atkins & de paula: atkins’ physical chemistry 9e chapter 19: materials 2: solids

35
Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Upload: jovany-howie

Post on 15-Dec-2015

318 views

Category:

Documents


27 download

TRANSCRIPT

Page 1: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Atkins & de Paula:

Atkins’ Physical Chemistry 9e

Chapter 19: Materials 2: Solids

Page 2: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Crystallography19.1 Lattices and unit cells space lattice, the pattern formed by points representing the locations of structural

motifs (atoms, molecules, or groups of atoms, molecules, or ions). unit cell, an imaginary parellelepiped that contains one unit of a translationally

repeating pattern.

unit cell

Page 3: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

crystal system, a classification based on the rotational symmetry elements of a unit cell.

essential symmetry, the elements a unit cell must possess to belong to a particular crystal system.

cubic system monoclinic system

triclinic system

Trigonal

Page 4: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Bravais lattice, the 14 distinct space lattices in three dimensions. primitive unit cell (P), formed by joining neighbouring lattice points by straight lines. body-centred unit cell (I), with lattice points at the corners and at the centre. face-centred unit cell (F), with lattice points at the corners and on each face. side-centred unit cell (A,B,C), with lattice points at the corners and on two opposite faces.

Page 5: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.2 The identification of lattice planes Miller indices (hkl), indices that distinguish planes in a lattice.

5. Negative directions are denoted with a bar on top of the number, e.g. 100

How to define Miller Indices

Page 6: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

(110) (230)

(010)(110)

(110)

(111)

Page 7: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Some Examples

Page 8: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: SolidsCommon crystallographic terms (hkl); parenthesis designate a crystal face or a family of planes throughout a crystal

lattice. [uvw]; square brackets designate a direction in the lattice from the origin to a point. Used

to collectively include all the faces of a crystals whose intersects (i.e., edges) parallel each other. These are referred to as crystallographic zones and they represent a direction in the crystal lattice.

{hkl}; "squiggly" brackets or braces designate a set of faces that are equivalent by the symmetry of the crystal.

[111]

{111}

Page 9: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

separation of planes (d-spacing)

2

2

2

2

2

2

2

2/12222

222

2

2/12202

22

20

1

)(

1

)(

1

c

l

b

k

a

h

d

lkh

ador

a

lkh

d

kh

ador

a

kh

d

hkl

hklhkl

hkhk

Page 10: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.3 The investigation of structure19.3(a) X-ray diffraction diffraction, interference caused by an object in the path of waves. diffraction pattern, the pattern of varying intensity that results from diffraction. Bremsstrahlung, X–radiation generated by the deceleration of electrons. K–radiation, X–radiation emitted when an electron falls into a K shell.

Page 11: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

four-circle diffractometer, a device used in X–ray crystallography.

Page 12: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.3(b) Bragg’s law reflection, an intense beam arising from constructive interference. glancing angle, θ, the angle of incidence of a beam of radiation. Bragg’s law, λ = 2d sin θ.

AB+BC = 2d sin θnλ = 2d sin θn = 1; first-order reflection

19.3(c) Scattering factors, f, a measure of the ability of an atom to diffract radiation

ondistributidensityelectronr

kdrrkr

krrf

:)(

sin4

,sin

)(40

2

f; equal to the total # of e in the atom at θ=0(Justification 19.1)

Page 13: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.3(d) The electron density Structure factor, overall amplitude of a wave diffracted by the {hkl} planes.

)(2)()(jjjhkl

j

jijhkl lzkyhxjwhereefF hkl

Example 19.2

lkhotherforF

lkhoddforffF

lkhevenforffF

hkl

hkl

hkl

,,0

,,)(4

,,)(4

iBA

BABAti

Bti

Ati

Bti

A

tiB

tiA

effA

ffffefefefefAI

efefA

hxhx

differencephase

pathindifferencehxaxh

ad

cos2))((

22)(

;sin2sin2sin2

22)()(2

)(

A

A

Bax a/h

Page 14: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

systematic absences, reflections with values of h + k + l that are absent from the powder diffraction pattern.

Pcubicoflkhoddfromreflectionno

lkhzyxIcubic

ffffeeffffI

effeffFFI

hkl

hklBABAii

BABAhkl

iBA

iBAhklhklhkl

hklhkl

hklhkl

)(

)(),,(),,(;

cos2)(

))((

21

21

21

2222

*

Au Nanooctahedron

Page 15: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Fourier synthesis, the construction of the electron density distribution from structure factors .

hkl

lzkyhxihkleF

Vr )(21)(

phase problem, the ambiguity in phase of structure factors obtained from intensities.

structure refinement, the adjustment of structural parameters to give the best fit between the observed intensities and those calculated from the model of the structure deduced from the diffraction pattern.

