HREM images are phase contrast due to interference of electron waves, and direct information on atomic arrangements in crystals can be obtained. HREM images are sensitive to defocus values, crystal thickness, crystal tilting, and other parameters.

HREM images of TlBa₂Ca₃Cu₄O₁₁ superconductor [15], which has the almost highest transition temperature of 123 K are shown in Figure 1. Although these three images were taken at the same magnification for the same sample, the image contrast is very different due to the imaging conditions. Figure 1A is a one-dimensional lattice image taken perpendicular to the c-axis of the crystal by 200 kV TEM. Tl and Ba layers show dark contrast, and Ca layers together with oxygen vacancies (Ov) show white lines. Figure 1B is a two-dimensional HREM image taken along the a-axis and perpendicular to the c-axis by 200 kV TEM. Although oxygen vacancy positions are imaged as bright dots due to dynamical diffraction effect, the image does not show the direct atomic arrangements. Figure 1C is a structure image taken along the a-axis and perpendicular to the c-axis by 400 kV TEM. This HREM image is imaged by the interference of multielectron waves, and the potential in the crystal is clearly imaged. When the atomic arrangements of the superconducting oxides are discussed, structure images, which show potential clearly in the crystal, are needed, as shown in Figure 1C. On the other hand, lattice images like Figure 1A and B are suitable for HREM observation in the unit cell scale such as defects, interface, and modulated structures.

Figure 1

HREM images of TlBa₂Ca₃Cu₄O₁₁ (T_c=123 K). (A) One-dimensional lattice image taken by 200 kV TEM. (B) Two-dimensional HREM image taken by 200 kV TEM. (C) Structure image taken by 400 kV TEM with the incident beam parallel to the a-axis, together with a projected structure model. Brighter spots indicated by Ov correspond to the oxygen vacant positions.

Necessary conditions to observe the structure images, which can be used to obtain information of crystal structures in the present work, are investigated by calculating high-resolution images with the multislice method. For the image calculations, a large computer (ACOS-2020) was used. Basic parameters used for the image calculations are as follows: accelerating voltage=400 kV, radius of the objective aperture=5.9 nm^-1, spherical aberration C_s=1.0 mm, spread of focus Δ=8 nm, semi-angle of convergence α=0.55 mrad, crystal thickness t=1.9 nm, and defocus value of the objective lens Δf=-49 nm (Scherzer defocus).

Figure 2 shows simulated images based on a structural model of TlBa₂Ca₃Cu₄O₁₁ with the incident beam parallel to the a-axis. Structure parameters in the calculations were used with values determined by X-ray diffraction [16]. In Figure 2A, the images calculated with various thicknesses under the Scherzer defocus condition (Δf=-45 nm) are shown, whereas in Figure 2B, the images are calculated as a function of defocus value for a crystal thickness of 1.92 nm. In Figure 2A, the images of thinner crystals than 2 nm faithfully represent the projection of crystal structure. The darkness or size of dark spots corresponding to Tl, Ba, Cu, and Ca positions can be identified to be nearly proportional to their atomic numbers. This type of high-resolution structure images are mainly used in the present paper hereafter. On the other hand, in the images of thicker than about 3 nm, the cation positions cannot be identified as dark spots. The calculations show that only images taken at nearly the Scherzer defocus (Δf=-45 nm) and from thinner crystals than 2 nm can be used for structure analysis. In Figure 2B, it is interesting to note that the image contrasts at Δf=15 nm and -75 nm are almost reversed to that of the Scherzer condition, and the cation positions appear as bright spots. As these types of wrong images have been occasionally reported in some papers, one should keep it in mind.

Figure 2

Calculated images of TlBa₂Ca₃Cu₄O₁₁ with the a-axis incidence as functions of (A) crystal thickness and (B) defocus value.

Unfortunately, oxygen atoms cannot be represented as dark spots in structure images taken with the present microscope. However, information on oxygen atom positions is contained in the structure images. Figure 3 is calculated images of TlBa₂Ca₃Cu₄O_x, and two types of models with oxygen vacancies and with oxygen atoms on the Ca layers are shown in Figure 3A and B, respectively. Image calculations were performed under the condition of a defocus value of -45 nm and crystal thickness of 1.92 nm. Intensity profiles along the lines through Tl and Cu atoms parallel to the c-axis are also shown at the right side of the calculated images. By the comparison between Figure 3A and B, one can notice that the oxygen vacant positions indicated by Ov show brighter contrast than the oxygen positions, and the intensity of the vacant positions shows higher peaks in the intensity profile. In order to confirm the above results of image calculations, an observed structure image of TlBa₂Ca₃Cu₄O₁₁ in Figure 1C is examined [14]. In the observed image, the oxygen vacant positions indicated by Ov show brighter contrast than the other bright regions corresponding to oxygen positions. Therefore, the image clearly shows the existence of ordering of oxygen vacancies on the Ca layers.

Figure 3

Models and calculated images of TlBa₂Ca₃Cu₄O₁₁ with oxygen vacancies on the Ca layers (A), and those of TlBa₂Ca₃Cu₄O₁₄ with oxygen atoms on the Ca layers (B). Intensity profiles along the lines through Tl and Cu atoms parallel to the c-axis are also shown at right side.

Bulk samples of Tl-based copper oxides were prepared by reacting Tl₂O₃, CaO, BaO₂, CuO, and BaCuO₂ [15, 17–22]. The samples of Tl₂Ba₂CuO₆ and TlBa₂CaCu₂O₇ were reheated in the range of 500–850°C, and then quenched in liquid nitrogen in order to control the oxygen content and to obtain the highest T_c. The Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, and TlBa₂CaCu₂O₇ samples showed the superconductivity at transition temperatures. Samples for high-resolution observation were prepared by dispersing crushed materials on holey carbon films [23].

Figure 4A and B are high-resolution structure images of Tl₂Ba₂CuO₆ (T_c=80 K) taken with the incident beam parallel to the [100] and [110] directions, respectively. To observe the atomic arrangements clearly, a crystallographic image processing was carried out. The digital images were masked and fast Fourier transformed. The reciprocal lattice was indexed according to a unit cell, and the lattice parameters were determined using the positions of the strongest peaks in the analysis. The local background was subtracted, and the amplitudes and phases of the peaks were corrected using symmetrization [24, 25]. Before correcting the phases, the phase origin was determined by investigating the origin shift that gave the best accordance with the phase conditions for the two-dimensional plane group. Averaged symmetrized images were reconstructed from the corrected Fourier transforms. Crystallographic symmetrization based on the two-dimensional space group was used for the reconstruction of the Fourier transform, as shown in Figure 4C and D, respectively. Tl, Ba, and Cu atoms are clearly observed, and the darkness and size of the dark spots corresponding to the metal atom positions can be identified to be nearly proportional to their atomic numbers.

Figure 4

High-resolution structure images of Tl₂Ba₂CuO₆ (T_c=80 K) taken with the incident beam parallel to the (A) [100] and (B) [110] directions. (C, D) HREM images after crystallographic image processing of (A) and (B), respectively.

A high-resolution structure image of Tl₂Ba₂CaCu₂O₈ (T_c=114 K) is shown in Figure 5A, which was taken with the incident beam parallel to the a-axis. Figure 5B is a HREM image after crystallographic image processing of Figure 4A, and metal atom positions are clearly observed. In addition to the metal atom positions, oxygen vacancies are clearly observed as bright white dots on the Ca layers.

Figure 5

High-resolution structure image of Tl₂Ba₂CaCu₂O₈ (T_c=114 K) taken with the incident beam parallel to the a-axis. (B) HREM image after crystallographic image processing of (A).

