Crystalline Materials

what does amorphous mean

give a value

no long range structure

2nm is a reasonable measure of the cut-off

word describing a material with no long range structure

amorphous

how is a crystal defined

a material in which the atoms are organised in a regular, three-dimensional structure

what is a symmetry operation

an operation that can be performed to give no change in the appearance of an object

what are the 3 types of symmetry operations

rotation, reflection, inversion

what is rotational symmetry and what is its associated element

if an object can be rotated about an axis (which is the element) such that it appears unchanged

how is rotational symmetry described & calculated

n-fold rotation axis

fold = 360/degrees of rotation

angle = 360/fold

available rotations for crystal lattices + their angles

1-fold = 360 - every structure has this symmetry

3-fold = 120

4-fold = 90

6-fold = 60

no 5-fold 

why is there no 5-fold rotation

with this type of rotation, the atoms cannot be close packed and the unit cell cannot be translated into 3 dimensions

what is mirror symmetry + its element

reflection of the structure in a mirror plane (the element) which reproduces the entire structure

what is inversion symmetry and how is it done

inversion through a point

lines are drawn from all points on the object through a point in the centre of the object (called the centre of symmetry, i)

the lines each have lengths that are equidistant from the original points

when the ends of the lines are connected, the original object is reproduced inverted from its original appearance

define a lattice

an infinite, regular arrangement of points, each of which has identical surroundings

define lattice points

points having identical surroundings in the crystal

could be 1 atom or a collection of atoms (which is more common)

what is a unit cell

the building block of the lattice

a parallelepiped (3D) or parallelogram (2D) with lattice points at its vertices, which when translated in all directions creates the lattice

what is needed to describe the whole structure of a crystal

lattice and motif

the motif is the arrangement of atoms associated with a lattice point