Module also offered within study programmes:
General information:
Annual:
2017/2018
Code:
MIM-2-109-AM-s
Name:
Diffusion in materials
Faculty of:
Metals Engineering and Industrial Computer Science
Study level:
Second-cycle studies
Specialty:
Advanced Materials - Processing and Characterization
Field of study:
Materials Science
Semester:
1
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
dr hab. inż. Kowalski Kazimierz (kazimierz.kowalski@agh.edu.pl)
Academic teachers:
Gut Stanisław (gut@agh.edu.pl)
Radziszewska Agnieszka (radzisze@agh.edu.pl)
WRóbel Mirosław (mwrobel@agh.edu.pl)
dr hab. inż. Kowalski Kazimierz (kazimierz.kowalski@agh.edu.pl)
dr inż. KĄC Sławomir (slawomir.kac@agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 Student is able to pass on his knowledge and skills concerning the diffusion in materials for students of technical sciences and for engineers. IM2A_K03 Presentation,
Scientific paper,
Participation in a discussion
Skills
M_U001 Student is able to determine the diffusion coefficient from experimental data using solutions of diffusion equations for some model systems. IM2A_U05, IM2A_U08 Test,
Report
M_U002 Student is able to designe the experiments for determining the diffusion coefficients. IM2A_U05, IM2A_U08 Test,
Report
M_U003 Student is able to determine the activation energy of bulk and grain boundary diffusion using the experimentally determined diffusion coefficients. IM2A_U01, IM2A_U05, IM2A_U08 Test,
Report
M_U004 Basing on his own knowledge and the scientific literature the student is able to develop selected topics of diffusion in materials. IM2A_U01, IM2A_U06 Presentation,
Scientific paper,
Participation in a discussion
Knowledge
M_W001 Student understands natural phenomena and technological processes where diffusion plays an important role and where it controls these phenomena. IM2A_W03 Examination
M_W002 Student knows the basic phenomenological laws of diffusion (Fick's laws) and is able to present solutions of the diffusion equations in the simplest cases. IM2A_W03 Examination
M_W003 Student knows the random walk theory of diffusion and can relate the results of this theory (Einstein-Smoluchowski equation) with phenomenological laws of diffusion. IM2A_W03 Examination
M_W004 Student understands the diffusion process in the frame of the irreversible thermodynamics concepts. IM2A_W03 Examination
M_W005 Student knows the atomic mechanisms of diffusion in solids, knows how the diffusion coefficient depends on the diffusion mechanism and can explain the temperature dependence of the diffusion coefficient. IM2A_W03 Examination
M_W006 Student knows and is able to explain the specific phenomenon of diffusion in different types of materials: metals and their alloys, semiconductors, ceramics (including solid electrolytes) and amorphous materials. IM2A_W03 Examination
M_W007 Student understands the influence of external forces such as: electric field, stress field, chemical potential and temperature gradient on the process of diffusion. IM2A_W03 Examination
M_W008 Student understands and can explain such phenomena of matter transport in solids as: chemical diffusion (mutual diffuzion), Kirkendall effect, the role of diffusion in phase transitions and chemical reactions involving solids (reactive diffusion). Student knows the Darken equation and is able to use the Boltzmann-Matano method. IM2A_W03 Examination
M_W009 Student understands the role of the fast diffusion paths in solids: dislocations, grain and phase bounadries and surface. Student knows the Fisher model of diffusion and its application to the polycrystalline materials. IM2A_W03 Examination
M_W010 Student knows the most popular experimental methods of determining the bulk and grain bounadry diffusion coefficients. IM2A_W03, IM2A_W05 Examination
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 Student is able to pass on his knowledge and skills concerning the diffusion in materials for students of technical sciences and for engineers. + - + - - - - - - - -
Skills
M_U001 Student is able to determine the diffusion coefficient from experimental data using solutions of diffusion equations for some model systems. - - + - - - - - - - -
M_U002 Student is able to designe the experiments for determining the diffusion coefficients. - - + - - - - - - - -
M_U003 Student is able to determine the activation energy of bulk and grain boundary diffusion using the experimentally determined diffusion coefficients. - - + - - - - - - - -
M_U004 Basing on his own knowledge and the scientific literature the student is able to develop selected topics of diffusion in materials. - - + - - - - - - - -
Knowledge
M_W001 Student understands natural phenomena and technological processes where diffusion plays an important role and where it controls these phenomena. + - - - - - - - - - -
M_W002 Student knows the basic phenomenological laws of diffusion (Fick's laws) and is able to present solutions of the diffusion equations in the simplest cases. + - - - - - - - - - -
M_W003 Student knows the random walk theory of diffusion and can relate the results of this theory (Einstein-Smoluchowski equation) with phenomenological laws of diffusion. + - - - - - - - - - -
M_W004 Student understands the diffusion process in the frame of the irreversible thermodynamics concepts. + - - - - - - - - - -
M_W005 Student knows the atomic mechanisms of diffusion in solids, knows how the diffusion coefficient depends on the diffusion mechanism and can explain the temperature dependence of the diffusion coefficient. + - - - - - - - - - -
M_W006 Student knows and is able to explain the specific phenomenon of diffusion in different types of materials: metals and their alloys, semiconductors, ceramics (including solid electrolytes) and amorphous materials. + - - - - - - - - - -
M_W007 Student understands the influence of external forces such as: electric field, stress field, chemical potential and temperature gradient on the process of diffusion. + - - - - - - - - - -
M_W008 Student understands and can explain such phenomena of matter transport in solids as: chemical diffusion (mutual diffuzion), Kirkendall effect, the role of diffusion in phase transitions and chemical reactions involving solids (reactive diffusion). Student knows the Darken equation and is able to use the Boltzmann-Matano method. + - - - - - - - - - -
M_W009 Student understands the role of the fast diffusion paths in solids: dislocations, grain and phase bounadries and surface. Student knows the Fisher model of diffusion and its application to the polycrystalline materials. + - - - - - - - - - -
M_W010 Student knows the most popular experimental methods of determining the bulk and grain bounadry diffusion coefficients. + - - - - - - - - - -
Module content
Lectures:
  1. Introduction to diffusion

