Basin Pigment Density

Where the red of the Sonoran meets the math of the bind

Cracked red earth in Hanksville desert, Utah — the grain of hematite revealed

The Ground Beneath the Color

In the Phoenix Basin, the red is not decoration. It is hematite (Fe₂O₃), crystallized in trigonal symmetry, with a density of 5.26 g/cm³. When I grind this soil for paint, I am not mixing dust—I am calculating the critical packing fraction.

This tool computes the binder-to-pigment mass ratio required for a stable film at your chosen Pigment Volume Concentration (PVC). At the Critical Packing Density (CPD ≈ 0.74 for spheres), the film achieves maximum strength without cracking. Go higher, and the binder starves. Go lower, and the pigment floats free.

The Calculator

Hematite Purity (%) Raw soil from the Sonoran floor rarely exceeds 95%

Target PVC (Pigment Volume Conc.)

0.30 (Rich Oil) 0.74 (Critical Packing) 0.85 (Dry Film)

Binder Density (g/cm³) Stand oil: 0.96 • Walnut: 0.93

0.50

Parts Binder : Parts Pigment (by mass)

At PVC 0.74 with 92% pure hematite: weigh 50g linseed to 100g ground red

The Formula

ρ_pigment = 5.26 g/cm³ (α-Fe₂O₃, hematite) ρ_binder = user-defined (default: 0.94 for linseed) Effective ρ_pigment = ρ_pigment × (purity/100) Volume_fraction_pigment (PVC) = V_pig / (V_pig + V_bind) Mass_ratio = (ρ_binder / Effective_ρ_pig) × (PVC / (1 − PVC))

Constants Ledger (Agent-Legible)

Property	Value	Source
Crystal System	Trigonal	Wikidata Q103223
Density (bulk)	5.26 g/cm³	Hematite mineral species
CAS Registry	1317-60-8	Q103223
Chemical Formula	Fe₂O₃	Q103223 / Q419170
Critical Packing	0.74 (Kepler limit)	Sphere packing theory

Download constants as JSON for agent consumption

A Worked Example

Scenario: You have ground 200g of raw Phoenix Basin soil (assumed 90% hematite purity). You wish to formulate a stable landscape paint using cold-pressed linseed oil (ρ = 0.94).

Step 1: Effective pigment density = 5.26 × 0.90 = 4.734 g/cm³
Step 2: Target PVC = 0.74 (critical packing for maximum film integrity)
Step 3: Mass ratio = (0.94 / 4.734) × (0.74 / 0.26) = 0.565
Result: Mix 113g linseed oil with 200g pigment (ratio 0.565:1)

This is not guesswork. This is the geometry of survival.