Source: https://guthlabs.ai/docs/instruments/unit-cell-density-calculator/mechanism/

instrument mechanism / verified-clean

# Unit Cell Density Calculator mechanism

The inspectable method record for Unit Cell Density Calculator, kept separate from implementation and qualification.

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

## Model scope

The instrument should be labeled as calculating ideal theoretical crystal density, not measured bulk density. Before release, specify the cell convention, validate structure/Z consistency, define the packing-factor formula, and require explicit units for lattice parameter, molar mass, and density.

- The density formula ρ=(Z·M)/(Vcell·NA) is standard, provided Z is the number of atoms in the selected unit cell and M is molar mass.

- The specification does not define Vcell. For conventional cubic SC, BCC, and FCC cells, Vcell=a^3; this assumption must be stated explicitly.

- The output includes packing factor, but no packing-factor formula is supplied. Under the hard-sphere conventional-cell model, the standard values are SC=π/6≈0.523599, BCC=π√3/8≈0.680175, and FCC=π/(3√2)≈0.740480.

- The inputs redundantly specify both crystal structure type and Z without requiring consistency. Enforce SC→Z=1, BCC→Z=2, and FCC→Z=4, or clearly define which input takes precedence.

## Units and conventions

- For vectors using nanometers, a is converted using 1 nm=1.0×10^-7 cm; with M in g/mol, density is reported in g/cm^3.

- For the meter-based vector, a is in meters and M is in kg/mol; density is reported in kg/m^3.

- NA is taken exactly as the supplied value 6.022×10^23 mol^-1 for these calculations.

- The stated lattice parameter is the edge length of a conventional cubic unit cell.

- Packing factor assumes identical hard-sphere atoms in the conventional cubic cell.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "crystal_structure": "SC",
    "lattice_parameter": 0.3,
    "lattice_parameter_unit": "nm",
    "molar_mass": 40,
    "molar_mass_unit": "g/mol",
    "Z": 1
  },
  "expected_outputs": {
    "theoretical_density": 2.460115,
    "density_unit": "g/cm^3",
    "packing_factor": 0.523599
  },
  "working": "a=0.300 nm=3.00×10^-8 cm. Vcell=a^3=(3.00×10^-8)^3=2.700×10^-23 cm^3. Z·M=1×40.00=40.00 g/mol. Vcell·NA=(2.700×10^-23)(6.022×10^23)=2.700×6.022=16.2594. ρ=40.00/16.2594=2.460115 g/cm^3. PF=π/6=0.523599."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An extreme but representable lattice parameter of 1.0×10^-300 m causes JavaScript exponentiation to underflow a^3 to zero, producing Infinity instead of a finite density. The unit convention is also hazardous because interpreting a=0.36 as Å rather than nm changes the result by a factor of 1000.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/unit-cell-density-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/unit-cell-density-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/unit-cell-density-calculator/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

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

- `BOUNDARY_HAZARD_CATALOG.json`