SOLID STATES

Most solids can be divided into two types:

Crystalline solids are made of repetitive units, and sometimes these featuresare visible on the macroscopic scale.Example: salt crystals, snow, gemstones.

Amorphous solids don’t have well-defined 3-D unit structure. Examples areplastic polymers, glass.

The strength of any solid depends on the molecular forces that hold the solidtogether, whether they are:

- Physical or intermolecular forces or bonds

- Chemical or intramolecular forces or bonds

- Which types of solids do you think would be stronger - solids held together with physical bonds, or solids held together with chemical bonds? Can you give examples of each?

REMEMBER - ELEMENTS AND COMPOUNDS CAN CRYSTALLIZE!

4 TYPES OF CRYSTALLINE SOLIDS………Molecular Solids - solids that consist of atoms or molecules held together by intermolecular forces…

The solid is caused by weak physical bonds!

Types: solid neon, solid water and CO2

Metallic Solids - solids that consist of a positive core of atoms held together by a surrounding sea of electrons….

Held together with metallic bonds….

Types: Iron, silver, copper

Ionic Solids - solids that consist of cations and anions held together by the electrical attraction of opposite charges…..

Held together by intramolecular forces….

The solid is caused by chemical ionic bonds!

Types: Cesium chloride, sodium chloride

TYPES OF CRYSTALLINE SOLIDS CONTINUED….

Covalent Network Solids - Solids that consist of atoms held together chemically in large networks or chains by chemical covalent bonds….

Types: diamond, graphite, asbestos, quartz

PROPERTIES OF MOLECULAR SOLIDS….

Low melting point…..Low melting point….. Brittle…..Brittle….. Soft……Soft…… Non-Conducting…..Non-Conducting….. Why are these solids soWhy are these solids so

weak, brittle, and have weak, brittle, and have

such low melting points…?such low melting points…?

MOLECULAR SOLIDS……..

NAMELY, ICE!

PROPERTIES OF METALLIC SOLIDS….

Variable melting point….Variable Hardness….Variable melting point….Variable Hardness…. Malleable - not brittle….Conducts electricity…..Malleable - not brittle….Conducts electricity….. Why are some metals so incredibly strong, with high Why are some metals so incredibly strong, with high

melting points?melting points?

METALLIC SOLIDS……….

PROPERTIES OF IONIC SOLIDS…. High melting point…..High melting point….. Brittle…..Brittle….. Hard……Hard…… Non-conducting solid Non-conducting solid Conducting liquid…..Conducting liquid….. Why is the solid non-Why is the solid non-conducting, but the liquidconducting, but the liquidis conducting?is conducting?do you remember why these do you remember why these Are hard but brittle?Are hard but brittle?

IONIC SOLIDS…..NAMELY, SODIUM CHLORIDE!

PROPERTIES OF COVALENT NETWORK SOLIDS…. Very high melting point….Very high melting point…. Very Hard….Very Hard…. Typically non-conducting…..Typically non-conducting….. Why are these hard, with high MP, but not Why are these hard, with high MP, but not

conducting…?conducting…?

COVALENT NETWORK SOLIDS…

Quartz and quartz glass… SiO2

The diagram shows a ball-and-stick model of a nanotube with carbon atoms in six-membered rings bonded in honeycomb-shaped, cylindrical structures. Nanotubes having strands narrower than a human hair and 10 times stronger than steel were first prepared in 1997.

What is a crystal lattice, in simple terms….?

The crystal lattice is the ordered structure we call a CRYSTAL…..The crystal lattice is the ordered structure we call a CRYSTAL….. One unit of that crystal lattice is called a unit cell - the unit cell is the One unit of that crystal lattice is called a unit cell - the unit cell is the

repeating pattern that repeats throughout the crystal or crystal latticerepeating pattern that repeats throughout the crystal or crystal lattice The crystal lattice is the collection of all of the unit cells - This is the large, The crystal lattice is the collection of all of the unit cells - This is the large,

macroscopic crystal your eye seesmacroscopic crystal your eye sees The frame of reference for each unit cell must be the same - whether it is The frame of reference for each unit cell must be the same - whether it is

the center of an atom, the corner of an atom, etc.the center of an atom, the corner of an atom, etc.

