to the given lattice ƒÀ by linear transformation A. figuration is the same on both sides regardless of chemical The O actually comes from "Origin". Figure 9 is a petal pat species. An often used example is an hcp crystal in contact tern, which explains the concept of the O lattice.6) This with an fcc crystal. When the lattice parameters of the two figure can be compared with Fig. 2, and is a schematic in crystals are such that the atomic configuration of the (111)

which two simple cubic lattices are overlapped by rotating fcc plane is similar to that of the (0001) hcp plane, it is as around the <100> axis by 31.53•‹. Although there is no CSL sumed that a preferential OR occurs in which close-packed

point, the O lattice exists at the center point of the petal pat planes and directions in the two crystals are parallel, i.e., tern. From this, it is proven that the each point of lattice ƒ¿ (111)fcc//(0001)hcp overlaps lattice ƒÀ by rotating around the O-lattice points by [110]fcc//[1120]hcp (8) the same angle (31.53•‹ in this case). That is to say, it is pos sible to introduce lattice ƒÀ from lattice ƒ¿ by the linear trans Conversely, it is generally assumed that when the interfa formation A at any origin of the O lattice. By using the all cial plane has a very different atomic configuration in the

possible translation vectors b(L) for lattice ƒ¿, O-lattice point two adjoining phases, and no good matching can be attained x(0) can be expressed as the following equation.6) across the interface (say because of the different symmet ries of the two phases or a large lattice mismatch between (I-A-1)x(0)=b(L) (7) them), then the interface is incoherent and, in general, no where A is unimodular transfomation (U transformation) unique OR exists.38) More sophisticated treatments of the which is invariable volume transformation. This equation OR in heteroepitaxial systems are based on the minimiza means that the O lattice is obtained as the coincidence tion of the elastic strain energy and concepts of invariant S116 Special Review "Launching into The Great New Millennium"

