Disorder in crystals Disorder in crystals All lattice

Disorder in crystals Disorder in crystals All lattice

Disorder in crystals Disorder in crystals All lattice points are not always the same. Apatite Ca3(PO4)2 Ca2+ Apatite Ca3(PO4)2

Ca2+ Apatite Ca3(PO4)2 0.98 Apatite Ca3(PO4)2 Ca2+

0.98 Sr2+ 1.12 Apatite Ca3(PO4)2 Ca2+

0.98 Sr2+ 1.12 Group II Be Mg Ca

Sr Ba Ra Group II Be Mg Ca Sr Ba

Ra 2+ in ionic compounds Group II Be Mg Ca Sr Ba

Ra 2+ in ionic compounds Sr 86% of naturally 38 occuring 88

Group II Be Mg Ca Sr Ba Ra 2+ in ionic compounds

Sr 86% of naturally 38 occuring 88 Sr radioactive isotope 38 product of nuclear weapons testing

90 Apatite Ca3(PO4)2 If Sr replaces Ca2+ consistently, the structure changes. 2+

Ca2+ 0.98 Sr2+ 1.12 Apatite Ca3(PO4)2

If Sr replaces Ca2+ consistently, the structure changes. This is not disorder. 2+ Ca2+ 0.98

Sr2+ 1.12 Apatite Ca3(PO4)2 If Sr replaces Some Ca2+ randomly, the structure is disordered. 2+

Ca2+ 0.98 Sr2+ 1.12 If a crystal contains 90% Ca and 10% Sr, each

M2+ site will appear to be Ca/Sr 90/10% based on diffraction data. Defects in Crystals Defects in Crystals Disorder implies that all positions are occupied, but the occupation of some sites may not be consistent.

Defects in Crystals A defect is a break in the infinite lattice. Defects in Crystals A defect is a break in the infinite lattice. Some sites that would normally be occupied in a perfect lattice, are open.

Color center defect - h + ClCl + e- Color center defect - h + ClCl + e-

Cl Cl- 0.99 1.81 The uncharged Cl is not affected by the + charges and is considerably smaller than the Cl-.

The uncharged Cl is not affected by the + charges and is considerably smaller than the Cl-. The Cl can move through, and leave, the lattice. The uncharged Cl is not affected by the + charges and is considerably smaller than the Cl-. The Cl can move through, and leave, the lattice. The

electron can be trapped in the octahedral vacancy left by the Cl-. Anion missing; replaced by e-. Anion missing; replaced by e-. The overall lattice is not disturbed. This does not have to be the same site vacated By the Cl-.

Anion missing; replaced by e-. Anion missing; replaced by e-. Color center defect Color center defect The presence of e- in a void leads to an electronic transition in the visible range.

In a real (as opposed to a perfect) Crystal, a small portion of the sites will be unoccupied. In a real (as opposed to a perfect) Crystal, a small portion of the sites will be unoccupied. This is called a Shottky defect. Perfect

+ - Real Perfect + -

Real Perfect + - In ionic crystals, charges still must balance.

Shottky Defect Shottky Defect: a void that does not disturb the structure. Shottky Defect in metal. Other defects may alter the lattice.

+ - Interstitial site: + - Interstitial site: position between ions or atoms which can be occupied by another

ion or atom. + - Interstitial site: position between ions or atoms which can be occupied by another ion or atom. +

- Move ion from normal site to interstitial site. Frenkel defect: lattice is distorted when an ion is moved to an interstitial site. Defects tend to be dynamic.

