Chapter 12: Crystalline Solids & Modern Materials Flashcards
Define crystalline lattice.
A crystalline lattice is the regular arrangement of atoms within a crystalline solid. The crystalline lattice of any solid is nature’s way of aggregating the particles to minimize their energy.
Define unit cell.
A unit cell is a small collection of atoms, ions, or molecules used to represent the crystalline lattice.
What is a simple cubic unit cell?
The simple cubic unit cell consists of a cube with one atom at each corner. The atom touch along each edge of the cube, so the edge length is twice the radius of the atoms (l = 2r).
How many atoms are in a simple cubic unit cell?
One. Each corner atom is shared by eight other cells, so any one unit cell actually contains only one-eighth of each of the eight atoms at its corners, for a total of just one atom per unit cell.
Define coordination number.
The coordination number is the number of atoms with which each atom is in direct contact. This number is also the number of atoms with which a particular atom can strongly interact.
What is the coordination number of a simple cubic unit cell?
6.
Define packing efficiency.
The packing efficiency is the percentage of the volume of the unit cell occupied by the spheres.
How is coordination number related to packing efficiency?
The higher the coordination number, the greater the packing efficiency.
What is the packing efficiency of a simple cubic unit cell?
52%.
What is the edge length of a simple cubic unit cell in terms of r?
2r.
What is the edge length of a body-centered cubic unit cell in terms of r?
4r/√3
What is the edge length of a face-centered cubic unit cell in terms of r?
2√2r
How many atoms are in a body-centered cubic unit cell?
2 atoms.
How many atoms are in a face-centered cubic unit cell?
4 atoms.
What is the coordination number of a body-centered cubic unit cell?
8.
What is the coordination number of a face-centered cubic unit cell?
12
What is the packing efficiency of a body-centered cubic unit cell?
68%.
What is the packing efficiency of a face-centered cubic unit cell?
74%.
What is a body-centered cubic unit cell?
The body-centered cubic unit cell consists of a cube with one atom at each corner and one atom (of the same kind) in the very center of the cube. The atoms do not touch along each edge of the cube, but instead along the diagonal line that runs from one corner through the middle of the cube to the opposite corner.
What is a face-centered cubic unit cell?
The face-centered cubic unit cell is a cube with one atom at each corner and one atom (of the same kind) in the center of each cube face. In the face-centered unit cell (like the body-centered unit cell), the atoms do not touch along each edge of the cube. Instead, the atoms touch along the diagonal face.
What is the pattern of hexagonal closest packing?
The pattern from one layer to the next is ABAB, with the third layer aligning exactly above the first. The central atom in layer B of this structure is touching six atoms in its own layer, three atoms in the layer above it, and three atoms in the layer below, for a coordination number of 12.
What is the pattern of cubic closest packing?
The third layer of atoms is offset from the first in an ABCABC pattern. Every fourth layer aligns with the first.
What is the cubic closest-packed structure identical to?
The face-centered cubic unit cell structure.
What are the three subcategories of crystalline solids?
Molecular, ionic, and atomic.
What are the three subcategories of atomic solids?
Nonbonding, metallic, and network covalent.
Define molecular solids.
Solids whose composite units are molecules. The lattice sites in a crystalline molecular solid are occupied by molecules. These solids are held together by intermolecular forces like dispersion forces, dipole-dipole forces, and hydrogen bonding.
Define polymorphs.
Polymorphs refers to the different structures molecular solids can crystallize into. Polymorphs have different properties, such as melting points and solubilities.
What are the forces holding ionic solids together?
Strong coulombic forces (or ionic bonds), and because these forces are much stronger than intermolecular forces, ionic solids tend to have much higher melting points than molecular solids.
What type of forces holds together nonbonding atomic solids?
Relatively weak dispersion forces. This means these solids have low melting points that increase uniformly with molar mass.
What type of forces holds together metallic atomic solids?
Metallic bonds: the interaction of metal cations with the sea of electrons that surrounds them.
How does the electron sea model explain the conductivity of metals?
In contrast to ionic solids where electrons are localized on an ion, the electrons in a metal are free to move. The movement or flow of electrons in response to an electric potential (or voltage) is an electric current. Metals are also excellent conductors of heat.
How does the electron sea model explain the malleability and ductility (the capacity to be drawn into wires) of metals?
Since there are no localized or specific bonds in a metal, we can deform it relatively easily by forcing the metal ions to slide past one another.
What type of force holds together network covalent atomic solids?
Covalent bonds. This causes the solids to have very high melting points.
Why don’t network covalent atomic solids tend to form closest-packed structures?
The crystal structures of these solids are more restricted by the geometrical constraints of the covalent bonds (which tend to be more directional than intermolecular forces, ionic bonds, or metallic bonds).
Describe graphite’s structure.
Graphite’s structure consists of flat sheets of carbon atoms covalently bonded together as interconnected hexagonal rings.
What is the bond length within a graphite sheet?
142 pm.
How do the forces between graphite sheets compare to the forces within sheets?
The forces between sheets are much different than the bonds within sheets. There are no covalent bonds between sheets, only relatively weak dispersion force, and the separation between sheets is 341 pm.
Why is graphite a good electrical conductor?
The electrons in the extended pi bonding network within a sheet make graphite a good electrical conductor in the direction of the plane of the sheets.
Describe the unit cell of diamonds.
The unit cell is a face-centered cubic structure with an additional carbon atom in half of the eight tetrahedral holes located directly in each corner atom. Each carbon atom is covalently bonded to four other carbon atoms at the corners of a tetrahedron.
Why does diamond conduct heat but not electricity?
