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Critical point theory (Mathematical analysis) --- Morse theory --- Variational inequalities (Mathematics) --- Geodesics (Mathematics)

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The phase behaviour of materials and their thermodynamic properties are a central subject in all fields of materials research. The first Volume of the work, meant for graduate students in chemistry, geology, physics, and metallurgy, and their engineering counterparts, is split up in three levels, such that from level to level the portion and importance of thermodynamics and mathematics are increased. In the ground level it is shown that the basic principles of phase equilibria can be understood without the use of thermodynamics – be it that the concept of chemical potential is introduced right from the beginning. The intermediate level is an introduction to thermodynamics; culminating in the Gibbs energy as the arbiter for equilibrium – demonstrated for systems where the phases in equilibrium are pure substances. In the third level the accent is on binary systems, where one or more phases are solutions of the components. Explicit relationships between the variables are derived for equilibria involving ideal mixtures and ideal dilute solutions. Non-ideal systems are treated from three different angles – geometrically, analytically, and numerically. Throughout the work high priority is given to the thermodynamic assessment of experimental data; numerous end-of-chapter exercises and their solutions are included. The work is useful for scientists as an introduction and a reference book. Audience: Students, teachers, and scientists in chemistry, chemical engineering, geology and geophysics, metallurgy, and related branches of materials science.

Phase rule and equilibrium. --- Thermodynamics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Critical phenomena (Physics) --- Equilibrium --- Chemical equilibrium --- Chemical systems --- Critical point --- Chemistry, Physical organic. --- Materials. --- Geology. --- Physical geography. --- Physical Chemistry. --- Materials Science, general. --- Geophysics/Geodesy. --- Geography --- Geognosy --- Geoscience --- Earth sciences --- Natural history --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Chemistry, Physical organic --- Chemistry, Organic --- Materials --- Physical chemistry. --- Materials science. --- Geophysics. --- Geological physics --- Terrestrial physics --- Material science --- Physical sciences --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry

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This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The latter include the renormalisation group approach to critical phenomena, the density functional theory of interfaces, the topological defects of nematic liquid crystals and the kinematic aspects of the phase transformation process. This textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. References include suggestions for more detailed treatments and four appendices supply overviews of the mathematical tools employed in the text.

Phase transformations (Statistical physics) --- Phase rule and equilibrium. --- Chemistry, Physical and theoretical --- Critical phenomena (Physics) --- Equilibrium --- Chemical equilibrium --- Chemical systems --- Critical point --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Thermodynamics. --- Statistics. --- Statistical physics. --- Condensed Matter Physics. --- Complex Systems. --- Soft and Granular Matter, Complex Fluids and Microfluidics. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistical Physics and Dynamical Systems. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Mathematical statistics --- Condensed matter. --- Dynamical systems. --- Amorphous substances. --- Complex fluids. --- Statistics . --- Complex liquids --- Fluids, Complex --- Amorphous substances --- Liquids --- Soft condensed matter --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Matter --- Solids