Chapter 3 The Structure of Crystalline Solids

Question 1

What are the two main types of atomic arrangements in solids?

Answer 1

Amorphous (non-crystalline) and crystalline.

Question 2

How are atoms arranged in amorphous materials?

Answer 2

Atoms are bonded but lack a repeating pattern, exhibiting only short-range order.

Question 3

How are atoms arranged in crystalline materials?

Answer 3

Atoms are bonded in a regular 3D pattern with long-range order.

Question 4

What is the relationship between energy and packing in atomic structures?

Answer 4

Dense, ordered packing tends to have lower energy, while non-dense, random packing has higher energy.

Question 5

How does the arrangement of atoms affect material properties?

Answer 5

The arrangement determines mechanical, optical, and chemical properties (e.g., ductility, transparency).

Question 6

What is the difference between atomic structure and crystal structure?
physical state

Answer 6

Atomic structure refers to protons, neutrons, and electrons, while crystal structure pertains to atomic arrangement in solids.

Question 7

What types of materials are typically crystalline?

Answer 7

Most metals, many ceramics, and some polymers.

Question 8

What is a lattice?

Answer 8

A 3D array of points coinciding with atom positions or sphere centers.

Question 9

What is a unit cell?

Answer 9

The smallest repetitive volume containing the complete lattice pattern of a crystal.

Question 10

What are lattice constants?

Answer 10

The lengths of the unit cell sides (a, b, c). In cubic systems, all three are equal.

Question 11

What is a simple cubic arrangement?

Answer 11

A unit cell with equal sides and 90° angles.

Question 12

Why are metals typically densely packed?

Answer 12

Due to non-directional metallic bonding, leading to small nearest-neighbor distances to minimize bond energy.

Question 13

What are the three common metallic crystal structures?

Answer 13

Body-Centered Cubic (BCC), Face-Centered Cubic (FCC), and Hexagonal Close-Packed (HCP).

Question 14

What is the Body-Centered Cubic (BCC) structure?

Answer 14

Atoms touch along cube diagonals, with close-packed directions along the space diagonal.

Question 15

What is the Face-Centered Cubic (FCC) structure?

Answer 15

Atoms touch along face diagonals, with close-packed directions along the face diagonal.

Question 16

What is the Hexagonal Close-Packed (HCP) structure?
visually

Answer 16

ABAB… stacking sequence, with an extra plane of atoms in the middle.

Question 17

What is the coordination number for a simple cubic structure?

Answer 17

6

Question 18

What is the Atomic Packing Factor (APF) for a simple cubic structure?

Answer 18

0.52

Question 19

How many atoms are in a BCC unit cell?

Answer 19

2 atoms per unit cell

Question 20

What is the coordination number for a BCC structure?

Answer 20

8

Question 21

What is the APF for a BCC structure?

Answer 21

0.68

Question 22

How many atoms are in an FCC unit cell?

Answer 22

4 atoms per unit cell

Question 23

What is the coordination number for an FCC structure?

Answer 23

12

Question 24

What is the APF for an FCC structure?

Answer 24

0.74

Question 25

What is the stacking sequence for an FCC structure?

Answer 25

ABCABC...

Question 26

What is the stacking sequence for an HCP structure?

Answer 26

ABAB...

Question 27

What is the coordination number for an HCP structure?

Answer 27

12

Question 28

How many atoms are in an HCP unit cell?

Answer 28

6 atoms per unit cell

Question 29

What is the APF for an HCP structure?

Answer 29

0.74

Question 30

What is the formula for calculating crystal density?

Answer 30

ρ = (n * A) / (Vc * NA), where n = number of atoms, A = atomic weight, Vc = unit cell volume, NA = Avogadro's number.

Question 31

What is Avogadro's number?

Answer 31

6.022 × 10²³ atoms/mol.

Question 32

How does the density of metals compare to ceramics and polymers?

Answer 32

ρ(metals) > ρ(ceramics) > ρ(polymers).

Question 33

What is polymorphism?

Answer 33

When elements or compounds exist in more than one crystal form, often requiring changes in temperature or pressure.

Question 34

What is allotropy?

Answer 34

Polymorphism found in elemental solids (single element) (e.g., carbon as graphite or diamond).

Question 35

How are point coordinates in a crystal lattice defined?

Answer 35

By their positions relative to the x, y, and z axes, using unit cell dimensions.

Question 36

How are crystallographic directions determined? (vector)

Answer 36

By projecting a vector onto the x, y, and z axes, reducing indices to the smallest integers.

Question 37

What is the notation for crystallographic directions?

Answer 37

Square brackets [uvw], with negative numbers indicated by a bar (e.g., [1̅00]).

Question 38

How do you reduce crystallographic direction indices to the smallest integers?

Answer 38

Divide or multiply indices by a common factor to achieve the smallest integers.

Question 39

What is the vector algorithm for crystallographic directions? how do you find the vector

Answer 39

Subtract tail coordinates from head coordinates, normalize by lattice parameters, reduce to smallest integers.

Question 40

What is the notation for a family of directions?

Answer 40

Angle brackets .

Question 41

What are Miller indices?

Answer 41

(hkl) describes planes in a crystal.

Question 42

How are Miller indices determined for a plane?

Answer 42

Find plane intercepts, take reciprocals, and reduce to smallest integers.

Question 43

What is the notation for Miller indices?

Answer 43

Parentheses (hkl).

Question 44

What is the notation for a family of planes?

Answer 44

Curly brackets {hkl}.

Question 45

What is linear atomic density?

Answer 45

The number of atoms centered on a given direction divided by the line length in that direction.

Question 46

What is planar atomic density?

Answer 46

The number of atoms centered on a given plane divided by the area of that plane.

Question 47

What are the close-packed planes in FCC and HCP structures?

Answer 47

FCC: {111} planes; HCP: (0001) plane.

Question 48

What is the difference between single crystals and polycrystals? (gd)

Answer 48

Single crystals have an uninterrupted lattice; polycrystals consist of many small grains with different orientations.

Question 49

How is X-ray diffraction used to study crystal structures?

Answer 49

X-rays are directed at a sample, and diffraction angles/intensities are measured. Using Bragg's law, the crystal structure and interplanar spacing can be determined.