Types of each unit cell shapes in crystal systems…

Cubic - NaCl, CuCubic - NaCl, Cu Tetragonal - TiOTetragonal - TiO22 (rutile), Sn (rutile), Sn

Orthorhombic - CaCOOrthorhombic - CaCO33 (argonite), (argonite),

BaSOBaSO44

Monoclinic - PbCrOMonoclinic - PbCrO44

Hexagonal - C (graphite), ZnOHexagonal - C (graphite), ZnO Rhombohedral - CaCORhombohedral - CaCO33 (calcite), (calcite),

HgSHgS Triclinic - CinnabarTriclinic - Cinnabar

All four types of basic solids can All four types of basic solids can form these seven crystal form these seven crystal systems….. systems…..

Which do you think is the most Which do you think is the most common, and the most common, and the most symmetrical, and the most stable symmetrical, and the most stable of the seven crystal systems?of the seven crystal systems?

The cubic unit cell!The cubic unit cell! Let’s examine the cubic unit cell Let’s examine the cubic unit cell

in more detail - there are actually in more detail - there are actually three types of cubic unit cell!three types of cubic unit cell!

Cubic Unit Cells….. There are three possible There are three possible

cubic unit cells:cubic unit cells: Simple cubic unit Simple cubic unit

cell - lattice points cell - lattice points are at the cornersare at the corners

Body-centered cubic Body-centered cubic unit cell - lattice unit cell - lattice point at center of cell point at center of cell as well as cornersas well as corners

Face-centered cubic Face-centered cubic unit cell - lattice unit cell - lattice points at center of points at center of each face and in the each face and in the cornerscorners

Crystal packing and crystal order

Our lattice point, or frame of reference for our unit cell, is the center of the atom!

Let’s look at some types of cubic unit cells….

This frame of reference will be the same for all unit cells!

SIMPLE CUBIC UNIT CELL

each corner of the unitcell is occupied by 1/8of an atom

The coordination number is the number of nearest neighbors surroundingan atom of interest. Here the coordination number =……… 6

-52% packing efficiency

-What types of substances would form this type of packing efficiency?

-Why is the packing efficiency so poor?

Each unit cell contains….. 1 atom.

BODY-CENTERED CUBIC

1/8 atom at each corner

Coordination number = …

68% packing efficiency1 whole atom at center

8 Each unit cell contains… 2 atoms

each corner of the unit cell isoccupied by 1/8 atom

FACE CENTERED CUBIC…..

• Coordination Number is….?

• 12!

• Each unit cell contains how many atoms…?

• 4 atoms total!

FACE CENTERED CUBIC…..74% packing efficiency - the most efficient of the cubic unit cells….

What kind of substances would give you this type of cubic cell?

The radius of tungsten is 137.2 pm and the The radius of tungsten is 137.2 pm and the density is 19.3g/cmdensity is 19.3g/cm33. Does elemental . Does elemental tungsten have a face-centered cubic tungsten have a face-centered cubic structure or a body centered cubic structure or a body centered cubic structure?structure?

If face centered:

• 1 atom W = 183.84 amu x 1.67 x 10-24g = 3.07 x 10-22 grams• 3.07 x 10-22 grams x 1 cm3/ 19.3 g = 1.59 x 10-23 cm3

• 1.59 x 10-23 cm3 x .741 = 1.1787 x 10-23 cm3

•1.1787 x 10-23 cm3 = 4/3 r3 = 141 pm

If body centered:

•1 atom W = 183.84 amu x 1.67 x 10-24g = 3.07 x 10-22 grams• 3.07 x 10-22 grams x 1 cm3/ 19.3 g = 1.59 x 10-23 cm3

• 1.59 x 10-23 cm3 x .68 = 1.0817 x 10-23 cm3

•1.0817 x 10-23 cm3 = 4/3 r3 = 137 pm

X-rays Scattered from Two Different Atoms may Reinforce (Constructive Interference) or Cancel (Destructive Interference) One Another

How are dimensions of crystals and atoms experimentally determined?

