Structures of Solids
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Transcript of Structures of Solids
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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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Structures of SolidsStructures of Solids
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Structures of SolidsStructures of Solids
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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Structures of SolidsStructures of Solids
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Structures of SolidsStructures of Solids
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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Structures of SolidsStructures of Solids
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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Structures of SolidsStructures of Solids
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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Structures of SolidsStructures of Solids
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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Structures of SolidsStructures of Solids
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Structures of SolidsStructures of Solids
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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Structure of Crystals
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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Structure of Crystals
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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Structure of Crystals
Face centered cubic (fcc)
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Structure of Crystals
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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Ionic SolidsIonic Solids
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Ionic SolidsIonic Solids
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