Course A - Atomic Structure of Materials Flashcards
define a crystalline and non-crystalline solid
“A crystalline solid is one in which the atoms are arranged in a periodic fashion - they have long range order”
“A non-crystalline solid is one in which no ‘long range order’ occurs but short range order can occur”
give 2 different 2D packing arrangments
Square, packing efficiency = 79%
Hexagonal, packing efficiency = 90.6%
define what a simple hexagonal structure is, do any examples exist?
- Layers of simple 2D hexagonal stacked
- no examples exist because layers just drop into gaps, not efficient or stable
define hexagonal close-packed (hcp) packing, give the stacking sequence, give the ideal layer separation
- ABAB arrangement of the 2D simple hex.
- ideally d = sqrt(2/3) a
define cubic close-packed (ccp), give the stacking sequence
ABCABC stacking sequence of 2D simple hex.
cubic symmetry on rotation
give the packing efficiencies of hcp and ccp
both 74%
explain the structure of bcc, give its packing efficiency
one square layer, single atom in middle of square, another square layer
packing efficiency = 68%
define goldschmidt’s packing principle
“The number of anions surrounding a cation tends to be as large as possible subject to the condition that all anions touch the cation”
i.e. interstitial not touching (too small) = unstable
just touching = ideal
too big = stable but not ideal
what are the interstitial sites in ccp
- 8 tetrahedral sites between 1 corner atom, 3 mid-face atoms at 1/4(1,1,1) and 3/4(1,1,1) etc.
- 4 octahedral interstices - found in centre, and 12(1/4) interstices at edges
what are the interstitial sites in hcp
the same as ccp
define a lattice
“A lattice is an infinite array of points repeated periodically throughout space, the view from each lattice point is the same as from any other”
what is a good way to think about constructing a structure
structure = lattice + motif
give the 3 main 3D lattice types and define them
cubic p = 1 lattice point per cell (simple cubic)
cubic f = 4 lattice points per cell (ccp)
cubic I = 2 lattice points per cell (bcc)
what are the lattice types called in 3D, how are they classified
Bravais Lattices
they are defined based on their symmetry
e.g. a cubic lattice has 3 fold symmetry
what are the 4 possible rotational symmetries, why are we limited to only these
diad = 2-fold
triad = 3-fold
tetrad = 4-fold
hexad = 6-fold
we are limited to only these due to the crystallographic restriction theorem (CRT)
this is where in a lattice, any linear combination of defined lattice vectors MUST take you to another lattice point
what is mirror symmetry
reflection in a mirror plane
what is the action of a glide line
combines translational and mirror symmetry
reflection about a line and a translation by 1/2 a lattice spacing parallel to line
e.g. footsteps in sand
what is a screw axis, define what each number does
given classification Rn
R = order of rotation/ number of rotations for 360 degrees
n = number of translations for 1 complete turn of helix/ number of repeat distances risen through in 1 full rotation
what is a centre of symmetry in a crystal
a centre of symmetry in a crystal is where any line from a point to the centre (of sym.) can be repeated the other side of the centre (of sym.) and you will reach the exact same of environment
contains centre of sym = centrosymmetric
does not = non-centrosymmetric
how is a direction vector written
[UVW]
for negative number, put a bar on top
how can we find the angle between two lattice directions
take the dot product as normal
what are miller indices, how do we write them
they define a plane
each number gives the reciprocal of the (fractional) intercepts for each unit cell
NOTE: the origin can always be moved but if the intercept is on -ve x,y,z, a bar should be placed on top as usual
what is the notation for a set of directions or a set of planes
a set of directions = < > brackets (triangular)
a set of planes = {} brackets (curly)
give the formula for interplanar spacing (IN FORMULA BOOK)
1/d(hkl)^2 = (h/a)^2 + (k/b)^2 + (l/c)^2
for some plane (hkl)
Note: this does not work for hexagonal crystals
give the definition of the Weiss Zone law
“A zone may be defined as a set of faces or planes in a crystal whose intersections are all parallel, the common direction of the intersections is the zone axis”
“If a lattice vector [UVW] is contained within a plane of set (hkl) then
hU + kV + lW = 0 “
what is the lattice vector to move from an atom in A position in hcp or ccp to B position in hcp or ccp
(this also applies for B to C in ccp)
a/6 <112>
Define a unit cell
“A Parallepiped in a lattice having lattice points at all vertices”
explain why the smallest unit cell isn’t always used
- A subset of the structure (not necessarily the smallest) which can be used to build the entire crystal is known as a unit cell
- It is conventional to choose a unit cell which contains the defining (rotational) symmetry of the
crystal, even if it has more than one lattice point per cell
although lattices cannot contain 5-fold symmetry, can motifs contain 5-fold symmetry
yes, they are not periodic structures
