- 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
- (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
- (a) Cite two important quantum-mechanical concepts associated with the Bohr model of the atom.(b) Cite two important additional refinements that
- 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.
- 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
- 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
- (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
- 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
- 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
- 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.
- 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,
- (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
- Using Table 2.2, determine the number of covalent bonds that are possible for atoms of the following elements: germanium, phosphorus, selenium, and
- What type(s) of bonding would be expected for each of the following materials: brass (a copper-zinc alloy), rubber, barium sulfide (BaS), solid
- 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
- 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
- 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,
- 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
- Using atomic weight, crystal structure, and atomic radius data tabulated inside the front cover, compute the theoretical densities of lead, chromium,
- 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
- 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,
- 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
- 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
- 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
- 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”
- 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
- (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
- 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
- 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
- Here are shown the atomic packing schemes for several different crystallographic directions for some hypothetical metal. For each direction the
- Below are shown three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms:(a) To what crystal
- 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
- (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R.(b) Compute and compare linear density
- (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
- (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
- (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
- 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
- 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)
- 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)
- 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
- 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;
- 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,
- 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
- 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
- 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
- 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
- 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
- Below, atomic radius, crystal structure, electro negativity, and the most common valence are tabulated, for several elements; for those that are
- 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
- 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?