Debye–Callaway Simulator v2.1.0

Version 2.1.0 introduces substantial GUI responsiveness improvements, enhanced parameter-selection logic, improved fitting workflow guidance, and numerous bug fixes.

Release Notes

Important Notice

Although Version 2.1.0 introduces substantial performance improvements and reduced GUI lag, the software remains computationally intensive due to the underlying Debye–Callaway thermal conductivity calculations.

Users should expect:

• Approximately 10–15 seconds for most button clicks and parameter changes to fully respond.
• Approximately 20–25 seconds for Auto Fit χ² operations to complete and update fitted parameters.
• Longer response times when multiple scattering mechanisms are activated simultaneously or when fitting large experimental datasets.

Please allow calculations to complete before issuing additional commands.

Major Improvements in Version 2.1.0

Reduced GUI Lag

This release continues to focus on improving software responsiveness and reducing unnecessary computational overhead.

Key improvements include:

• Reduced lag associated with parameter updates.
• Faster plot refresh operations.
• Improved handling of slider interactions.
• Improved management of active scattering mechanisms.
• More efficient experimental data processing.
• Reduced overhead associated with repeated Debye–Callaway calculations.
• Improved stability during intensive fitting operations.
• Enhanced responsiveness during manual parameter tuning and fitting.

Nanopore Scattering Mechanism

Version 2.1.0 introduces a nanopore scattering model for the simulation of phonon transport in porous and nanostructured materials.

The implementation extends the Debye–Callaway framework by incorporating an additional phonon relaxation process arising from nanoscale pores and pore-induced phonon scattering.

New Parameters

Porosity (%)

Represents the pore volume fraction within the material.

• May be selected for fitting using the Master Slider.
• Can participate in Auto Fit χ² optimization.

pole_l — Nanopore Length Scale (nm)

Represents the characteristic pore length scale governing phonon–pore interactions.

• Tuned manually using the Mini Slider.
• Can also be edited through the numerical input box.

Activation of Nanopore Scattering

Nanopore scattering behaves as an optional scattering mechanism.

To activate:

1. Right-click the Nanopore fitting parameter button.
2. The mechanism becomes active and available for fitting.
3. Select Porosity (%) or Pore Length (pore_l) (nm) for manual tuning if desired.

When deactivated, nanopore scattering contributes no additional phonon scattering to the thermal conductivity calculation.

Important Note on Porosity

Although Porosity (%) appears in the fitting-parameter section of the interface, it is fundamentally a physical parameter, not a fitting parameter.

Porosity has been placed within the fitting-parameter section solely to allow convenient activation and deactivation of the nanopore scattering mechanism, in a manner consistent with the other optional scattering processes.

Whenever possible, users are encouraged to determine porosity experimentally and use the measured value during modelling.

Automatic fitting of porosity should primarily be used for:

• Exploring porosity–κₗₐₜₜ relationships.
• Sensitivity analysis.
• Investigating the influence of pore volume fraction on phonon transport.
• Preliminary studies where experimental porosity data are unavailable.

For physically meaningful modelling and publication-quality analysis, experimentally measured porosity values are recommended.

Scientific Basis

The nanopore relaxation-time formulation implemented in Version 2.1.0 follows the methodology described in:

Wu, G., Li, A., Wang, L. et al. Modulating phonon dynamics: tailoring lattice vibrations to enhance thermoelectric efficiency in Mg₃(Sb,Bi)₂ alloy. Nat Commun 16, 10366 (2025). DOI: 10.1038/s41524-026-01992-4

Users employing the nanopore scattering model in publications are encouraged to cite this work.

Benefits

The nanopore model enables:

• Simulation of porous thermoelectric materials.
• Investigation of pore-size effects on lattice thermal conductivity.
• Improved fitting of materials containing engineered nanoscale porosity.
• More realistic modelling of phonon scattering in microstructurally complex systems.

Enhanced Experimental Data Handling

Experimental data entry has been significantly improved.

Users can now:

• Paste data directly from Microsoft Excel.
• Paste data from Microsoft Word.
• Paste data from Notepad and other text editors.
• Modify experimental datasets without restarting the application.

