Characteristics of Solids The Classification of Solids Preferred for characterization of structure and properties Polycrystalline Powder (Highly crystalline) Electrons in Solids Used for characterization when single crystal ean not be easily obtained, preferred for industrial production and nd Theory Polycrystalline Powder Large Surface Area) Desirable for further reactivity and certain applications such catalysis and electrode materials Semiconducto Amorphous(Glass) No long range translationalorder Thin Film widespread use in microelectronics, telecommunications, 18, coatings, etc. Molecular solid Covalent Types of Crystals According to the ionic bonding in solids (a)ion crystalNaCD olid state Ar crystal(H, BO (mixed bond crystals(graphite) Bo Bonding onding aPrimary bonds-strong attractions between atoms ovalent donic- Metal ion(+)& Nonmetallic ion H) Covalent- local sharing of electrons between atoms MEtallic- global sharing of electrons by all atoms Secondary bonds-attraction forces between
1 Characteristics of Solids Bonding Electrons in Solids Band Theory Defects Semiconductor Classification of Solids There are several forms solid state materials can adapt ßSingle Crystal -Preferred for characterization of structure and properties. ßPolycrystalline Powder (Highly crystalline) -Used for characterization when single crystal can not be easily obtained, preferred for industrial production and certain applications. ßPolycrystalline Powder (Large Surface Area) -Desirable for further reactivity and certain applications such as catalysis and electrode materials ßAmorphous (Glass) -No long range translationalorder. ßThin Film -Widespread use in microelectronics, telecommunications, optical applications, coatings, etc. Molecular solid Ionic Covalent Metallic Types of Crystals (a)ion crystal(NaCl) (b)metallic crystal (c)covalent crystal(InSb) (d)molecule crystal (solid state Ar) (e)hydrogen bond crystal(H3BO3 ) (f)mixed bond crystals (graphite) According to the ionic bonding in solids Bonding Electrons transfer between atoms Between many atoms Electrons sharing two atoms Bonding Primary bonds ¾ strong attractions between atoms Ionic ¾ Metal ion(+) & Nonmetallic ion (-) Covalent ¾ local sharing of electrons between atoms Metallic ¾ global sharing of electrons by all atoms Secondary bonds ¾ attraction forces between molecules
Primary Bonding Solid State- Strength TThe strength of the solid depends on the molecular forces that hold the solid together monic interactions are strong because the opposite charges resist breaking of the intermolecular bonds. For I example, the melting temperature of salts is very high Covalent typically400to800°C a Some molecular interactions are strong because of the 3 ngement of the atoms. For example, diamonds ar atoms. The bonds are molecular not ion Metallic Types of Non Bonded (intermolecular, van der waals)Interactions Ion-dipole interactions Dipole-dipole lon-dipole Induced dipole Dispersion Hydroger When polar molecules e er ions he positive end of the dipole is attracted to negative ions and vice versa. hen two polar molecules with net dipoles 甲 es to be present, one to provide ions &HH closer, one end of the dipole in one lin the second molecule than ion ion interactions in io Q o (b). These forces decrease with distance as Dispersion or London forces In non-polar molecules, electrons are distributed Noble gases are atomic gases and do not have dipole metrically. This symmetry can be distorted by an liquefied suggests that forces of attraction exist between These forces are weak and are of short range. atoms of a noble gas. These forces are called Dispersio cThe distribution of electrons in an atom/ molecule uctuate over time. These fluctuations set up temporary forces. These forces exist between all atoms and molecules electrons in atoms/molecules. "Dispersion force ncre group. Thus, forr down a g ases, dispersion forces ase as Xe> Kr> Ar> Ne He