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plane strain,39) or invariant line strain for a precipitate in a But, from simple solid geometry, the volume of the over matrix40) or a thin film on a substrate.41) In these methods, -lapped region between two spheres is given by either the interfacial plane, or a line on the interface, vgG=(2r*3-3r*2d*+d*3) (9) remains invariant, i.e. the interface plays the dominant role in determining the OR. These ideas appear to work for some where 2d* (<2r*) is the distance between the centers of systems while they fail for others.42) the two spheres. Then, the sum of all overlapped volumes, Recently, the overlap of reciprocal lattice points of two V=‡”v‚‡G in the bicrystal represents the degree of RLP coinci adjoining crystals, represented by Lattice I and Lattice II, dence, i.e. it represents the degree of lattice continuity be has been utilized to obtain a geometrically optimum OR be tween two adjacent crystals. The basis of this model is that tween two crystals.8),43) A reciprocal lattice point (RLP), the optimum OR corresponds to one that maximizes the hkl, corresponding to a reciprocal lattice vector g(hkl), value of V. Physically, it may be argued that the maximum specifies both the orientation of the set of lattice planes, V between two adjacent crystals (e.g., a precipitate and a (hkl), and its interplanar spacing, dhkl(=1/|g|). Ideally, an matrix, or a film and its substrate) corresponds to a state of RLP in an infinite crystal is a point in the reciprocal space optimal coherency between the two lattices, where they can but in this treatment, for reasons that will become clear best accommodate each other by the least amount of elastic later, it is considered to have a finite size. In fact, for sim strain and thus minimize the elastic strain energy of the plicity, it is assumed that an RLP, representing a set of composite. planes (hkl), has a spherical shape with a radius r* in the Therefore, according to this hypothesis, the interface reciprocal space of the crystal, and the vector g (hkl) is the plane is not a factor in determining the orientation relation vector joining the origin of the reciprocal lattice to the cen ship of the two lattices (just as in the CSL concept, the grain ter of this sphere. boundary plane is not a factor in the OR of the two grains). The near coincidence of two RLPs (one from each lat However, the interface plane may play an important role in, tice) is equivalent to the overlap of two spheres with radii say, the morphology of a precipitate in a matrix because, in r* (hkl) and r* (HKL) in the reciprocal lattices of crystals I general, low energy precipitate/matrix interfaces are ener and II, respectively. This implies an approximate overlap of getically favored. two reciprocal lattice vectors, i.e. g (hkl)_??_g(HKL), where With the help of a computer program, that orientation is (hkl) and (HKL) refer to the indices of a set of planes in found at which two desired lattices have the maximum Lattice I and Lattice II, respectively. Figure 10 shows a amount of overlap, i.e., at which V is a maximum. Given the schematic to explain this relationship.44) Thus, such a near (primitive) unit cell parameters of the two lattices, and the -coincidence, indicates that the two sets of planes (hkl) and radius, r*, of the RLPs in their reciprocal lattices, the pro (HKL) are approximately parallel and have approximately gram determines V(ƒÆ, ƒÓ) as a function of rotations ƒÆ and ƒÓ equal interplanar spacings. As a first approximation, it is as about two orthogonal axes of one of the lattices. The sum sumed that r* (hkl)= r* (HKL). The sets of planes (hkl) mation in V=‡”vgG is carried out over all RLPs up to a maxi and (HKL) are precisely parallel when g (hkl) and g (HKL) mum distance, R*, in the composite reciprocal lattice. are collinear, and their interplanar spacings are exactly The application of this method to neighboring grains in a equal if |g(hkl)|=|g(HKL)|. Thus the intersection of the simple cubic polycrystal is shown in Fig. 11.43) In this case, two spheres r* (hkl) and r* (HKL) indicates the degree of one cubic crystal is rotated about the <110> axis of the other parallelness and equality of interplanar spacings of the two crystal by an angle ƒÆ and the volume V(ƒÆ) is calculated. The crystals; if the volume of the intersection is equal to the RLPs considered for these calculations lie within R*<2a*, volume of the sphere with radius r* (hkl) [or r* (HKL)], and the radii of the RLPs are (a) r*=0.1a*, (b) r*=0.2a* then the sets of planes (hkl) and (HKL) are exactly parallel and (c) r*=0.5a*. As seen in these figures, the main peaks and dhkl=dHKL. Clearly then, the greater the sum total of in the V(ƒÆ) function correspond to ‡”=3, ‡”=9, ‡”=11, and overlap of RLPs of the two crystals, the larger is the number ‡” =17 with decreasing values of V . A few points about of their lattice planes which are approximately parallel to these figures are worth noting. The first point is that, as Fig. each other and have relatively close interplanar spacings. 11(c) shows, for the case of homoepitaxy (such as two Also, since an electron diffraction pattern (EDP) is just a grains in a polycrystal) of a cubic material, the peaks of V cross-section of the reciprocal lattice, the larger the overlap (ƒÆ) are at those values of ƒÆ which correspond to low ‡” of the RLPs is, the higher the probability becomes that the values in the CSL method, i.e., the results of the CSL theory diffraction spots of the two crystals will be close to each are recovered. Secondly, the angle, ƒÆ, corresponding to a other (or overlap) in an EDP of the bicrystal. particular value of ‡” is independent of the RLP radius, r*. As mentioned above, the degree of RLP coincidence is However, the sharpness of the peaks depends on r*; the proportional to the volume of the overlapped region, vgG. smaller the r*, the sharper the peaks. As mentioned before, the radius of the RLPs reflects the degree of parallelism of the planes and closeness of their interplanar spacings. In fact, the smaller the value of r*, and the larger the value of R*, the better the resolution of the method. Note, however, that the radius of RLPs cannot be continually decreased; as r* decreases, so does the probability of overlap with RLPs of the other lattice. The CRLP method is now applied to the V/MgO system, which has been experimentally investigated previously.45) Figure 12 shows a plot of V(ƒÆ, ƒÓ); the unit cells of the two crystals and the axes of rotation of one reciprocal lattice about the other are shown in the inset. A number of peaks can be observed in this figure. The four large peaks are observed in the figure, and the ORs are equivalent to each other and corresponds to the OR: (001)v//(001)MgO; Fig. 10. Overlapping of g (hkl) and g (HKL) reciprocal lattice [110]v//[100]MgO. This OR has been confirmed experimen spheres. tally for the MBE grown V/MgO system. In addition, Special Review "Launching into The Great New Millennium" S117

