Homework 1
1.1 What are materials? List eight commonly encountered engineering materials.
Answer1.1: Materials are substances of which something is composed or made. Steels, aluminum alloys, concrete, wood, glass, plastics, ceramics and electronic materials.
1.2 What are the main classes of engineering materials?
Answer1.2: Metallic, polymeric, ceramic, composite, and electronic materials are the five main classes.
1.3 What are some of the important properties of each of the five main classes of engineering materials? Answer1.3: Metallic Materials
? many are relatively strong and ductile at room temperature ? some have good strength at high temperature
? most have relatively high electrical and thermal conductivities
Polymeric Materials
? generally are poor electrical and thermal conductors ? most have low to medium strengths ? most have low densities
? most are relatively easy to process into final shape ? some are transparent Ceramic Materials
? generally have high hardness and are mechanically brittle ? some have useful high temperature strength
? most have poor electrical and thermal conductivities
Composite Materials
? have a wide range of strength from low to very high
? some have very high strength-to-weight ratios (e.g. carbon-fiber epoxy materials) ? some have medium strength and are able to be cast or formed into a variety of sha (e.g. fiberglass-polyester materials)
? some have useable strengths at very low cost (e.g. wood and concrete)
Electronic Materials
? able to detect, amplify and transmit electrical signals in a complex manner ? are light weight, compact and energy efficient
1.8 What are nanomaterials? What are some proposed advantages of using nanomaterials over their conventional counterparts?
Answer1.8: Are defined as materials with a characteristic length scale smaller than 100 nm. The length scale could be particle diameter, grain size in a material, layer thickness in a sensor, etc. These materials have properties different than that at bulk scale or at the
molecular scale. These materials have often enhanced properties and characteristics because of their nano-features in comparison to their micro-featured counterparts. The structural, chemical, electronic, and thermal properties (among other characteristics) are often enhanced at the nano-scale.
Homework 2
Chapter 3, Problem 4
What are the three most common metal crystal structures? List five metals that have each of these crystal structures. Chapter 3, Solution 4
The three most common crystal structures found in metals are: body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP). Examples of metals having these structures include the following. BCC:
??iron,vanadium, tungsten, niobium, and chromium.
FCC: copper, aluminum, lead, nickel, and silver. HCP: magnesium,
Chapter 3, Problem 5
For a BCC unit cell, (a) how many atoms are there inside the unit cell, (b) what is the coordination number for the atoms, (c) what is the relationship between the length of the side a of the BCC unit cell and the radius of its atoms, and (d) APF = 0.68 or 68%
Chapter 3, Solution 5
(a) A BCC crystal structure has two atoms in each unit cell. (b) A BCC crystal structure has a coordination number of eight. (c) In a BCC unit cell, one complete atom and two atom eighths touch each other along the cube diagonal. This geometry translates into the relationship
Chapter 3, Problem 6
For an FCC unit cell, (a) how many atoms are there inside the unit cell, (b) What is the coordination number for the atoms, (c)
??titanium,zinc, beryllium, and cadmium.
3a?4R.
a?4R2, and (d) what is the atomic packing factor?
Chapter 3, Solution 6
(a) Each unit cell of the FCC crystal structure contains four atoms. (b) The FCC crystal structure has a
coordination number of twelve. (d) By definition, the atomic packing factor is given as:
Atomic packing factor?
volume of atoms in FCC unit cell
volume of the FCC unit cellThese volumes, associated with the four-atom FCC unit cell, are
?4?16Vatoms?4??R3???R3
?3?3 and Vunit cell?a3
4R, 2where a represents the lattice constant. Substituting
a?Vunit cell
64R3 ?a?223The atomic packing factor then becomes,
?16?R3??12??2APF (FCC unit cell)???=0.74 ??3???6?3??32R?Chapter 3, Problem 7
For an HCP unit cell (consider the primitive cell), (a) how many atoms are there inside the unit cell, (b) What is the coordination number for the atoms, (c) what is the atomic packing factor, (d) what is the ideal c/a ratio for HCP metals, and (e) repeat a through c considering the “larger” cell.
Chapter 3, Solution 7
The primitive cell has (a) two atoms/unit cell; (b) The coordination number associated with the HCP crystal structure is twelve. (c)the APF is 0.74 or 74%; (d) The ideal c/a ratio for HCP metals is 1.633; (e) all answers remain the same except for (a) where the new answer is 6.
Homework 3 Chapter 3, Problem 25
Lithium at 20?C is BCC and has a lattice constant of 0.35092 nm. Calculate a value for the atomic radius of a lithium atom in nanometers.
Chapter 3, Solution 25
For the lithium BCC structure, which has a lattice constant of a = 0.35092 nm, the atomic radius is,
R?33a?(0.35092 nm)?0.152 nm44
Chapter 3, Problem 27
Palladium is FCC and has an atomic radius of 0.137 nm. Calculate a value for its lattice constant a in nanometers.
Chapter 3, Solution 27
Letting a represent the FCC unit cell edge length and R the palladium atomic radius,
2a?4R or a?44R?(0.137 nm)?0.387 nm22
Chapter 3, Problem 31 Draw the following directions in a BCC unit cell and list the position coordinates of the atoms whose centers are intersected by the direction vector: (a) [100] (b) [110] (c) [111]
Chapter 3, Solution 31
错误！未找到引用源。
(a) Position Coordinates:
Chapter 3, Problem 32
Draw direction vectors in unit cells for the following cubic directions:
(b) Position Coordinates:
(c) Position Coordinates:
(0, 0, 0), (1, 0, 0) (0, 0, 0), (1, 1, 0) (0, 0, 0), (1, 1, 1)
?111?? (b) ??110?? (a) ?
Chapter 3, Solution 32
Chapter 3, Problem 46
?121?? (d) ??113?? (c) ?z y
x
(a) (b)
x = +1
y = -1 z = -1 x = +1 y = -1 z = 0
[111](c)
? ?
[110](d)
? [113]Dividing by 2, 2Dividing by 3, a?1, b??, c?1[121]332. What are the Miller indices A cubic plane has the following axial intercepts: x = -? x = – ? y = 1 of this plane? y = – ?
Chapter 3, Solution 46
? 1?3,xGiven the axial intercepts of (?, -?, ?), the reciprocal intercepts are:
Multiplying by 2 to clear the fraction, the Miller indices are (634).
13??,y21?2.z
