Calculator Inputs
Plotly Graph
The line uses the equivalent-frequency form of E = hf. Your submitted result and chosen reference appear as markers.
Example Data Table
| Case | Frequency (THz) | Energy (meV) | Wavenumber (cm⁻¹) | Equivalent Temperature (K) |
|---|---|---|---|---|
| Low acoustic example | 0.5000 | 2.0678 | 16.6782 | 24.00 |
| Mid acoustic example | 1.5000 | 6.2035 | 50.0346 | 71.99 |
| High acoustic example | 3.0000 | 12.4070 | 100.0692 | 143.98 |
| Near upper acoustic range | 6.0000 | 24.8140 | 200.1385 | 287.95 |
| Ge optical reference benchmark | 8.9986 | 37.2151 | 300.1600 | 431.86 |
Formula Used
E = hf converts phonon frequency into energy.
E = ℏω converts angular frequency into energy.
f = cṽ uses spectroscopic wavenumber, where ṽ is in cm⁻¹ and c is the speed of light.
f = v / λ uses phonon wavelength with a user-supplied branch velocity.
E ≈ kBT gives a thermal energy scale for quick comparison.
Unit conversions shown by the calculator include joules, electronvolts, millielectronvolts, kelvin, THz, GHz, and cm⁻¹.
How to Use This Calculator
- Choose the input mode that matches your data source.
- Enter the primary value and select the correct unit.
- For wavelength mode, provide a realistic phonon velocity.
- Keep or edit the reference wavenumber for comparison.
- Optionally label the branch or test case.
- Select decimal precision and click the calculate button.
- Review the result card, graph, and example table.
- Export the finished calculation as CSV or PDF.
FAQs
1) What does this calculator compute?
It converts frequency, angular frequency, wavenumber, wavelength with velocity, or temperature into phonon energy. Outputs include joules, eV, meV, THz, cm⁻¹, and equivalent kelvin.
2) Why is velocity required for wavelength mode?
A wavelength alone does not determine phonon energy. In crystals, wave speed depends on branch and direction, so the calculator asks you to supply the appropriate phonon velocity.
3) Is kBT the same as a single phonon energy?
No. kBT is a thermal energy scale, not a guaranteed single-mode phonon energy. It is most useful for quick comparisons against measured or modeled phonon energies.
4) Why compare with a reference wavenumber?
A reference helps you benchmark your value against a familiar germanium spectral feature or a laboratory target. You can replace the default reference with any custom wavenumber.
5) Which mode should I choose?
Use frequency or wavenumber for spectroscopy data, angular frequency for theory work, wavelength plus velocity for wave analysis, and temperature for a rough thermal estimate.
6) Are the outputs branch-specific?
The conversion math is universal. Branch-specific meaning enters through the velocity you choose, the reference you compare against, and the physical context of your data.
7) Why show wavenumber and equivalent temperature together?
Different fields use different energy languages. Showing cm⁻¹, meV, and kelvin together makes it easier to cross-check spectroscopy, device, and thermal calculations.
8) Can I export my results?
Yes. After calculation, use the CSV button for spreadsheet analysis or the PDF button for a compact summary you can save or share.