Nanowire design by dislocation technology

Progress in Materials Science 54 (2009) 770–791

Contents lists available at ScienceDirect

Progress in Materials Science journal homepage: www.elsevier.com/locate/pmatsci

Nanowire design by dislocation technology Yuichi Ikuhara * Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656, Japan Nanostructures Research Laboratory, Japan Fine Ceramic Center, Nagoya 456-8575, Japan WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

a r t i c l e

i n f o

a b s t r a c t We proposed new guidelines for designing ceramic devices with a high-density of nanowires or periodically aligned nanowires in single crystals by controlling dislocation distribution, type and composition. Insulating sapphire and YSZ single crystal were used as model systems in which high-densities of dislocations and periodically aligned dislocations were introduced by high-temperature compression tests and fabrication of bicrystals with low-angle grain boundaries. The electron and ion conductivities were measured for the dislocation introduced crystals, and it was concluded that the proposed techniques are very useful for giving new functions to any single crystal. Ó 2009 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dislocation introduction method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. High-temperature compression test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Fabrication of low-angle grain boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction of high-density dislocation into sapphire and fabrication of nanowire . . . . . . . . . . . . . . 3.1. High-density dislocation introduction using high-temperature compression method . . . . . . . 3.2. High-resolution TEM characterization of the dislocation core structure . . . . . . . . . . . . . . . . . . 3.3. Fabrication of metal nanowire and the electric properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Fabrication of periodic grain boundary dislocation using bicrystal . . . . . . . . . . . . . . . . . . . . . . 3.5. High-resolution STEM characterization of the GB dislocation core structures . . . . . . . . . . . . . 3.6. Periodically aligned conductible nanowires in sapphire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

771 772 772 773 773 773 774 777 779 781 784

* Address: Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656, Japan. Tel.: +81 3 5841 7688; fax: +81 3 5841 7694. E-mail address: [email protected] 0079-6425/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.pmatsci.2009.03.001

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

4.

5.

Introduction of high-density dislocation into zirconia and ion conductivity . . . . . . . . . . . . . . . . . . . . . 4.1. High-density dislocation introduction by high-temperature compression method . . . . . . . . . 4.2. Grain boundary dislocations in YSZ bicrystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

771

786 786 788 790 790

1. Introduction Since a low dimensional quantum structure such as a quantum wire and a quantum dot has received attention because it shows completely different properties from the ones of the bulk even with the same crystal structure and the composition, a lot of studies have been conducted so far [1–3]. To prepare low dimensional quantum structures like these, the surface or interface of the materials are often used. For example, various methods such as a method to use the Scanning Tunneling Microscope (STM) [4], a method to use a surface step of the crystal [5], and ion implantation to the interface [6] have been tried. However, with every these methods, since a low dimensional structure is formed just on the surface or interface, some difficulties often arise to apply them to actual devices. On the other hand, if the low dimensional structures can be confined in the solid, not only it has a great advantage from the point of device applications and the handling but also specific interaction at the interface in the solid/quantum structure is expected; there is a possibility that it can develop to the creation of new solid devices provided with unique physical properties. In this paper, a method to form a high-density or periodic quantum nanowire by controlling the distribution of ‘‘dislocation”, which is a line defect in the crystal, is described. Dislocation is a line defect, with which the atomic bond on the lattice plane is cut, and there is a bonding defect line in its core region; thus, a large elastic strain field is formed around it [7–11] and the dislocation itself has a different electronic state from the one in the crystal, having potential to express peculiar physical properties. Shockley has pointed out that a bonding defect line aligned with the edge dislocation brings about one-dimensional electron conduction for diamond [12]. After that, the electrical conduction characteristics of the samples, to which dislocation was introduced by plastic deformation at various conditions, were reported for various semiconductors such as CdS [13–16], Si [17], Ge [18], and SmS [19]. Elbaum [13] has found that as much as about 108 times of the anisotropic difference in electric conduction was generated in the plastically deformed sample of a CdS crystal. Furthermore, Döding and Labusch [15,16] also have performed the same experiments systematically and showed that the electric conductivity in the direction parallel to the introduced dislocation line is significantly high compared with the one in the direction perpendicular to it. From a series of these studies, it was demonstrated that the dislocation in the semiconductor can be paths for electric conduction. On the other hand, Little [20] has proposed a model (the Excitonic Superconducting), which shows superconduction even at high-temperature, if one-dimensional metal element chains are formed in the organic compound. Furthermore, Fukuyama [21] has pointed out a potential of the expression of the excitonic superconducting by forming one-dimensional metal conduction paths along the dislocation of the semiconductor and the insulator crystal in the same way. However, as far as the author knows, there has been no report that second element was doped along the dislocation intentionally to fabricate dislocation nanowire with the dopant in its core, and to provide special properties in matrix materials. This is probably due to the fact that such studies so far were mainly performed for semiconductor crystals and after that, the researches regarding the physical properties of dislocation have not been paid much attention. In addition, the difficulty in the distribution control technology of dislocation, the atomic-level microstructure analysis, and the evaluation of electrical properties from a single dislocation is believed to have been a contributory factor as well. The recent resolution of the microstructural characterization and evaluation technology has improved drastically; for example, using the Scanning Transmission Electron Microscopy (STEM), by combining it with the Energy Dispersive Spectroscopy (EDS) or the

772

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

Electron Energy Loss Spectroscopy (EELS), chemical composition and bonding state analyses are possible to be performed with the probe diameter of 0.5 nm or less. The resolution of Scanning Probe Microscope (SPM) is already less than 1 nm as well. If these characterization technologies are utilized successfully, a quantitative evaluation of dislocation itself and the structure, the composition, the chemical bonding state, the properties, etc. of nanowires along the dislocations are expected to be possible. In this paper, recent studies are reviewed to focus on the introduction of high-density and periodically aligned dislocations to oxide ceramics and their properties, in which I will show that electric conductivity and ionic conductivity can be provided by introducing dislocations into the insulating crystals. As model systems, we selected insulating sapphire and Y2O3 Stabilized Zirconia (YSZ) single crystal, expected as an ion conductor, respectively, to introduce dislocations by various methods [22–33]. We will show the results such as fabrication method of the high-density nanowires with which the dislocation distribution is controlled, the diffusion method of the metal elements to the dislocation, and fabrication method of periodically aligned nanowires by the bicrystal fabrication method. With these methods, it is possible to form high-density quantum nanowires or periodically aligned quantum nanowires in the crystalline solid. Furthermore, since there are innumerable combinations of crystals, to which dislocation is introduced, and the atomic species, doped by diffusion, creation of unprecedented nanowires with completely new properties is expected as well; we believe that it will lead to the design and creation of new, highly functional nano device materials in future. 2. Dislocation introduction method 2.1. High-temperature compression test High-temperature compression test is one of the effective methods to introduce dislocation into the crystalline solid. In this study, since we intend to arrange linear dislocation with high-density, experiments using single crystals are performed to activate the primary slip. In this case, consideration regarding the slip system is required; for example, it is recommended to select the compression direction, which makes the Schmidt factor of the target primary slip system the maximum. Fig. 1 shows a schematic view of the dislocation introduction method by the compression test. On the other hand, in case that the application as a device is considered, although the introduction of high-density of dislocations is effective for the device, attention should be taken because if the strain amount is too much, it makes the secondary slip system active, making the dislocations are clasped intricately. Accordingly,

Compression

Dislocation

Single Crystal

Fig. 1. Schematic of compression test to introduce high-density of dislocations.

