Semiconductor Phase Separation Spinodal Calculator
Audit local unequal-grid discrete free-energy curvature/spinodal candidates, not global common-tangent coexistence or inferred stability outside sampled composition.
Description
Local free-energy curvature describes how a sampled composition branch bends.
Local free-energy curvature describes how a sampled composition branch bends.1
Negative discrete curvature marks spinodal candidates under the supplied free-energy model, while phase coexistence requires a separate analysis.
When to use Semiconductor Phase Separation Spinodal Calculator
Use this tool when you need to calculate the stated measurement summary or conditional model from matched observations. Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
How to use Semiconductor Phase Separation Spinodal Calculator and understand its results
- Prepare independently matched device or specimen measurements, units, branch selection, and model or calibration conventions.
- Enter observedCompositionFractions, observedFreeEnergy, following the field table and calculation rules below, then run the tool.
- Read discreteFreeEnergySecondDerivatives, negativeCurvatureInteriorCompositionFractions. Use the output table and calculation rules below to interpret units, signs, crossings, and flags.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedCompositionFractions | Observed composition fractions | list of number | Required |
| observedFreeEnergy | Observed free energy | list of number | Required |
Use at least three strictly increasing composition fractions in [0,1] and aligned free energies. Compute adjacent secant slopes and their unequal-grid second difference at each interior sample. Return all interior coordinates with strictly negative curvature; endpoints and zero curvature are excluded.
g″_i=2×((g_(i+1)−g_i)/(x_(i+1)−x_i)−(g_i−g_(i−1))/(x_i−x_(i−1)))/(x_(i+1)−x_(i−1)) Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| discreteFreeEnergySecondDerivatives | Discrete free energy second derivatives | list of number |
| negativeCurvatureInteriorCompositionFractions | Negative curvature interior composition fractions | list of number |
{
"input": {
"observedCompositionFractions": [
0,
0.25,
0.5,
0.75,
1
],
"observedFreeEnergy": [
1,
0.5,
0,
0.5,
1
]
},
"output": {
"discreteFreeEnergySecondDerivatives": [
0,
16,
0
],
"negativeCurvatureInteriorCompositionFractions": []
}
}Limitations and assumptions
Measurements, branch identification, units, and model applicability must be independently established. Results do not supply universal material constants, a complete physical model, or operating-condition approval.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Numeric lists allow at most 10000 entries, subject to smaller tool-specific bounds above.
Alternative or Complementary methods
For a related task, use Semiconductor Eutectic Composition Calculator: A sampled liquidus minimum can locate eutectic composition candidates on a verified eutectic branch. A generic valley is insufficient evidence to assign that reaction type. For a complementary step, use Semiconductor Peritectic Temperature Calculator: A peritectic equilibrium involves a particular reactant-product phase reaction. Zero crossings of its matched free-energy difference identify equilibrium candidates only after that reaction branch has been independently established.
References
Similar or alternative tools
- Semiconductor Eutectic Composition Calculator
A sampled liquidus minimum can locate eutectic composition candidates on a verified eutectic branch. A generic valley is insufficient evidence to assign that reaction type.
- Semiconductor Peritectic Temperature Calculator
A peritectic equilibrium involves a particular reactant-product phase reaction. Zero crossings of its matched free-energy difference identify equilibrium candidates only after that reaction branch has been independently established.