SOLID STATES Most solids can be divided into two types: Crystalline solids are made of repetitive units, and sometimes these features are visible on the macroscopic scale. Example: salt crystals, snow, gemstones. Amorphous solids don’t have well-defined 3-D unit structure. Examples are plastic polymers, glass. The strength of any solid depends on the molecular forces that hold the solid together, 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 CO 2 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 so Why are these solids so weak, brittle, and have 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 melting points? Why are some metals so incredibly strong, with high 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 liquid is conducting? do you remember why these 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 conducting…? Why are these hard, with high MP, but not conducting…?

COVALENT NETWORK SOLIDS… Quartz and quartz glass… SiO 2

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 repeating pattern that repeats throughout the crystal or crystal lattice 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 lattice The crystal lattice is the collection of all of the unit cells - This is the large, macroscopic crystal your eye sees The crystal lattice is the collection of all of the unit cells - This is the large, macroscopic crystal your eye sees 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 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.

Types of each unit cell shapes in crystal systems… Cubic - NaCl, Cu Cubic - NaCl, Cu Tetragonal - TiO 2 (rutile), Sn Tetragonal - TiO 2 (rutile), Sn Orthorhombic - CaCO 3 (argonite), BaSO 4 Orthorhombic - CaCO 3 (argonite), BaSO 4 Monoclinic - PbCrO 4 Monoclinic - PbCrO 4 Hexagonal - C (graphite), ZnO Hexagonal - C (graphite), ZnO Rhombohedral - CaCO 3 (calcite), HgS Rhombohedral - CaCO 3 (calcite), HgS Triclinic - Cinnabar Triclinic - Cinnabar

All four types of basic solids can form these seven crystal systems….. All four types of basic solids can form these seven crystal systems….. Which do you think is the most common, and the most symmetrical, and the most stable of the seven crystal systems? Which do you think is the most common, and the most symmetrical, and the most stable of the seven crystal systems? The cubic unit cell! The cubic unit cell! Let’s examine the cubic unit cell in more detail - there are actually three types of cubic unit cell! Let’s examine the cubic unit cell in more detail - there are actually three types of cubic unit cell!

Cubic Unit Cells….. There are three possible cubic unit cells: There are three possible cubic unit cells:  Simple cubic unit cell - lattice points are at the corners  Body-centered cubic unit cell - lattice point at center of cell as well as corners  Face-centered cubic unit cell - lattice points at center of each face and in the corners

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 unit cell is occupied by 1/8 of an atom The coordination number is the number of nearest neighbors surrounding an 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 is occupied 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 pm and the density is 19.3g/cm 3. Does elemental tungsten have a face-centered cubic structure or a body centered cubic structure? If face centered: 1 atom W = amu x 1.67 x g = 3.07 x grams 3.07 x grams x 1 cm 3 / 19.3 g = 1.59 x cm x cm 3 x.741 = x cm x cm 3 = 4/3  r 3 = 141 pm If body centered: 1 atom W = amu x 1.67 x g = 3.07 x grams 3.07 x grams x 1 cm 3 / 19.3 g = 1.59 x cm x cm 3 x.68 = x cm x cm 3 = 4/3  r 3 = 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: n  2d sin 

X-Rays with a = 2.63 Angstroms were used to analyze an unknown crystal. The angle of first-order diffraction (n=1) was degrees. What is the spacing between crystal planes, and what would be the angle for second- order diffraction (n=2)? D = 4.9 Angstroms  =

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 formed…..? What would determine the type of cubic unit cell that would be 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 atoms that surround an ion, determines the type of cubic unit cell that will be formed Coordination number, which is the number of oppositely charged atoms that surround an ion, determines the type of cubic unit cell that will be formed This is determined by the charge and size that the atoms have in the compound! This is determined by the charge and size that the atoms have in the compound!

Covalent Network Solids….. Covalent network solids form crystals as well Covalent network solids form crystals as well These crystalline structures are dependent on the direction of the covalent bonds These crystalline structures are dependent on the direction of the covalent bonds Diamond is an example - the carbon bonds give the molecule its shape….what is the molecular geometry of a carbon molecule…..? Diamond is an example - the carbon bonds give the molecule its shape….what is the molecular geometry of a carbon molecule…..? Tetrahedral! Tetrahedral! Graphite contains carbons bonded in a hexagonal ring, much like…… Graphite contains carbons bonded in a hexagonal ring, 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 freely and in all directions! Metallic bonding is non-directional - the electrons flow freely and in all directions! Maximum bonding and attraction can occur when each metal nucleus is surrounded by as many other electrons as possible! Therefore, they pack as tightly into a given space as possible…. Maximum bonding and attraction can occur when each metal nucleus is surrounded by as many other electrons as possible! Therefore, they pack as tightly into a given space as possible…. Metal form both body centered and face centered cubic – giving them either 68% or 74% packing efficiency! Metal form both body centered and face centered cubic – giving them either 68% or 74% packing efficiency! INSTEAD of forming cubic crystals, though, sometimes they can also form what we call layering systems, where they literally layer on top of one another INSTEAD of forming cubic crystals, though, sometimes they can also form what we call layering systems, where they literally layer on top of one another These layering systems are called packing systems These layering systems are called packing systems Metals can also form either cubic or hexagonal close-packed packing systems Metals can also form either cubic or hexagonal close-packed packing 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, aka hexagonal close packed Structure (HCP). This type of packing gives rise to the hexagonal unit cell. It has An ABABAB…. stacking arrangement. Examples are magnesium, titanium, and zinc. This is abcabc, aka cubic close packed Structure (CCP). This type of packing gives rise to the face-centered cubic unit 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 and cations of differing size and charge, as in ionic compounds Crystallization would not be so even and repetitive with anions and 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 above, and the cations fill the empty holes that are left What happens is the anions form packing systems as described above, and the cations fill the empty holes that are left There are three types of holes that cations normally fill in between anions in packing systems There are three types of holes that cations normally fill in between anions in packing systems  Trigonal Holes  Tetrahedral Holes  Octahedral 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 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 the unit cell = 1 whole cation + 12 cations x ¼ cation = 4 cationsThere are four cations within the unit cell, and four anions within the unit cell = 1 whole cation + 12 cations x ¼ cation = 4 cations If all holes were filled, that would yield 4 cations per unit cell If all holes were filled, that would yield 4 cations per unit cell

What is the formula for a compound that exhibits a CCP array of sulfur ions, and contains zinc atoms in 1/8 of the tetrahedral holes, and aluminum atoms in ½ of the octahedral holes? ZnAl 2 S 4

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 X2Y1X2Y1

Molecular solids….. Molecules that are physically bonded to one another by intermolecular bonds, can maximize those intermolecular bonds by getting as close to one another as possible! Molecules that are physically bonded to one another by intermolecular bonds, can maximize those intermolecular bonds 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 maximize the number of physical bonds they can form…. Therefore, they pack as tightly into a given space as possible, to maximize the number of physical bonds they can form…. They like to form either cubic or hexagonal close-packed layers, or these packing systems as well! They like to form either cubic or hexagonal close-packed layers, or these packing systems as well! The strength of these crystals are completely dependent on the closeness of the molecules, and the strength of the physical bonds - the strength is not dependent at all on the strength of the chemical bond - ie) ice The strength of these crystals are completely dependent on the closeness of the molecules, and the strength of the physical bonds - the strength is not dependent at all on the strength of the chemical 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 Semiconduct or

A Schematic of Two Circuits Connected by a Transistor

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