Solid-State Electrochemistry: Essential Course Notes and Solved Exercises

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Solid-State Electrochemistry: Essential Course Notes and Solved Exercises
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Grenoble Sciences Series
Preface
Table of contents
Base quantities, units, and symbols from the international system (IS)
Physical-chemistry: Symbols and units
Acronyms and abbreviations used in this book
1. Description of ionic crystals
	Course notes
		1.1 – Definitions
			1.1.1 – The perfect crystal
			1.1.2 – The real crystal
			1.1.3 – Structure elements and effective charge
		1.2 – Reactions and equilibria
			1.2.1 – Atomic disorder and electronic disorder
			1.2.2 – Writing the reactions
			1.2.3 – Presence of foreign atoms
			1.2.4 – Equilibrium with the environment
		1.3 – Brouwer diagram
			1.3.1 – Equilibria
			1.3.2 – Electroneutrality relation and the Brouwer approximation
			1.3.3 – Diagram for MX2 crystal
			1.3.4 – Case of solid solution (MX2)1−x(DX)x
		1.4 – Stoichiometry and departure from stoichiometry
	Exercises
		Exercise 1.1 – Notation for structure elements and structure defects
		Exercise 1.2 – Notation for doping reactions
		Exercise 1.3 – Sitoneutrality and expression of chemical formulas
		Exercise 1.4 – Calculation of defect concentrations
		Exercise 1.5 – Doping strontium fluoride
		Exercise 1.6 – Variation of the concentration of structure defects in pure zirconium dioxide ZrO2 as a function of oxygen partial pressure
		Exercise 1.7 – The non-stoichiometry of iron monoxide
		Exercise 1.8 – Departure from stoichiometry of barium fluoride BaF2
		Exercise 1.9 – Crystallographic and thermodynamic study
of thorium dioxide ThO2
	Solutions to exercises
		Solution 1.1 – Notation for structure elements and structure defects
		Solution 1.2 – Notation for doping reactions
		Solution 1.3 – Sitoneutrality and notation for chemical formulas
		Solution 1.4 – Calculation of defect concentrations
		Solution 1.5 – Doping strontium fluoride
		Solution 1.6 – Variation of the concentration of structure defects in pure zirconium dioxide ZrO2 as a function of oxygen partial pressure
		Solution 1.7 – The non-stoichiometry of iron monoxide
		Solution 1.8 – Departure from stoichiometry of barium fluoride BaF2
		Solution 1.9 – Crystallographic and thermodynamic study 
of thorium dioxide ThO2
2. Methods and techniques
	Course notes
		2.1 – Complex impedance spectroscopy
			2.1.1 – Time domain: principal passive linear dipole devices in sinusoidal regime
			2.1.2 – Complex notation
			2.1.3 – Graphical representation of complex impedance
			2.1.4 – Other dipole devices
			2.1.5 – Physical meaning of complex impedance spectra
		2.2 – Methods to measure transport number
			2.2.1 – Electromotive force method
			2.2.2 – Using the results of total conductivity
			2.2.3 – Tubandt method
			2.2.4 – Dilatocoulometric method to measure cationic transport number
			2.2.5 – Electrochemical semipermeability
			2.2.6 – Blocking electrode method
	Exercises
		Exercise 2.1 – Determination of conductivity by four-electrode method
		Exercise 2.2 – Measurement of electric quantities by complex impedance spectroscopy
		Exercise 2.3 – Measurement of electronic conductivity in a mixed conductor
		Exercise 2.4 – Measurement of ionic conductivity in a mixed conductor
		Exercise 2.5 – Determination of cationic transport numberby dilatocoulometry
		Exercise 2.6 – Determination of cationic transport number in CaF2 by dilatocoulometry
		Exercise 2.7 – Electrochemical semipermeability
		Exercise 2.8 – Determination of transport number by electrochemical semipermeability
		Exercise 2.9 – Determination of conduction mode in α-AgI by Tubandt method
	Solutions to exercises
