Close Packing Of Spheres, Atoms Or Ions And Simple Ionic Structures

Front 1

If a number of equally sized spheres (representing atoms) are placed in a rectangular box with the restriction that they must be in a regular arrangement, what are the two most efficient forms of packing and how are their layers describes respectively?

Back 1

Hexagonal close packing (HCP), has ABAB packing. Cubic close packing (CCP), has ABCABC packing.

Front 2

What type of lattice do HCP and CCP lattices have respectively?

Back 2

HCP: primitive lattice (P)

CCP: Face-centred subic lattice (FCC)

Front 3

What is the coordination of each sphere for both CCP and HCP structures?

Back 3

12

Front 4

HCP and CCP are the most efficient forms of packing known as 'close-packing'. What is another form of packing?

Back 4

Body centred packing (BCC) which has a body-centred cubic lattice.

Front 5

What is important to note about CCP and BCC respectively when considering volume calculations of a single unit cell?

Back 5

In CCP atoms are in contact along the diagonal of the face of the unit cell. Diagonal = 4r.

In BCC atoms are touching along body diagonal of unit cell =4r.

Front 6

Calculate the percentage space filled in a CCP lattice:

Back 6

As cubic can assume length of all sides = 1.

4r² = 1² + 1²

r=(√2)/4

Volume of a sphere = (4/3)πr³ = 0.185cm³

Number of atoms in unit cell = 4. Total volume of spheres = 0.74cm³. Total volume of cube = 1³ therefore = 74% filled.

Front 7

What can be noted about the percentage space filled in an HCP lattice?

Back 7

Both methods equally efficient, 74% also filled.

Front 8

Calculate the percentage of space filled in a BCC lattice

Back 8

Front 9

Distinguish between tetrahedral and octahedral holes in close-packed structures. how many of each do CCP and HCP have respecitvely?

Back 9

Twice as many tetrahedral holes as octahedral. For n anions, there will be 2n tet sites and n oct sites

CCP: 8 tet holes and 4 oct.

HCP: 4 tet holes and 2 oct

Front 10

Describe the simple ionic structure of NaCl in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations. Describe the layering in the strucutre.

Back 10

CCP array of Cl- with Na+ in all octahedral holes. 4 of each ion per unit cell with coordination of 6,6. Ions in alternate layers parallel to {111} planes

Front 11

Describe the simple ionic structure of NiAs in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations. Describe the layering in the strucutre.

Back 11

HCP array of As atoms with Ni in all octahedral holes. 6,6, coordination with 2 of each atom per unit cell and alternate layers parallel to {001} planes.

Front 12

Describe the simple ionic structure of CdCl2 in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations. Describe the layering in the strucutre.

Back 12

CCP array of Cl- anions with Cd2+ cations in half of octahedral holes. 6,3 coordination with 4 Cl- and 2 Cd+ per unit cell, alternate layers parallel to {111} planes. Rhombohedral lattice not cubic.

Front 13

Describe the simple ionic structure of CdI2 in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations. Describe the layering in the strucutre.

Back 13

HCP array of I- anions with Cd2+ cations in half of octahedral holes. 6,3 coordination with 2I- and 1 Cd2+ per unit cell. Alternate layers with {001} planes.

Front 14

Describe the simple ionic structure of ZnS (zinc blende) in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 14

CCP array of S2- anions with Zn2+ in half of the tetrahedral holes. 4,4 coordination with 4 of each ion per unit cell.

Front 15

Describe the simple ionic structure of diamond in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 15

CCP array of C atoms with more C atoms in half of tetrahedral holes. Coordination is 4,4 with 8 C atoms per unit cell.

Front 16

Describe the simple ionic structure of ZnS (Wurtzite) in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 16

HCP array of S2- anions with Zn2+ in half of tetrahedral holes. Coordination 4,4 and 2 of each atom per unit cell

Front 17

Describe the simple ionic structure of 'hexagonal diamond' in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 17

HCP array of C atoms with more C atoms in half of tetrahedral holes, gives 4,4 coordination and 4 C atoms per unit cell.

