Encyclopedia of Smart Materials (Vols 1 and 2) - M. Schwartz (2002) Episode 12 pps

P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 SMART PEROVSKITES 1001 BaCeO 3 can be good conductors of ions and electrons or protons by simply changing the valence of the B cations to mixed valency. Superconductivity Superconductivity is the phenomenon of vanishing elec- trical resistance below the superconducting transition emperature (T c ). Superconductivity has important applica- tions in power transmission, nuclear magnetic resonance, extremely strong magnets, and high-speed computing. High-temperature superconductors, such as YBa 2 Cu 3 O 7 , Bi 2 Sr 2 CaCu 2 O 8+d and Tl 2 Ba 2 Ca 2 Cu 3 O x , are the focus of today’s research (22). Most ceramic superconductors are based on the perovskite structure. The structure of YBa 2 Cu 3 O 7 will be used as an example to show the construction of its structure from anion-deficient perovskites (see later section). A superconductor is characterized by three physical quantities. The first is the critical transition temperature T c , below which superconductivity appears. The second is the critical magnetic field H c , below which a superconducting body exhibits perfect diamagnetism and excludes a magnetic field. If the applied magnetic field is higher than H c , the materials revert to the normal state. H c is temperature-dependent. The third is the critical current density J c , above which superconductivity is destroyed and the superconductor reverts to the normal state. Polycrys- talline superconducting materials are limited mainly by low J c due to the weak link between grain boundaries. Im- proving J c in the field is the essential task of current research in superconductivity. THE FUNDAMENTAL STRUCTURAL CHARACTERISTICS OF ABO 3 PEROVSKITE Perovskite and related structures cover a large portion of smart materials, and their crystal structures can vary to a large extent. The key questions are do the perovskite- type structures have smart properties and are there any intrinsic connections among the structures? The answers may be found in the following areas: (1) nonstoichiometry (a) B O (b) A B O (c) A B O Figure 16. ABO 3 perovskite structure formed by corner-sharing octahedron chains. The corners of the Bravais cell are the B cations. (a) A postulated structure where the A cation is absent at the center, and (b) a structure that has the A cation. The anions shadowed by the octahedra are not shown for clarity. (c) ABO 3 perovskite structure drawn by setting the A cations as the corners of the Bravais cell, showing the BO 6 octahedron located in the A-cation cube. of the cation and/or the anions; (2) distortion of the cation configuration; and (3) the mixed valence and the valence mixture electronic structure. From the viewpoint of crystal structure, each of these features can be introduced by doping a third type of cation into the stoichiometric phase of a base structure. It is important to understand how oxygen stoichiometry and lattice distortion are introduced as a re- sult of doping another type of cation that has different valence states. First, we explore the fundamental perovskite structure (2). Vertex Sharing of Oxygen Octahedra In the ABO 3 type structure, the cation B whose valence is 4+ is usually a transition-metal element that prefers to form a six-coordinated octahedron with its neighboring oxygen anions, and itself is located at the center. The octahedron is the basic unit of these structures. The geometric configuration of the arrangement of the octahedra that has the lowest interactive energy is a linear 180˚ vertex- sharing connection. If the octahedra are connected to each other at every vertex, they form a 3-D network (Fig. 16a). Because the oxygen at every vertex is shared by adjacent octahedra, the composition of this configuration is BO 3 , and the unit cell is a simple cubic, as given in Fig. 16a. This structure, however, cannot exist unless B has a valence of 6+ because the valence charges are not balanced. Thus, a cation of valence 2+ must be introduced into the structure to