**Crystalline solids** represent structures with well-organized patterns and shapes.

Concept #1: Crystalline Solids

Unlike **crystalline solids**, **amorphous solids** represent structures that lack an organized patterns or shapes.

When examining the particles within a crystal you may observe them tightly packed in an organized pattern. The smallest portion of which is termed the **unit cell**.

There are 7 crystal systems and 14 types of unit cells that naturally occur. The **simple** **cubic unit cell **represents one of the simplest types.

Concept #2: Simple Cubic Unit Cell

The **Simple Cubic Unit Cell** is composed of a cube with an atom at each corner. In the **Lattice Diagram** each of the unit cells are combined to form a crystal lattice. In the **Space Filling Unit Cell Diagram** we are shown that the unit cell uses only 1/8 of each of the 8 corner atoms.

The **body-centered cubic unit cell **is composed of a cube with one atom at each of its corners and one atom at the center of the cube.

Concept #3: Body Centered Cubic Unit Cell

The **face-centered cubic unit cell** is composed of a cube with one atom at each of its corners and one atom in the center of each cube face.

Concept #4: Face Centered Cubic Unit Cell

Example #1: Unit Cell Calculations 1

Example #2: Unit Cell Calculations 1

Example #3: Unit Cell Calculations 1

Example #4: Unit Cell Calculations

Example #5: Unit Cell Calculations 2

Example #6: Unit Cell Calculations 2

Example #7: Unit Cell Calculations 2

Example #8: Unit Cell Calculations 3

Example #9: Unit Cell Calculations 3

Example #10: Unit Cell Calculations 3

Aluminum has a face-centered cubic unit structure and a density of 2.716 g/cm3. Calculate the edge length of the unit cell.
a) 4.041 x 10 -8 cm
b) 3.992 x 10 -8 cm
c) 3.615 x 10 -8 cm
d) 3.247 x 10 -8 cm
e) 2.836 x 10 -8 cm

What is the number of nearest neighbors in a body-centered-cubic lattice?
(A) 12
(B) 8
(C) 6
(D) 4

Determine the radius of an Al atom (in pm) if the density of aluminum is 2.71 g/cm 3. Aluminum crystallizes in a face centered cubic structure with an edge length of 2√2 r.
a) 143 pm
b) 227 pm
c) 96 pm
d) 172 pm
e) 193 pm

Gold crystallizes in a face-centered cubic structure. What is the edge length of the unit cell if the atomic radius of gold is 144 pm?
a) 204 pm
b) 288 pm
c) 333 pm
d) 407 pm

Which one of the following elements is considered an insulator?
a. Fe
b. Ga
c. N
d. Ge
e. Si

Which of the following statements about crystalline and amorphous solids is TRUE?
A) A crystalline solid is composed of atoms or molecules arranged with long-range repeating order.
B) An example of a crystalline solid is glass.
C) An example of an amorphous solid is table salt (NaCl).
D) An amorphous solid is composed of atoms or molecules with a majority of its volume empty.
E) All of the above statements are TRUE.

Rank the three cubic crystalline structures in order of increasing space between the particles of the crystal.
Note: FCC = face-centered cubic, BCC = Body-centered cubic, and SC = simple cubic.
a) SC < BCC = FCC
b) FCC < BCC < SC
c) BCC < FCC < SC
d) FCC < SC < BCC
e) SC = BCC < FCC

Sodium chloride, NaCl, crystallizes in a face-centered cubic lattice of chloride ions, with the smaller sodium ions occupying holes between the chloride ions. How many Cl – ions are in contact with any single Na+ ions?
a) 4
b) 6
c) 8
d) 12

Which term describes the number of atoms surrounding an atom in a crystal lattice
a) Unit cell
b) Coordination number
c) Crystalline solid
d) Packing efficiency

What is the edge length of a face-centered cubic unit cell made up of atoms having a radius of 128 pm?
A) 181 pm
B) 362 pm
C) 512 pm
D) 1020 pm
E) 81 pm

Vanadium crystallizes in a body centered cubic structure and has an atomic radius of 131 pm. Determine the density of vanadium, if the edge length of a bcc structure is 4r/√3.
A) 3.06 g/cm3
B) 12.2 g/cm3
C) 6.11 g/cm3
D) 2.77 g/cm3
E) 8.46 g/cm3

The edge of a body-centered-cubic unit cell (which contains two atoms per unit cell) of an element Y was found to be 3.16 x 10 –8 cm. The density of the metal is 19.35 g•cm –3. What is the approximate molar mass of Y?
a) 65.4 g•mol –1
b) 92.0 g•mol –1
c) 184 g•mol –1
d) 238 g•mol –1

Which one of the following cannot form a solid with a lattice based on the sodium chloride structure?
A. CuO
B. NaBr
C. LiF
D. CuCl2
E. RbI

Potassium metal crystallizes in a body-centered cubic structure with a unit cell edge length of 5.31 angstroms. The radius of a potassium atom is __________ angstroms.
A. 2.30
B. 2.66
C. 5.31
D. 1.33
E. 1.88

The density of solid Ag is 10.5 g/cm3.a. How many atoms are present per cubic centimeter of Ag?b. As a solid, Ag adopts a face-centered cubic unit cell. How many unit cells are present per cubic centimeter of Ag?c. What is the volume of a unit cell of this metal?d. What is the edge length of a unit cell of Ag?

Consider a body-centered cubic unit cell as shown here.a. How many corner atoms (orange) are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube? c. How many body atoms shown in this image? d. What fraction of each body atom is inside the boundaries of the cube? e. If you sum all the fractions of atoms, how many atoms are actually inside a body-centered cubic unit cell?

How many atoms are in one body-centered cubic unit cell of a metal?
A) 1
B) 2
C) 3
D) 4

Consider a simple cubic (a.k.a, primitive cubic) unit cell as shown here.
(i) How many atoms are shown in this image?
(ii) What fraction of each atom is inside the boundaries of the cube?
(iii) If you sum all (the fractions of atoms, how many atoms are actually inside a simple cubic unit cell?

Rank the crystal lattice structures in order of decreasing efficiency of space in the structure.Simple cubic, Body centered cubic, Face centered cubic, Hexegonal close packed

The density of solid W is 19.3 g/cm3. a) How many atoms are present per cubic centimeter of W? b) As a solid, W adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of W? c) What is the volume of a unit cell of this metal? d) What is the edge length of a unit cell of W?

Consider a face-centered cubic unit cell as shown here.a. How many corner atoms are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube?c. How many face atoms are shown in this image?d. What fraction of each face atom is inside the boundaries of the cube?e. If you sum all the fractions of atoms, how many atoms are actually inside a face-centered cubic unit cell?

Lithium crystallizes in a body-centered cubic unit cell. What is the mass of one unit cell in grams?

Lithium crystallizes in a body centered cubic unit cell. What is the mass of one unit cell? Report answer in grams.

Determine the number of atoms per unit cell for each of the following metals.a. Tungstenb. Nickel

Metallic copper crystallizes in a face-centered cubic lattice, with one Cu atom per lattice point. If the edge length of the unit cell is found to be 362 pm, what is the metallic radius of Cu in pm?

The substance lithium is found to crystallize in a cubic lattice, with an edge length of 346.0 pm. If the density of solid lithium is 0.5565 g/cm3, how many Li atoms are there per unit cell?

Arrange the three common unit cells in order from least dense to most dense packing.