- 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
- (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?
- Allowed values for the quantum numbers of electrons are as follows:The relationships between n and the shell designations are noted in Table 2.1. Relative to the subshells,
- Give the electron configurations for the following ions: Fe2+, Al3+, Cu+, Ba2+, Br-, and O2-.
- 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.
- (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 O2- ion the centers of which are separated by a distance of 1.5 nm.
- The net potential energy between two adjacent ions, EN, 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
- 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
- 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
- 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 ? are constants whose values depend on the
- (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 for the body-centered cubic crystal structure that the unit cell edge length a and the atomic radius R are related through a =4R/√3.
- For the HCP crystal structure, show that the ideal c/a ratio is 1.633
- Show that the atomic packing factor for BCC is 0.68.
- Show that the atomic packing factor for HCP is 0.74.
- 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
- 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
- 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.
- Below are listed the atomic weight, density, and atomic radius for three hypothetical alloys. For each determine whether its crystal structure is FCC, BCC, or simple cubic and then justify your
- 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
- 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
- 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
- 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.
- Below is a unit cell for a hypothetical metal.(a) To which crystal system does this unit cell belong?(b) What would this crystal structure be called?(c) Calculate the density of the
- Sketch a unit cell for the body-centered orthorhombic crystal structure.
- List the point coordinates for all atoms that are associated with the FCC unit cell(figure).
- List the point coordinates of the titanium, barium, and oxygen ions for a unit cell of the perovskite crystal structure(figure).
- List the point coordinates of all atoms that are associated with the diamond cubic unit cell(figure).
- 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
- 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],
- Determine the indices for the directions shown in the following cubic unitcell:
- Determine the indices for the directions shown in the following cubic unitcell:
- 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.
- Using Equations 3.6a, 3.6b, 3.6c, and 3.6d, derive expressions for each of the three primed indices set (u′, v′, and w′) in terms of the four unprimed indices (u, v, t, and w).
- (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)
- Determine the Miller indices for the planes shown in the following unitcell:
- Determine the Miller indices for the planes shown in the following unitcell:
- Determine the Miller indices for the planes shown in the following unitcell:
- 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)
- 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
- 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
- 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
- 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:(a)(b)(c)(d)
- Sketch the (1101) and (1120) planes in a hexagonal unit cell.
- (a) Derive linear density expressions for FCC [100] and [111] directions in terms of the atomic radius R.(b) Compute and compare linear density values for these same two directions for silver.
- (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R.(b) Compute and compare linear density values for these same two directions for tungsten.
- (a) Derive planar density expressions for FCC (100) and (111) planes in terms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for nickel.
- (a) Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for vanadium.
- (a) Derive the planar density expression for the HCP (0001) plane in terms of the atomic radius R.(b) Compute the planar density value for this same plane for magnesium.
- 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.
- Determine the expected diffraction angle for the first-order reflection from the (113) set of planes for FCC platinum when monochromatic radiation of wavelength 0.1542 nm is used.
- Using the data for aluminum in Table 3.1, compute the interplanar spacing’s for the (110) and (221) sets of planes.
- The metal iridium has an FCC crystal structure. If the angle of diffraction for the (220) set of planes occurs at 69.22( (first-order reflection) when monochromatic x-radiation having a wavelength of
- The metal rubidium has a BCC crystal structure. If the angle of diffraction for the (321) set of planes occurs at 27.00( (first-order reflection) when monochromatic x-radiation having a wavelength of
- For which set of crystallographic planes will a first-order diffraction peak occur at a diffraction angle of 46.21( for BCC iron when monochromatic radiation having a wavelength of 0.0711 nm is used?
- Figure shows an x-ray diffraction pattern for a-iron taken using a diffract meter and monochromatic x-radiation having a wavelength of 0.1542 nm; each diffraction peak on the pattern has been
- 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
- Figure shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used. (a) Index
- 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
- 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)
- 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
- For both FCC and BCC crystal structures, there are two different types of interstitial sites. In each case, one site is larger than the other, and is normally occupied by impurity atoms. For FCC,
- Derive the following equations: (a) Equation 4.7a (b) Equation 4.9a (c) Equation 4.10a (d) Equation4.11b
- What is the composition, in atom percent, of an alloy that consists of 30 wt% Zn and 70 wt% Cu?
- What is the composition, in weight percent, of an alloy that consists of 6 at% Pb and 94 at% Sn?
- Calculate the composition, in weight percent, of an alloy that contains 218.0 kg titanium, 14.6 kg of aluminum, and 9.7 kg of vanadium.
- What is the composition, in atom percent, of an alloy that contains 98 g tin and 65 g of lead?

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