3D Thermal Stress Local Model

This project establishes a workflow for evaluating thermal stress in a 3D crystal geometry, based on boundary conditions extracted from an earlier 2D axisymmetric simulation.

This repository contains CsI Czochralski crystal growth cases using Elmer.

• CsI-reference case : 2D simulation of CsI Czochralski growth
• CsI-optimized case : 2D simulation of optimized CsI Czochralski growth

Referencing

If you use this code in your research, please cite our open-access publication:

N. Sagias, A. Sabanskis, and K. Dadzis, “ Optimization of Thermal Stresses During Czochralski Growth of Oxides and Halides.” Cryst. Res. Technol. 61, no. 1 (2026): e70061. https://doi.org/10.1002/crat.70061

Computational setup (Docker)

The setup for the simulations is provided in form of a docker image, so just an installation of Docker is required on your system. The image nemocrys/opencgs:v1.0.1 is used (see opencgs for more information).

On Windows, the container can be started with the following command:

docker run -it --rm -v ${PWD}:/home/workdir nemocrys/opencgs:v1.0.1 bash

On Linux, the container can be started with:

docker run -it --rm -v $PWD:/home/workdir -e LOCAL_UID=$(id -u $USER) -e LOCAL_GID=$(id -g $USER) nemocrys/opencgs:v1.0.1 bash

This will map the current working directory (e.g., a copy of this repository) into the container and, on Linux, set the user's group and user id. The simulation can then be executed using the provided python3.

Workflow Overview

The simulation pipeline consists of the following steps:

1. 2D-axisymmetric Simulation: A 2D Electromagnetic-thermal axisymmetric simulation is performed to obtain the thermal field and phase interface. The reference case is located at 2D/Csi_reference_case.

2. Thermal Boundary Extraction: Temperature boundaries are extracted from the 2D simulation. Specifically, temperature profiles for the crystal side, top, and the crystal-melt interface are processed.

3. 3D Geometry Generation: A 3D mesh of the crystal is generated. The shape of the crystal bottom is determined by the extracted boundary conditions.

4. 3D Thermal Stress Calculation: The 3D geometry and boundary conditions are used to run a thermal stress simulation.

Directory Structure

sim-cz-stress/
├── 2D/                          # 2D simulation EM-Thermal simulations
│   ├── Csi_reference_case/      # Reference case for CsI crystal
│   │   ├── geometry.py          # 2D geometry generation
│   │   ├── setup.py             # 2D simulation Elmer setup
│   │   ├── my_tools.py          # 2D utility functions
│   │   ├── post.py              # Post-processing scripts
│   │   ├── run.py               # 2D simulation runner
│   │   ├── config_geometry.yml  # 2D geometry configuration
│   │   ├── config_sim.yml       # 2D simulation parameters
│   │   ├── config_mat.yml       # 2D material properties
│   │   ├── config_elmer.yml     # 2D Elmer solver configuration
│   │   └── simdata/             # 2D simulation output
│   │       └── 01_case/         
│   │           └── results/     # Results (.dat, .vtu files)
│   └── Csi_optimum/             # Optimized case for CsI crystal (same structure as reference case)
│       └── ...                  
├── 3D/                          # 3D Thermal stress simulations 
│   ├── geo_3D.py                # 3D geometry generation from 2D results
│   ├── T_boundary_from2Dto3D.py # Temperature boundary condition extraction from 2D
│   ├── setup.py                 # Elmer simulation setup
│   ├── my_tools.py              # 3D utility functions
│   ├── run.py                   # 3D simulation runner
│   ├── config_geometry.yml      
│   ├── config_sim.yml           
│   ├── config_mat.yml           
│   ├── config_elmer.yml         # Elmer solver configuration
│   └── simdata/                 # 3D simulation output directory
│       └── <case_name>/         # Results                   
├── runAll.py                    # Top-level script to run 2D + 3D workflow
└── README.md

Usage

Running Individual Simulations

1. Prepare 2D Results:

   First, run the 2D simulation to generate the required boundary condition files:

   cd 2D/Csi_reference_case
   python3 setup.py

   This will create the necessary .dat files (e.g., crystal_T_boundary_side.dat, phase-if.dat) in the 2D/Csi_reference_case/simdata/01_case/results/ directory, which are required for the 3D simulation.

2. Configure Simulation:

   • Navigate to the 3D/ directory.
   • Edit run.py to select the desired simulation case from the simulations list.
   • Adjust config_geometry.yml, config_sim.yml, and config_mat.yml as needed.

3. Run the 3D Simulation: Execute the 3D simulation script:

   cd 3D
   python3 run.py

   This script will:

   • Create a directory for the simulation in 3D/simdata/.
   • Generate the 3D crystal mesh (mesh.msh).
   • Create the temperature boundary condition files from 2D simulation.
   • Generate the Elmer simulation files (case.sif, etc.).
   • Run ElmerGrid to convert the mesh.
   • Run ElmerSolver to perform the simulation.

Running the Complete Workflow

To run both the 2D and 3D simulations sequentially, use the top-level script:

python3 runAll.py

This will:

1. Execute the 2D simulation in 2D/Csi_reference_case/
2. Execute the 3D simulation in 3D/ using the 2D results

Output

The simulation results are stored in the following locations:

2D Simulation Results:

• Location: 2D/<case_name>/simdata/01_case/results/
• Files: Temperature and field data (.dat files), ParaView visualization files (.vtu) and phase-if.dat, crystal_T_boundary_side.dat, crystal_T_boundary_top.dat

3D Simulation Results:

• Location: 3D/simdata/<case_name>/
• Files: ParaView visualization files (.vtu) regarding thermal stress calculation.

You can visualize both 2D and 3D results using ParaView.

Results

2D temperature fields for 60 mm and the entire crystal (117 mm). Reference case (left) and optimized case (right).

3D thermal stress fields for 60 mm and the entire crystal (117 mm). Reference case (left) and optimized case (right).

Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 851768).