EVOLUTION OF RUTILE-TYPE STRUCTURES

Sodium Chloride and Rutile-Related Structure Systems

2.5. EVOLUTION OF RUTILE-TYPE STRUCTURES

82

CHAPTER 2

(a)

(b)

Figure 2.11. Arrays of edge-sharing octahedra. (a) The linear, zigzag, ring, and sheet of octahedra formed by edge-sharing. (b) The linear edge-sharing octahedra with cation distortion because of strong interaction.

2.4.3. FACE SHARING

The face-sharing octahedra hardly occur in rutile-related structures because the adjacent cations are too close to each other and the screening effect from the anions is small. The interaction energy is too high. However, NaCl and CsCI have the face-sharing octahedral arrays due to the radius ratio (rM/rX > 0.414) and pure ionic bonding.

build the rutile structure except with overlaps, as indicated by the overlaps between circles. In other words, the type 2 group can be taken as the typical structure unit of rutile, which can be either connected differently or combined with other types of polyhedra to build different structures. Hollandite and ramsdellite structures can be visualized as the rutile mosaic rotated for different angles to join. Al2 Ti70 1S is a connection of the distorted rutile mosaic with tetrahedra chains.

Hollandite structure shown in Fig. 2.13a is made of rutile mosaic with edge sharing.

This process creates a large square tunnel. The unit cell can be chosen from the center to the center of the rutile mosaics or the newly created large tunnels. The large tunnel is surrounded by oxygen anions. The large tunnel may absorb some cations, organic molecules, and/or water molecules. Therefore, the formula of hollandite is A2B^g[O(OH)h6' The A cation should be ionic and the number of A cations is usually non stoichiometric.

The ramsdellite structure has rectangle tunnels (Fig. 2. 13b). The structure is made from the rutile mosaic with edge sharing in one direction to form a slab, but the slabs are stacked with an overlap, equivalent to take away some octahedra. Manganate is a very interesting and useful example of rutile structure. P-Mn02 has rutile structure, but the same mosaics rotate 16° to connect together, forming a:-Mn02 with ramsdellite-type structure. If these mosaics do not overlap in one direction the structure should be hollandite and some ionic cations and water molecules should be absorbed into the large tunnels. Therefore, it has a composition of (Ba,Na,K)Mns(O,OH)16' If one more parallel edge-sharing .octahedron chain is inserted into the middle of the two edge-sharing rutile mosaics, as shown in Fig. 2.13c, it forms the psilomelane structure with a composition of (Ba,H20)zMnsOlO' If two parallel edge-sharing octahedron chains are inserted in the two directions of the rutile mosaics, as shown in Fig. 2.13d, the structure is todorokite with a composition of (Na,Ca,KMMn,Mg)6012' nH20 (x

=

0.3-0.7). The large tunnels of these

Figure 2.12. A complex of 3 x 3 rutile unit cells. The large dashed circles represent the rutile "mosaic."

The square is the unit cell viewed along [001], which also represents the normal mosaic of rutile. The 90°

rotation between the chains along the viewing direction is apparent. The unit cell can also be taken as small dashed circles superimposed with crosses.

[001 J r

83

SODIUM CHLORIDE AND RUTILE-

RELATED STRUCTURE SYSTEMS

84

CHAPTER 2

manganates make them good candidates for energy storage, catalysis, and molecular filtering.

As presented, using the rutile basic mosaics one can construct the rutile-related structures. The dioxides of transition metals such as Ti, V, and Mn usually have rutile- type structures. When they form ternary oxides with other elements, such as AI, they can keep the octahedron chain or modify the chain to connect with other polyhedra, such as tetrahedra, to form new structures. AlzTi70 I5 is an example.

Tetravalent titanium cations form a rutile structure, but trivalent aluminum sesquioxide can have corundum and ~-GaZ03 structures. In these structures, Ae+ can have two types of coordination polyhedra: octahedron and tetrahedron. When A13+ is doped into titanium dioxide to form AlzTi70 I5 compound, one would wonder what will the structure be. The structure of AlzTi70 I5 has been determined by x-ray diffraction (Remy et al., 1988) and confirmed later by HRTEM (Kang et al., 1989). Figure 2.14 shows the structure of Alz ThOI5. This structure can be understood by the evolution of the rutile structure. First, we introduce the structure of ~-GaZ03 in Figure 2.15, where half of the Ga3+ cations are in tetrahedra and the other half are in octahedra. Two edge-sharing

Figure 2.13. (a) The hollandite structure formed by rutile mosaics with edge sharing. (b) The structure of ramsdellite formed by rutile mosaics with edge sharing. (c) The structure of psilomelane (Ba,H20hMnsOlO. (d) The structure of todorokite (Na,Ca,K)iMn,Mg)6012· nH20 (x

=

O.3....().7).