2 Primary Bonding e + Na+ e e e e e e e e e e + e e e e e e e e e F- Ionic + + e e Covalent e + + + + + + + + + e e e e e e e e Metallic Solid State ¾ Strength The strength of the solid depends on the molecular forces that hold the solid together. Ionic interactions are strong because the opposite charges resist breaking of the intermolecular bonds. For example, the melting temperature of salts is very high, typically 400 to 800°C. Some molecular interactions are strong because of the 3- D arrangement of the atoms. For example, diamonds are exceptionally hard because the solid state forms, a 3-D network such that each carbon is held close to 4 other atoms. The bonds are molecular, not ionic. Types of Non-Bonded (intermolecular, van der Waals) Interactions Dipole-dipole Ion-dipole Induced dipole Dispersion or London Hydrogen bonding H Cl + - H + Cl - Dipole-dipole interactions: when two polar molecules with net dipoles come closer, one end of the dipole in one molecule will be attracted to the opposite end in the second molecule. (a). These forces are strong, but are weaker than ion-ion interactions in ionic compounds. (b). These forces decrease with distance as 3 r 1 Ion-dipole interactions: When polar molecules encounter ions, the positive end of the dipole is attracted to negative ions and vice versa. The ion-dipole interactions require two species to be present, one to provide ions and another to provide dipoles. O H H d+ d+ d- Na+ ClInduced dipole interactions: In non-polar molecules, electrons are distributed symmetrically. This symmetry can be distorted by an ion/dipole, by inducing dipole in non-polar molecule. These forces are weak and are of short range. e e e e e e + e e e e e e + e e Dispersion or London forces: Noble gases are atomic gases and do not have dipole moments or net charges. The fact that they can be liquefied suggests that forces of attraction exist between atoms of a noble gas. These forces are called Dispersion or London forces. The distribution of electrons in an atom/molecule fluctuate over time. These fluctuations set up temporary dipoles which induce dipoles in others. The attraction between temporary dipoles is responsible for dispersion forces. These forces exist between all atoms and molecules. Strength of dispersion forces increases with number of electrons in atoms/molecules. “Dispersion force increases down a group”. Thus, for rare gases, dispersion forces increase as Xe > Kr > Ar > Ne > He
Types of Non- Bonded Interactions Interaction "ion Interaction A hydrogen atom covalently bonded to N, O, or F is attracted to the lone pair of a different atom nearby H-bonding rming a hydrogen bond. 2k/mol Dispersion/London ydrogen bonding is stronger than any other non- bonds/interaction, yet weaker than covalent Induced dipole Hydrogen bonding Hydrogen bond o covalent HF(g) covalent Hydrogen bonding Variation of ionic radii with Some general trends for Ionic radii Coordination Number 1. lonic radii increase on going down a group (Lanthanide contraction restricts the increase of heavy 2. Radii of equal charge ions decrease across a period 3. lonic radii increase with increasing coordination lumber (the higher its CN the bigger the ions seems to The radius of one ion has to be 4. The ionic radius of a given atom decreases with fixed to a reasonable value increasing charge(r(Fe2+)>rFe3+)) (O2)=1.40A→ Linus 5. Cations are usually the smaller ions in a cation/anion That value is then combination(exceptions: r(Cs*)>r(F).1 compile a set of self 6. Frequently used for rationalization of structures nt values for all other oolA rcation)/r(anion)(< 1) 81012 Ion bond and Ion Crystal ome Properties of lonic Crystals Some Properties of lon Crystal rElative stable and hard crystals Lattice energy of ion crystal Poor electrical conductors (lack of free electrons) Ionic radii in crystals High melting and vaporization temperatures ← Pauling' s Rule Transparent to visible light but absorb strongly on bonds with part covalent bond infrared light n water and polar liquids
