ch 12 solids and modern materials

Ch. 12 Solids and Modern Materials

12.1 Classification of Solids

12.2 Structures of Solids

• Polymers contain long chains of atoms (usually carbon), where the atoms within a given chain are connected by covalent bonds and adjacent chains are held to one another largely by weaker intermolecular forces. Polymers are normally stronger and have higher melting points than molecular solids, and they are more flexible than metallic, ionic, or covalent-network solids.

•  Nanomaterials are solids in which the dimensions of individual crystals have been reduced to the order of 1–100 nm.

12.2.1 Crystalline and Amorphous Solids

12.2.2 Unit Cells and Crystal Lattices

• Ions pack to minimize repulsions

• Once ions are packed, x ray diffraction is used to determine the arrangement of atoms

Diffraction: When light waves pass through a narrow slit, they are scattered in such a way that the wave seems to spread out. 

• A unit cell is the smallest piece of the crystal required to show a repeating pattern

• A crystal lattice is the long range pattern shown by repeating the unit cell

• In two dimensional lattices the lattice can take 5 shapes, oblique is most common

• The seven three-dimensional primitive lattices

12.2.3 Filling the Unit Cell

• Motif: In a crystal, the group of atoms associated with each lattice point

12.3 Metallic Solids

12.3.1 The Structures of Metallic Solids

• Structures of metals. Only looking at cubic unit cells: all sides equal + all angles 90^o

• Metals with a primitive cubic structure are rare, one of the few examples being the radioactive element polonium. Body-centered cubic metals include iron, chromium, sodium, and tungsten. Examples of face-centered cubic metals include aluminum, lead, copper, silver, and gold.

• The empirical formula is based on the # of atoms inside the unit cell

  • Fraction of atoms in the unit cell based on location:

    • Center: 1

    • Face: ½

    • Edge: ¼

    • Corner: ⅛  

• Primitive (aka simple cubic structure) 

  • Lattice pts only on corners. Each corner shared by 8 cells

  • 8 atoms x ⅛ atom (corner) = 1 atom per unit cell

• Body center

  • Lattice pts on 8 corners + center

  • 8 atoms x ⅛ atom (corner) = 1 atom in u.c.

  • 1 atom x 1 atom (center) = 1 atom in u.c.

  • Total of 2 atoms per u.c.

• Face-center

  • Lattice pts on faces + corners

  • 8 atoms x ⅛ atom (corner) = 1 atom in u.c.

  • 6 atoms x ½ atom (face) = 3 atoms in u.c.

  • Total of 4 atoms per u.c.

12.3.2 Close Packing

Hexagonal (left) close packing and cubic (right) close packing are equally efficient ways of packing spheres. The red and yellow dots indicate the positions of depressions between atoms.

• For the third layer, we have two choices for where to place the spheres. One possibility is to put the third layer in the depressions that lie directly over the spheres in the first layer. This is done on the left-hand side of above as shown by the dashed red lines in the side view. Continuing with this pattern, the fourth layer would lie directly over the spheres in the second layer, leading to the ABAB stacking pattern seen on the left, which is called hexagonal close packing (hcp).

• Alternatively, the third-layer spheres could lie directly over the depressions that were marked with red dots in the first layer. In this arrangement, the spheres in the third layer do not sit directly above the spheres in either of the first two layers, as shown by the dashed red lines on the lower right-hand side of above. If this sequence is repeated in subsequent layers, we derive an ABCABC stacking pattern shown on the right known as cubic close packing (ccp).

• The coordination number is the number of atoms immediately surrounding a given atom in a crystal structure.

The solid lines indicate the unit cell boundaries. Colors are used to distinguish one layer 

of atoms from another.

• the structure that results from cubic close packing possesses a unit cell that is identical to the face-centered cubic

• Packing efficiency is the fraction of space in a crystal that is actually occupied by 

Atoms

• Equation for volume atoms occupies (face-centered cubic) above

• Equation for volume of unit cell. diagonal across a face of the unit cell is equal to four times the atomic radius. Above

• Packing efficiency equation. Above

• The length of a side of the unit cells equation is given as: l=2r1+2r2=2(r1+r2), where r1 is the ionic radius of the corner ion and r2 is the ionic radius of the edge ion 

• The length of the unit cell edge can be estimated using the formula: Unit Cell Edge Length = 2 × Atomic Radius for close-packed structures.