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

773

Fig. 2. Schematic of a simple low-angle grain boundary (misorientation angle h, and dislocation spacing h).

for the crystals with high-symmetry like cubic structure, even if the Schmidt factor of the primary slip system is the maximum, some ideas like the shift of the compression axis slightly to make the particular primary slip system active is required since many equivalent slip systems are present in the cubic system. Furthermore, the density and the substructure of the dislocations introduced by the mechanical test strongly depend on the deformation conditions such as temperature and a strain rate as well. For example, to obtain a high-density dislocation, deformation at low temperature and with the highstrain rate is required. However, in case that the target crystals are ionic or covalent bonded, the crystals are easily fractured under such conditions. It is therefore needed to find the optimum deformation conditions, under which fracture does not occur, by systematic deformation tests. As described above, in order to obtain the one-dimensionally arranged, high-density dislocations, the optimum control of the high-temperature deformation conditions, the compression direction, and the strain amount is required. 2.2. Fabrication of low-angle grain boundary Fabrication of the low-angle grain boundary is effective method to arrange dislocations periodically as well. Since the misorientation angle of the two crystals is small, the low-angle grain boundary compensates the misorientation angle by introducing periodic array of dislocations. Fig. 2 shows a schematic view of a simple low-angle grain boundary. If the edge dislocation with Burgers vector b is periodically lined at intervals of h along the low-angle grain boundary with the misorientation tilt angle 2h, the following relationship is obtained between h, h, and b [34]:

2h ¼ tan1 bh ’ b=h

ð1Þ

Accordingly, if the low-angle grain boundary can be fabricated by bonding the two single crystals, it is possible to arrange dislocation linearly with regularity along its bonded interface. The bicrystal method is thus useful to introduce periodically located dislocations. In this case, it is also possible to control the periodicity of the dislocations by controlling the misorientation tilt angle, and to make the dislocation arrays with the different Burgers vector by bonding the interface of the different directions as well. 3. Introduction of high-density dislocation into sapphire and fabrication of nanowire 3.1. High-density dislocation introduction using high-temperature compression method Here, the method to introduce high-density dislocations into sapphire is described [22,25]. As the primary slip systems of sapphire, the basal slip ((0 0 0 1), b = 1/3h1 1 2 0i) and the prismatic plane slip

774

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

({1 1 2 0}, b = h1 1 0 0i) are known, but the basal slip system is dominantly activated at high-temperature above 700 °C [35,36]. In order to form the dislocations by introducing only the basal slip, deformation was performed along the compression axis with the 45° tilted direction to both the basal plane and the slip direction so that the Schmidt factor is 0.5. This is the condition where other slip systems do not occur easily from the fact that sapphire has a rhombohedral structure. To introduce dislocations into the crystal with high-density, in general, deformation at low temperature with the high-strain rate is recommended. However, in case of the compression deformation to the above described direction, for example, with 10% deformation under the conditions of the temperature of 1200 °C and the strain rate of 1.0  105 s1, many R (rhombohedral) twins are formed to partially fracture the sample. However, if it is deformed at 1400 °C with the strain rate of the same 1.0  105 s1, although only the basal slip is activated and it shows the uniform plastic deformation even with 10% deformation, the dislocation density of this case will be about 108 cm2. In case that after deformation at 1400 °C to introduce many mobile dislocations into the crystal, if it is deformed again at 1200 °C, it plastically deforms uniformly without the formation of twin crystals even with the 10% deformation [25]. In this case, the dislocation density increases about more than 10 times compared with that of the deformation only at 1400 °C. By the high-temperature deformation with two steps like this, it becomes possible to introduce about 109–1010 cm2 of the dislocation density into sapphire. Fig. 3a shows the TEM bright field image of the dislocation, which was introduced in this way, viewed from the [0 0 0 1] direction (the direction perpendicular to the slip plane) [22]. It is recognized in the figure that although the introduced dislocations is about aligned to the constant direction (parallel to the [1 1 0 0] axis), it still shows rather wavy shape. As a result of the g  b analyses, it is confirmed that almost all of these dislocations are provided with the Burgers vector of b = 1/ 3[1 1 2 0]. However, to form one-dimensional nanowires, these dislocations are required to be arranged linearly. In this study, heat treatment, with which the surface effect is utilized, was performed to linearize the wavy dislocations in the crystal [22,25]. At first, the sample, to which high-density dislocations were introduced by the two step compression test, was sliced in the direction perpendicular (parallel to the (1 1 0 0) plane) to the basal plane to about 10 lm in thickness to make it plates and both surfaces were mirror polished. Next, this plate shape sample was filled in the high-purity alumina crucible and 30 min of heat treatment was performed at 1400 °C in air. Fig. 3b is a TEM bright field image of the sample, to which heat treatment like this was performed, viewed from the [1 1 0 0] direction perpendicular to the (1 1 0 0) plane. In this image, a lot of dot contrasts are observed; they correspond to the dislocations arranged perpendicular to the paper plane [22]. Fig. 3c is a TEM bright field image of the sample viewed from the direction ([4 4 0 1] direction) slightly tilted around the [1 1 2 0] rotation axis in the same area in (b) [22]. It is recognized that the contrast, observed as dots in (b), is the linearly arranged dislocations. Linearization of dislocations by this heat treatment is believed to be caused by the strong image force [7,8,11] due to the surface effect. 3.2. High-resolution TEM characterization of the dislocation core structure As for the basal slip, Kronberg first predicted [37] that a basal dislocation with b = 1/3h1 1 2 0i would dissociate into two half partial dislocations by glide as the following reaction:

1=3h1 1 2 0i ! 1=3h1 0 1 0i þ 1=3h0 1 1 0i

ð2Þ

But the dissociation on the (0 0 0 1) basal plane caused by glide has not been observed yet. As pointed out by Phillips et al. [38], the separation distance by the glide dissociation is considered to be too narrow to distinguish by the conventional electron microscopy techniques. On the other hand, Lagerlöf et al. [39] confirmed the dissociation of a basal dislocation by self-climb using the weak-beam dark field technique. According to their results, a basal dislocation dissociated into the two partials with b1 = 1/3h1 0 1 0i and b2 = 1/3h0 1 1 0i perpendicularly to the (0 0 0 1) slip plane. But it remains unclear whether the glide dissociation takes place or not since the separation distance between the two partials is seemingly very narrow. Thus, it is needed to reveal the core structure of a basal dislocation in order to clarify this point. Meanwhile, High-Resolution Transmission Electron Microscopy (HRTEM) is one of the most powerful techniques to analyze microstructure at atomistic level. Here, a basal

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

775

Fig. 3. TEM bright field images showing the dislocation structures formed by the two-stage deformation technique and the post-annealing process [22]. (a) The image taken in a sapphire deformed up to e = 5% at 1400 °C and subsequently up to e = 10% at 1200 °C. The incident beam is parallel to the [0 0 01] direction. (b) The image along [1 1 0 0] taken after the annealing of plate specimens cut out along (1 1 0 0) plane. (c) The image along [4 4 0 1] taken with slightly tilting the beam direction around the axis of [1 1 2 0] from the same area of the image in (b).

dislocation was directly observed by HRTEM from the direction parallel to the dislocation line in order to clarify the atomic structure of the basal dislocation in sapphire. Fig. 4a shows a typical HRTEM image around the basal dislocation observed along the [1 1 0 0] parallel to the dislocation line [36]. It is noted that the two disconnected contrasts clearly appeared on the HRTEM image, which implies that the dislocation dissociated into two partial dislocations. Burgers