This greatly simplifies importing literature and laboratory measurements.

Improved Auto-Fit Workflow

Version 2.1.0 employs a hybrid fitting strategy:

1. Differential Evolution (Global Search)
2. L-BFGS-B Refinement (Local Optimization)

Benefits include:

• Better convergence reliability.
• Reduced likelihood of becoming trapped in poor local minima.
• Improved fitting performance for complex scattering models.
• More stable fitting after large changes to experimental datasets.

Simplified Slider Control System

Version 2.1.0 replaces the previous multiple-slider layout with two shared sliders:

Master Slider

• Tunes the selected fitting parameter.

Mini Slider

• Tunes the selected physical parameter or empirical constant.

This reduces interface crowding, lowers GUI overhead, and improves software responsiveness compared with earlier versions that used many individual sliders.

Only active parameters can be selected. Optional scattering parameters must first be activated before they can be assigned for tuning or fitting.

Parameter Activation Rules

Deactivated optional scattering parameters cannot be selected or tuned.

To use an optional parameter:

1. Activate the corresponding scattering mechanism by right clicking the yellow button.
2. Select the parameter by left clicking.
3. Adjust it using the appropriate slider or numerical input box.

This prevents inactive mechanisms from unintentionally affecting theoretical κₗₐₜₜ calculations or optimization routines. Activated optional scattering parameters can be deactivated by right clicking.

Optional Scattering Mechanisms

The following mechanisms may be enabled or disabled as required:

• ε — Point Defect Scattering
• Aₙₐₙₒ — Nano-Inclusion Scattering
• s² — Vacancy Scattering
• A — Dislocation Scattering
• Nanopore Scattering

Only activated mechanisms participate in fitting calculations.

Typical Workflow

Step 1 — Enter Experimental Data

At the upper-left section of the interface:

• Enter or paste temperature data.
• Enter or paste corresponding lattice thermal conductivity data.
• Click Modify Data.

The experimental curves will be updated for subsequent calculations.

Step 2 — Adjust the Temperature Range and Number of Points

Before fitting, adjust the minimum and maximum temperature limits so that the theoretical temperature range adequately covers the experimental dataset.

This ensures that:

• The theoretical κₗₐₜₜ curve is evaluated over the appropriate temperature range.
• χ² calculations are performed using the correct temperature window.
• Comparisons between experimental and theoretical data remain physically meaningful.

Number of Points (No. points)

The Number of Points (No. points) controls the number of temperature values used to generate the theoretical κₗₐₜₜ curve.

Higher values of No. points produce smoother curves but also increase computational demand because the Debye–Callaway integrals must be evaluated at more temperature points.

As a result:

• Larger No. points values increase calculation time.
• Slider response becomes slower.
• Auto Fit χ² operations require more time to complete.
• Overall GUI responsiveness may decrease.

For most fitting applications, a relatively low value of No. points is sufficient and is strongly recommended during parameter tuning and optimization.

Recommended workflow:

1. Use a lower No. points value during fitting to improve responsiveness and reduce waiting time.
2. After obtaining a satisfactory fit, increase No. points if a smoother theoretical curve is desired for visualization, publication-quality figures, or data export.

Reducing No. points is one of the most effective ways to decrease computational load and improve the overall user experience.

Step 3 — Update Physical Properties

Before fitting, users are strongly encouraged to update the physical parameters using experimentally measured values whenever available.

Both fitting parameters and physical parameters may be edited directly through their corresponding numerical input boxes and pressing the ENTER button.

When a parameter value is entered manually:

• The parameter value is updated immediately.
• The associated Master Slider or Mini Slider range is automatically recalculated and recentered around the new value.
• Subsequent slider adjustments will therefore operate relative to the newly entered value rather than the previous parameter range.

This feature allows users to rapidly move to physically meaningful parameter regions without requiring extensive slider adjustments, particularly when working with parameters that span several orders of magnitude.

Only active (gray) physical parameters can be selected and edited directly.