This formula works because in close-packed structures, the atoms touch each other along the edge of the unit cell, so the edge length is twice the atomic radius.

12.3.3 Alloys

• When atoms of the solute in a solid solution occupy positions normally occupied by a solvent atom, we have a substitutional alloy. homogeneous mixture (aka solid solutions)

  • formed when the two metallic components have similar atomic radii and chemical-bonding characteristics.

  • When two metals differ in radii by more than about 15%, solubility is generally more limited.

• When the solute atoms occupy interstitial positions in the “holes” between solvent atoms, we have an interstitial alloy. homogeneous mixture (aka solid solutions)

  • solute atoms must have a much smaller bonding atomic radius than the solvent atoms. 

  • Typically, the interstitial element is a nonmetal that makes covalent bonds to the neighboring metal atoms. The presence of the extra bonds provided by the interstitial component causes the metal lattice to become harder, stronger, and less ductile.

• In a heterogeneous alloy, the components are not dispersed uniformly.

  • the properties of heterogeneous alloys depend on both the composition and the manner in which the solid is formed from the molten mixture.

• Intermetallic compounds are compounds rather than mixtures. 

  • have definite properties and their composition cannot be varied. 

  • Furthermore, the different types of atoms in an intermetallic compound are ordered rather than randomly distributed. The ordering of atoms in an intermetallic compound generally leads to better structural stability and higher melting points than what is observed in the constituent metals. These features can be attractive for high-temperature applications. 

  • On the negative side, intermetallic compounds are often more brittle than substitutional alloys.

12.4 Metallic Bonding

Which are molecules?

12.4.1 Electron Sea Model

• A simple model that accounts for some of the most important characteristics of metals is the electron-sea model, which pictures the metal as an array of metal cations in a “sea” of valence electrons 

  • The electrons are confined to the metal by electrostatic attractions to the cations, and they are uniformly distributed throughout the structure. The electrons are mobile, however, and no individual electron is confined to any particular metal ion. 

  • When a voltage is applied to a metal wire, the electrons, being negatively charged, flow through the metal toward the positively charged end of the wire.

• high thermal conductivity of metals is also accounted for by the presence of mobile electrons. 

• The ability of metals to deform (their malleability and ductility) can be explained by the fact that metal atoms form bonds to many neighbors.

12.4.2 Molecular Orbital Model

• electron-sea model does not adequately explain many properties of metals. It said strength of bonding between metal atoms should steadily increase as the number of valence electrons increases, resulting in a corresponding increase in the melting points. However, elements near the middle of the transition metal series, rather than those at the end, have the highest melting points in their respective periods. This trend implies that the strength of metallic bonding first increases with increasing number of electrons and then decreases. Similar trends are seen in other physical properties of the metals, such as the boiling point, heat of fusion, and hardness.

Rules of molecular orbital theory:

1. Atomic orbitals combine to make molecular orbitals that can extend over the entire molecule.

2. A molecular orbital can contain zero, one, or two electrons.

3. The number of molecular orbitals in a molecule equals the number of atomic orbitals that combine to form molecular orbitals.

4. Adding electrons to a bonding molecular orbital strengthens bonding, while adding electrons to antibonding molecular orbitals weakens bonding.

• As the length of the chain increases, the number of molecular orbitals increases.

• If the chain becomes very long, there are so many molecular orbitals that the energy separation between them becomes vanishingly small. As the chain length goes to infinity, the allowed energy states become a continuous band. Band: an array of closely spaces molecular orbitals occupying a continuous range of energy

• The electronic structure of a bulk solid is referred to as a band structure.

• The molecular orbital model predicts that bonding first becomes stronger as the number of valence electrons increases and the bonding orbitals are increasingly populated. Upon moving past the middle elements of the transition metal series, the bonds grow weaker as electrons populate antibonding orbitals. Strong bonds between atoms lead to metals with higher melting and boiling points, higher heats of fusion, higher hardness, and so forth.

• the more delocalised electrons present and the smaller the radius of the atom, the higher the melting point of the metal. As we move across periods the number of delocalised electrons per metal atom increases and the radius of the elements decreases. This means the melting point increases.

12.5 Ionic Solids 490

• Because the valence electrons in ionic compounds are confined to the anions, rather than being delocalized, ionic compounds are typically electrical insulators.

