Solid State Materials Chemistry 1st Edition Patrick M. Woodward, Pavel Karen, John S. O. Evans, Thomas Vogt - Solutions

With a structure-drawing program, determine which of the three most common tilts the perovskite prototype CaTiO3 (ICSD 62149) adopts.
Analyze hole filling in the spinel structure of ccp oxygens. (a) Given the general formula [tetrahedron]1[octahedron]2O4, calculate the total fractions of tetrahedral and octahedral holes filled. (b) Use a structure-drawing program to orient the structure and identify the type of filled holes
Rewrite the chemical formulas in Table 1.7 into simplified crystal-chemical formulas of spinel.Table 1.7 Tetrahedron 1 2 2 3 4 5 6 Octahedron 4 3 3 4 2 2 1 1 NNWNWA 3 2 3 2 2 1 Chemical formula of an example LiMnO4 (a = 8.245 ) ZnFeO4 (a = 8.442 ) FeTiO4 (a = 8.521 ) Fe3O4 (a = 8.394 ) NiSiO4 (a =
Which type of similarity do you see between the Laves phase MgCu2 (Fd3m, a = 7.034 Å, Mg in 8a at 0 0 0, Cu in 16d at ⅝⅝⅝) and the spinel in Figure 1.47?Figure 1.47 Mg2+[41] A12+180) O(1,3) MgALO Fd3m (227, origin 1) cubic (ICSD # 56116) a= 8.086 A At. Wyck. x Al 16d 5/8 5/8 Mg 8a 0 0 O 32e
ReO3 has a 3D network of octahedrally coordinated rhenium. Determine the N, M-connectivity for this binodal network
In β-Li3N, nitrogen is 11-coordinated. Write down the Niggli formula of the NLi3 polyhedron.
Write the Niggli formula for C3N4 made of identical CN4 tetrahedra. How many different types of nitrogen vertices are there? What is the coordination number of each?
Using the Niggli formula and the rule of parsimony, determine the stoichiometry that results from sharing (a) All corners, (b) All edges,(c) All faces of a cation-centered cube of anions. Note the structure prototype where you recognize it.
Construct a bond graph or Niggli formula to determine if it is possible for all anions to be equivalent in a structure of tetrahedrally coordinated cations and stoichiometry of C2A3? Which alternative Niggli formula complies best with the rule of parsimony?
Write the Niggli formula and the simple crystal-chemical formula for the CrO3 structure that contains chains of corner-sharing chromium-centered tetrahedra.
La in solid LaBr3 has a tricapped trigonal-prismatic coordination. What is the coordination number of Br? Is it possible that the tricapped trigonal prisms share only corners, or would you expect sharing of edges and/or faces? Check the result by viewing the structure and constructing polyhedra
In the low-temperature form of CrCl3, every second plane of octahedral holes is occupied. What is the filling fraction of the occupied planes? Check the result by a sideon view of the closest-packed layers perpendicular to their subsequent shifts (R3 in hexagonal setting; a = 5.94, c = 17.3 Å, Cr
Determine the stacking sequence of Br in trigonal CdBr2 (R3m in hexagonal setting; a = 3.965, c = 18.70 Å, Cd in 3a at 0 0 0, Br in 6c at 0 0 0.25).
With a structure-drawing program, determine the stacking sequence in Tb (data for plotting: P63/mmc, a = 3.068, c = 14.87 Å, Tb in 2b at 0 0 ¼ and 4f at ⅓ ⅔ 0.083). Suggest the Ramsdell symbol and the Jagodzinski–Wyckoff notation.
From unit-cell parameters in figures in this chapter, calculate the following shortest distances: (a) Na–Cl and Na–Na in NaCl, (b) Ni–Ni in NiAs, (c) Ca–F in CaF2,(d) C–C in diamond, (e) Ti–Ti in TiO2 (rutile), (f) Ti–O, Sr–O, and O–O in the cubic perovskite SrTiO3 (a = 3.90
Imagine a coordination polyhedron with a cation at the center. Now treat the ions as hard spheres and reduce the size of the cation until the anions just touch. What is the radius r of the cation for anions of unit radius in the following coordinations: (a) Cube, (b) Octahedron,(c)
Calculate the percentage of available space that’s taken up by touching spheres in primitive and body-centered cubic arrangements.
Suggest the anion bonding that might occur in MgB2 and MgC2.
Use the generalized 8−N rule to identify whether anion–anion or cation–cation bonds are present for the following compounds (assume no cation-localized nonbonding electron pairs): (a) Na2Tl, (b) SrSb2, (c) BaTe2, (d) InSe.
Describe or sketch a structure for layered V2O5 that is consistent with the bond-graph representation in Figure 1.15.Figure 1.15 SIO TiO Ca LL CaF O O AI=O=AI AlO3 Pt Pt Pt04 Pt 28889 02 03 V05 V
Convert the bond graphs in Figure 1.15 into crystal-chemical formulas.Figure 1.15 SIO TiO Ca LL CaF O O AI=O=AI AlO3 Pt Pt Pt04 Pt 28889 02 03 V05 V
Draw the bond graph for the mineral spinel MgAl2O4 (Figure 1.47).Figure 1.47 Mg2+14A2+160)(1,3) MgAlO Fd3m (227, origin 1) cubic (ICSD #56116) a= 8.086 A At. Wyck. X y z Al 16d 5/8 5/8 5/8 000 Mg Ba O 32e 0.384 0.3840.384 MA 240
Write down the three balances expressed in the crystal-chemical formulas of the phases in the previous problem.
Is it possible for a c glide plane to have the direction of: (a) a axis, (b) b axis, (c) c axis? If not, why is this not allowed?
Sketch a set of equidistant 113 planes in a cubic unit cell.
Sketch a set of equidistant 113 planes in a cubic unit cell.
Write down indices for the following sets of equidistant planes: e e e
By analogy with Table 1.1, determine the number and type of 2D crystal systems via considering their possible minimum symmetry elements and sketching their Bravais lattices.Table 1.1 Crystal system Triclinic Monoclinic Orthorhombic Tetragonal Hexagonal Trigonal Cubic Minimum symmetry 1 2, m 222 4,4
Write down the ⟨111⟩ set of symmetry-equivalent directions in a cubic lattice.

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