Growth II Twinning, defects, and polymorphism Jon Price

Congratulations…it’s twins! Rational, symmetrical intergrowth of structures This raises the internal energy Growth twins - free growth accidents, where a lattice becomes offset during nucleation Transformation twins - movement of parts of the lattice when internal symmetry changes These may be contact (planar face) or penetration (throughgoing) twins. Gliding twins - offsets in the lattice as a strain (in response to a stress). Polysynthetic Chromite contact twins Staurolite penetration twins

Common Twin Laws Triclinic Common Twin Laws Triclinic Albite twinning: plagioclase feldspars (CaAl,NaSi)AlSi 2 O 8 commonly show b-axis perpendicular polysynthetic twinning Pericline twinning: microcline, KAlSi 3 O 8, develops twining around the [010] axis when it transforms from a monoclinic structure X-polar photomicrograph by K. Hollocher, Union

Common Twin Laws Monoclinic Common Twin Laws Monoclinic Manebach twinning: orthoclase, KAlSi 3 O 8, contact twin. Very common. Formed from accidental growth. Carlsbad twinning: orthoclase and sanidine, KAlSi 3 O 8, develop penetration twining around the [001]. Formed from accidental growth. Baveno twinning: orthoclase, KAlSi 3 O 8, develops contact twin during accidental growth.

Common Twin Laws Monoclinic Common Twin Laws Monoclinic Swallow tail twinning: gypsum, CaSO 4 2H 2 O, develops contact twin during accidental growth. Most are cyclical contacts on {011}. Rutile (TiO 2 ) and cassiterite (SnO 2 ) are examples. Tetragonal

Common Twin Laws Hexagonal Common Twin Laws Hexagonal Calcite twinning: Common contact twins are {0001} and rhombohedron. The right from can also can be stress Induced. Brazil twinning and daupine twinning: Penetration quartz twins resulting from transformation.

Common Twin Laws Isometric Common Twin Laws Isometric Spinel twinning: contact twin parallel to an octahedron common to spinel (MgAl 2 O 4 ) Iron cross twin: Pyrite (FeS 2 ), 2/m class, may have pentration twinning of the forms with appearant 3A 4 symmetry.

Defects Missing atoms (vacancies) Impurities Edge dislocations Screw dislocations Interlayered structures Twins

Non-stoichiometric atoms Schottky defect Image from Perkins, 1998

Frenkle defect Edge defect Image from Perkins, 1998

Edge defect Screw dislocation AFM image of growth spiral on graphite along [001]. MIT STM image of PtNi alloy edge defects Michael Schmid, IAP/TU Wien

Importance of defects Incorporation of non-stoichiometric elements (non substitution) Color Incorporation of foreign materials inclusions Can produce diagnostic characteristics Twinning in feldspar

Energy Minimization Everything explained in the course thus far is the result of energy minimization! Examples? In nature, energy is the only commodity.

Energy Minimization - a system will assume a state of minimum energy. Parameterizing energy - the Gibb’s Free Energy equation G = E + PV - TS E is a measurement of lattice energy, or the sum of bond energy P is pressure V is molar volume T is temp S is entropynote: E + PV = H

So Free Energy is dependent on: 1. The nature of the bonding 2. Pressure 3. Temperature 4. Degree of disorder

The Carbon System Graphite - steep dG/dP Diamond - higher initial G, shallow dG/dP

Image modified from Zoltai and Stout, 1984 Diamond’s excited state

Poly morph -  many forms These abound in Earth Materials and can be of great use in pinning down the conditions at which the mineral formed.

Why can we observe graphite and diamond at the same time? There is a place where both phases share the same G, but at room T, this is ~14 kbar!

At P = 5 kbar

Image from Pauling, 1970

Phase Diagram Recall that as you go into the Earth, both P and T increase These two variables control phase stability of compositions in the earth. On the left is a map for phases of carbon

Reconstruction vs. displacement Displacement requires less transition energy because lattices are just “tweaked” Reconstruction requires substantial excess energy to move things to new configuration

Polymorphs

From Blackburn & Dennen, 1998

Silica Polymorphs

More ‘morphs CaCO 3 AlSiO 5

Order-disorder Reorganization of atoms into more ordered arrangements Decrease in T produces higher order G = E + PV - TS Change in structure accompanies change in order.

Alkali Feldspar Order-disorder M T T

Polytypism Polymorphs that differ only in the stacking of identical, two-dimensional sheets or layers. Cell dimensions parallel to sheets are identical Spacing between sheets is related by multiples.

1. Increasing P results in structures with high densities and large CN are favored 2. Increasing T favors low density and CN 3. High-T modifications often has highest symmetry

In summary - Polymorphism is a reconfiguration of chemical components in response to changing energy. Polymorphs therefore have the same composition but differing structures.