Geology Mixing Hyperbola Calculator

Concentration-weighted two-endmember isotope mixing hyperbola on declared common denominator, not arithmetic isotope mean. Caller independently establishes matching units, evidence, method edition and applicability; output is not compliance, diagnosis, work-safety approval, geological identity or validated hazard prediction.

Description

Two-endmember isotope mixing weights each isotope ratio by its contributing element concentration.

Two-endmember isotope mixing weights each isotope ratio by its contributing element concentration.^[1]

Equal material fractions therefore need not contribute equally to the mixed isotope ratio. Use this tool to calculate mixing hyperbola from the supplied measurements and assumptions.

When to use Geology Mixing Hyperbola Calculator

Use this tool to calculate mixing hyperbola from the supplied measurements and assumptions. Establish the measurement units, sampled interval, calibration or model edition and geological assumptions before entering data.

How to use Geology Mixing Hyperbola Calculator and understand its results

Establish the measurement units, sampled interval, calibration or model edition and geological assumptions before entering data.
Enter isotopeRatios, elementConcentrations, firstMassFractions, using the field meanings and rules below, then run the tool.
Read mixedConcentrations, mixedRatios. Interpret the fields using their units, signs and evidence conventions below.
If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.

Input field	Meaning	Value type	Requirement
isotopeRatios	Isotope ratios	list of number	Required
elementConcentrations	Element concentrations	list of number	Required
firstMassFractions	First mass fractions	list of number	Required

Supply exactly two finite isotope ratios and positive element concentrations, plus first-endmember mass fractions from 0 through 1. For each fraction calculate the linear concentration mixture and the concentration-weighted isotope ratio. Fractions 0 and 1 reproduce the second and first endmembers respectively; no endmember identification or fraction fitting occurs.

C=fC1+(1−f)C2; R=[fC1R1+(1−f)C2R2]/C

Use the exact units, boundary rules, ordering and missing-evidence conventions above.

Output field	Meaning	Value type
mixedConcentrations	Mixed Concentrations; follow the units, sign, ordering and evidence convention stated above	list of number
mixedRatios	Mixed Ratios; follow the units, sign, ordering and evidence convention stated above	list of number

json

{
  "input": {
    "isotopeRatios": [
      1,
      3
    ],
    "elementConcentrations": [
      1,
      3
    ],
    "firstMassFractions": [
      0,
      0.5,
      1
    ]
  },
  "output": {
    "mixedConcentrations": [
      3,
      2,
      1
    ],
    "mixedRatios": [
      3,
      2.5,
      1
    ]
  }
}

Limitations and assumptions

Equal material fractions therefore need not contribute equally to the mixed isotope ratio. Interpretation depends on the units, sampling scope and exact model described above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.

Alternative or Complementary methods

Use Geology Fractional Melting Calculator for this related task: Fractional melting removes successive melt increments from a reservoir under a specified partition coefficient.

Use Geology Batch Melting Calculator when its separate inputs and assumptions fit the question: Batch melting keeps melt and residue in equilibrium under a specified bulk partition coefficient.

References

Geology Mixing Hyperbola Calculator — tool.io

Similar or alternative tools

Geology Fractional Melting Calculator
Fractional melting removes successive melt increments from a reservoir under a specified partition coefficient.
Geology Batch Melting Calculator
Batch melting keeps melt and residue in equilibrium under a specified bulk partition coefficient.