Crystallography And Diffraction Flashcards
How can we observe crystals?
Regular form of the faces of mineral specimens.
Scattering of light by periodic objects (eg opals).
Diffraction experiments.
High resolution electron microscope images.
What makes a material crystalline?
Ordered arrangement of atoms.
Atoms stack together to form regular networks.
Atomic arrangement is often reflected in the macroscopic geometry.
What makes a material amorphous?
Random arrangement of atoms.
What makes a material polycrystalline?
It is made up of many small crystals.
What is a lattice?
An infinite array of points in space in which the environment of every point is identical.
What is a motif?
A repeating unit of pattern (eg the arrangement of atoms that is placed on each lattice point).
What is a mesh?
The arrangement of lines that joins the lattice points.
What is a unit mesh?
One unit which, when repeated, makes up the mesh.
Where can the motif be placed on the lattice?
The motif can be placed anywhere in relation to the lattice point as long as the same position is chosen for every motif.
Can there be more than one unit mesh for a lattice?
Yes, it is possible, however we generally use the primitive mesh.
What is the primitive mesh?
The unit mesh with only one lattice point.
What is a centred mesh?
A square mesh with a lattice point in the middle.
How can lattice points be reached on a lattice?
With a combination of lattice vectors.
What method can we use to project 3D to 2D?
We can use crystal plans or crystal projections.
How do we draw crystal projections?
We view the cell in a set plane and label elevations for each point not at 1 or 0.
What is the most efficient way to pack in 2D?
Hexagonal packing (91%).
What are the most efficient ways to pack in 3D?
HCP and FCC (74%).
What interstices do both HCP and FCC possess?
Octahedral and Tetrahedral interstices?
What are interstices?
Small spaces within a lattice that may be able to accommodate another atom.
Example of an interstice:
Na+ in a FCC Cl- lattice inside the octahedral interstice.
What symmetry elements are there in 2D?
Rotational and Mirror.
If when does a body have n-fold symmetry?
When the final and initial forms of the body are identical when it is rotated 360º/n around the axis of rotation.
How does mirror symmetry work?
When an object is reflected along a mirror plane and its image in that plane is identical.
Pure rotation operations generate what?
4 2D plane point groups (2-fold, 3-fold, 4-fold 6-fold).
Why can’t 5-fold symmetry exist in crystallography?
5-fold rotation does not cause tessellation of the lattice.
Combining mirror and rotational elements generates how many more 2D crystallographic plane point groups?
5 more: m, 2mm, 3m, 4mm and 6mm.
What is the most basic (asymmetrical) 2D lattice we can draw?
It is oblique ( the haggle between two of its sides is >90º and <180º) and the two adjacent sides have different lengths.
What symmetry does the primitive unit mesh of the asymmetrical shape have?
P21 as it has a diad.
What does the presence of the first diad in the p2 cell cause?
3 more dads to be generated automatically, making it in effect p222, however the nomenclature is p2 as these are automatically generated and implied.
What symmetry does a primitive 90º, unequal adjacent sided cell show?
p2mm.
Why does a primitive, 90º unequal adjacent sided cell show p2mm symmetry?
It has a diad axis on its vertices and generated additional diad axes at the centre of the edges and at the cell centre. It also possesses a horizontal and vertical mirror plane thus p2mm as the second mirror is caused by the first.
If a motif has rotational symmetry 2 and the lattice it is applied to is oblique, whet is the symmetry of the crystal?
p2 as the oblique lattice has symmetry p2.
What happens when you place a motif of lower symmetry on a lattice that has higher symmetry?
The symmetry of the crystal is lowered.
Can you apply a motif of higher symmetry to a lattice of lower symmetry and get a crystal that shows symmetry?
No.
Where to find the list of lattice point groups with possible crystal point groups:
Lecture 2 back page.
Directions are given in what brackets?
[ ]
Sets of directions related by symmetry are given in what brackets?
< >
Sets of symmetrically arranged planes are given in what brackets?
{ }
Planes are given in what brackets?
( )
What is different about directions and planes in the hexagonal system?
They use the Miller-Bravais indices: hkli
Equation for the Weiss Zone Law:
hU + kV + lW = 0
Define the Weiss Zone Law.
If [UVW] lies in the plane (hkl) then hU+kV+lW=0. Alternatively, if [UVW] is parallel to (hkl) then the Weiss Zone Law is satisfied.
A set of planes with a common axis (direction) is known as what?
A zone.
Equations for direction at intersection of two planes:
U = k1l2-k2l1 V = l1h2-l2h1 W = h1k2-h2k1
or use cross product trick.
How to find the plane parallel to two directions:
(hkl) = (V1W2 – V2W1 W1U2 – W2U1 U1V2 – U2V1)
or use cross product trick.
Two planes lie in the same zone if:
h1U+k1V+l1W=0
and
h2U+k2V+l2W=0
Addition rule of planes:
(ph1+qh2)U + (pk1+qk2)W + (pl1+ql2)V = 0
so, p(h1k1l1) + q(h2k2l2) = 0
What is wave number?
Aka the propagation constant, it is 1/λ in radians per metre. Given letter k.
De Broglie’s equation
λ=h/p
General form that describes a travelling wave:
ψ=F(x–vt)
can also be written as:
ψ=F(t–x/v)
where ψ=F(x,t)
Write the equation that describes a sine wave travelling at speed v, with amplitude A.
ψ(x,t)=AsinK(x–vt)
K is constant to avoid taking sine of physical units.
What happens to a periodic wave if it’s position, x is increased by the wavelength, λ?
ψ(x,t)=ψ(x±λ,t)
which for a sine wave alters the argument of the wave by ±2π hence:
sinK(x–vt)=sinK[(x±λ)–vt]=sin[K(x-vt)±2π]
