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 – Energy must be supplied to change the local environment. This results in no temperature change.

1 st order Phase Transitions… BaTiO 3 : Volume change at Tc Thus expect first order phase change with discontinuity in P s at T c LaTaO 3 shows second order phase transition

Phase Transitions in BaTiO 3 T cf [001] [011][111] PHONONS Introduction to Solid State Physics, 6 th Ed., Kittel

K x Na 1-x NbO 3 monoclinic tetragonal cubic Dan Baker, PhD Thesis 2009, University of Warwick

2 nd Order Phase Transitions Ehrenfest classification: Discontinuity in the 2 nd 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

2 nd Order – FM transition

Magnetic Ordering Critical Exponents:  =0.326(1) MFA,  =0.5  =1.2378(6) MFA,  =1 Critical Point 

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).

Metastable State

Final Structures: Thermo vs. Kinetics Energy to remain on surface, E a Energy to diffuse on surface, E d Cohesive energy, E c Strain Energy – modification of U

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 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. Activation Energy

Allotropes - Sn T<13.2°C Tin Disease – Buttons, Cathedral organ pipes

HPHT Synthetic Diamonds

Polymorphs - ZnS Zincblende Cubic, Diamond like Wurtzite Hexagonal, hcp like, different number of 2 nd nearest neighbours

Calcite Polymorphs: CaCO 3 Calcite AragoniteVaterite Orthorhombic TrigonalHexagonal

Tetragonal Rhombohedral Amorphous Silica Polymorphs: SiO 2

Paracetamol

MnSb – polymorph structures n-MnSb(hexagonal) Niccolite (P6 3 /mmc) c-MnSb (cubic) Zincblende (F-43m) w-MnSb (hexagonal) Wurtzite (P6 3 mc) Mn Sb MnSb on GaAs(111)A Cubic MnSb GaAs MnSb(0001) GaAs (111)B MnSb on GaAs(111)B

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

-adatom Crystal growth happens at steps (001) (111) (101) (011) 5μm5μm CdTe in N 2

Ce 0.5 Zr 0.5 O 2 Figures adapted from W.D. McAllister, Materials Science and Engineering, 7 th edition, Wiley. Figures after M. Boudart Kinetics of Heterogeneous Catalytic Reactions, Princeton University Press,1984 and W.J. Stark et al. Chem Comm (2003)

-Impurity species -adatom Blocking of step flow by impurities Cohesive energy, E c

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