Get questions and answers for Materials Science Engineering

Cite the difference between atomic mass and atomic weight.

Chromium has four naturally-occurring isotopes: 4.34% of ⁵⁰Cr, with an atomic weight of 49.9460 amu, 83.79% of ⁵²Cr, with an atomic weight of 51.9405 amu, 9.50% of ⁵³Cr, with an atomic weight of 52.9407 amu, and 2.37% of ⁵⁴Cr, with an atomic weight of 53.9389 amu. On the basis of these data, confirm that the average atomic weight of Cr is 51.9963 amu.

(a) How many grams are there in one amu of a material?

(b) Mole, in the context of this book, is taken in units of gram-mole. On this basis, how many atoms are there in a pound-mole of a substance?

(a) Cite two important quantum-mechanical concepts associated with the Bohr model of the atom.

(b) Cite two important additional refinements that resulted from the wave-mechanical atomic model.

Relative to electrons and electron states, what does each of the four quantum numbers specify?

Give the electron configurations for the following ions: Fe²⁺, Al³⁺, Cu⁺, Ba²⁺, Br^-, and O^2-.

Sodium chloride (NaCl) exhibits predominantly ionic bonding. The Na⁺ and Cl^- ions have electron structures that are identical to which two inert gases?

With regard to electron configuration, what do all the elements in Group VIIA of the periodic table have in common?

To what group in the periodic table would an element with atomic number 114 belong?

Without consulting figure or Table 2.2, determine whether each of the electron configurations given below is an inert gas, a halogen, an alkali metal, an alkaline earth metal, or a transition metal. Justify your choices.

(a) 1s²2s²2p⁶3s²3p⁶3d⁷4s²

(b) 1s²2s²2p⁶3s²3p⁶

(c) 1s²2s²2p⁵

(d) 1s²2s²2p⁶3s²

(e) 1s²2s²2p⁶3s²3p⁶3d²4s²

(f) 1s²2s²2p⁶3s²3p⁶4s¹

(a) What electron subshell is being filled for the rare earth series of elements on the periodic table?

(b) What electron subshell is being filled for the actinide series?

Calculate the force of attraction between a K⁺ and an O^2- ion the centers of which are separated by a distance of 1.5 nm.

The net potential energy between two adjacent ions, E_N, may be represented by the sum of Equations 2.8 and 2.9; that is,

Calculate the bonding energy E₀ in terms of the parameters A, B, and n using the following procedure:

(a). Differentiate E_N with respect to r, and then set the resulting expression equal to zero, since the curve of E_N versus r is a minimum at E₀.

(b). Solve for r in terms of A, B, and n, which yields r₀, the equilibrium interionic spacing.

(c). Determine the expression for E₀ by substitution of r₀ into Equation 2.11.

For a K⁺–Cl^– ion pair, attractive and repulsive energies EA and ER, respectively, depend on the distance between the ions r, according to

For these expressions, energies are expressed in electron volts per K⁺–Cl^– pair, and r is the distance in nanometers. The net energy E_N is just the sum of the two expressions above.

(a) Superimpose on a single plot E_N, E_R, and E_A versus r up to 1.0 nm.

(b) On the basis of this plot, determine (i) the equilibrium spacing r₀ between the K⁺ and Cl^– ions, and (ii) the magnitude of the bonding energy E₀ between the two ions.

(c) Mathematically determine the r₀ and E₀ values using the solutions to Problem 2.14 and compare these with the graphical results from part (b).

Consider a hypothetical X⁺-Y^- ion pair for which the equilibrium interionic spacing and bonding energy values are 0.35 nm and -6.13eV, respectively. If it is known that n in Equation 2.11 has a value of 10, using the results of Problem 2.14, determine explicit expressions for attractive and repulsive energies E_A and E_R of Equations 2.8 and 2.9.

The net potential energy EN between two adjacent ions is sometimes represented by the expression

in which r is the interionic separation and C, D, and ρ are constants whose values depend on the specific material.