776

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

(a)

(b) [1120]

[0001] [1120] [1100]

2nm

Observation [1100]

Fig. 4. (a) Typical HRTEM image taken from the edge-on basal dislocation. Two lattice discontinuity are clearly observed from the Burgers circuits described in the image. (b) A schematic of the atomic arrangement projected along the [0 0 0 1] direction of a-Al2O3, in which large open circles, small fill circles and small open circles represent oxygen atoms, Al atoms and Al vacancies, respectively. This schematic well explains that the lattice discontinuity of 1/6[1 1 2 0] is present at each center of two Burgers circuits. The vector of 1/6[1 1 2 0] corresponds to the projection of the two partials with b1 = 1/3h1 0 1 0i and b2 = 1/3h0 1 1 0i.

circuits are schematically described around each partial and also two partials. Fig. 4b shows a schematic of the atomic arrangement projected along the [0 0 0 1] direction of a-Al2O3, in which large open circles, small fill circles and small open circles represent oxygen atoms, Al atoms and Al vacancies, respectively. The HRTEM image in (a) is observed along the heavy arrow in (b). The size of the perfect dislocation thus corresponds to the fine arrow perpendicular to the [1 1 0 0] observation direction ([1 1 2 0] direction), and the size of partials correspond to the two thick arrows tilted by 30° from the [1 1 2 0] direction. In the figure (a), the two circuits have clear lattice discontinuity in their centers, and the edge segment on the (1 1 0 0) plane is estimated to be 1/6[1 1 2 0]. Here, the b1 and b2 of the two half partials, which were produced from a basal dislocation according to the reaction (2), also have the edge segment of 1/6[1 1 2 0] on the (1 1 0 0) plane. Thus, it was reconfirmed that the basal dislocation dissociate into two half partials, as reported in the past [38,39]. The two partials separate with a distance of 4.7 nm along the [0 0 0 1] in Fig. 4a [36]. Defining ‘the dissociation by self-climb’ as the dissociation perpendicular to the (0 0 0 1) slip plane, which can be caused by the climbing with diffusion, it can be said that the basal dislocation is dissociated by self-climb as suggested in the past [38,40]. On the other hand, in general, ‘the dissociation by glide’ means the dissociation on the slip plane by dislocation glide. Here, the two partials were located at the nearest neighbor position along the [1 1 2 0] direction, which is parallel to the (0 0 0 1) slip plane. That is, the dissociation by glide is not developed in the basal dislocation. Thus, it can be concluded that the dissociation by self-climb is developed but the dissociation by glide is not in a basal dislocation, on the relaxed condition where compressive stresses are removed and the motion of the dislocation is ceased. In addition, they were located adjacently to each other along the [1 1 2 0]. Here, the spacing between (1 1 2 0) layers is 0.235 nm, which corresponds to the projected spacing of cation or anion sublattice along the [1 1 2 0] direction. Thus, the two half partials are located at the nearest neighbor position along the [1 1 2 0], and in addition no stacking fault is formed if the two partials exists on the same (0 0 0 1) plane. Fig. 5a and b shows schematic illustrations of cation sublattice, which are viewed from the [0 0 0 1] direction [36]. In the figure (a), the Burgers vectors of a perfect dislocation with b = 1/3[1 1 2 0] and two partials with b = 1/3[1 0 1 0] and b = 1/3[0 1 1 0] are shown, and obviously there are two kinds of stacking sequences along the [1 1 2 0] direction as indicated with a and b, respectively. In the figure (b), the 1/3[0 1 1 0] stacking fault on the (1 1 2 0) plane is shown, and it must be noted that this fault involves only the cation sublattice since the vectors belonging to the b1 and b2 such as the 1/3[0 1 1 0] correspond to perfect vector in the idealized anion sublattice. As seen in Fig. 4a, the dissociation of a basal

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

777

Fig. 5. Atomic structure of the cation sublattice projected along the [0 0 0 1] direction, indicating the perfect cation sublattice in (a) and the 1/3[0 1 1 0] stacking fault formed on the (1 1 2 0) plane in (b). These structures can be constructed by the stacking sequence of a and b. The filled and gray circles represent Al ions upper and lower between two oxygen layers, respectively, while the open circles correspond to the unoccupied octahedral sites. (c) A schematic illustration showing an actual structure in the basal dislocation [36].

dislocation is caused by self-climb along the [0 0 0 1] direction. Thus, a stacking fault is formed on the {1 1 2 0} climbing plane between the two partials. In general, a fault vector of a stacking fault usually exists on the fault plane since it is needed to maintain the lattice continuity outside the stacking fault. But, the Burgers vectors of the two partials do not exist on the climbing plane. However, owing to the threefold inversion symmetry of sapphire, it can be said that the stacking faults with the fault vectors belonging to b1 such as the 1/3[1 1 0 0] are equal in structure. In the same way, the faults with b2 are equal to that with the 1/3[1 1 0 0]. Thus, just two type of stacking faults with fault vectors of b1 or b2 can be formed on the {1 1 2 0} climbing plane between two partials. On the other hand, the 1/3[1 1 0 0] fault and the 2/3[1 1 0 0] fault are equivalent in structure on the (1 1 2 0) plane, as reported by BildeSørensen et al. [41]. In this respect, it is obvious that these two faults become same by the reflection operation to the (1 1 2 0) fault plane. Here, note that it is needless to consider anion site since the position of the anion reverts by the 1/2[0 0 0 1] translation. Moreover, the 2/3[1 1 0 0] fault and the 1/ 3[1 1 0 0] fault are equal on the (1 1 2 0) plane since [1 1 0 0] (or [1 1 0 0]) are perfect vectors in sapphire. That is, the 1/3[1 1 0 0] fault and the 1/3[1 1 0 0] fault are equivalent, as noticed by Phillips et al. [38]. Thus, stacking faults with fault vectors of b1 or b2 are equivalent in structure on the {1 1 2 0} plane according to the symmetry of sapphire. As a consequence, the stacking faults on the {1 1 2 0} plane between the two partials are essentially always equivalent in structure. Considering the circumstances mentioned above, an actual structure of a basal dislocation on the relaxed condition where the external stresses are removed is schematically illustrated in Fig. 5c [36]. Here, the [0 0 0 1] view of the stacking fault in the figure corresponds to the fault in (b). It was confirmed that a basal dislocation dissociates into two half partials with the Burgers vectors of b1 and b2. The partials separate with a certain distance along the [0 0 0 1] direction due to the dissociation by self-climb. As a result, only one type of the stacking fault with fault vectors of 1/3h1 0 1 0i (or 1/3h0 1 1 0i) is formed on the {1 1 2 0} plane between the two partials. On the other hand, the dissociation by glide is not developed in a basal dislocation. 3.3. Fabrication of metal nanowire and the electric properties By above described two step deformation and heat treatment, it was possible to arrange straight dislocations with high-density into sapphire. Since it is expected that the dislocation itself shows different properties from the ones of the bulk, the dislocation can be regarded as nanowire already as

778

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

(a)

Deposited metal (Ti)

Sapphire

Dislocation

(b)

Sapphire

Ti enriched nano-wires Fig. 6. Concept illustrations showing fabrication processes of one-dimensional nanowires. (a) Metallic Ti film deposited on the sapphire plate containing straight dislocations and (b) Ti atoms segregate in the vicinity of the dislocations by the rapid pipe diffusion process during the heat treatment.

