Ch. 12: Crystalline Solids and Modern Materials

Dr. Namphol Sinkaset Chem 200: General Chemistry I

I. Chapter Outline

I. Introduction II. X-Ray Crystallography III. Unit Cells and Basic Structures IV. Types of Crystalline Solids V. Semiconductors and Band Theory

I. Materials Science • Materials of the day literally shape

society. • History of metallurgy: from gold to

copper to bronze to iron to steel. • Porcelain revolutionizes dishware. • Cement revolutionizes construction. • Semiconductors gives us today’s

society.

II. Crystalline Solids • Recall that crystalline solids have atoms

or molecules arranged with long-range order.

• Sharp angles and edges in minerals are dictated by specific patterns at the atomic and molecular level.

• Structure of crystalline solids can be determined with x-ray crystallography.

II. Interference

• Recall that EM radiation can constructively or destructively interfere.

• When coupled with diffraction, interference patterns form.

II. X-ray Diffraction

• Method to find spacing between planes, d. • Ray 2 travels a distance that is 2a longer

than Ray 1. • If 2a is an integral # of wavelengths, rays

will be in phase.

II. Bragg’s Law • We derive an important equation used

to solve crystal structures.

𝑛𝑛λ = 2𝑎𝑎 Necessary for constructive interference

sin θ =𝑎𝑎𝑑𝑑

𝑎𝑎 = 𝑑𝑑 sin θ

𝑛𝑛λ = 2𝑑𝑑 sin θ

II. Finding d Between Layers

• Rearrangement of Bragg’s law allows calculation of d.

• X-ray crystallography involves creating diffraction patterns from different angles to find the entire crystalline structure.

𝑑𝑑 =𝑛𝑛λ

2 sin θ

II. X-ray Crystallography

III. Unit Cells

• X-ray crystallography reveals the crystalline lattice, how atoms are regularly spaced in a crystalline solid.

• To represent this lattice in the simplest way possible, we use unit cells.

• If a unit cell is repeated, it will reconstruct the entire crystalline lattice.

III. Unit Cells as a Base Unit

• Unit cells are 3D analogs of floor tiles. • Individual floor tiles together create an

extended pattern.

III. Simple Cubic Unit Cell

III. Body-Centered Cubic Unit Cell

• Colored spheres are used for clarity; each sphere is the same atom!

III. Face-Centered Cubic Unit Cell

III. Summary of Cubic Unit Cells

III. Closest-Packed Structures

• Another way to envision crystal structures is to think about it as stacking layers – like fruit at grocery store.

• This is useful in atomic solids like metals.

• There are different ways we can “pack” these atoms.

III. Simple Cubic Packing

• For example, we can stack atoms directly on top of each other.

• This packing is the same as a simple cubic unit cell.

III. Hexagonal Closest Packing • In this packing, we offset by half an atom in

each layer and between layers.

III. Hexagonal Closest Packing

III. Cubic Closest Packing

III. CCP = FCC • It’s hard to see, but cubic closest packing is the

same as face-centered cubic.

IV. Types of Crystalline Solids

IV. Structures of Ionic Solids

• Crystalline structures of ionics are closely related to the unit cells we covered.

• Three things need to be accommodated: Maximize coordination number Electroneutrality Relative sizes of cation and anion

IV. Cesium Chloride • The ions of cesium chloride are of similar size

(radii of 167 pm and 181 pm, respectively). • BCC-type structure maximizes coordination

number (8) and keeps electroneutrality.

IV. Sodium Chloride

• Na+ and Cl- are not so similar in size, 97 and 181 pm, respectively.

• Cl-’s are FCC and Na+’s occupy holes in between for CN = 6.

• Known as rock salt structure.

IV. Zinc Blende

• In ZnS the radii are 74 and 184 pm, respectively.

• S2-’s are FCC and Zn2+’s occupy tetrahedral holes (CN = 4).

IV. Fluorite and Antifluorite

• For 1:2 ionics like CaF2, Ca2+’s are FCC with F-’s occupying 8 tetrahedral holes.

• Antifluorite would be for 2:1 ionics.

IV. Metallic Atomic Solids

• Metallic solids are held together via metallic bonds.

• Metal atoms donate valence e- to an e- “sea.”

• Metal cations float in this “sea of e-’s.”

IV. Malleability of Metals

• This e- sea model of metals explains the malleability of metals.

IV. Explaining Other Properties of Metals

• Group 2 metals have higher melting points than group 1 metals.

• Metals have high electrical conductivity. • Metals conduct heat well.

IV. Network Covalent Solids

• These are solids in which atoms are held together with covalent bonds.

• Network solids have very high melting points due to extended covalent bonding.

• Two most common examples are the different allotropes of carbon and silicates.

IV. Carbon

• Two most common crystalline forms are graphite and diamond.

• Graphite held together by σ and π bonds and dispersion forces.

• Diamond held together by σ bonds – like one giant molecule.

IV. Silicates • Silicates are extended arrays of Si and O. • These are the most common network solids. • Si single bonds to 4 O’s in a tetrahedral

arrangement.

V. Semiconductors

• To explain semiconductors, we apply molecular orbital theory to atoms in crystalline solid.

• When two atomic orbitals are combined, how many molecular orbitals form?

• We extend this idea to a large number of atomic orbitals.

V. Band Theory • As more molecular orbitals are formed,

they start to coalesce into a band. • These bands extend across the entire

crystalline solid.

V. Promotion to Conduction Band

• If there’s a small or no band gap, it’s easy for an e- to jump into the conduction band if the T is high enough.

• Once there, it’s free to move along the entire solid.

• This freedom of movement explains high thermal and electrical conductivity.

V. Importance of the Band Gap

• The band gap determines whether the material is a conductor, semiconductor, or insulator.

V. Doped Semiconductors

• Si has a fairly large band gap, so only a few e-’s are promoted to the conduction band at room T; thus, it is a poor electrical conductor.

• We can add a small amount of a different element to improve it’s conductivity.

• This process is called doping.

V. n-Type Semiconductors

• If we add some P to Si, it brings an extra valence e-.

• This extra e- must go into the conduction band because the valence band is full.

• This doped Si now conducts well. • Called n-type because have electrons

as negative charge carriers.

V. p-Type Semiconductors • We could also add Ga to Si to increase

the conductivity. • Ga has one less e-, so it creates holes

(empty MO’s) in the valence band. • Since e-’s can now move from hole to

hole, this doped Si is a better conductor. • Called p-type because each hole acts

as a positive charge that moves in the opposite direction of the e-’s.