A technique called X-Ray Diffraction is used….Sir W.H. Bragg and his son first developed this still-used technique in 1913…

Reflection of X-rays of Wavelength from a Pair of Atoms in Two Different Layers of Crystal

xy + yz = n

where n is an integer and is the wavelength of the x-rays

Trigonometry shows that:

xy + yz = 2d sin

d is the distance between atoms and is the angle of incidence and reflection

Combining both equations gives us:

n2d sin

X-Rays with a X-Rays with a = 2.63 Angstroms were = 2.63 Angstroms were used to analyze an unknown crystal. used to analyze an unknown crystal. The angle of first-order diffraction The angle of first-order diffraction (n=1) was 15.55 degrees. What is the (n=1) was 15.55 degrees. What is the spacing between crystal planes, and spacing between crystal planes, and what would be the angle for second-what would be the angle for second-order diffraction (n=2)?order diffraction (n=2)?

D = 4.9 Angstroms

= 32.40

Ionic solids….. The majority of ionic solids form your basic 7 types of crystal unit cells!The majority of ionic solids form your basic 7 types of crystal unit cells! The most common is the cubic unit cell!The most common is the cubic unit cell! The positions of both the cations and anions are important!The positions of both the cations and anions are important! What would determine the type of cubic unit cell that would be What would determine the type of cubic unit cell that would be

formed…..?formed…..? We have talked about this in depth before!We have talked about this in depth before! Coordination number, which is the number of oppositely charged Coordination number, which is the number of oppositely charged

atoms that surround an ion, determines the type of cubic unit cell that atoms that surround an ion, determines the type of cubic unit cell that will be formedwill be formed

This is determined by the charge and size that the atoms have in the This is determined by the charge and size that the atoms have in the compound! compound!

Covalent Network Solids….. Covalent network solids form crystals as wellCovalent network solids form crystals as well These crystalline structures are dependent on the direction These crystalline structures are dependent on the direction

of the covalent bondsof the covalent bonds Diamond is an example - the carbon bonds give the Diamond is an example - the carbon bonds give the

molecule its shape….what is the molecular geometry of a molecule its shape….what is the molecular geometry of a carbon molecule…..?carbon molecule…..?

Tetrahedral!Tetrahedral! Graphite contains carbons bonded in a hexagonal ring, Graphite contains carbons bonded in a hexagonal ring,

much like……much like…… Cyclohexane and benzene!Cyclohexane and benzene!

Diamond and Graphite 3-D

Metallic solids….. Ask yourself - why are metals so dense?Ask yourself - why are metals so dense? Metallic bonding is non-directional - the electrons flow Metallic bonding is non-directional - the electrons flow

freely and in all directions!freely and in all directions! Maximum bonding and attraction can occur when each Maximum bonding and attraction can occur when each

metal nucleus is surrounded by as many other electrons as metal nucleus is surrounded by as many other electrons as possible! Therefore, they pack as tightly into a given space possible! Therefore, they pack as tightly into a given space as possible….as possible….

Metal form both body centered and face centered cubic – Metal form both body centered and face centered cubic – giving them either 68% or 74% packing efficiency!giving them either 68% or 74% packing efficiency!

INSTEAD of forming cubic crystals, though, sometimes they INSTEAD of forming cubic crystals, though, sometimes they can also form what we call layering systems, where they can also form what we call layering systems, where they literally layer on top of one anotherliterally layer on top of one another

These layering systems are called packing systemsThese layering systems are called packing systems Metals can also form either cubic or hexagonal close-packed Metals can also form either cubic or hexagonal close-packed

packing systemspacking systems

Three dimensional crystal packing…..

In a molecular solid or metallic solid crystal the unit cells are packed such that interactions are maximized. This is achieved by minimizing the distances between atoms which exhibit attractive forces.

This is ababab, akahexagonal close packedStructure (HCP).This type of packinggives rise to thehexagonal unit cell. It hasAn ABABAB…. stackingarrangement.Examples are magnesium,titanium, and zinc.

This is abcabc, akacubic close packedStructure (CCP).This type of packinggives rise to theface-centered cubicunit cell. It has an ABCABC… stacking Arrangement.Examples are nickel,copper, and lead.

These cubic structures and layering structures only hold true for pure substances….Usually not ionic compounds….