• When stress is applied to an ionic solid, the planes of atoms, which before the stress were arranged with cations next to anions, shift so that the alignment becomes cation–cation, anion–anion. The resulting repulsive interaction causes the planes to split away from each other, a property that lends itself to the carving of certain gemstones (such as ruby).

• The most favorable structures are those where the cation–anion distances are as close as those permitted by ionic radii, but the anion–anion and cation–cation distances are maximized.

• The sodium chloride (NaCl; also called the rock salt structure) and zinc blende (ZnS) structures are based on a face-centered cubic lattice.

• the coordination number changes from 8 to 6 to 4 on moving from CsCl to NaCl to ZnS. As the cation size decreases further, eventually the coordination number ((The Coordination number of an atom in a given molecule or a crystal refers to the total number of atoms, ions, or molecules bonded to the atom in question. 'Ligancy' is another term used to refer to the coordination number of an atom) 

• must be reduced again, this time from 6 to 4. in ionic crystals, ions of opposite charge touch each other but ions of the same charge should not touch.

• Magnesium fluoride, however, has two anions for every cation, resulting in a tetragonal crystal structure called the rutile structure.

• To get side length when you know the volume of a cube cube root it (the 3 besides a sq root sign)

12.6 Molecular Solids

• Molecular solids have  intermolecular forces that are weak, are soft and have relatively low melting points (lower than 200degreesC)

• molarity = moles of solute / liters of solution

12.7 Covalent Network Solids

• Many solids, however, conduct electricity somewhat, but nowhere near as well as metals, which is why such materials are called semiconductors.

• The band that forms from bonding molecular orbitals is called the valence band, and the band that forms the antibonding ​orbitals is called the​ conduction band 

• These two bands are separated by the energy band gap E_g

• Band gaps greater than ~3.5 eV are so large that the material is not a semiconductor; it is an insulator and does not conduct electricity.

• Semiconductors can be divided into two classes: elemental semiconductors, which contain only one type of atom, and compound semiconductors, which contain two or more elements.

• As the difference in electronegativity of the elements increases, the bonding becomes more polar and the band gap increases.

The band gap will increase when either of the following conditions is met:

1. The elements are located higher up in the periodic table, where enhanced orbital overlap leads to a larger splitting between bonding and antibonding orbital energies, or

2. the horizontal separation between the elements increases, which leads to an increase in the electronegativity difference and bond polarity.

• 12.7.2 Semiconductor doping

• The electrical conductivity of a semiconductor is influenced by the presence of small numbers of impurity atoms. The process of adding controlled amounts of impurity atoms to a material is known as doping

• The semiconductor industry uses “nine-nines” silicon to make integrated circuits; what this means is that Si must be 99.999999999% pure (nine nines after the decimal place) to be technologically useful!

• Aluminum has only three valence electrons compared to silicon’s four. Thus, there are electron vacancies, known as holes, in the valence band when silicon is doped with aluminum.

  • Since the negatively charged electron is not there, the hole can be thought of as having a positive charge. Any adjacent electron that jumps into the hole leaves behind a new hole. Thus, the positive hole moves about in the lattice like a particle

  • A material like this is called a p-type semiconductor, p signifying that the number of positive holes in the material has increased.

• 12.8 Polymers

• The word polymers was created to denote molecular substances of high molecular weight formed by the polymerization (joining together) of monomers, molecules with low molecular weight.

• Types of plastics:

  • Thermoplastics can be reshaped through application of heat and pressure

  •  thermosetting plastic (also called a thermoset) is shaped through irreversible chemical processes and, therefore, cannot be reshaped readily.

  • elastomer, which is a material that exhibits rubbery or elastic behavior

• 12.8.1 Making Polymers

• Here n represents the large number—ranging from hundreds to many thousands—of monomer molecules (ethylene in this case) that react to form one polymer molecule.

• In a condensation reaction two molecules are joined to form a larger molecule by elimination of a small molecule, such as H2O

• Polymers formed from two different monomers are called copolymers.

• Forming bonds between chains is called cross-linking-method of stiffening polymers

• Resonance leads to delocalization

• 12.9 Nanomaterials 506

• It turns out that the properties of semiconductors and metals change in this size range. Nanomaterials—materials that have dimensions on the 1–100-nm scale

•  in small molecules, electrons occupy discrete molecular orbitals, whereas in macroscale solids the electrons occupy delocalized bands. 