Front 18

Describe the simple ionic structure of CaF2 (fluorite) in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 18

CCP array of Ca2+ cations with F- anions in all tetrahedral holes. 8,4 coordination with 8 F- and 4 Ca2+ per unit cell

Front 19

Describe the simple ionic structure of Li2O (anti-fluorite) in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 19

CCP array of O2- anions with Li+ cations in all tetrahedral holes, 8,4 coordination with 8 Li+ and 4 O2- per unit cell

Front 20

Describe the simple ionic structure of TiO2 (rutile) in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 20

HCP array of O2- anions with Ti4+ in half of octahedral holes. 6,3 coordination with 4O2- and 2 Ti4+ per unit cell.

Front 21

Describe the simple ionic structure of CsCl in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.

Back 21

Looks body centred cubic but actually primitive cubic array of Cl- anions with Cs+ in the body centre of the unit cell. 8,8 coordination with 1Cs+ and 1 Cl- per unit cell.

Front 22

Describe the simple ionic structure of SrTiO3 (perovskite) in terms of the array of the anions, the position of the cations, how many of each atom per unit cell and their respective coordinations.How else can this be viewed?

Back 22

Primitive cubic structure overall.

Ti4+ at cell vertices, Sr2+ at body centre and O2- along cell edges.

Sr2+ coordinated to 12 O2- anions

Ti4+ coordinated to 6 O2- anions

O2- coordinated to 4 Sr and 4 Ti cations.

Can be viewed as TiO6 octahedra with Sr in the intersects.

Front 23

What's a simple way of finding number of octahedral holes filled for an anionic array? How can this be used to find number of tetrahedral holes filled?

Back 23

Number of octahedral holes filled = Number of cations / number of anions.

Number of tetrahedral holes = octahedral/2

Front 24

Calculate the density of CsCl with an NaCl type lattice given that the internuclear distance is 3.47 Å

Back 24

Density = Mr * z / V * NA

z = number of formula units, v = volume, NA = Avagadros.

NaCl has a CCP structure for each ion, with an arrangement of Na+ Cl- Na+ along a unit cell edge. Length of cell there is 2(3.47 Å).

Volume =

Density = 168.35g/mol * 4 / 0.602 x (6.94Å)³ = 3.35gcm-³

Front 25

Calculate the density of CsCl with a primitive lattice given that the internuclear distance is 3.56 Å

Back 25

Density = Mr * z / V * NA

Diagonal length of body (r) = 2(3.56).

Diagonal of base of cube can be found in terms of r: 2a² = r² so r=√2a

Can now use r in terms of a and the length of the body diagonal to find a.

7.12² = a² r² therefore 50.69=a² + (√2a)²

3a² = 50.69 so a=√(50.69/3) = 4.11Å

Density = 168.35g/mol * 1 / 0.602 x (4.11Å)³ = 4.03g/cm³

Front 26

Explain the thermodynamics of defect formation

Back 26

Defect formation enthalpically unfavourable but this is counteracted by the associuated increase in entropy. However, as the concentration of defects increases enthalpic cost outweighs entropic gain.

Front 27

What is an intrinsic defect?

Back 27

A defect due to thermodynamic effects

Front 28

What is an extrinsic defect?

Back 28

Defects due to imperfections in stoichiometry

Front 29

Define a point defect

Back 29

Local distortions and localised charge imbalance

Front 30

Define an extended defect

Back 30

When defect sites cluster or accumulate into lines or planes

Front 31

Name 3 important intrinsic defects

Back 31

1) Schotty defect

2) Frenkel defect

3) Interchange defect

Front 32

What is a Schotty defect and what is it most common for?

Back 32

A pair of cation/anion vaccancies with no change in the stoichiometry. Common for alkali/metal halide compounds.

Front 33

What is a Frenkel defect and for which compounds is it most common?

