Chapter 12: Crystalline Solids & Modern Materials

Question 1

Define crystalline lattice.

Answer 1

A crystalline lattice is the regular arrangement of atoms within a crystalline solid. The crystalline lattice of any solid is nature’s way of aggregating the particles to minimize their energy.

Question 2

Define unit cell.

Answer 2

A unit cell is a small collection of atoms, ions, or molecules used to represent the crystalline lattice.

Question 3

What is a simple cubic unit cell?

Answer 3

The simple cubic unit cell consists of a cube with one atom at each corner. The atom touch along each edge of the cube, so the edge length is twice the radius of the atoms (l = 2r).

Question 4

How many atoms are in a simple cubic unit cell?

Answer 4

One. Each corner atom is shared by eight other cells, so any one unit cell actually contains only one-eighth of each of the eight atoms at its corners, for a total of just one atom per unit cell.

Question 5

Define coordination number.

Answer 5

The coordination number is the number of atoms with which each atom is in direct contact. This number is also the number of atoms with which a particular atom can strongly interact.

Question 6

What is the coordination number of a simple cubic unit cell?

Answer 6

6.

Question 7

Define packing efficiency.

Answer 7

The packing efficiency is the percentage of the volume of the unit cell occupied by the spheres.

Question 8

How is coordination number related to packing efficiency?

Answer 8

The higher the coordination number, the greater the packing efficiency.

Question 9

What is the packing efficiency of a simple cubic unit cell?

Answer 9

52%.

Question 10

What is the edge length of a simple cubic unit cell in terms of r?

Answer 10

2r.

Question 11

What is the edge length of a body-centered cubic unit cell in terms of r?

Answer 11

4r/√3

Question 12

What is the edge length of a face-centered cubic unit cell in terms of r?

Answer 12

2√2r

Question 13

How many atoms are in a body-centered cubic unit cell?

Answer 13

2 atoms.

Question 14

How many atoms are in a face-centered cubic unit cell?

Answer 14

4 atoms.

Question 15

What is the coordination number of a body-centered cubic unit cell?

Answer 15

8.

Question 16

What is the coordination number of a face-centered cubic unit cell?

Answer 16

12

Question 17

What is the packing efficiency of a body-centered cubic unit cell?

Answer 17

68%.

Question 18

What is the packing efficiency of a face-centered cubic unit cell?

Answer 18

74%.

Question 19

What is a body-centered cubic unit cell?

Answer 19

The body-centered cubic unit cell consists of a cube with one atom at each corner and one atom (of the same kind) in the very center of the cube. The atoms do not touch along each edge of the cube, but instead along the diagonal line that runs from one corner through the middle of the cube to the opposite corner.

Question 20

What is a face-centered cubic unit cell?

Answer 20

The face-centered cubic unit cell is a cube with one atom at each corner and one atom (of the same kind) in the center of each cube face. In the face-centered unit cell (like the body-centered unit cell), the atoms do not touch along each edge of the cube. Instead, the atoms touch along the diagonal face.

Question 21

What is the pattern of hexagonal closest packing?

Answer 21

The pattern from one layer to the next is ABAB, with the third layer aligning exactly above the first. The central atom in layer B of this structure is touching six atoms in its own layer, three atoms in the layer above it, and three atoms in the layer below, for a coordination number of 12.

Question 22

What is the pattern of cubic closest packing?

Answer 22

The third layer of atoms is offset from the first in an ABCABC pattern. Every fourth layer aligns with the first.

Question 23

What is the cubic closest-packed structure identical to?

Answer 23

The face-centered cubic unit cell structure.

Question 24

What are the three subcategories of crystalline solids?

Answer 24

Molecular, ionic, and atomic.

Question 25

What are the three subcategories of atomic solids?

Answer 25

Nonbonding, metallic, and network covalent.

Question 26

Define molecular solids.

Answer 26

Solids whose composite units are molecules. The lattice sites in a crystalline molecular solid are occupied by molecules. These solids are held together by intermolecular forces like dispersion forces, dipole-dipole forces, and hydrogen bonding.

Question 27

Define polymorphs.

Answer 27

Polymorphs refers to the different structures molecular solids can crystallize into. Polymorphs have different properties, such as melting points and solubilities.

Question 28

What are the forces holding ionic solids together?

Answer 28

Strong coulombic forces (or ionic bonds), and because these forces are much stronger than intermolecular forces, ionic solids tend to have much higher melting points than molecular solids.

Question 29

What type of forces holds together nonbonding atomic solids?