3 Hydrogen bonding: A hydrogen atom covalently bonded to N, O, or F is attracted to the lone pair of a different atom nearby forming a hydrogen bond. Hydrogen bonding is stronger than any other nonbonded interaction, yet weaker than covalent bonds/ionic bonds O H H .. H O H Hydrogen bond Types of Non-Bonded Interactions Interaction Energy Ion-ion interaction ~250 kJ/mol H-bonding ~20 kJ/mol Ion-dipole Dipole-dipole ~2 kJ/mol Dispersion/London <2 kJ/mol Induced dipole Examples: Compound/element Type Dominant Interaction NaH ionic Ion-ion ClBr covalent Dipole-dipole Rn noble gas Dispersion NH3 covalent Hydrogen bonding NH4Cl ionic Ion-ion HBr(g) covalent Dipole-dipole HF(g) covalent Hydrogen bonding Variation of Ionic Radii With Coordination Number The radius of one ion has to be fixed to a reasonable value (r(O2- ) = 1.40Å) ® Linus Pauling. That value is then used to compile a set of self consistent values for all other ions. 1. Ionic radii increase on going down a group. (Lanthanide contraction restricts the increase of heavy ions !!) 2. Radii of equal charge ions decrease across a period 3. Ionic radii increase with increasing coordination number (the higher its CN the bigger the ions seems to be !!) 4. The ionic radius of a given atom decreases with increasing charge (r(Fe2+) > r(Fe3+)) 5. Cations are usually the smaller ions in a cation/anion combination (exceptions: r(Cs+) > r(F- ) ...!!!) 6. Frequently used for rationalization of structures: “radius ratio” r(cation)/r(anion) (< 1) Some General Trends for Ionic Radii Ion Bond and Ion Crystal Some Properties of Ion Crystal Lattice energy of ion crystals Ionic radii in crystals Pauling’s Rules Ion bonds with part covalent bond Some Properties of Ionic Crystals Relative stable and hard crystals Poor electrical conductors (lack of free electrons) High melting and vaporization temperatures Transparent to visible light but absorb strongly infrared light Soluble in water and polar liquids!
Lattice Enthalpy Equilibrium Distance Cohesive Energy AH is the standa molar enthalpy change for the following proces Mtas+Xgas→Ma △H<0 - otal derations are neglected the most stable crystal structure of a given compound is the Lattice Energy(U)of Ionic Compounds emble one mole of a crystalline ionic compound nto free ZTe 1 ZTe Bohr-Madelung equation LAttice Energy of lonic Compounds: Bohr-Madelung Z+z-e- equation ANZ'Z'e Find B and n at equilibrium. dE N=6.02x10=moh cThe Madelung constant endent of the ionic charges 0→B=2ze2 elf know the crystal structure, you can choose a suitable ladelung constant, and the distance between the ions r you can estimate the lattice energy of ion compoun Total energy at ro Azel To What is n? Compressibility= zns (wurtzite) 2ns (ine blende) igg Applications of lattice Enthalpy The Kapustinskii Equation Calculations Kapustinskii noticed that A/v, is almost athermal stabilities of ionic solids constant for all structures v is the number of ions in the formula unit stabilities of oxidation states of cations r=r+r, unit.pm Solubility of salts in water Variation in A /v with structure is partially calculations of electron affinity data canceled by change in ionic radii with coordination number stabilities of "non existent 125200uZZ,34.5