well. Here, moreover, for example, by diffusing heterogeneous metals along the dislocation, nanowires composed of the doped metal elements are possible to be obtained. Around the dislocation, a strain field exists; under its influence, it is known that the phenomena such as Cottrell effect [8,42] which induces segregation of solute elements, and the pipe diffusion [43,44], with which the diffusion rate becomes faster than the one in the bulk, occurs. Utilizing the characteristics of dislocation like these, it is possible to diffuse various metals along the dislocation. We have tried diffusion of various metal elements; here, the results of the metal Ti diffusion [22] are introduced. In the meantime, it is reported that the pipe diffusion of Ti along the dislocation in sapphire is 106–107 times faster than the one in the bulk [44]. Fig. 6 shows a schematic of the method to diffuse Ti element along the dislocations [22]. At first, as shown in figure (a), a film of metal Ti was deposited by the vacuum deposition method on the plane (in this case, the (1 1 0 0) plane), into which dislocation lines are penetrated. Next, in order to form the Ti rich nanowire like the one in Fig. 6b by diffusing Ti along the dislocation, 2 h of heat treatment was performed at 1400 °C in an Ar atmosphere to the sample with which the metal film was deposited. After the heat treatment, remained Ti on the surface was removed by such as mechanical polishing and the sapphire substructure was observed with the TEM. The result was that it showed almost the same dislocation substructure to the ones in Fig. 3b and c and there were no drastic change in the distribution or the arrangement of dislocations by this heat treatment. Fig. 7a and b shows EDS spectra obtained from a basal dislocation and an area 20 nm off the dislocation in the plate, respectively, after the infiltration process [22]. It should be noteworthy that the Ti Ka-peak was clearly observed in Fig. 7a, whereas that was not found in Fig. 7b. Fig. 7c also shows distribution of elements taken across the dislocation by line EDS analyses. It can be seen that Ti atoms were localized in a region of about 5 nanometers around the dislocation. Moreover, the amount of Al decreased in that region in an opposite way of Ti. This indicates that Ti atoms infiltrated along the dislocations from the plate surface, and that Ti atoms intensely segregated throughout the dislocation lines. That is, nanometer-sized wires enriched by Ti, namely, ‘‘Ti-enriched nano-wires”, were formed along high-density of unidirectional dislocations in the sapphire plate. The striking infiltration behavior of Ti atoms along the dislocations would be attributed to the rapid pipe diffusion in sapphire, which was found to be faster by 106–107 times than bulk-diffusion [44]. In addition, ionic radii of Ti ions (such as Ti3+ or Ti4+) are by 30–50% larger than that of Al3+ ions, depending on the charge states

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

779

Fig. 7. Composition and chemical state analyses around the unidirectional dislocations after the Ti infiltration process [22]. (a) and (b) show EDS spectra obtained at a dislocation and an area 20 nm off the dislocation, respectively. (c) EDS line profile across the dislocation, indicating that Ti atoms intensely segregate along the dislocation to form a ‘‘Ti-enriched nanowire”. (d) The ELNES spectrum of Ti–L2,3 edge obtained from the nanowire. (e) The reference profiles of NEXAFS in Ti2O3 and TiO2 [46].

of Ti [45]. This difference in ionic size likely gives rise to an attractive interaction between Ti and the dislocation due to Cottrell effect. In this case, it is expected that Ti ions are present as substitutional solutes for Al, not as interstitial solutes, because Ti ions with the larger ionic size are more favourably located at the Al sites. As a result, Ti infiltrates into a crystal along the dislocation and remains in the vicinity of it. To investigate electronic states of Ti in the nanowires, electron-energy loss near-edge structures (ELNES) of Ti L2,3-edge were also measured as shown in Fig. 7d. As a reference, near-edge X-ray absorption fine structure (NEXAFS) of Ti L2,3-edge in Ti2O3 and TiO2 [46] are displayed in Fig. 7e. The ELNES spectrum is comparable with those of NEXAFS because both spectra reflect local atomic structures and partial density of states for Ti in respective materials. As seen in the figures, spectrum from the Ti-enriched nanowire shows four separated peaks, which was similar to that of TiO2 rather than Ti2O3. This means that valance state of Ti in the nanowire is closely similar to Ti4+ in TiO2. Here, TiO2 itself is an insulator (<1010 X1 cm1). However, Ti in the nanowires should be slightly reduced to form TiO2x like bonding state since the heat treatment for infiltration of Ti was conducted in a reduced atmosphere (1400 °C in Ar) [47]. Accordingly, the nanowires are considered to include both Ti4+ and a small amount of Ti3+. In addition, TiO2x containing Ti3+ ion is known to exhibit electronic conduction, which can be classified into semiconductors [48]. Thus, the present Ti-enriched nanowires could exhibit unusual electric conduction even inside sapphire insulator. In order to evaluate the electric characteristics of the above described nanowire, evaluation of conductivity was performed using the contact current mode of the AFM. During probe scanning, the measurement was performed applying the voltage of 1–10 V. Fig. 8 shows the current image of the scanning in the case of applied voltage of 10 V and the measurement region of 5  5 lm [22]. From this image, it is recognized that the current value rapidly increases discretely at the particular site only. Since this distribution is almost equal to the introduced dislocation distribution, it is suggested that current is flowing along these nanowires. Furthermore, by rough estimate of current, it has been revealed that the current flowing along the nanowires reached as much as 1013 times or more of the one in sapphire. In this way, it has become possible to form conductive nanowires with high-density arranged linearly in sapphire, an insulator. Despite that innumerable nanowires are introduced in this sample, it is still provided with perfect transparency equivalent to the one of sapphire as well. Applications as a new functional device are therefore expected in the future. 3.4. Fabrication of periodic grain boundary dislocation using bicrystal By bonding two pieces of sapphire, the bicrystals provided with the low-angle grain boundary of 0 to 10° of the misorientation angle around the [0 0 0 1] axis were prepared [26]. Before bonding, each single crystal was cut in the given direction and the surface was polished with diamond paste up to

780

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

Fig. 8. Current mapping image obtained from the sapphire plate by using the contact current mode of APM. It can be seen that electrons drastically flow at the localized positions. The separation distance between the positions is about 450 nm, which corresponds to the average separation distance of the dislocations that were introduced in the sapphire plate. This suggests that conductible one-dimensional nanowires bundle is formed in sapphire insulator.

