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Modelling crystallization: When the normal growth velocity depends on the supersaturation
- The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the material excess, the supersaturation. Using a conservation constraint for the transformation ratio α∈[0,1] as complementing the rescaled supersaturation to 1 and a kinetic law for the normal growth velocity as function of the supersaturation raised to power g, the growth order, we derive an equation for the rate of transformation dα/dt. We integrate it for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of g = 1, 2 towards obtaining expressions for αDg. The same equation, with g = 1 and D = n (n is the so called Avrami exponent) is obtained when taking only the linear in α term from the Taylor’s expansion around α = 0 of the model equation of Johnson-Mehl-Avrami-Kolmogorov (JMAK). We verify our model by fitting datasets of α21 and α31 (from α = 0 to αupper = 0.999) with JMAK to obtain from the fit n = 1.725, 2.43, resp. WeThe crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the material excess, the supersaturation. Using a conservation constraint for the transformation ratio α∈[0,1] as complementing the rescaled supersaturation to 1 and a kinetic law for the normal growth velocity as function of the supersaturation raised to power g, the growth order, we derive an equation for the rate of transformation dα/dt. We integrate it for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of g = 1, 2 towards obtaining expressions for αDg. The same equation, with g = 1 and D = n (n is the so called Avrami exponent) is obtained when taking only the linear in α term from the Taylor’s expansion around α = 0 of the model equation of Johnson-Mehl-Avrami-Kolmogorov (JMAK). We verify our model by fitting datasets of α21 and α31 (from α = 0 to αupper = 0.999) with JMAK to obtain from the fit n = 1.725, 2.43, resp. We show further how the values of n depend on the value of αupper to which the fit is performed starting always from 0. Towards building a validation protocol, we start with validating α21 with published results.…
Autor*innen: | V.V. Ivanov, Christopher Tielemann, K. Avramova, Stefan ReinschORCiD, V. Tonchev |
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Dokumenttyp: | Zeitschriftenartikel |
Veröffentlichungsform: | Verlagsliteratur |
Sprache: | Englisch |
Titel des übergeordneten Werkes (Englisch): | Journal of Physics and Chemistry of Solids |
Jahr der Erstveröffentlichung: | 2023 |
Organisationseinheit der BAM: | 5 Werkstofftechnik |
5 Werkstofftechnik / 5.6 Glas | |
Veröffentlichende Institution: | Bundesanstalt für Materialforschung und -prüfung (BAM) |
Verlag: | Elsevier Ltd. |
Jahrgang/Band: | 181 |
Aufsatznummer: | 111542 |
Erste Seite: | 1 |
Letzte Seite: | 10 |
DDC-Klassifikation: | Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurwissenschaften und zugeordnete Tätigkeiten |
Freie Schlagwörter: | Crystallization; Growth kinetics; Growth rate; JMAK model; Supersaturation |
Themenfelder/Aktivitätsfelder der BAM: | Material |
DOI: | 10.1016/j.jpcs.2023.111542 |
URN: | urn:nbn:de:kobv:b43-581706 |
ISSN: | 0022-3697 |
Verfügbarkeit des Dokuments: | Datei für die Öffentlichkeit verfügbar ("Open Access") |
Lizenz (Deutsch): | Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International |
Datum der Freischaltung: | 06.09.2023 |
Referierte Publikation: | Ja |
Datum der Eintragung als referierte Publikation: | 06.09.2023 |
Schriftenreihen ohne Nummerierung: | Wissenschaftliche Artikel der BAM |