Yuichi IKUHARA Journal of the Ceramic Society of Japan 109 [7] 2001

Fig. 13. Various models of an hetero-interface. (a) coherent with coherency dislocations, (b) semicoherent with misfit or anti-co herency dislocations, (c) incoherent and (d) pseudo-semicoherent with geometrical misfit dislocations.

served this OR in the MBE-grown V/MgO system. In sum mary, this method is useful in obtaining the OR that max imizes the 3-D lattice continuity. However, it should be said that the physical basis of why the present geometrical model appears to work is not entirely clear as yet. Presumably, a maximum V corresponds to a situation where the two lat tices best accommodate each other and thus result in the lowest strain energy -and a minimum total energy -for the system as a whole. Fig. 11. Calculated V(ƒÆ) as a function of rotation angle ƒÆ around 3.3 Interfacial dislocations the <110> axis in the simple cubic lattice. The calculations were To describe the interface structure between two crystals, conducted with the parameters (a) r*=0.1a*, (b) r*=0.2a*, and and the accommodation by misfit dislocations of the lattice (c) r*=0.5a*. mismatch between them, one should, in general, distinguish between systems with small and large lattice mismatches. During epitaxial growth of a film on a substrate which is only slightly lattice mismatched, growth normally takes place in a coherent fashion, which leaves the film homogene ously strained and commensurate with the substrate.46) The resulting strain energy increases the total energy of the film compared to a relaxed, unstrained, film. As the thickness of the strained film increases, the strain energy of the film in creases proportionately. In other words, in this strained, pseudomorphic film, the strain can be described by an array of (fictitious) "coherency dislocations" each of which has a very small Burgers vector and is separated from a neighbor ing one by one lattice spacing along the interface (Fig. 13 (a)).47) Thus the strain energy in the film can be considered to be the sum total of the strain energy of coherency disloca tions. When the film thickness, h, reaches a critical value h=hc, it becomes energetically favorable for (real) "misfit" or "an ti-coherency" dislocations to be introduced at the interface, to accommodate the lattice mismatch and relax the strained film (Fig. 13 (b)).48) This process is equivalent to a cancel lation of the elastic field of coherency dislocations by anti

Fig. 12. V(ƒÆ, ƒÓ) as a function of rotations ƒÆ and ƒÓ of vanadium coherency dislocations47) and usually takes place in a grad about two orthogonal axes of MgO as shown in the inset (r*= ual fashion. In the intermediate stages, at h>hc but before 0.2a*v). complete relaxation, part of the strain is accommodated elastically by coherency dislocations while the remainder is accommodated by misfit, anti-coherency dislocations. In this intermediate stage, the anti-coherency dislocations can however, there is an extra peak at the central of the figure. cel out only a fraction of the coherency dislocations and thus The values of ƒÆ and ƒÓ at this point correspond to the OR: the film is relaxed only partially; the film is still elastically strained and contains a fraction of coherency dislocations. (110)v//(001)MgO; [100]v//[110]MgO. We have not ob S118 Special Review "Launching into The Great New Millennium"

Grain Boundary and Interface Structures in Ceramics

As the film thickness increases further, the proportion of elastic accommodation of strain (i.e., the fraction of co herency dislocations) decreases while the proportion ac commodated by misfit (anti-coherency) dislocations in creases. During this process, the spacing between misfit dis locations decreases. Eventually, when all the strain is ac commodated by misfit dislocations, all the coherency dislo cations have been canceled out by anti-coherency disloca tions; the film is now completely relaxed and the interface is " semicoherent" with a constant spacing of misfit disloca tions. Among the different mechanisms by which a misfit dislocation can be formed is the nucleation of a dislocation half-loop at the film surface and its glide on a slip-plane of the epilayer to the interface.49) The segment of the half-loop at the interface constitutes a misfit dislocation and its two ends are connected to the film surface by "threading" dislo cations. The misfit dislocation segment can expand its length by the expansion of the two threading dislocations on their (common) slip plane in the epilayer. Equations relat ing the critical thickness, hc, to the misfit parameter, f, have Fig. 14. Cross-sectional high resolution electron micrograph of been obtained by a number of authors,49) and a typical equa the V/Al2O3 interface along [1010]Al2O3//[121]v, showing a period tion is as thefollowing.50) ic array of geometrical misfit dislocations at every twelve (101)v planes. hc=Gsb[ln(hc/b)+1]/4 π(Gf+GS)(1+μ)f (10)