Figure 6 has high-resolution structure images of TlBa₂CaCu₂O₇, Tl₂Ba₂Cu₃O₁₀, TlBa₂Ca₄Cu₅O₁₃, and Tl₂Ba₂Ca₃Cu₄O₁₂, taken with the incident beam parallel to the a-axis, together with projected structure models [26]. Metal atoms positions are clearly observed, and brighter spots indicated by asterisks correspond to the oxygen vacant positions. It is well known that the Tl-based superconductors have various layered structures, TlBa₂Ca_n-1Cu_nO_2n+3 (n=1–5) with single Tl layers and Tl₂Ba₂Ca_n-lCu_nO_2n+4 (n=1–4) with double Tl layers. Their structure models were proposed, as shown in Figure 7. In the TlBa₂Ca_n-lCu_nO_2n+3 (n=1–5) system, structure parameters of TlBa₂CaCu₂O₇ (Tl-1212) [27], TlBa₂Ca₂Cu₃O₉ (Tl-1223) [16], and TlBa₂Ca₃Cu₄O₁₁ (Tl-1234) [16] have been determined by X-ray diffraction. On the other hand, in the Tl₂Ba₂Ca_n-lCu_nO_2n+4 (n=1–4) system, Tl₂Ba₂CuO₆ (Tl-2201) [28], Tl₂Ba₂CaCu₂O₈ (Tl-2212) [28], and Tl₂Ba₂Ca₂Cu₃O₁₀ (Tl-2223) [28] have been examined in detail by X-ray diffraction. Although crystal structures of TlBa₂Ca₄Cu₅O₁₃ [15] and Tl₂Ba₂Ca₃Cu₄O₁₂ [26] structures were proposed, their structure parameters were not determined from diffraction analysis because they are always formed as the intergrowth with other structures. Here, the structure models of TlBa₂CaCu₂O₇, Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, and Tl₂Ba₂Ca₂Cu₃O₁₀ proposed by X-ray diffraction was examined, and next, the structure parameters of TlBa₂Ca₄Cu₅O₁₃ and Tl₂Ba₂Ca₃Cu₄O₁₂ were determined from observed high-resolution structure images.

Figure 6

High-resolution structure images of (A) TlBa₂CaCu₂O₇ (T_c=110 K), (B) Tl₂Ba₂Ca₂Cu₃O₁₀ (T_c=122 K), (C) TlBa₂Ca₄Cu₅O₁₃, and (D) Tl₂Ba₂Ca₃Cu₄O₁₂ taken with the incident beam parallel to the a-axis, together with a projected structure model. Brighter spots indicated by asterisks correspond to the oxygen vacant positions.

Figure 7

Structure models of TlBa₂Ca_n-1Cu_nO_2n+3 (n=1–5) and Tl₂Ba₂Ca_n-1Cu_nO_2n+4 (n=1–4).

Figures 4, 5, and 6A and B are high-resolution structure images of Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈, TlBa₂CaCu₂O₇, and Tl₂Ba₂Ca₂Cu₃O₁₀, taken with the incident beam parallel to the a-axis. In the images, a good correspondence between the arrangement of dark spots in the image and that of cations in the projected structure model proposed by X-ray diffraction is clearly observed. The larger black spots correspond to the Tl atoms and Ba atoms, and Cu and Ca atoms with smaller atomic numbers are represented as small dark spots. Oxygen atom positions are located on bright regions between the dark spots of the cations. In addition, positions of the dark spots corresponding to cations faithfully reflect the coordinates of the cations, determined with X-ray diffraction, as listed in Table 1. The z coordinates of cations, measured from the observed images, are listed in Table 1, together with values determined by diffraction methods [27, 28]. Good correspondences between the z coordinates of cations were determined from the observed high-resolution images and from diffraction methods. From Table 1, it can be seen that the dark spot positions in the structure images, reflect the real positions of cations within an error of 0.01 nm, which may be in a measured error. This result shows that the cation positions can be determined with the precision of 0.01 nm from the structure images. The oxygen vacant positions, which are located on the Ca layers, can be distinguished as brighter regions from the other bright regions corresponding to the oxygen sites.

Figures 6C and D are high-resolution structure images of TlBa₂Ca₄Cu₅O₁₃ and Tl₂Ba₂Ca₃Cu₄O₁₂, respectively. They were observed as the intergrowth with other structures having smaller numbers of Cu layers. The z coordinates of cations determined from the images are shown in Tables 2 and 3, respectively. Oxygen vacancies on the Ca layers can be observed in the images. In Tables 2 and 3, the z coordinates of oxygen atoms in Tl-O and Cu-O layers were assumed to be the same as those of cations, and oxygen positions in the Ba layer were assumed to be shifted by 0.07 nm along the c-axis from the results of other Tl-based superconductors [16, 27–29]. Tl-1201 structures and other substitution-type structures had also been reported for the Tl-based superconductors [30–34].

In addition to the basic layer structures of Tl-based copper oxides, modulated structures accompanied with the satellite spots have also been observed [35–41]. Figure 8 is electron diffraction patterns of Tl₂Ba₂CuO₆ taken along the various directions of the crystal [42]. In addition to the fundamental reflections, sharp satellite spots are observed in Figure 8A, B, and C, which indicate the modulated superstructure. The electron diffraction pattern of Figure 8C can be obtained from Figure 8D by rotation of 18° along the c-axis. There is no satellite spot in Figure 8D, and the satellite spots along the [3 1 0] appear by the 18°-rotation along the c-axis as observed in Figure 8C. The Tl₂Ba₂CuO₆ has both tetragonal and orthorhombic structures, and the modulated structure is observed in the orthorhombic phase. The fundamental structure with the modulated structure is distorted a little, and the indices are those of an orthorhombic unit cell (a=0.545 nm, b=0.549 nm, c=2.318 nm) as observed in the electron diffraction pattern of Figure 8A. The fundamental lattice has a twin structure with a twin plane of {110} as observed in Figure 8B. The superstructure reflections are observed along the <1 3 0>, and the modulated wave vector was determined as q=[±0.07 0.22 1]=1/6.2 <1 3 0>, i.e., the modulation is incommensurate.

Figure 8

Electron diffraction patterns of Tl₂Ba₂CuO₆ taken with the incident beam parallel to the (A) [001], (B) [001], (C) [1̅30], and (D) [11̅0] directions. The electron diffraction pattern (B) showing the modulated structure and its twinning.

Figure 9A is a HREM image of Tl₂Ba₂CuO₆ taken along the c-axis. An enlarged image of Figure 9A is shown in Figure 9B. In addition to the fundamental lattice fringes, dark and bright contrasts with a distance of ∼1.2 nm and their twin relations can be seen. This HREM images show the direction of the modulated structure is near [130]. Although twinning of the modulated structure appears on both {110} and near {100} planes, the twinning of fundamental lattice appears only on {110} planes, as indicated by the arrows in Figure 9A and B. Figure 9C is a high-resolution image of Tl₂Ba₂CuO₆ 2201 taken with the [1̅30] incidence. Dark and bright contrasts with a distance of ∼2.4 nm are observed, and the modulated region (a) and the nonmodulated region (b) are clearly distinguishable. By careful observation of the modulation contrast, changes in both the darkness and position of Tl atoms can be seen, as indicated by arrows in the region (a) of Figure 9C. This indicates that the origin of modulated structure would exist on the Tl-O planes.

Figure 9

HREM image of Tl₂Ba₂CuO₆ taken along c-axis. (B) Enlarged image of (A). (C) HREM image of with the incident beam parallel to the [31̅0] direction.

