Chapter #16 Liquids and Solids 16.1) Intermolecular Forces 16.2) The Liquid State 16.3) An Introduction to Structures and Types of Solids 16.4) Structure and Bonding of Metals 16.5) Carbon and Silicon: Network Atomic Solids 16.6) Molecular Solids 16.7) Ionic Solids 16.8) Structures of Actual Ionic Solids 16.9) Lattice Defects 16.10) Vapor Pressure and Changes of State 16.11) Phase Diagrams What happens when substances freeze into solids? Less thermal energy available Less motion of the molecules More ordered spatial properties Crystals (or Glasses) 1
Properties of Crystals Unit Cell: The smallest repeating unit needed to describe the complete extended structure of a crystal (through repetition and translation). Some Common Crystal Lattices Figure 16.9 2
How do we know what crystals look like? x-ray diffraction Figure 16.10 Why x-rays? To satisfy the diffraction conditions, the wavelength of light needs to be comparable to the unit cell dimensions Ångstroms (10-10 meters) Diffraction Conditions Figure 16.11 From trigonometry: nl = 2d sinq Key Point: Typical interatomic and intermolecular distances are d 1.0 to 20Å Typical x-ray wavelengths are l 0.01 to 10Å 3
The X-ray Diffraction Experiment Crystal structure Molecular structure 3 Types of Crystalline Solids Atomic Solids e.g. all metals, Si, Carbon (diamond, graphite) Ionic Solids e.g. salts like NaCl Molecular Solids e.g. protein crystals, sucrose Figure 16.12 4
Crystal structure Physical properties of crystals Bonding forces Physical Properties melting point mechanical strength electrical properties Example: Copper and Diamond are both atomic solids, but they have very different physical properties: Copper: very soft, lower melting point (1083 C), excellent conductor Diamond: hardest known substance, higher m.p. (3500 C), insulator The BIG Picture/A Summary 5
Rank by energy 7/3/2012 Recalling Intra/Inter-molecular Forces Structure and Bonding in Metals Metals in solids can be treated as hard spheres that (usually) pack in a way to minimize the empty space between spheres. This is called closest packing. Two distinct structures can be formed by closest packing of atomsa cubic structure and a hexagonal structure Cubic: x = y = z All unit cell angles = 90 Hexagonal: x = y z some unit cell angles 90 (60 or 120 instead) 6
Cubic Closest Packed Structure (ccp) Figure 16.13 Figure 16.15 Face Centered Cubic (fcc) Hexagonal Closest Packed Structure Figure 16.13 Figure 16.14 Hexagonal Prism (hcp) 7
Close-packing of equal spheres (Wikipedia) Top-down Top-down Front/Corner Top and Front Top and Corner Both fcc and hcp have the same number of nearest neighbor interactions = 12 Figure 16.16 8
How many atoms are in the fcc unit cell? 6(atoms on faces) + 8(atoms on corners) = 6(1/2) + 8(1/8) = 3 + 1 = 4 Figure 16.17 Some Common Crystal Lattices Figure 16.9 9
How many atoms are in: Simple cubic unit cell? Body-centered cubic unit cell? 8 atoms in corners 8(1/8) = 1 8 atoms in corners + 1 atom 8(1/8) +1 = 2 Packing Efficiency The fraction of the volume (often expressed as %) of the unit cell that is occupied by atoms, ions, or molecules PE = f v = volume of space occupied by particles volume of unit cell Example: the face centered cubic unit cell PE = f v = (#atoms in unit cell)(volume of atom) (edge of cubic unit cell) 3 (4)(4/3 pr 3 ) = e 3 e 10
Example (cont d): the face centered cubic unit cell e 4r e e e So, PE = f v = (4)(4/3 pr3 ) e 3 e 2 + e 2 = (4r) 2 e = r 8 = 0.74 or 74% for the face centered cubic unit cell Cubic Crystal Lattices PE = 52% 6 nearest neighbors PE = 68% 8 nearest neighbors Figure 16.9 PE = 74% 12 nearest neighbors 11