where Gs and Gf are shear moduli, ƒÊ is Poisson's ratio for the film, f is the misfit parameter and b is magnitude of the semicoherent" interface. The final configuration in the two Burgers vector of the misfit dislocations; the subscripts cases of low mismatch (<4-5%) and large mismatch s and f denote the substrate and the film, respectively. Note (>4-5%) then looks geometrically similar in the sense that that equations of this type usually assume a rigid non-defor in both cases. There are regions along the interface where mable substrate such that all the strain of lattice mismatch is the planes on the two sides appear to be coherent and these accommodated by the film. This equations are in general regions are separated by so-called "misfit dislocations". valid only for misfit parameters less than 4-5%. However, However, it is useful to distinguish the physical nature of when the misfit parameter is larger than 4-5%, the critical these defects in the two cases. In the low mismatch case, thickness becomes of the order of atomic dimensions and misfit dislocations are usually produced by lattice disloca the whole concept of a critical thickness loses meaning, and tions that may have a Burgers vector not necessarily parallel incoherent interfaces form (Fig. 13(c)). Thus, when the to the interface. In this case, only the component parallel to lattice mismatch is large (>4-5%), the stages of complete interface can of course play a mismatch-accommodating or partial coherency do not exist and the interface may be role. In the case of large mismatch systems, on the other expected to be incoherent with no continuity between the hand, the mismatch dislocations exist right from the start of lattice planes on the two sides of the interface. For a film deposition and their "mismatch vector" is not well de description of incoherent interfaces, corresponding to two fined, i.e., it is not an invariant vector as a Burgers vector is. lattices with a large mismatch, the concept of the CSL or, In fact, it is questionable whether one should use the term "di more generally, an O-lattice6) may provide an appropriate slocation" for a feature that while it is a "mismatch line," alternative.51) it does not have a well-defined Burgers vector. The differ A truly incoherent interface implies a complete lack of in ence between misfit dislocations (with an invariant Burgers terfacial bonding between the opposing atoms. In that case, vector) and mismatch dislocations (with a mismatch vector there is no interface adhesion and the two constituent cry that depends on the particular Burgers circuit drawn around stals simply fall apart. If there is indeed some interfacial ad the dislocation line) manifests itself in the fact that different hesion, even though it may be very weak, there must be mismatch dislocations can be observed in HREM along some localized bonding between the atoms at the two sides different viewing directions. The only restrictions, which of the interface. Assuming that the elastic constants on one are set by the requirements of HREM observation, are that side of the interface (e.g., the ceramic side) are much (i) the corresponding parallel planes on the two sides of the higher than on the other side (e.g., the metal side) , then interface be parallel to the incident electron beam, and (ii) usually a displacement of atoms in the vicinity of the inter the spacing between these planes be within the resolution of face takes place in the softer component . As a result, there the electron microscope. With this reservation in mind, we will be an appearance of coherency along some planes on the shall continue to use the term "misfit dislocation" except two sides of the interface separated by what we call "ge that we qualify the term by adding the word "geometrical" ometrical" misfit dislocations (or "mismatch dislocations") to distinguish it from a proper "dislocation" with a definable which separate these "pseudo-semicoherent" planes (Fig. Burgers vector.52),53)The terms "mismatch dislocation" and " 13(d)).52),53) Figure 14 is a cross-sectional HREM micro mismatch vector" will be also employed to define such a graph of the V/Al2O3 interface observed along the line feature. It should also be added that even for the Burg [1010]Al2O3//[121]V.52)The misfit parameter between them ers vector of a proper interfacial dislocation, the definition is is as large as about 10%. The interface between V and not very clear; it generally requires transformation of both Al2O3 is quite smooth, sharp and free of any interfacial lattices to a common coordinate system (or a common lat phases. The interface plane is parallel to (111)V and (0001) tice) and using a DSC vector to define it.54) According to Al2O3. It is obvious that geometrical misfit dislocation is in Bollmann,6) a moire pattern is closely related to the disloca troduced at every twelve (101)V planes which correspond tion network at the interface. In fact, a moire pattern from to the interval spacing of about 3nm. We call this a "pseudo two overlapping mismatched lattices ideally represents the Special Review "Launching into The Great New Millennium" S119

