Respectively the atomic packing factor and atomic radius are and

3.14					3.21	Questions and Problems


						+z
	Rhodium has an atomic radius of 0.1345 nm (1.345 A˚ ) and a density of 12.41 g/cm3. De- termine whether it has an FCC or BCC crys-					90�
						90�

	and atomic radius for three hypothetical alloys. For each determine whether its crystal
	structure is FCC, BCC, or simple cubic and					90�		+y
						90�		+y
						0.30 nm
						+x	0.30 nm
	Atomic		Atomic			+x	0.30 nm
						(a) To which crystal system does this unit cell belong?
	A	77.4	8.22
		107.6	13.42
		127.3	9.23	0.142		(b) What would this crystal structure be called?
					3.22	(b) What would this crystal structure be called?


	0.318 nm, respectively. If its density, atomic weight, and atomic radius are 7.30 g/cm3,
						Using the Molecule Definition File (MDF)
3.17						on the CD-ROM that accompanies this book, generate a three-dimensional unit cell
						for the intermetallic compound AuCu3 given the following: 1) the unit cell is cubic with

					3.23
						an edge length of 0.374 nm, 2) gold atoms
						an edge length of 0.374 nm, 2) gold atoms
						are situated at all cube corners, and 3) copper atoms are positioned at the centers of all unit

						cell faces.
						Using the Molecule Definition File (MDF)
	unit cell.					Using the Molecule Definition File (MDF)
	unit cell.					on the CD-ROM that accompanies this book, generate a three-dimensional unit cell

						for the intermetallic compound AuCu given
					3.24	the following: 1) the unit cell is tetragonal with a � 0.289 nm and c � 0.367 nm (see


						Table 3.6), 2) gold atoms are situated at all unit cell corners, and 3) a copper atom is
	the radius of the Ti atom is 0.1445 nm, (a) determine the unit cell volume, and (b) cal-culate the density of Ti and compare it with the literature value.
						positioned at the center of the unit cell.
						Sketch a unit cell for the body-centered or-

					3.25	For a ceramic compound, what are the two
	late the atomic radius for Zn.					characteristics of the component ions that determine the crystal structure?

					3.26	Show that the minimum cation-to-anion ra-dius ratio for a coordination number of 4
					3.26

70	Chapter 3 / Structures of Metals and Ceramics				3.36	Compute the theoretical density of diamond
3.27						Compute the theoretical density of diamond
3.27
3.28					3.37	are 0.154 nm and 109.5�, respectively. How does this value compare with the mea-
	ions are just touching along cube edges and across face diagonals.



3.29	of 8 is 0.732.				3.38	How does this value compare with the mea-


	ing materials: (a) CsI, (b) NiO, (c) KI, and (d) NiS. Justify your selections.					and from x-ray diffraction data it is known that the cell edge length is 0.582 nm. If the
3.30					3.39
3.30	chloride choices.	crystal	structure?	Justify	3.39
3.31	Compute the atomic packing factor for the cesium chloride crystal structure in which				3.40	cation of the result of Problem 3.4.


3.32

	as 0.138 and 0.140 nm, respectively. What					sured one?


3.33					3.41
						A hypothetical AX type of ceramic material
	Using the Molecule Definition File (MDF) on the CD-ROM that accompanies this					A hypothetical AX type of ceramic material





3.34	the unit cell is tetragonal with a � 0.397				3.42
	the unit cell is tetragonal with a � 0.397					respectively. On the basis of this informa-
						respectively. On the basis of this informa-



	of the other opposing faces (rectangular) at
	of the other opposing faces (rectangular) at					The unit cell for MgFe2O4 (MgO-Fe2O3) has cubic symmetry with a unit cell edge length




						factor. For this computation, you will need
	Calculate the density of FeO, given that it has the rock salt crystal structure.					factor. For this computation, you will need

3.35					3.43
					3.43
	(a) Determine the unit cell edge length.				3.44	material is 3.99 g/cm3, calculate its atomic packing factor. For this computation use



						diamondcubiccrystalstructure(Figure3.16).