From detailed composition analysis of the Tl-2201 phase, the orthorhombic with modulated structure and the tetragonal without the modulation had the composition of Tl_1.7Ba₂CuO_5.7 and Tl_1.6Ba₂CuO_5.6, respectively. The modulated structure has 0.3 oxygen and 0.3 Tl deficiencies per unit cell. The electron diffraction and high-resolution observation showed the 6.2 times superstructure along the [130] direction. These results indicated that the modulation would be due to the atomic ordering of oxygen and Tl in the Tl-O layers along the [130] with a period of 6.2 times. If the oxygen and Tl deficiencies are assumed along the [130] direction, the deficiencies are calculated as 0.36 per the unit cell, which agree well with the composition analysis. Therefore, the modulated superstructure is believed to be due to Tl and oxygen vacancies in the Tl-O layers along the [130] with a period of 6.2 times (∼2.4 nm). On the other hand, the tetragonal phase had more atomic deficiencies randomly and did not show the modulated structure.

Electron diffraction patterns of Tl₂BaSrCuO₆ taken with the incident beam parallel to the [001] and [010] directions are shown in Figure 10A and B, respectively. When Sr atoms are doped at the Ba sites, the fundamental structure has a tetragonal structure. Satellite reflections due to a modulated structure are observed, which are weak and diffuse compared to the Tl-2201 phase. In addition, the modulation wave vector was changed as q=<1/6 0 1>.

Figure 10

Electron diffraction patterns of Tl₂BaSrCuO₆ taken with the incident beam parallel to the (A) [001] and (B) [010] directions. (C) Electron diffraction pattern and (D) HREM image of Tl₂Ba₂CaCu₂O₈ taken with the incident beam parallel to the [010] direction. Electron diffraction patterns of (E) TlBa₂CaCu₂O₇ and (F) TlBa₂Ca₂Cu₃O₉ taken along the c-axis.

For Tl₂Ba₂CaCu₂O₈ (Tl-2212) [35, 36] and Tl₂Ba₂Ca₂Cu₃O₁₀ (Tl-2223) [35], weak diffuse scatterings were also observed, and the modulation wave vector is determined to be q=<l/6 0 1> as observed in Figure 10C. This modulation shows two-dimensional character, and the symmetry of the fundamental lattice remains tetragonal (a=0.385 nm, c=2.92 nm). A HREM image corresponding to Figure 10C is shown in Figure 10D. Modulation contrast with a distance of ∼2.3 nm is observed in the Tl-O layer along the a-axis. Models for the modulated superstructures were reported as follows: short-range ordering due to displacements of Tl and O in the Tl-O planes [36], extra oxygen in the Tl-O planes [35], a partial substitution of Tl³⁺ by Tl⁺ [35, 38], the mutual substitution of Tl and Ca atoms [10, 41]. The compositional analysis of the present samples showed that the Tl-2212 and Tl-2223 phases had compositions of Tl_1.7Ba₂Ca_1.3Cu₂O₈ and Tl_1.7Ba₂Ca_2.3Cu₃O₁₀, respectively. This implies that the excess 0.3 Ca atoms are doped at the Tl sites per the unit cell. The electron diffraction and HREM observation showed 6 times superstructure along the a-axis. If the Tl atoms are substituted by Ca atoms with a period of 6 times along the axis, the substitution atoms are 0.33 per unit cell, which agreed well with the measured composition of the samples. Therefore, the modulated superstructure is believed to be due to the Tl substitution by Ca atoms along the a-axis with a period of 6 times (∼2.3 nm).

Figure 10E and F are electron diffraction patterns of TlBa₂CaCu₂O₇ (Tl-1212) and TlBa₂Ca₂Cu₃O₉ (Tl-1223) taken along the c-axis, respectively. Weak, diffuse satellite scatterings are observed as indicated by arrows, and the observed modulation wave vector is approximately q=<0.28 0 0.5> [42]. Almost the same incommensurate diffuse scattering was observed for the TlBa₂Ca₃Cu₄O₁₁ (Tl-1234) phase. As the modulation shows a two-dimensional character, the symmetry of the fundamental lattice remains tetragonal. The diffuse scattering becomes stronger as the oxygen loss is increased, and also the Tc increases. Oxygen deficiencies δ of Tl-based superconductors calculated from electron diffractions of Figure 10 and iodimetric measurements of oxygen contents are summarized in Table 4. From the compositional analysis for the Tl-1212, 1223, and 1234 phases, the atomic ratios of Tl:Ba:Ca:Cu were determined to be 1:2:1:2, 1:2:2:3, and 1:2:3:4 (stoichiometry), respectively. However, 0.29 oxygen atoms are deficient per unit cell, as summarized in Table 4, which implies that the oxygen vacant positions are the same for these structures. In the present work, oxygen atoms in the Tl-O layers would be deficient, and the measured modulation from the electron diffraction patterns are summarized in Table 4. As listed in Table 4, assumed oxygen vacancies in the Tl-O layers measured by electron diffraction agreed well with the measured oxygen vacancies by iodimetric measurements. Therefore, it is believed that the modulation superstructure would be due to oxygen vacancy ordering in the Tl-O layer along the a-axis with a period of 3.6 times (=0.28^-1) and 2 times along the c-axis. The period of 3.6 times is incommensurate, which implies the mixture of 3- and 4-times superstructures. In fact, modulations with periods of 3.1∼4.2 times (=0.32^-1∼0.24^-1) are observed for electron diffraction patterns, as listed in Table 4.

Pb-based superconductors and related oxides have been discovered and investigated [5], and various new types of crystal structures of PbBaSr(Y,Ca)Cu₃O_y (y=7–8.4) and Pb₂(Ba,Sr)₂(Ln,Ce)₂Cu₃O_y (Ln: Lanthanoid, y=9–10.4) [43–45] were determined by high-resolution electron microscopy, with the aid of electron and X-ray diffraction, and quantitative analysis of compositions of cations and oxygen. Some results of the determination of crystal structures are shown here. Samples were prepared from a mixture of PbO, BaO₂, Sr₂CuO₃, Y₂O₃, Eu₂O₃, CeO₂, and CuO by solid state reaction. After heating at 830°C in a 1% O₂-N₂ mixed gas, the specimens were slowly cooled in a furnace, quenched into liquid nitrogen or annealed in a flowing O₂ gas at 400°C. Electron probe microanalysis and iodide titration method are used for quantitative analysis of the element.

Figure 11A and B are high-resolution structure images of PbBaSrYCu₃O₇ [43] and Pb₂Sr₂Y_0.5Ca_0.5Cu₃O₈ taken with the incident beam parallel to the a-axis. The PbBaSrYCu₃O₇ shows superconductivity at 65 K by Ca substitution for Y sites [44], and the Pb₂Sr₂YCu₃O₈ also showed superconductivity at 75 K by Ca substitution for Y sites [46]. HREM images after crystallographic image processing of Figure 11A and B are shown in Figure 11C and D, respectively. PC, BS, YC, and Ov represent (Pb, Cu), (Ba, Sr), (Y, Ca), and oxygen vacancy, respectively, and the image directly shows an arrangement of cations. The indicated atomic arrangements were proposed from the structure image, X-ray diffraction, and energy-dispersive spectroscopy (EDS) analysis. In Figure 11C, zigzag arrays consisting of larger black spots correspond to (Pb, Cu) layers, and on both sides of the (Pb, Cu) layers, there are layers of a mixture of Ba and Sr atoms [43]. In this image, Cu and Y atoms, with smaller atomic numbers, are represented as small dark spots. Oxygen atom positions are located at bright regions between the cation sites of the dark spots. In addition, the oxygen vacant positions on the Y layers, indicated by Ov, can be distinguished as brighter regions from the other bright regions corresponding to the oxygen-occupied sites in Figure 11C and D.

Figure 11

HREM images of (A) PbBaSrYCu₃O₇ and (B) Pb₂Sr₂Y_0.5Ca_0.5Cu₃O₈ taken with the incident beam parallel to the a-axis. (C, D) HREM images after crystallographic image processing of (A, B), respectively.

