Crystalline SolidsWhen cooled slowly, atomic and molecular building blocks can assemble into well-ordered minimum-energy structures:CrystalsExamplesCuSO4 5H2OQuartz SiO2CholesterolAgCuMnB(OH)3

5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile6 polymorphic formsmore generallyPharmaceutical Example: ROY

Comparison: Amorphous solidsTar, molten glass, molten plastics, and molten butter, consist of large molecules or a mixture of molecules that cannot move readily. As the temperature is lowered, their molecules move more and more slowly and finally stop in random positions. The resulting materials are called amorphous solids or glasses. Such solids lack an ordered internal structure. Common examples include candle wax, butter, glass, and plastics.

Crystalline SolidsMetallic crystalsCrystals of packed moleculesIonic crystalsAg, Cu: metallic bonds, soft to hard, low to high melting points, good conductors of heat and electricityCH4, cholesterol: dispersion, dipole-dipole, H-bonds, soft, low melting, poor conductorsNaCl, CuSO4: electrostatic attraction, hard, brittle, poor conductors of heat and electricityNetwork covalent crystalsDiamond, -SiO2-: hard, high melting, poor electrical conductors, poor to excellent heat conduction

DefinitionsUnit Cell:The smallest repeating unit in a three dimensional structure (lattice)Characterized by a coordination number (number of nearest neighbors) and a lattice parameter, a (edge length)Bonding Atomic radius -- Bulk density Different geometric arrangements depending on the crystal type

The crystal lattice and the unit cellThe unit cell is the minimum repeating unit necessary to describe the crystal.

DefinitionsCrystal Systems:Arrangements for stacking spheres, each one characterized by a packing efficiency (percentage of total volume occupied by spheres) Cubic Systemsa=b=c, a=b=g=90Body-centered Cubic (BCC) 868%Face-centered Cubic (FCC) 1274%

There are 7 types of crystal systems, 14 units cells, but we will look at cubic and the hexagonal systems.

1) Simple cubic unit cell8 atoms define corners atoms touch along edges, but not along diagonalCoordination # = 6. 4 in layer, 1 above, 1 below1 atom/unit cell (1/8 8 atoms)

2) Body-centered cubic unit cell8 atoms define corners plus one in center atoms touch central atom, not each otherCoordination # = 8. 4 above and 4 below.2 atoms/unit cell (1/8 8 atoms + 1 atom in center)

3) Face-centered cubic unit cell8 atoms define corners plus 6 in center of each face Corner atoms touch face atom, not each otherCoordination # = 12. 4 in layer, 1 above, 1 below, 6 faces4 atoms/unit cell (1/8 8 crnr atoms + 6 face atoms)Crystal Systems

Simple Cubic (SC)SC lattice and crystal structure aPacking fraction = 54%Coordination number = 6

Body Centered Cubic (BCC)aPacking fraction = 68%Coordination number = 8Where does this come from?

Cubic Packing - BCC

Face Centered Cubic (FCC)A close-packed structure with a packing fraction of 74%Coordination number = 12

How do these packing arrangements arise?Start always with a layer of atoms, separated center to center by the lattice parameter, a.Then, place a layer on top, over atoms or over spaces.Packing Arrangements

Thus, for a simple cubic lattice (SC):The first layer is spaced with a = 2RThen the second layer is placed with every atom directly atop the one belowNot a close-packed structure.Coordination number = 6 (octahedral) Packing fraction = 54%

For a body-centered cubic lattice (BCC):The first layer is spaced withThen, the second layer is placed over the spaces between atoms.Still not a close-packed structure.Packing fraction = 68%

The close-packed crystal systemsCubic closest packing or face-centered cubic, FCCTilt to find unit cellA close-packed structure with a packing fraction of 74%abcabc

The close-packed crystal systemsHexagonal closest packing, HCPShift every other row in the first layer to compress packingPlace second layer over triangular spacesThird layer directly over the atoms of the firstA close-packed structure with a packing fraction of 74%ababRhombic unit cellCoordination # = 12 (3 above, 6 in the plane, 3 below)

Packing efficiencyDescribes the total volume occupied by atoms in the unit cell.

For a given atom radius, the higher the coordination, the higher the packing efficiency:You can calculate these from simple geometry, like you did in lab, by relating the unit cell and atomic radius information.

Most metallic elements pack in hexagonal closest packing lattice. Many ionic compounds are fcc. (NaCl two interspersed fcc lattices.)

Cell TypeCoordination #Packing EfficiencySimple cubic652%Body-centered cubic868%Face-centered cubic aka, (cubic closest packing)1274%Hexagonal1274%

Packing of spheres.simple cubic(52% packing efficiency)body-centered cubic(68% packing efficiency)

closest packing of first and second layers

The structures of simple ionic compounds In simple ionic structures space is filled as compactly as possible ions of one charge are surrounded by as many ions as possible of the opposite charge positive and negative ions touchIonic structures are determined by two principal factorsthe relative sizes of the ionsthe ratio of the numbers of positive and negative ions in the compound

The structures of simple ionic compounds In simple ionic structures we usually find the anions, which are normally larger than the cations, arranged in a simple cubic or a closest packed array. Relatively small cations occupy tetrahedral holesLarger cations occupy octahedral holesEven larger cations occupy larger cubic holes in a simple cubic array of anions

Holes Tetrahedral holesOctahedral holeCubic hole

The CsCl structure

The CsCl unit cellCsCl: Cs+ ions occupy all the cubic holes in a simple cubic array of Cl ions.A unit cell contains 1 Cs+ ion and 1 Cl ion. Ions touch along the body diagonal.

The CaF2 structure

The CaF2 unit cellCaF2: F ions occupy all the cubic holes in a simple cubic array of Ca2+ ions.

The fluorite (CaF2) structure.A unit cell contains 4 Ca2+ ions and 8 F ions. Ions touch along the body diagonal.F- ions are tetrahedral coordinated, Ca2+ are octahedrally coordinated.

The NaCl structure

The NaCl unit cell

The NaCl unit cell

The sodium chloride structure.expanded viewspace-fillingA unit cell contains 4 Na+ ions and 4 Cl ions. Ions touch along the cell edge

The ZnS, zinc blende, structure

The zinc blende unit cellA unit cell contains 4 Zn2+ ions and 4 S2 ions. Ions touch along the body diagonal.Zn2+ ions fit in tetrahedral holes

This research comes from the Lilly laboratories and Purdues own Dr. Steven Byrn an international expert in polymorphism. He is in the pharmacy department and runs SSCI in the Purdue Research park.

Note that not only are the colors different (The red, orange, yellow ROY), but the crystal habit is different too. You can see the needles, prisms, and plates. In the Cambridge structural Database in May 1999 the authors discovered using C, H, N, O, F, and S that 291 systems were dimorphic, 27, trimorphic, 3 had four polymorphs, and none had 5 or more. This ROY system exhibits a high degree of polymorphism.