Figure 2.14. The structure of A12Ti70'5 viewed along [010].

octahedra are grouped and they share corners with tetrahedra, as shown in Fig. 2.15a. The octahetra also share both opposite edges to form a chain as in the rutile structure. We can say that it is similar to the rutile structure, but the connection between the octahedron chains is different. If we use the basic rutile mosaic as shown in Fig. 2.12 to build a slab in which two rutile mosaics share an edge to form a new group, as given in Fig. 2.16a, and these groups are connected to each other by tetrahedra to create the structure of AlzTi7015 (Fig. 2.14). In this procedure the octahedra must be rotated and distorted to

(a) The structure of ~-Ga203 projected on (010) (b) The stereoscopic view of the structure of ~-Ga203

Figure 2.15. The structure of ~-Ga203 projected onto (010) (a), and the stereoscopic view (b), where the rutile slabs are clearly seen.

85

SODIUM CHLORIDE AND RUTILE-

RELATED STRUCTURE SYSTEMS

86

CHAPTER 2

match comers with the tetrahedra (Fig. 2.16b). This kind of stacking creates large tunnels in which the tetrahedra can be inserted into the octahedra family and share all of their comers with adjacent octahedra. As a result, the characteristics of both rutile and ~­

Ga203 are contained in this structure. The mosaic of ~-Ga203 is a combined result of the rutile units. In Al2Ti70 15, AI3+ has two types of coordination sites-octahedron and tetrahedron-and Ti⁴+ are usually present at the octahedral sites. This compound is a mixed valent compound, but At3+ and Ti⁴+ cations are crystallographic ally indistinguishable in some special cases. Some A13+ can reside in octahedra, replacing Ti. Thus, Ah ThOl5 may belong to the second class mixed valent compounds, which are semiconductive.

The structural evolution process was revealed by HRTEM (Kang et al., 1989a, b).

The AhTi70 15 compound was first synthesized by Monnereau et al. (1985). The structure

(a) Rutile mo aie

(b) Oi torted rutile mo aie Rutile mo aies with one octahedron mi ing

~~ ~

(c)

Figure 2.16. (a) Two rutile mosaics sharing an edge to form the structural blocks of f3-Ga203' (b) Distorted rutile mosaic and the mosaics with one octahedron missing. (c) Defects are introduced in Al2Ti⁷015 by shifting the rutile-type slabs to create ramsdellite-type and hollandite-type tunnels.

was determined by x-ray diffraction (Remy et al., 1988). The lattice parameters are a

=

1.77 nm, b

=

0.297 nm, C

=

0.936 nm, and ~

=

98.7°. The physical measurement showed that it is a semiconductor. An electron diffraction pattern of the crystal is shown as an inset in Fig. 2.17a. In the [010] orientation there are some spots with stronger intensity that form a parallelogram with 81.3° (or 98.7°) instead of 90°, and there are three intervals between the stronger spots, indicating that the rutile mosaic has heen distorted from 90° to 81.3° and the number of the octahedra sheets is tripled in the unit cell. A high-resolution image recorded along [010] demonstrates this type of pattern, where the white blocks correspond to rutile-type tunnels. At the thin-edge region of the

Figure 2.17. High-resolution TEM images and the corresponding electron diffraction patterns of Al2 Ti7015

compound oriented along (a) [010] and (b) [001]. The superlattice unit cell is indicated and the rutile reflections are indicated by circles.

87

SODIUM CHLORIDE AND RUTlLE-

RELATED STRUCTURE SYSTEMS

88

CHAPTER 2

specimen, only rutile tunnels are shown. The lattice image in [001] orientation (Fig.

2.17b) clearly shows that the triple spacing of the octahedra slabs in the unit cell. The crystal could contain some defects, as shown in Fig. 2.l6c. High-resolution image and rnicrodiffraction pattern revealed that the defects are due to shifting of the rutile-type slabs to create ramsdellite-type and hollandite-type tunnels (Kang et al., 1989b).

