Source: https://guthlabs.ai/docs/instruments/alloy-density-rule-of-mixtures-calculator/

instrument / verified-clean

# Alloy Density Rule-of-Mixtures Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/alloy-density-rule-of-mixtures-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/alloy-density-rule-of-mixtures-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/alloy-density-rule-of-mixtures-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/alloy-density-rule-of-mixtures-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Chemistry & Materials

**Tranche**: tranche-5

**Evidence ID**: t5-036

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The mathematical formulas are correct for ideal rule-of-mixtures calculations. The catalog entry needs an explicit mode selector, validation rules for fraction normalization and density positivity, and an honest label such as ideal estimated density rather than guaranteed measured alloy density. Temperature, phase, composition, and porosity assumptions for the ASM density reference table should also be specified.

### Formula and scope findings

- Both formulas are standard ideal rule-of-mixtures formulas, but they require the selected fractions to be dimensionless, nonnegative, and normalized so that Σwᵢ=1 or Σvᵢ=1.

- The input specification does not identify an explicit calculation mode, so it is ambiguous whether supplied fractions are weight fractions or volume fractions.

- The formulas assume additive constituent volumes, no porosity, and no excess-volume or shrinkage effects; actual alloy/composite density may differ under nonideal mixing.

### Unit assumptions

- All constituent densities must use the same density unit, and the output density has that same unit.

- Weight and volume fractions are dimensionless.

- For the weight-fraction formula, wᵢ are mass fractions and must sum to 1.

- For the volume-fraction formula, vᵢ are volume fractions and must sum to 1.

- Reference densities must correspond to specified composition, temperature, phase, and porosity state if an accurate physical density is claimed.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A zero constituent density creates an undefined division in the weight-fraction formula, and ambiguous percentage-versus-unit fraction input can produce a physically nonsensical result if not normalized or rejected.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "mode": "weight_fraction",
    "densities": [
      7.8,
      2.7
    ],
    "density_unit": "g/cm³",
    "fractions": [
      0.7,
      0.3
    ]
  },
  "expected_outputs": {
    "rho_alloy": 4.9787234043,
    "density_unit": "g/cm³"
  },
  "working": "ρ = 1/(0.7/7.8 + 0.3/2.7) = 1/(0.0897435897 + 0.1111111111) = 1/0.2008547008 = 4.9787234043 g/cm³."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`