Course Information

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
In-person direct teaching

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Tue 8:00–9:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Students will obtain ability to solving phase and chemical equilibria. At the student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Students will obtain ability to solving phase and chemical equilibria. At the student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Tue 8:00–9:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Students will obtain ability to solving phase and chemical equilibria. At the student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Students will obtain ability to solving phase and chemical equilibria. At the student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Wed 8:00–9:50 prace doma

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Students will obtain ability to solving phase and chemical equilibria. At the student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Tue 14:00–15:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Students will obtain ability to solving phase and chemical equilibria. At the student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 19 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Learning outcomes

Student will be able to: - use thermodynamic functions to describe the behavior of mixed systems. - read and understand phase diagrams - to use basic experimental methods of experimental study of phase equilibrium. - use and real phase diagrams for practical applications in laboratory and at technological conditions. - Understand diffusion by controlled processes and transformations in materials.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis, cooling curves. Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.
General note: Předmět alternuje k přednášce C6335 Nanočástice. Tj koná se obvykle v lichý rok.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 19 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.
General note: Předmět alternuje k přednášce C6335 Nanočástice. Tj koná se obvykle v lichý rok.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Mon 19. 9. to Sun 18. 12. Thu 8:00–9:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 19 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Tue 13:00–14:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 15 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• GASKELL, David R. Introduction to the thermodynamics of materials. 5th ed. New York: Taylor & Francis, 2008, xv, 618. ISBN 9781591690436. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Mon 10:00–11:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Mon 12:00–13:50 C12/311

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

After completing this course, the student should manage problem-solving phase and chemical equilibria. At the same student gains knowledge about how they work   SW calculations of phase equilibria materials based on metals and alloys.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programs and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualization, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick's laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programs (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimization of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures. Group discussion.

Assessment methods

Oral exam. Final assessment - oral examination. The successful evaluation should demonstrate knowledge of at least 50% of the lectures.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures.

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures.

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures.

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures.

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria Thermodynamics

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Language of instruction

Czech

Further Comments

The course is taught once in two years.
The course is taught: every week.

C6730 Phase Equilibria Thermodynamics

Extent and Intensity

2/0/0. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science

Prerequisites

C3140 or C3401 (Physical Chemistry I)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 25 fields of study the course is directly associated with, display

Course objectives

Thermodynamic conditions of phase equilibrium. Phase diagrams. Calculations and predictions of phase diagrams. Kinetic of reaching up to an equilibrium state. Stable and metastable phase equilibria. The influence of diffusion and nucleation on reaching up equilibrium state. Theory of phase equilibria in real systems. Examples of phase equilibria calculations in real systems. Experimental ways of phase equilibrium study. Chemical equilibria calculations.

Syllabus (in Czech)

• Termodynamické základy teorie fázových rovnováh: Termodynamické stavové funkce soustavy, Gibbsova energie soustavy a její vlastnosti, molární a parciální molární veličiny, závislost Gibbsovy energie čistých složek na teplotě a tlaku. Termodynamika mísení, stavové chování směsi: vyjádření složení směsi, Gibbsova-Duhemova rovnice, závislost Gibbsovy energie reálné soustavy na teplotě, tlaku a složení soustavy, aktivitní koeficienty, dodatkové funkce, mg. příspěvek, fázové pravidlo a stabilita fází. Zákony zachování hmoty, náboje a stechiometrie v termodynamických soustavách. Termodynamická podmínka stability fázové rovnováhy: Kritéria rovnováhy: diferenciální podmínka fázové rovnováhy, integrální podmínka fázové rovnováhy. Matematické řešení problému fázové rovnováhy. Fázové diagramy heterogenních soustav, základní typy fázových, diagramů, geometrická termodynamika, znázornění fázových diagramů, možné průběhy fázových hranic.Výpočty a predikce fázových diagramů. Kinetika dosažení rovnovážného stavu: Stabilní a metastabilní fázové rovnováhy, bezdifúzní fázové přeměny, role difúze a nukleace při ustavování rovnovážných stavů. Nukleace fází. Simulace difůzních procesů v heterogenních soustavách. Metody experimentálního studia fázových rovnováh: Získávání fázových dat, získávání termodynamických dat, měřitelné termodynamické veličiny. Zdroje dat a jejich přesnost. Reálné fázové rovnováhy: Hranice fázových oblastí jednosložkových soustav: stavové chování čisté látky, standardní stavy. Fázové rovnováhy v binárních soustavách: rovnováha kapalina-pára, kapalina-kapalina, směsi těkavých kapalin, destilace, pásmové čistění, roztoky netěkavých látek, koligativní vlastnosti, rovnováha kapalina-pevná látka a pevná látka-pevná látka. Fázové diagramy s neomezenou rozpustností v tuhé fázi, s částečnou a úplnou nerozpustností v tuhé fázi a s intermetalickými sloučeninami. Fázové rovnováhy ve vícesložkových soustavách, řezy fázovými diagramy. Příklady výpočtů fázových rovnováh a fázových diagramů v reálných systémech. Výpočty chemických rovnováh: Rovnovážná konstanta, homogenní systém, reakční koordináta, reakce v plynné fázi a v heterogenní soustavě. Algoritmy výpočtu chemických rovnováh.. Příklady výpočtů chemických rovnováh.

