Crystallography Flashcards

Question

ionic solids: Li2O (anti-fluorite strucure) + CaF2 (fluorite structure)

Answer 1

Li2O - cubic close-packed layers of O2- with Li+ in all Td holes - 4:8 coordination CaF2 - anion and cation sites are swapped with each other to give an 8:4 coordination - primitive cubic array of F- - cubic close-packed layers of Ca2+ with F- in all td holes

Answer 2

CdI2 - hexagonal close-packed (ABABAB) layers of I- with Cd2+ in Oh holes - but in alternate layers i.e. 100%, 0%, 100%, 0%... CdCl2 - cubic close-packed (ABCABC) layers of Cl- with Cd2+ in Oh holes - but in alternate layers

Answer 3

structure O2- anions with two types of cation A is normally 2+ B is normally 3+ face-centred cubic - close-packed layers of oxide anions can be seen when model is viewed perpendicular to body diagonal of cube (a 2D view) structure 1: - close-packed O2- anions - all Oh holes filled with cations structure 2: - close-packed O2- anions - half of Oh holes filled with cations structure 3: - close-packed O2- anions - all Td holes filled with cations structure 4: - close-packed O2- anions - 1/8 (12.5%) Td holes filled with cations structure 5: - close-packed O2- anions - half of Oh holes filled with cations - 1/8 (12.5%) Td holes filled with cations

Answer 4

close-packed O2- anions (shown as 2x2x2 fcc cube) BUT 3+ cations on Td site 2+ and 3+ cations on Oh site (disordered)

Answer 5

A = 2+ cation B = 3+ cation NORMAL: spinel structure - MgAl2O4 - larger Mg2+ ion prefers tetrahedral geometry - smaller Al3+ ion prefers octahedral geometry INVERSE: spinel structure - CoFe2O4 - larger Co2+ ion prefers octahedral geometry - smaller Fe3+ ion swaps to tetrahedral geometry (whilst other stays octahedral)

Answer 6

close sphere packing works well for low charged cations (1+ and 2+) - not good for highly charged cations (Ti4+ or Si4+ - ionic with some covalency)

Answer 7

sum charges ABO3 oxides: A + B = 6+ ABX3 (less common) halides A + B = 3+ examples: SrCoO3 NaMgF3 cubic, tetragonal, orthorhombic or monoclinic

Answer 8

ceramic high Tc superconductors YBa2Cu3O7-x perovskites of recent interest: MAPI Methyl Ammonium Lead (Pb) Iodide

Answer 9

corner shared octahedrons of [BO6] units - form a primitive unit cell with a = 3.7 - 4.5 Å large cation A at the centre of the cube (1/2, 1/2, 1/2) smaller cation B is at (0,0,0) O2- anions are at (1/2, 0, 0), (0, 1/2, 0), and (0,0,1/2) can be viewed as cubic close packed layers of AO3 with B in 25% Oh holes

Answer 10

if A cation too small: cooperative rotations lower the symmetry - tilting of [BO6] octahedra - reduces distance between A site cation and O2- - O2- can get closer to A site - many tilt combinations possible other distortions caused by the B cation moving slightly off the centre of the O6 octahedron - results in interesting electrical and magentic properties

Answer 11

simple corner-sharing octahedra: perovskite structure mixing corner-sharing with edge-sharing: several permutations possible -Anatase -Rutile -Brookite

Answer 12

Tetragonal Bravais Lattice - TiO6 octahedra with both corner and edge sharing slice through structure parallel to c - within the slice, [TiO6] units are corner linked double slice through the structure parallel to c - slices are linked together along c via edge-shared [TiO6] units

Answer 13

- distorted internal angles within octahedron - coordination around O2- deviates from 120° Ti-O-Ti: 101.9° (×2), 156.2°

Answer 14

Tetragonal Bravais Lattice - TiO6 octahedra with both corner and edge sharing slice through structure parallel to c - within the slice [TiO6] units are corner linked (but differently to Anatase) edge sharing occurs in 1D columns

Answer 15

- less distorted angles within octahedron - coordination around O2- has smaller deviation from 120° (compared to anatase) Ti-O-Ti: 130.6° (×2), 98.8.2° density comparison Rutile: 4.25 g cm-3 Anatase 3.89 g cm-3 Rutle is the thermodynamically stable form Anatise is the kinetic form

