Plan & usage
Current plan
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Runs this month
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API Access
API Reference →
Use your API key to integrate Criticality Engine into your workflows.
Select domain
Choose the screening module to activate
LIVE
Percolation / Materials
Critical exponents for composites, 2D/3D networks, superfluids and magnetic transitions.
Percolation 2D / 3D
Ising 3D, O(2)
σ(p) curve + CSV export
LIVE
Alloys / HEA Screen
Solid-solution viability for multi-component alloys. OLTP v2 + Miedema ΔH + Ω gate. Phase prediction via VEC rule.
ΔH_mix + Ω stability
FCC / BCC prediction
IM former detection
LIVE
Chemistry / Ligands
Trans-influence prediction for Pt(II) metal-ligand systems. Formula v3: 0 inversions, r²=0.98 vs Appleton (1973).
I_trans = θ_σ − λ·i_π·θ_π
λ = 0.25 (derived, no free params)
12 ligands · CSV export
BETA
Cosmology / CPF
Ontological coherence filter for cosmological parameter sets. PLO v2 / TDSL framework. H₀ tension detector.
Ω_m, H₀, S₈, n_s
NI / DA scoring
H₀ tension detector
BETA
Alloy Inverse Design
Target-driven HEA search. Set phase, density and strength — engine returns ranked candidates with Hume-Rothery and solubility filters.
FCC / BCC / HCP / MIXED
Hume-Rothery · δr · Δen
Up to 50 000 samples
BETA
Criticality Inverse
Input an experimental exponent value — engine identifies the matching universality class, scaling law and system within tolerance.
Percolation 2D / 3D
Ising 3D · O(2) · SU(2)
Adjustable tolerance
BETA
Ligand Trans-influence
Inverse I_trans prediction from donor atom, hybridization and period. σ / π channel decomposition with D3 boost and halogen penalty.
θ_σ · θ_π · D3 boost
λ = 0.25 · no free params
High / Medium / Low regime
Workflow
1
System2
Target3
Result4
Candidates5
Export
Analyzing: —
Material type
Select the system you want to analyse
Dimensionality
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Symmetry
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Scaling law
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Reference
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Parameters
Operating conditions and target
Load example (optional — fills the fields, you still press Calculate)
No hay ejemplos cargados todavía para este sistema — completá los campos manualmente.
Percolation threshold pc
0.015
0.001vol fraction0.100
Volume fraction at which the system transitions from insulator to conductor. Typically 0.01–0.05 for CNT composites.
Prefactor σ₀ (S/m)
1.0
0.1S/m10.0
Intrinsic conductivity of the filler material. Higher values yield more conductive composites above threshold.
Target property (S/m)
0.030
0.001S/m0.099
Desired property value for your application. The engine finds the optimal filler concentration to reach this target.
Analysis range pmax
×8 p_c
×2multiples of pc×20
Upper bound of the concentration scan, expressed as a multiple of pc. Wider range gives more complete curves at higher compute cost.
Result
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Design equation
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σ (S/m)
p (vol frac)
p_opt
Some exponents require a Pro plan
Candidates
Ranked by cost/performance ratio
Additional candidates available on Pro
Export
Download your screening results
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CSV / Excel
Universal · all plans
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PDF Report
Pro
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XML — ANSYS
Pro
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JSON — API
Pro
Preview CSV
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Alloys / HEA Screen — ASF v2
OLTP + Miedema ΔH_mix + Ω gate · Verified 17/18 HEA cases
Load example (optional — fills the fields, you still press Compute)
Composition (element: fraction, one per line)
Fractions must sum to 1.0 · Supported: Co Cr Fe Ni Mn Al Ti Cu Mo Nb V W Ta Zr Hf Re Ru Si Li Mg Sc Y Zn Pd Pt Ag Au
Mediation T² (surface / solvent / network)
0.20
0.0 — none1.0 — max
Crystal symmetry (prior)
Thermodynamic Parameters
ΔH_mix (kJ/mol)—
ΔS_mix / R—
Ω = TΔS/|ΔH|—
δ_r — atomic size mismatch (%)—
VEC—
Compatibility score components—
Stability score—
Estimated Physical Properties
Melting point Tfus (rule of mixtures)—