(a) Derive an expression for the bonding energy E₀ in terms of the equilibrium interionic separation r₀ and the constants D and ρ using the following procedure:

1. Differentiate E_N with respect to r and set the resulting expression equal to zero.

2. Solve for C in terms of D, ρ, and r₀.

3. Determine the expression for E₀ by substitution for C in Equation 2.12.

(b) Derive another expression for E₀ in terms of r₀, C, and ρ using a procedure analogous to the one outlined in part (a).

(a) Briefly cite the main differences between ionic, covalent, and metallic bonding.

(b) State the Pauli Exclusion Principle.

Compute the percents ionic character of the interatomic bonds for the following compounds: TiO₂, ZnTe, CsCl, InSb, and MgCl₂.

Make a plot of bonding energy versus melting temperature for the metals listed in Table 2.3. Using this plot, approximate the bonding energy for copper which has a melting temperature of 1084°C.

Using Table 2.2, determine the number of covalent bonds that are possible for atoms of the following elements: germanium, phosphorus, selenium, and chlorine.

What type(s) of bonding would be expected for each of the following materials: brass (a copper-zinc alloy), rubber, barium sulfide (BaS), solid xenon, bronze, nylon, and aluminum phosphide (AlP)?

Explain why hydrogen fluoride (HF) has a higher boiling temperature than hydrogen chloride (HCl) (19.4 vs. –85°C), even though HF has a lower molecular weight.

What is the difference between atomic structure and crystal structure?

If the atomic radius of aluminum is 0.143 nm, calculate the volume of its unit cell in cubic meters.

Show that the atomic packing factor for BCC is 0.68.

Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. Compute and compare its theoretical density with the experimental value found inside the front cover.

Calculate the radius of an iridium atom, given that Ir has an FCC crystal structure, a density of 22.4 g/cm³, and an atomic weight of 192.2 g/mol.

Calculate the radius of a vanadium atom, given that V has a BCC crystal structure, a density of 5.96 g/cm³, and an atomic weight of 50.9 g/mol.

Some hypothetical metal has the simple cubic crystal structure shown in figure. If its atomic weight is 70.4 g/mol and the atomic radius is 0.126 nm, compute itsdensity.

Zirconium has an HCP crystal structure and a density of 6.51 g/cm³.

(a) What is the volume of its unit cell in cubic meters?

(b) If the c/a ratio is 1.593, compute the values of c and a.

Using atomic weight, crystal structure, and atomic radius data tabulated inside the front cover, compute the theoretical densities of lead, chromium, copper, and cobalt, and then compare these values with the measured densities listed in this same table. The c/a ratio for cobalt is 1.623.

Rhodium has an atomic radius of 0.1345 nm and a density of 12.41 g/cm³. Determine whether it has an FCC or BCC crystal structure.

The unit cell for tin has tetragonal symmetry, with a and b lattice parameters of 0.583 and 0.318 nm, respectively. If its density, atomic weight, and atomic radius are 7.30 g/cm³, 118.69 g/mol, and 0.151 nm, respectively, compute the atomic packing factor.

Iodine has an orthorhombic unit cell for which the a, b, and c lattice parameters are 0.479, 0.725, and 0.978 nm, respectively.

(a) If the atomic packing factor and atomic radius are 0.547 and 0.177 nm, respectively, determine the number of atoms in each unit cell.

(b) The atomic weight of iodine is 126.91 g/mol; compute its theoretical density.

Titanium has an HCP unit cell for which the ratio of the lattice parameters c/a is 1.58. If the radius of the Ti atom is 0.1445 nm,

(a) Determine the unit cell volume, and

(b) Calculate the density of Ti and compare it with the literature value.

Zinc has an HCP crystal structure, a c/a ratio of 1.856, and a density of 7.13 g/cm³. Compute the atomic radius for Zn.

Rhenium has an HCP crystal structure, an atomic radius of 0.137 nm, and a c/a ratio of 1.615. Compute the volume of the unit cell for Re.

Sketch a unit cell for the body-centered orthorhombic crystal structure.

Sketch a tetragonal unit cell, and within that cell indicate locations of the ½ 1 ½ and ¼ ½ ¾ point coordinates.

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 a three-dimensional unit cell for the intermetallic compound AuCu3 given the following:

(a). The unit cell is cubic with an edge length of 0.374 nm,

(b). Gold atoms are situated at all cube corners, and

(c). Copper atoms are positioned at the centers of all unit cell faces.