Answer 29

Relatively weak dispersion forces. This means these solids have low melting points that increase uniformly with molar mass.

Question 30

What type of forces holds together metallic atomic solids?

Answer 30

Metallic bonds: the interaction of metal cations with the sea of electrons that surrounds them.

Question 31

How does the electron sea model explain the conductivity of metals?

Answer 31

In contrast to ionic solids where electrons are localized on an ion, the electrons in a metal are free to move. The movement or flow of electrons in response to an electric potential (or voltage) is an electric current. Metals are also excellent conductors of heat.

Question 32

How does the electron sea model explain the malleability and ductility (the capacity to be drawn into wires) of metals?

Answer 32

Since there are no localized or specific bonds in a metal, we can deform it relatively easily by forcing the metal ions to slide past one another.

Question 33

What type of force holds together network covalent atomic solids?

Answer 33

Covalent bonds. This causes the solids to have very high melting points.

Question 34

Why don't network covalent atomic solids tend to form closest-packed structures?

Answer 34

The crystal structures of these solids are more restricted by the geometrical constraints of the covalent bonds (which tend to be more directional than intermolecular forces, ionic bonds, or metallic bonds).

Question 35

Describe graphite's structure.

Answer 35

Graphite's structure consists of flat sheets of carbon atoms covalently bonded together as interconnected hexagonal rings.

Question 36

What is the bond length within a graphite sheet?

Answer 36

142 pm.

Question 37

How do the forces between graphite sheets compare to the forces within sheets?

Answer 37

The forces between sheets are much different than the bonds within sheets. There are no covalent bonds between sheets, only relatively weak dispersion force, and the separation between sheets is 341 pm.

Question 38

Why is graphite a good electrical conductor?

Answer 38

The electrons in the extended pi bonding network within a sheet make graphite a good electrical conductor in the direction of the plane of the sheets.

Question 39

Describe the unit cell of diamonds.

Answer 39

The unit cell is a face-centered cubic structure with an additional carbon atom in half of the eight tetrahedral holes located directly in each corner atom. Each carbon atom is covalently bonded to four other carbon atoms at the corners of a tetrahedron.

Question 40

Why does diamond conduct heat but not electricity?

Answer 40

The electrons in diamond are confined to the covalent bonds and are not free to flow, so it does not conduct electricity. However, because the bonds are strong and the connectivity between atoms so extensive, diamond is an excellent conductor of heat.

Question 41

What are fullerenes?

Answer 41

Carbon clusters containing from 36 to over 100 carbon atoms.

Question 42

What are nanotubes?

Answer 42

Nanotubes are synthesized long carbon structures that consist of sheets of interconnected C6 rings that assume the shape of a cylinder.

Question 43

What are the two types of nanotubes?

Answer 43

1. Single-walled nanotubes that have one layer of interconnected C6 rings forming the walls. 2. Multiwalled nanotubes that have concentric layers of interconnected C6 rings forming the walls.

Question 44

What are silicates?

Answer 44

Silicates are extended arrays of silicon and oxygen that form a network covalent structure in which a silicon atom bonds to four oxygen atoms at the corner of a tetrahedron. The silicon atom bonds to each oxygen with a single covalent sigma bond.

Question 45

What is silica?

Answer 45

Commonly called quartz, silica has the formula unit of SiO2. Each Si atom is in a tetrahedron surrounded by four O atoms, and each O atom acts as a bridge connecting the corners of two tetrahedrons.

Question 46

How is band theory similar to molecular orbital theory?

Answer 46

In MOT, molecular orbitals are not localized on individual atoms but delocalized over the entire molecule. Similarly, in band theory, we combine the atomic orbitals of the atoms within a solid crystal to form orbitals that are not localized on individual atoms but delocalized over the entire crystal.

Question 47

What is the band in band theory?

Answer 47

This refers to the band of energy levels that forms when there are no longer discrete energy levels between atoms.

Question 48

What is the valence band?

Answer 48

The orbitals in the band that are bonding molecular orbitals and contain N number of valence electrons.

Question 49

What is the conduction band?

Answer 49

The orbitals in the band that are antibonding and completely empty.

Question 50

How many valence and conduction bands are there per solid?

Answer 50

The number of valence and conduction bands is equal.

Question 51

How are mobile electrons in the conduction band responsible for the thermal conductivity of metals?

Answer 51

When a metal is heated, electrons are excited to higher-energy molecular orbitals. These electrons quickly transport the thermal energy throughout the crystal lattice.