Nonstoichiometric Compounds Wstite Wstite FeO =O = Fe

Wstite FeO =O = Fe Wstite +2 -2 FeO

=O = Fe Wstite Fe0.85-0.95O +2 -2 If there is less than 1 Fe per O, FeO Fe must be in more than 1 ox. State. =O = Fe2+, Fe3+

Wstite +2 -2 FeO Fe0.85-0.95O Fe0.85-0.95O Fe0.85O

Fe0.85-0.95O Fe0.85O Fe2+x ; Fe3+0.85-x Fe0.85-0.95O Fe0.85O Fe2+x ; Fe3+0.85-x 2x + 3(0.85-x) = 2 Fe0.85-0.95O

Fe0.85O Fe2+x ; Fe3+0.85-x 2x + 3(0.85-x) = 2 2x + 2.55 3x = 2 Fe0.85-0.95O Fe0.85O Fe2+x ; Fe3+0.85-x 2x + 3(0.85-x) = 2 2x + 2.55 3x = 2

-x = -0.55 Fe0.85-0.95O Fe0.85O Fe2+x ; Fe3+0.85-x 2x + 3(0.85-x) = 2 2x + 2.55 3x = 2 x = 0.55 Fe0.85-0.95O

Fe0.85O (Fe2+0.55, Fe3+0.30 )O Fe2+x ; Fe3+0.85-x 2x + 3(0.85-x) = 2 2x + 2.55 3x = 2 x = 0.55 Fe0.85O

(Fe2+0.55, Fe3+0.30 )O Fe0.95O (Fe2+0.85, Fe3+0.10 )O Thermodynamics of Crystals Na+ Cl-

ionic bond Na+ Account for ionic attractions and repulsions based on the distance of the ions and their charges. -

r + - r +

The energy of this pair depends on coulombic attraction and repulsion. 2 z z e b 1

2 + Ep = - r rn - r +

The energy of this pair depends on coulombic attraction and repulsion. 2 z z e b 1

2 + Ep = - r rn attraction term (decreases energy) - r

+ The energy of this pair depends on coulombic attraction and repulsion. 2 z z e

b 1 2 + Ep = - r rn attraction term Repulsive term (decreases energy) (increases energy)

- r + 2 z z

e b 1 2 + Ep = - r rn z = charge number

- r + 2 z z e

b 1 2 + Ep = - r rn z = charge number e = electron charge

- r + 2 z z e

b 1 2 + Ep = - r rn z = charge number e = electron charge r = internuclear separation

- r + 2 z z

e b 1 2 + Ep = - r rn z = charge number e = electron charge

r = internuclear separation b, n are repulsion constants - r + 2

z z e b 1 2 + Ep = - r rn

z = charge number e = electron charge r = internuclear separation b, n are repulsion* constants * repulsion due to physical contact, not coulombic repulsion 2 z z

e b 1 2 + Ep = - r rn The lattice energy for a mole of NaCl can be evaluated by multiplying

the energy by No and including a factor that accounts for all ion-ion interactions. 2 z z e b 1

2 + Ep = - r rn U = No 2 Az z

e B 1 2 + r rn 2 z

z e b 1 2 + Ep = - r rn U = No

Lattice energy 2 Az z e B 1 2

+ r rn 2 z z e b 1

2 + Ep = - r rn U = No Az1z2e2+ B - r rn

Avagadros number Lattice energy 2 z z e b 1

2 + Ep = - r rn U = No 2 Az z

e B 1 2 + r rn Avagadros number Lattice energy

Madelung constant Repeat S&P pg 80 When an individual ion is considered in a cubic lattice, there is a group of oppositely charged ions at a given distance followed by a group of like charged ions at a longer distance.

If r = a in NaCl then there are 6 Cl- at distance a from Na+. If r = a in NaCl then there are 6 Cl- at distance a from Na+. There are 12 Na+ at a distance of 2 a from the initial Na+. a

a 2 a Madelung constant for NaCl Potential energy for nearest neighbors = -6e2 a Potential energy for next-nearest = 12e2 2 a Madelung constant for NaCl

Potential energy for nearest neighbors = -6e2 a Potential energy for next-nearest = 12e2 2 a e2 a 6 1

+ 12 2 8 3 + ......... Madelung constant for NaCl

Potential energy for nearest neighbors = -6e2 a Potential energy for next-nearest = 12e2 2 a e2 a 6 1

+ 12 2 8 3 + ......... 1.75

U = No Az1z2e2+ B - a an Az1z2e2 n-1 a B=

n U = No Az1z2e2+ B - a an Az1z2e2 n-1 a

B= n U = No 2 Az z e Az1z2e + 1 2

n-1 a - a nan 2 U = No Az1z2e2+ B - a

an Az1z2e2 n-1 a B= n U = No 2 Az

z e Az1z2e + 1 2 n-1 a - a nan 2

Az z e U = -No 1 2 a 2 1

1n 2 Az z e U = -No 1 2 a

1 1n n varies from 9 to 12; it is determined from the compressibility of the material 2 Az z e

