Chapter 13: Solids and Modern Materials

graphene

a new material that consists of a single sheet of carbon atoms (similar to a sheet of graphite) one atom thick; it is both the thinnest and strongest known material

X-ray diffraction

a powerful laboratory technique that allows for determining the arrangement of atoms in a crystal and for measuring the distance between them

Bragg's law

nλ = 2dsinθ

X-ray crystallography

the process of using X-ray diffraction to determine the structure of a crystal

crystalline lattice

the regular arrangement of atoms in a crystalline solid

unit cell

the smallest divisible unit of a crystal that, when repeated in three dimensions, reproduces the entire crystal lattice

simple cubic

a unit cell that consists of a cube with one atom at each corner

coordination number

the number of atoms with which each atom in the crystal lattice is in direct contact

packing efficiency

the percentage of volume of a unit cell occupied by the atoms, assumed to be spherical

body-centered cubic

a unit cell that consists of a cube with one atom at each corner and one atom at the center of the cube

face-centered cubic

a crystal structure that has a unit cell that consists of a cube with one atom at each corner and one atom in the center of every face

hexagonal closest packing structure

a closest-packing arrangement in which the atoms of the third layer align exactly over those in the first layer

cubic closest packing

a closest-packed arrangement in which the third layer of atoms is offset from the first; the same structure as the face-centered cubic

molecular solids

solids whose composite units are molecules; they generally have low melting points

polymorphs

the different crystal structures that can sometimes exist for the same compound

ionic solids

solids whose composite units are ions; they generally have high melting points

atomic solids

solids whose composite units are atoms; they include nonbonding atomic solids, metallic atomic solids, and network covalent solids

nonbonding atomic solids

atomic solids held together by dispersion forces; they have low melting points

metallic atomic solids

atomic solids held together by metallic bonds; they have variable melting points

network covalent atomic solids

atomic solids held together by covalent bonds; they have high melting points

How many atoms per unit cell in a simple cubic cell?

1

How many atoms per unit cell in a body-centered cubic cell?

2

How many atoms per unit cell in a face-centered cubic cell?

4

What is the coordination number of a face-centered cubic cell?

12

What is the coordination number of a body-centered cubic cell?

8

What is the coordination number of a simple cubic cell?

6

What is the edge length for a simple cubic cell in terms of r?

l = 2r

What is the edge length for a body-centered cubic cell in terms of r?

4r/√3

What is the edge length for a face-centered cubic cell in terms of r?

2√2 × r

What is the packing efficiency of a face-centered cubic cell?

74%

What is the packing efficiency of a body-centered cubic cell?

68%

What is the packing efficiency of a simple cubic cell?

52%

graphite

an elemental form of carbon consisting of flat sheets of carbon atoms, bonded together as interconnected hexagonal rings held together by intermolecular forces, that can easily slide past each other

diamond

an elemental form of carbon in which each carbon atom is covalently bonded to four other carbon atoms at the corners of a tetrahedron

fullerenes

carbon clusters, such as C₆₀, bonded in roughly spherical shapes containing from 36 to over 100 carbon atoms

nanotubes

long, tubular structures consisting of interconnected C₆ rings

silicates

network covalent atomic solids that contain silicon, oxygen, and various metal atoms

quartz

a silicate crystal that has a formula unit of SiO₂

silica

a silicate crystal that has a formula unit of SiO₂

ceramics

inorganic metallic solids that are prepared from powders usually mixed with water, formed into the desired shape, and then heated

clay

a powdered form of a mineral (such as an aluminosilicate) mixed with water

Portland cement

a powdered mixture consisting mostly of limestone (CaCO₃) and silica (SiO₂), with smaller amounts of alumina (Al₂O₃), iron (III) oxide (Fe₂O₃), and gypsum (CaSO₄ × 2H₂O)

concrete

a mixture of Portland cement combined with sand and pebbles

glass

an amorphous form of silica with a randomly ordered structure

vitreous (fused) silica

a type of glass that is hard, resists high temperatures, has a low thermal expansion, and is transparent to both visible light and ultraviolet light

soda-lime glass

a type of glass that is about 70% SiO2 with the balance being mostly Na2O and CaO; this type is transparent to visible light (not ultraviolet) and has a high thermal expansion, but it is less expensive to make form into desired shapes than vitreous silica

borosilicate glass

a type of glass containing boric oxide (B2O3); expands less when heated and can withstand heating and cooling cycles without shattering

leaded glass

a type of glass (often called crystal) that contains PbO; has a higher index of refraction (it bends light more than ordinary glass), which results in more brilliant-looking glassware

band theory

a model for bonding in atomic solids based on molecular orbital theory in which atomic orbitals combine and become delocalized over the entire crystal

valence band

in band theory, the band of energy levels that forms from bonding molecular orbitals

conduction band

in band theory, the band of energy levels that forms from antibonding molecular orbitals

band gap

an energy gap that exists between the valence band and conduction band of semiconductors and insulators

n-type semiconductor

a semiconductor that employs negatively charged electrons in the conduction band as the charge carriers

p-type semiconductor

a semiconductor that employs positively charged "holes" in the valence band as the charge carriers

p-n junctions

tiny areas in electronic circuits that have p-type semiconductors on one side and n-type on the other

diodes

a device that allows the flow of electrical current in only one direction

amplifier

a device that amplifies a small electrical current into a larger one

polymers

a long chain-like molecule composed of repeating units called monomers

monomers

a repeating unit in a polymer

addition polymer

a polymer in which the monomers link together without the elimination of any atoms

dimer

the product that forms from the reaction of two monomers

condensation polymers

a polymer formed by elimination of an atom or small group of atoms (usually water) between pairs of monomers during polymerization