Darkness of the spots in the double (Pb,Cu) layers in Figure 11A suggests that the zigzag double layers contain some light element, Cu in addition to Pb. A random mixture of Pb and Cu in the double Pb layers is unlikely because of their different ionic radii and coordination schemes. Careful examination of contrast for the double Pb layers in a thin part near the crystal edges, as indicated by arrows in Figure 11A, suggests the pairwise distribution of Pb and Cu layers [47]. Some of these spots are large and dark, while some others are small and faint, which would correspond to Pb and Cu, respectively. The observed HREM image indicates that small domains of Pb and Cu layers alternate every several unit cells. This short-range ordering seems to be two-dimensional in the Pb and Cu layers, and Pb and Cu layers are not distinguishable due to an averaging effect in a thicker part of the specimen.

Atomic coordinates of PbBaSrYCu₃O₇ determined from the high-resolution structure image of Figure 10C are shown in Table 5. The z coordinates of oxygen atoms in (Pb, Cu) and Cu-O layers were assumed to be the same as those of cations, and oxygen positions in (Ba, Sr) layers were assumed to be shifted by 0.03 nm along the c-axis from the results of other Pb-based oxides [5].

Figure 12A and B are electron diffraction patterns of PbBaSrY_0.7Ca_0.3Cu₃O₇ taken with the incident beam parallel to the [001] and [110] directions, respectively. Satellite reflections at 1/2 1/2 0 are observed, and weak reflections at 1/4 1/4 0 are also observed in Figure 12A, which indicates a modulated superstructure with a modulation wave vector of q=1/4<1 1 0>, and the modulation would be due to oxygen ordering. Weak streaks at 1/2 1/2 0 along the c-axis are also observed in Figure 12B, which indicates stacking faults of the superstructure along the c-axis. The similar modulated superstructure with a modulation wave vector of q=1/4<1 1 0> was also observed in PbBa_0.7Sr_1.3EuCeCu₃O₉ [45].

Figure 12

Electron diffraction patterns of PbBaSrY_0.7Ca_0.3Cu₃O₇ taken with the incident beam parallel to the (A) [001] and (B) [110] directions.

A high-resolution structure image of PbBa_0.7Sr_1.3EuCeCu₃O₉, which was taken with the incident beam parallel to the a-axis, is shown in Figure 13A. Here, the foil thickness increases from the top to the bottom in the picture. The image contrast of the thin region directly represents the projected potential. The structure model of PbBa_0.7Sr_1.3EuCeCu₃O₉ was determined from the structure image by the aid of X-ray diffraction. The structure has a characteristic layer structure formed by alternate stacking of (Eu, Ce) double layers and (Pb, Cu) double layers, which are separated by (Ba, Sr) and Cu layers. In Figure 13A, (Eu, Ce) atoms are represented as the largest dark spots.

Figure 13

HREM images of (A) PbBa_0.7Sr_1.3EuCeCu₃O₉, (B) PbBa_0.7Sr_1.3YCe₂Cu₃O₁₁, and (C) Pb₂Sr₂(Y,Ce)₅Cu₃O₁₆ taken with the incident beam parallel to the a-axis, together with projected structure models. Calculated images of two models of (D) PbBa_0.7Sr_1.3EuCeCu₃O₉ and (E) Pb₂Sr₂(Y,Ce)₅Cu₃O₁₆ with the a-axis incident, together with projected structure models.

Figure 13B is a high-resolution structure image of PbBa_0.7Sr_1.3YCe₂Cu₃O₁₁, which was taken with the incident beam parallel to the a-axis, together with a structure model. A good correspondence between the arrangement of dark spots in the image and that of cations in the projected structure model of PbBa_0.7Sr_1.3YCe₂Cu₃O₁₁ is clearly observed. The image shows a layer structure with three (Y, Ce) layers between Cu-O layers. The atomic coordinates were directly determined from the observed high-resolution images as summarized in Table 6. Structure models of Pb(Ba,Sr)₂(Ln,Ce)_nCu₃O_5+2n (n=1–5) determined by the present work are summarized in Figure 14A.

Figure 14

Structure models of (A) Pb(Ba,Sr)₂(Ln,Ce)_nCu₃O_5+2n (n=1–5) and (B) Pb₂Sr₂(Ln,Ce)_nCu₃O_6+2n (n=1–5) determined from high-resolution electron microscopy.

In addition to the Pb(Ba,Sr)₂(Ln,Ce)_nCu₃O_5+2n (n=1–5) with double (Pb, Cu) layers, Pb₂Sr₂(Ln,Ce)_nCu₃O_6+2n (n=1–7) with triple (Pb,Cu) layers were investigated by high-resolution electron microscopy. Figure 13C is a HREM image of the Pb₂Sr₂YCe₄Cu₃O₁₆ [48] taken with the incident beam parallel to the a-axis, together with a determined structure model, as listed in Table 7. This structure can be characterized as a layer structure formed by stacking of fivefold (Y, Ce) fluorite layers between (PbO-Cu-PbO) blocks. Structure models of Pb₂Sr₂(Ln, Ce)_nCu₃O_6+2n (n=1–5) determined by the present work are summarized in Figure 14B. In addition, Pb single-layer structures were synthesized and reported [49–53], and new types of structures with (Ce, Y) fluorite layers were also reported [54, 55].

The observed image of Figure 13A was examined in detail with the aid of computer simulations. Multislice calculations were carried out with the z coordinates obtained from high-resolution image. Two types of oxygen positions (left: tetrahedral sites, right: octahedral sites) between (Eu, Ce) layers were assumed, as shown in Figure 13D. The calculated image of Figure 13D with oxygen positions at tetrahedral sites, under the condition of a defocus of -35 nm and a crystal thickness of 1.93 nm, is in good agreement with the observed image of Figure 13A, compared with Figure 13B. This result shows that the positions of oxygen atoms can be determined by comparing calculated images with observed images. The detailed structure of PbBa_0.7Sr_1.3EuCeCu₃O₉ was investigated by imaging plates. The observed image of PbBa_0.7Sr_1.3YCe₂Cu₃O₁₁ in Figure 13B was also investigated by comparing with computer simulations. The z coordinates obtained from the high-resolution image of Figure 13B were used, and two types of oxygen positions at tetrahedral sites (left) and octahedral sites (right) between (Y, Ce) layers were assumed. The calculated image of oxygen positions at tetrahedral sites in Figure 11E agrees well with the observed image of Figure 13B.

Various types of lanthanoid-based copper oxides have been reported [56–58], and electron-doped Nd_2-xCe_xCuO₄ superconductors were discovered [59–61]. In order to clarify the microstructures, single crystals of Ln₂CuO₄ prepared with various heat treatments are investigated by means of high-resolution electron microscopy and electron diffraction.

Single crystals of Ln₂CuO₄ (Ln=Pr, Nd, Sm) were grown by the traveling-solvent-floating-zone technique using an infrared-heating furnace [62, 63]. To reduce oxygen content, parts of the Ln₂CuO₄ (Ln=Pr, Nd, Sm) samples were annealed at 1100°C for 18 h in air and quenched in liquid nitrogen. The rests of the samples were annealed at 400°C in air for 38–140 h to saturate oxygen content in the crystals. SmLa_0.75Sr_0.25CuO₄ was also synthesized from a mixture of La₂O₃, Sm₂O₃, CuO, and SrCO₃ [64]. Mixed powder was first calcined at 950°C in air for 10 h, then pressed into pellets, and finally sintered at 1130°C in air for 15 h. The pellets were quenched to room temperature in air and subsequently annealed at 550°C in the atmosphere with various oxygen pressures.