balance the local excess negative charge. A vertex-sharing octahedral network, on the other hand, has a large cavity in the center of the unit cell. A cation of valence 2+ can occupy this cavity. Then , the unit cell still preserves the simple cubic structure, and the composition is ABO 3 , simply the basic model of the perovskite structure (Fig. 16b). It is clear, therefore, that six-coordinated octahedra are essential structural and compositional building blocks, and sharing of all of the vertexes is required for the stoichiometry and the structure of the perovskite. Based on this ideal, we can outline some characteristics of the perovskite structure: 1. Any cation, that prefers to have six coordination could occupy the B position even if its valence is P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 1002 SMART PEROVSKITES different from 4+, but to balance the valence charges, the average valence at the B site usually equals 4+. 2. The A cation of valence 2+ is expected to have a larger radius because, as a general rule, the valence increases as the radius of the cation decreases and vice versa. The coordination number of the A cation is 12. Elements that have a coordination number of more than six are likely to bond ionically. This is possible because the A cation in the perovskite structure is usually an alkaline-earth metal element. From this viewpoint, we may say that any cation, of higher ioni- city or less polarity could occupy the position of the A cation, although its valence is different from 2+. But to balance the charge, the average valence at this site is likely to be 2+. 3. From 1 and 2, we can see that B cations have some degree of covalency, or in other words, they are easier polarize than A cations, and bonding between the B cation and the adjacent oxygen is stronger than that of the A cation. The octahedron of oxygen is the basic unit of the perovskite structure although it may be distorted, as is discussed later. Oxygen anions have significant influence on the cation valence if it can be changed. For example, a vacancy of oxygen can re- sult in modifying the valence state of the B cation. The A cation may not be easily modified because it bonds ionically to the adjacent oxygen. However, if the A cation changes valence, the surrounding oxygen anions must be affected to balance the valence charges by creating vacancies. Because the oxygen anion cannot have a valence other than −2, an oxygen deficiency must form to balance the local charge. The roles of the A and B cations in the structural evolution of ABO 3 type perovskite can be understood as follows. The A cation plays a key role in oxygen deficiency because of its stronger ionic interaction with oxygen anions. We will see later that the A cation is closely packed together with oxygen. The B cation prefers six-coordination (i.e., an octahedron) although its valence can vary. The flexibility in the valences of the B cation makes the oxygen anion deficiency acceptable, and in a reverse process, the oxygen deficiency is autocontrolled by adjusting the valence of the B cation. This process makes the perovskite structure the most fas- cinating structural configuration for smart materials. If the A cation changes its valence, for example, from +2 to +3, the oxygen anion must modify its occupancytomatch the valence variation of the A cation and to balance the local charge, resulting in oxygen deficiency. But this change will feed back to the B cation, leading to disproportionation of the local valence state. The disproportionation of the B cation’s oxidation state usually changes the electronic band structure of the perovskite compound, resulting in a transition from an insulator to a semiconductor, conductor, or even superconductor. CaMnO 3 is an insulator, but when the Ca (i.e., A 2+ cation) is totally replaced by La(+3), LaMnO 3 could be a conductor if the monovalence Mn 4+ were replaced by mixed valent states of Mn 3+ and Mn 4+ . From the viewpoint of charge balance, if the valence of the Mn cations is +3 and +4, the relative content of the oxygen anions should be more