    Macroscopic (phenomenological) and microscopic description of diffusion process; characteristics of diffusion in gases, liquids and solids; importance of diffusion in nature and technology; history of diffusion studies.

  2. Diffusion equations

    Derivation of classic (Fick) equations of diffusion, the equation of continuity of matter; macroscopic definition of diffusion coafficient; anisotropy of diffusion and tensor of diffusion coefficient.

  3. Most important solutions of Fick's equations

    Steady-state diffusion and its solutions, examples; non-steady-state diffusion: cases of constant, instantenous and finite sources and their solutions; homogenisation of materials; the role of initial and boundary conditions; mean diffussion distance.

  4. Microscopis interpretatiom of diffusion

    Random-walk theory; derivation of Einstein-Smoluchowski equation and its interpretation; microsopic definiotion of the diffusion coefficient; equivalence of microscopic and macrosopic desription of diffusion; application of the random-walk theory to the diffusion in solids.

  5. Temperature dependance of diffusion

    Thermodynamic description of atom migration process in solid; atomic jump process; activation energy and entropy factor; jumping frequency; correlation factor. Equation of the temperature dependance of diffusion and its Arrhenius presentation.

  6. Mechaisms of diffusion

    Defects in solids and their role in the diffusion; interstitial, vacancy and divacancy, interstitialty, inetrstitial-substitutional exchage and some other collective mechanisms of diffusion; dependency of the correlation effect on diffusion mechanism and crystal structure.

  7. Isotope effect of diffusion. Dependemce of diffusion on pressure

    Self-diffusion and hetero-diffusion; tracer diffusion; method of the isotope effect parameter determination and its importance in diffusion mechanism investigation. Influence of pressure on diffusion process and its therodynamic description; activation volume of diffusion.

  8. Diffusion in different types of materials

    Empirical correlations between diffusion coefficient and other macroscopic properties of materials. Characteristics of diffusion and its mechanisms in different types of materials: metals and alloys, semiconductors and ceramics.

  9. Interdiffusion (chemical diffusion)

    Binary diffusion couple – determination of the chemical diffusion (interdiffusion) coefficient by the Boltzmann-Matano method; advantages and limitations of the method.

  10. Kirkendall effect

    Kirkendall experiment and its interpretation: Kirkendall plane,intrinsic diffusion coefficients, Kirkendall pores, vacancy wind. Importance of the Kirkendall effect in the theory of diffusion and its practical consequences. Darken equation.

  11. Diffusion and irreversible thermodynamics

    Influence of the gradients of chemical potentials, temperature, pressure and other physical potentials on the diffusion flux in multicomponent systems; role of the kinetic (phenomenological) constants; up-hill diffusion.

