Chapter 12: Problem 7
Compute the atomic packing factor for the rock salt crystal structure in which \(r_{\mathrm{C}} / r_{\mathrm{A}}=0.414\).
Chapter 12: Problem 7
Compute the atomic packing factor for the rock salt crystal structure in which \(r_{\mathrm{C}} / r_{\mathrm{A}}=0.414\).
All the tools & learning materials you need for study success - in one app.
Get started for freeCite one reason why ceramic materials are, in general, harder yet more brittle than metals.
Using the Molecule Definition Utility found in both "Metallic Crystal Structures and Crystallography" and "Ceramic Crystal Structures" modules of VMSE, located on the book's web site [www.wiley.com/college/callister (Student Companion Site)], generate (and print out) a three-dimensional unit cell for lead oxide, \(\mathrm{PbO}\), given the following: (1) The unit cell is tetragonal with \(a=0.397 \mathrm{nm}\) and \(c=0.502 \mathrm{nm},(2)\) oxygen atoms are located at the following point coordinates: $$\begin{array}{ll} 000 & 001 \\ 100 & 101 \\ 010 & 011 \\ 110 & 111 \\ \frac{1}{2} \frac{1}{2} 0 & \frac{1}{2} \frac{1}{2} 1 \end{array}$$ and (3) \(\mathrm{Pb}\) atoms are located at the following point coordinates: $$\frac{1}{2} 00.763 \quad 0 \frac{1}{2} 0.237$$ $$\frac{1}{2} 10.763 \quad 1 \frac{1}{2} 0.237$$
Using the data given below that relate to the formation of Schottky defects in some oxide ceramic (having the chemical formula \(\mathrm{MO}\) ), determine the following: (a) The energy for defect formation (in eV), (b) the equilibrium number of Schottky defects per cubic meter at \(1000^{\circ} \mathrm{C},\) and (c) the identity of the oxide (i.e., what is the metal M?) $$\begin{array}{rcc} \hline \boldsymbol{T}\left(^{\circ} \boldsymbol{C}\right) & \boldsymbol{\rho}\left(\boldsymbol{g} / \mathrm{cm}^{3}\right) & \boldsymbol{N}_{\boldsymbol{s}}\left(\boldsymbol{m}^{-3}\right) \\ \hline 750 & 3.50 & 5.7 \times 10^{9} \\ 1000 & 3.45 & ? \\ 1500 & 3.40 & 5.8 \times 10^{17} \\ \hline \end{array}$$
A three-point bending test is performed on a spinel (MgAl_O_) specimen having a rectangular cross section of height \(d 3.8 \mathrm{mm}\) \((0.15 \text { in. })\) and width \(b 9 \mathrm{mm}(0.35 \text { in. }) ;\) the distance between support points is \(25 \mathrm{mm}\) \((1.0 \text { in. })\) (a) Compute the flexural strength if the load at fracture is \(350 \mathrm{N}\left(80 \mathrm{lb}_{\mathrm{f}}\right)\) (b) The point of maximum deflection \(\Delta y\) occurs at the center of the specimen and is described by $$\Delta y=\frac{F L^{3}}{48 E I}$$ where \(E\) is the modulus of elasticity and \(I\) is the cross-sectional moment of inertia. Compute \(\Delta y\) at a load of \(310 \mathrm{N}\left(70 \mathrm{lb}_{f}\right)\)
Briefly explain (a) why there may be significant scatter in the fracture strength for some given ceramic material, and (b) why fracture strength increases with decreasing specimen size.
What do you think about this solution?
We value your feedback to improve our textbook solutions.