Draw an orthorhombic unit cell, and within that cell a [121] direction.

Sketch a monoclinic unit cell, and within that cell a [011] direction.

What are the indices for the directions indicated by the two vectors in the sketch below?

Within a cubic unit cell, sketch the following directions:

(a)[110],

(b)[121],

(c)[012],

(d)[133],

(e)[111],

(f)[122],

(g)[123],

(h)[103],

For tetragonal crystals, cite the indices of directions that are equivalent to each of the following directions:

(a) [001]

(b) [110]

(c) [010]

Convert the [100] and [111] directions into the four-index Miller–Bravais scheme for hexagonal unit cells.

Determine indices for the directions shown in the following hexagonal unit cells:

Sketch the [1123] and [1010] directions in a hexagonal unit cell.

(a) Draw an orthorhombic unit cell, and within that cell a (210) plane.

(b) Draw a monoclinic unit cell, and within that cell a (002) plane.

What are the indices for the two planes drawn in the sketchbelow?

Sketch within a cubic unit cell the following planes:

(a) (011),

(b) (112),

(c) (102),

(d) (131),

(e) (111),

(f) (122),

(g) (123),

(h) (013)

Cite the indices of the direction that results from the intersection of each of the following pair of planes within a cubic crystal:

(a) (100) and (010) planes,

(b) (111) and (111) planes, and

(c) (101) and (001) planes.

Sketch the atomic packing of

(a) The (100) plane for the BCC crystal structure, and

(b) The (201) plane for the FCC crystal structure (similar to Figures 3.10b and3.11b).

Consider the reduced-sphere unit cell shown in Problem 3.20, having an origin of the coordinate system positioned at the atom labeled with an O. For the following sets of planes, determine which are equivalent:

(a) (001), (010), and, (100)

(b) (110), (101), (011), and (110)

(c) (111), (111), (111), and (111)

Here are shown the atomic packing schemes for several different crystallographic directions for some hypothetical metal. For each direction the circles represent only those atoms contained within a unit cell, which circles are reduced from their actual size.

(a) To what crystal system does the unit cell belong?

(b) What would this crystal structure becalled?

Below are shown three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms:

(a) To what crystal system does the unit cell belong?

(b) What would this crystal structure be called?

(c) If the density of this metal is 8.95 g/cm³, determine its atomic weight.

Convert the (010) and (101) planes into the four-index Miller–Bravais scheme for hexagonal unit cells.

Determine the indices for the planes shown in the hexagonal unit cells below:

Sketch the (1101) and (1120) planes in a hexagonal unit cell.

Explain why the properties of polycrystalline materials are most often isotropic.

Using the data for molybdenum in Table 3.1, compute the interplanar spacing for the (111) set ofplanes.

The diffraction peaks shown in figure are indexed according to the reflection rules for BCC (i.e., the sum h + k + l must be even). Cite the h, k, and l indices for the first four diffraction peaks for FCC crystals consistent with h, k, and l all being either odd oreven.

Would you expect a material in which the atomic bonding is predominantly ionic in nature to be more or less likely to form a non-crystalline solid upon solidification than a covalent material? Why?

Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327°C (600 K). Assume an energy for vacancy formation of 0.55 eV/atom.

Calculate the number of vacancies per cubic meter in iron at 850°C. The energy for vacancy formation is 1.08 eV/atom. Furthermore, the density and atomic weight for Fe are 7.65 g/cm³ and 55.85 g/mol, respectively.

Calculate the activation energy for vacancy formation in aluminum, given that the equilibrium number of vacancies at 500°C (773 K) is 7.57 ´ 10²³ m^-3. The atomic weight and density (at 500°C) for aluminum are, respectively, 26.98 g/mol and 2.62 g/cm³.

Below, atomic radius, crystal structure, electro negativity, and the most common valence are tabulated, for several elements; for those that are nonmetals, only atomic radii are indicated.

Which of these elements would you expect to form the following with copper?

(a) A substitutional solid solution having complete solubility

(b) A substitutional solid solution of incomplete solubility

(c) An interstitial solidsolution