  12. Diffusion and external driving forces

    Examples of external driving forces; drift motion of atomes; Fick’s equations with drift; Nernst-Einstein relation and its applications; electromigration, effects of Gorsky and Soret.

  13. Reactive diffusion

    Diffusion in multiphase systems; formation of new phases and phase boundary motion; changes of concentration and chemical potential across the phase boundary. Role of diffusion in solid state chemical reactions; oxydation; diffusional phase transformations.

  14. Diffusion along high-diffusivity paths

    Dependance of the diffusion activation energy on the type of high diffusivity path: surface, dislocations, grain and phase boundaries. Fisher’s model of diffusion in an isolated grain boundary and its extrapolation to plycrystalline materials, Harrison’s classification of diffusion kinetic regimes. Diffusion in nanomaterials. Models of diffusion along dislocations and on the surface.

  15. Experimental methods in diffusion

    Classification of direct and indirect methods. Tracer methods: section (mechanical, chemical, electrochemical, SIMS and EPMA) and autoradiography methods. Metallographical methods. Use of some physico-chemical processes: sintering, discontinues precipitation and high temperature creep for determination of diffusion coefficients.

Laboratory classes:
  1. Binary diffusion couple
  2. Kirkendall effect
  3. Homogenization
  4. Oxdation and diffusion
  5. Reactive oxidation
  6. Grain boundary diffusion
Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 89 h
Module ECTS credits 3 ECTS
Participation in lectures 28 h
Participation in laboratory classes 14 h
Examination or Final test 2 h
Realization of independently performed tasks 20 h
Preparation of a report, presentation, written work, etc. 15 h
Contact hours 10 h
Additional information
Method of calculating the final grade:

Final grade = 0.3 x (laboratory classes grade) + 0.7 x (exam grade)

Prerequisites and additional requirements:

Completed course in physics or physical chemistry

Recommended literature and teaching resources:

1. John Crank, Mathematics of Diffusion
2. Jean Philibert, Atom movements, Diffusion and mass transport in solids
3. Helmut Mehrer, Diffusion in Solids. Fundamentals, Methods, Materials, Diffusion-Controlled Processes
4. P. Heitjans, J. Kärger (Eds), Diffusion in Condensed Matter. Methods, Materials, Models
5. J. S. Kirkaldy, D. J. Young, Diffusion in the Condensed State
6. Devendra Gupta (Ed.), Diffusion Processes in Advanced Technological Materials
7. R. W. Baluffi, S. A. Allen, W. C. Carter, Kinetics of Materials, Part I: Motion of Atoms and Molecules by Diffusion
8. R.W. Cahn, P. Haasen (Eds), Physical metallurgy, Vol. 1, Chapter 7: J.L. Bocquet, Y. Limoge, G. Brébec, Diffusion in Metals and Alloys
9. I. Kaur, Y. Mishin, W. Gust, Fundamentals of Grain and Interphase Boundary Diffusion

Scientific publications of module course instructors related to the topic of the module:

http://www.bpp.agh.edu.pl/

1. K. Kowalski, K. Obal, Z. Pędzich, K. Schneider, M. Rękas, Lattice and grain-boundary diffusion of Al in tetragonal Yttria-Stabilized Zirconia polycrystalline ceramics (3Y-TZP) analyzed using SIMS, Journal of the American Ceramic Society, vol. 97 iss. 10 (2014) pgs 3122–3127

2. K. Kowalski, Oxygen diffusion and surface exchange in yttria-stabilized zirconia and gadolinia-doped ceria ceramics at low temperatures, Defect and Diffusion Journal, 2009 vols. 289–292 s. 769–774

3. K. Kowalski, A. Bernasik, J. Camra, M. Radecka i J. Jedliński, Diffusion of niobium in yttria-stabilized zirconia and in titania-doped yttria-stabilized zirconia polycrystalline materials, Journal of the European Ceramic Society 26 (2006) 3139-3143

4. K. Kowalski, A. Bernasik i A. Sadowski, Diffusion of calcium in yttria fully stabilized zirconia ceramics, Journal of the European Ceramic Society 20 (2000) 2095-2100

5. K. Kowalski, A. Bernasik i A. Sadowski, Bulk and grain boundary diffusion of titanium in yttria stabilized zirconia, Journal of the European Ceramic Society 20 (2000) 951-958

Additional information:

None