X-ray Diffraction- Basic Crystallography Flashcards
What is a crystalline solid?
One composed of a three dimensional periodic array of matter. The matter may be atoms, ions or molecules.
What is an amorphous solid?
One that shows no long range order but the short range order (chemical bonds) are well defined
Types of crystalline solid
Single crystal: unique entity
Polycrystalline material: composed of many contiguous crystals
How are lattices defined?
Use non co-linear vectors a, b, c separated by angles α, β, γ. Use one for one-dimensional lattice, two for lattice plane, three for lattice array. The vectors define the unit cell. Translation by a sum of the vectors to an equivalent lattice point.
What are Miller planes?
A series of planes in a 3D periodic lattice which contain an infinite number of lattice points. Infinite number of ways to generate the series of planes.
How do Miller indices work?
They are the reciprocals of the fractional intercepts the plane makes with the unit cell axes. (2 2 1) intercepts a at 1/2, b at 1/2 and c at 1. If plane parallel to an axis the reciprocal of infinity is 0.
Miller indices if a plane intercepts the origin of the unit cell
Consider the adjacent parallel plane. If this plane makes a negative intercept the index is written with a bar
Inter-planar spacing
The spacing of the Miller planes. Symbol d subscript hkl
Link between inter-planar spacing and the unit cell parameters and angles
Depends on the crystal system so there are 7 different formulae for 1/d^2. Involve h, k, l and a, b, c and if the angles aren’t all 90 α, β, γ
What is true about two different sets of lattice planes which have integer multiples of Miller indices?
They have exactly the same orientation.
d h,k,l = nd nh,nk,nl
4 types of symmetry operations
Reflection, inversion centre, rotation, rotation inversion
What is rotation-inversion?
A body has an n-fold rotation-inversion axis if rotation by 360/n followed by inversion through the centre of the axis brings it into coincidence with itself
How many lattice points in each type of Bravais lattice?
Primitive: 1 point per unit cell
Body centred: 2 points per unit cell
Face centred: 4 points per unit cell
Side centred: 2 points per unit cell
Minimum symmetry elements required for each crystal system
Cubic: four 3-fold rotation axes
Tetragonal: one 4-fold rotation(-inversion) axis
Orthorhombic: three mutually perpendicular 2-fold rotation(-inversion) axes
Rhombohedral: one 3-fold r(-i) axis
Hexagonal: one 6-fold r(-i) axis
Monoclinic: one 2-fold r(-i) axis
Triclinic: none
Which axes are the vectors a, b and c on in a unit cell?
a is x axis, b is y axis, c is z axis
