What are unit cells
Bonds that occur between atoms, molecules, or ions in an ordered arrangement form the basic building block
Explain unit cells fully
- 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
What are lattice points
A point in space where atoms, ions or molecules are positioned in a repeating pattern to form a crystal lattice
Explain the lattice parameter
- 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 a and c , with b omitted
- Different lattice parameters of unit cell form different crystal systems
What are the 7 crystal lattice systems
- Cubic
- Tetragonal
- Orthorhombic
- Rhombohedral
- Hexagonal
- Monoclinic
- Triclinic
Explain the cubic crystall lattice system
- a=b=c,
- α = β = γ = 90°
- Three sides are equal, so the three lattice parameters are designated ONLY as a with b, c omitted
OR
b and c are also considered to be “a”
Explain the Tetragonal crystall lattice system
a = b ≠ c
α = β = γ= 90°
Explain the Orthorhombic crystall lattice system
a ≠ b ≠ c
α = β = γ= 90°
Explain the Rhombohedral crystall lattice system
a = b = c
α = β = γ ≠ 90°
Explain the Hexagonal crystall lattice system
a = b ≠ c
α = β = 90°, γ = 120°
Explain the Monoclinic crystall lattice system
a ≠ b ≠ c
α = γ = 90°, β ≠ 90°
Explain the Triclinic crystall lattice system
a ≠ b ≠ c
α ≠ β ≠ γ
What is crystal structure
- 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
What are the types of cubic structures
- Simple cubic
- Body centered cubic
- Face centered cubic
What are miller indices
Planes in a crystal can be specified using a notation called Miller indices
Explain the Miller indices
- The Miller index is indicated by the notation [hkl] where h, k, and l are reciprocals of the plane with the x, y, and z axes
- Miller indices directions may be grouped in families
- Individual Miller indices are given in parentheses (hkl), while braces {hkl} are placed around the indices of a family of planes
For example, (001), (100), and (010) are all in the {100} family of planes, for a cubic lattice
What are the steps To obtain the Miller indices of a given plane
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
Desribe the crystal structure
- 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
What is closed packing
Atoms (ions) are arranged so as to have the maximum density
What are the closed packing structures
- Hexagonal Close Packing
- Cubic Close Packing
Explain “ The most efficient way for equal sized spheres to be packed in
two dimensions “
- It can be seen that each sphere (the dark gray shaded sphere) is surrounded by, and is in contact with, six other spheres (the light
gray spheres ) - Each sphere is in contact with six other spheres the maximum possible is the spheres are the same size, although lower density
packing is possible - Close packed layers are formed by repetition to an infinite sheet
Within these close packed layers, three close packed rows are present, shown by the dashed lines
Explain the Hexagonal Close Packing
- If two close packed layers A and B are placed in contact with each other so as to maximize the density, then the spheres of layer B will rest in the hollow (vacancy) between three of the spheres in layer A
- Atoms in the second layer, B (shaded light gray), may occupy one of two possible positions but not both together or a mixture of each
- If a third layer is placed on top of layer B such that it exactly covers layer A, subsequent placement of layers will result in the following
sequence …ABABAB…. This is known as hexagonal close packing or hcp
Explain the Cubic Close Packing
- 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….
- The unit cell of cubic close packed structure is actually that of a face-centered cubic (fcc) Bravais lattice
- In the fcc lattice the close packed layers constitute the {111} planes
- As with the hcp lattice packing fraction in a cubic close packed (fcc) cell is 74.05%
Packing Fraction / Packing Density
The packing fraction or density is derived by assuming that each atom is a hard sphere in contact with its nearest neighbours
-
Lecture 1 - Catalysis44
-
Lecture 2 Health and Nutrition69
-
Lecture 4 - Green Chemistry35
-
Lecture 5 - Crystal Structure30
-
Lecture 3 - Reactors18
-
Lecture 4b - Green Chemistry24
-
Lecture 2 test stuff39
-
Leecture 3 - Test 1 stuff20
-
Chapter 6 - Group Theory ( Test )31
-
Chapter 5 - Test ( Crystal structure )38
-
Extra for chapter 5&610
-
Test 2 Memo answers15