Determining Atomic Radius from a Crystal Structure Problem: Barium it has a body-centered cubic unit cell and a density of 3.62g/cm 3. What is the atomic radius of barium? Plan: Since an atom is spherical, we can find its radius from its volume. 1. From the density (mass/volume) and the molar mass (mass/mole), we find the molar volume of Ba metal. 2. Since it crystallizes in the body-centered cubic structure, 68% of this volume is occupied by Ba atoms, and the rest is empty. 3. Dividing by Avogadro s number gives the volume of one Ba atom, from which we determine the atomic radius. 4. Volume of a sphere is V = 4/3 pr 3 Solution: 1 Volume/mole of Ba metal = = density MM 1 cm 3 137.3 g Ba 3.62 g Ba 1 mol Ba = 37.9 cm 3 /mol Ba Volume/mole of Ba atoms = (volume/mol Ba) * (packing efficiency) = 37.9 cm 3 / mol Ba * 0.68 = 26 cm 3 /mol Ba atoms 26 cm Volume/Ba atom = 3 1 mol Ba atoms * 1 mol Ba atoms 6.022 x 10 23 Ba atoms = 4.3 x 10-23 cm 3 /Ba atom Finding the atomic radius of Ba from the volume of a sphere: V of Ba atom = 4/3pr 3 and r 3 = 3V 4p 3 3V 3 3(4.3 x 10 r = = - 23 cm 3 ) = 2.17 x 10-8 cm = 2.17Å 4p 4 x 3.14159 12
Properties of metals Conductivity, malleability and ductility are all a result of the bonding forces between particles being strong and non-directional It is difficult to separate metal atoms, but fairly easy to move them as long as they stay in contact. MO theory helps explain this. Each atom brings its own set of orbitals, the varying energy levels of each set combine to make bands of filled and empty orbitals As a result, there are large numbers of highly mobile electrons they move from filled orbitals to empty ones. Metallic Bond: Cations in a Sea of Electrons Group 1A Metals (Li, Na, K etc.) Group 2A Metals (Be, Mg, Ca etc.) 13
ENERGY BANDS IN SOLIDS Band theory MO theory applied to solid crystals (nearly infinite groups of atoms). Instead of well-separated bonding, nonbonding, and antibonding MOs, a large group of close-packed atoms has very closely spaced orbitals: a lower-energy valence band of filled MOs and a higher-energy conduction band of empty MOs. Metals have no band gap (energy separation) between the valence and conduction bands. Nonmetals and most compounds have a large band gap. Metalloids (semiconductors) have a small band gap. Metalloid elements are B, Si, Ge, As, Sb, and Te (along periodic-table metalnonmetal line). Orbital energy levels 14
Easily movable ( conduction band ) Localized at atom ENERGY BANDS IN SOLIDS Electrical conductivity (e movement across a crystal lattice) requires excitation of a few e to mostly empty orbitals (the conduction band). Because of the different-sized band gaps, this occurs easily in metals, to some extent in metalloids, and not at all in nonmetals and most compounds. Conductivity of metals decreases with increasing T because atomic motion slows down the cross-lattice electron movement. Conductivity of metalloids increases with increasing T because higher T provides more excitation energy. You can make an e - jump to the conduction band by giving it energy. One way is for it to absorb light E photon = hn= hc/l In a laser: electrons jump down from the conductance band to emit a photon of light with E=hn 15
CLOSE PACKING: METALS In alloys, some atoms of another element fit into closepacked lattice of a metal. Types: o substitutional: where two metal atoms have similar r atomic, one can simply replace the other; strengthens metal by adding bond polarity. Example: brass = 1/3 Zn, 2/3 Cu o interstitial: element with small r atomic can fit into metallattice holes; strengthens metal by adding new elementmetal bonds Example: in steel, n C = 1 6% n Fe Examples of Metal Alloys Crystals formed by different atoms or ions; Contains a mixture of elements and has metallic properties 16
Chapter #16 Liquids and Solids 16.1) Intermolecular Forces 16.2) The Liquid State 16.3) An Introduction to Structures and Types of Solids 16.4) Structure and Bonding of Metals 16.5) Carbon and Silicon: Network Atomic Solids 16.6) Molecular Solids 16.7) Ionic Solids 16.8) Structures of Actual Ionic Solids 16.9) Lattice Defects 16.10) Vapor Pressure and Changes of State 16.11) Phase Diagrams Network Atomic Solids Unlike metals, network atomic solids contain strong covalent bonds. These solids tend to be brittle and relatively non-conductive (heat and electricity). Representative elements for these types of solids are: carbon and silicon. 17