Neutron and electron diffraction

Page 16: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.5 Metallic solids19.5(a) Close packing close-packed, a layer of spheres with maximum utilization of space. polytype, structures that are identical in two dimensions but differ in the third dimension. hexagonally close-packed (hcp), the sequence of layers ABABAB.... cubic close-packed (ccp), the sequence of layers ABCABC....

hcp

ccp

Page 17: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

coordination number, the number of nearest neighbours. packing fraction, the fraction of space occupied by hard spheres.

19.5(b) Less closely packed structures; bcc (cubic I) & cubic P

Page 18: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Primitive CubicCoordination Number 652% Packing Fraction

Body-Centered CubicCoordination Number 868% Packing Fraction

Close-Packed (CCP or HCP)Coordination Number 1274% Packing Fraction

CCP

HCP

Page 19: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids19.6 Ionic solids19.6(a) Structure (n+,n–)–coordination, the number of nearest neighbours of opposite charge; n+ is the

coordination number of the cation and n– that of the anion. . caesium-chloride structure, an ion of one charge occupies the centre of a cubic unit cell

with eight counter ions at its corners: (8,8)–coordination rock-salt structure, of two interpenetrating slightly expanded fcc arrays, one of cations and

the other of anions: (6,6)–coordination radius ratio, γ = rsmaller/rlarger. radius-ratio rule, a rule suggesting which type of structure is likely based on the radius

ratio: γ < 0.414 (zinc blende); 0.414 < γ < 0.732 (rock salt); γ > 0.732 (caesium chloride).

Page 20: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.6(b) Energies lattice energy, the difference in potential energy of ions packed together in a solid and

widely separated as a gas. lattice enthalpy, ΔHL, the change in molar enthalpy for MX(s) Mz+(g) + Xz–(g).

):(4

;3

42ln2)()(

2

1

42ln2)(

2ln44

1

3

1

2

11

4

4324

1)(

0

2

0

22

0

22

0

22

0

22

22222222

0

constantMadelungAd

eNzzAEarrayDFor

d

eNzanionEcationENE

d

ezcationE

d

ez

d

ez

d

ez

d

ez

d

ez

d

ezcationE

ABAp

AppAp

p

p

Page 21: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Born–Mayer equation, for the total potential energy of an ionic crystal. Born–Haber cycle, a closed path of transformations starting and ending at the same point,

one step of which is the formation of the solid compound from a gas of widely separated ions.

Ad

d

d

eNzzEEtotalMinimun

eCNEoncontributirepulsive

ABAp

ddAp

)1(4

,*

0

2

min,

/* *

Page 22: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.7 Molecular solids and covalent networks covalent network solid, a solid in which covalent bonds in a definite spatial orientation

link the atoms in a network extending through the crystal. molecular solid, a solid consisting of discrete molecules held together by van der Waals

interactions.

Ice(molecular solid)

Diamond

CNT

Graphite

Page 23: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

Impact on Nanotechnology; CNTs Strong & light: 100 times stronger than steel but 1/6 as heavy. High electrical & thermal conductivities: far better than Cu.

[CVD growth]

[Mechanical properties of CNTs]

[SWCNTs] [MWCNTs]

metallic

semiconducting

[Electrical properties of CNTs][Nanotube field-effect transistor]

Page 24: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

I19.1 X-ray crystallography of biological macromolecules

DNA

Proteins

TLR3

Page 25: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

THE PROPERTIES OF SOLIDS19.8 Mechanical properties stress, the applied force divided by the area to which

it is applied. strain, the distortion of a sample resulting from an

applied stress. rheology, the study of the relation between stress

and strain. uniaxial stress, stress applied in one direction. hydrostatic stress, a stress applied simultaneously in

all directions. pure shear, a stress that tends to push opposite faces

of the sample in opposite directions.

uniaxial stress

hydrostatic stress

shear stress

Page 26: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

elastic deformation, a deformation that disappears when the stress is removed. plastic strain, a strain from which recovery does not occur when the stress is removed. Young’s modulus, E = (normal stress)/(normal strain). bulk modulus, K = pressure/(fractional change in volume). shear modulus, G = (shear stress)/(shear strain). Poisson’s ratio, vP = (transverse strain)/(normal strain).