Answer 16

Orthorhombic lattice - TiO6 octahedra with both corner and edge sharing

Answer 17

tetrahedral [SiO4] group - either as a discrete anion, (SiO4)2- or as oxygen-linked tetrahedral neutral/anionic species -O-Si(-O-)2-O-Si(-O-)2-O-

Answer 18

common crystalline form of SiO2 its crystalline nature can be seen in PXRD pattern

Answer 19

tough clear solid with very high melting point (softens at > 950°C) no sharp diffraction peaks in PXRD pattern - indicates a purely amorphous (glassy) substance

Answer 20

multiple crystalline forms + an amorphous (glassy) form local structure is the same for all forms difference in the way the [SiO4] tetrahedra are linked random [SiO4] linking occurs when cooling from the liquid state - leads to a glass as evidenced by the lack of Bragg peak in PXRD pattern [SiO4] tetrahedra may be linked so as to lead to solids varying from high to low density

Answer 21

[SiO4] or [AlO4]- tetrahedra (often simplified to [TO4]) T = Si or Al primary building unit: [TO4] unit linked via O bridging secondary building unit: T-O-T rings

Answer 22

Al-O-Al linkages in zeolitic frameworks are forbidden - all [AlO4]- must be linked to 4 [SiO4] units

Answer 23

simplest zeolite framework structure Na8(Al6Si6O24)Cl2 [Si]/[Al] ratio is 1:1 cubic with a = 8.9 Å

Answer 24

cubic, naturally occuring zeolite with a = 24.7 Å (Na2,Ca,Mg)3.5[Al7Si17O48].32(H2O) synthetic versions are known as zeolites X/Y X is where [Si]/[Al] = 2 to 3 Y is where [Si]/[Al] > 3

Answer 25

x-rays are scattered by electrons in an atom incoming x-ray photon acts as a plane wavelet as source is a long way from the sample scattered x-ray photon acts as a spherical wavelet

Answer 26

multiple slits: a 1-D optical diffraction grating optical grating: nλ = dsinθ n - order d - slit spacing if atoms are in a regular array, diffraction will occur if an appropriate wavelength source is used

Answer 27

2-D optical diffraction grating useful to demonstrate how symmetry information can be derived from a single image - inversion symmetry added during the process of diffraction - diffraction space unit cell vectors are in a different direction to real space ones when the unit cell angle is not 90 - diffraction space has natural origin (0,0,0) - small dimensions become big and vice versa (property of diffraction space: e.g. volume, V* = 1/V) - translational symmetry in 2-dimensional space due to a centred lattice leads to missing intensity spots in a systematic matter in 2-D diffractional space

Answer 28

(not exact when object itself has no inversion symmetry but very close to inversion symmetry) diffraction pattern contains a point of inversion in the absence of anomalous dispersion, even when this symmetry element is not present in the crystal structure

Answer 29

diffraction space indicated with * b* perpendicular to a a* perpendicular to b c and c* are colinear and perpendicular to the plane of the screen unit cell angles that are 90° in the crystal will exhibit 90° angles in reciprocal space

Answer 30

crystalline objects produce diffraction spots symmetry relationship between crystal (real) space and diffraction (reciprocal) space crystal space: 3-dimensional symmetry across all space diffraction space: 3-dimensional symmetry around a point (h,k,l = 0,0,0) amorphous objects (glasses) do not produce diffraction spots

Answer 31

modern single-crystal x-ray diffractometer has 3 rotation axes (ω, κ (or χ), φ) rotate crystal in 3-dimensional space, plus a rotation axis 2θ for the detector orient the crystal with respect to the incident x-ray beam so as to satisfy Bragg's law by rotations about the different instrument axes - as the crystal is slowly rotates, the intensity of the diffracted x-rays is measured using an area detector 2θ value for every spot provides d spacing via Braggs law λ = 2d_hkl sinθ_hkl d-spacing relates to the 6 unit cell parameters: a, b, c α, β, γ