Literature

• Physical chemistry (Orig.) : Fizičeskaja chimija : Fyzikální chemie [Moore, 1979] : Fyzikální chemie [Moore, 1981]. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria Thermodynamics

Extent and Intensity

2/0/0. 3 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science

Prerequisites

C3140 or C3401 (Physical Chemistry I)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 16 fields of study the course is directly associated with, display

Syllabus

• Thermodynamic conditions of phase equilibrium. Phase diagrams. Calculations and predictions of phase diagrams. Kinetic of reaching up to an equilibrium state. Stable and metastable phase equilibria. The influence of diffusion and nucleation on reaching up equilibrium state. Theory of phase equilibria in real systems. Examples of phase equilibria calculations in real systems. Experimental ways of phase equilibrium study. Chemical equilibria calculations.

Literature

• Physical chemistry (Orig.) : Fizičeskaja chimija : Fyzikální chemie [Moore, 1979] : Fyzikální chemie [Moore, 1981]. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

The course is not taught in Autumn 2005

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria Thermodynamics

The course is not taught in Spring 2004

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), graded credit, z (credit), -.

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

C3140 or C3401 (Physical Chemistry I)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course ofers to students knowledge about nucleation, kinetics, and evolution of stable/metastable phase equilibria.

Syllabus

• Basic nomenclature: system, specie, phase, phase diagram,... Phase rules. Phase diagram geometry. Thermodynamic phase equilibrium constrains. Thermodynamic descriptions of non-ideal phases. Methods for phase diagram calculation and prediction. Stable and metastabile equilibria. Phase nucleation. Kinetic of reaching up to an equilibrium state. The influence of diffusion on equilibrium state. Theory of phase equilibria in real systems. Examples of phase equilibria calculations in real systems. Experimental ways of phase equilibrium study. Chemical equilibria calculations. Material design and technology applications.

Literature

• Physical chemistry (Orig.) : Fizičeskaja chimija : Fyzikální chemie [Moore, 1979] : Fyzikální chemie [Moore, 1981]. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
The course is taught annually.
Information on the per-term frequency of the course: v podzimním semestru.
The course is taught: every week.
General note: Je vhodné, aby zájemci mimo Př.fak.MU kontaktovali vyučujícího předem.

C6730 Phase Equilibria Thermodynamics

The course is not taught in Spring 2003

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science

Prerequisites

C3140 or C3401 (Physical Chemistry I)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 25 fields of study the course is directly associated with, display

Course objectives

The course ofers to students knowledge about nucleation, kinetics, and evolution of stable/metastable phase equilibria.

Syllabus

• Basic nomenclature: system, specie, phase, phase diagram,... Phase rules. Phase diagram geometry. Thermodynamic phase equilibrium constrains. Thermodynamic descriptions of non-ideal phases. Methods for phase diagram calculation and prediction. Stable and metastabile equilibria. Phase nucleation. Kinetic of reaching up to an equilibrium state. The influence of diffusion on equilibrium state. Theory of phase equilibria in real systems. Examples of phase equilibria calculations in real systems. Experimental ways of phase equilibrium study. Chemical equilibria calculations. Material design and technology applications.

Literature

• Physical chemistry (Orig.) : Fizičeskaja chimija : Fyzikální chemie [Moore, 1979] : Fyzikální chemie [Moore, 1981]. info

Language of instruction

Czech

Further Comments

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria Thermodynamics

The course is not taught in Spring 2001

Extent and Intensity

2/0/0. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Chemistry Section – Faculty of Science

Prerequisites

C3140 or C3401 (Physical Chemistry I)

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 25 fields of study the course is directly associated with, display

Course objectives

Thermodynamic conditions of phase equilibrium. Phase diagrams. Calculations and predictions of phase diagrams. Kinetic of reaching up to an equilibrium state. Stable and metastable phase equilibria. The influence of diffusion and nucleation on reaching up equilibrium state. Theory of phase equilibria in real systems. Examples of phase equilibria calculations in real systems. Experimental ways of phase equilibrium study. Chemical equilibria calculations.

