x-ray crystallography - crystal structure Flashcards
(28 cards)
unit cell definition
smallest repeating volume unit (box shape) in a crystal
how many types of unit cells are there?
7 different geometric shapes of unit cell, known as the 7 crystal systems
what is important about the stacking of unit cells?
when stacked in 3D, all the space will be filled
how are unit cell shapes defined?
the 3 sides of the unit cell = a, b, c
the 3 angles between the sides = α, β, γ
the 3 faces of the unit cell = A, B, C
(so α is the angle made by b and c, β by a and c, γ by a and b - similarly for faces)
what are unit cell parameters?
a, b, c, α, β, γ are collectively known as unit cell parameters
how many faces do unit cells have?
all unit cells have 6 faces (3 sets of parallel faces)
what are the 7 crystal systems/unit cell shapes?
cubic
tetragonal
orthorhombic
trigonal/rhombohedral
hexagonal
monoclinic
triclinic
what are the unit cell parameters for cubic crystal systems?
a = b = c
α = β = γ = 90
what are the unit cell parameters for tetragonal crystal systems?
a = b =/= c
α = β = γ = 90
what are the unit cell parameters for orthorhombic crystal systems?
a =/= b =/= c
α = β = γ = 90
what are the unit cell parameters for trigonal / rhombohedral crystal systems?
a = b = c
α = β = γ =/= 90
what are the unit cell parameters for monoclinic crystal systems?
a =/= b =/= c
α = γ = 90, β =/= 90
what are the unit cell parameters for hexagonal crystal systems?
a = b =/= c
α = β = 90, γ = 120
what are the unit cell parameters for triclinic crystal systems?
a =/= b =/= c
α =/= β =/= γ =/= 90
lattice point definition
the environments at all corners of a unit cell - which are always identical
how can lattice points be used to simplify a structure?
crystals are simplified into 2D using grids of lattice points
what is the miller index?
in 2D representations of crystals, lines can be drawn that connect certain lattice points
sets of parallel lines are a miller index, each set/index has different spacing between adjacent lines and belongs to a different family
how are miller indices written + described?
miller indices are given as (h, k) which can be found by taking reciprocals of where the line intersects the a and b axes, and clearing any fractions
lines in the same set/family will have the same miller index /(h, k)
so individual lines in a family = x(reciprocals of miller index), where x = integer
how does miller indices affect diffraction?
lines in the same family will all diffract at the same angle and produce spots of the same intensity
how does miller indices change for 3D systems?
indices are now given by (h, k, l) for axes a, b, and c respectively
what is d-spacing + how can it be found?
planes in the same miller index will all cut an axis at particular regular intervals (depending on the index) - these intervals relative to the axis being cut = d-spacing
e.g. planes in (1, 0, 0) index cut the a axis at integer intervals so d-spacing = a
what is braggs law?
braggs law is a derived mathematical relationship governing the conditions required to observe diffraction from a set of miller planes using monochromatic radiation - essentially radiation enters a crystal structure and is reflected out at the same angle it came in at
what is the braggs equation + how does it describe diffraction?
equation: nλ = 2dsinθ
where n = integer
d = spacing between planes/lines
θ = angle that x-ray comes in at/makes with planes/lines
λ = wavelength of radiation
for reflected beams to constructively interfere to give a diffraction spot, the difference in distance travelled that the x-ray beam must travel before being reflected must = nλ where n=integer
how does θ change between 2D and 3D systems?
in 3D, θ will be different for each (h, k, l) as all have different d-spacing
