PHASE STABILITY IN ALLOYS

Mehrabov Ə.

  • Kursun Səviyyəsi: Doctorate
  • Dizayn edilən dərs kodu: Met E 540
  • Təhsil növü: Formal Education (Day Education)
  • Kursun Məzmunu: Theoric and Application
  • Akademik il: 1994 - 1995
  • Dərsin məzmunu:

    MIDDLE EAST TECHNICAL UNIVERSITY

    Department of Metallurgical and Materials Engineering

     

    MetE 540 Phase Stability in Alloys (3-0) 3

     

    Course Content

     

    I.                Introduction

    -        Concept of Alloy. Types of alloys. Solid Solutions

    -        Intermediate and Interstitial Phases

    -        The free energy of solid solutions. Phase mixtures

    -        The stable state of an alloy

    -        Equations of phase equilibrium. The phase rule

     

                                                               (2 week)

     

    II.             Order- Disorder transformations in Solids

                 -  Order-disorder phase transformation.

                 -  Long-range order (LRO) in solid solutions.

                 -  Short range order (SRO) in solid solutions.

                 - Elementary theory of SRO (Homework).

     

                                                      (1 week)

     

    III.           Interatomic interactions in the metals and alloys

    -        Introduction

    -        Statistico-thermodynamical theory of binary alloys

               - A. Gorsky-Bragg-Williams (GBW) Theory

               - B. Kirkwood’s Theory

               - C. Quasi-Chemical Theory

    -        Quantum mechanical model of interatomic interactions for metals and binary solid solutions.

                                                                                             (2 week)

     

     

                     Homework: Interatomic Interactions in the Metals and Alloys

     

     

    IV.           The pseudopotential theory of interatomic interactions

    -        Potential seen by an atomic electron

    -        Dielectric screening

    -        Interatomic interaction potential

    -        Screening in alloys

                                                                                                                       (2 week)

     

    V.              The use of pseudopotential theory for crystal structure stability calculations

    -        Basic assumption

    -        Band structure energy of pure metals and binary alloys

    -        Application of the theory for crystal-structure energy calculations of pure Al.

    -        Electrostatic energy calculations for metals and binary alloys

    -        The total internal energy of an alloy with perfect long-range order

    -        The total internal energy of an alloy with short-range order

    -        The total internal energy of a fully random alloy

                                          

                                                                                                               (3 week)

     

                   Project I. Crystal-Structure energy calculations for pure metals in the pseudopotential

                                  method approximation

     

     Midterm I (Project 1)

     
     

    Midterm I (Project 1)

     

       VI.        The calculation of phase boundary energies in terms of pseudopotential theory

    -     Basic assumption

    -     Theory of phase boundary energy calculations

    -     Application of the theory to Cu-Al alloys

    -     Application of the theory to In-Mg and Al-Mg alloys

     

                                                                                                                                 (1 week)

     

    Project II. Phase boundary energy calculation for the different binary alloys

     

     Midterm II (Project 2)

     
     

     


     Midterm II (Project 2)

     

     

    VII.     Ordered phases, their structures and existence conditions calculation in terms of pseudopotential theory of alloys

    -        Basic assumption

    -        Calculation of the ordered phases energy for binary alloys

    -        Application of the theory to the ordered phase analysis for Hg-Mg alloys

    -        Calculation of the short-range ordering energy for binary alloys

    -        Application of the theory to the short-range order problems in Ni-Al, Fe-Al, Ti-Al, etc. alloys

     

                                                                                                                                          (2 week)

     

                       Project III. Pairwise alloying potential calculations for binary alloys

     

    VIII.    The interatomic interaction potential calculation in the fiber reinforced metal matrix composites (Homework)

    -             Experimental data analysis

    -             The choice of matrix for composite materials

    -             Application of the pseudopotential theory to the solubility process analysis in composites

    -             Interatomic interaction parameters in the statistical theory of alloys

    -             The calculation of the interatomic interaction parameters in the composites with Al and Mg matrixes.

     

                                                                                                                                    (1 week)

     

           Project IV. The calculation of the interatomic interaction parameters for different metal  

                             matrix composites

     

     

    REFERENCES

     

    1. Cottrell, A., An Introduction to Metallurgy, E. Arnold Ltd., London, 1979.
    2. Girifalco, L. A., Statistical Physics of Materials, John Wiley and Sons., N. Y., 1973.
    3. Animaln, A.O. E., Intermediate Quantum Theory of Crystal-Line Solids, Englewood Cliffs, N.J., 1977.
    4. Harrison, W. A., Pseudopotential in the Theory of Metals, N. Y. , W. A. Benjamin, 1966.
    5. Krivoglaz, M. A., The Theory of Order-Disorder in Alloys, N. Y. , 1964
    6. Khachaturyan, A. G., Theory of Structural Transformations in Solids, N.Y., 1983
    7. Yastrebov, L.I., Katsnelson A.A. Foundations of one-electron theory of solids, Mir Publisher, Moscow, 1987
    8. Heine, V., Cohen, M.L., Weaire., Solid State Physics, vol. 24, ed. by H. Ehrenreich et al., Academic Press, N. Y., 1970.
    9. Hayes T.M., Brooks, H., and Bienenstock, Phys. Rev., vol. 175, p. 699, 1968.
    10. Inglesfield, J. K. , J. Phys. C,  vol. 1, p. 1837, 1968; vol. 2, p. 1285, 1969; vol. 2, p. 1293, 1969.
    11. Kogachi, M. J. Phys. Chem. Solids, vol. 32, p. 2393, 1971; vol. 34, p. 67, 1973; vol. 35, p. 109, 1974
    12. Krasco, G. L., Machnovetskii A. B., Phys. Stat. Sol. (b), vol. 65, p. 869, 1974.
    13. Kastnelson, A. A. , Silonov, V. M., Farid, A., Khawaja, Phys. Stat. Sol. (b), vol. 91, p.11, 1979.
    14. Mekhrabov Amdulla O. O., Doyama M. , Phys. Stat. Sol. (b), vol. 126, p. 453, 1984.
    15. Mekhrabov A.O., Akdeniz M.V. and Arer M.M., Acta Mater., vol. 45, No. 3, p. 1077-1083, 1997
    16. Mekhrabov A.O. and Akdeniz M.V., Acta Mater., vol. 47, No. 7, p. 2067-2075, 1999
    17. Portnoy K. I., Bogdanov V. I.,  and Fuks D. L., Rachet Vsaimodeytivie and Stabilnosti faz, Metallurgiya, Moscow, 1981 (in Russian).
    18. Akdeniz M.V. and Mekhrabov A.O., Acta Mater., Vol. 46, No. 4, p. 1185-1192, 1998

     

     

     

    Schedule: Tuesday, 13:40 - 17:30, B-208

     

    GRADING:

     

    Project I: 15%

    Project II: 20%

    Project III: 15%

    Homework: 10%

    Attendance: 5%

    Final Exam: 35%