4 Two definitions: The lattice enthalpy change is the standard molar enthalpy change for the following process: M+ (gas) + X- (gas) ® MX(solid) If entropy considerations are neglected the most stable crystal structure of a given compound is the one with the highest lattice enthalpy. Lattice Energy (U) of Ionic Compounds: disassemble one mole of a crystalline ionic compound at 0K into free components o DHL H 0 o D L < Lattice Enthalpy o U = -DHL Equilibrium Distance & Cohesive Energy ) n 1 (1 r Z Z e E E E 0 2 attractive repulsive = - - = + + - Ep r n r B r Z Z e + - 2 - total At equilibrium: (Erepulsive) (Eattractive) 0 2 attractive r Z Z e E + - = - Find B and n at equilibrium: repulsive n r B E = n 2 Total attractive repulsive r B r Z Z e E = E + E = - + + - 0 dr dE Total = 0 r = r n 1 0 2 n 1 0 2 0 2 r n Z Z e 0 B r nB r Z Z e - + - + + - Þ - + = Þ = Total energy at r0 : ) n 1 (1 r Z Z e E 0 2 r r0 = - - + - = What is n? Compressibility Þ n » 9 Bohr-Madelung equation Lattice Energy of Ionic Compounds: Bohr-Madelung equation： N = 6.02x1023 mol-1 The Madelung constantis independent of the ionic charges and the lattice dimensions, but is only valid for one specific structure type If know the crystal structure, you can choose a suitable Madelung constant, and the distance between the ions ro , you can estimate the lattice energy of ion compound. ) n 1 (1 r ANZ Z e U 0 2 = - + - Structure Type Madelung Constant CsCl 1.763 NaCl 1.748 ZnS (Wurtzite) 1.641 ZnS (Zinc Blende) 1.638 thermal stabilities of ionic solids stabilities of oxidation states of cations solubility of salts in water calculations of electron affinity data stabilities of “non existent”compounds Applications of Lattice Enthalpy Calculations The Kapustinskii Equation Kapustinskii noticed that A /n, is almost constant for all structures νis the number of ions in the formula unit ro = r++r-, unit: pm Variation in A /n with structure is partially canceled by change in ionic radii with coordination number ) r 34.5 (1 r 125200 Z Z U 0 0 - u = + -
BONDS Coord. No Length(A Limiting and Optimal radius Ratios for Specific Coordinations 464666 ot"in touch in touch Notes: alon radii for given element increase with coordination Ion radii for given element decrease with increasing oxidation state/positive charge Anions often bigger thancations Radius ratio rules fr Rationalization for octahedral "rattle inside the octahedral site coordination: R= radius of large alf r/R>0.414, the anions are pushed apart ion. Gradius of small ion Coordination Minimum r/R Linear. 2 R+r-c0s45= Trigonal 3 Tetrahedral, 4 0.225 √ER=R+r Octahedral. 6 0.414 Cubic. 8 0.732 Close packed, 12 1.000 A simple prediction tool, but beware- it doesn't always work us Rati ZnS 4:4 miting Radius Ratios anions in the coordination polyhedron of cation are in contact with the cation d with each other Radius ratio Coordination lary (AB) agenda 2 body diagonal a rA/=1 1>x+h。>0732 073>r/>044 0414>r/E>025 篱 七/·3-1.1 0.414 0225
5 BONDS Coord. No. Length (Å) C-O 3 1.32 Si-O 4 1.66 Si-O 6 1.80 G e-O 4 1.79 G e-O 6 1.94 SnI V -O 6 2.09 PbI V -O 6 2.18 PbII -O 6 2.59 Notes: Ion radii for given element increase with coordination number (CN) Ion radii for given element decrease with increasing oxidation state/positive charge Radii increase going down a group Anions often bigger thancations not “in touch” in touch Limiting and Optimal Radius Ratios for Specific Coordinations Radius Ratio Rules Rationalization for octahedral coordination: R= radius of large ion, r=radius of small ion 0.414 R r ( 2 1)R r 2R R r 2 1 cos45 R r R Þ = Þ - = Þ = + = = + o If r/R < 0.414, the cation is too small and can “rattle”inside the octahedral site If r/R > 0.414, the anions are pushed apart If r/R £ or ³ 0.414, coordination changes: Coordination Minimum r/R Linear, 2 - Trigonal, 3 0.155 Tetrahedral, 4 0.225 Octahedral, 6 0.414 Cubic, 8 0.732 Close packed, 12 1.000 A simple prediction tool, but beware ¾ it doesn’t always work! Limiting Radius Ratios - anions in the coordination polyhedron of cation are in contact with the cation and with each other Radius Ratio Coordination no. Binary (AB) Structure-type r+/r- = 1 12 none known 1 > r+/r- > 0.732 8 CsCl 0.732 > r+/r- > 0.414 6 NaCl 0.414 > r+/r- > 0.225 4 ZnS