		Solution 2.1 – Determination of conductivity by four-electrode method
		Solution 2.2 – Measurement of electric quantities by complex impedance spectroscopy
		Solution 2.3 – Measurement of electronic conductivity in a mixed conductor
		Solution 2.4 – Measurement of ionic conductivity in a mixed conductor
		Solution 2.5 – Determination of cationic transport number by dilatocoulometry
		Solution 2.6 – Determination of cationic transport number in CaF2 by dilatocoulometry
		Solution 2.7 – Electrochemical semipermeability
		Solution 2.8 – Determination of transport number by electrochemical semipermeability
		Solution 2.9 – Determination of conduction mode in α-AgI by Tubandt method
3. Transport in ionic solids
	Course notes
		3.1 – Phenomenological approach to ionic transport
in ionic crystals
			3.1.1 – Electrochemical mobility and flux density
			3.1.2 – Electrical conductivity and transport number
		3.2 – Microscopic approach to ionic transport in crystals: Activated-hopping model
			3.2.1 – Electric mobility
			3.2.2 – Ionic conductivity
			3.2.3 – Conductivity and temperature
			3.2.4 – Conductivity and environment
			3.2.5 – Ionic conductivity and composition
			3.2.6 – Other parameters
		3.3 – Basic description of Wagner theory
	Exercises
		Exercise 3.1 – Influence of geometric factor
		Exercise 3.2 – Study of oxygen mobility in solid solutions (ThO2)1−x(YO1.5)x
		Exercise 3.3 – Study of electronic conductivity in solid solutions (CeO2)1−x(CaO)x
		Exercise 3.4 – Electronic transport number in a glass
		Exercise 3.5 – Electrical properties of potassium chloride KCl
		Exercise 3.6 – Application of Nernst-Einstein relation to LiCF3SO3
in poly(ethylene oxide) P(EO)
		Exercise 3.7 – Electrical conductivity as a function of composition
in (CeO2)1−x(YO1.5)x
		Exercise 3.8 – Conductivity of nickel oxide
		Exercise 3.9 – Ionic conductivity-activity relationship of glass modifier in oxide-based glasses
		Exercise 3.10 – Electrochemical coloration
		Exercise 3.11 – Oxygen diffusion in gadolinia-doped ceria
		Exercise 3.12 – Electrical conductivity of solid vitreous solution (SiO2)1−x(Na2O)x
		Exercise 3.13 – High-temperature protonic conductor SrZrO3
		Exercise 3.14 – Free-volume model
		Exercise 3.15 – Study of single-crystal calcium fluoride CaF2
in the presence of oxygen
		Exercise 3.16 – emf of a membrane crossed by an electrochemical semipermeability flux
		Exercise 3.17 – Determination of electronic conductivityby electrochemical semipermeability
	Solutions to exercises
		Solution 3.1 – Influence of geometric factor
		Solution 3.2 – Study of oxygen mobility in solid solutions (ThO2)1−x(YO1.5)x
		Solution 3.3 – Study of electronic conductivity in solid solutions (CeO2)1−x(CaO)x
		Solution 3.4 – Electronic transport number in a glass
		Solution 3.5 – Electrical properties of potassium chloride KCl
		Solution 3.6 – Application of Nernst-Einstein relation to LiCF3SO3
in poly(ethylene oxide) P(EO)
		Solution 3.7 – Electrical conductivity as a function of composition in (CeO2)1−x(YO1.5)x
		Solution 3.8 – Conductivity of nickel oxide
		Solution 3.9 –  Ionic conductivity-activity relationship of oxide modifier in oxide-based glasses
		Solution 3.10 – Electrochemical coloration
		Solution 3.11 – Oxygen diffusion in gadolinia-doped ceria
		Solution 3.12 – Electrical conductivity of solid vitreous solution (SiO2)1−x(Na2O)x
		Solution 3.13 – High-temperature protonic conductor SrZrO3
		Solution 3.14 – Free-volume model
		Solution 3.15 – Study of single-crystal calcium fluoride CaF2 
in the presence of oxygen
		Solution 3.16 – emf of membrane crossed by an electrochemical semipermeability flux
		Solution 3.17 – Determination of electronic conductivity by electrochemical semipermeability
4. Electrode reactions
	Course notesThermodynamics and electrochemical kinetics
