Description
Return the mass-weighted concentration and the concentration-weighted isotope-ratio average.
An isotope ratio depends on which isotope is in the numerator and denominator. Delta notation compares a ratio with a reference on a per-mil scale, while mixing and decay models require explicit amount and system assumptions.
Return the mass-weighted concentration and the concentration-weighted isotope-ratio average.
When to use this tool
Use Isotope Mixing Two Endmember Fraction when you need a stated isotope-reference, mixing, or one-step decay calculation.
How to use the tool and how it works
- Enter firstRatio, secondRatio, firstConcentration, secondConcentration, firstMassFraction. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read mixedConcentration, mixedRatio. Use the output convention below.
Require nonnegative ratios and concentrations and firstMassFraction in [0, 1], with positive concentration-weighted total. Return the mass-weighted concentration and the concentration-weighted isotope-ratio average.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstRatio | First Ratio | Required. Finite number; minimum 0. |
| secondRatio | Second Ratio | Required. Finite number; minimum 0. |
| firstConcentration | Concentration weight; exact ratio mixing requires proportionality to denominator-isotope amount per sample mass. | Required. Finite number; minimum 0. |
| secondConcentration | Same concentration basis and unit as the first endmember. | Required. Finite number; minimum 0. |
| firstMassFraction | First Mass Fraction | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| mixedConcentration | Mixed Concentration | Required. Finite number. |
| mixedRatio | Mixed Ratio | Required. Finite number. |
{
"input": {
"firstRatio": 0.1,
"secondRatio": 0.2,
"firstConcentration": 2,
"secondConcentration": 1,
"firstMassFraction": 0.5
},
"output": {
"mixedConcentration": 1.5,
"mixedRatio": 0.13333333333333333
}
}Limitations and assumptions
- Ratios share an isotope orientation and concentrations share units. Exact ratio mixing requires concentration weights proportional to denominator-isotope amounts per sample mass; total-element concentration weighting can be an approximation, unlike explicit denominator-isotope mixing.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the appropriate reference materials and full isotope model for interpretation. Preserve ratio orientation, reference scale, denominator-isotope weighting, uncertainty, and any open-system or fractionation effects.
References
Similar or alternative tools
- Isotope Ratio Mixing Weight
Scale both amounts by their maximum, form normalized weights, and interpolate the two ratios stably; return mixedRatio and firstWeight.
- Isotope Reference Delta Offset
Reconstruct the sample ratio from first delta and reference, divide by the second reference, subtract one, and multiply by 1000.