Page 27: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.9 Electrical properties metallic conductor, a substance with an

electrical conductivity that decreases as the temperature is raised.

semiconductor, a substance with an electrical conductivity that increases as the temperature is raised.

insulator, a semiconductor with a very low electrical conductivity.

superconductor, a solid that conducts electricity without resistance.

Page 28: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.9(a) The formation of bands nearly-free-electron approximation, a model of a metal in which the valence electrons are

assumed to be trapped in a box with a periodic potential. tight-binding approximation, a model of a metal in which the valence electrons are

assumed to occupy molecular orbitals delocalized throughout the solid. s- and p-bands, a band formed from overlap of s- and p-orbitals, respectively. band gap, a range of energies to which no orbital corresponds.

NasEE

NkN

kE

N

k

4

,...,2,11

cos2

1

From Hückel secular determinant

Page 29: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.9(b) The occupation of orbitals Fermi level, the highest occupied molecular orbital in a solid at T = 0. Fermi–Dirac distribution, P = 1/(e(E – μ)/kT + 1); a version of Boltzmann distribution that

takes into account the effect of the Pauli principle.

Page 30: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.9(c) Insulators and semiconductors valence band, a filled band in a solid. conduction band, an empty band in a solid. intrinsic semiconductor, where semiconduction is a property of the pure material. compound semiconductor, an intrinsic semiconductor being a compound of different elements. extrinsic semiconductor, becomes semiconducting when it is doped with other atoms. dopant, introduced atoms. p- and n-type semiconductivity, conduction by holes and particles, respectively. p–n junction, a junction between p- and n-type semiconductors.

n-typep-type Reverse bias Forward bias

Page 31: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.10(a) Light absorption by excitions in molecular solids exciton, an electron–hole pair. Frenkel exciton, the electron and hole jump together from molecule to molecule. Wannier exciton, the electron and hole are on different but nearby molecules. exciton bands, the structure of an absorption spectrum due to exciton formation: there are N

exciton bands when there are N molecules in each unit cell Davydov splitting, the splitting between exciton bands.

Page 32: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.10(b) Light absorption by metals and semiconductors

19.10(c) Nonlinear optical phenomena frequency doubling (or second harmonic generation), the process in which an intense

laser beam is converted to radiation with twice its initial frequency as it passes though a suitable material.

optical Kerr effect, the change in refractive index of a well chosen medium (Kerr medium) when it is exposed to intense electric fields .

Kerr lens, the self-focussing of the laser beam by using the Kerr effect.

)2cos1(2

1cos

:2

1

2220

2

2

tt

izabilityhyperpolar

doublingfrequency

EEE

EE

Page 33: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.11 Magnetic properties19.11(a) Magnetic susceptibility magnetization, the magnetic dipole moment density, M = χH. volume magnetic susceptibility, the proportionality constant χ. molar magnetic susceptibility, χm = χVm. magnetic flux density, B = μ0(H + M) = μ0(1 + χ) H. paramagnetic, a material for which χ is positive. diamagnetic, a material for which χ is negative. magnetizability, ξ, a measure of the extent to which a

magnetic dipole moment may be induced in a molecule. Curie law, χm = A + C/T, A = NAμ0ξ and C = NAμ0m2/3k. Gouy balance, a device for determining the magnetic

susceptibility of a sample. superconducting quantum interference device (SQUID), a

superconducting device for determining the magnetic susceptibility of a sample.

Gouy balance

Page 34: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.11(b) The permanent magnetic moment ferromagnetism, strong, persistent magnetization arising from the cooperative alignment of

spins. antiferromagnetic phase, a phase in which spins are locked into a low–magnetization

arrangement. Curie temperature, the temperature of a ferromagnetic transition. Néel temperature, the temperature of an antiferromagnetic transition. Temperature–independent paramagnetism (TIP), orbital paramagnetism.

paramagnetic

ferromagnetic

antiferromagnetic

Page 35: Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids

Chapter 19: Materials 2: Solids

19.12 Superconductors superconductor, a substance that conducts electricity without resistance. high-temperature superconductor (HTSC), a substance that is superconducting at

relatively high temperatures. Type I superconductor, a superconductor that shows an abrupt loss of superconductivity

when exposed to a magnetic field above a critical value; completely diamagnetic below Hc

Meissner effect, the exclusion of a magnetic field from a superconductor. Type II superconductor, a superconductor that shows a gradual loss of superconductivity

when exposed to a magnetic field. Cooper pair, a pair of electrons that exists as a result of interactions with the lattice.

YBa2Cu3O7 Cooper pair