A simple model to describe isothermic phase transformations in binary alloys

Simmich, O.; Löffler, H.

doi:10.1002/pssa.2210480153

Cited by 1 publication

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“…2. (7) converges well for t > t k 2 = ( 4 L 2 /~2 D ) (7b) (8) and in these cases (7) can be fitted well by…”

Section: Later Stages Of Decompositionmentioning

confidence: 86%

“…From (8) it can be concluded that the growth law R = at1/?, which holds for the initial stage of ageing (see (5d)), does not graduate into the JMA equation (2) with m = 1/2 for later ageing times. Indeed (8) is of JMA type, but with rn = 1 and a back-shifted time scale.…”

Section: Discussionmentioning

confidence: 99%

“…I n 0. SIMMICH and H. LOFFLER the interval R > 0.6Ren,1 (8) can be applied instead of (7). The JMA formula ( 2 ) with m = 1/2 does not f i t well (7).…”

Section: Discussionmentioning

confidence: 99%

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On the one-dimensional diffusion-controlled growth of parallel plates

Simmich

Löffler

1980

Phys. Stat. Sol. (a)

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The one-dimensional growth of a set of infinite parallelly arranged plates of uniform distance 2L is comidered taking into account the interaction between neighbouring plates by means of the diffusion controlled impoverishment of the alloyed atoms in the matrix (soft impingement) as well as the movement of the interface between plates and matrix in time and supposing that the concentration a t the interface as well as the diffusion constant D are independent of time. The diffusion equation is solved in two manners, namely by combination and repeated use of the methods of reflection and superposition as well as that of separation of variables. The main results are the following. 1. The parabolic growth law ( R = atlln) holds only in the time range t < LZ/D. 2. At later ageing times ( t > 4L2/Dn2) the growth law of the thickness 2R of the plates can be approximately described by a formulae of Avrami type, namely R/R,,d = 1 -exp (--It -0.21), taking into account a shift of the time scale. 3. In case R < L and Dt < L2 holds the consideration of the movement of the interface in time does not essentially influence the growth kinetics (i.e. R = = atW holds as well). Es wird das eindimensionale Wachstum eines Satzes unendlicher parallel angeordneter Platten mit einheitlichem Abstand 2L betrachtet, unter Beriicksichtigung der Wechselwirkung zwischen benachbarten Platten (ausgedriickt durch die diffusionskontrollierte Verarmung der Matrix a n Legierungsatomen, sog. soft impingement) und der Wanderung der Interface zwischen Platte und Matrix mit der Zeit und unter der Annahme, daO sowohl die Konzentration ander Interface als auch die Diffusionskonstante D zeitunabhangig sind. Die Diffusionsgleichung wird sowohl durch Kombination und wiederholte Anwendung der Methode der Reflexion und Superposition als auch nach der Methode der Variablenseparation gelost. Folgende Hauptresultate werden erzielt. 1. Das parabolische Wachstumsgesetz ( R = atllz) gilt nur im Zeitbereich t < L2/D. 2. Bei spaten Alterungszeiten ( t > 4L2/Dn2) wird das Wachstumsgesetz der Plattendicke (3R) nlherungsweise durch eine Formel vom Avrami-Typ erfaDt, namlich R/R,,d = 1exp (-W -0,21), wenn man die Verschiebnng der Zeitskala beriicksichtigt. 3. Sind die Bedingungen R< L und Dt< Lz erfiillt, 80 beeinflu& die Bewegung der Interface nicht wesentlich die Wachstumskinetik, d. h. R = atllz gilt ebenfalls.

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“…2. (7) converges well for t > t k 2 = ( 4 L 2 /~2 D ) (7b) (8) and in these cases (7) can be fitted well by…”

Section: Later Stages Of Decompositionmentioning

confidence: 86%

Section: Discussionmentioning

confidence: 99%