A mathematical model for chalcopyrite disease within sphalerite is developed. As one main result, by analyzing the system enthalpy, correct expressions for the reaction terms in a system undergoing phase transitions are worked out. For the resulting equations, the thermodynamical validity is shown and the existence of a unique solution is proved.
REFERENCES
1.
Alt
, H. W.
and Luckhaus
, S.
, “Quasilinear elliptic parabolic differential equations
,” Math. Z.
183
, 311
–338
(1983
).2.
Bente
, K.
and Doering
, T.
, “Diffusion induced segregation in Cu-In systems
,” Contrib. Mineral. Petrol.
53
, 285
–305
(1995
).3.
Blesgen
, T.
, “Modeling and numerical simulation of diffusion induced segregation
,” Cryst. Res. Technol.
37
, 570
–580
(2002
).4.
Blesgen
, T.
, Luckhaus
, S.
, and Bente
, K.
, “Diffusion induced segregation in the case of the ternary system sphalerite, chalcopyrite and cubanite
,” Cryst. Res. Technol.
39
, 969
–979
(2004
).5.
Elliott
, C. M.
and Luckhaus
, S.
, “A generalized diffusion equation for phase separation of a multi-component mixture with interfacial free energy
,” Report No. SFB 256, University Bonn
, 1991
.6.
Elliott
, C. M.
and Songmu
, Z.
, “On the Cahn–Hilliard equation
,” Arch. Ration. Mech. Anal.
96
, 339
–357
(1986
).7.
Garcke
, H.
, Habilitation thesis, Bonn, 2001
.8.
Grindrod
, P.
, The Theory and Application of Reaction-Diffusion Equations, Patterns and Waves
, 2nd ed. (Clarendon
, Oxford, 1996
).9.
Kirkaldy
, J. S.
and Young
, D. J.
, Diffusion in the Condensed State
(The Institute of Metals
, London, 1987
).10.
O’Keefe
, M.
and Navrotsky
, A.
, Structures and Bonding in Crystals
(Academic
, New York, 1981
).11.
Onsager
, L.
, “Reciprocal relations in irreversible processes I
,” Phys. Rev.
37
, 405
–426
(1931
).12.
Onsager
, L.
, “Reciprocal relations in irreversible processes II
,” Phys. Rev.
38
, 2265
–2279
(1931
).13.
Protter
, M. H.
and Weinberger
, H. F.
, Maximum Principle in Differential Equations
, 2nd ed. (Springer
, New York, 1999
).© 2005 American Institute of Physics.
2005
American Institute of Physics
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