than 3, in other words, its formula should be LaMnO 3+x . Based on the crystallography of the perovskite structure illuminated discussed before, the excess oxygen anions have no place to locate because the existing oxygens have already been closely-packed in the structure. Therefore, if Mn 3+ and Mn 4+ must coexist in the system, the only choice is to change the A cation’s valence state from La 3+ to a mixture of La 3+ and A 2+ , a divalent cation. For example, if a small portion of La 3+ is replaced by Ca 2+ , the La 3+ stoichiometry will change from 1 to 1 − x. Then we can have a perovskite type structure that has +3 and +4 mixed Mn cations at the B site. Unit Cell by Taking the A Cation as the Origin The perovskite structure has a simple cubic Bravais cell, in which the octahedra share corners and the origin of the Bravais cell is at the B cation, as shown in Fig. 16a. Alter- natively, we can also take the A cation as the origin, and the unit cell is transformed into the form given in Fig. 16c. In this configuration, the A cations locate at the cubic vertexes, and the oxygens occupy the face centers of the six faces to form an octahedron where the B cation is at thecen- ter. This geometric arrangement makes the oxygen form linear O 2− –B 4+ –O 2− triples parallel to the x, y, and z axes, and the oxygens are located at the centers of the squares formed by the A 2+ cations. If an electric field is applied parallel to the z axis, for example, the O 2− –B 4+ –O 2− chain parallel to the z axis is polarized, but the O 2− –B 4+ –O 2− chains parallel to the x and y axes may not be disturbed, resulting in polarization of the crystal parallel to the z axis (ferroelectricity). Moreover, the displacement of the oxygen anions could cause a distortion in the configuration of the A cations, resulting in a change in the shape of the unit cell (the piezoelectric effect). Oxygen Cubic Close Packing Now, we reexamine the ABO 3 perovskite structure from a different viewpoint. We use the structural model of perovskite formed by the corner-sharing chains of octahedra, for example, the unit cell that has B cations as the origin, as shown in Figure 16b, in which the octahedron is sketched for clarity. The relationship between the oxygen anions and A cations in the {111} stacking layers are re- vealed in Fig. 17a, where an A cation is surrounded by six oxygen anions and forms a closely packed structure. Note that three oxygen atoms form a triangular unit. Naturally, the A cations also form a hexagonal array, but are separated by the triangularly packed oxygen anions. The chemical composition of this layer is AO 3 . Because the charge ofAis2+, the valencecharge of thelayer is (AO 3 ) 4− . To balance the local negative charge, a layer that has a charge of 4+ must be introduced. Therefore, a B 4+ cation layer (without oxygen anions) should be the next stacking layer (Fig. 17b). The A cation has three stacking positions, indicated by α, β, and γ , respectively, and the B cation has similar stacking. An A cation hexagon contains six apex- sharing oxygen triangles. This characteristic of the fundamental stacking layer (AO 3 ) 4− determines the features of the perovskite structure. The (AO 3 ) 4− and the B 4+ layers are stacked together to form a combined layer, and the perovskite structure is obtained by stacking the new layers following a sequence of αβγby translating the cation P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 SMART PEROVSKITES 1003 (a) α γ β (AO 3 ) 4− (111) stacking layer (b) α γ β B 4+ (111) stacking layer Figure 17. (a) The fundamental (AO 3 ) 4− (111) close-packing layer, and (b) the B 4+ (111) close-packing layer in the perovskite structure. The shadowed area represents the hexagonal unit from stacking the two layers into one. α, β, and γ represent the three cation stacking positions for forming the three-dimensional perovskite structure. sites (similar to the stacking to form a face-centered-cubic lattice). Anion Close Packing and Formation of Tetrahedra and Octahedra The introduction of oxygen vacancies in the unit cell can create a wide