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Solid State ChemistrySolid State ChemistryChem 331Chem 331

Koloman Moser

Wall decorations in the Sala del Reposo, Alhambra.

Mauritis C. Escher

Introduction to the Solid State

• There are ~20,000,000 known chemical substances.– ~95% are molecular (predominantly

containing C).– ~4% are inorganic molecular.– ~1% are non-molecular extended structures

(e.g. solid salts and most elements).

Single Element PackingSquare Lattice first layer

second layer(directly abovefirst)

Simple Cubic Lattice Packing used by e.g. Po.

Single Element Packing

Square Lattice first layersecond layer(sitting in indentations)third layer(directly above first)

BCC Lattice Packing used by e.g. Li, K, V, Fe, W, etc.


Closest Packed Latticefirst layer

second layer(over any indentation)

Two types of indentationsA.Directly over first layer.B.Over first layer indentation.

So, two different places to start third layer!

A A AB B B






A A A

IF directly over A, get ABAB packing, also known as hexagonal closest packed (hcp).Used by Mg, Ca, Co, Zn, etc.






IF third layer directly over B, get ABCABC packing, also known as face centered cubic (fcc).Used by Al, Cu, Ni, Ag, Au etc.

Lattice Packing

• Elemental Cu and Ni each uses fcc packing and both have very similar lattice parameters (e.g. internuclear distances).

• If we heat the two elements to melting and then mix together and cool slowly, the fcc packing is retained, but with a random placement of the two elements.

• Known as a solid solution ≈ alloy.

Lattice Packing

• Elemental Cu and Au each uses fcc packing but have very different lattice parameters (Au >> Cu).

• Upon reaction (melt and cool) yields a specifically ordered arrangement = an intermetallic compound, which may not conform to oxidation state rules.

Binary Compounds (MX)

• Which elements do we need to be concerned about?– ignore noble gases; no known extended structures.– ignore radioactive elements.– this leaves about 80 elements of possible interest.

• mathematically, this results in ~3,160 possible binary elemental combinations (not taking into account various stoichiometries, AB, AB2, A2.3B3, etcetera).

• 90% of known binary compounds have simple stoichiometries: MX, MX2, MX3, M3X5, etcetera.

• For MX there are 20 common structure types (we’ll look at 3).

• For MX2 there are 26 common structure types (we’ll look at 2).

• Each of these structural types can be thought of as starting from single element packing lattices.

Most Common MX Structures

NaCl structureNa+ in fcc latticeCl- in Oh “holes”

CsCl structureCl- in simple cubic latticeCs+ in cubic “hole”

Zinc blende (ZnS) structureS-2 in fcc latticeZn+2 in alternating Td “holes”

Most Common MX2 Structures

Rutile (TiO2) structureTi+2 in body centered cubic latticeOxygens in lower symmetry array.

Fluorite (CaF2) structureCa+2 in fcc latticeF- in all Td “holes”

Ternary Compounds (ABC)• 82,160 potential combinations; ~20,000 known.• ~700 structural types known (so far and growing fast);

very few examples of each type.• Synthesis: grind together and heat Li2O and MoO3, for

example. Reacts before melting.• Forms one of three compounds, depending on ratio on

mixing:– 1 Li2O : 1 MoO3 → Li2MoO4 100%yield– 1 Li2O : 4 MoO3 → Li2Mo4O13 100%yield– 2 Li2O : 5 MoO3 → Li4Mo5O17 100%yield

• If react with other ratios, get mixtures of these 3 plus startting material.

• If use Na2O instead of Li2O, get entirely different compounds.

Pseudoternary Compounds.

• Both sodium chloride and silver chloride utilize NaCl structure.

• If react (melt and re-cool) non-stoichiometric amounts, get solid solution of NaCl structure type, but with random occupation of Na/Ag sites.

• Called pseudoternary because it contains 3 types of elements, but still adopts binary-type structure.

(1-x) NaCl + xAgCl → Na1-xAgxCl

• Consider superconductors (a metal that, when cooled to a low enough temperature, Tc, will carry a charge with no resistance). – best single element superconductor is Nb, Tc = 9 K.– best binary superconductor is Nb3Ge, Tc ≈ 20 K.– best ternary superconductor is La2CuO4, Tc ≈ 40 K.– best quarternary superconductor is Ba2YCu3O4, Tc ≈ 92

K; above N2(l).– best superconductor is Tl2Ba2Ga2Cu3O10, Tc ≈ 135 K.

– to extrapolate out to room temperature, would need 8 elements, which means 2.90 x 1010 possible combinations… before stoichiometry!

– what are the most “complicated” compounds in nature (max # cations in different crystallographic environments)?

Asbecaite: Cu3TiAs6Be2Si2O30

Mordite: LaSrNa3ZnSi6O17

Future? Why Do We Care?

Synthesis of Non-Molecular Solids

• Typically start with powdered reactants, mix together, press together, heat, and then let cool (aka “shake and bake”).– See West Ch 9 for specifics of many methods.– By convention, high temp ≈ 800oC; low temp ≈ 200-600oC.

• Don’t want material to react with container, so common to use fused quartz (up to 1200oC), but do use other materials.

• Often start with oxides that are stable in air.– 3CuO + 2BaO2 + Y(OH)3

– mix well and press into a pellet; heat in aluminum oxide container 920oC for 24 hours.

– yields YBa2Cu3O6, which when reacted with 3/2H2O + 5/2O2 and annealed below 500oC in O2 produces YBa2Cu3O4 (superconductor).

Nucleation and Diffusion• These solid state reactions occur in two steps: first nucleation,

where product forms within a few nm of where the reactants contact one another, then product growth through diffusion.

• The reason the material is pressed is to get points of contact (on the molecular scale) as the reaction only occurs when contact occurs.

• Very little is known about nucleation, but diffusion is reasonably well understood.

• Different atoms diffuse at different rates, but typically D ~ 10-

10 to 10-12 cm2/sec at 2/3Tm (in K).• Therefore, it would take ~320 years to move 1cm in a solid.

But, they ARE moving! Atomic scale on order of Ǻ.• Atoms can also diffuse (migrate) in crystalline solids because

of defects (more later).

d ≈ √ D tdiffusiondistance

diffusionconstant

time

Melting Points

• Compounds may melt congruently (Tm) , with a single melting point. Changes from solid to liquid of same composition.

• e.g. H2O(s) → H2O(l); all elements melt congruently.

• Some compounds melt incongruently (Tin), decomposing on heating to components with different composition.

• e.g. solid → solid and liquid of different composition.• e.g. YBa2Cu3O4 melts incongruently.

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