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Material operators

8 operators in the material category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
ALLOY_MIXTUREVoigt upper bound rule of mixtures estimating composite elastic modulus as the volume-weighted average of fiber and matrix moduli.E_c = V_f E_f + V_m E_m
CRYSTAL_DIFFRACTIONBragg's law relating X-ray wavelength and crystal lattice spacing to the diffraction angle for constructive interference.n\lambda = 2d\sin\theta
CRYSTAL_LATTICEInterplanar spacing for cubic crystal systems computed from the lattice parameter and Miller indices of the diffracting plane.d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}
HARDNESS_VICKERSVickers hardness number calculated from the applied test force divided by the surface area of the pyramidal indentation.HV = \frac{1.854F}{d^2}
MATERIAL_MODULUSYoung's modulus defining the ratio of uniaxial stress to strain in the linear elastic region of a material's response.E = \frac{\sigma}{\epsilon}
MATERIAL_STRENGTHHall-Petch equation predicting yield strength increase with decreasing grain size through a square-root inverse relationship.\sigma_y = \sigma_0 + k_y d^{-1/2}
NANO_SURFACETotal surface area of a collection of spherical nanoparticles calculated from individual particle radius and particle count.SA = 4\pi r^2 \times N
THERMAL_EXPANSIONLinear thermal expansion giving the change in length of a material as the product of original length, expansion coefficient, and temperature change.\Delta L = L_0 \alpha \Delta T

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["ALLOY_MIXTURE"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​