A physically rigorous seven-parameter Crystal Intelligence Septuplet for equation-of-state modelling, lattice thermodynamics, and mantle phase transition prediction across Earth's full pressure-temperature interior.
Every cubic centimetre of mineral material inside the Earth is subject to forces no surface laboratory can sustain indefinitely. MINERALCO integrates all seven governing parameters into a single unified framework.
Pressures reach 363 GPa at the inner-core boundary — 3.6 million Earth atmospheres. Temperatures climb to ~6,000 K at the core. Minerals operating under these conditions control everything from seismic wave speed to mantle viscosity to volcanic eruption dynamics.
MINERALCO provides the first unified seven-parameter framework — the Crystal Intelligence Septuplet (CIS) — that simultaneously encodes all information required to predict a mineral's equation of state, thermal expansion, phase stability, and lattice energy under any P-T condition accessible within Earth.
Validated against 3,200 experimental P-V-T data points from synchrotron diamond anvil cell and multi-anvil press studies, MINERALCO achieves mean RMS volumetric accuracy of 0.19% across the full mantle pressure range.
Seven physically independent parameters, each capturing a distinct aspect of mineral behaviour under extreme pressure and temperature — from the crystallographic unit cell to thermodynamic coupling between lattice vibrations and volume.
Zero-pressure incompressibility — the foundational EOS stiffness parameter. Determines seismic velocity and mineral density at depth. Every major mantle phase transition is driven by a K₀ discontinuity between competing phases.
Bridgmanite: K₀ = 261 GPaThe three edge lengths and angles of the crystallographic unit cell — encoding atomic bond lengths, densities, and elastic anisotropy. Measured by synchrotron X-ray diffraction to ±0.001 Å precision above 100 GPa.
Bridgmanite: 4.775 × 4.929 × 6.897 ÅFirst pressure derivative ∂K/∂P at P=0 — the non-linear stiffening rate under compression. Critical for EOS accuracy above ~10 GPa. The MINERALCO Symmetry-Stiffness Paradigm predicts K' from crystal system alone (r = −0.88).
Cubic: K' = 4.01 ± 0.24 universallySpace group (1–230) and crystal system (cubic → triclinic). Governs the Madelung constant, elastic anisotropy, and the number of independent elastic constants (3 to 21). Neumann's Principle: all physical properties must exhibit the crystal's symmetry.
7 crystal systems · 230 space groupsVolumetric thermal expansion ∂(lnV)/∂T|ₚ (K⁻¹). Governs volume change with temperature — critical for the mantle adiabat and phase boundary Clapeyron slopes. A mineral at 2,500 K in the lower mantle has a volume ~3–5% larger than at 300 K.
Bridgmanite: α = 2.0 × 10⁻⁵ K⁻¹The most physically fundamental parameter in the CIS. Dimensionless thermodynamic coupling γ = αK₀Vₛ/Cᵥ — the backbone of the Mie-Grüneisen EOS. Links thermal pressure to volume; quantifies how strongly thermal energy contributes to pressure.
Mantle minerals: γ ≈ 1.0–2.0 typicalMolar volume Vₛ = M/ρ (cm³/mol) — the primary observable in synchrotron P-V diffraction experiments and the dependent variable in all EOS curve-fitting procedures. The net volumetric outcome of all competing pressure and thermal forces.
Bridgmanite: 24.45 cm³/mol (ambient)Together, these seven parameters fully parameterise the third-order Birch-Murnaghan EOS and the Mie-Grüneisen thermal correction — providing a complete thermodynamic description of any mineral across Earth's full P-T interior.
0–363 GPa · 300–6,000 KThe CSI has been calibrated against all four major seismic discontinuity-producing transitions in Earth's mantle. A mineral whose CSI reaches 0.85 is within ±2 GPa of a phase transition in 87% of benchmark cases.
| Phase Transition | P_exp (GPa) | P_MINERALCO (GPa) | CSI | Seismic Feature |
|---|---|---|---|---|
| Olivine → Wadsleyite | 13.5 ± 0.3 | 13.8 | 410 km discontinuity | |
| Wadsleyite → Ringwoodite | 18.0 ± 0.5 | 18.3 | 520 km discontinuity | |
| Ringwoodite → Bridgmanite + FP | 23.5 ± 0.4 | 23.2 | 660 km — most precise test | |
| Bridgmanite → Post-perovskite | 125 ± 2 | 124 | D'' layer · ~2,600 km | |
| ε-Fe → Liquid Iron (melting) | 330 ± 5 | 327 | Inner Core Boundary · ~5,150 km |
| Crystal System | K' Mean | Std Dev | N Minerals | Key Minerals |
|---|---|---|---|---|
| Cubic (highest symmetry) | 4.01 | ± 0.24 | 11 | MgO, FeO, garnet, spinel, diamond |
| Tetragonal | 4.18 | ± 0.31 | 4 | Rutile TiO₂, stishovite, scheelite |
| Hexagonal / Trigonal | 4.29 | ± 0.38 | 8 | ε-Fe, corundum, calcite, quartz |
| Orthorhombic | 4.44 | ± 0.41 | 15 | Bridgmanite, forsterite, enstatite |
| Monoclinic | 4.67 | ± 0.52 | 6 | Wadsleyite, diopside, jadeite |
| Triclinic (lowest symmetry) | 4.91 | ± 0.61 | 3 | Feldspars, kyanite, rhodonite |
Key results from the 47-mineral benchmark validate the CIS framework and establish findings with profound implications for planetary interior modelling.
Mean volumetric prediction error of 0.19% across 3,200 experimental P-V-T data points at pressures from 0 to 363 GPa and temperatures from 300 to 5,000 K. Best-in-class: periclase MgO achieves 0.07% — near-experimental accuracy from seven crystallographic numbers alone.
The Crystal Stability Index correctly predicts phase transition onset within ±1.5 GPa for 43 of 47 benchmark minerals, including the 660 km discontinuity (ringwoodite → bridgmanite + ferropericlase) at 23.2 GPa vs 23.5 ± 0.4 GPa experimental. Mean CSI at transition: 0.88 ± 0.03.
Thermodynamic and phonon Grüneisen parameters agree to r² = 0.971 across 28 minerals with both data types — confirming that MINERALCO CIS is thermodynamically internally consistent rather than empirically over-parameterised. Mean discrepancy: |Δγ| = 0.063.
"The bridgmanite seven-parameter CIS predicts PREM seismic velocities at 660 km depth to within 0.4% for Vₚ and < 0.1% for Vₛ — without any empirical adjustment."
— MINERALCO, Section 6.4 · Bridgmanite PREM ComparisonAll code, datasets, CIS parameter databases, and 15 Jupyter notebooks reproducing manuscript figures are fully open-access and reproducible from the archived repository.
"Seven parameters to decode the Earth's solid core."
— Samir Baladi, March 2026All 15 Jupyter notebooks reproduce manuscript figures and statistical outputs without external dependencies beyond the archived data. Fully reproducible mineral physics.