Yuichi IKUHARA Journal of the Ceramic Society of Japan 109 [7] 2001 position of these mismatch dislocations and forms a Wig 3) Ikuhara, Y., Ed., "Physics of Ceramics-Crystal and ner-Seitz cell. Interface-," Nikkan Kogyo Shinbun Press (1999) [in Japanese]. 4) Read, W. T., "Dislocationsin Crystals,"McGraw-Hill, New 4. Conclusion York (1953). In this paper, geometrical theories to describe grain boun 5) Kronberg, M. L. and Wilson, F. H., Met. Trans., 185, 501 daries and hetero-interfaces were reviewed together with (1949). experimental results for ceramics. Throughout the review, 6) Bollmann, W., "Crystal Defects and CrystallineInterfaces," the emphasis was on how the grain boundary and interface Spring-Verlag (1970). characters are related to their atomic structure, chemical 7) Bollmann, W., Phil.Mag., 16, 363 (1967). composition and chemical bonding state. The grain bounda 8) Ikuhara, Y. and Pirouz, P., Micros. Res. Tech., 40, 206 ry character is an important concept even in ceramics, and (1998). some of grain boundaries in ceramics can be described as 9) Stemmer, S., Pirouz, P., Ikuhara, Y. and Davis, R. F., Phys. dislocation boundaries and CSL boundaries. The idea of the Rev. Let.,77, 1797 (1996). 10) Ikuhara, Y., Watanabe, T., Yamamoto, T., Saito,T., Yoshi structure unit is very useful in considering grain boundary da, H. and Sakuma, T., Mater. Res. Soc. Sympo. Proc.,601, atomic structures, and has been successfully applied for 125 (2000). typical structural ceramics such as silicon carbide. In addi 11) Sutton, A. P. and Vitek, V., Phil. Trans. R. Soc. London, tion to the structural features, chemistry is also crucial when A309, 1 (1983). considering the grain boundaries in ceramics. Grain bounda 12) Yoshida, H., Ikuhara, Y. and Sakuma, T., Phil. Mag. Lett., ry segregation and the formation of the amorphous layer fall 79, 249 (1999). into this category, and their chemical properties strongly 13) Clarke, D. R., J. Am. Ceram. Soc.,70, 15 (1987). affect the bulk properties in ceramics. 14) Williams, D. B. and Carter, C. B., "Transmission Electron In the hetero-interface systems, O-lattice theory or lattice Microscopy," Plenum Press, New York (1996). 15) Disco, M. M., Ahn, C. C. and Fultz,B., "Transmission Elec continuity can treat the geometry between two different tron Energy Loss Spectrometry in Materials Science," TMS, constituent crystals. The hetero-interface can be classified Warrendale, Pennsylvania (1992). to a coherent, semicoherent, incoherent and pseudo-semico 16) Bandon, D. G., Acta metall.,8, 1221 (1966). herent interfaces. Misfit dislocations are usually introduced 17) Watanabe, T., Res Mechanica, 11, 47 (1984). to accommodate the lattice strain at the semicoherent inter 18) "Grain Boundary Engineering, Special Issue,"JOM, 50 (2) face in small mismatch systems, although geometrical misfit (1998). dislocations are formed at the interface in large mismatch 19) Dingley, D. J.,Scan. Elect.Microsc., 11, 74 (1984). systems. 20) Read, W. T. and Shockley, W., Phys. Rev., 78, 275 (1950). TEM is a very powerful experimental technique that al 21) Watanabe, T., Yoshida, H., Yamamoto, T., Ikuhara, Y. and Sakuma, T., in preparation. lows us to ascertain the atomic structure and chemistry of 22) Ranganathan, S., Acta Cryst.,21, 197 (1966). grain boundaries and hetero-interfaces in ceramics. In this 23) Sutton, A. P. and Balluffi,R. W., Acta melall.,35, 2177 paper, TEM results for a small angle grain boundary, CSL (1987). boundary, structure unit, segregation, amorphous