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Atkins & de Paula: Atkins’ Physical Chemistry 9e

Atkins & de Paula: Atkins’ Physical Chemistry 9e. Chapter 19: Materials 2: Solids. Chapter 19: Materials 2: Solids. Crystallography 19.1 Lattices and unit cells

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Atkins & de Paula: Atkins’ Physical Chemistry 9e

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

  2. Chapter 19: Materials 2: Solids 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. Trigonal monoclinic system cubic system triclinic system

  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. How to define Miller Indices 5. Negative directions are denoted with a bar on top of the number, e.g. 100

  6. Chapter 19: Materials 2: Solids (110) (230) (010) (110) (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. A B a/h ax A Example 19.2

  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 CCP Primitive Cubic Coordination Number 6 52% Packing Fraction Close-Packed (CCP or HCP) Coordination Number 12 74% Packing Fraction Body-Centered Cubic Coordination Number 8 68% Packing Fraction 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 = 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).

  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, ΔHL, the change in molar enthalpy for MX(s)  Mz+(g) + Xz–(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. Graphite Diamond Ice (molecular solid) CNT

  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. [MWCNTs] [CVD growth] [SWCNTs] metallic semiconducting [Nanotube field-effect transistor] [Electrical properties of CNTs] [Mechanical properties of CNTs]

  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 shear stress hydrostatic 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,vP = (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. p-type Reverse bias Forward bias n-type

  31. Chapter 19: Materials 2: Solids 19.10(a) Light absorption by excitions in molecular solids exciton, an electron–hole pair. Frenkelexciton, the electron and hole jump together from molecule to molecule. Wannierexciton, the electron and hole are on different but nearby molecules. exciton bands, the structure of an absorption spectrum due to exciton formation: there are Nexciton 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 • 19.11 Magnetic properties • 19.11(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

  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 • 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

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