mirror finish; after that, mechanochemical polishing was performed using colloidal silica to obtain the flat surface at the atomic level. A bicrystal was prepared by fixing these two crystals to conduct diffusion bonding. The bonding conditions in this case were under a load of 0.2 MPa, at 1500 °C, and 10 h. Fig. 9 shows bright field images for (a) 2°, (b) 6° and (c) 8° tilt grain boundaries [26]. A periodic array of dislocations can be seen for all three grain boundaries, and the spacing between dislocations decreases with increasing tilt angles. Fig. 10a is the bright field image of the [0 0 0 1] 2° tilt grain boundary. From this figure, it is recognized that dislocations are formed along the grain boundary with a period of about 13 nm. Fig. 10b is a magnified image of this region. It is recognized that the dislocation contrast has been made of two pairs as shown by the arrows. Fig. 10c shows the HRTEM image, with which this region is further magnified [26]. From this figure, the paired dislocations can be apparently identified even with the high-resolution image. To analyze the atomic structure of this pair dislocations, the Burgers circuit was made around each dislocation; as a result, it was recognized that each dislocation has the 1/3h1 0 1 0i type Burgers vector as shown in Fig. 10d. It suggests that the dislocations formed here are not perfect dislocations, but partial dislocations. In other words, it is expected that perfect dislocations have dissociated to two partial dislocations in the reaction described in Eq. (2) in Section 3.2. The top figure shown in Fig. 10e is the low-angle grain boundary model formed by perfect dislocations. But, experimental results revealed that the actual structure is like shown in the bottom figure. It is recognized in the figure that stacking faults (in this case, the faults on the (1 1 2 0) plane) of the distance d1 are formed between partial dislocations, and partial dislocation pairs exist with the period of the distance d. It has been confirmed that the above described pairs of partial dislocations are introduced periodically in all the angle range of 0–10°, observed this time. Considering the balance between the repulsive force of each dislocation and the attractive force due to the stacking fault energy, the relationship among the misorientation angle, the separation width, and stacking fault energy can be analyzed quantitatively. Similar low-angle grain boundary has been reported to be fabricated by utilizing the grain growth at single crystal–polycrystal interface [49]. These arguments have been described in detail elsewhere [26]. It should be noted in this section that by controlling the misorientation angle, the dislocation interval can be precisely controlled in the nanometer order as well. It means that with the method using a bicrystal, it is possible to arrange straight dislocations located periodically along a particular plane with high-density. The nanowire design using dislocation arrangement like this will open up so called ‘‘Dislocation Technology”.

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

781

Fig. 9. Bright field TEM images for (a) 2°, (b) 6° and (c) 8° low-angle tilt grain boundaries. Note that dislocations are periodically introduced along the grain boundaries [26].

3.5. High-resolution STEM characterization of the GB dislocation core structures In order to investigate the grain boundary dislocations formed on the different plane and around different rotation axis, sapphire bicrystal with a [1 1 0 0] 2° tilt grain boundary were also fabricated using diffusion bonding [31,50,51]. Fig. 11 shows a typical HRTEM image obtained from the GB dislocation. In the image, the pair lattice discontinuities are observed, which is similar to the pair partials formed in the [0 0 0 1] low-angle GB. It was found from the Burgers circuits in the figure that the total edge component of the lattice discontinuities is 1/3[1 1 2 0], which corresponds to the Burgers vector of the perfect basal dislocation that is expected to be formed for compensating the misorientation angle between two adjacent crystals. As mentioned in Section 3.2, it is known that the basal dislocation dissociates into two partial dislocations [41,36,40] according to Eq. (2). The size of the edge component of each lattice discontinuity in Fig. 11 is 1/6[1 1 2 0] and corresponds to the projection of the two partial dislocations with b = 1/3[1 0 1 0] or b = 1/3[0 1 1 0]. It is thus considered that the lattice discontinuities from the pair are due to the dissociated basal dislocation, which were formed for compensating the given tilt angle of the grain boundary as expected from the orientation relationship of the fabricated bicrystals. It is considered that this dislocation structure is exactly the same as the basal dislocation in the crystal lattice. We applied recent Scanning Transmission Electron Microscopy (STEM) technique to quantitatively determine the dislocation core structures for the basal dislocation in the present specimen. STEM method is the technique to scan the electron probe, which is focused down to 0.2 nm or less, on the sample and collect the scattered electrons in each probe position by the Annular Dark Field (ADF) detector in the bottom of the sample to form the image on the monitor by synchronizing with the scanning probe. In this case, the atomic resolution image can be obtained by focusing the electron

782

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

Fig. 10. (a) Bright field TEM images and (b) magnified bright field image for 2° tilt grain boundary. Note that dislocations form pair contrast as indicated by the arrows. (c) HRTEM image for 2° tilt grain boundary, indicating the formation of pair dislocations along the boundary as indicated by the arrows. (d) Burgers circuits around the pair dislocations and individual dislocation, indicating that a dislocation is dissociated into two partials to form a stacking fault between them. (e) Dislocation models of the [0 0 0 1] low-angle tilt grain boundaries with (upper) perfect dislocations and (bottom) partial dislocations plus stacking faults between them in Al2O3. The grain boundary plane is (1 1 2 0) for both cases. In the actual model (upper), d1 represents the length of stacking fault between two partials, d2 the length of coherent region, and then, d is d1 + d2.

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

783

Fig. 11. A typical HRTEM image of the partial dislocations in the [1 1 0 0] 2° low-angle grain boundary. It is seen from the Burgers circuit that the total size of the lattice discontinuity is 1/3[1 1 2 0], which is the perfect translation vector of the corundum structure, and that the size of each lattice discontinuity is 1/6[1 1 2 0].

probe down to below the atomic column interval. In addition, the image contrast corresponding to about the square of the atomic number Z can be obtained by detecting the electrons scattered to the high angle (High Angle ADF (HAADF)-STEM) [52]. Contrast like this is called Z-contrast as well, making the observation of the distribution of single atomic column possible in the region where the local composition is changed. Since sapphire is composed of Al and O, to understand its dislocation core structure at the atomic level, an analysis including the structure of the sublattice of oxygen, a light element, is required. Fig. 12 shows (a) atomic structure model of a sapphire crystal viewed from [1 1 0 0] direction, (b) HAADF-STEM and (c) Bright Field (BF)-STEM image observed along the [1 1 0 0] direction [33]. In this case, BF and the corresponding HAADF image were obtained from the same observation area simultaneously. As shown in the crystal structure model, the atomic columns of Al and O can be distinguished

Fig. 12. (a) Atomic structure model of sapphire crystal projected along the [1 1 0 0] direction, and (b) HAADF-STEM and (c) BFSTEM images of a sapphire single crystal viewed from [1 1 0 0] direction [33].

784

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

Fig. 13. BF-STEM images of partial core structures of a dissociated basal dislocation (b1 and b2), indicating that each core terminates at Al and O, respectively [33].

from the present incident axis. In the HAADF-STEM image shown in (b), the position of the O columns and the Al columns is apparently discriminated. In this case, although the S/N ratio is lower compared with the one of the BF-STEM image of (c), the atom position can be directly determined because it is the image under incoherent conditions. On the other hand, although the S/N of the BF-STEM image is good, it is optically equivalent to the image of the high-resolution transmission electron microscopy (HRTEM) due to the reciprocity theorem. Therefore the contrast varies widely according to the defocus and the sample thickness. Accordingly, by simultaneously taking the BF image and the HAADF-STEM image to compare their contrast, the correspondence of the contrast of the BF-STEM image and the atom position can be directly determined. Under this observation condition, the position of the bright contrast in the BF-STEM image is confirmed to directly correspond to the atomic column position. In this way, the simultaneous observation of both HAADF- and BF-STEM images enables us to determine the atomic species including light element such as oxygen. The basal dislocation of sapphire has the Burgers vector of b = 1/3h1 1 2 0i as mentioned above. However, it was confirmed in the HRTEM image that the dislocation core climbed and dissociated along the [0 0 0 1] direction to form partial dislocations of b1 = 1/3h0 1 1 0i, b2 = 1/3h1 0 1 0i and stacking faults on the {1 1 2 0} plane. Fig. 13 shows the BF-STEM image of each dislocation edge for the dissociated partials [33]. In the BF-STEM image, since the oxygen column and the aluminum column can be identified, the atomic columns at the dislocation edge can be determined directly. As apparent from the experimental image, two partial dislocations terminate at the aluminum and the oxygen atomic columns, respectively. It is noted that each partial dislocation core has the structure with local composition change of aluminum-rich or oxygen-rich from the stoichiometric ratio. In case of ionic crystals, the structure like this has been considered to be energetically unstable so far. But, the present results demonstrate that the nonstoichiometric local structure can exist. However, if the perfect dislocation between the partial dislocations is considered altogether, the stoichiometric ratio is satisfied in total, which suggests that the stoichiometric is maintained when the basal dislocation moves. The glide mechanism of the basal dislocation of sapphire can be considered by the present direct observation [33]. It will bring a great breakthrough to the study of ceramic dislocation in future. It is also expected that the STEM observation, which combines the BF image with the HAADF image, will become a useful technique for an atomic resolution characterization in future. 3.6. Periodically aligned conductible nanowires in sapphire We have systematically fabricated sapphire bicrystals with misorientation angles from 0° to 15° around the [1 1 0 0] axis [31,50]. Fig. 14 shows a bright field TEM image for the grain boundary with