		4.1 – Electrode thermodynamics
			4.1.1 – Electrode
			4.1.2 – Electrode potential
			4.1.3 – Electrode polarization
			4.1.4 – Electrode overpotential
			4.1.5 – Current density
		4.2 – Electrochemical kinetics
			4.2.1 – Review
			4.2.2 – Pure-charge-transfer regime (extreme case)
			4.2.3 – Mixed transfer-diffusion regime
			4.2.4 – Regime of pure diffusion kinetics (extreme case)
			4.2.5 – Regime of adsorption of gaseous species
	Exercises
		Exercise 4.1 – Oxygen-diffusion-limited electrode
		Exercise 4.2 – Study of oxygen-electrode reaction
		Exercise 4.3 – Overpotential in an oxygen electrochemical pump
		Exercise 4.4 – Determination of exchange current
		Exercise 4.5 – Reduction of water vapor at the M / YSZ interface with M = Pt, Ni
		Exercise 4.6 – Hydrogen oxidation at Ni / YSZ interface
	Solutions to exercises
		Solution 4.1 – Oxygen-diffusion-limited electrode
		Solution 4.2 – Study of oxygen-electrode reaction
		Solution 4.3 – Overpotential in an oxygen electrochemical pump
		Solution 4.4 – Determination of exchange current
		Solution 4.5 – Reduction of water vapor at the M / YSZ interface with M = Pt, Ni
		Solution 4.6 – Hydrogen oxidation at Ni / YSZ interface
5. Applications
	Course notes
		5.1 – Electrochemical sensors
			5.1.1 – Definition and characteristics
			5.1.2 – Potentiometric sensor for gas analysis
			5.1.3 – Amperometric sensor
			5.1.4 – Coulometric sensor
			5.1.5 – Conductometric sensor for gas analysis
		5.2 – Electrochemical generators
			5.2.1 – Definition and characteristics
			5.2.2 – Discharge and (re)charge of electrochemical generators
			5.2.3 – Primary batteries, fuel cells, and secondary batteries
	Exercises
		Exercise 5.1 – Determination of standard free enthalpy of formation for AgCl
		Exercise 5.2 – Measurement of thermodynamic quantities of metal fluorides
		Exercise 5.3 – Measurement of O2− ion activity in a molten salt
		Exercise 5.4 – Calculation of equilibrium constants for defect formation in Cu2O
		Exercise 5.5 – TiS2: insertion material
		Exercise 5.6 – Chlorine sensor based on doped strontium chloride
		Exercise 5.7 – CO2 sensor (a)
		Exercise 5.8 – CO2 sensor (b)
		Exercise 5.9 – Sulfur oxide sensor
		Exercise 5.10 – Oxygen semiconductor sensor
		Exercise 5.11 – Amperometric oxygen sensor
		Exercise 5.12 – Coulometric oxygen sensor
		Exercise 5.13 – Nitrogen oxide sensor
		Exercise 5.14 – The sodium-sulfur battery
		Exercise 5.15 – General information on fuel cells
		Exercise 5.16 – Solid oxide fuel cell (SOFC)
		Exercise 5.17 – Use of hydrocarbons in SOFCs
		Exercise 5.18 – Thermodynamic study of methane reforming in SOFC
		Exercise 5.19 – Electrochemical integrator
	Solutions to exercises
		Solution 5.1 – Determination of standard free enthalpy of formation for AgCl
		Solution 5.2 – Measurement of thermodynamic quantities of metal fluorides
		Solution 5.3 – Measurement of O2− ion activity in a molten salt
		Solution 5.4 – Calculation of equilibrium constants for defect formation in Cu2O
		Solution 5.5 – TiS2: insertion material
		Solution 5.6 – Chlorine sensor based on doped strontium chloride
		Solution 5.7 – CO2 sensor (a)
		Solution 5.8 – CO2 sensor (b)
		Solution 5.9 – Sulfur oxide sensor
		Solution 5.10 – Oxygen semiconductor sensor
		Solution 5.11 – Amperometric oxygen sensor
		Solution 5.12 – Coulometric oxygen sensor
		Solution 5.13 – Nitrogen oxide sensor
		Solution 5.14 – The sodium-sulfur battery
		Solution 5.15 – General information on fuel cells
		Solution 5.16 – Solid oxide fuel cell (SOFC)
		Solution 5.17 – Use of hydrocarbons in SOFCs
		Solution 5.18 – Thermodynamic study of methane reforming in SOFC
		Solution 5.19 – Electrochemical integrator
Appendix – Fick’s laws of diffusion
Bibliography
Glossary
Index