1 structures of solids n solids have maximum intermolecular forces. n molecular crystals are formed...

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Structures of SolidsStructures of Solids

Solids have maximum intermolecular forces. Molecular crystals are formed by close packing of

the molecules (model by packing spheres). We rationalize maximum intermolecular force in a

crystal by the close packing of spheres. When spheres are packed as closely as possible,

there are small spaces between adjacent spheres. The spaces are called interstitial holes.

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A crystal is built up by placing close packed layers of spheres on top of each other.

There is only one place for the second layer of spheres.

There are two choices for the third layer of spheres:– Third layer eclipses the first (ABAB arrangement).

This is called hexagonal close packing (hcp);– Third layer is in a different position relative to the first

(ABCABC arrangement). This is called cubic close packing (ccp).

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Close Packing of SpheresClose Packing of Spheres Each sphere is surrounded by 12 other spheres (6 in

one plane, 3 above and 3 below). Coordination number: the number of spheres

directly surrounding a central sphere. Hexagonal and cubic close packing are different

from the cubic unit cells. If unequally sized spheres are used, the smaller

spheres are placed in the interstitial holes.

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X-Ray DiffractionX-Ray Diffraction When waves are passed through a narrow slit they are

diffracted. When waves are passed through a diffraction grating

(many narrow slits in parallel) they interact to form a diffraction pattern (areas of light and dark bands).

Efficient diffraction occurs when the wavelength of light is close to the size of the slits.

The spacing between layers in a crystal is 2 - 20 Å, which is the wavelength range for X-rays.

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X-ray diffraction (X-ray crystallography):– X-rays are passed through the crystal and are detected on

a photographic plate.– The photographic plate has one bright spot at the center

(incident beam) as well as a diffraction pattern.– Each close packing arrangement produces a different

diffraction pattern.– Knowing the diffraction pattern, we can calculate the

positions of the atoms required to produce that pattern.– We calculate the crystal structure based on a knowledge

of the diffraction pattern.

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X-Ray DiffractionX-Ray Diffraction

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Unit CellsUnit Cells Crystalline solid: well-ordered, definite

arrangements of molecules, atoms or ions. Crystals have an ordered, repeated structure. The smallest repeating unit in a crystal is a unit cell. Unit cell is the smallest unit with all the symmetry

of the entire crystal. Three-dimensional stacking of unit cells is the

crystal lattice.

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Structures of SolidsStructures of SolidsUnit CellsUnit Cells

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Three common types of unit cell.– Primitive cubic, atoms at the corners of a simple cube,

each atom shared by 8 unit cells;

– Body-centered cubic (bcc), atoms at the corners of a cube plus one in the center of the body of the cube,

corner atoms shared by 8 unit cells, center atom completely enclosed in one unit cell;

– Face-centered cubic (fcc), atoms at the corners of a cube plus one atom in the center of each face of the cube,

corner atoms shared by 8 unit cells, face atoms shared by 2 unit cells.

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Structure of Crystals

Simple cubic

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Simple cubic– each particle at a corner is shared by 8 unit cells– 1 unit cell contains 8(1/8) = 1 particle

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Body centered cubic (bcc)– 8 corners + 1 particle in center of cell– 1 unit cell contains 8(1/8) + 1 = 2 particles

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Face centered cubic (fcc)

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Face centered cubic (fcc)– 8 corners + 6 faces– 1 unit cell contains 8(1/8) + 6(1/2) = 4 particles

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Bonding in SolidsBonding in Solids

Molecular (formed from molecules) - usually soft with low melting points and poor conductivity.

Covalent network (formed from atoms) - very hard with very high melting points and poor conductivity.

Ions (formed form ions) - hard, brittle, high melting points and poor conductivity.

Metallic (formed from metal atoms) - soft or hard, high melting points, good conductivity, malleable and ductile.

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Bonding in SolidsBonding in Solids

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Molecular Solids

Intermolecular forces: dipole-dipole, London dispersion and H-bonds.

Weak intermolecular forces give rise to low melting points.

Room temperature gases and liquids usually form molecular solids and low temperature.

Efficient packing of molecules is important (since they are not regular spheres).