A high-resolution image of Sm₂CuO₄ taken with the [100] incidence is shown in Figure 15A. The specimen thickness increases from the top to the bottom in this HREM image. The observed image shows the projected arrangement of metal atoms. There are two kinds of dark spots in the image. The larger ones in the zigzag arrays correspond to the Sm atoms. Cu atoms, with a smaller atomic number, are represented as less dark spots between the double Sm layers. Figure 15B is a HREM image of SmLa_0.75Sr_0.25CuO₄ taken along the a-axis. Fairly large separation between two lines of La ions is clearly observed in the HREM image, which is in accord with X-ray diffraction analysis [64].

Figure 15

HREM images of (A) Sm₂CuO₄ and (B) SmLa_0.75Sr_0.25CuO₄ taken along the a-axis. (C) Structure models and calculated images of the (D) Sm₂CuO₄ and (E) SmLa_0.75Sr_0.25CuO_3.95, respectively.

Based on the crystal structure models of Figure 15C, image calculations on the Sm₂CuO₄ and SmLa_0.75Sr_0.25CuO₄ were carried out to confirm the structures, as shown in Figure 15D and E, respectively. The images of Figure 15D and E calculated at a Scherzer defocus of -45 nm and a crystal thickness of 1.2∼2.7 nm, agree well with the observed image contrast for both thin and thick regions. For the SmLa_0.75Sr_0.25CuO₄ structure, the difference of oxygen atom positions in the Sm and La-Sr layers are clearly observed both in the observed and calculated image, which indicates the HREM image includes information both on metal and oxygen atoms in the crystal.

Modulated superstructures are also observed in the lanthanoid-based copper oxides [65–68]. The domains of superlattice with sizes of 5∼60 nm in diameter were observed, and the smaller domains (5∼10 nm) are observed around a large one and seem to grow into larger ones (40∼60 nm). A representative superstructure domain in Nd₂CuO₄ is shown in Figure 16A, and B is an electron diffraction pattern of Figure 16A. Sharp satellite reflections with a wave vector q=<1/4 1/4 0> are observed in Figure 16B. In Figure 16A, repeated dark and bright contrasts separated at a distance of 1.1 nm (≃2√2×a) are observed in the [110] direction. The high-resolution image and the diffraction pattern reveal that the basic lattice spacing of the superlattice lengthen as much as 101.5% and 100.3% in the [110] and [11̅0] directions, respectively, compared with the fundamental lattice. Therefore, the contrast due to strain field is observed around the domain. Two-directional superlattice domain is also observed as shown in a HREM image in Figure 16C, and an electron diffraction pattern of the superlattice domains along two directions is shown in Figure 16D, which also indicates a modulation wave vector of q=<1/4 1/4 0>. It can be considered that such domain structure is due to non-uniformity of oxygen content in the specimens.

Figure 16

(A) HREM image and (B) electron diffraction pattern of a single domain of the superlattice in Nd₂CuO₄, taken with the [001] incidence. (C) HREM image and (D) electron diffraction pattern of superlattice domains along two directions.

Various types of modulated superstructures were observed in the Ln₂CuO₄, as listed in Table 8. Figure 17A–D are electron diffraction patterns of Nd₂CuO₄, Pr₂CuO₄, Pr_1.85Ce_0.15CuO₄, and Sm₂CuO₄, taken along the [11̅0] direction. For the Pr₂CuO₄, Pr_1.85Ce_0.15CuO₄, and Sm₂CuO₄ crystals, satellite reflections at 0.24 0.24 0.72, 1/3 1/3 0, and 1/2 1/2 1 are observed, as shown in Figure 17B, C, and D, respectively. Figures 17E and F are electron diffraction patterns of Pr₂CuO₄ taken along the [010] and [1̅11] directions, respectively, which also indicates weak diffuse scattering and sharp satellite reflections at 1/2 0 1/2 and 1/4 1/4 1/2, respectively. A superstructure have been observed and characterized for Nd_2-xCe_xCuO₄ by a wave vector q=<1/4 1/4 0> [62] and was suggested that the modulation is due to ordering of oxygen vacancy and/or Ce. However, the satellite reflections were not observed in the diffraction patterns of Nd₂CuO₄ and Pr₂CuO₄ quenched from 1100°C. The result indicates that the appearance of superstructures is sensitive to the oxygen content and unrelated to ordering of Ce atoms. As neutron diffraction study shows the deficiency of oxygen in Cu-O planes, it can be supposed that the superlattices are due to ordering of oxygen atoms in the Cu-O planes.

Figure 17

Electron diffraction patterns of (A) Nd₂CuO₄, (B) Pr₂CuO₄, (C) Pr_1.85Ce_0.15CuO₄, and (D) Sm₂CuO₄, taken with the [11̅0] incidence. Electron diffraction patterns of Pr₂CuO₄ taken along the (E) [010] and (F) [1̅11] directions.

Superconducting thin films can be used for electronic devices and other applications [69–73]. Chemically, vapor deposited (CVD) YBa₂Cu₃O₇ thin films with high critical current density (J_c) of 6.5×10⁴ A/cm² at 77.3 K and 27 T were investigated [74, 75]. The films were deposited on the SrTiO₃(100) substrate. β-diketonate complexes (2, 2, 6, 6-tetramethy 1-3, 5-heptanedionate chelated Y³⁺, Ba²⁺, and Cu²⁺) were used as the three vapor sources [76]. The films were deposited in a mixed gas atmosphere or Ar/O₂=3/1 at 10 Torr on the substrate, which was heated at 900°C close to the melting point of YBa₂Cu₃O_7-y. The post-annealing was carried out in the O₂ atmosphere at 1 atm. To view the cross-section of the CVD film, two pieces of cut substrate and film were pasted together, film to film, then cut again perpendicular to the film and polished in an Ar ion sputtering mill.

Figure 18A is a low-magnification image obtained with the incident beam perpendicular to the substrate. Relatively large grains of 20∼100 nm in size are observed in the image. Many observed precipitates showed Moiré fringes, which indicates that the precipitates are semicoherent with the matrix and have very similar crystal lattice. A cross-sectional high-resolution image is shown in Figure 18B. Relatively large precipitates ∼30 nm in size are embedded parallel to the c-planes. These precipitates could act as the flux-pinning centers, which would result in the high J_c. Many defect regions are formed parallel to c-planes, as shown in Figure 18C. The defect regions consist of extra layers and ∼20 nm in diameter with deformed regions adjacent to them. Those faulted regions may also act as the flux-pinning centers. Figure 18D is a cross-sectional HREM image of a grain in the CVD film, and most of the grains have a preferred c-axis orientation perpendicular to the SrTiO₃(100) substrate, as indicated by region 1. On the other hand, the c-axis is oriented parallel to the SrTiO₃(100) substrate in a region 2. An enlarged HREM image at the grain boundary interface is shown in Figure 18E, and the c-axis of the YBa₂Cu₃O₇ structure is perpendicular to one another. A structure model and a structure image of YBa₂Cu₃O₇ are shown in Figure 18F and G, respectively. Undeformed YBa₂Cu₃O_7-x domains, interleaved by the faulted regions, are ∼50 nm in size. The electron diffraction pattern taken with the incident beam parallel to [010] did not change when the specimen was tilted by 5°, which is appreciably wider than the usual crystals. Such morphology indicates that the sample was grown quickly at a temperature just below the melting point or YBa₂Cu₃O_7-x where the homogeneous nucleation process followed by the preferential crystal growth in the c-planes occurs.

Figure 18

(A) Low magnification image of CVD-YBa₂Cu₃O₇ film taken with the electron beam perpendicular to the substrate. Round precipitates with Moiré fringes on them are observed. (B) Cross-sectional HREM image of CVD-YBa₂Cu₃O₇ film taken with the electron beam parallel to the a-axis. (C) Stacking faults in the film. HREM image of (D) a grain and (E) grain boundary of the film. (F) Structure model and (G) structure image of YBa₂Cu₃O₇ together with a projected structure model.

