The equation describes the time evolution of a scalar-valued state variable on a domain during a time interval , and is given by:[1][2]
where is the mobility, is a double-well potential, is the control on the state variable at the portion of the boundary , is the source control at , is the initial condition, and is the outward normal to .
^Allen, S. M.; Cahn, J. W. (1972). "Ground State Structures in Ordered Binary Alloys with Second Neighbor Interactions". Acta Metall. 20 (3): 423–433.
doi:
10.1016/0001-6160(72)90037-5.
^Allen, S. M.; Cahn, J. W. (1973). "A Correction to the Ground State of FCC Binary Ordered Alloys with First and Second Neighbor Pairwise Interactions". Scripta Metallurgica. 7 (12): 1261–1264.
doi:
10.1016/0036-9748(73)90073-2.
Allen, S. M.; Cahn, J. W. (1975). "Coherent and Incoherent Equilibria in Iron-Rich Iron-Aluminum Alloys". Acta Metall. 23 (9): 1017.
doi:
10.1016/0001-6160(75)90106-6.
Allen, S. M.; Cahn, J. W. (1976). "On Tricritical Points Resulting from the Intersection of Lines of Higher-Order Transitions with Spinodals". Scripta Metallurgica. 10 (5): 451–454.
doi:
10.1016/0036-9748(76)90171-x.
Allen, S. M.; Cahn, J. W. (1976). "Mechanisms of Phase Transformation Within the Miscibility Gap of Fe-Rich Fe-Al Alloys". Acta Metall. 24 (5): 425–437.
doi:
10.1016/0001-6160(76)90063-8.
Cahn, J. W.; Allen, S. M. (1977). "A Microscopic Theory of Domain Wall Motion and Its Experimental Verification in Fe-Al Alloy Domain Growth Kinetics". Journal de Physique. 38: C7–51.
Allen, S. M.; Cahn, J. W. (1979). "A Microscopic Theory for Antiphase Boundary Motion and Its Application to Antiphase Domain Coarsening". Acta Metall. 27 (6): 1085–1095.
doi:
10.1016/0001-6160(79)90196-2.
The equation describes the time evolution of a scalar-valued state variable on a domain during a time interval , and is given by:[1][2]
where is the mobility, is a double-well potential, is the control on the state variable at the portion of the boundary , is the source control at , is the initial condition, and is the outward normal to .
^Allen, S. M.; Cahn, J. W. (1972). "Ground State Structures in Ordered Binary Alloys with Second Neighbor Interactions". Acta Metall. 20 (3): 423–433.
doi:
10.1016/0001-6160(72)90037-5.
^Allen, S. M.; Cahn, J. W. (1973). "A Correction to the Ground State of FCC Binary Ordered Alloys with First and Second Neighbor Pairwise Interactions". Scripta Metallurgica. 7 (12): 1261–1264.
doi:
10.1016/0036-9748(73)90073-2.
Allen, S. M.; Cahn, J. W. (1975). "Coherent and Incoherent Equilibria in Iron-Rich Iron-Aluminum Alloys". Acta Metall. 23 (9): 1017.
doi:
10.1016/0001-6160(75)90106-6.
Allen, S. M.; Cahn, J. W. (1976). "On Tricritical Points Resulting from the Intersection of Lines of Higher-Order Transitions with Spinodals". Scripta Metallurgica. 10 (5): 451–454.
doi:
10.1016/0036-9748(76)90171-x.
Allen, S. M.; Cahn, J. W. (1976). "Mechanisms of Phase Transformation Within the Miscibility Gap of Fe-Rich Fe-Al Alloys". Acta Metall. 24 (5): 425–437.
doi:
10.1016/0001-6160(76)90063-8.
Cahn, J. W.; Allen, S. M. (1977). "A Microscopic Theory of Domain Wall Motion and Its Experimental Verification in Fe-Al Alloy Domain Growth Kinetics". Journal de Physique. 38: C7–51.
Allen, S. M.; Cahn, J. W. (1979). "A Microscopic Theory for Antiphase Boundary Motion and Its Application to Antiphase Domain Coarsening". Acta Metall. 27 (6): 1085–1095.
doi:
10.1016/0001-6160(79)90196-2.