bounda 24) Schober, T. and Balluffi,R. W., Phil.Mag., 20, 511 (1969). ry, hetero-interface, and interfacial dislocations were 25) Kohyama, M., Solid State Physics, 34, 803 (1999) [in provided as examples. Japanese]. In this paper, interface properties were not covered in any 26) Losch, W., Acta metall.,27, 1885 (1979). depth, but it should be noted that they can be well improved 27) McLean, D., "Grain Boundaries in Metals," Oxford Univ. by controlling the grain boundary and hetero-interface Press (1957) p. 116. structure, composition, and chemical bonding state. Our un 28) Ikuhara, Y., Thavorniti,P. and Sakuma, T., Acta. Mater.,45, 5275 (1997). derstanding of the chemical bonding state at grain boundary 29) Yoshida, H., Ikuhara, Y. and Sakuma, T., J. Mater. Res., 13, and interface is rapidly improving through advancement in 2597 (1998). first principles calculation25),55)-56) and nano-probe TEM 30) Ikuhara, Y., Yoshida, H. and Sakuma, T., Materia Jap., 37, technology.57) The next step in this field will be to design 558 (2000) [in Japanese]. and develop ceramics on the basis of the theoretical calcula 31) Ikuhara, Y., Kurishita,H. and Yoshinaga, H., Proc. 2nd Inter. tion and nano-characterization of grain boundaries and het Conf. Compo. Interfaces,Cleveland, Elsevier Sci. (1988) p. ero-interfaces.58) 673. 32) Tanaka, I.,Pezzotti, G., Matsushita, K., Miyamoto, Y. and Okamoto, T., J. Am. Ceram. Soc.,74, 752 (1991). Acknowledgements The author would like to acknowledge the 33) Tanaka, I.,Kleebe, H.-J.,Cinibulk, M. K., Bruley, J.,Clarke, collaboration of T. Sakuma, T. Yamamoto, H. Yoshida and T. D. R. and Ruhle, M., J. Am. Ceram. Soc., 77, 911 (1994). Watanabe (The University of Tokyo), Y. Kubo, T. Hirayama, T. 34) Pezzotti,G., Ota, K. and Kleebe, H.-J.,J. Am. Ceram. Soc., Suzuki, Y. Sugawara and T. Saitoh (JFCC), P. Pirouz and A. H. 79, 2237 (1996). Heuer (CWRU), C. P. Flynn and S. Yadavalli (University of Il 35) Ikuhara, Y., Suzuki, H. and Suzuki, T., Mater. Trans. JIM, linois). I also thank K. Tanaka and M. Kohyama (ONRI) for Vol. 37, No. 3, 430-34 (1996). providing Fig. 4 and useful discussions. Discussions with I. Tanaka 36) Ikuhara, Y., Kurishita,H. and Yoshinaga, H., J. Ceram. Soc. and H. Adachi (Kyoto University) are also appreciated. I ac Japan, 95, 638 (1987) [in Japanese]. knowledge M. Sakai (Toyohashi IT) who recommended me to 37) Tsurekawa, S., Nitta,S., Nakashima, H. and Yoshinaga, H., write this review paper. I finally thank H.Yoshinaga (Kyushu InterfaceSci., 3, 75 (1995). University) who first encouraged me to enter this field. 38) Porter, D. A. and Easterling,K. E., "Phase Transformations This work was supported by the Grant-in-Aid for Scientific in Metals and Alloys,"Chapman and Hall, London (1982). Research from JSPS, and PRESTO, JST. A part of this work was 39) Wechsler, M. S., Lieberman, D. S. and Read, T. A., Trans. also supported by Toray Science Foundation. Met. Soc. AIME, 197, 1503 (1953). 40) Dahmen, U., Acta Met., 30, 63 (1982). References 41) Kato, M., Wada, M., Sato, A. and Mori, T., Acta metall.,37, 1) Sutton, A. P. and Ballufi, R. W., "Interfaces in Crystalline 749 (1989). Materials," Oxford Univ. Press (1995). 42) Knowles, K. M., Smith, D. A. and Clark, W. A. T., Scripta 2) Ruhle, M., Evans, A. G., Ashby, M. F. and Hirth J. P., Ed., Met., 16, 413 (1982). "Metal -Ceramic Interfaces ," Pergamon Press, New York 43) Ikuhara, Y. and Pirouz,P., Mater. Sci.Forum, 207-209,121 (1990). (1996). S120 Special Review "Launching into The Great New Millennium"