Bulk types of YBa₂Cu₃O_7-x superconductors with high J_c were also investigated. Oxide powders or Y, Ba, and Cu were mixed with the composition of YBa₂Cu₃O_7-x phase. The mixture was calcined at 900°C for 24 h and then reground. After this process was repeated twice, a small amount of additive oxide powder with a perovskite structure BaZrO₃ was added, 3 mol%, to the YBa₂Cu₃O_7-x powder [77]. Again, grinding and calcining were repeated, and the pellets were sintered at 950°C for 24 h and then cooled slowly. The bulk sample showed high critical current density of 2.0×10⁵ A/cm² at 77.3 K and 0.1 T.

Figure 19A is a TEM image of an YBa₂Cu₃O_7-x bulk specimen with BaZrO₃ additive, where two types of fine particles with spherical and irregular shapes are lying in the YBa₂Cu₃O_7-x matrix. Their minimum size was ∼20 nm, and the average size was roughly estimated to be ∼100 nm, and they were confirmed to be BaZrO₃ phase from electron diffraction. Figure 19B is a HREM lattice image near the grain boundary between the BaZrO₃ phase and the YBa₂Cu₃O_7-x matrix, where both lattice planes generating a lattice fringe are assigned as indicated in the figure. The lattice plane continues across the interface, but the extra half plane is inserted in every 20 fringes within the BaZrO₃ phase, while the interval for the extra half plane is theoretically suggested to be every 14 fringes. Therefore, the interface in this region was suggested to be semi-coherent. The mechanism of fine dispersion of ABO₃ oxides in the matrix is not yet fully understood. It is suggested that the grain growth takes place during sintering, and ABO₃ phase is dragged into the growing grain as the same species as the matrix because both phases have a similar crystal structure and have a semi-coherent interface as mentioned above. Several types of pinning centers like Y₂BaCuO₅ [78], CuO [79], SnO₂ [80], ZrO₂ [81], and irradiation-induced defects [82] have been reported to be effective for the YBa₂Cu₃O_7-x superconductor [83–87]. A perovskite-type oxide, ABO₃, seems to be a promising candidate as pinning center for the superconducting copper oxides because the crystal structure is similar to the host superconducting phase. A remarkable flux-pinning effect could be expected by introducing the oxide. Homogeneous distribution of non-superconducting fine particles is very effective, when they distribute in the same dimension with the fluxoid lattice. In addition, the matrix is distorted around the particles with different unit volume by the coherent interface with the matrix, and a significant change of the superconducting property is expected around the coherent particles.

Figure 19

(A) TEM image of 3 mol%-BaZrO₃ dispersed YBa₂Cu₃O_6+x. (B) HREM image at the BaZrO₃ nanoparticles and YBa₂Cu₃O_6+x matrix interface.

The crystal structure of YBa₂Cu₃O₇ is based on a triple perovskite structure and is characterized by the ordering of oxygen vacancies, as shown in Figure 18F, that is, the oxygen positions on the Y atom layer and between two Ba atoms are vacant. In addition, oxygen orderings in the Cu-O basal planes were observed [7]. Bulk samples of YBa₂Cu₃O_7-x superconductors were prepared by mixing BaCO₃, Y₂O₃, and CuO powders with the composition of YBa₂Cu₃O_7-x phase. The mixture pellets were calcined at 930°C for 12 h in air and then cooled slowly in a furnace. After crushing the pellets to form powders, the process was repeated once more. The obtained pellets were reheated at 500∼900°C and quenched into liquid nitrogen, and subsequently annealed at 500∼300°C in the vacuum seal. The pellets were also annealed in a flowing N₂ gas at various temperatures to control the oxygen contents. The oxygen contents were investigated by iodimetric measurements and mass change.

As the consequence of the tetragonal-to-orthorhombic phase transition of YBa₂Cu₃O_7-x at ∼600°C [88, 89], twin boundaries are often observed. Figures 20A and B are TEM image and lattice image of YBa₂Cu₃O_7-x taken with the incident beam parallel to the c-axis. Twin boundaries (TB) are coherent and indicated by arrows. The twin boundaries show distinct contrast in the TEM image, and the existence of boundaries is evident from kinks of the lattice fringes. In the oxygen-deficient YBa₂Cu₃O_7-x compounds, oxygen vacancy ordering was observed. Figure 20C and D are electron diffraction patterns of YBa₂Cu₃O_6.68 taken with the incident beam parallel to the c-axis and b-axis, respectively. The electron diffraction pattern shows orthorhombic structure with a- and b-axis and a twin structure with a {110} twin plane. Both electron diffraction patterns in Figure 20C and D shows diffuse satellite reflections at 1/2 0 0 along the a-axis. This indicates the existence of modulated superstructure with a modulation wave vector q=<1/2 0 0>, which would be due to ordering of oxygen vacancies on the basal Cu-O planes. Figure 20E is a Fourier transform of HREM image of Figure 20B, and filtered inverse Fourier transform of Figure 20E is shown in Figure 20F, in which linear bright stripes with the distance of 2a are observed along the a-axis. The twin boundary can be clearly seen at a glancing view parallel to the a- or b-axis in Figure 20F.

Figure 20

(A) TEM image and (B) lattice image of YBa₂Cu₃O_7-x taken with the incident beam parallel to the c-axis. Twin boundaries (TB) are indicated by arrows. Electron diffraction patterns of YBa₂Cu₃O_6.68 taken with the incident beam parallel to the (C) c-axis and (D) b-axis. (E) Fourier transform of (B). (F) Filtered inverse Fourier transform of (E).

Electron diffraction patterns of oxygen-deficient YBa₂Cu₃O_6.80, YBa₂Cu₃O_6.47, YBa₂Cu₃O_6.23, and YBa₂Cu₃O_6.29 taken along the c-axis are shown in Figure 21A–D, respectively. In Figure 21A, weak diffuse streaks are observed along the a-axis, which would indicate short-range ordering of oxygen atoms. In Figure 21B and C, superstructures with a modulation wave vector q=<1/3 0 0> and <0 1/3 0>, which indicates the superstructure are formed along the a-axis and b-axis of the orthorhombic cell, respectively. In addition, a superstructure with a modulation wave vector q=<1/4 0 0> is observed along the a-axis, as shown in Figure 21D. These modulated structures are summarized as listed in Table 9.

Figure 21

Electron diffraction patterns of (A) YBa₂Cu₃O_6.80, (B) YBa₂Cu₃O_6.47, (C) YBa₂Cu₃O_6.23, and (D) YBa₂Cu₃O_6.29 taken along the c-axis. (E) HREM lattice image and (F) electron diffraction pattern of YBa₂Cu₃O_6.47 taken along the c-axis.

Figure 21E and F are a lattice image and an electron diffraction pattern of YBa₂Cu₃O_6.47 taken with the [001] incidence. Satellite peaks with a modulation wave vector q=<1/3 0 0> are observed together with q=<1/2 0 0> in the diffraction pattern. Linear bright stripes with the distance of 3a are observed along the two principal lattice directions in the HREM image of Figure 21E.

From these observations, a model for the ordered arrangement of oxygen vacancies is proposed, as shown in Figure 22A. The fundamental unit cell is orthorhombic, with a dimension of 2a×b×c. Other oxygen-ordering models of basal planes (Cu-O) of the YBa₂Cu₃O_7-x are also proposed as shown in Figure 22B, which depends on the oxygen content. These phases would correspond to the ortho-II phase and ortho-III phases [90–96], which results in the changes of Tc, and the control of oxygen atoms in the oxide crystals is important [97–99].

Figure 22

Models for ordered arrangement of oxygen vacancies in YBa₂Cu₃O_7-x. (A) A 2-times model along the a-axis. (B) Oxygen-ordering models of basal planes (Cu-O) of the YBa₂Cu₃O_7-x.

