Annealing Thermal Budget
Convert an annealing step to an Arrhenius-equivalent thermal budget.
Description
Arrhenius equivalent time compares process temperature with a reference using an activation energy.
Arrhenius equivalent time compares process temperature with a reference using an activation energy. It assumes the same thermally activated process at both temperatures.1
Convert an annealing step to an Arrhenius-equivalent thermal budget.
When to use Annealing Thermal Budget
Use this tool to convert an annealing step to an Arrhenius-equivalent thermal budget.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Annealing Thermal Budget and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter processTemperatureKelvin, processSeconds, referenceTemperatureKelvin, activationEnergyEv using the field table and calculation rules, then run the tool.
- Read rateRatioToReference, equivalentReferenceSeconds. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| processTemperatureKelvin | Process temperature (K) | number; minimum: 0 | Required |
| processSeconds | Process duration (s) | number; minimum: 0 | Required |
| referenceTemperatureKelvin | Reference temperature (K) | number; minimum: 0 | Required |
| activationEnergyEv | Activation energy (eV) | number; minimum: 0 | Required |
Enter positive kelvin temperatures and nonnegative seconds/activation eV. Use kB=8.617333262145e−5 eV/K. Return ratio and reference-equivalent seconds.
rateRatio=exp(−Ea/kB×(1/Tprocess−1/Tref)); equivalentTime=time×ratio Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| rateRatioToReference | Arrhenius rate ratio | number; minimum: 0 |
| equivalentReferenceSeconds | Equivalent reference-temperature time (s) | number; minimum: 0 |
{
"input": {
"processTemperatureKelvin": 1000,
"processSeconds": 10,
"referenceTemperatureKelvin": 1000,
"activationEnergyEv": 1
},
"output": {
"rateRatioToReference": 1,
"equivalentReferenceSeconds": 10
}
}Limitations and assumptions
No temperature ramp, reaction mechanism, prefactor change or material validation is supplied.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Ablation Threshold Fit: Fit a Liu ablation-threshold line from pulse energy and squared crater radius. For a complementary task, use Photothermal Diffusivity: Infer thermal diffusivity from photothermal-wave phase lag at a known offset.
References
-
Annealing Thermal Budget — tool.io
Similar or alternative tools
- Ablation Threshold Fit
Fit a Liu ablation-threshold line from pulse energy and squared crater radius.
- Photothermal Diffusivity
Infer thermal diffusivity from photothermal-wave phase lag at a known offset.