Chapter 7 - Crystals

Question 1

Answer 1

Hexagonal Close Packing

Question 2

Hexagonal Close Packing

Answer 2

Atoms: 2

Lattice points: (0,0,0), (1/3, 2/3, 1/2)

Dimensions: 2r, 2r, 2.83r

Angle of 120º in parallelogram base

Question 3

Answer 3

Cubic Close Packing

Question 4

Cubic Close Packing

Answer 4

Atoms: 4

Lattice-points: (0,0,0), (1/2, 1/2, 0), (0,1/2,1/2), (1/2, 0, 1/2)

Question 5

What are the types of holes?

Answer 5

Question 6

In a single layer, what are the different ways we can pack atoms?

Answer 6

Question 7

How can we calculate the lengths of the sides/radius of the atom able to fit in the center of a unit cell?

Answer 7

Question 8

Packing efficiency

Answer 8

Question 9

Primitive Cubic Structure

Answer 9

Atoms: 1

Lattice points: (0,0,0)

Sides: 2r

Question 10

Body centered cubic

Answer 10

Atoms: 2

Lattice Points: (0,0,0), (1/2,1/2,1/2)

Sides: 2.31r

Question 11

For a close-packed structure, how many holes are there per atom?

Answer 11

Two tetrahedral holes + one octahedral hole per atom

Question 12

Metallic crystals

Answer 12

Most metals crystallize in body-centered cubic, cubic close-packed, and hexagonal close-packed structure

Changes in pressure/temperature can change the structure of many metallic crystals

Bonding in metals is nondirectional (each atom is bonded to all neighboring atoms, rather than to individual atoms), so dislocations –> deformation is possible

Question 13

Dislocations

Answer 13

imperfections in crystals where atoms are out of place, but persist due to crystal rigidity

Question 14

What effect do dislocations have on metals?

Answer 14

Dislocations make the metal more susceptible to physical deformation

This effect is heightened by added impurity atoms (especially with a size different from that of the host). These foreign atoms tend to accumulate at crystal dislocations, making the crystal structure even less uniform.

Question 15

Describe sodium chloride NaCl crystal structure

Answer 15

Face-centered cubes of sodium ions and face-centered cubes of chloride atoms, offset by half a unit cell length in one direction

Question 16

Describe the Zinc Blende (ZnS) crystal structure

Answer 16

Zinc blende is one of the two common crystalline forms of ZnS. It is also the most common zinc ore and has the same geometry as diamond, with alternating layers of zinc and sulfide.

A face-centered lattice of sulfide ions with each zinc ion in a tetrahedral hole (4). Half of the total tetrahedral holes in the cell (4 atoms/unit cell x 2 tetrahedral holes/atom = 8 tetrahedral holes available) are occupied.

Question 17

Describe the wurtzite form of ZnS

Answer 17

Wurtzite is one of the two common crystalline forms of ZnS. However, wurtzite is much rarer than zinc blende and is formed at higher temperatures.

The zinc and sulfide ions each occupy the tetrahedral holes of the other ion’s hexagonal close-packed lattice.

Half of the total tetrahedral holes in each lattice is occupied.

Per unit cell there are (1/8)x8 + 1 = 2 atoms per hexagonal packing unit cell. Thus, there are 4 available tetrahedral holes, 2 of which are occupied by the other ion.

Question 18

Describe the fluorite (CaF₂) crystal structure

Answer 18

Calcium ion in a cubic close-packed lattice, with eight fluoride ions surrounding each calcium ion and occupying all of the tetrahedral holes (face centered cubic = 4 atoms/unit cell, 4atoms x 2 tetrahedral holes/atom = 8 tetrahedral holes/unit cell)

Or, can also be thought of as the fluoride ions in a simple cubic array with calcium ions in alternate body centers.

Found in all the oxides and sulfides of Li, Na, K, and Rb, and in Li₂Te and Be₂C

Question 19

What crystal structure can you expect for alkali halides (e.g. LiCl)?

Answer 19

Like the structure for NaCl. Face-centered cubic unit cells for each atom offset by half a unit cell.

Question 20

What compound has a crystal structure with ions in face-centered lattices and the other ion in the tetrahedral holes of this lattice?

Answer 20

ZnS Zinc Blende and Diamond (except with the same atom instead of ions).

Question 21

What compound has a crystal structure with a hexagonal unit cell and the other ion occupying half of the tetrahedral holes?

Answer 21

ZnS Wurtzite

Question 22

Antifluorite structure

Answer 22

The cation-anion stoichometry of CaF₂ is reversed. That is, for compounds like Li₂Te, Be₂C

Every tetrahedral hole in the anion lattice is occupied by a cation.

Common for structures with X₂F stoichometry (for oxiodes and sulfides)

Question 23

Born-Haber cycle

Answer 23

A cycl that considers the series of component reactions that can be imagined as “steps” for compound formation, to give the final heat of formation. It basically applies Hess’s law (which states that the overall change in energy of a process can be determined by breaking the process down into steps, then adding the changes in energy of each step) to an ionic solid.

Question 24

What enthalpies are positive and what enthalpies are negative for the reactions in the Born Haber cycle?

Answer 24

Positive:

• Sublimation ( Na(s) —> Na(g) )
• Ionization ( Na(g) —> Na⁺(g) + e^- )
• Bond dissociation ( 1/2 Cl₂ (g) —> Cl (g) )

Negative:

• Electron affinity ( Cl (g) + e^- —> Cl^- (g) )
• Lattice enthalpy ( Na⁺ (g) + Cl^- (g) —> NaCl (s) )
• Heat of formation ( Na (s) + 1/2 Cl₂ (g) –> NaCl (s) )

Question 25

Valence band theory

Answer 25

Molecular orbital theory works fine when only two atoms are involved. But what if there are many atoms? When many atoms interact, the number of orbitals is also large, and the discrete MOs combine to form a band of orbitals of similar energy rather than the discrete energy levels of small molecules ( kind of how sum –> integral).

Valence Band = highest energy band that contains electrons

Conduction Band = the next higher, empty band below the valence band

Question 26

Valence band

Answer 26

The highest energy band containing electrons

Question 27

Conduction band

Answer 27

The next higher, empty band above the valence band

Question 28

Band gap

Answer 28

The gap between the valence and conduction bands

Question 29

Use valence band theory to describe insulators

Answer 29

Insulators have a filled valence band and an empty, higher energy conduction band. Thus, electrons are restricted in their motion.

Question 30

Use valence band theory to describe conductors.

Answer 30

Conductors have a partially filled valence band and a higher energy conduction band. Since the valence band still has “empty space”, the electrons are free to move throughout the conductor.

Question 31

Use valence band theory to describe semiconductors.

Answer 31

For semiconductors, they have valence and conduction bands that are very close in energy. Therefore, electrons in the valence band (which can be filled or partially filled) can enter the conduction band. Higher temperature encourages the electrons to jump up into the conduction band, and conductance increases.

Question 32

Doping

Answer 32

Replacing a few atoms of the original element with atoms having either more or fewer electrons.