CHEM 511 Chapter 6
page 1 of 22
Chapter 6 Structures and energetics of metallic and ionic solids Types of bonding ● Metallic
● Ionic (non-directional bonding)
● Covalent (directional bonding) Significant sharing of electrons between atoms. Can form vast arrays (e.g. C—diamond, graphite; SiO2—quartz, cristobalite) or molecular solids (e.g. CO2, SO2, H2O) Two cases for covalent: amorphous crystalline
Packing of spheres Lattice: three dimensional infinite array of points (atoms) where each atom is surrounded in an identical way by neighboring points Unit cell: the smallest repeating unit in a solid state lattice from which the entire crystal structure can be built by purely translational displacements There are seven basic crystal systems that are described by lengths (a,b,c) and angles (α,β,γ)—(this information is not in your book)
CHEM 511 Chapter 6
Close packed unit cell: less wasted space each atom will have 12 nearest neighbors
Types of cp unit cells Hexagaonally close packed (hcp) layer A is set down layer B is in the “dimples” of layer A 3rd layer is exactly the same as A
page 2 of 22
CHEM 511 Chapter 6
page 3 of 22
Cubic close packed (ccp) aka, face centered cubic (fcc) set down layer A layer B is placed in “dimples” of layer A layer C is placed in “dimples” of layer B, but not directly above atoms in the A layer
Often, atoms can be squeezed in the empty spaces between atoms (holes). Calculate the volume of space occupied by the atoms in a ccp structure.
Holes in close packed structures Octahedral holes (Oh holes): lie between 2 planar triangles
CHEM 511 Chapter 6
For ccp, Oh holes are located at midpoints of each edge of the cube AND in the center
Tetrahedral hole (Td): lies between a planar triangle capped with a single atom
Non-close-packed structures Body centered cubic (bcc or cubic-I): atoms at each corner and in the center
Simple or primitive cubic (cubic-P): atoms only at corners
page 4 of 22
CHEM 511 Chapter 6
page 5 of 22
Packing of spheres applied to the elements We will focus mainly on the metallic elements as shown below. Atoms typically crystallize in the hcp or ccp structure type, but not exclusively. More importantly, multiple crystallization phases may be possible—depending on the temperature and pressure.
Polymorphism: the ability to adopt different crystalline forms at various temperatures and pressures. This is the phase diagram for Fe. What do you notice about the packing of higher pressure forms? Does this make sense?
(1 bar = 0.987 atm)
Typically a transition to a higher temperature would result in less close-packed structures. Is this borne out on the figure?
CHEM 511 Chapter 6
page 6 of 22
Metallic radii rmetal: one half the distance between the nearest-neighbor atoms in a solid state metallic lattice This value is dependent on the coordination number (i.e., the nearest neighbor atoms) Coordination Number Relative Ratio
12 1.00
8 0.97
6 0.96
4 0.88
The periodic table on previous page shows rmetal for 12-coordinate species. What is the CN for a bcc lattice?
So if the tabulated value for the rmetal of Na is 191 pm, what would the sodium radius in the bcc lattice be at 1 bar and 298 K?
What is the periodic trend for size on going down a group?
What is the correlation between lattice type and melting point?
Alloys and intermetallic compounds Alloy: an intimate mixture or compound of two or more metals or metals and nonmetals. Properties will be different that the elements separately. ● can be homogeneous ● can be made of definite compounds (definite composition and internal (crystalline) structure)
CHEM 511 Chapter 6
page 7 of 22
Classification of alloys (a) Substitutional alloy atomic radii must be within 15% of size crystal structures of the elements must be the same electronegativity should be similar
(b) Interstitial alloy (also, interstitial solid solutions) need one atom to be very small compared to the lattice atoms, otherwise distortion will occur
(c) Intermetallic compounds formation of a stoichiometric compound (i.e., one with a specific composition) between two or more metals.
CHEM 511 Chapter 6
page 8 of 22
Bonding in metals and semiconductors Extended solids, whether metallic, covalent, or ionic can be modeled with molecular orbitals. Metallic conductor: a substance whose electrical conductivity decreases with rising temperature (or it can be said conversely: the resistivity increases with rising temperature) Semiconductor: a substance whose electrical conductivity increases with rising temperature (or: the resistivity decreases with rising temperature) Insulators are just a special category of semiconductors
Ge
To understand this, imagine forming a molecular orbital system for a collection of lithium atoms.