• At what point does a molecule get so large that it starts behaving as though it has delocalized bands rather than localized molecular orbitals? For semiconductors, both theory and experiment tell us that the answer is roughly at 1 to 10 nm (about 10–100 atoms across).

• Because these effects become important at 1 to 10 nm, semiconductor particles with diameters in this size range are called quantum dots.

• As the particle gets smaller, the band gap gets larger, and emitted light shifts to a shorter wavelength

• Another way to make semiconductors emit light is to illuminate them with light whose photons have energies larger than the energy of the band gap of the semiconductor, a process called photoluminescence

• Semiconductors do not have to be shrunk to the nanoscale in all three dimensions to show new properties. They can be laid down in relatively large two-dimensional areas on a substrate but be only a few nanometers thick to make quantum wells. 

• Quantum wires, in which the semiconductor wire diameter is only a few nanometers but its length is very long, have also been made by various chemical routes.

  •  In both quantum wells and quantum wires, measurements along the nanoscale dimension(s) show quantum behavior, but in the long dimension, the properties seem to be just like those of the bulk material.

• 12.9.2 Metals on the nanoscale

• Metals also have unusual properties on the 1–100-nm-length scale. Fundamentally, this is because the mean free path (find more in Section 10.8) of an electron in a metal at room temperature is typically about 1–100 nm. So when the particle size of a metal is 100 nm or less, one might expect unusual effects because the “sea of electrons” encounters a “shore” (the surface of the particle).

• Macroporous is visible to the human eye.  Microporous solids have pores up to 2 nm in size, whereas mesoporous solids have pore sizes in the range 2 to 50 nm.

• Microporous and mesoporous materials have a large surface area relative to their volume because of their numerous pores and cavities. Nanomaterials, on the other hand, have a large surface area relative to their volume because of their small particle size.

• Zeolites, which occur naturally and can also be synthesized, are a class of aluminosilicates

  • may be synthesized with weakly interacting ions occupying the cavities. Upon exposure to ions that interact more strongly with the interior surfaces, there is a preferential exchange of weakly interacting ions for more strongly interacting ions. This effectively creates what we might think of as an ionic sponge

• 12.9.3 Carbon on the nanoscale

• pure solid carbon was thought to exist in only two forms: the covalent-network solids diamond and graphite. However, scientists vaporized a sample of graphite with an intense pulse of laser light and used a stream of helium gas to carry the vaporized carbon into a mass spectrometer. The mass spectrum showed peaks corresponding to clusters of carbon atoms, with a particularly strong peak corresponding to molecules composed of 60 carbon atoms, C₆₀

  • Formed an almost perfectly spherical ball with 32 faces, 12 pentagons, and 20 hexagons

  • They named these buckyballs. These molecules are now known as fullerenes.

  • Appreciable amounts of buckyball can be prepared by electrically evaporating graphite in an atmosphere of helium gas. About 14% of the resulting soot consists of buckyball

• After discovering C₆₀ scientists discovered carbon nanotubes. You can think of these as sheets of graphite rolled up and capped at one or both ends with by half of a C₆₀ molecule.

  • Multiwall carbon nanotubes consist of tubes within tubes, nested together, whereas single-walled carbon nanotubes consist of single tubes. 

  • Single-walled carbon nanotubes can be 1000 nm long or even longer but are only about 1 nm in diameter. 

  • Depending on the diameter of the graphite sheet and how it is rolled up, carbon nanotubes can behave as either semiconductors or metals.

• The two-dimensional form of carbon, graphene, is the most recent low- dimensional form of carbon to be experimentally isolated and studied.

•  the technique they used to isolate single-layer graphene was to successively peel away thin layers of graphite using adhesive tape.

  • Individual layers of graphene were then transferred to a silicon wafer having a precisely defined overcoat of SiO₂ 

  • The properties of graphene are remarkable. It is very strong and has a record thermal conductivity, topping carbon nanotubes in both categories. Graphene is a semimetal, which means its electronic structure is like that of a semiconductor in which the energy gap is exactly zero. The combination of graphene’s two-dimensional character and the fact that it is a semimetal allows the electrons to travel very long distances, up to 0.3 picometers without scattering from another electron, atom, or impurity. Graphene can sustain electrical current densities six orders of magnitude higher than those sustainable in copper. Even though it is only one atom thick, graphene can absorb 2.3% of sunlight that strikes it