Network Solids: Carbon Network solid: not close-packed. Each atom s environment is determined instead by covalentbond geometry (think VSEPR ). Carbon occurs in three different atomic forms (allotropes): Diamond Graphite Fullerenes (molecular solid) Diamond One giant molecule: web of C C single bonds, one connecting each pair of C atoms, tetrahedral, sp 3 C Hardest natural substance; must break bonds to deform mp = 4,440 C; secondhighest-melting natural substance Graphite Planar sheets of fused hexagonal rings, sp 2 C Sheets held together by delocalized p bonds (conducts electricity along sheets); Soft mp = 4,492 C; highestmelting natural substance 18
Fig. 16.26 Atomic Networks (Typical metal) Fig. 16.27 Graphite consists of layers of carbon atoms 19
p-electron System in Graphite Fig. 16.28 Network Solids: Silicon Silicon is to geology what carbon is to biology Silicon is right below carbon on the periodic table So why is SiO 2 so different from CO 2? SiO 2 at room temperature CO 2 at room temperature Si is too big to form strong p bonds to oxygen no double bonds as in CO 2 20
Si O Bond Network in Quartz Ring structures Tetrahedral geometry Examples of silicate anions, all of which are based on SiO 4 4- tetrahedra 21
Two-dimensional representations of (a) a quartz crystal and (b) a quartz glass When silica is heated above melting and then cooled rapidly, the result is a glass cooled too quickly for regular crystalline patterns to form. soda-lime aluminosilicate borosilicate optical 22
Ceramic another siliconbased substance Ceramics are made of clays fired at high temperatures. They are brittle, non-metallic materials that consist of minute crystals of silicates suspended in a glassy cement. Unlike regular glass, ceramic cannot be melted and remelted. Silicon - continued Elemental silicon has the same structure as diamond, but the gap between filled and empty MOs is smaller in silicon: Diamond Silicon The smaller band gap means some electrons can cross the gap silicon is a semiconductor. 23
Semiconductors Pure semiconductors allow only a few electrons to cross the band gap, BUT they can be doped with other elements to create greater or fewer valence electrons available for movement More electrons: n-type Fewer electrons: p-type n-type: conductivity is increased by doping it with elements that have more valence electrons than the host crystal. For example, silicon doped with arsenic (1 more e - ) p-type: conductivity is increased by doping it with elements that have less valence electrons than the host crystal, creating a hole. For example, silicon doped with boron (1 less e - ) 24
Semiconductors n-dopant (electron rich, like arsenic) p-dopant (electron deficient, like boron) Semiconductors Why are n-type and p-type semiconductors useful? When you put one of each together, you get a p-n junction. When is a p-n junction useful? Only in those rare circumstances when you want to plug something into an AC outlet in the wall! p-n junctions are used in rectifiers to convert AC to DC They also form the building blocks of diodes, transistors, solar cells, LEDs and integrated circuits. 25
p-n junction good rectifier (converts AC to DC) Charge buildup on p = contact potential; prevents further migration Reverse bias = no current flow through system Forward bias = current flows easily Chapter #16 Liquids and Solids 16.1) Intermolecular Forces 16.2) The Liquid State 16.3) An Introduction to Structures and Types of Solids 16.4) Structure and Bonding of Metals 16.5) Carbon and Silicon: Network Atomic Solids 16.6) Molecular Solids 16.7) Ionic Solids 16.8) Structures of Actual Ionic Solids 16.9) Lattice Defects 16.10) Vapor Pressure and Changes of State 16.11) Phase Diagrams 26