Band: a group of MOs in which the energy difference is so small that the system behaves as if a continuous, non-quantized variation of energy is possible
If each atom gives 1 electron, then the orbital array should be half-full. This level is called the Fermi level (technically, this level is measured at absolute zero, but it is impossible to reach this temperature).
CHEM 511 Chapter 6
page 9 of 22
Which letter in the figure links the band diagram to the appropriate type of conductor?
For metals, electrons are filled to the Fermi level and thermal energy can promote the electron to allow them to conduct around the metal. So why will an increase in temperature decrease the conductivity?
Semiconductors Intrinsic semiconductors (no doping necessary): small band gap, therefore thermal energy used to promote electrons to the conduction band (upper band) Extrinsic semiconductors (doping necessary)-results in p- or n-type semiconductors
CHEM 511 Chapter 6
page 10 of 22
Why does heat cause these to increase conductivity?
Ionic radius What happens to the size of an atom when it loses an electron? Why?
What happens to the size of an atom when it gains an electron? Why?
Measuring the size of an ion is complicated—and made more complicated since coordination number will change the size of an ion. One system uses oxygen as a standard and measures other ions against it.
Ionic Solids
Contain cations and anions in crystalline arrays Often one ion will be in fcc or hcp and the other ion fills in Oh or Td holes.
Rock Salt structure Named for NaCl, but many ionic compounds conform to this crystal structure (LiCl, KBr, RbI, AgCl, AgBr, MgO, CaO, TiO, NiO, BaS, UC, ScN) Consists of fcc array of anions. Cations occupy Oh holes (or vice versa!)
CHEM 511 Chapter 6
page 11 of 22
Cesium Chloride structure Named for CsCl, but many ionic compounds conform to this crystal structure (CsBr, CsI, NH4Cl, NH4Br, TlCl, TlBr, and some intermetallics: CuZn, CuPd, AuMg) Each anion occupies a vertex and the cation is in the center of the box (or vice versa !)
Fluorite structure Named for the mineral CaF2 (others: BaCl2, HgF2 , PbO2, ThO2, CeO2, PrO2, UO2, ZrO2, HfO2, NpO2, PuO2, AmO2) Ca occupy fcc array and F occupy both types of Td holes
Anti-fluorite structure Has basically the same structure as fluorite, but cations and anions switched positions K2O, Na2O, Na2S, K2S
CHEM 511 Chapter 6
page 12 of 22
Sphalerite (aka zinc blende) structure Named for the mineral ZnS. Other compounds that adopt this structure: CuCl, CdS, HgS
Variants of zinc blende: diamond and β-cristobalite (SiO2)
CHEM 511 Chapter 6
Wurtzite structure Another type of ZnS mineral ZnO, AgI, SiC, NH4F
Rutile structure (TiO2) Others: SnO2, MgF2, NiF2, MnO2
page 13 of 22
CHEM 511 Chapter 6
Layered Structures CdI2 and CdCl2
CdI2 structures: MgBr2, MgI2, CaI2, Mg(OH)2, many d-metal iodides CdCl2 structures: FeCl2, CoCl2
Perovskite structure (ABX3) Perovskite is a class of compounds, but the prototype is calcium titanate (CaTiO3) Others: BaTiO3, SrTiO3
BaTiO3 is a ferroelectric material...
page 14 of 22
CHEM 511 Chapter 6
page 15 of 22
Rationalizing Structures Ionic radii As noted earlier, a reference value is needed. Usually oxygen is assumed to be 140 pm Trends are: 1. ionic radii increase going down a group (lanthanide contraction notwithstanding) 2. the radii of ions of the same charge decreases across a period 3. for a given ion, a larger coordination number results in a larger radius 4. an ionic radius will decrease as the positive charge increases for a given cation Radius ratio: taking a ratio of the ions' sizes, you can “predict” the coordination of the ions CN 8 6 4 3 2
Ratio >0.73 0.41-0.73 0.22-0.41 0.15-0.22
