Unit Cells and Bravais Lattices in Crystallography

1. How many distinct Bravais lattices can exist in three dimensional space

7

10

14

32

While there are 7 crystal systems defined by symmetry there are exactly 14 unique ways to arrange points in space such that every point has an identical environment.

Explanation

While there are 7 crystal systems defined by symmetry there are exactly 14 unique ways to arrange points in space such that every point has an identical environment.

2. A primitive unit cell contains lattice points only at its corners

True

False

By definition a primitive cell labeled P has lattice points only at the corners. The total number of points per primitive cell is exactly one because each corner is shared by eight adjacent cells.

Explanation

By definition a primitive cell labeled P has lattice points only at the corners. The total number of points per primitive cell is exactly one because each corner is shared by eight adjacent cells.

3. Which crystal system is characterized by the conditions where all axes are of equal length and all angles are 90 degrees

Tetragonal

Orthorhombic

Cubic

Monoclinic

The cubic system is the most symmetric. It requires a equals b equals c and alpha equals beta equals gamma equals 90 degrees.

Explanation

The cubic system is the most symmetric. It requires a equals b equals c and alpha equals beta equals gamma equals 90 degrees.

4. Which of the following are types of centered unit cells

Body centered I

Face centered F

Side centered C

Primitive P

Centered cells contain lattice points in addition to the corners. Primitive cells are not considered centered because they only have points at the corners.

Explanation

Centered cells contain lattice points in addition to the corners. Primitive cells are not considered centered because they only have points at the corners.

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5. What is the effective number of atoms in a Body Centered Cubic BCC unit cell

1

2

4

8

In a BCC cell there is one atom at the center and one eighth of an atom at each of the eight corners. This sums to a total of two atoms per unit cell.

Explanation

In a BCC cell there is one atom at the center and one eighth of an atom at each of the eight corners. This sums to a total of two atoms per unit cell.

6. In the monoclinic crystal system all three lattice vectors are of unequal length

True

False

For a monoclinic system a is not equal to b and b is not equal to c. Additionally two angles are 90 degrees while the third is not.

Explanation

For a monoclinic system a is not equal to b and b is not equal to c. Additionally two angles are 90 degrees while the third is not.

7. Which crystal systems can have a base centered C Bravais lattice

Cubic

Orthorhombic

Monoclinic

Triclinic

Only the orthorhombic and monoclinic systems have base centered variations. The cubic system does not have a base centered lattice because it would violate cubic symmetry.

Explanation

Only the orthorhombic and monoclinic systems have base centered variations. The cubic system does not have a base centered lattice because it would violate cubic symmetry.

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8. Which crystal system is the least symmetric with no equal axes or angles

Monoclinic

Triclinic

Hexagonal

Rhombohedral

The triclinic system has a b and c all unequal and alpha beta and gamma all unequal and not equal to 90 degrees.

Explanation

The triclinic system has a b and c all unequal and alpha beta and gamma all unequal and not equal to 90 degrees.

9. The packing efficiency of a Simple Cubic lattice is higher than that of a Body Centered Cubic lattice

True

False

Simple cubic has a packing efficiency of about 52 percent while BCC is more densely packed at about 68 percent. FCC is the highest at 74 percent.

Explanation

Simple cubic has a packing efficiency of about 52 percent while BCC is more densely packed at about 68 percent. FCC is the highest at 74 percent.

10. What is the relationship between axes in the Tetragonal crystal system

A equals b equals c

A equals b but not c

A is not equal to b or c

All angles are different

A tetragonal cell looks like a stretched cube. Two axes are equal in length but the vertical axis c is either longer or shorter. All angles remain 90 degrees.

Explanation

A tetragonal cell looks like a stretched cube. Two axes are equal in length but the vertical axis c is either longer or shorter. All angles remain 90 degrees.

11. Which parameters define the geometry of a unit cell

Edge lengths a b c

Interaxial angles

Atomic mass

Color of the crystal

A unit cell is fully defined by its six lattice parameters which include the lengths of the three edges and the angles between those edges.

Explanation

A unit cell is fully defined by its six lattice parameters which include the lengths of the three edges and the angles between those edges.

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12. How many atoms are contained within a single Face Centered Cubic FCC unit cell

1

2

4

14

In an FCC cell there is one eighth of an atom at each of the 8 corners and one half of an atom on each of the 6 faces. This results in a total of 4 atoms.

Explanation

In an FCC cell there is one eighth of an atom at each of the 8 corners and one half of an atom on each of the 6 faces. This results in a total of 4 atoms.

13. What is the total number of lattice points in a primitive hexagonal unit cell

1

2

3

6

A primitive cell by definition always contains exactly one lattice point regardless of the crystal system it belongs to.

Explanation

A primitive cell by definition always contains exactly one lattice point regardless of the crystal system it belongs to.

14. What is the coordination number of an atom in a Face Centered Cubic FCC lattice

6

8

12

14

In an FCC or cubic close packed structure each atom is in direct contact with 12 nearest neighbors. This represents one of the most efficient ways to pack spheres.

Explanation

In an FCC or cubic close packed structure each atom is in direct contact with 12 nearest neighbors. This represents one of the most efficient ways to pack spheres.

15. A rhombohedral unit cell is also known as a trigonal unit cell

True

False

In the rhombohedral or trigonal system the axes are all equal in length but the angles are equal to each other while being different from 90 degrees.

Explanation

In the rhombohedral or trigonal system the axes are all equal in length but the angles are equal to each other while being different from 90 degrees.

Crystal Foundations Unit Cells and Bravais Lattices Quiz

1. How many distinct Bravais lattices can exist in three dimensional space

2.

What first name or nickname would you like us to use?

2. A primitive unit cell contains lattice points only at its corners

3. Which crystal system is characterized by the conditions where all axes are of equal length and all angles are 90 degrees

4. Which of the following are types of centered unit cells

5. What is the effective number of atoms in a Body Centered Cubic BCC unit cell

6. In the monoclinic crystal system all three lattice vectors are of unequal length

7. Which crystal systems can have a base centered C Bravais lattice

8. Which crystal system is the least symmetric with no equal axes or angles

9. The packing efficiency of a Simple Cubic lattice is higher than that of a Body Centered Cubic lattice

10. What is the relationship between axes in the Tetragonal crystal system

11. Which parameters define the geometry of a unit cell

12. How many atoms are contained within a single Face Centered Cubic FCC unit cell

13. What is the total number of lattice points in a primitive hexagonal unit cell

14. What is the coordination number of an atom in a Face Centered Cubic FCC lattice

15. A rhombohedral unit cell is also known as a trigonal unit cell