range of perovskite structures. If one of the oxygen sublattices is vacant, the layer composition is (AO 2 ) 2− (see Fig. 18b). If two of the oxygen sublattices are vacant, the layer composition is AO; thus, the layers are neutral, provided the valence of cation A is 2+. There is no electrostatic force attracting the B 4+ cation layers, and thus, the perovskite structure cannot be formed. If oxygen vacancies are partially formed in the (AO 3 ) 4− layer, the close-packing layer should be (AO 3−x ) (4−2x)− (Fig. 18c,d where x = 0.67 and x = 0.33, respectively). Therefore, there are two choices to have oxygen vacancies in the three oxygen sublattices. If one oxygen vacancy is formed in the oxygen sublattice, it can locate in different layers and/or different sublattices of oxygen. The symmetry of oxygen triangles makes vacancies possible at different corners of the triangles that belong to alternate stacking layers. This creates the five- and four-coordinated oxygen polyhedra, shown in Fig. 19, where the structure of the B cations does not change, but their valence states may change to balance the local charge. The A cations in the (a) (AO 3 ) 4− layer (b) (AO 2 ) 2− layer (c) (AO 2.33 ) 2.67− layer (d) (AO 2.67 ) 3.33− layer Figure 18. Two-dimensional oxygen sublattices in the (AO 3 ) 4− layers (a) no vacancy [(AO 3 ) 4− ], (b) one vacancy [(AO 2 ) 2− ], and (c, d) partial vacancies. (AO 3 ) 4− layer may change their valence states and/or their total number in the layer (e.g., stoichiometry). Therefore, the substitution of the A cations by an element of different valence may be the optimum choice to induce oxygen deficiency and/or the mixed valence statesoftheBcations. This is the tailoring characteristic of the perovskite structure. In the ABO 3 structure, the A cations are closely packed with the oxygen anions and are dominated by ionic bonding. The B cations may be regarded as the dependent subordinations that rely on the structure of the (AO 3 ) 4− layer. Bonding of B cations with the surrounding oxygens may be ionic, covalent, or partially covalent. If the (AO 3 ) 4− layer has defects, such as vacancies, stacking these layers will form distorted or deficient oxygen octahedra. Thus, the B cation must have the flexibility of modifying its valence state to balance the local charge. In other words, if we intend to modify the valence of the B cation, changing the structure surrounding the A cations via doping is recommended. This is an important principle for modifying the structure and properties of perovskites. ANION-DEFICIENT PEROVSKITE STRUCTURAL UNITS—THE FUNDAMENTAL BUILDING BLOCKS FOR NEW STRUCTURES Perovskite types of structures are the basis of many oxides, in which oxygen-deficient perovskites are a key group of materials that possess functionality. Anion-deficiency can change the coordination number of the B cation octahedra and the size and type of the Bravais unit cell of the compounds. It is important to elucidate the possible types of anion-deficient perovskite structures to enhance insight into fabricating new materials. As shown in Fig. 18, there are three equivalent stacking positions for the layers parallel to the (111) plane. Fig- ure 19a shows an αβ stacking of the (AO 3 ) 4− layers (the P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 1004 SMART PEROVSKITES (a) 1 2 V 2 V 1 2 2 2 V 2 V 2 V 1 2 α β γ Figure 19. The local oxygen vacancy arrange- ments and the stacking of the (AO 3 ) 4− type layers (with vacancies). (a) Single and double oxygen vacancies in BO 6 octahedron, where 1, 2, and 3 represent the anions in the α, β, and γ layers, respectively. (b, c) Connections of the octahedra without, with one, and with two oxygen vacancies. (b) (c) 3 3 33 2 3 3 3 3 3 3 2 22 2 3 2 2 2 2 2 3 3 3 3 3 V 3 V 3 V 2 V 3 V 2 B cation Anions in first, second and third stacking layers, respectively A cation in the first stacking layer α, β, and γ positions are indicated in the left part of this figure). The octahedra are formed by superimposed oxygen triangles that belong to the α and β layers (this is most easily seen in Fig. 18). If