Other types of solids While metals and networked solids can be thought of often as one giant molecule, a few other types of solids also exist Molecular solids: covalently-bonded molecules occupy the lattice positions held together in the solid state by intermolecular forces Examples: ice, sulfur (S 8 ), and white phosphorous (P 4 ) Molecular Solids The same intermolecular forces at work in liquids exist in solids: London dispersion forces are fairly weak in nonpolar molecules (like CO 2, I 2, P 4, S 8 ), but increased molecular weights causes many to be solids at room temperature Polar molecules have greater intermolecular forces (especially when H-bonding is possible) These intermolecular forces are still not as strong as the covalent bonds that hold each molecule together as discrete units. 27
Other types of solids Ionic solids: stable, high-melting substances held together by strong electrostatic forces between oppositely charged ions Examples: salt (NaCl), zinc sulfide (ZnS), calcium fluoride (CaF 2 ) 28
IONIC CRYSTALS Ionic solid: array of B ions (not quite close-packed), with A ions in a fraction of the holes between the B s. A is usually (not always) the + ion and B the ion, since + ions are normally smaller than ions. Example: the two types of holes in a ccp/fcc array of B ions. Octahedral holes: total of 6 holes around each B ion, each shared with 5 other B ions net of 1 hole per B (or 1 hole/cps) Tetrahedral holes: total of 8 holes around each B ion, each shared with 3 other B ions net of 2 holes per B (or 2 holes /cps) Think: Pack basketballs in a container, then fill holes with smaller balls One type of hole has 6 basketballs around it (oct), one has 4 (tet) Whether the holes are occupied depends on the relative sizes of the anions and cations Ionic Solids (NaCl) 29
The locations of the octahedral holes (gray x) in the face-centered cubic unit cell Tetrahedral Holes (a) The location (x) of a tetrahedral hole in the face centered cubic unit cell (b) One of the tetrahedral holes 30
Tetrahedral Holes (c) The unit cell for ZnS, S 2- are closest packed, Zn 2+ fill alternate tetrahedral holes (half the tetrahedral holes are filled) (d) The unit cell for CaF 2, Ca 2+ are closest packed, F fill tetrahedral holes (all of the tetrahedral holes are filled) Tetrahedral and Octahedral Holes in a Single Face-Centered-Cubic Lattice 31
SOLIDS AND LIQUIDS BY BOND TYPE In solids and liquids, many atoms, molecules, or ion pairs join together. Properties depend on bond type. Ionic Compounds. Nearly always solids at room T, with: no discrete molecules, just alternating + and ions; each ion surrounded by as many of opposite charge as fit. Example: NaCl. Na + and Cl alternate This non-directional close packing occurs because electrical force is equal in all directions outward from an ion s center. SOLIDS AND LIQUIDS BY BOND TYPE Covalent Substances (some elements, some compounds). Can be solids, liquids, or gases at room T. 3 types of solids/liquids: Molecular: Electrons held tightly within individual molecules. Weak forces, large distances between usually close-packed molecules. Examples: CO 2, HCl, H 2, Ne. For the noble gases such as Ne, the molecule is a single atom. Metallic: Sea of valence e delocalized over (shared equally among) close-packed nuclei. Examples: Mg, Cu. Network: All atoms interconnected by limitless web of strong bonds, each localized between two atoms. Not close-packed; specific e -group geometry around each atom. Whole crystal is one giant molecule. Examples: C(diamond), SiO 2 (quartz, sand). 32
BOND TYPE AND PHYSICAL PROPERTIES Structure 1 Molecular substances melt at < 200 o C. Other substances melt at 300 4000 o C, except certain metals: Column I, Ga, In, and Hg [ 40 (Hg) to +180 o C (Li)]. 2 C graphite and metalloids (B, Si, Ge, As, Sb, Te) conduct electricity slightly. Room-T Phase MP/BP 1 Conduct Electricity? Mechanical Properties Molecular g, l, or s Low No Soft Network s Highest No 2 Hard/Brittle Metallic l or s Low High s, l 2 Soft Hard/ Workable Ionic s High l,aq Hard/Brittle BOND TYPE AND PHYSICAL PROPERTIES Element Bond Type MP ( C) S 8 Purely Covalent (Molecular) 113 Si Purely Covalent (Network) 1,414 Fe Metallic 1,538 Na Metallic 98 Oxide Bond Type MP ( C) SO 2 Polar Covalent (Molecular) 76 SiO 2 Polar Covalent (Network) 1,713 Fe 2 O 3 Polar Covalent (Network) 1,565 Na 2 O Ionic 1,132 33