Why……?Why……? Crystallization would not be so even and repetitive with anions Crystallization would not be so even and repetitive with anions

and cations of differing size and charge, as in ionic compoundsand cations of differing size and charge, as in ionic compounds What types of crystals ionic compounds form, then?What types of crystals ionic compounds form, then? What happens is the anions form packing systems as described What happens is the anions form packing systems as described

above, and the cations fill the empty holes that are leftabove, and the cations fill the empty holes that are left There are three types of holes that cations normally fill in There are three types of holes that cations normally fill in

between anions in packing systemsbetween anions in packing systems Trigonal HolesTrigonal Holes Tetrahedral HolesTetrahedral Holes Octahedral holesOctahedral holes

Let’s look at each….Let’s look at each….

The Holes that Exist in packing systems…

Trigonal holes are too small to fill….

Whether tetrahedral or octahedral holes are filled depends on the size difference between the cations and anions

The Location (x) of a Tetrahedral Hole in the Face-Centered Cubic Unit Cell (same as layered packing systems)

• This creates 8 tetrahedral cation holes per unit cell….• There are twice as many tetrahedral holes as packed anions in this unit cell, as the face centered cubic structure has only 4 anions per cell•Since the atoms are completely enclosed in the unit cell, that gives us 8 cations if all 8 holes are filled!

The Locations (gray X) of the Octahedral The Locations (gray X) of the Octahedral Holes in the Face-Centered Cubic Unit Cell Holes in the Face-Centered Cubic Unit Cell

• This creates 13 octahedral cation holes per unit cell….This creates 13 octahedral cation holes per unit cell….• However, the cations aren’t completely within the unit cell…However, the cations aren’t completely within the unit cell…•There are four cations within the unit cell, and four anions within There are four cations within the unit cell, and four anions within the unit cell = 1 whole cation + 12 cations x ¼ cation = 4 cationsthe unit cell = 1 whole cation + 12 cations x ¼ cation = 4 cations• If all holes were filled, that would yield 4 cations per unit cellIf all holes were filled, that would yield 4 cations per unit cell

What is the formula for a compound thatWhat is the formula for a compound that

exhibits a CCP array of sulfur ions, and exhibits a CCP array of sulfur ions, and

contains zinc atoms in 1/8 of the tetrahedral contains zinc atoms in 1/8 of the tetrahedral

holes, and aluminum atoms in ½ of the holes, and aluminum atoms in ½ of the

octahedral holes?octahedral holes?

ZnAl2S4

Given the pictorial of the unit cell to the right, What is the empirical formula of this

compound?

•8 corners x 1/8 anion per corner = 1 anion

•6 faces x ½ anion per face = 3 anions

•8 cations in unit cell = 8

•4 total anions

•8 total cations

X2Y1

Molecular solids….. Molecules that are physically bonded to one another by Molecules that are physically bonded to one another by

intermolecular bonds, can maximize those intermolecular bonds intermolecular bonds, can maximize those intermolecular bonds by getting as close to one another as possible! by getting as close to one another as possible!

These bonds are non-directional…(what does that mean….?)These bonds are non-directional…(what does that mean….?) Therefore, they pack as tightly into a given space as possible, to Therefore, they pack as tightly into a given space as possible, to

maximize the number of physical bonds they can form….maximize the number of physical bonds they can form…. They like to form either cubic or hexagonal close-packed layers, They like to form either cubic or hexagonal close-packed layers,

or these packing systems as well!or these packing systems as well! The strength of these crystals are completely dependent on the The strength of these crystals are completely dependent on the

closeness of the molecules, and the strength of the physical closeness of the molecules, and the strength of the physical bonds - the strength is not dependent at all on the strength of the bonds - the strength is not dependent at all on the strength of the chemical bond - ie) icechemical bond - ie) ice

Partial Representation of the Molecular Orbital Energies in (a) Diamond and (b) a Typical Metal

Energy-Level Diagrams for (a) an N-Type Semiconductor and (b) a P-Type Semiconductor

The P-N Junction Involves the Contact of a P-Type and an N-Type Semiconductor

A Schematic of Two Circuits Connected by a Transistor

The Steps for Forming a Transistor in a Crystal of Initial Pure Silicon