an oxygen vacancy is created in the β layer, as indicated by V 2 ,afive-coordinated polyhedron is formed. By the same token, oxygen vacancies can be created in the octahedra formed by the superposition of the β and γ layers, as shown in Fig. 19a,b, where the sequence numbers 1, 2, and 3 represent the anions in the α, β, and γ layers, respectively. As discussed before, any (AO 3 ) 4− stacking layer can have oxygen vacancies. A five-coordinated polyhedron is formed if only one oxygen vacancy is created in the β layer, and the α layer is perfect. If two oxygen vacancies (V 1 and V 2 ) are created in the two adjacent layers within the same octahedron, a four-coordinated square is formed, as shown in Fig. 19a. It is impossible to have more than two vacancies in one octahedron because four apexes are the minimum to form a 3-D connection for the perovskite type of frame. The geometric assemblies of the four-, five-, and six-coordinated A cations are given in Fig. 19c. Figure 20a,b shows the BO 5 and BO 4 structures, respectively, in an octahedral sheet. The lack of one oxygen at a vertex forms a five-coordinated unit (Fig. 20a), and the lack of two oxygens located at two opposite vertexes results in a four-coordinated square (Fig. 20b). The lack of three oxygens in one octahedron forces the unit to break its connections to other octahedra. Figure 20c shows a cluster constructed on the basis of the symmetrical distribution of two oxygen octahedra, resulting in four 5-coordinated polyhedra and two 4-coordinated squares. It has the composition AB 8 O 30 , and it demonstrates how the different coordinated polyhedra may be connected to each other in 3-D. Figure 20d–n shows eight possible interconnecting configurations of the five- and four-coordinated polyhedra (2). Any of these types of anion-deficient perovskite-like P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 SMART PEROVSKITES 1005 (a) BO 5 unit V O B (b) BO 4 unit (c) O A AB 8 O 30 cluster B BO 5 unit (d) B B (e) (f) (g) BO 4 unit (h) (i) (j) (k) (l) Figure 20. A total of 14 perovskite-type structural modules that have oxygen vacancies, where the oxygen anions are represented by different patterns to distinguish their stacking layers and V stands for vacancy. The combination of these modules can reproduce the crystal structures of many compounds (see text). P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 1006 SMART PEROVSKITES (m) (n) Figure 20. (Continued ) structural modules may be connected to the ideal perovskite structure’s unit cells to form a new structure. The compound YBaCuFeO 5 (23), for example, has a structure that contains CuO 5 and FeO 5 units, corresponding to configuration (f) shown in Fig. 20. LaBa 2 Cu 2 TaO 8 (24) and Ba 2 La 2 Cu 2 Sn 2 O 11 (25) belong to the module shown in Fig. 20(l). The idealized structure of this compound contains TaO 6 or SnO 6 octahedra and five-coordinated CuO 5 . The structure of YBa 2 Cu 3 O 7 (26) is built by the unit in Fig. 20(l), and it contains five-coordinated CuO 5 and four- coordinated CuO 4 squares. The compound La 2 Ni 2 O 5 is constructed by the (h) type in Fig. 20, and it contains NiO 6 octahedra and NiO 4 four-coordinated squares. These types of anion-deficient perovskite-like units can be combined with tetrahedra, octahedra, or others including themselves to form a variety of different structures. The compound Ca 2 Mn 2 O 5 (27), for example, contains distorted MnO 5 units similar to the (m) type unit shown in Figure 20. The modules shown here are based the squares, tetrahedra, square-based pyramids (half-octahedra) and octahedra. These are the most fundamental “bricks” for constructing anion-deficient perovskite structures. It must be pointed out that although the structural modules proposed in Fig. 20 assume that the atom sites are the same as in perfect perovskite structures, in practice, lattice relaxation/distortion is possible due to unbalanced anion coordination and oxygen vacancies. Fine-tuning of the structure must rely on quantitative fitting of X-ray or neutron diffraction data. STRUCTURAL EVOLUTION IN THE FAMILY