Bi-based copper oxides with Ag are expected for wire application [100–102]. A spray-dried aqueous solution of nitrates with atomic ratio Bi_1.5Pb_0.5Sr₂Ca₂Cu₃ was calcined at 650°C for 15 h, resulting in a mixture of oxides [103–105]. The resulting precursor powder with a grain size of 3 μm was mixed with 30 vol% Ag whiskers with a diameter of 20–50 μm and a length of a few hundred micrometers. The Ag whiskers were synthesized via an electrochemical reduction of a Ag nitrate solution by a copper wire at pH 2. The mixture was pressed into bars and sintered at 853°C for 170 h in air to obtain the Bi-2223/Ag composites.

Figure 23A is a TEM image of the Bi-2223/Ag whisker interface in a sintered composite. A thin layer with a different contrast is observed at the Bi-2223/Ag interface. Electron diffractions of Ag and Bi-2223 phase are also shown in Figures 23B and C, respectively. Figure 23B is observed along the [11̅0] of the face-centered cubic Ag crystal. The diffraction pattern of Bi-2223 phase in Figure 23C was taken along the a-axis, which indicates a modulated structure with a modulation wave vector of q∼<0 1/4 0>. The origin of the modulated superstructure would be metal atom displacements in the crystal [106–114].

Figure 23

(A) TEM image of (Bi,Pb)₂Sr₂Ca₂Cu₃O_x/Ag whisker interface in a sintered composite. Electron diffraction of (B) Ag and (C) (Bi,Pb)₂Sr₂Ca₂Cu₃O_x.

Figure 24A is a TEM image of the Bi-2223/Ag whisker composite with Ag-rich phase. Lattice fringes of c-planes of Bi-2223 phase are observed, and an amorphous/nanocrystalline (AM-NC) structure is observed at the Ag/Bi-2223 interface. The white areas are the result of preferential ion milling, probably of amorphous phases, which are more easily removed compared to Bi-2223. The superconducting phase is oriented with the c axis perpendicular to the interface. An EDX spectrum of the AM-NC phase in Figure 24A is shown in Figure 24B, which indicates a composition of Ag₂Bi_2.4Pb_0.6Sr₂Ca_0.8Cu_4.3 and an increase of Ag, Bi, Pb and Cu concentration in the amorphous phase. An enlarged HREM image and an electron diffraction pattern at the interface are shown in Figure 24C and D, respectively. The Bi-2223/AM-NC interface exhibits small steps of half or one unit cell of Bi-2223, and such intermediary phase was also observed [115]. The diffraction pattern exhibits [110] incident of the Bi-2223 crystal, and the observed streak along the c-axis indicates that there is a small amount of Bi-2212 or Bi-2234 phase to form an intergrowth structure. A diffuse ring is also observed as indicated by arrows, which exhibits the amorphous-like structure of AM-NC phase. The influence of Ag on the yield in Bi-2223 synthesis can be explained in terms of the shift in the incongruent melting point.

Figure 24

(A) TEM image of the Bi-2223/Ag whisker composite with Ag-rich phase. (B) EDX spectrum of the AM-NC phase in (A). (C) HREM and (D) electron diffraction pattern at the interface.

In order to observe the atomic arrangements of the Bi-2223 phase more clearly, crystallographic image processing was carried out for the Fourier transform of the HREM image. Figure 25A is a HREM image after crystallographic image processing of Bi2223, together with a projected structure model and a simulated image enclosed by a white square. The HREM image clearly shows the metal atom arrangements in the crystal, and the lines indicate the unit cell. The shading and size of the black spots corresponding to (Bi, Pb), Sr, Cu, and Ca positions can be identified as being nearly proportional to their atomic numbers. Although oxygen atoms are not represented as dark spots in Figure 25A, information on the oxygen positions should be included in the image [14, 116]. In the Ca layers, oxygen positions indicated by Ov show a brighter contrast than the other white regions, which indicates the existence of an ordering of oxygen vacancies in the (Bi, Pb) layers. A structure model of Bi(Pb)-2223 determined by X-ray diffraction [117] is inserted into Figure 25A and agrees well with the arrangements of the black dots. To investigate the observed HREM image in detail, HREM images were calculated based on the structure model for Bi-2223. Figure 25B shows calculated HREM images for Bi-2223 along the [11̅0] direction. Image calculations were carried out for various defocus values (under defocus) and crystal thickness to determine the imaging conditions of the observed images. The contrast changes of the images are very sensitive to both defocus value and crystal thickness, and (Bi, Pb) double layers are observed as dark dots around the defocus value of 30 nm. The simulation image calculated at the defocus value of -30 nm and crystal thickness of 2.7 nm is inserted into Figure 25A and agrees well with the observed HREM image.

Figure 25

(A) HREM image after crystallographic image processing of Bi2223, together with a projected structure model and a simulated image enclosed by a white square. Oxygen vacancies are indicated by Ov. (B) Calculated image of Bi-2223 as a function of crystal thickness and defocus values of the TEM objective lens.

As mentioned in the previous sections, the perovskite-type superconducting copper oxides have many types of layer structures with slightly different compositions. Thus, their crystals always include a high density of intergrowth with various types of structures, in addition to well-ordered regions. A typical example of such disordered regions is shown in Figure 26A, which is a one-dimensional lattice image of TlBa₂Ca₃Cu₄O₁₁ taken with the incident beam perpendicular to the c-axis. Although the image does not represent each atom, stacking sequence of the layered structure can be distinguished; that is, thick black lines correspond to Tl and Ba layers, and thin white lines correspond to Ca layers with oxygen vacancy. In Figure 26A, two-, three-, five-, and six-fold Cu sequences (white lines) between Tl and Ba layers (thick black lines) are observed in addition to the usual fourfold Cu sequences. This intergrowth gives rise to steps decreasing of electron conductivity near T_c, showing multiple transition temperatures [15] because the structures with different numbers of Cu-O layers show different transition temperatures. This defect is very sensitive to annealing condition of the sample. The lattice images such as Figure 26A can be easily observed and have enough information on the intergrowth of various layer structures. Figure 26B is also a HREM image of TlBa₂Ca₃Cu₄O₁₁, which has a higher resolution than that of Figure 26A. Although the HREM image is a two-dimensional image, it is not a structure image. It is interesting that the periodic intergrowth forms a new ordered structure with a long period. It would be difficult to synthesize this type of crystal with a single phase.

Figure 26

High-resolution lattice images of TlBa₂Ca₃Cu₄O₁₁ taken with the incident beam (A) perpendicular to the c-axis and (B) parallel to the a-axis.

It is well known that Tl atoms in the Tl-based superconductors are easily vapored at high temperatures, and Tl content deceases by annealing at high temperatures. Figures 27 are one-dimensional lattice images of Tl-vaporized regions. Starting composition of the sample was Tl:Ba:Ca:Cu=2:2:2:3 and was sintered at 890°C for 10 h. In the lattice image in Figure 27A, black strain contrasts are observed, which resulted from lattice deformation around the terminations of Tl-O layers, being about to disappear by the vaporization of Tl, as indicated by small arrows. In Figure 27B, the vaporization of Tl progressed furthermore. The regions of Cu-O layers were expanded, and the strain field contrasts become stronger. After Tl-O layers disappear, the remaining Ba-O layers are observed, as indicated by arrows in Figure 27B.

Figure 27

(A) High-resolution lattice images taken with the incident beam perpendicular to the c-axis. (B) More Tl-vaporized region.

