GTBL042-03 GTBL042-Callister-v2 September 6, 2007 15:33
Questions and Problems • 933.8Indium has a tetragonal unit cell for which the
aandclattice parameters are 0.459 and 0.495
nm, respectively.
(a)If the atomic packing factor and atomic ra-
dius are 0.693 and 0.1625 nm, respectively,
determine the number of atoms in each
unit cell.
(b)The atomic weight of indium is 114.82
g/mol; compute its theoretical density.
3.9Magnesium has an HCP crystal structure, a
c/aratio of 1.624, and a density of 1.74 g/cm^3.
Compute the atomic radius for Mg.Ceramic Crystal Structures
3.10Show that the minimum cation-to-anion ra-
dius ratio for a coordination number of 4 is
0.225.
3.11Demonstrate that the minimum cation-to-
anion radius ratio for a coordination number
of 8 is 0.732.
3.12On the basis of ionic charge and ionic radii,
predict crystal structures for the following ma-
terials:
(a)CaO
(b)KBr.
Justify your selections.Density Computations–Ceramics
3.13Compute the atomic packing factor for the
rock salt crystal structure in whichrC/rA=
0.414.
3.14Compute the atomic packing factor for cesium
chloride using the ionic radii in Table 3.4 and
assuming that the ions touch along the cube
diagonals.
3.15Iron oxide (FeO) has the rock salt crystal struc-
ture and a density of 5.70 g/cm^3.
(a)Determine the unit cell edge length.
(b)How does this result compare with the
edge length as determined from the radii
in Table 3.4, assuming that the Fe^2 +and
O^2 −ions just touch each other along the
edges?
3.16One crystalline form of silica (SiO 2 ) has a
cubic unit cell, and from x-ray diffraction
data it is known that the cell edge length is
0.700 nm. If the measured density is 2.32 g/cm^3 ,how many Si^4 +and O^2 −ions are there per unit
cell?
3.17A hypothetical AX type of ceramic material
is known to have a density of 2.10 g/cm^3 and
a unit cell of cubic symmetry with a cell edge
length of 0.57 nm. The atomic weights of the
A and X elements are 28.5 and 30.0 g/mol, re-
spectively. On the basis of this information,
which of the following crystal structures is
(are) possible for this material: sodium chlo-
ride, cesium chloride, or zinc blende? Justify
your choice(s).Silicate Ceramics
3.18Determine the angle between covalent bonds
in an SiO^44 −tetrahedron.Carbon
3.19Compute the theoretical density of ZnS given
that the Zn—S distance and bond angle
are 0.234 nm and 109.5◦, respectively. How
does this value compare with the measured
density?
3.20Compute the atomic packing factor for the di-
amond cubic crystal structure (Figure 3.16).
Assume that bonding atoms touch one an-
other, that the angle between adjacent bonds
is 109.5◦, and that each atom internal to the
unit cell is positioneda/4 of the distance away
from the two nearest cell faces (ais the unit
cell edge length).Crystal Systems
3.21Sketch a unit cell for the face-centered or-
thorhombic crystal structure.Point Coordinates
3.22List the point coordinates of both the sodium
and chlorine ions for a unit cell of the sodium
chloride crystal structure (Figure 3.5).
3.23Sketch a tetragonal unit cell, and within that
cell indicate locations of the 1 1^12 and^121412
point coordinates.
3.24Using the Molecule Definition Utility found in
both “Metallic Crystal Structures and Crystal-
lography” and “Ceramic Crystal Structures”
modules ofVMSE, located on the book’s web
site [www.wiley.com/college/callister (Student