Crystallisation

Question 1

Crystal Habit

Answer 1

Describes general external shape of crystal

Question 2

Gibbs crystal habit theory

Answer 2

Crystal growth attempts to minimise total free energy of the surface
High surface energy = low morphological importance

Question 3

Wulff crystal habit theory

Answer 3

Distance of facet from its centre is proportional to surface energy

Question 4

BFDH crystal habit theory

Answer 4

facet growth is inversely proportional to the interplanar spacing, d_hkl

Question 5

Hartman & Perdock crystal habit theory

Answer 5

Growth rate is proportional to the attachment energies of crystal facets

Question 6

Miller Indices

Answer 6

Integers that are inversely proportional to the intercepts of the crystal face

h = a/x, k = b/y, l = c/z

Question 7

Miller Indices methodology

Answer 7

• Determine the intercepts of the face along the crystallographic axes
• Take reciprocals
• Clear fractions
• Reduce to the lowest terms

Question 8

Polymorphs

Answer 8

Molecularly identical crystals with different lattice structure

Question 9

Dihedral angle

Answer 9

Angle between 2 facets

consistent irrespective of particle size

Question 10

Supersaturation

Answer 10

Solution containing more solute than thermodynamically stable in solutions (and able to overcome energy barrier to form crystal surface)

Question 11

Saturation

Answer 11

Crystal is at thermodynamic equilibrium with solution (maximum concentration that is thermodynamically stable)

Question 12

Degree of Supersaturation

Answer 12

Delta_C = C - C*

Question 13

Supersaturation Ratio

Answer 13

S = C/C*

Question 14

Relative Supersaturation

Answer 14

Phi = Delta_C/C* = S - 1

Question 15

Moyers & Rousseau (van’t Hoff Relationship)

Answer 15

ln(x) = Hf/RT * (T/Tm - 1)

Hf = Latent heat of fusion
Tm = melting point

Question 16

Predicition of solubility for very small particles

Answer 16

ln (cr/c) = 2Msigma/(niRTro_sr)

Question 17

Supersaturation Equation (Sigma)

Answer 17

sigma = Delta(mu)/RT

Question 18

Primary Nucleation

Answer 18

In the absence of seeded crystals

Question 19

Homogeneous nucleation

Answer 19

formation of crystals from supersaturation only

Question 20

Heterogeneous nucleation

Answer 20

formation of crystals from the presence of insoluble material

Question 21

Secondary nucleation

Answer 21

Occurs in the presence of seeded crystals

Question 22

Empirical equation for secondary nucleation

Answer 22

dN/dt = k_n(c - c)^i = B

Question 23

Classical Nucleation Theory

Answer 23

Surface energy of small crystals provides a thermodynamic barrier to forming new surface

Delta Gr = - 4/3 pir^3 * Delta Gv + 4pir^2 *sigma

(Assumes Nucleus to be spherical and interacial tension to isotropic - non directionally dependent)

Question 24

Critical Radius

Answer 24

Minimum size of crystal for it to be more energy beneficial to grow than redissolve

Question 25

Method of solving for r_crit and Delta Gr_crit

Answer 25

``` Set d(delta Gr)/dr = 0 Solve for r_crit put equation for r_crit into delta Gr equation to solve for delta Gr_crit ```

Question 26

Homogeneuous rate of nucleation

Answer 26

J = F*exp((-16*pi*sigma^3 *vm^2)/(3*k^3 *T^3*(lnS)^2)

Question 27

Heterogeneous rate of nucleation

Answer 27

J = K_n * delta(c)^n

Question 28

Derivation of homogeneous nucleation rate

Answer 28

- Start with Arrhenius: J = F*exp(-delta G/kT) - Insert delta G_crit - Rearrange ln(cr/c*) for r and insert - Use molar volume to remove terms and insert some constants in pre-exponential factors

Question 29

Define induction period

Answer 29

Delay between supersaturation & first crystal formation ti is proportional to 1/J

Question 30

2 Stage process of crystallisation

Answer 30

- Birth = Nucleation | - Growth (Volume Diffusion & Surface diffusion)

Question 31

3 Crystal growth regimes

Answer 31

- Continuous Growth (lots of kink sites) - Surface Nucleation (several nuclei on suface) - Spiral growth (single nucleus on surface)

Question 32

Crystal habit modification

Answer 32

- growth rates are not constant along facets | - Specific adsorption of species on particular facets modifies crystal growth

Question 33

Crystal Yield Equation

Answer 33

y = R*w1* (c1 - c2*(1 - E))/(1 - c2*(R - 1)) ``` R = ratio of hydrate: anhydrous MW E = ratio of solvent evaporated to initial solvent ```

Question 34

Crystal yield derivation

Answer 34

- Solute balance w1*c1 = w2*c2 + y/R - Solvent Balance w1 = w2 + y*(R - 1)/R + w1*E - Rearrange solvent balance for w2 - Insert w2 into solute balance - rearrange for y

Question 35

Derivation of mass of seeds required equation:

Answer 35

- Take the mass of crystal assuming spherical m_s = ro*pi/6 * d_s^3 - Take equation for yield based on volume difference: y = ro*pi/6*(d_p^3 - d_s^3) - Write out m_s/y - Then multiply both sides by y

Question 36

Optimum cooling curve

Answer 36

- Growth rate will increase as crystal grows - dC/dT of solubility curve decreases as C decreases, therefore need to increase (-dT/dt) to accommodate - Need to cool faster to remain in metastable region - Slow initial cooling but increasing over time

Question 37

Practice sketching crystallisation curves

Answer 37

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