Back 33

An atom or ion is displaced into an interstitial site with no change in stoichiometry. Most common for AgCl and fluorite/antifluorite conformations.

Interstitial sites can sometimes attract each other and form clusters.

Front 34

What is an interchange defect and for which compounds does it usually occur?

Back 34

An interchange of two different atom sites, no change in stoichiometry and common for alloys of Au-Cu

Front 35

Name two forms of extrinsic defects:

Back 35

1) Doping

2) Crystal impurities

Front 36

Describe the cause of crystal impurity

Back 36

Perfect purity is generally unattainable for crystals of any significant size, impurity atoms or ions incorporated during crystal growth.

Front 37

What is doping? Give a common example

Back 37

The deliberate introduction of impurities to change the properties of a compound. For example changing the electrical/optical properties of Si by introducing B and As atoms.

Front 38

When is a doped compound considered a solid solution?

Back 38

When dopant concentrations are higher than 1%

Front 39

What are colour centres? For which compounds are they most common?

Back 39

Colour centres are extrinsic defects that give rise to changes in optical properties (IR, UV or vis absorption). Most common for alkali metal compounds.

Front 40

What is an F-centre colour defect, how can it be induced for NaCl and what does it result in?

Back 40

Some anion sites are replaced by e-. E.g. by heating NaCl in Na vapour some Cl- sites are replaced by e- . The electron behaves like a particle in a box with quantized energy levels accessible by absorption in the visible part of the spectrum. NaCl with F-centre colour defects appears yellow.

Front 41

Name another compound that is analagous with NaCl in terms of F-centre defects and what colour it appears?

Back 41

KCl, appears violet

Front 42

What is an H-centre colour defect for NaCl?

Back 42

A Cl2- anion fills an anion site

Front 43

What is a V-centre colour defect for NaCl?

Back 43

A Cl2- anion fills a pair of anion sites

Front 44

What is band theory?

Back 44

A description of bonding and conduction in solids

Front 45

What can be noted about the difference in energy between bonding and anti-bonding orbitals for strong and weak interactions?

Back 45

Larger difference in energy between bonding and antibonding for stronger interactions that weaker interactions

Front 46

For a simple solid with only one atom type, what bands would appear?

Back 46

Separate bands resulting from each set of atomic orbitals, i.e. an s-band, a p-band, a d-band etc.

Front 47

What effects the width of the bands?

Back 47

The strength of the interaction, i.e. a strong interaction gives a wide band and a weak interaction a narrow band.

Front 48

Some bands tend to overlap in energy, e.g. 3s and 3p, whilst there are also energy gaps where no orbitals are present. What are these known as?

Back 48

Band gaps.

Front 49

Energy levels are filled from lowest to highest bands as for molecular orbitals. What is the highest occupied energy level (at absolute zero) known as?

Back 49

The Fermi level

Front 50

At temperatures above absolute zero what can be noted about the population of the bands?

Back 50

They follow Fermi-Dirac distribution

Front 51

What are phonons?

Back 51

Lattice vibrations in particle form, increase with temperature.

Front 52

What are the properties of metallic conductors? Give some examples:

Back 52

High conductivity with a significant proportion of valence electrons delocalised. Conductivity decreases with temperature due to resistance from phonon-electron collisions. Includes metals, alloys, sulfides

Front 53

What are the properties of semiconductors? Give some examples:

Back 53

Moderate conductivity

Conductivity increases with temperature

Conductivity can be modified by impurities

Includes transition metals, Si, Ge

Front 54

What are the properties of insulators? Give some examples:

Back 54

Very low conductivity, conductivity increases with temperature, valence electrons tightly bound, includes many solid covalent networks and ionic solids.

Front 55

What are the properties of ionic conductors? Give some examples:

Back 55

Moderate conductivity, rigid framework with one set of mobile ions. Vacant sites and atoms in interstitial sites increase ion mobility and low energy barriers for high ionic conductivity. Most common in doped materials. Conductivity increases with temperature due to higher concentration of defects.

