Periodic Reporting for period 3 - NEMOCRYS (Next Generation Multiphysical Models for Crystal Growth Processes)
Reporting period: 2023-02-01 to 2024-07-31
For the development of new NUMERICAL MODELS, the Finite Element software Elmer has been mainly applied so far, in particular for thermal and electromagnetic phenomena. While Elmer is a generally ready-to-use open source code with wide multiphysical capabilities, the setup of simulations becomes increasingly difficult for complex geometries and large-scale parametric studies. Therefore, a new Python-based interface pyelmer has been developed and published under an open-source license. pyelmer facilitates the automation of the pre-processing and post-processing phases of simulations, hence saving time and reducing errors in model setup and implementation. The OpenFOAM software is based on the Finite Volume Method and is applied for modeling the melt and gas flows. Furthermore, models for a simplified description of high-frequency induction heating as well as for free surface shapes are being developed for the floating zone process. The selected simulation programs together with tools for pre-processing (e.g. Gmsh for grid generation) and post-processing (e.g. ParaView for visualization) are integrated into a Python-based SOFTWARE PLATFORM for open-source crystal growth simulation - OpenCGS.
One of the main overarching goals of the project is the VALIDATION of numerical models. To that end, we have developed a new methodology consisting of three steps: (1) sensitivity analysis to identify the most relevant model parameters; (2) parameter adjustment using in-situ measurements during a growth process or using dedicated experimental setups; (3) global accuracy estimation by comparing simulations with growth experiments. Recently, we have applied this approach to thermal modeling of the Czochralski process for tin and developed routines of parameter adjustment for convective heat transfer in the gas and in the melt in particular. This allowed us to reach a new level of accuracy for such practically relevant quantities as global power balance and crystal diameter. Another study addressed Czochralski growth of caesium iodide as a low-temperature model materials for oxides and halides. In-situ measurements of crucible temperature and inductor current allowed us to validate various modeling assumptions related to melt flow and semi-transparency of the crystal.
The development of numerical models was preceded by a careful analysis of the current state of the art in the relevant literature to obtain an overview of the open questions and unresolved challenges. We first addressed the effects of convective heat transfer which have historically been neglected or simplified without adequate justification in most cases. Models for complex three-dimensional shapes of inductive and resistive heaters were validated using measurements of the temperature distributions and magnetic fields. Finally, after analyzing many other open modeling questions, we expect to develop a "recipe book" of high practical relevance and large physical and technological scope leading to a new generation of multiphysical models for crystal growth processes. All these models, along with the validation experiments, will be made available under open source licenses and documented in open access publications. Our goal is to provide an alternative to the commonly-used commercial multi-physics packages (which require significant adaptations for crystal growth simulations) and to the very few specialized commercial tools for crystal growth.