Answer 32

a* b* c* a* is perpendicular to b and c in the crystal b* is perpendicular to c and a in the crystal c* is perpendicular to a and b in the crystal the vector dot products are unity a.a* = 1 b.b* = 1 c.c* = 1 the diffraction coordinate space has a 'reciprocal' relationship to crystal coordinate space (hence, the name reciprocal space)

Answer 33

d* = ha* + kb* + lc* hkl correspond to the same Miller indices hkl of the lattice planes from which the diffraction intensity I(hkl) arises

Answer 34

diffraction space axes (a* ,b* ,c*) are orthogonal and in the same direction lengths of the axes are given by: a* = 1/a b* = 1/b c* = 1/c

Answer 35

if cell angles are 90,

Answer 36

real space (crystal) → reciprocal space (diffraction) atoms → scattering factor unit cell and lattice → interference term atomic displacements → Debye-Waller factors

Answer 37

x-rays interact strongly with the electrons in an atom (or ion) elastic interaction → diffraction absorption & re-emittance → fluorescence (loss of coherent scattering) elastic interaction is proportional to number of electrons (atomic number, Z) - scattering factor given by symbol, f

Answer 38

electron density of atom has gaussian distribution fourier transform of the electron cloud corresponds to the X-ray form factor

Answer 39

position of the atoms is determined by I(hkl) - peak maximum is the position of the peak at 2θ - position of the peaks, 2θ, determined by Bragg's Law peak area is the intensity of the peak I(hkl) peak has height H and width W (for powder diffracion) - I(hkl) ∝ H ∝ W intensity of the peak, I(hkl) is given by the 'Structure Factor' equation (symbol F(hkl))

Answer 40

the proportionality terms are: c - the scale factor ~ counting time ~ amount of diffracting material j_hkl - multiplicity (this only applies to PXRD) ~ number of symmetry equivalent reflections Lp(2θ) - geometric factors - Lorentz, L - polarisation, p

Answer 41

summation is taken over all atoms, n within a single unit cell summation could be taken over all atoms in the crystal, but since all unit cells are the same: multiply F_hkl by the number of unit cells

Answer 42

amount of constructive/destructive interference of X-ray wave depends on the scattering power of each atom, and its relative position (r_n) within the unit cell also depends on the diffracting planes hkl whose normal can be defined in terms of d* as d* = ha* + kb* + lc*

Answer 43

the Fourier transform of the electron density ρ_xyz - x-rays 'see' electrons NOT atoms F_hkl is a vector quantity - can be thought of a wave expression with magnitude IF_hklI and a relative phase angle Φ

Answer 44

consider the hypothetical case where the atoms(/or ions) are stationary in space Debye-Waller factor exp(-Wn)=1 since the atomic displacements are zero (e^0=1)

Answer 45

Cs atoms lie in the planes with the Cl atoms half-way between them - therefore destructive interference occurs

Answer 46

both the Cs atoms and Cl atoms lie in the same planes - therefore constuctive interference occurs

Answer 47

reflection intensities from planes such as 110, 220, 211, 220, etc. (even) of Fe will be strong reflection intensities from planes such as 100, 111, 210, 300, etc. (odd) of Fe have zero intensity such reflections are said to be missing/extinct or SYSTEMATICALLY ABSENT for the cases of non-zero intensities, they are usually referred to as a REFLECTION CONDITION

Answer 48

effect of atomic motion atoms vibrate - usually as harmonic oscillators - giving rise to a normal (Gaussian) distribution about a point - Fourier transform of this motion is a normal distribution simplest case is for isotropic vibration

Answer 49

structure factor has a marked effect on the RELATIVE intensity of peaks in a PXRD - e.g. CsCl: weak 100 but strong 110 Lorentz-polarisation term also has a big effect

Answer 50

PDF database consists of a set of cards, one for each material with its powder diffraction pattern parameters contains: - file number for the database entry - chemical formula, chemical name, and mineral/common name (if one exists) - quality factor of the data entry: star indicates data of the highest quality and data is indexed with hkl values - experimental details on how the data was obtained (radiation used - Cu Kα1 and wavelength - 1.5405Å) - crystallographic information: crystal system, lattice parameters, no. formula units per unit cell, calculated density - physical properties: mp, optical refraction indices and colour - the PXRD data