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Molecular Solids

– molecules occupy unit cells– low melting points,volatile & insulators– examples:

water, sugar, carbon dioxide, benzene

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Covalently Bonded SolidsCovalently Bonded Solids

Intermolecular forces: dipole-dipole, London dispersion and H-bonds.

Atoms held together in large networks. Examples: diamond, graphite, quartz (SiO2), silicon

carbide (SiC), and boron nitride (BN). In diamond:

– each C atom has a coordination number of 4;– each C atom is tetrahedral;– there is a three-dimensional array of atoms.– Diamond is hard, and has a high melting point (3550 C).

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Covalent Network SolidsCovalent Network Solids

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Covalently Bonded SolidsCovalently Bonded Solids

In graphite– each C atom is arranged in a planar hexagonal ring;– layers of interconnected rings are placed on top of each

other;– the distance between C atoms is close to benzene (1.42 Å

vs. 1.395 Å in benzene);– the distance between layers is large (3.41 Å);– electrons move in delocalized orbitals (good conductor).

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Ionic SolidsIonic Solids

Ions (spherical) held together by electrostatic forces of attraction:

– The higher the charge (Q) and smaller the distance (d) between ions, the stronger the ionic bond.

There are some simple classifications for ionic lattice types:

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d

QQkF

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NaCl Structure Each ion has a coordination number of 6. Face-centered cubic lattice. Cation to anion ratio is 1:1. Examples: LiF, KCl, AgCl and CaO.

CsCl Structure Cs+ has a coordination number of 8. Different from the NaCl structure (Cs+ is larger than

Na+). Cation to anion ratio is 1:1.

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Crystal Structure of Sodium ChlorideCrystal Structure of Sodium Chloride

Face-centered cubic lattice. Two equivalent ways of defining unit cell:

– Cl- (larger) ions at the corners of the cell, or– Na+ (smaller) ions at the corners of the cell.

The cation to anion ratio in a unit cell is the same for the crystal. In NaCl each unit cell contains same number of Na+ and Cl- ions.

Note the unit cell for CaCl2 needs twice as many Cl- ions as Ca2+ ions.

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Crystal Structure of Sodium ChlorideCrystal Structure of Sodium Chloride

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Metallic SolidsMetallic Solids

Metallic solids have metal atoms in hcp, fcc or bcc arrangements.

Coordination number for each atom is either 8 or 12.

Problem: the bonding is too strong for London dispersion and there are not enough electrons for covalent bonds.

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Metallic Solids

Resolution: the metal nuclei float in a sea of electrons.

Metals conduct because the electrons are delocalized and are mobile.

positively charged nuclei surrounded by a sea of electrons– positive ions occupy lattice positions

– examples: Na, Li, Au, Ag, ……..

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Metallic SolidsMetallic Solids

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Bonding in Solids

Variations in Melting Points Molecular Solids

Compound Melting Point (oC)

ice 0

ammonia -77.7

benzene, C6H6 5.5

napthalene, C10H8 80.6

benzoic acid, C6H5CO2H 122.4

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Bonding in Solids

Covalent Solids

Substance

sand, SiO2

carborundum, SiC

diamond

graphite

Melting Point (oC)

1713

~2700

>3550

3652-3697

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Bonding in Solids Ionic SolidsCompoundLiFLiClLiBrLiICaF2

CaCl2

CaBr2

CaI2

Melting Point (oC) 842 614 547 4501360 772 730 740

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Bonding in Solids

Metallic Solids

Metal

Na

Pb

Al

Cu

Fe

W

Melting Point (oC)

98

328

660

1083

1535

3410

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Band Theory of Metals Na’s 3s orbitals can interact to produce

overlapping orbitals

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Band Theory of Metals

Can also overlap with unfilled 3p orbitals

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Band Theory of Metals Insulators have a large gap - forbidden zone Semiconductors have a small gap

1 structures of solids n solids have maximum intermolecular forces. n molecular crystals are formed...

Documents

packing spheres

cubic unit cells

layer of spheres

smallest unit

unit cellsbody

unit cellface

number of spheres

close packing arrangement