Density ρ (rule of mixtures)—
Lattice parameter a₀ (FCC approx.)—
Result
Solid solution stability—
Phase prediction (VEC rule)—
IM former risk—
— Enter composition and press Compute
ArXe Internal Analysis
max_prime(Z elements)—
NI Zone (OLTP layer)—
OLTP score (raw)—
dH gate (kJ/mol)—
IM pairs (H_ij < −30)—
Alloys / Property Evolution
Sweep one element's fraction · ASF v2 engine · 11-point resolution
Load example (optional — fills the fields, you still press Compute)
Base composition (element: fraction, one per line)
Fractions must sum to 1.0 · Supported: Co Cr Fe Ni Mn Al Ti Cu Mo Nb V W Ta Zr Hf Re Ru Si Li Mg Sc Y Zn Pd Pt Ag Au
Element to sweep
Sweep range (fraction of swept element)
0.00
0.50
0.0 — none0.9 — max
Thermodynamic Parameters vs Composition
— Compute to plot
Estimated Physical Properties vs Composition
Stability Score & Phase vs Composition
— Set base composition, choose an element to sweep, and press Compute
Chemistry / Ligands — I_trans v3
Formula: 0 order inversions vs Appleton (1973) · r²=0.98 · Pt(II) square-planar
Load example (optional)
Ligand (select to profile)
λ = 0.25 — derived, no free parameters
Metal: Pt(II) square-planar (default)
Ref: Appleton, Clark & Manzer (1973)
Verified: 0 inversions / 66 pairs
Ligand Profile
Ligand—
σ-donation strength—
π-character intensity—
π-redistribution factor—
π-correction term—
I_trans (predicted)—
Lit. normalized (Appleton 1973)—
Rank in series—
Class—
Full Series (ranked)
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— Select a ligand to compute
Compare two ligands
A vs B
Ligand A
Ligand B
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σ-donation
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σ-donation
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Δ σ
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π-correction
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π-correction
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Δ π
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I_trans
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I_trans
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ΔI_trans
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ArXe Internal Analysis
θ_σ (T⁻⁵ projection)—
intensity_π (T⁻³ activation)—
θ_π (π redistribution)—
λ (coupling T⁻³/T⁻⁵)0.25
π penalty (λ·i_π·θ_π)—
FormulaI_trans = θ_σ − λ·i_π·θ_π
T⁻³/T⁻⁵ class—
Cosmology — CPF / PLO v2
Ontological coherence filter for cosmological parameters
Ω_m — Matter density
0.315
0.200dimensionless0.500
Ω_Λ — Dark energy density
0.685
0.400dimensionless0.900
H₀ — Hubble constant (km/s/Mpc)
67.4
60.0km/s/Mpc80.0
S₈ — Structure growth parameter
0.810
0.600dimensionless0.950
Analysis
Parameter coherence—
H₀ tension—
S₈ tension—
— Adjust parameters and press Compute
ArXe Internal Analysis — PLO v2
Naturality Index (NI)—
NI Zone (PLO v2)—
Axiomatic Distance (DA)—
Scaled integers (Ω_m, Ω_Λ)—
NI definition: max_prime(scale_to_int(Ω_m, Ω_Λ, digits=4))
NI is NOT a Bayesian fine-tuning index. NI=137 means Ω_Λ=0.685 → scaled integer 137 (prime). Arithmetic structure, not statistical probability.
DA definition: Sum of normalized observational tension contributions.
DA = 350×min(ΔH0/5.6,1) + 200×min(ΔS8/0.072,1). NOT Mahalanobis distance. Ref: ArXe CPF §PLO v2.
NI is NOT a Bayesian fine-tuning index. NI=137 means Ω_Λ=0.685 → scaled integer 137 (prime). Arithmetic structure, not statistical probability.
DA definition: Sum of normalized observational tension contributions.
DA = 350×min(ΔH0/5.6,1) + 200×min(ΔS8/0.072,1). NOT Mahalanobis distance. Ref: ArXe CPF §PLO v2.
Examples
Target Constraints
Element Pool
Forbidden Elements
searching composition space…
Ranked Candidates
| # | Formula | Phase | N | ρ (g/cm³) | σ (MPa) | δr | Δen | Max Prime | S_ArXe | Score | Warnings |
|---|
Candidates ranked by combined stability score. Export to CALPHAD / DFT for final validation.
Column guide ·
δr Hume-Rothery radius mismatch (<0.066 = solid solution stable) ·
Δen max electronegativity diff (<0.40 = miscible) ·
SOL exceeds solid solution limit ·
TOX processing hazard ·
HR Hume-Rothery violation ·
PGM platinum-group / critical cost
Unlock PDF & JSON export — Pro plan
Examples
Target Observable
Matching Systems
Examples
Ligand Parameters
Metal Center (optional)
Trans-Influence Prediction