Growing Crystalline Materials

Jon Price

Growth and the construction of defects

• How are crystals made?

• What types of irregularities are possible?

• Why are irregularities so important?

Transition between the three states of matter

•Gas-solid Condensation

•Liquid-solid Precipitation

Crystallization

•Solid-solid Transformation

The SOLUBILITY is defined as the concentration that is reached in a saturated solution (for T and P).

SaturationSaturation - the amount of solute going into solution is equal to that which comes out of solution.

UndersaturatedCrystal dissolves b/c more atoms leave than attach

SaturatedCrystal unchanged b/c as many atoms leave as attach

OversaturatedCrystal grows b/c fewer atoms leave than attach

So how does a crystal start growing?

In a solution, random motions will create crystallite clusters.

If undersaturated, the clusters disperse.

The solution is oversaturated, clusters hang around, bump into each other, and begin to grow.

Nucleation

Nucleation Barrier

It takes additional energy to form nuclei. This can limit when and how many crystals form.

Growth has started. Next stop: the surface - where all the action is.

Unsatisfied bonds

Charge distribution upset

Incomplete coordination polyhedra

Crystalline structure - lowers G

Crystalline edges - raises G

What makes a bubble round?

Controls on external shape

Could those same forces work for crystals?

What’s the difference between this atom

And this one

The greater the anisotropy of the structure, the more this is a problem!

Which is the more stable configuration of 36 atoms?

Four crystals growing in melt. Note angular faces typical of the 2/m crystals as seen from the 001 plane.

Planes (facets) result from energy minimization along a crystallographic plane - depends on T, P, and X.

Hornblende

Ca2(Mg, Fe, Al)5 (Al, Si)8O22(OH, F)2

On this phase diagram, there are two phases, a solid and a liquid.

The line represents the conditions where both will be present at equilibrium

From Blackburn & Dennen, 1998

Crystal growth results from diffusion of components to the crystal surface

Crystals can grow in any medium - solids, liquids, gasses, supercritical fluids. Liquids and fluids may be melted rocks, C-O-H or aqueous fluids, or a mixture. All are contingent on component transport.

Diffusion

In any matter over 0 K, atoms migrate. The rate of movement depends on how well the atoms are bonded.

In a gas, atoms or molecules may dance around each other, or switch places.

Although diffusion happens everywhere, we can see diffusion in places where atoms are initially separated

The atoms will move in random directions. As a consequence, the atoms are no longer in distinct domains.

With time, the random movements of the atoms lead to complete random dispersion of the atoms

However, if there is a chemical gradient, the diffusion may become directional.

This is not to say that the diffusion rate changes.

From Blackburn & Dennen, 1998

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

LLNL

Calcite - step growth

Corners are higher energy - if diffusion cannot keep up with growth, the corners may grow much more rapidly than the faces.

Dendritic growth

Potential F

ace

Crystal

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Silver

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Ice I

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Several material scientists, like Nikolas Provatas at McMaster are exploring this type of growth numerically

This is a really simplified model - but extremely computationally intensive.

Grain size

General principles

The slower the change in conditions, the larger the grain size

e.g. - slowly cooled rocks have bigger crystals than ones cooled rapidly

Problems: it depends on the material - don’t compare apples and oranges

More than one crystal… more than one bubble

Image from Smith, 1964

In polycrystalline systems, atoms diffuse along the boundaries between crystals. To minimize energy, the chemical potential is to the center of curvature

Net result: the boundary moves in the convex direction.

Smaller crystals are consumed by larger ones

1. Equal forces - boundary is pinned

2. Fr<<Fm - particle included

3. Fr<Fm particle is swept

If there is a smaller grain of another insoluble material on the boundary, it resists the movement of the boundary

The growing grain exerts a force Fm, the particle exerts a force Fr

The entire system is trying to minimize energy

Where three crystals meet, the forces generated by the energy along their boundaries must cancel to reach a minimum value.

In three dimensions, grains that minimize their energy have near tetrakeidecahedral shapes

An example from an amphibolite

Image from Kretz, 1968

MyrmekiteMyrmekite

An intergrowth of quartz and feldspar

Likely result of too few nucleation sites

Undercooling

Viscosity contrasts

Rapid diffusion

An intergrowth of quartz and feldspar

Likely result of too few nucleation sites

Undercooling

Viscosity contrasts

Rapid diffusion

Growth rates for albite crystals in an undercooled silicate melt = 10-6 cm/sec (Fenn, 1977)

That’s 10 nm/sec. Compare that to the ionic radii in a SiO2 tetrahedron.

Ostwald RipeningOstwald Ripening

Minimizing energy requires that smaller crystals are resolved so that bigger crystals may grow.

Reactive growthReactive growth

New minerals may form from recrystallization of reaction of preexisitng grains.

Overgrowth, mantling, coronas

This is a diffusion driven process.

A not so natural example follows

Periclase (MgO) + Corundum (Al2O3) reacts to Spinel (MgAl2O4)

Prolonged runs at high temperature produce a solid state reaction between MgO and Al2O3, forming a layer of spinel

Imp

etu

s

Gro

wth The width of the spinel layer is linear to

the square root of time.

Implies a diffusion controlled process.

Gro

wth

Co

nst

ant

Pressure

Growth rate may be parameterized following Tammann (1920)

k = (X2 / 2t)

k has the units of diffusivity

Apparent Ea = ~410 kJ/mol

Apparent Va changes, dependent on T.

Bo

un

dar

y co

mp

osi

tio

ns

EMPA traverses of spinel

Stoich. spinel

Al enriched

1400 oC4 GPa89 hr30 m

600 oC3.2 GPa16 hr66 m

1978 oC2.5 GPa0.4 hr115 m

Bo

un

dar

y co

mp

osi

tio

ns

Ratio of the slopes is always -0.661 (~ -2/3) for all runs

Maintains charge balance (Mg 2+ vs. Al 3+)

Formula for the spinel:

Mg1-3x, Al2+2x, [_]x, O4

Growth requires local oversaturation of the chemical components.

Initial crystallization begins with nucleation - energy intensive

Post-nucleation growth is controlled by the surface of the phase.

Growth is always a trick to reduce the energy of the system

Atoms are added to reduce unsatisfied bonds and coordination through diffusion

Rapid growth may produce crystals with high surface energy.

Adjacent crystals must also minimize their energy