Literature

• Physical chemistry (Orig.) : Fizičeskaja chimija : Fyzikální chemie [Moore, 1979] : Fyzikální chemie [Moore, 1981]. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.
General note: v a.r.01/02.

C6730 Phase Equilibria

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Physical Chemistry (programme PřF, N-CH)
• Macromolecular Chemistry (programme PřF, D-CH) (2)

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures.

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught once in two years.
Information on the per-term frequency of the course: v podzimním semestru lichého roku.
The course is taught: every week.
General note: Přednáška alternuje k předmětu C6335 Nanočástice.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info
• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info

Teaching methods

Lectures.

Assessment methods

Oral exam

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

C6730 Phase Equilibria

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).

Teacher(s)

prof. RNDr. Jiří Sopoušek, CSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Sopoušek, CSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: prof. RNDr. Jiří Sopoušek, CSc.

Prerequisites

It is recommended knowledge of physical chemistry and mathematics (for example in scope of study on Faculty of Sciences MU or Brno University of Technology).

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 22 fields of study the course is directly associated with, display

Course objectives

The course is especially designed for students of chemistry and material engineering. The contents consists chiefly of following items: thermodynamics of non-ideal several-component systems, essential conditions for phase coexistence, phase diagrams, phase transformations, kinetics of phase formation and disappearing, diffusion inside solid state, thermal analysis and its applications, methods of calculations and predictions of phase diagrams, and potency of kinetic simulations. The themes are complemented by examples (rectification, extraction, material heat treatment, separation, material microstructures, nucleation, optimisation of mechanical properties, material design, life-time of materials, ). An attained knowledge allows to understand correctly and to solve a great group of practical problems, which occurs in chemical laboratory, technical practice or during new material production qualifiedly.

Syllabus

• 1. Basic terms. Thermodynamic functions of pure substance and several component mixtures. Standard state. Phase nomenclature. Gibbs-Duhem equation. Gibbs energy of real system. Excess functions. 2. Phase structures and their crystallography. Lattice defects. Thermodynamics of stoichiometry and non-stoichiometry phases and chemical compounds. Conservation laws of mass, charge, and stoichiometry in thermodynamic systems. Phase rule and phase stability. 3. Gibbs energy of system. Chemical potential and activity. Differential equations of phase equilibrium, integral equation of phase equilibrium. Phase equilibrium formation. 4. Mathematical solution of phase equilibrium. Calculations and predictions of phase diagrams. Methods, programmes and thermodynamic databases for phase equilibrium calculations. CALPHAD approach. 5. Phase diagrams. Fundamental types of phase diagrams, visualisation, possible phase boundaries, and phase diagram cross-sections. Use of phase diagrams. 6. Experimental methods of phase equilibria study. Gain of phase data and thermodynamic data. Measurements of thermodynamic functions. Thermal analysis (cooling curves, DTA, DSC, ...). Data sources and their accuracy. 7. Real phase equilibria. Unary systems, binary systems (coexistence of gas, liquid, and solid phases; mixture of volatile liquids; distillation; sublimation; dissolutions). Phase diagrams of several component systems (coexistence of solid phases; extraction; purification; chemical compounds inside phase diagram; intermetallics). 8. Examples of phase equilibrium and phase diagram calculations for systems. Relationship between phase, physical, and mechanical properties. 9. Phase transformations. Stable and metastable phase equilibria. Diffusion-less phase transformations. Role of diffusion and nucleation at equilibrium establishing. 10. Diffusion. Essentials. Atomic mechanisms of diffusion. Fick`s laws of diffusion. Boundary conditions. Analytical and numerical solutions of diffusion equations. 11. Diffusion in real systems. Atomic mobility. Mass fluxes. Kinetic and thermodynamic factors of diffusion. 12. Diffusion controlled phase transformations. Heterogeneous real systems. Diffusion and equilibrium at high and low temperatures. Simulation programmes (DICTRA). 13. Phase equilibria and diffusion controlled processes in chemical laboratory and technology. Coarsening and dissolving of phases, optimisation of material technology treatment, homogenization, nitriding, weld stability, protective layers, transformation diagrams, ...

Literature

• SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
• PORTER, David A. Phase Transfformations in Metal and Alloys. New York: Van Nostrand Reinhol, 1981, 445 s. ISBN 0-442-30439-0. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.
The course is taught: every week.

• Enrolment Statistics (recent)