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

785

Fig. 14. Bright field TEM image for the grain boundary with the misorientation angle of 0.4° with the incident beam parallel to (a) [1 1 0 0] edge-on direction and (b) [1 2 1 0] direction which is tilted from the edge-on direction to confirm that a dot contrast in (a) corresponds to a straight dislocation (b).

the misorientation angle of 0.4°. In the image, the observations were made along (a) [1 1 0 0] edge-on direction and (b) [1 2 1 0] direction which was tilted from the edge-on direction to confirm that a dotlike contrast in (a) corresponds to a straight dislocation (b). It is seen that the dislocations are periodically introduced with an interval spacing of 90 nm along the {1 1 2 0} boundary plane. These dislocations are also composed of two partial dislocations with b = 1/3[1 0 1 0] or b = 1/3[0 1 1 0]. According to the Eq. (2) by Frank’s model [34], the misorientation angle can be estimated to be 0.31°, which is close to the intended angle of 0.4°, indicating that the initial misorientation angle can be precisely controlled within 0.1° in the present experimental procedures. As well as the results shown in Section 3.3, nano-probe EDS and EELS measurement revealed that Ti segregate in the vicinity of the present dislocation core within 3–5 nm. This indicates that Ti rich nanowire is formed along the respective dislocation. Next, the electron conductivity was measured using the contact current mode of the AFM, which was the same technique described in Section 3.3. The measurement was performed applying the voltage of 1–100 V. Fig. 15 shows an example of the electron current mapping image for the [1 1 0 0] 2° tilt grain boundary. This image was obtained at an applied voltage of 100 V from the measurement region of 10  10 lm. From this image, it is recognized that the electron current value increases discretely at the grain boundary region, indicating that electron current flows along the dislocation nanowires at the grain boundary. Although the structure and the properties of the present nanowire are similar to those in the nanowires formed in the lattice as described in the Section 3.3, another unique and special properties are expected to appear when the dislocation distance is controlled more closer or the dislocation core structure is changed by using another rotation axis. These studies will be performed in the future.

786

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

Fig. 15. Electron current mapping image for the [1 1 0 0] 2° tilt grain boundary observed by AFM-contact mode under the applied voltage of 100 V. The scanning area is 10  10 lm, and it is recognized that the electron current increases discretely along the dislocations on the grain boundary.

4. Introduction of high-density dislocation into zirconia and ion conductivity 4.1. High-density dislocation introduction by high-temperature compression method Cubic zirconia has a fluoric type structure, and has the {0 0 1}h1 1 0i slip system and the {1 1 1}h1 1 0i slip system, in which the multiple slip can easily occurs [53]. For introducing the straightly aligned dislocations, it is required to make only the single slip active and suppress the secondary slip. The main slip system of the cubic YSZ used in this study is the {0 0 1}h1 1 0i system. There is a possibility that the multiple slip becomes active if it is compressed in the direction with the Schmidt factor of 0.5. Therefore, the compression axis was slightly tilted to be the h1 1 2i direction, and it was selected as a compression axis [27,28]. In this case, although the compression axis is tilted by 55°against the {0 0 1} plane and its Schmidt factor is 0.47, the single slip is expected in the beginnings of deformation. In this study, the dislocation density and its distribution were controlled by compression deformation tests systematically at various temperatures and at different strain rates. Fig. 16 shows the microstructure with strain amount of (a) 1% and (b) 10% in the case where deformation was made at the temperature of 1300 °C at the strain rate of 8  106 s1, respectively [27,28]. The observations were made along the [1 1 0] direction, in which the electron was transmitted from the direction parallel to the slip plane. If the direction of the incident beam and the dislocation line are parallel, dislocation should be observed as like black dots in the figure. As shown in (a), it is recognized that almost all dislocations are arranged upright in the case of a strain amount of 1%. On the other hand, in case of applying 10% deformation, the dislocations themselves intertwine each other because of the activity of the secondary slip system. Here, the dislocation densities of the samples with the strain amount of 1% and 10% were 8  108 cm2 and 1.2  109 cm2, respectively. In addition, as a result of the g  b analysis, it has been confirmed that all the dislocation of the present samples with the strain amount of 1% has the Burgers vector of b = a/2[1 1 0]. Recently, the YSZ is paid attention as a conductor of oxygen ions. If the fast pipe diffusion along the dislocations occurs, the ion conductivity should be increased along the dislocation line in the sample, in which high-density dislocations were introduced. Then, the ion conductivity in the parallel direction (the [1 1 0] direction) to the introduced dislocation was measured at various temperatures using an impedance analyzer. Fig. 17 shows a graph of the ion conductivity plotted against the amount of the deformation strain [27]. The ion conductivity of the deformed sample at each temperature was normalized by the ion conductivity of the undeformed sample measured at the same temperature. In this way, it was revealed that the ion conductivity of the deformed sample actually increases with

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

787

Normalized conductivity

Fig. 16. Bright field images of the dislocation structures for the specimens deformed up to (a) 1% and (b) 10% strain with the incident beam parallel to the [1 1 0] direction, which is parallel to the dislocation lines introduced by primary slip [27].

1.10 1.08 1.06 1.04

○ 406 oC ● 456 ooC 504 C ▲ 551 ooC □ 597 oC ■ 642 C

1.02 1.00

0

2

4

6

8

10

Plastic strain / % Fig. 17. Normalized ion conductivity as a function of plastic strain obtained in the temperature range of 400–650 °C [27].

the increase in the strain amount at every temperature. For example, the ion conductivity of the sample with the strain amount of 10% at 600 °C increases about 10% compared with the one of the undeformed sample. This result suggests that the ion conductivity is possible to be improved if the highdensity dislocations can be introduced. We examine how highly the improvement in ion conductivity can be expected based on these experimental results. Since the dislocation is aligned almost straight with the sample with the strain amount of 1%, we take this sample as a model for the present evaluation. In case where the dislocations are straight and they penetrate the sample, the diffusion path of oxygen ions can be evaluated by dividing it into the dislocation part and the bulk part as shown in the inset of Fig. 18. Accordingly, the total resistance Rtotal of the sample is regarded as a parallel circuit of the resistance Rbulk of the bulk and the resistance Rdis of the dislocation. On the assumption of the parallel circuit, by substituting the