Physical parameters associated with optional scattering mechanisms remain inactive until their corresponding fitting parameter has been activated.

Physical Parameter Dependencies

To edit these physical parameters:

1. Activate the corresponding scattering mechanism by right-clicking the yellow button.
2. Select the desired physical parameter.
3. Adjust it using the Mini Slider or numerical input box.

Step 4 — Select Dataset for Fitting

Choose whether optimization targets:

• Pristine dataset
• Doped dataset

The selected dataset becomes the reference for χ² calculations and parameter optimization.

Step 5 — Activate Scattering Mechanisms

Activate only the scattering mechanisms required for the material being modelled.

Universal Scattering Mechanisms

These are always active:

• NP (Normal Processes)
• U_m (Umklapp Processes)
• C_eph (Electron–Phonon Scattering)

Optional Scattering Mechanisms

The following mechanisms may be enabled or disabled as required:

• ε — Point Defect Scattering
• A_nano — Nano-Inclusion Scattering
• S² — Vacancy Scattering
• A — Dislocation Scattering
• Nanopore Scattering

Only activated mechanisms participate in fitting calculations.

Step 6 — Select Parameters for Manual Adjustment

Left-click any parameter button to assign that parameter to:

• Master Slider
• Mini Slider

The selected parameter may then be adjusted interactively.

This enables rapid exploration of parameter sensitivity.

Important Note on Slider Response

Due to the computational demands of the Debye–Callaway calculations, a short delay may occur before the sliders become responsive after a parameter is assigned.

When using either the Master Slider or Mini Slider:

1. Click and hold the slider handle.
2. Continue holding for a few seconds until the slider becomes responsive.
3. Once activated, drag the slider normally.

Avoid repeatedly clicking the slider handle during this activation period, as multiple rapid clicks may temporarily reduce interface responsiveness.

Alternatively, parameter values may be entered directly into the corresponding numerical input boxes. Manual entry automatically updates the associated slider range, allowing efficient exploration of parameter values outside the current slider limits.

Step 7 — Manual Model Tuning

Adjust selected parameters using:

• Master Slider
• Mini Slider
• Direct numerical input boxes

The theoretical κₗₐₜₜ curve updates automatically after calculations complete.

Note: Parameters may be adjusted using either the sliders or the numerical input boxes. Manual entry automatically updates the corresponding slider range, enabling efficient exploration of parameter values that lie far outside the current slider limits.

Step 8 — Calculate Current χ²

Click Calculate χ² to evaluate agreement between:

• Experimental κₗₐₜₜ
• Theoretical κₗₐₜₜ

Lower χ² values indicate improved agreement.

Step 9 — Automatic Optimization

Click Auto Fit χ².

The software will:

• Perform a Differential Evolution global search.
• Refine the solution using L-BFGS-B optimization.
• Update fitted scattering parameters.
• Refresh the theoretical κₗₐₜₜ curve.

Typical completion time is approximately 20–25 seconds.

Step 10 — Evaluate the Fit

After optimization:

• Examine χ².
• Inspect agreement between theoretical and experimental curves.
• Fine-tune parameters manually if desired.

Users are encouraged to assess the physical realism of fitted parameters rather than relying solely on χ² values.

Step 11 — Export Theoretical κₗₐₜₜ Data

Once a satisfactory fit has been obtained:

• Generate the theoretical lattice thermal conductivity curve.
• Export the calculated κₗₐₜₜ dataset.

Final Remarks

Version 2.1.0 delivers significantly improved responsiveness, more reliable optimization, streamlined experimental data handling, and introduces nanopore scattering for modelling porous and nanostructured materials within the Debye–Callaway framework.

Feedback, feature requests, and bug reports are welcome and will continue to guide future development of the Debye–Callaway Simulator.

Citation

If this software contributes to your research, publications, presentations, or data analysis, please cite the following work:

Kahiu, J. N., Lee, H.S. Debye-Callaway model simulator: an interactive slider-based program for fitting theoretical and experimental lattice thermal conductivity. npj Comput Mater 12, 118 (2026). https://doi.org/10.1038/s41524-026-01992-4