SO7 Diff Transform 2
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Diffusional Transformations - 2SOLID STATE
Overall Transformation KineticsProgress of isothermal phase transformations can be represented by plotting Fraction transformed (f) as a function of time (t) and temperature (T)TTT Diagrams
(cellular) + (cellular) +
Volume fraction f varies from 0 to 1
Overall Transformation KineticsFactors that determine f(t, T)Nucleation rateGrowth rateDensity & distribution of nucleation sitesOverlap of diffusion fieldsImpingement of adjacent transformed volumesf depends on nucleation rate and growth ratef depends on number of nucleation sites and growth rate
Solid-State Transformation KineticsMany of the reactions of interest to materials scientists involve transformations in the solid state.e.g. Recrystallization of a cold worked material Precipitation of a crystalline polymer from an amorphous phase Growth of an equilibrium phase from a non-equilibrium structure
The driving force is usually brought about by cooling from one temperature to another.Lets consider the initial phase to be and resulting phase to be .The total volume of the sample is:V = V + VThen the fraction transformed can be written as:
Assume that the transformation of to is controlled by nucleation and growth
i.e. nucleation of phase within and then growth of .Let,
The equation relating the fraction transformed to nucleation rate, growth rate, and time is given by:Johnson-Mehl equation
A similar treatment of the subject is given by Avrami.In general, he expresses the fraction transformed aswhere n is called the Avrami n n may vary from 1-4k is equivalent to
Johnson-Mehl EquationAvrami EquationThe variation of n from 4 (as in Johnson-Mehl eqn) can occur for a number of reasons.
In some solid-state reactions, the nucleation rate is a decaying function of time. In that case the Avrami n would be 4 early in the reaction, but decreasing to 3 as the nucleation decreases as a function of time, and the transformation is governed by the growth rate.
In general, for 3-dimensional solids, the Avrami n is between 3 and 4.
In case of a growth of a phase in 2-dimensions such as in a sheet or a film, the Avrami n is between 2 and 3.
In the case of wire, a 1-dimentional solid, the Avrami n is between 1 and 2.
Determine the value of the Avrami n.Thus the Avrami n is the slope of the plot of the ln ln 1/(1 F) versus ln t
Overall Transformation KineticsTTT Diagrams
+ Volume fraction f varies from 0 to 1Value of n is numerical exponent that varies from ~1 to 4
Precipitation in Age-Hardening AlloysAl-4Cu (1.7 at%) alloy-phase-phase
Precipitation in Age-Hardening Alloys Transition PhasesGP zonesFully coherentVery low interfacial energyTwo atomic layers thick10 nm diameter
Precipitation in Age-Hardening Alloys Transition PhasesGP zones are formed as first ppt during low temperature aging of many technologically important alloys.
Precipitation in Age-Hardening Alloys Transition PhasesPrecipitation process are fully coherent plate-like pptsVisible through coherency-strain fieldsOrientation relationship with the matrixGo G1 G2 G3 G4
Precipitation in Age-Hardening AlloysActivation energy barrier
Precipitation in Age-Hardening Alloys Tetragonal
TetragonalComposition approx CuAl2
Precipitation in Age-Hardening AlloysNucleation sites
Precipitation in Age-Hardening AlloysEffect of aging temperature on the sequence of precipitatesFastest transformation rates are associated withhighest nucleation rates and therefore the finest ppt distributions
Precipitate Free Zone (PFZ)
Spinodal DecompositionTransformations having no barrier to nucleationPhase diagram with a miscibility gapTemperature lowered from T1 to T2Alloy will immediately become unstableSmall fluctuation in composition can produce A-rich and B-rich regionsUp-hill diffusion takes placeFree-energy has a negative curvature
Spinodal DecompositionFor spinodal decomposition the alloy must lie between the two points of inflectionLocus of the points on the phase diagram is known as the chemical spinodalFor alloys outside spinodalSmall variation in composition will lead to an increase in free-energyThus alloy is metastableNucleation & growth processDown-hill diffusion occursFree-energy has a positive curvature
Spinodal Decomposition vs N & G
Particle CoarseningMicrostructure of a 2-phase alloy is not completely stable unless the total interfacial free energy is minimumHigh density of fine ppt will tend to coarsen into a lower density of larger pptReduces overall interfacial area
Gibbs-Thomson effectTotal number of ppts decreases and the mean radius r increases with timeIf r0 is the mean radius at t=0 thenWhere,
Rate of ppt Coarsening