The electrons in diamond are confined to the covalent bonds and are not free to flow, so it does not conduct electricity. However, because the bonds are strong and the connectivity between atoms so extensive, diamond is an excellent conductor of heat.
What are fullerenes?
Carbon clusters containing from 36 to over 100 carbon atoms.
What are nanotubes?
Nanotubes are synthesized long carbon structures that consist of sheets of interconnected C6 rings that assume the shape of a cylinder.
What are the two types of nanotubes?
- Single-walled nanotubes that have one layer of interconnected C6 rings forming the walls.
- Multiwalled nanotubes that have concentric layers of interconnected C6 rings forming the walls.
What are silicates?
Silicates are extended arrays of silicon and oxygen that form a network covalent structure in which a silicon atom bonds to four oxygen atoms at the corner of a tetrahedron. The silicon atom bonds to each oxygen with a single covalent sigma bond.
What is silica?
Commonly called quartz, silica has the formula unit of SiO2. Each Si atom is in a tetrahedron surrounded by four O atoms, and each O atom acts as a bridge connecting the corners of two tetrahedrons.
How is band theory similar to molecular orbital theory?
In MOT, molecular orbitals are not localized on individual atoms but delocalized over the entire molecule. Similarly, in band theory, we combine the atomic orbitals of the atoms within a solid crystal to form orbitals that are not localized on individual atoms but delocalized over the entire crystal.
What is the band in band theory?
This refers to the band of energy levels that forms when there are no longer discrete energy levels between atoms.
What is the valence band?
The orbitals in the band that are bonding molecular orbitals and contain N number of valence electrons.
What is the conduction band?
The orbitals in the band that are antibonding and completely empty.
How many valence and conduction bands are there per solid?
The number of valence and conduction bands is equal.
How are mobile electrons in the conduction band responsible for the thermal conductivity of metals?
When a metal is heated, electrons are excited to higher-energy molecular orbitals. These electrons quickly transport the thermal energy throughout the crystal lattice.
What is the band gap?
In metals, the energy difference between the top of the valence band and the bottom of the conduction band is infinitesimally small. In semiconductors and insulators, however, there is an energy gap between the two; this is the band gap.
How does the size of the band gap compare between insulators and semiconductors?
In insulators, the band gap is large, but in semiconductors, the band gap is smaller.
How does the size of the insulator band gap affect conductivity?
In insulators, the band gap is large, and electrons are not promoted into the conduction band at ordinary temperatures, resulting in no electrical conductivity.
How does the size of the semiconductor band gap affect conductivity?
Since the band gap is small, the conductivity of semiconductors increases with increasing temperature because heat allows a greater number of electrons to be thermally promoted into the conduction band.
What is the relationship between band gap length and position on a periodic column? Why?
The band gap decreases as we move down the column of elements. Atomic radius increases as we move down a column in the periodic table. The increasing radius reduces the overlap between orbitals on neighboring atoms, which in turn reduces the energy difference between the antibonding orbitals (the conduction band) and the bonding orbitals (the valence band).
What are doped semiconductors?
Doped semiconductors are semiconductors that contain minute amounts of impurities that result in either additional electrons in the conduction band or electron “holes” in the valence band.
What is an n-type semiconductor?
A type of semiconductor in which additional electrons are added to conduct electrical current. The charge carriers are negatively charged electrons in the conduction band.
What is a p-type semiconductor?
Through doping, empty molecular orbitals are added to the valence band. The presence of these holes allows for the movement of electrical current because electrons in the valence band can move between holes. In this way, the holes move in the opposite direction as the electrons. Because each hole acts as a positive charge, these semiconductors are named p-type.
What is the relationship between the intermolecular forces a solid is experiencing and the energy of the system?
The more force, the less the energy.
To move around in a solid, which band must electrons be in?
The antibonding conduction band.
What is the relationship between coordination number and lattice energy?
The higher the coordination number, the greater the attractive forces (lattice energy) are holding it together.
What is the only type of matter known to assemble into a simple cubic unit cell?
Polonium (Po).
Name some examples of elements that assemble into a body-centered cubic unit cell.
Iron (Fe), tungsten (W), and chromium (Cr).
Name some examples of elements that assemble into a face-centered cubic unit cell.
Aluminium (Al), copper (Cu), nickel (Ni), gold (Au), and silver (Ag).
Define allotropes.
A type of polymorphism specific to elements. Different arrangements of the crystal lattice gives them different properties.
What is the relationship between conductivity and temperature?
Conductivity drops as temperature increases.
What is the band of bonding orbitals called?
The valence band.
What is the band of antibonding orbitals called?
The conduction band.
In a highly conjugated system, what happens as you add more atomic orbitals?
The energy gap between the resulting molecular orbitals decreases (gets closer to one another).
What does HOMO stand for?
Highest occupied molecular orbital.
What does LUMO stand for?
Lowest unoccupied molecular orbital.
How does the distinction between the bonding and antibonding bands change from metals to semimetals and semiconductors?
For metals, the distinction is infinitesimally small. Semimetals and semiconductors are different in that they have a band gap: large for insulators and small for semiconductors.
At 0 K, which band are electrons located in?
The valence band. With thermal energy, some will move up to the conduction band.
How do N-type semiconductors affect the band gap?
They raise the valence band through the use of negative electrons as major charge carriers.
How do P-type semiconductors affect the band gap?
They lower the conduction band through the use of “positive” holes as major charge carriers.
How do you induce directionality in a semiconductor?
If a p-type and n-type are next to each other, you can induce directionality in electron flow since electrons flow downhill relative to potential energy and holes flow uphill relative to potential energy.
What does applying a current to a semiconductor generate?
Photons equal in energy to its band gap.