Similar structures were often observed in the Pb-based superconductors. An intergrowth of (Pb, Cu) layers is observed in PbBaSrYCu₃O₇ (Pb-2212), as shown in Figure 28A. In the image, the intergrowth of two types of units, (a) and (b), which have double (Pb, Cu) layers and stacks of two (Pb, Cu) and one Cu layers is observed. A high density intergrowth in PbBa_0.7Sr_1.3YCe₃Cu₃O₁₃ is also shown in Figure 28B. In this image, the intergrowth of various numbers of (Y, Ce) layers was observed, and disappearance of (Pb, Cu) layers is also observed as indicated by arrows, and extended regions of the (Y, Ce) layers can be seen. Observations of the intergrowth give us variable information on the possibility of appearance of new unknown structures and on the transitional structures to the equilibrium state.

Figure 28

HREM images of (A) PbBaSrYCu₃O₇ and (B) PbBa_0.7Sr_1.3YCe₃Cu₃O₁₃ taken with the incident beam parallel to the a-axis. Number of (Y, Ce) layers are shown in (B).

Lattice defects, particularly dislocations in the superconductors having complex structures, are an interesting subject to study mechanical and electrical properties of these materials. Figure 29A is an end-on view of a dislocation observed in the Tl₂Ba₂CuO₆. The dislocation is laid along the [11̅0] direction parallel to the incident beam direction. An extra plane can be seen by obliquely viewing Figure 29A along the vertical direction. Figure 29B is a Fourier transform of Figure 29A, and Figure 29C is an image reconstructed by using 110 and 1̅1̅0 reflection in the Fourier diffractogram of Figure 29B. Figure 29D is an enlarged image of Figure 29C. In the image of Figure 29D, a long range strain field over 4 nm in diameter is observed around the dislocation core. Although a Burgers vector of this dislocation cannot be determined from only this image, it would be [100] of the perovskite unit. The smallest Burgers vector in the perovskite unit is 1/2 [111] position, but the dislocation with the [100] Burgers vector is possibly stable in this structure because a different type of atom is placed at the 1/2 [111] position. This dislocation would be considered to be formed during crystal growth, and it would be placed in the most stable state.

Figure 29

(A) High-resolution image of an end-on view of a dislocation in Tl₂Ba₂CuO₆, taken with the incident beam parallel to the [11̅0] direction. (B) Fourier transform of (A). (C) Image reconstructed by using 110 and 1̅1̅0 reflection in the Fourier diffractogram of (A). (D) Enlarged image of (C).

Understanding of interface and surface structures is important for application of the superconductors to electronic devices such as Josephson junction and superconducting transistor [118–122], as illustrated in Figure 30A and B, respectively. Recently, the surface structure has been widely studied with scanning tunneling microscopy in the atomic scale. High-resolution electron microscopy has also made possible to observe atomic structures of interfaces and surfaces in the superconductors. Figure 30C is a one-dimensional lattice image of an anti-phase boundary in Tl₂Ba₂CuO₆, which was observed perpendicular to the c-axis. Tl layers are indicated by arrows, and the phase displacement is 0.2c along the c-axis at the interface. This indicates that the displacement corresponds to one block of the perovskite cell, and the Tl layers are connected with Cu layer at the interface. Figure 30D is a structure image of an anti-phase boundary in TlBa₂CaCu₂O₇ taken along the a-axis. The interface is {103} of the TlBa₂CaCu₂O₇ structure, and the phase displacement is 0.21c+0.5a. This indicates that the displacement corresponds to half block of the perovskite cell, and the Tl layers are connected with the Ba layers at the interface. Small disordering of atoms is observed at the interface within ∼2 nm, which would work as insulator layers between two crystals. These interfacial structures with distances of a few nanometers are suitable for the Josephson junction devices as shown in Figure 30A.

Figure 30

Schematic illustration of (A) Josephson junction and (B) superconducting transistor. HREM images at the interfaces of (C) Tl₂Ba₂CuO₆ and (D) TlBa₂CaCu₂O₇.

Surface structures are important information on the superconducting transistors as illustrated in Figure 30B. Figure 31A is a HREM structure image of TlBa₂Ca₃Cu₄O₁₁ taken with the incident beam parallel to the a-axis. The image is observed without any contamination layers at the sample edge, and an atomic arrangement can be directly observed at the crystal surface. High-resolution images were obtained from thin samples, which were selected from crushed materials dispersed in a solution of n-butanol and dropped on holely carbon films. A mixing of Tl, Ba, Ca, and Cu atoms near the surface is observed. Figure 31B is a HREM structure image of Tl_0.5Pb_0.5Sr₂CuO₅ taken along the a-axis together with a projected structure model, which indicates no preferential surface structure. Figure 31C is a HREM structure image of Pb₂Sr₂Y_0.5Cu₃O₈, and a characteristic surface structure with valleys at Pb layers and hills at between the Pb layers is observed. In the region of the hills, mixing of atoms appears to occur. A HREM structure image of PbBa_0.7Sr_1.3EuCeCu₃O₉ taken along the a-axis is shown in Figure 31D, which indicates preferential atomic arrangements on the c-plane of the crystal. A HREM structure image of TlBa₂CaCu₂O₇ is also shown in Figure 31E. At the crystal edge, preferential fracture occurs between Tl and Ba layers, as indicated by arrowheads, and the fracture surface has steps with Tl layers. This result shows that the fracture surface parallel to the c-plane in the superconductor is stable and chemically unreactive to the solution and the atmosphere. On the other hand, the surface structures of the fracture nearly perpendicular to the c-axis show complex structures formed by rearrangement of atoms near the edge. However, Hg-based copper oxides showed stable surface [123, 124]. The characteristics of various surface structures should be taken into consideration, when the properties are sensitive to surface structures.

Figure 31

HREM images of (A) TlBa₂Ca₃Cu₄O₁₁, (B) Tl_0.5Pb_0.5Sr₂CuO₅, (C) Pb₂Sr₂Y_0.5Ca_0.5Cu₃O₈, (D) PbBa_0.7Sr_1.3EuCeCu₃O₉, and (E) TlBa₂CaCu₂O₇, taken along the a-axis together with projected structure models.

The microstructural information on the perovskite-type copper oxide superconductors is useful for the materials’ development for superconducting devices such as high-performance superconducting wires, nuclear electromagnetic resonance analytical systems, linear motor car and the international thermonuclear experimental reactor [125–127], and for the theoretical analysis of superconducting mechanism [128–130]. High-resolution electron microscopy and electron diffraction are quite useful for characterization of structures of high-T_c superconducting oxides on the atomic scale. Valuable information on crystal structures from the observed high-resolution images, severe conditions, such as thinner crystals than 2 nm, and definite defocus values of -35 to -45 nm are required. The structure images taken under the severe conditions include information not only on arrangements and accurate coordinates of cations but also on ordered arrangements of oxygen atoms and oxygen vacancies. Many examples of crystal structure analysis of the perovskite-type superconductors were presented from the observed structure images and electron diffractions. Defects, surface, interface, intergowth, and dislocations, which cannot be investigated by diffraction methods, were observed and examined. Modulated superstructures were also observed in various copper oxides, which showed satellite reflections with various modulation wave vectors. The appearance of superstructures is sensitive to the oxygen content, and the superlattices would be due to the ordering of oxygen atoms in the Cu-O planes. Thin films and bulk materials with high J_c were also investigated, and many precipitates showing Moiré fringes were observed in the image, which could act as the flux-pinning centers resulting in the high J_c. Such nanostructural analysis will have an important role for the future development of perovskite-type superconducting copper oxide materials.

The author would like to acknowledge K. Hiraga, S. Nakajima, A. Tokiwa, M. Kikuchi, D. Shindo, M. Hirabayashi, Y. Syono, T. Kajitani, H. Yamane, K. Takagi, T. Hirai, Y. Tokura, E. Bruneel, S. Hoste, K. Osamura, T. Kizu, K. Kosuge, N. Kobayashi, and S. Hosoya for excellent collaborative works, providing samples and fruitful discussion.