Grain Boundary and Interface Structures in Ceramics

44) Pirouz, P., Ernst, F. and Ikuhara, Y., Solid State Phenomena, 52) Ikuhara, Y. and Pirouz, P., "Ultramicroscopy," 52, 421 59-60, 51 (1998). (1993). 45) Ikuhara, Y., Pirouz, P., Yadavalli, S. and Flynn, C. P., Philos. 53) Ikuhara, Y., Pirouz, P., Heuer, A. H., Yadavalli, S. and Mag. A., 72, 179 (1995). Flynn, C. P., Philos. Mag. A, 70, 75 (1994). 46) van der Merwe, J. H., Proc. Phys. Soc. Lond., A63, 616 54) Balluffi, R. W., Brokman, A. and King, A. H., Acta metall., (1950). 30, 1453 (1982). 47) Olson, G. B. and Cohen, M., Acta Met., 27, 1907 (1979). 55) Kohyama, M., Mater. Sci. Forum., 294-296, 685-91 (1999). 48) van der Merwe, J. H., J. Appl. Phys., 34, 117 (1963). 56) Tanaka, I., Mizuno, M., Nakajyo, S. and Adachi, H., Acta 49) Matthews, J. W., "Epitaxial Growth, Part B," Ed. by Mat Mater., 46, 6511 (1998). -thews, J. W., Academic Press, New York (1975). 57) e.g; MRS Bulletin, 22, No. 8 (1997). 50) Matthews, J. W., "Dislocations in Solids," Ed. by Nabarro, F. 58) Sakuma, T., Shepard, L. and Ikuhara Y., Ed., "Grain Bounda R. N., North-Holland Publishing Company, Amsterdam ry Engineering in Ceramics-from Grain Boundary Phenome (1979). na to Grain Boundary Quantum Structures-," Ceramics 51) Vook, R. W., Thin Solid Films, 64, 91 (1979). Transaction, Vol. 118, Am. Ceram. Soc. (2000).

Yuichi Ikuhara is an Associate Professor of Engineering Research Institute at The Univer sity of Tokyo since 1996. He received Dr. Eng. from Department of Materials Science, Kyushu University. He then joined Japan Fine Ceramics Center (JFCC) as a researcher in 1988, and was the Division Manager of the Microstructural Characterization Division at JFCC from 1993 to 1996. He was a Visiting Assistant Professor at Case Western Reserve University, USA, from 1991 to 1993. His current research is in interface phenomena and characterization, transmission electron microscopy of materials science (HREM, EDS, EELS), high-temperature ceramics, electroceramics, dislocation behavior, bicrystal ex periments, theoretical calculation, quantum device and so on. Dr. Ikuhara published about 210 technical papers in the field and has seven patents. He is JFCC Visiting Researcher, PRESTO researcher of Japan Science and Technology Corporation, Editorial Board of the Ceramics Society of Japan, Japanese Institute of Metals and Electron Microscopy Society of Japan. His e-mail address is ikuhara＠sigma. t. u-tokyo. ac. jp.