Question 52

What is the band gap?

Answer 52

In metals, the energy difference between the top of the valence band and the bottom of the conduction band is infinitesimally small. In semiconductors and insulators, however, there is an energy gap between the two; this is the band gap.

Question 53

How does the size of the band gap compare between insulators and semiconductors?

Answer 53

In insulators, the band gap is large, but in semiconductors, the band gap is smaller.

Question 54

How does the size of the insulator band gap affect conductivity?

Answer 54

In insulators, the band gap is large, and electrons are not promoted into the conduction band at ordinary temperatures, resulting in no electrical conductivity.

Question 55

How does the size of the semiconductor band gap affect conductivity?

Answer 55

Since the band gap is small, the conductivity of semiconductors increases with increasing temperature because heat allows a greater number of electrons to be thermally promoted into the conduction band.

Question 56

What is the relationship between band gap length and position on a periodic column? Why?

Answer 56

The band gap decreases as we move down the column of elements. Atomic radius increases as we move down a column in the periodic table. The increasing radius reduces the overlap between orbitals on neighboring atoms, which in turn reduces the energy difference between the antibonding orbitals (the conduction band) and the bonding orbitals (the valence band).

Question 57

What are doped semiconductors?

Answer 57

Doped semiconductors are semiconductors that contain minute amounts of impurities that result in either additional electrons in the conduction band or electron "holes" in the valence band.

Question 58

What is an n-type semiconductor?

Answer 58

A type of semiconductor in which additional electrons are added to conduct electrical current. The charge carriers are negatively charged electrons in the conduction band.

Question 59

What is a p-type semiconductor?

Answer 59

Through doping, empty molecular orbitals are added to the valence band. The presence of these holes allows for the movement of electrical current because electrons in the valence band can move between holes. In this way, the holes move in the opposite direction as the electrons. Because each hole acts as a positive charge, these semiconductors are named p-type.

Question 60

What is the relationship between the intermolecular forces a solid is experiencing and the energy of the system?

Answer 60

The more force, the less the energy.

Question 61

To move around in a solid, which band must electrons be in?

Answer 61

The antibonding conduction band.

Question 62

What is the relationship between coordination number and lattice energy?

Answer 62

The higher the coordination number, the greater the attractive forces (lattice energy) are holding it together.

Question 63

What is the only type of matter known to assemble into a simple cubic unit cell?

Answer 63

Polonium (Po).

Question 64

Name some examples of elements that assemble into a body-centered cubic unit cell.

Answer 64

Iron (Fe), tungsten (W), and chromium (Cr).

Question 65

Name some examples of elements that assemble into a face-centered cubic unit cell.

Answer 65

Aluminium (Al), copper (Cu), nickel (Ni), gold (Au), and silver (Ag).

Question 66

Define allotropes.

Answer 66

A type of polymorphism specific to elements. Different arrangements of the crystal lattice gives them different properties.

Question 67

What is the relationship between conductivity and temperature?

Answer 67

Conductivity drops as temperature increases.

Question 68

What is the band of bonding orbitals called?

Answer 68

The valence band.

Question 69

What is the band of antibonding orbitals called?

Answer 69

The conduction band.

Question 70

In a highly conjugated system, what happens as you add more atomic orbitals?

Answer 70

The energy gap between the resulting molecular orbitals decreases (gets closer to one another).

Question 71

What does HOMO stand for?

Answer 71

Highest occupied molecular orbital.

Question 72

What does LUMO stand for?

Answer 72

Lowest unoccupied molecular orbital.

Question 73

How does the distinction between the bonding and antibonding bands change from metals to semimetals and semiconductors?

Answer 73

For metals, the distinction is infinitesimally small. Semimetals and semiconductors are different in that they have a band gap: large for insulators and small for semiconductors.

Question 74

At 0 K, which band are electrons located in?

Answer 74

The valence band. With thermal energy, some will move up to the conduction band.

Question 75

How do N-type semiconductors affect the band gap?

Answer 75

They raise the valence band through the use of negative electrons as major charge carriers.

Question 76

How do P-type semiconductors affect the band gap?

Answer 76

They lower the conduction band through the use of "positive" holes as major charge carriers.

Question 77

How do you induce directionality in a semiconductor?

Answer 77

If a p-type and n-type are next to each other, you can induce directionality in electron flow since electrons flow downhill relative to potential energy and holes flow uphill relative to potential energy.

Question 78

What does applying a current to a semiconductor generate?

Answer 78

Photons equal in energy to its band gap.