788

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

104

Dislocation region

σdis / σ bulk

Bulk region

103 Oxygen diffusion Rtotal

102

Rbulk

Rdis

10

0

2

4

6

8

10

Effective dislocation core radius, r / b Fig. 18. Effective radius ‘‘r” dependence of rdis/rbulk, in which the insets show the diffusion path of oxygen ions is by dividing into the dislocation part and the bulk part. The total resistance Rtotal is evaluated as a parallel circuit of the resistance Rbulk and Rdis [27].

result obtained by the experiment, ‘‘rdis/rbulk,” the ratio of the ion conductivity of the one of the dislocation to the one of the bulk, can be calculated as a function of ‘‘r”, an effective radius of the dislocation core. Fig. 18 shows the result of the present calculation. It is recognized that as ‘‘r” decreases, ‘‘rdis/rbulk” increases. From the result, although the ion conductivity along the dislocation line depends on ‘‘r,” it can be estimated to be as large as 102–104 times compared with the bulk one. Using these results, a trial calculation was made regarding the relationship between the dislocation density and ion conductivity. With the dislocation density of about 109 indicated this time, it only improved ion conductivity of the bulk by about 10%. However, it is suggested that there is a possibility that if the dislocation density of about 1011 can be introduced for example, 10–20 times, and if with the dislocation density of about 1012, 100 times or more of the ion conductivity of the bulk one can be achieved. This will be a unique technique to improve the ionic conductivity of ceramic materials. 4.2. Grain boundary dislocations in YSZ bicrystals It is possible to form various dislocation arrays by preparing a bicrystal provided with the low-angle grain boundary for the YSZ as well. We have prepared the YSZ bicrystals composed of various tilt grain boundaries around the axes of such as the [1 1 0], [0 0 1], and [1 1 1] axes and evaluated their atomic structures and properties so far. It is possible to arrange dislocations with various Burgers vectors periodically by controlling the common rotation axis, the grain boundary plane, and the inclination angle. The structures characterized so far are described in detail elsewhere [54–58]. In this section, we will introduce grain boundaries, of which the structure transforms according to the angle in the low-angle grain boundary even with the same rotation angle [57]. This is interesting phenomenon from the point of dislocation structure control. The low-angle grain boundary of the YSZ was obtained by preparing a bicrystal by diffusion bonding as well. The grain boundary introduced here is a low-angle grain boundary with the misorientation angle from 0° to 10° around the [0 0 1] common axis. By cutting each single crystal in the given direction prior to the preparation of a bicrystal, a flat surface at the atomic level was obtained by the mechanochemical polishing, the same as the case of sapphire, in this case as well. A bicrystal was prepared by fixing these two single crystals to perform diffusion bonding under the conditions of 0.2 MPa at 1600 °C for 15 h. Fig. 19 shows the HREM images for the [0 0 1] low-angle grain boundaries with the misorientation angle of (a) 1° and (b) 5°, respectively [57]. As can bee seen in the figure, both of the boundaries are composed of periodically introduced dislocation arrays. It is found that the dislocation interval in the grain boundary with 5° is far shorter than the one in the grain boundary with 1°. Burgers circuit of the

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

789

Fig. 19. HRTEM images of the [0 0 1] low-angle grain boundary with the misorientation angle of (a) 1° and (b) 5°. The insets show the Burgers circuits in the respective dislocation. Grain boundary dislocation models for the [0 0 1] low-angle grain boundary with the misorientation angle of (c) 1° and (d) 5°.

dislocation is shown in the inset of each image. Fig. 19a shows that the dislocation has the Burgers vector of a/2[1 0 0]. However, if the a/2[1 0 0] type dislocations are periodically introduced, the stacking faults with high-energy are considered to be introduced alternately. On the other hand, if this dislocation has the a/2[0 0 1] component, stacking faults are not formed between the dislocations, and it is expected that the energy of the present dislocation arrangement will be much lower. Although the a/2[0 0 1] component is a screw component, if the a/2[0 0 1] component, which is opposite sign to it, is introduced alternately, the screw component as a whole will not exist. Therefore, it means that the grain boundary dislocation with the misorientation angle of 1° has a structure like the one in Fig. 19c, where the perfect dislocations of b = a/2[1 0 1] and b = a/2[1 0 1], including the screw component, are alternately introduced along the boundary. On the other hand, there is a slightly elongated contrast to the direction of the grain boundary as indicated by the arrows in Fig. 19b. As a result of the detailed analysis, it was revealed that the contrast indicates the stacking faults formed on the

790

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

(1 0 0) plane, and partial dislocation with b = a/2[1 0 0] type partial dislocations are present at both sides of the stacking faults (Fig. 19d). In other words, the grain boundary with 5° is formed by the array of partial dislocations and stacking faults in between. Considering the fact that the [0 0 1] low-angle grain boundary with the misorientation angle of 1° is formed by the perfect dislocation arrays, the dislocation structure of the present low-angle grain boundary must transform with the misorientation angle of between 1° and 5°. The structure transformation is expected to be determined by the balance of strain energy of the dislocation and stacking fault energy. As described above, in the particular axis, by controlling the misorientation angle, not only the periodicity of the dislocation arrangement but also the types of dislocations introduced can be controlled. Further systematic studies are expected in future. 5. Summary In this review paper, the fabrication method and the properties of high-density nanowires using the dislocation arrangement were introduced with the focus on our recent results. Many studies have been reported regarding such as quantum wires and the quantum dots, with which the fabrication has been tried by various techniques so far. However, since most of them are to form these low dimensional quantum structures on the surface or interface in a solid, they are considered to be accompanied by much difficulty, if practical applications as a functional device are considered. On the other hand, if it becomes possible to form a low dimensional structure inside the solid with high-density, since the handling also becomes easy, there is a potential for various applications as a device as well. Although the techniques introduced here are in the incunabula of the study, they are one of the effective methods, which can introduce high-density or periodically aligned nanowire into the crystal. Dislocation, if anything, has been used to understand the mechanical properties of materials in particular so far. However, if the specific atomic and electronic structure of the dislocation core, the elastic strain field of dislocation, and the one-dimensional linear nanostructure etc. are used actively, the fabrication of novel functional materials and devices with a new idea will be possible as described here. We believe that this field has an innumerable potential and that the development of the functional materials, with which the structures of dislocation and grain boundary can be arbitrarily controlled, will be possible in future. In this process, it is expected that new academic frameworks like ‘‘Dislocation Technology” or ‘‘Grain Boundary Technology” will be created as well. On the other hand, from the industrial aspect, by the development of the revolutionary nano devices and energy materials such as unprecedented nano devices for example, high-performance nano devices, which bring about the epoch-making technology revolution, the development of high-efficiency ion conductors, with which the low temperature operation is possible, investment of electric conductivity to insulators, and the development of the superconductive nanowire, etc., we believe that there is a potential to build new industry as well. As far as the author knows, it is in situations that few researches have been conducted in this field yet; we hope that this paper will be a lead to have an interest in this study. Acknowledgements The author would like to acknowledge the collaboration with N. Shibata, T. Mizoguchi, K. Matsunaga, T. Yamamoto throughout the present studies, and with A. Nakamura, H. Nishimura, T. Nakagawa, J. Thoma, M. Tamura, E. Uehara, E. Tochigi, K.P.D. Lagerlof, M.F. Chisholm, S.J. Pennycook for sapphire studies, and with A. Kuwabara, S. Ii, K. Otsuka for YSZ studies. The author also thanks T. Sakuma, R.M. Cannon, A.M. Glaeser, P. Pirouz, A.H. Heuer, P.B. Hirsch for valuable discussions and comments. A part of this work was supported by the Grants-in-Aid for Scientific Research on Priority Areas ‘‘Nano Materials Science for Atomic-scale Modification” (No. 19053001) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT). References [1] Turton R. The quantum dot: a journey into the future of microelectronics. Oxford University Press; 1995. [2] Heinrich H, Bauer G, Kuchar F. Physics and technology of submicron structures. Berlin: Springer-Verlag and Heidelberg GmbH & Co.; 1988.

