Towards the Thermodynamic Modeling of Nucleation and Growth of Liquid Droplets in Single Crystals

Dreyer, Wolfgang; Duderstadt, Frank

doi:10.1007/978-3-0348-7893-7_9

Cited by 4 publications

(7 citation statements)

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“…A jump of the chemical potential was also observed numerically in [9] on studies of stress assisted diffusion in Gallium Arsenide single crystals where unwanted liquid droplets grow in the solid surrounding. Because contrary to the solid phase the liquid phase does not contain any dislocations and vacancies, this leads to a jump of the chemical potential across the solid-liquid interface.…”

Section: Introductionmentioning

confidence: 64%

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On reconstitutive phase transitions and the jump of the chemical potential

Blesgen¹

2008

Analysis

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Summary:This article studies diffusion in solids in the case of two phases under isothermal conditions where due to plastic effects the number of vacancies changes when crossing a transition layer, i.e. a reconstitutive phase transition. A segregation model is derived and the equations are studied in the limit of a sharp interface. A Gibbs-Thomson law is derived and it is shown that the vacancy component of the chemical potential jumps across the transition layer thereby explaining recent experimental observations. The thermodynamic correctness of the model is shown as well as the existence of weak solutions with logarithmic free energies.

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Section: Introductionmentioning

confidence: 64%

“…Because contrary to the solid phase the liquid phase does not contain any dislocations and vacancies, this leads to a jump of the chemical potential across the solid-liquid interface. For the chemical potential of the Gallium phase and the Arsenide phase, [9] postulates the constitutive relations…”

Section: Introductionmentioning

confidence: 99%

On reconstitutive phase transitions and the jump of the chemical potential

Blesgen¹

2008

Analysis

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“…Jumps of the chemical potential that depend on the particular structure of the sub-lattice were observed and studied before in References [12,13] for models of Ga=As precipitates, where the defects are very important for the macroscopic properties of the material.…”

Section: T Blesgen and S Luckhausmentioning

confidence: 98%

The dynamics of transition layers in solids with discontinuous chemical potentials

Blesgen

Luckhaus

2006

Math. Meth. Appl. Sci.

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SUMMARYWe derive a two-phase segregation model in solids under isothermal conditions where due to plastic e ects the number of vacancies changes when crossing a transition layer, i.e. a reconstitutive phase transition. We show the thermodynamic correctness of the model and review the existence of weak solutions in suitable spaces. By a formal asymptotic analysis we study the dynamics of the interface and its dependence on the unsymmetric vacancy distribution.

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“…the stiffened gas equation of state for component i is specified. According to (10), (12) and (14) it holds…”

Section: Equation Of Statementioning

confidence: 99%

“…Step 2: Determine the integration constant c(ρ i , T 0 ) by plugging (24) into (10) c and integrating the resulting ODE…”

Section: Remarkmentioning

confidence: 99%

Analysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions

Hantke

Müller

2018

Quart. Appl. Math.

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Starting in 2007, the MFO publishes a preprint series which mainly contains research results related to a longer stay in Oberwolfach. In particular, this concerns the Research in Pairs-Programme (RiP) and the Oberwolfach-Leibniz-Fellows (OWLF), but this can also include an Oberwolfach Lecture, for example. A preprint can have a size from 1-200 pages, and the MFO will publish it on its website as well as by hard copy. Every RiP group or Oberwolfach-Leibniz-Fellow may receive on request 30 free hard copies (DIN A4, black and white copy) by surface mail. Of course, the full copy right is left to the authors. The MFO only needs the right to publish it on its website www.mfo.de as a documentation of the research work done at the MFO, which you are accepting by sending us your file. In case of interest, please send a pdf file of your preprint by email to or , respectively. The file should be sent to the MFO within 12 months after your stay as RiP or OWLF at the MFO. ri There are no requirements for the format of the preprint, except that the introduction should contain a short appreciation and that the paper size (respectively format) should be DIN A4, "letter" or "article". On the front page of the hard copies, which contains the logo of the MFO, title and authors, we shall add a running number (20XX-XX). We cordially invite the researchers within the RiP or OWLF programme to make use of this offer and would like to thank you in advance for your cooperation.

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Towards the Thermodynamic Modeling of Nucleation and Growth of Liquid Droplets in Single Crystals

Cited by 4 publications

References 1 publication

On reconstitutive phase transitions and the jump of the chemical potential

On reconstitutive phase transitions and the jump of the chemical potential

The dynamics of transition layers in solids with discontinuous chemical potentials

Analysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions

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