A dynamic model for evolution of crystal shape

Gadewar, Sagar B.; Doherty, Michael F.

doi:10.1016/j.jcrysgro.2004.03.019

Cited by 43 publications

(31 citation statements)

References 15 publications

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“…Further model reduction was applied to form three coupled single PB equations using a predefined function for the 2-D crystal-size distribution. Recently, a new approach was developed by Zhang and Doherty 58 to combine a separate shape evolution model 31 with a standard 1-D PB model for the simultaneous prediction of crystal shape evolution and size distribution in solution crystallization processes. The method was applied to track both the crystal size and shape evolution of 2-D tabletlike succinic acid crystals, as grown from water, with fixed relative face growth rates being applied to all faces.…”

Section: Population Balance Modelingmentioning

confidence: 99%

Morphological population balance for modeling crystal growth in face directions

2007

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in Wiley InterScience (www.interscience.wiley.com).A morphological (or polyhedral) population balance (PB) model is presented for modeling the dynamic size evolution of crystals grown from solution in all crystal growth directions. The morphological PB approach uses the crystal shape information for a single crystal obtained from morphology prediction, or experiment as the initial face locations, as well as face growth rates to predict the shape evolution of the crystal population. For each time instant during the crystallization process, the prediction uses its shape at the previous time moment, and the growth rate for the specific crystal habit plane. The methodology is demonstrated through a study of potash alum (KAl (SO 4 ) 2 Á12H 2 O), for which literature data is available for comparison and validation. The discretization method, method of classes, was used to convert the equations to ordinary differential form with the computational domain being discretized into small meshes. The ordinary differential equations ([1.5 million) were then solved simultaneously using the Runge-Kutta-Fehlbergh 4th/5th-order solver with automatic time-step control. The results obtained clearly demonstrate that the morphological PB model developed can predict crystal growth and surface area of individual habit faces in detail, together with crystal shape and size evolution.

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Section: Population Balance Modelingmentioning

confidence: 99%

Morphological population balance for modeling crystal growth in face directions

2007

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“…Instead, these freely grown grains are somewhat similar to the grown single crystals scaled down, scarcely observed in ceramics. Furthermore, as such crystalline grains are still on a micrometer scale that only corresponds to the initial stages of growth of bulk single crystals, valuable information is thus expected to help a better understanding of the growth process of crystal counterparts, since all habitual faces, including those in the transitional form with high growth rates, should appear on the growth morphology in such stages [19,20].…”

Section: Article In Pressmentioning

confidence: 99%

Growth mechanism of relaxor-PbTiO3 single crystals shown by morphology of crystalline grains in ceramics

Pan

Zhang

Chen

2005

Journal of Crystal Growth

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“…In literature, the so-called multidimension is often interpreted as multiple-variables, i.e., a single-size dimension as volume equivalent spherical diameter plus other variables, such as particle location, porosity and fraction ratio. Crystal morphology has been a very important research area, but the focus has been on shape prediction for single crystals [10,[75][76][77][78][79][80] rather than for all the crystal population within a crystalliser. On the other hand, although population balance (PB) modeling for crystallisation processes is for all crystals in a crystalliser, crystal shape was often ignored with an over-simplified crystal-size definition, i.e., the volume equivalent diameter of spheres (see for example [54,[81][82][83][84][85][86][87][88]).…”

Section: Multi-dimensional and Morphological Population Balance Modelsmentioning

confidence: 99%

“…Faceted crystal shape evolution and manipulation during dissolution or growth were studied by Snyder et al [78,97]. Zhang and Doherty [98] developed a method to combine a separate shape evolution model [77] with a standard 1D PB model for the simultaneous prediction of crystal shape evolution and size distribution in crystallisation processes of succinic acid.…”

Section: Multi-dimensional and Morphological Population Balance Modelsmentioning

confidence: 99%

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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A dynamic model for evolution of crystal shape

Cited by 43 publications

References 15 publications

Morphological population balance for modeling crystal growth in face directions

Morphological population balance for modeling crystal growth in face directions

Growth mechanism of relaxor-PbTiO3 single crystals shown by morphology of crystalline grains in ceramics

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

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