OF PEROVSKITES High-Temperature Superconductors In high T c superconductors, the B cation is Cu that has +1, +2, and +3 valence states and coordination numbers 2, 3, and 4 for Cu(I) and 4 and 6 for Cu(II) and Cu(III). If the A and B cations in ABO 3−x have valences +3 and +2, respectively, the (AO 3 ) 4− layers must be replaced by(AO 3−x ) (3−2x)− . Because the Cu cation (the B cation) may have valence +1, +2, and +3, the perovskite- type cell that contains oxygen vacancies gives the Cu cation the possibility of disproportionating its valence from +2to+1 plus +3. Figure 21a gives the module shown previously in Fig. 20(l). The B cation in this module has two types of coordinations: BO 5 and BO 4 .Ifweflip this module over, as shown in Fig. 21b, and combine these two by superimposing the BO 4 units of the two, we ob- tain the new module given in Fig. 21c. This new module is the building block for the Y–Ba–Cu–O system of high T c superconductors and introduces Ba cations between the modules. The structure of YBa 2 Cu 3 O 7 is given in Fig. 21d. Combining BO 4 units and the YBa 2 Cu 3 O 7 module (Fig. 21d) produces the structure of YBa 2 Cu 4 O 8 (Fig. 21f). Stacking YBa 2 Cu 3 O 7 and the YBa 2 Cu 4 O 8 modules creates the structure of Y 2 Ba 4 Cu 7 O 15 (Fig. 21g). Anion Deficiency-Induced Brownmillerite Structure As we discussed before, the ABO 3 type perovskite has a fundamental stacking layer (AO 3 ) 4− in which the A cations play a key role in creating oxygen vacancies. In general, the A cations have the valence +2 and an ionic character, which means that their coordination numbers are higher than six, for instance, 12. If the A cations have the valence +3 and an ionic character, the oxygen in the (AO 3 ) 4− layers must be modified by creating oxygen vacancies. The charge of the layer is (AO 3 ) 3− ; thus, the B cation layers must be modified to balance the local excess positive charge. The B cations usually have polarization or partial covalence, and they have favorable coordination numbers for reduc- ing energy. If the valence of partial A cations is changed from +3to+2, the negative charge of (AO 3 ) layers increases from −3to−(3 + x), where x depends on the relative population of A 2+ . Simultaneously, part of the B cations should modify their valence state from +3to+4 to balance the local charge. The percentage of B cations whose valence is modified is related to the x value, as La 1−x Sr x MnO 3 .Mn 3+ and Mn 4+ cations are both favorable for six-coordinated octahedra, but the situation is different for Co cations. Both Co 3+ and Co 4+ can have six and four coordinations. Four-coordinated Co 4+ requires the presence of oxygen vacancies; thus, the (AO 3 ) layer is replaced by (A 3+ 1−x A 2+ x O 3−y ) (3+x−2y)− . On the other hand, if some B cations are reduced and their valence state is decreased from +3to+2, the (AO 3 ) 3− layers are required to compensate for the excess negative charge, resulting in oxygen vacancies and the change in P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 SMART PEROVSKITES 1007 (a) Module (1) (b) Flip (a) vertically and horizontally (c) (f) YBa 2 Cu 4 O 8 (g) Oxygen anion Vacancy Y cation Cu cation Ba cation Y 2 Ba 4 Cu 7 O 15 Y123 type block Y124 type block YBa 2 Cu 3 O 7 (d) (e) Figure 21. Evolution of the oxygen-deficient perovskite modules into the crystal structures of the Y–Ba–Cu–O system. (a) The module given in Fig. 20(l); (b) the module is flipped over vertically and horizontally. (c) The modules in (a) and (b) are combined by superimposing the BO 4 units to form a new module, which is the structural building block for YB 2 Cu 3 O 7 . (d) The structure of YB 2 Cu 3 O 7 . (e) A new module created by combining the two modules in (a) and (b) to share the edges of the BO 4 units. This new module is the building block of the structure of YBa 2 Cu 4 O 8 . (f) The structure of YBa 2 Cu 4 O 8 . (g) The structure of Y 2 Ba 4 Cu 7 O 15 is a combination of the modules in (c) and (e). P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 1008 SMART PEROVSKITES Perovskite Tetrahedron chain (a) ABO 3-x (b) ABO 2.75 (c) ABO 2.5 brownmillerite structure (d) Figure 22. Structural evolution from perovskite and tetrahedron chains to form ABO 3−x , ABO 2.75 , and ABO 2.5 (brownmillerite) structures owing to ordered anion deficiency. In all of these structures, the A and B cation lattice remains the same as that in standard perovskite, although for clarity they are not shown in the models; the only change is the introduction of anion vacancies. the coordination number of the B cations. If the percentage of reduced B cations is small, the perovskite structure still holds. If the percentage of reduced B cations reaches an upper limit, the perovskite structure has to be changed to another structure that might be related to perovskite. The structural evolution from perovskite into the brownmillerite structure is an example. ACoO 3 (A = La, Pr, Nd, Gd) perovskite is a typical example. Methane gas can be oxidized by LaCoO 3 above 1000 ◦ C. This means that LaCoO 3 can release lattice oxygen (28,29). Co 2+ cations can have coordinationnumbersofsix,five,and four. During the reduction process, Co 3+ can be reduced to Co 2+ and Co 0 . The coordination is changed from octahedral to tetrahedral. During the reduction process, the anion framework should hold, but it can have vacant sites. The perovskite unit and the possible corner-sharing tetrahedron chain are shown in Fig. 22a. When these chains are connected to neighboring octahedra, the remaining two corners of each tetrahedron are shared. If we randomly insert these tetrahedra chains into the perovskite structure (Fig. 22b), the compound is ABO 3−x . As the number of tetrahedron chains increases and reaches a number at which two octahedron slabs (that have the thick- ness of the perovskite unit cell) and one corner-sharing octahedron slab are separated by a “slab” of the tetrahedron chains, as shown in Fig. 22c, the ABO 2.75 structure is formed. Ordered structures of A 2+ (B  3+ 0.5 B  4+ 0.5 )O 2.75 and A 2+ (B  2+ 0.5 B  5+ 0.5 )O 2.75 can be formed. If the octahedron slab and the slab of the tetrahedron chains are stacked alternately via corner-sharing, the brownmillerite structure ABO 2.5 is constructed (Fig. 22d). As the relative number of the tetrahedron chains increases, the interaction between A cations also increases. If the number of the tetrahedron slabs is more than that of the octahedron slabs, the system will be unstable. Then, LaCoO 3−y is likely to be reduced to two phases: La 2 O 3 and CoO. In other words, all of the Co 2+ will have tetrahedral coordination, and there is no octahedral-coordinated Co 2+ . P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB091-S-DRV-II January 23, 2002 21:38 SMART PEROVSKITES 1009 Tailoring Perovskite-Related Structures In general, compounds that have perovskite-like structures can be represented by the chemical formula A m B m O 3m−x . In this formula the (AO 3 ) 4− and the B 4+ layers are the basic stacking layers, and they are stacked alternately following the sequence αβγ , respectively, as defined by the three positions shown in Fig. 17. If the compound contains m layers of (AO 3 ) 4− and m layers of B 4+ and they are stacked together in the sequence αβγ , respectively, alternately, we can have A m B m O 3m , such as ABO 3 when m = 1, the perovskite structure. If oxygen vacancies are introduced, an (AO 3 ) 4− layer may have one oxygen sublattice possessing a vacancy, and the layer (AO 3 ) 4− is transformed into (AO 2 ) 2− . If these types of anion-deficient layers are mixed with the ideal (AO 3 ) 4− layers, the new compounds should have the formula A m B m O 3m−n (where n ≤ m), in which n represents the number of the (AO 2 ) 2− layers that contain sublattices that have oxygen vacancies. Ca 2 Mn 2 O 5 (m = 2 and n = 1), YBa 2 Cu 3 O 6 or YBa 2 Cu 3 O 6 (m = 3 and n = 3), YBa 2 Cu 3 O 7 (m = 3 and n = 2), LaBa 2 Cu 2 TaO 8 (m = 3, n = 1), and Ba 2 La 2 Cu 2 Sn 2 O 11 (m = 4 and n = 1) are typical examples. Furthermore, if the (AO 3 ) 4− layer lack only a portion of the oxygens, the composition and the charge of the layer becomes (AO 3−x ) (4−2x)− . If