Hollandite and ramsdellite structures are very useful ionic conductors for solid-state electrolytes. Groutite MnOOH and ramsdellite cx-Mn02 can be doped with Li to form LixMn02, an important cathode material for lithium batteries.

Our discussion in this book covers little about corundum structure because of its lower possibility for structural evolution. The corundum structure of cx-A1203 can be

~'_b~

To hare an octahedron face

~

Corundum tI\Icrure of a-A12OJ

Figure 2.18. The relationship between tbe rutile blocks and tbe corundum structure of at-AI203 . The heavy lines and circles mean tbe modules and atoms at tbe front. The projected unit cell is indicated.

deduced from the rutile structure as shown in Fig. 2.18. The rutile structural slabs with two-octahedra thickness share an octahedron face, resulting in the structure of (X-Ah03 corundum. B-Nb20S and Sb20 s also can be visualized as the rutile"related structure.

2.6.

NONSTOICHIOMETRY AND CRYSTALLOGRAPHIC SHEAR PLANES It seems that compounds with rutile-related structure always have oxygen anion close-packing layers, which can be stacked following different stacking sequences. The cations always distribute between these anion close-packing layers. The cation-packing configurations determine the structure and the packing of the oxygen octahedra by comer (edge) sharing into edge (comer) sharing. The "reduced rutiles" are some examples (Andersson et al., 1957a, b; Bursill and Hyde, 1972; Hyde and Andersson, 1989). Ti02

can be reduced to TiOx, or in a general formula Tin02n -p , where nand p are integers.

They can be sorted into three groups:

a. 1.75:'S x:'S 1.89, with p

=

^1, n

=

^{4 to 9}

b. 1.93 :'S x:'S 1.98, with p

=

1, n

=

16 to 40-60, probably with only even values of n c. 1.89:'S x:'S 1.93, with p > 1 and 9 < nip < 16

All of these structures can evolve from ideal rutile slabs by various crystallographic shear (CS) planes: (i) (121)r; (ii) (132)r; (iii) (hkl)r

=

p(121)r

+

q(Oll)r' where p and q are integers. If p

=

1 and q

=

0, it is (121)r; if p

=

1 and q

=

1 it is (l32)yo The values of p and q are related to oxygen content in TiOx' When x is lower, for example 1.89, q

= °

^and

p

=

1, the CS plane is (121)r; as x increases to 1.93 it becomes (132)r'

The change in CS planes can be clearly shown by the oxygen close-packing layers with different cation arrangements. Figure 2.19 shows the ideal rutile structure projected along [lOO]yo The unit cell in this projection is outlined as a rectangle in which the longer side is the b axis and the short one is the c axis. In this figure the oxygen anions have a

Figure 2.19. Oxygen close-packing layer in an ideal rutile structure, where the voids, cation distribution, and the edge sharing octahedron chains are indicated.

89

SODIUM CHLORIDE AND RUTILE-

RELATED STRUCTURE SYSTEMS

90

CHAPTER 2

close packing of hexagonal network. Three anions form a triangle void, and seven anions create six triangle voids as marked by 1, 2, 3, 4, 5, and 6. The cations can occupy these positions, but positions 1, 3, 5 or 2, 4, 6 can only be occupied simultaneously due to the strongest charge interactions and space limitation. If the 1, 3, and 5 voids are occupied by a layer, another close-packing oxygen layer can stack on its top by shifting to the 2, 4, and 6 void positions. Repeating this process gives the rock salt structure, in which all the octahedral faces are shared. We may understand the rutile structure as cations occupying only the 1 and 3 void positions of the oxygen closest-packing layer and leaving the 5 void position empty. Therefore, the ratio OIM

=

^{2 or M0}2.

As Ti02 is reduced with oxygen loss, the ratio of oxygen to titanium cations is decreased. That means the system of TiOx is denser than Ti02. The experimental data of Tin02n -p indicate that the smallest x value is 1.75, implying a loss of 12.5% oxygen.

Based on previous discussion, some cations should occupy not only position 2 void but also 4 and 6 void positions. Figure 2.20a shows a situation in which part of the cations in rutile is shifted from position 2 voids to position 4 voids, with a displacement of ~[OIl]r in the (12I)r plane. In the (I2I)r plane, the cations have close packing as in rock salt, but only limited to one atomic layer. The structures on both sides of the shear plane are still perfect rutile structure, but the cation occupied voids have been changed to 2, 4, and 6 void positions. The interval between two CS planes determines the total amount of oxygen loss. On the other hand, CS plane is close packing so that the x value cannot be smaller than 1.75.

