Lecture 5 - Crystal Structure

Question 1

What is crystal structure

Answer 1

• It is ordered OR repeating arrangement of atoms / ions / molecules [consider these as particles] in a crystalline material
• Structure refers to the internal arrangement of particles and not the external appearance of the crystal
• However, these are not entirely independent since the external appearance of a crystal is often related to the internal arrangement.
• For example, crystals of cubic rock salt (NaCl) are physically cubic in appearance

Question 2

Explain unit cells

Answer 2

• Is the smallest group of atoms, ions or molecules that, when repeated at regular
  intervals in three dimensions, will produce the LATTICE POINTS of a crystal system / structure/ Lattice
• Bonds that occur between atoms, molecules, or ions in an ordered arrangement form the basic building block

Question 3

What is a lattice point

Answer 3

A point in space wher atoms; ions or molecules are positioned in a repeating pattern to form a cyrstal lattice

Question 4

Explain attice parameters

Answer 4

• Is the length between two points on the corners of a unit cell
• If two sides are equal, such as in a tetragonal lattice, then the lengths of the two lattice
  parameters are designated aand c , with bomitted
• Different lattice parameters of unit cell form different crystal systems

Question 5

What are Atom positions

Answer 5

Within the unit cell, the atomic arrangement is expressed using coordinates

Question 6

What are Two systems of coordinates

Answer 6

1. Cartesian or orthogonal coordinates (X, Y, Z)
2. Atomic coordinates are usually expressed in terms of fractional coordinates, (x, y, z)

Question 7

Explain the Cartesian or orthogonal coordinates (X, Y, Z) co-ordinate system

Answer 7

• It is the distance in each direction between the origin of the unit cell and the atom
• These coordinates may be manipulated in the same fashion are used with two- or three-dimensional graphs
• It is very simple, therefore, to calculate inter-atomic distances and angles given the Cartesian coordinates of the atoms
• Unfortunately, the repeating nature of a crystal cannot be expressed easily using such coordinates

Question 8

Explain the Atomic coordinates are usually expressed in terms of fractional coordinates, (x, y, z) co-ordinate system

Answer 8

• This coordinate system is coincident with the cell axes (a, b, c) and relates to the position of
  the atom in terms of the fraction along each axis
• Fractional coordinates, therefore, are used to retain and manipulate crystal information

Question 9

What are Miller indices

Answer 9

• Planes in a crystal can be specified using a notation
• Are indicated by the notation [hkl] where h, k, and l are reciprocals of the plane with the x, y, and z axes

Question 10

How do you obtain the Miller indices of a given plane

Answer 10

1.The plane in question is placed on a unit cell

2.Its intercepts with each of the crystal axes are then found

3.The reciprocal of the intercepts are taken

4.These are multiplied by a scalar to insure that is in the simple ratio of whole numbers

Question 11

Provide a Description of crystal structure

Answer 11

• The most common manner is to refer to the size and shape of the unit cell and the positions of the atoms (or ions) within
  the cell
• However, this information is sometimes insufficient to allow for an understanding of the true structure in three
  dimensions
• Consideration of several unit cells, the arrangement of the atoms with respect to each other, the number of other atoms
  they in contact with, and the distances to neighboring atoms, often will provide a better understanding
• A number of methods are available to describe extended solid-state structures.
  The most applicable with regard to elemental and compound semiconductor, metals and the majority of insulators is the
  CLOSE PACKING APPROACH

Question 12

What is closed packing

Answer 12

• Atoms (ions) are arranged so as to have the maximum density
• Most efficient way for equal sized spheres to be packed in two dimensions

Question 13

What is Cubic close packing

Answer 13

• Two close packed layers are stacked
• Third layer (C) is placed such that it does not exactly cover layer A
• The packing sequence will be …ABCABCABC….

Question 14

Explain what is Coordination Number is

Answer 14

• The coordination number of an atom or ion within an extended structure is the number of
  nearest neighbor atoms (ions of opposite charge) that are in contact with it
• A slightly different definition is often used for atoms within individual molecules: the number of donor atoms associated with the central atom or ion
• However, this distinction is rather artificial, and both can be employed

Question 15

Explain the coordination numbers for metal atoms

Answer 15

In a molecule or complex are commonly 4, 5,
and 6, but all values from 2 to 9 are known and a few examples of higher coordination
numbers have been reported

Question 16

Explain the common coordination numbers in the solid state

Answer 16

Are 3, 4, 6, 8, and 12

Question 17

What are interstitial sites or vacancies

Answer 17

• The unfilled lattice sites (interstices) between the atoms in a cell
• In both fcc and hcp cells most of the space within these atoms lies within two different sites known as octahedral sites and tetrahedral sites

Question 18

What are tetrahedral sites (vacancies)

Answer 18

Are surrounded by four atoms arranged at the corners of a tetrahedron

Question 19

Explain Octahedral sites

Answer 19

• Are surrounded by six atoms which make-up the apices of an octahedron
• For a given close packed lattice an octahedral vacancy will be larger than a tetrahedral vacancy

Question 20

What happens Within a face centered cubic lattice

Answer 20

• The eight tetrahedral sites are positioned within the cell, at the general fractional coordinate of (n/4,n/4,n/4) where n = 1 or 3

e.g., (1/4,1/4,1/4), (1/4,1/4,3/4), etc.

• The octahedral sites are located at the center of the unit cell (1/2,1/2,1/2), as well as at each of the edges of the cell

e.g., (1/2,0,0).

Question 21

What happens In the hexagonal close packed system

Answer 21

The tetrahedral sites are at (0,0,3/8) and (1/3,2/3,7/8), and the octahedral sites are at (1/3,1/3,1/4) and all symmetry equivalent positions

Question 22

Explain a diamond cubic crystal strcurure

Answer 22

• fcc lattice
• Half of the tetrahedral sites are filled
• All the octahedral sites remain vacan

Question 23

Explain a Zinc Blende crystal strcurure

Answer 23

• Archetype: zinc sulfide (ZnS)
• Fcc lattice of S atoms in which half of the tetrahedral sites are filled with Zn atoms
• This is a binary phase

Question 24

Explain a Chalcopyrite crystal strcurure

Answer 24

• Archetype: Chalcopyrite CuFeS2
• Structure is tetragonal
• Lattice is made-up of a lattice of sulfur atoms in which the tetrahedral sites are filled in layers…FeCuCuFe

Question 25

Explain a Wurtzite crystal strcurure

Answer 25

- This is a hexagonal form of the zinc sulfide - Identical in the number of and types of atoms - It is built from two interpenetrating hcp lattices as opposed to the fcc lattices in zinc blende - All the atoms in a wurtzite structure are 4-coordinate

Question 26

Explain a Rock Salt crystal strcurure

Answer 26

- Archetype: sodium chloride (NaCl) - It may also be described as face centered cubic lattice in which all of the octahedral sites are filled, while all the tetrahedral sites remain vacant, and thus each of the atoms in the rock salt structure are 6-coordinate

Question 27

Breifly explain defects

Answer 27

- Ordinarily exist in equilibrium between the crystal lattice and its environment

Question 28

Explain the two types of defects

Answer 28

1. Point defects are associated with a single crystal lattice site 2. Extended defects occur over a greater range

Question 29

What are the point defects

Answer 29

- Vacancy ( Missing atom at a certain crystal lattice position ) - Interstitial impurity ( Extra impurity atom in an interstitial position ) - Self-interstitial ( Extra atom in an interstitial position ) - Substitution impurity ( Impurity atom, substituting an atom in crystal lattice ) -- Frenkel defect ( Extra self-interstitial atom, responsible for the vacancy nearby )