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Solids and Surfaces Prof. John Foord Eight lectures 3rd year PTCL ‘core’ (for more (!), see PTCL option 1 “Interfaces” in HT )

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What is the interest in “Solids”? “Solids” are an important application of chemistry e.g. –Structural; steel, concrete, glass, plastics etc. etc. –Functional; semiconductors, superconductors, magnetic, optical, coatings, sensors etc. etc.

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The properties of solids are controlled by the chemical bonding Strength, hardness, melting point etc. Electrical properties Optical and Magnetic Changes with temperature and pressure Crown jewels “Great Star of Africa” 530 Carats

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Solid Surfaces Adhesion and coatings Functional solid state devices Nanotechnology Electrochemistry Detergent Action Catalysis Corrosion Etc.

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Aims of the course 1.Understanding some properties of solids in a physical chemical framework. {Revision of some statistical mechanics} 2.An introduction to surface chemistry Chemistry at the solid-gas interface {Foundations for PTCL Option 1}

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Books (Solids) Solid state inorganic texts, West etc. Smart and Moore, “Solid State Chemistry” Mandl, “Statistical Physics” Elliott, “The Physics and Chemistry of Solids”

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Solids 1.Heat capacity of solids –Solids possess a significant heat capacity even at low T –Must have a different origin to the that for gases, which mainly stems from translation and rotation at room T –Lattice vibrations –[Electronic excitations in metals]

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Early ideas - Dulong and Petit C for many monatomic solids is around 3R [Aside: for a gas C p -C v = R ; for a solid the two heat capacities are virtually identical since solids have small expansion effects]

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Each atom is vibrating in the x,y,z direction From energy equipartition expect C= 3R Deviations at low T later ascribed to “quantum” effects ElementCpCp CpCp Al24.4S22.7 Au25.4Si19.9 Cu24.5C (diamond) 6.1

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Formal model - Einstein theory for a pure monatomic solid Assume each atom in the solid vibrates independently in three independent directions x,y,z So that there are 3N Avo oscillators…..and they will all have the same frequency Assume the vibrations are harmonic

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Reminder about stat. mechs

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For a single oscillator

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And need the differential of q w.r.t. T So we know what q and its differential is. We can now get the energy

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And finally differentiate U w.r.t. to T to get the heat capacity.

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Notes Qualitatively works quite well Hi T 3R (Dulong/Petit) Lo T 0 Different crystals are reflected by differing Einstein T (masses and bond strengths)

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Heat capacity at constant volume

Heat capacity at constant volume

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