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a. Using your own words, explain why crystalline solids are grouped into four types: metallic solids, covalent network solids, ionic solids, and molecular solids.

b. A hypothetical metal has a crystal structure as shown in Figure Q1b. For the metal, determine the following relationships:

(i) Relationship between a and R.

(ii) The packing fraction/atomic packing factor (APF), assuming the atoms to be hard spheres.

Figure Q1b: Hypothetical metal has a crystal structure.

c. The density of BCC iron is 7.882 g/cm3. The atomic weight is 55.847 g/mol. Calculate:

(i) The lattice parameter, and

(ii) The atomic radius of iron.

d. Pure iron goes through a polymorphic change from BCC to FCC upon heating at 912Â°C. Calculate the volume change associated with the change in crystal structure from BCC to FCC. If at 912Â°C, the BCC unit cell has a lattice constant a = 0.293 nm and the FCC unit cell a = 0.363 nm.

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03:29

An unknown metal atom, labeled “A”, crystallizes by means of a body-centered cubic crystal lattice (BCC). a. Draw one metal unit cell and determine the number of atoms in one unit cell. b Draw the positions of the atoms giving the relation between the side lengths and the atomic radii. Then calculate the atomic radius if it is known that the side length of the unit cell is 305 pm c. It is known that the atomic density data in one unit cell of several metal atoms that crystallize with a body-centered cubic lattice. Li = 0.53 Na = 0.97 V = 5.96 Cr = 7.17 If you know the mass of 1 atom A is 8.46 x10-2 grams. Calculate the density or density of the atom A in one unit cell using the data from problems a and b. Estimate what atom is atom A if it is matched with the density data of several atoms above (choose the closest).

02:38

Activity 2:Check Your Understanding on Crystal Structure Self-Assessment No.Differentiate crystal structure, crystal system, and crystal form. 2. How to find what materials crystal structure is? (FCC, BCC or neither FCC or BCC or others) 3. Describe the crystal structure of iron; which crystallizes with two equivalent metal atoms in a cubic unit cell. Silver has a face-centered cubic unit cell. How many atoms of Ag are present in each unit cell? 5. Copper crystallizes in a face-centered cubic structure. What is the mass of one unit? 6. What is the edge length of a simple cubic unit cell made up of atoms having a radius of 158 pm? 7. State the number of atoms on a plane having the Miller indices of 110 in a BCC unit cell:

03:40

a) C60 fullerenes crystallize into an fcc lattice, also known as fullerite, with a lattice constant of a=14.17 Ã…. The diameter of a C60 molecule is about 0.71 nm. Calculate the density of fullerite. b) Metal ions can be inserted into the octahedral sites of the fullerite structure. What is the maximum ionic radius that can be accommodated without distorting the C60 lattice? c) C-C bonds in fullerenes are described as sp2-sp3 admixtures. Which do you expect to possess more sp3 character, C-C bonds in C60 fullerenes or C120 fullerenes? Briefly explain why.

04:21

BCC:DCHCP unit cell:HCP bonding configuration:What is the coordination number (number of nearest neighbors) for each structure? Remember that each unit cell is surrounded by identical unit cells_ b. Find the number of atoms per cell. Find the interatomic distance d for each structure in terms of the lattice spacing a This number depends on the structure, but is the same for each atom pair within the structure. Find the volume of each hard sphere that would pack into these structures in terms of the lattice spacing a. Find the volume of each unit cell. For HCP you must find € in terms of a f. Find the atomic packing fraction of hard spheres in each of these crystal structures_

02:30

A crystal is composed of two elements, A and B. The basic crystal structure is a facecentered cubic with element $A$ at each of the corners and element $B$ in the center of each face. The effective radius of element $\mathrm{A}$ is $r_{A}=1.035 \AA$ Å. Assume that the elements are hard spheres with the surface of each A-type atom in contact with the surface of its nearest A-type neighbor. Calculate ( $a$ ) the maximum radius of the B-type element that will fit into this structure, $(b)$ the lattice constant, and $(c)$ the volume density $\left(\# / \mathrm{cm}^{3}\right)$ of both the A-type atoms and the B-type atoms.

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