U = -No 1 2 a 1 1n Ucalc Uexp kJ/mol

NaCl 770 770 KF 808

803 NaH 845 812 Where do experimental values for U

come from? E E K(g) K+(g) + e-

419 kJ/mol K(g) K+(g) + e- 419 kJ/mol First ionization energy

K(g) Cl(g) + e- K+(g) + e- Cl-(g) 419 kJ/mol First ionization

energy 349 kJ/mol K(g) Cl(g) + e- K+(g) + e- Cl-(g)

419 kJ/mol First ionization energy 349 kJ/mol Electron affinity K(s)

K(g) Hsublimation K(s) Cl2(g) K(g) Hsublimation

Cl(g) Hdissociation K(s) K(g) Cl2(g) K(g) Cl(g) + e-

Hsublimation Cl(g) Hdissociation K+(g) + eCl-(g) 419 kJ/mol 349 kJ/mol K(s)

K(g) Cl2(g) K(g) Hsublimation Cl(g) Hdissociation K+(g) + e-

Cl(g) + eK+(g) + Cl-(g) 419 kJ/mol Cl-(g) 349 kJ/mol KCl(s)

U K+(g) + Cl-(g) I -e K(g) +e -A -U

KCl(s) - Hf Hsub+ D + Cl(g) K(s) + Cl2(g) K+(g) + Cl-(g) I -e K(g)

+e -A -U KCl(s) - Hf Hsub+ D + Cl(g)

K(s) + Cl2(g) Born-Haber Cycle K+(g) + Cl-(g) I -e K(g) +e -A -U Only term not from

KCl(s) experiment - Hf Hsub+ D + Cl(g) K(s) + Cl2(g) Born-Haber Cycle K+(g) + Cl-(g) I -e

K(g) +e -A -U Only term not from KCl(s) experiment - Hf Hsub+ D + Cl(g)

K(s) + Cl2(g) Born-Haber Cycle U = - Hf + Hsub+ D + I - A Born-Haber Cycle U = - Hf + Hsub+ D + I - A NaCl kJ/mol

-414 109 113 490 347 Born-Haber Cycle U = - Hf + Hsub+ D + I - A NaCl 779

kJ/mol -414 109 113 490 347 Born-Haber Cycle

U = - Hf + Hsub+ D + I - A NaCl 779 NaBr kJ/mol -414 -377 109

109 113 490 347 96 490 318 Born-Haber Cycle U = - Hf + Hsub+ D + I - A NaCl 779 NaBr 754 NaI

kJ/mol -414 -377 -322 109 109 109

113 490 347 96 490 318 71 490 297 Born-Haber Cycle U = - Hf + Hsub+ D + I - A NaCl 779 NaBr 754 NaI 695

kJ/mol -414 -377 -322 109 109 109

113 490 347 96 490 318 71 490 297 Born-Haber Cycle U = - Hf + Hsub+ D + I - A 2 Az z

e U = -No 1 2 a 1 1n Born-Haber Cycle U = - Hf + Hsub+ D + I - A

2 Az z e U = -No 1 2 a NaCl NaBr

NaI 1 1n Thermo(B-H) Theory 779

754 695 795 757 715 Homework problems for 10/3 1. Construct a diagram for the Born-Haber cycle for the various thermodynamic

properties associated with the formation of magnesium chloride. continued The important values are: Hsub Mg IE1 Mg IE2 Mg D Cl2

A Cl Hf MgCl2 147.7 kJ/mol 737.7 kJ/mol 1450.7 kJ/mol 243 kJ/mol 348.6 kJ/mol -642 kJ/mol

continued 2. In the CsCl structure, how many ions would be included in the first attractive term for the Madelung constant. continued CsCl

2. In the CsCl structure, how many ions would be included in the first repulsive term for the Madelung constant. CsCl

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