Answer 51

PXRD pattern represented as a set of d-spacings (from high to low values) relative peak intensities (I/I1) and hkl values for each observed peak (i.e. the fingerprint region) d spacings of the 3 most intense peaks in the powder pattern and their relative intensities are used to constuct HANAWALT search/match tables

Answer 52

most intense peaks from each phase are the easiest to identify in a mixture of phases sorted into d-spacing ranges (e.g. 3.74-3.60 Å) faster for manual search-match lists d-spacings for 4th-8th strongest peaks in addition

Answer 53

for a match, d-spacing values should match within experimental error reasons for mis-match - wrong material made - measurement error - instrumental error - not comparing like with like (e.g. if measurement and databse entry refers to different temperatures OR comparing doped vs pure phase materials)

Answer 54

material at lower temperatures is almost amorphous - peaks sharpen with increasing T narrower peaks indicate that crystallite size is getting bigger with higher T difficult to make definitive assignment with broad peaks using database - use the highest temperature dataset matching the strong peaks against a database entry can show the presence of a particular major componenet in a PXRD sample HOWEVER purity is demonstrated by accounting for ALL of the peaks in the measured PXRD pattern

Answer 55

concept of quantitative analysis by PXRD methods is based on the fact that scattering is proportional to the amount of material present

Answer 56

single crystal x-ray diffraciton (SXD) - IF(hkl)I^2 values provide detail of the material/compound/complex - atomic postions, average atomic motion, unit cell and crystal symmetry powder x-ray diffraction (PXRD) - used for qualitative and quantitative analysis - can determine: is this the right material? it is single phase? purity?

Answer 57

powder diffraction pattern yi(calc) can be calculated from: - peak positions (determined by unit cell and any instrument zero offsets) - peak intensities (determined by structure factor, scale factor, geometric factors etc)

Answer 58

analysis of PND data - mixed metal oxides (e.g. perovskites) used to fit all powder diffraction data - used for organic crystal structures - often done badly and data over interpreted

Answer 59

used in petroleum industry - heterogeneous catalyst for hydrocarbon isomerisation reactions low density crystal structure is not normally favoured - synthetic methods need to exploit kinetic (and other) effects 1. hydrothermal methods 2. silica and alumina gels (F- to act as a mineraliser) 3. templating organic molecules (amine based e.g. diethylamine to make ZMS22) - removed after synthesis by calcination 4. [PO4] to replace [SiO4] to give ALPOs

Answer 60

large, open pore network structures - created by (semi-) rigid organic linkers and metal cations syntheis is similar to that of zeolites - hydrothermal/solvothermal techniques used (crystals grow slowly from a hot solution) constructed from bridging organic ligands that remain intact throughout the synthesis and act as the templates - contrast with zeolites where amines are used and have to be removed later functionality built into MOF by an appropriate choice of ligand

Answer 61

oxalic acid malonic acid isophthalic acid terephthalic acid trimesic acid

Answer 62

cation's coordination preference influences size and shape of pores - dictates how many ligands can bind to metal structures descibed in terms of primary building blocks (ligands) and secondary building blocks

Answer 63

driven by materials for H2 storage/CO2 capture and storage large pore size - can store lots of gas pore size can change depending on whether absorbed gas is present or not

Answer 64

prepared from a solvothermal reaction of H3BTE, H2BPDC and zinc(II) nitrate hexahydrate - synthesis involved 2 topologically different organic linking groups (both carboxylic acids) has ultrahigh surface area

Answer 65

organic linker: 1,4-benzenedicarboxylate (BDC) framework formula: Zn4(O)(BDC)3 metal cluster: 4 tetrahedra of [ZnO4] corner shared by an O to give a tetrahedral arrangement of Zn around the central O prepared by diffusion of NEt3 into solution of Zn2+ nitrate and BDC in DMF/C6H5Cl + H2O2 cavity contains DMF and C6H5Cl solvents

Answer 66

diffraction - the Fourier transform of the whole unit cell and its contents - d-spacings do not relate to bond lengths - crystal structure determination gives structure of the WHOLE molecule - not just the metal and atoms bound to in an organometallic complex spectroscopy (NMR, IR) - measures local information - can be tuned to specific parts of a molecule (i.e. energy of a metal carbonyl bond)

Crystallography Flashcards

(97 cards)