If we see rutile structure as oxygen close packing with cations occupying the 2 and 4 void positions as shown in Fig. 2.19, we may say that the positions of the 2 and 4 voids form a row aligning along the c axis and the distance between adjacent rows is the b lattice constant. Two pairs of 2 and 4 voids form a projected unit cell of rutile. If the two rows are shifted into different void positions-the first shifting to the 4 void position, the other to the 6 void position with displacements HOII] and ~[OIl], respectively-a CS plane of (I32)r is created (Fig. 2.20b). The atom density in CS plane (132)r is lower than that in the CS plane (121)r but higher than rutile. The x value is 1.93 ~ x ~ 1.98. If the first row is shifted from position 2 to position 6, the second and third rows from position 2 to 4, the fourth one from position 2 to 6, and the four rows form a group repeatedly, a CS plane (253)r is obtained (Fig. 2.20c). Similarly five rows as a block can create CS plane (374)r (Fig. 2.20d). As the CS plane changes from (132)r to (374)r the cation density in these planes is increasing, and the x value decreases from 1.93 to 1.89. The interval between these CS planes may be regularly or irregularly distributed. However, as the number of these CS planes increases, the amount of oxygen loss is increased. This process causes cation displacement (or stacking faults), and a polycrystal is smashed into powders.

For functional materials, this type of compound can supply lattice oxygen from a crystal surface, but it will smash due to the loss in oxygen. Thus, the absorption and desorption of oxygen are irreversible.

Based on the discussion of rutile structural evolution, the oxygen octahedra with cations at the centers have been tightly connected with each other via corner sharing and edge sharing. As the number of edge-sharing octahedra decreases, the bandwidth might become wider, suggesting that rutile-related compounds are insulators and possibly with high dielectric constant. The oxygen deficiency or nonstoichiometry of rutile-type structure is due to CS planes and the intergrowth of different CS planes, and the intervals between these CS planes determine the composition of the nonstoichiometric phases.

Doping of another valence cation into rutile can form a structure built from the rutile mosaic and the basic unit of the doped cation. The oxygen octahedra with cations at the centers are still retained, but changing the connection configurations with original rutile mosaic and/or doped new units can form new compounds, such as Al2 Ti7015 . The bandwidth may be changed, possibly resulting in a transition from insulator to semiconductor. The high dielectric constant makes rutile a good insulator and microwave material.

The energy band structure of Ti02 is given in Fig. 2.21. The 0 2p band is full and the Ti 3d bands are empty. The 3d energy levels are delocalized and the lower 3d band

Figure 2.20. Models showing crystallographic shear planes of (a) (121)" (b) (132)" (c) (253)" and (d) (374)r (after Hyde and Anderson, 1989, reprinted with permission from Wiley & Sons, Inc.), where equivalent lattice sites are labeled with

*

and #, respectively.

91

SODIUM CHLORIDE AND RUTILE-

RELATED STRUCTURE SYSTEMS

92

CHAPTER 2

Energy

Unoccupied states

Occupied states

o

^{2p and2s}

Density of states N(E) Figure 2.21. Schematic electron band structure of Ti02.

fonns the conduction band. The band gap of Ti02 is 3.4eV. If another element is doped into the rutile structure, the donor energy levels may locate in the gap and the system will be semiconductive. If the 3d band and/or 2p band are broadened, it is possible to overlap the filled 0 2p band with the Ti 3d band, creating a partially filled conductive band.

Therefore, the system will be metallic. For example, V02 compound has rutile structure, but the vanadium cations are distorted to fonn pairs. The unit cell will be changed from tetragonal to monoclinic and the cation-to-cation distances in the pairs are shortened.

These two factors may broaden the 3d band and modify the band positions so that the bands can overlap, resulting in a metallic property (Goodenough, 1971).

Rutile structure has a pair of edge-sharing octahedral chains rotated 90⁰ with each other and are connected by corner sharing. The corner-sharing connection may be modified to create different deduced structures, but the chains still exist. If the chains have been destroyed the rutile structure should change to other types of structures, such as perovskite, as discussed in Chapter 3.