n and m are the numbers of the (AO 3−x ) (4−2x)− type and the (AO 3 ) 4− type layers, respectively, the compounds formed by stacking these layers and a total of (m+n) B cation layers alternately, should be A m+n B m+n O 3(m+n)−xn . For example, when n = m = 1, it is A 2 B 2 O 6−x (x < 1). These two types of oxygen-deficient perovskite compounds have been found. Compounds that have (AO 3−x ) (4−2x)− layers may be more stable than those that have (AO 2 ) 2− layers. The high T c superconductor is an example (21). Compounds that have some (AO 2 ) 2− layers may have an integral number of oxygens, but the compounds that have (AO 3−x ) (4−2x)− layers may have a nonintegral number of oxygens. As discussed before, the A cation can be substituted by cations that have different valences or by partial cation vacancies to satisfy the local electron orbital and charge balance requirements. These results may help us to understand the structure of oxide functional materials. Most of the useful compounds that have functionality contain anion-deficient perovskite-like structural units, especially those that contain (AO 3−x ) (4−2x)− layers. The 14 structural configurations shown in Fig. 10 are the fundamental building blocks for building these structures. The perovskite-related compounds that have A cation and/or oxygen anion deficiency may have the general formula A [(m+n)−yn] B (m+n) O 3(m+n)−xn where 0 ≤ x<1,0≤ y < 1, 0 ≤ n < m, and n and m are integral numbers. Although A or B cations can be partially substituted by another element, the average valences are usually close to +2 and +4 (see later), respectively. The A cation, for example, may be replaced by (A + 0 ,A 3+ )or(V + ,A  3+ ), where V stands for a positively charged vacancy site, and B cation Co Co Co La La Co Co Co Sr Sr Co Co Co La La Co Co Co Sr Sr Co Co Co 0.5 nm Figure 23. High-magnification TEM images of La 0.5 Sr 0.5 CoO 2.25 recorded along [100], where the white spots correspond to the projected atom columns. can be (B 3+ ,B 5+ )or(B 2+ ,B 6+ ). Substitution of these combinations can give a series of compounds that belong to the perovskite family. Cations of different valences usually have different sizes and electron configurations, and they tend to have a strong influence on the oxygen close packing, especially in the (AO 3 ) 4− layers. A change in the valence of the A cation should have a much stronger effect because it is in the fundamental stacking layer. Figure 23 shows a cross section of a TEM image of La 0.5 Sr 0.5 CoO 2.25 viewed along [100]. The La and Sr atoms are distributed in different (001) atomic planes and exhibit La–Co–Sr–Co–La–Co–Sr–Co– (001) layered structure (31). The crystal structure is based on a fundamental perovskite module of LaSrCo 2 O 6 (or La 0.5 Sr 0.5 CoO 3 ) without anion deficiency, as shown in Fig. 24a, which is a combination of two perovskite unit cells of LaCoO 3 and SrCoO 3 . The structure of La 0.5 Sr 0.5 CoO 2.25 is composed of eight of this type module that has ordered anion vacancies in each. Two anion-deficient modules of LaSrCo 2 O 4.5 are derived from this stoichiometric module, denoted by M 1 and M 2 (Fig. 24b). A divalent Co is likely to be coordinated by one oxygen, on average, in the top and bottom layers. These modules are the building blocks for constructing the full unit cell of La 0.5 Sr 0.5 CoO 2.25 (Fig. 24c). The unit cell is or- thorhombic. 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FCH/UKS T1: FCH PB0 9 1- S-DRV-II January 23, 2002 21: 38 10 10 SMART PEROVSKITES LaSrCo 2 O 6 (a) LaSrCo 2 O 4.5 Modules M 1 M 2 (b) La 8 Sr 8 Co 16 O 36 M 1 (c) M 2 M 1 M 2 M 1 M 1 M 2 M 2 La (d) Sr Co. Williams, J. Catal. 12 5: 265–275 (19 90). P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB0 9 1- S-DRV-II January 23, 2002 21: 38 10 14 SOIL-CERAMICS (EARTH), SELF-ADJUSTMENT OF HUMIDITY AND TEMPERATURE 29 cells of complex functional materials, such as high T c superconductors. P1: FCH/FYX P2: FCH/FYX QC: FCH/UKS T1: FCH PB0 9 1- S-DRV-II January 23, 2002 21: 38 SMART PEROVSKITES 10 13 BF-TEM (a) 10 0 nm (b) Co-L 2 (c) Co-L 3 (d) Post