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The Muppet’s Guide to:. The Structure and Dynamics of Solids. 4. Phase Transitions & Crystal Growth. 1 st Order Phase Transitions. Ehrenfest classification: Discontinuity in the 1 st derivative of Gibbs free energy. Transitions that exhibit LATENT HEAT

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the muppet s guide to

The Muppet’s Guide to:

The Structure and Dynamics of Solids

4. Phase Transitions & Crystal Growth

1 st order phase transitions
1st Order Phase Transitions

Ehrenfest classification:

Discontinuity in the 1st derivative of Gibbs free energy

  • Transitions that exhibit LATENT HEAT
    • – Energy must be supplied to change the local environment. This results in no temperature change.
first order
First Order

h

Discontinuity

Transitions in liquid crystals

phase transitions
Phase Transitions…

BaTiO3:

Volume change at Tc

Thus expect first order phase change with discontinuity in Ps at Tc

LaTaO3 shows second order phase transition

phase transitions in batio 3

[111]

[011]

[001]

Phase Transitions in BaTiO3

PHONONS

Tcf

http://www.camsoft.co.kr , Introduction to Solid State Physics, 6th Ed., Kittel

k x na 1 x nbo 3
KxNa1-xNbO3

monoclinic

cubic

tetragonal

Dan Baker, PhD Thesis 2009, University of Warwick

2 nd order phase transitions
2nd Order Phase Transitions

Ehrenfest classification:

Discontinuity in the 2nd derivative of Gibbs free energy

  • Transitions that exhibit NO latent heat
    • correspond to divergences in the susceptibility, an infinite correlation length, and a power law decay of correlations
magnetic ordering
Magnetic Ordering

h

Critical Point

Critical Exponents:

b=0.326(1) MFA, b=0.5

g=1.2378(6) MFA, g=1

phase transitions1
Phase Transitions

A phase change can occur for thermodynamic reasons:

- Ordering of ground state to reduce H

BUT

Kinetics may produce a non-thermodynamic (metastable) state during growth.

Thermodynamically this should decay to the ground state (eventually).

final structures thermo vs kinetics
Final Structures:Thermo vs. Kinetics

Energy to remain on surface, Ea

Energy to diffuse on surface, Ed

Cohesive energy, Ec

Strain Energy – modification of U

allotropes carbon
Allotropes - Carbon

Graphite

In-plane sp2

& van der Waals

Diamond

3D - sp3

Fullerenes

sp2:

Hexagons & pentagons

Carbon structures are stable under different bonding configurations

activation energy
Activation Energy

Activation Energy

Thermodynamically lowest energy state is the most stable, but must overcome the energy barrier to reach it. Multiple structures of the same material with an energy barrier separating the two.

allotropes sn
Allotropes - Sn

T<13.2°C

Tin Disease – Buttons, Cathedral organ pipes

hpht synthetic diamonds
HPHT Synthetic Diamonds

http://www.darmann.com/abrasives.html

http://www.diamondlab.org/80-hpht_synthesis.htm

polymorphs zns
Polymorphs - ZnS

Zincblende

Cubic, Diamond like

Wurtzite

Hexagonal, hcp like, different number of 2nd nearest neighbours

slide17

Calcite Polymorphs: CaCO3

Aragonite

Vaterite

Calcite

Trigonal

Hexagonal

Orthorhombic

http://www.u-bourgogne.fr/BIOGEOSCIENCE/images/stories/actu/calcite_polymorphs.jpg

slide18

Silica Polymorphs: SiO2

Rhombohedral

Amorphous

Tetragonal

paracetamol
Paracetamol

http://research.jonathanburley.com/files/Paracetamol_for_Web_Page.png

crystal growth
Crystal Growth
  • All growth processes require conditions that promote formation of a crystal such as:
    • Condensing from a supersaturated solution
    • Freezing from a melt
    • Evaporation
  • Different methods needed for different materials
crystal growth happens at steps

(101)

(001)

(111)

CdTe in N2

(011)

5μm

Crystal growth happens at steps

-adatom

ce 0 5 zr 0 5 o 2
Ce0.5Zr0.5O2

Figures adapted from W.D. McAllister, Materials Science and Engineering, 7th edition, Wiley. Figures after

M. Boudart Kinetics of Heterogeneous Catalytic Reactions, Princeton University Press,1984 and W.J. Stark et al. Chem Comm. 588-589 (2003)

blocking of step flow by impurities
Blocking of step flow by impurities

Cohesive energy, Ec

-adatom

-Impurity species

growth from solution
Growth from Solution

Evaporation of the solvent causes super-saturation and hence the solute comes out of solution