Chapter 21, Problem 17P

(a) Magnesium (Mg) has a hexagonal close-packed (HCP) crystal structure with the lattice parameter of a = 0.321 nm and c= 0.521 nm and the atomic radius is 0.173 nm. (i) What is the number of atoms per unit cell in HCP structure? (ii) Determine the atomic packing factor of the Mg unit cell. (iii) Is Mg containing an ideal atomic packing factor? You may justify your answer by evaluating the HCP c/a ratio. Subsequently, will slip be harder in Mg compared to the ideal HCP structure? Justify your answer.

The orthorhombic unit cell of NiSO4 has the dimensions a = 634 pm, b = 784 pm, and c = 516 pm, and the mass density of the solid is estimated as 3.9 g cm−3. Identify the number of formula units in a unit cell and calculate a more precise value of the mass density.

A metal X has an atomic radius of 0.126 nm. If the density and molar mass of X are 7.87 g cm3 and 55.85 g mol1, respectively. 1. (a) (i) Determine the number of atoms per unit cell and the crystal structure of metal X. (ii) Determine the volume of the unit cell. (ii) Determine its planar density in [100], [110] and [111] directions. (iv) Explain which direction would be the most possible slip direction when shear stress is applied. (b) Explain the role of matrix and reinforcement phase in a composite material.

A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.(a) What is the empirical formula of this compound? Explain your answer.(b) What is the coordination number of the Mn3+ ion?(c) Calculate the edge length of the unit cell if the radius of a Mn3+ ion is 0.65 A.(d) Calculate the density of the compound.

Gallium has an orthorhombic structure, with a0 = 0.45258 nm, b0 = 0.45186 nm, and c0 = 0.76570 nm. The atomic radius is 0.1218 nm. The density is 5.904 g cm3, and the atomic weight is 69.72 g mol. Determine (a) the number of atoms in each unit cell; and (b) the packing factor in the unit cell.

Sodium sulfate (Na2SO4) crystallizes in the orthorhombic system in a unit cell with a = 5.863 Å, b= 12.304 Å, and c=9.821 Å. The density of these crystals is 2.663 g cm-3. Determine how many Na2SO4 formula units are present inthe unit cell.

Protein crystal with 261 amino acids , dimensions 500 x500x20 um. The protein crystallized in monoclinic space group P21 (2 monomers per unit cell) with dimensions a=42.3, b=41.1, c=72.2 A and β = 103.8 degrees. Calculate the physical volume of your protein crystal How many copies of your protein are in your crystal?

The Structure of Crystalline Solids If the atomic radius of a metal that has the face-centred cubic crystal structure is 0.2782 nm, calculate the volume of its unit cell in nm3.

For the shown crystal structure, write down (a) the Bravais lattice and (b) the basis of the primitive unit cell. For this structure a=b= c and a=B=y%3D90°. The green (A) atoms at the vertices; blue (B) atom at the center, pink (C) atoms are the centers of two opposite faces; and brown (D) atoms at the centers of four edges of the unit cell. Note that the a, b and c translation vectors are along the positive x, y and z axes, respectively, as shown. COD