Front 56

What are the properties of ionic conductors? Give some examples:

Back 56

No electrical resistance below critical temperature (as no electron-phonon collisions). Valence shell delocalised, electrons move cooperatively.

Front 57

What are the properties of superconductors?

Back 57

No electrical resistance below critical temperature, as no electron phonon collisions. Valence shell electrons delocalised and electrons move cooperatively.

Front 58

What can be noted about the difference in energy level transition between band theory and molecular orbital theory?

Back 58

Electrons can be readily promoted to higher bands at thermal temperatures.

Front 59

What property of the bands allows metallic conduction? Give an example using Be

Back 59

Partially filled bands, athe bands must be partially filled. Most metals have partially filled atomic orbitals so partially filled bands, in other cases such as Be the 2s and 2p bands overlap to give partially filled bands and can conduct.

Front 60

Describe the bands of insulators?

Back 60

They have filled bands and empty bands with large gaps between them, limiting conduction of electrons.

Front 61

Describe the bands of intrinsic semi-conductors

Back 61

They have filled bands and empty bands but small band gaps that allows some conduction due to thermal excitation from the valence band to the conduction band. This can even occur at room temperature to some extent due to Boltzman distribution. Conductivity increases with temperature as increased population of conduction band outweighs increased vibrations.

Front 62

How can charge carriers be viewed?

Back 62

As electrons in the conduction band and as positive holes in the valence band.

Front 63

What is the equation for measuring conductivity?

Back 63

σ = A e^(-Ea/kT) activation energy is approx 0.5E(gap)

Front 64

How can promotion of electrons from valence band to conduction band with larger gaps be induced?

Back 64

Irradiation - photoconductivity. CdS absorbs visible light, used in photocells for solar power

Front 65

How is conduction in extrinsic semi-conductors determined?

Back 65

Semi-conductors are modified by introduction of a doping agent, conductivity generally greater than intrinsic due to decreased band gap. Controlled by the concentration of the dopant.

Front 66

What are P-type semi-conductors? Give an example.

Back 66

Intrinsic semi-conductors where the dopant has one electron fewer than the semiconductor. E.g. introduction of Ga to Si. electron defficient Ga-Si bond not part of valence band, forms discrete acceptor band above it. Electrons from valence band promoted to acceptor band, leaving positive holes to serve as charge carriers.

Front 67

What are N-type semi-conductors? Give an example.

Back 67

Intrinsic semi-conductors where the dopant has one electron more than the semi-conductor. E.g. introduction of As to Si. Extraa electron in energy band below valence band, electrons can be readily promoted into valence band to allow conduction with negative charge carriers.

Front 68

Which type of semi-conductor is best at low and high temps respectively?

Back 68

At low temperature extrinsic higher conductivity, at high temps intrinsic.

Front 69

What property allows solid electrolytes to show very high conductivities? Commeont on their stability

Back 69

Channel structures that permit facile ion mobility. Only stable at high tempertatures.

Front 70

How do superconductors work?

Back 70

Zero electrical resistance below critical temperature as no electron phonon collisions - power transmission without energy loss. Electrons associate into pairs to act cooperatively and travle throughout the structure. 'Cooper' pairs of electrons arise following a local distortion - a second electron is attracted in response.

Front 71

Give an example of a high Tc (critical temp) semi-conductor and state what structure its based on

Back 71

YBa2Cu3O7, based on perovskite ABO3 with oxygen site deficiencies.

Front 72

Comment on the positions of the atoms in YBa2Cu3O7

Back 72

Y3+ and Ba2+ in body centre with Cu2+/3+ in the cell vertex and O2- along some edges.

Front 73

What is a consequence of the oxygen site deficiencies? How does this result in conductivity?

Back 73

Some Cu ion sites are 2+ and so square pyramidal, and some are 3+ and so square planar. Conductivity due to transfer of electrons between these two structures.

Front 74

How can super conductivity of YBa2Cu3O7 be destroyed?

Back 74

Partial reduction