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

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Presentation on theme: "Atkins & de Paula: Atkins’ Physical Chemistry 9e Chapter 19: Materials 2: Solids."— Presentation transcript:

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

2 Crystallography 19.1 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

3 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

4 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.

5 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

6 Chapter 19: Materials 2: Solids (110)(230) (010)(110) (111)

7 Chapter 19: Materials 2: Solids Some Examples

8 Chapter 19: Materials 2: Solids Common 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}

9 Chapter 19: Materials 2: Solids  separation of planes (d-spacing)

10 Chapter 19: Materials 2: Solids 19.3 The investigation of structure 19.3(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.

11 Chapter 19: Materials 2: Solids  four-circle diffractometer, a device used in X–ray crystallography.

12 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 θ nλ = 2d sin θ n = 1; first-order reflection 19.3(c) Scattering factors, f, a measure of the ability of an atom to diffract radiation  f; equal to the total # of e in the atom at θ=0 (Justification 19.1) 

13 Chapter 19: Materials 2: Solids 19.3(d) The electron density  Structure factor, overall amplitude of a wave diffracted by the {hkl} planes. Example 19.2 A A B ax a/h

14 Chapter 19: Materials 2: Solids  systematic absences, reflections with values of h + k + l that are absent from the powder diffraction pattern. Au Nanooctahedron

15 Chapter 19: Materials 2: Solids  Fourier synthesis, the construction of the electron density distribution from structure factors.  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

16 Chapter 19: Materials 2: Solids 19.5 Metallic solids 19.5(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

17 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

18 Chapter 19: Materials 2: Solids Primitive Cubic Coordination Number 6 52% Packing Fraction Body-Centered Cubic Coordination Number 8 68% Packing Fraction Close-Packed (CCP or HCP) Coordination Number 12 74% Packing Fraction CCP HCP

19 Chapter 19: Materials 2: Solids 19.6 Ionic solids 19.6(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 = r smaller /r larger.  radius-ratio rule, a rule suggesting which type of structure is likely based on the radius ratio: γ (caesium chloride).

20 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, ΔH L, the change in molar enthalpy for MX(s)  M z+ (g) + X z– (g).

21 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.

22 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

23 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]

24 Chapter 19: Materials 2: Solids I19.1 X-ray crystallography of biological macromolecules DNA Proteins TLR3

25 Chapter 19: Materials 2: Solids THE PROPERTIES OF SOLIDS 19.8 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

26 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, v P = (transverse strain)/(normal strain).

27 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.

28 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. From Hückel secular determinant

29 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.

30 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-type p-typeReverse bias Forward bias

31 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.

32 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.

33 Chapter 19: Materials 2: Solids Magnetic properties 19.11(a) Magnetic susceptibility  magnetization, the magnetic dipole moment density, M = χ H.  volume magnetic susceptibility, the proportionality constant χ.  molar magnetic susceptibility, χ m = χV m.  magnetic flux density, B = μ 0 ( H + M ) = μ 0 (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, χ m = A + C/T, A = N A μ 0 ξ and C = N A μ 0 m 2 /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

34 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

35 Chapter 19: Materials 2: Solids 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 H c  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. YBa 2 Cu 3 O 7 Cooper pair


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