Y. Ikuhara / Progress in Materials Science 54 (2009) 770–791

791

[3] Harrison P. Quantum wells, wires and dots: theoretical and computational physics of semiconductor nanostructures. John Wiley & Sons Ltd.; 2000. [4] Eigler DM, Schweizer EK. Nature 1990;344:524. [5] Petroff PM, Gaines JM, Tsuchiya Simes MRJ, Coldren LA, Kroemer H, English J, et al. J Cryst Growth 1989;95:260. [6] Asahi H, Yu SJ, Takamura J, Kim SG, Okuno Y, Kaneko T, et al. Surf Sci 1992;267:232. [7] Hirth JP, Lothe L. Theory of dislocations. 3rd ed. New York: Krieger Pub. Co.; 1992. [8] Hull D, Bacon DJ. Introduction to dislocations. 4th ed. Butterworth–Heinemann; 2001. [9] Weertman J, Weertman J. Elementary dislocation theory. Oxford University Press; 1992. [10] Bulatov V, Cai W. Computer simulations of dislocations (Oxford series on materials modelling). Oxford University Press; 2006. [11] Suzuki H. Introduction to dislocation. AGNE Pub. Co.; 1967 [in Japanese]. [12] Shockley W. Phys Rev 1953;91:228. [13] Elbaum C. Phys Rev Lett 1974;32:376. [14] Hutson AR. Phys Rev Lett 1981;46:1159. [15] Döding G, Labusch R. Phys Stat Solidi (a) 1981;68:143. [16] Döding G, Labusch R. Phys Stat Solidi (a) 1981;68:469. [17] Grazhulis VA, Kveder VV, Mukhina VY, Osip’yan YA. JETP Lett 1977;24:142. [18] Osip’yan YA, Tal’yanskii VI, Shevchenko SA. Sov Phys JETP 1977;45:810. [19] Takeuchi S, Kimura K, Iwamoto K, Misawa Y. Superconducting materials. JJAP series, vol. 1; 1988. p. 158. [20] Little WA. Phys Rev 1964;134:A1416. [21] Fukuyama H. J Phys Soc Jpn 1982;51:1709. [22] Nakamura A, Matsunaga K, Tohma J, Yamamoto T, Ikuhara Y. Nat Mater 2003;2:453. [23] Matsunaga K, Nakamura A, Yamamoto T, Ikuhara Y. Phys Rev B 2003;68:214102. [24] Matsunaga K, Mizoguchi T, Nakamura A, Yamamoto T, Ikuhara Y. Appl Phys Lett 2004;84:4795. [25] Nakamura A, Lagerlof KPD, Matsunaga K, Tohma J, Yamamoto T, Ikuhara Y. Acta Mater 2005;53:455. [26] Ikuhara Y, Nishimura H, Nakamura A, Matsunaga K, Yamamoto T, Lagerlöf KPD. J Am Ceram Soc 2003;86:595. [27] Otsuka K, Kuwabara A, Nakamura A, Yamamoto T, Matsunaga K, Ikuhara Y. Appl Phys Lett 2003;82:877. [28] Otsuka K, Matsunaga K, Nakamura A, Ii S, Kuwabara A, Yamamoto T, et al. Mater Trans 2004;45:2042. [29] Mizoguchi T, Sakurai M, Nakamura A, Matsunaga K, Tanaka I, Yamamoto T, et al. Phys Rev B 2004;70:153101. [30] Nakamura A, Matsunaga K, Yamamoto T, Ikuhara Y. Appl Sur Sci 2005;241:38. [31] Nakamura A, Matsunaga K, Yamamoto T, Ikuhara Y. Philos Mag 2006;86:4657. [32] Nakagawa T, Nakamura A, Sakaguchi I, Shibata N, Lagerlof KPD, Yamamoto T, et al. J Cearm Soc Jpn 2006;1335:1013. [33] Shibata N, Chisholm MF, Nakamura A, Pennycook SJ, Yamamoto T, Ikuhara Y. Science 2007;316:82. [34] Frank FC. Philos Mag 1951;42:809. [35] Lagerlöf KPD, Heuer AH, Castaing J, Rivière JP, Mitchell TE. J Am Ceram Soc 1994;77:385. [36] Nakamura A, Yamamoto T, Ikuhara Y. Acta Mater 2002;50:101. [37] Kronberg ML. Acta Metall 1957;5:507. [38] Phillips DS, Mitchell TE, Heuer AH. Philos Mag A 1982;45:371. [39] Lagerlöf KPD, Mitchell TE, Heuer AH, Rivière JP, Cadoz J, Castaing J, et al. Acta metall 1984;32:97. [40] Mitchell TE, Pletka BJ, Phillips DS, Heuer AH. Philos Mag 1976;34:441. [41] Bilde-Sørensen JB, Thölen AR, Gooch DJ, Groves GW. Philos Mag 1976;33:877. [42] Blavette D, Cadel E, Fraczkiewicz A, Menand A. Science 1999;286:2317. [43] Balluffi RW, Granato AV. Dislocations in solids. In: Nabarrro FRN, editor. Amsterdam; 1989 [chapter 13]. [44] Tang X, Lagerlöf KPD, Heuer AH. J Am Ceram Soc 2003;86:560. [45] Shannon RD. Acta Crystallogr 1976;A32:751. [46] Lusvardi VS, Barteau MA, Chen JG, Eng JJ, Teplyakov A, Fruhberger B. Surf Sci 1998;397:237. [47] Li XL, Hillel R, Teyssandier F, Choi SK, Van Loo FJJ. Acta Metall Mater 1992;40:3149. [48] Blumenthal RN, Coburn J, Baukus J, Hirthe WM. J Phys Chem Solids 1996;27:643. [49] Marks A, Taylor ST, Mammana E, Gronsky R, Glaeser AM. Nat Mater 2004;3:682. [50] Tochigi E, Shibata N, Nakamura A, Yamamoto T, Ikuhara Y. Acta Mater 2008;56:2015. [51] Hirsch PB, Zhou Z, Cockayne DHJ. Phil Mag 2007;87:5421. [52] Pennycook SJ, Jesson DE. Phys Rev Lett 1990;64:938. [53] Dominguez-Rodriguez A, Lagerlöf KPD, Heuer AH. J Am Ceram Soc 1986;69:281. [54] Shibata N, Oba F, Yamamoto T, Sakuma T, Ikuhara Y. Philos Mag 2003;83:2221. [55] Ikuhara Y, Shibata N, Watanabe T, Oba F, Yamamoto T, Sakuma T. Ann Chim Sci Mater 2002;27:S21. [56] Shibata N, Oba F, Yamamoto T, Ikuhara Y, Sakuma T. Philos Mag Lett 2002;82:393. [57] Shibata N, Morishige M, Yamamoto T, Ikuhara Y, Sakuma T. Philos Mag Lett 2002;82:175. 2002. [58] Shibata N, Yamamoto T, Ikuhara Y, Sakuma T. J. Electron Microsc 2001;50:429.