The Muppet’s Guide to: The Structure and Dynamics of Solids Thomas Hase Room MAS

My Research X-ray (and neutron) scattering from thin films and multilayers…. Not much diffraction!

Objectives for part 1 1.Understand how thermodynamics and bonding are responsible for crystal structure and material properties 2.Have knowledge of simple crystal structures and how they relate to bonding requirements. Be able to reproduce the bcc, fcc, diamond and perovskite structures and be able to explain the concepts of the lattice and the basis. 3.Understand the structural origin of the ferroelectric effect. 4.Be able to explain the difference between a first and second order phase transition and justify why they occur from a thermodynamic point of view. 5.Be able to read and use a unary and binary phase diagram and calculate phase compositions and relative amounts. Understand the diffusive mechanisms in determining structure and predict the evolution of structure using a eutectic phase diagram. 6.Have an understanding of different crystal growth methods and the types of materials they produce. Be able to describe simple defect structures and how these relate to material properties. 7.Understand how x-rays, neutrons and electrons interact with matter. Appreciate the differences between probes and be able to compare x-ray and neutron scattering. 8.Be able to apply basic scattering concepts to the study of single crystal and powder materials. Be able to predict the likely scattering from simple structures and describe the changes it scattering as a material undergoes a phase transition. 9. Understand how scattering is related to reciprocal space. Know how to determine material properties such as lattice parameters, layer thickness, roughness, particle size and shape. Understand how sample shape affects the scattering. Determine strain and particle size from scattering data. 10.Understand the complementarity between x-rays and neutrons 11.Understand x-ray spectroscopy and spectroscopic probes

Recommended Books – Part 1 The Physics and Chemistry of Solids Stephen Elliott ISBN: , Wiley, Paperback June 1998 £47.50 / €71.30 (Wiley) Materials Science and Engineering - An Introduction, 7th Edition William D. Callister, Jr., ISBN: , Wiley, Hardback 2007 £37.95 / €58.50 (Wiley) Extended notes which cover all the course content and more are available on-line and a printed copy will be handed out soon

Feedback Please give honest and critical feedback during the course: –During the lectures –After the lectures

The Muppet’s Guide to: The Structure and Dynamics of Solids 1. Structure from a Thermodynamic Viewpoint

Bonding in Solids Arrangement of atoms in a solid (on a local atomic level) is driven by energy considerations Require a thermodynamical treatment of atomic positions and bonding….

Entropy: A measure of disorder or randomness in a system: Enthalpy: The total energy of a thermodynamic system. It is the sum of the internal energy of a body and the energy associated with displacing it from its environment: Thermodynamics U is the Internal energy of crystal

The Gibbs Free Energy Is a measure of the energy that depends on both enthalpy and entropy: Also known as the free enthalpy

Re-expression of 1 st Law Recall 1 st law of thermodynamics: Which using the definition of entropy,  S=  Q/T, becomes Consider small change in Gibbs free energy (G= H-TS)

Entropy, S Disorder in atomic positions / moments Thermal vibrations about average position Enthalpy, H Largest contribution comes from the internal energy U: Potential due to bonding Lattice vibrations (phonons and magnons) Initially we will assume that the lattice vibrations do not contribute to H

Gibbs free energy “Every system seeks to achieve a minimum of free energy.” Stable at x=0Unstable at x=0

Stable Phases At low temperatures the Gibbs free energy is lowered by minimising the enthalpy (H=U-PV) and this is associated with an ordered ground state. As the temperature rises it becomes more important to maximise the entropy (S). ORDERED DISORDERED Solid Liquid

Solid PhaseMinimum G when H is at optimum value U stabilised by bonding - ORDERED Liquid Phase:Disorder becomes more important Bonding requirements loosened Gas Phase:No-longer any real bonding requirements dominated by Sand high disorder - DISORDERED Low Temp, TS < H Minimise enthalpy High Temp, TS > H Maximise entropy

SOLIDS - Internal Energy Assume that the contribution to the internal energy of the lattice arising from vibrations is low (meV) Energy, U proportional to position of atoms in unit cell Position determined by bonding potential,  ij which only depends on separation, r ij. Expect  ij to depend on the type of bonding and to be different for ionic, covalent, etc.

S. Klotz et al. Europhys. Lett., 72 (4), p. 576 (2005) L. Pauling considered the packing of water molecules in ice in Developed the ‘Ice rules’ U(P,V) - Ice Structures

ICE Cubic Ice VII

Bonding For stable bonds balance attractive and repulsive forces: Bond energy: Figure adapted from Callister, Materials science and engineering, 7 th Ed. Stable bonds have a minimum in the total energy

Bonding or E A is bonding dependent Figure adapted from Callister, Materials science and engineering, 7 th Ed.

van der Waals Temporary time varying electric dipole created in neutral materials through zero point motion of the electrons.  =Potential energy at equilibrium separation  =distance between the two atoms at zero energy Figure adapted from Callister, Materials science and engineering, 7 th Ed. Lennard-Jones

van der Waals Materials Inert gases and Molecular crystals He, Ar, Ne, Xe, N 2, O 2, H 2, Cl 2, Graphitic Carbon No restriction on bond angles Want to maximise the number of nearest neighbours Maximise Packing Density: Simple Cubic Structures Fast fall-off Only nearest neighbours attract Weak bond Low melting temperatures

Ionic Bonds Small lattice parameters

Ionic Materials Range of materials such as NaCl, CsCl, MgO etc. Non-directional – bond strength same in all directions brittle and hard materials All positive ions surrounded by negative ions and want to maximise the number of nearest neighbours Simple Cubic Structures Moderate fall-off First and second nearest neighbours attract Strong bondHigh melting temperatures