2) Crystalline solids

What is a unit cell

smallest repeating unit which shows the full symmetry of the crystal structure; must repeatable and not isolated from each other

What is Z

the number of formula units in one unit cell; eg 4Na and 4Cl: Z=4

Give the equation for the density

rho = m/V = FW/V_molar = (FW.Z)/(V_C.N_A); FW = formula weight; Z = formula units in unit cell; V_C = unit cell volume; N_A = avodagros number

describe the orthorhombic structure

a,b,c all different; all angles 90

describe the hexagonal structure

a=b not c; gamma =120deg

describe the trigonal structure

a=b=c; all angles not 90

describe the monoclinic system

a,b,c all different; beta not 90

describe the triclinic system

a,b,c all different; all angles not 90

Describe rotational symmetry

rotation by 360/n; can be done n times;

What is 5 fold rotational symmetry

structure is ordered but not periodic; cannot be represented by a unit cell

What is mirror symmetry

reflection in a mirror plane m

What is the centre of symmetry

1bar; point through which any part of the crystal can be inverted to produce identical configuration

What are inversion axes

n_bar; combination of rotation by 360/n and inversion through central point

Describe screw axes

X_Y; translation by X/Y of a unit cell; rotate 360/X

Describe glide planes/transflections

translate along x,y,z axis (indicated by a,b,c) then reflect in that axis; can also occur along diagonals

What are the Bravais lattice types and their symbols

primitive P; fcc F; base centred (only one pair of opposing faces) C (B,A); body centred I

How to identify miller indices

identify lattice plane opposite origin; find intercepts in xyz axes; take the inverse

What is the notation for lattice planes

round brackets for individual; curly for families

How to identify a lattice direction

draw line parallel to direction that intercepts the origin and unit cell edge; find xyz values of where it intercepts the unit cell edge; convert to integers

What is the notation for lattice directions

square brackets; <> for family of directions

What are space groups

defines symmetry in structure and potential atomic locations

Hermann Mauguin notation

first letter = bravais lattice; subsequent letters = essential symmetries

Wyckoff notation

shows where atoms are found in the structure; coords in terms of lattice parameter; number gives multiplicity; letter is just a label

Which element is the only one to have simple cubic structure

polonium

metals

densely packed, isotropic interactions between atoms (maximum contact preferred); small nn distance lowers bond energy

describe fcc

ccp parallel to (111) planes; repeating ABC layers; a=2sqrt(2)R; CN=12

describe hcp

repeating ABA layers; a=2R; CN=12

describe bcc

not a close packing structure as atoms in contact along diameter; a=4/sqrt(3) R; CN=8

Which structures have the densest packing

fcc and hcp

Does close packing occur in ionic structures

many have close packing anions with cations on interstitial sites; often cations too large causing anion lattice to expand (no longer ideal close packing); anions may not be in contact (eutectic structure)

Describe a tetrahedral site

site between three atoms in one layer and one in another; CN=4

Describe an octahedral site

site between 3 atoms in layer above and 3 from below; CN=6

Polyhedra can fill space by sharing:

vertices; edges; faces

List the properties of electron diffraction

strong matter interactions; small sample size (<0.1um)

List the properties of XRD

weaker matter interaction; bulk (larger crystalline samples); arrangement of atoms in crystal lattice

What is elastic scattering

bound e; rayleigh scattering; no E lost; coherent; diffraction

What is inelastic scattering

free/loosely bound e; compton scattering; E lost by xray; incoherent

How does crystal size affect peak width in XRD

larger crystals produce sharper peaks