Crystal structures and diffraction, defects and diffusion, mechanical properties, phase diagrams, polymers, ceramics and composites, and electronic and thermal properties.
Materials Science (materials-science-ai999x) is an offline Python package for materials science. It covers crystal structures and diffraction, defects and diffusion, mechanical properties, phase diagrams, polymers, ceramics and composites, and electronic and thermal properties.
It has 87 capabilities — 87 computational procedures — in 13 topics, the largest being Crystal structures, Mechanical properties, Diffraction, Polymers, Diffusion and Fracture. Ask a question in words with ask(), or call a capability by name with typed inputs with solve(). Every answer carries its value and unit, the steps that produced it and the formula in LaTeX.
When a question is not determined — a value is missing, an input is out of range, or the request is outside the package — it says so and names what it needs, instead of guessing. It runs on an ordinary CPU without a network connection (Python >=3.10), and the same question always gets the same answer.
pip install materials-science-ai999x hf download AI999X/materials-science-ai999x --local-dir materials-science-ai999x
Each question below was put to materials-science-ai999x and the answer shown is the one it returned, with the steps it took.
Theoretical density: structure = FCC, A = 63.55 g/mol, R = 0.128 nm
structure = FCC, A = 63.55 g/mol, R = 0.128 nmrho = 8895.28269 kg/m^3, rho_gcc = 8.89528269, a_nm = 0.362038672Bragg angle: d = 0.2087 nm, lambda = 0.1542 nm
d = 0.2087 nm, lam = 0.1542 nmtheta_deg = 21.68045609, two_theta_deg = 43.36091219Fick's second law: C0 = 0.25 wt%, Cs = 1.2 wt%, x = 0.5 mm, D = 1.6e-11 m^2/s, t = 7 h
C0 = 0.25, Cs = 1.2, x = 0.5 mm, D = 1.6e-11 m^2/s, t = 7 hCx = 0.7987846097, z = 0.3937129927, ratio = 0.5776680102Iron-carbon microconstituents: C0 = 0.35 wt%
C0 = 0.35W_proeutectoid = 0.5555555556, W_pearlite = 0.4444444444, W_ferrite_total = 0.9508834981, W_cementite_total = 0.04911650195, proeutectoid_phase = ferritem.solve("planar_density", structure="BCC", h=1, k=1, l=0, a="0.2866 nm") structure = BCC, h = 1, k = 1, l = 0, a = 0.2866 nmPD_per_nm2 = 17.21720402, PD = 1.721720402e+19 1/m^2, PPF = 0.8330405509Ceramic density: prototype = rocksalt, rc = 0.102 nm, ra = 0.181 nm, Ac = 22.99 g/mol, Aa = 35.45 g/mol
prototype = rocksalt, rc = 0.102 nm, ra = 0.181 nm, Ac = 22.99 g/mol, Aa = 35.45 g/mola = 5.66e-10 m, a_nm = 0.566, rho = 2140.769963 kg/m^3, rho_gcc = 2.140769963Rule of mixtures: Ef = 69 GPa, Em = 3.4 GPa, Vf = 0.4
Ef = 69 GPa, Em = 3.4 GPa, Vf = 0.4E_long_GPa = 29.64, E_trans_GPa = 5.486435921, fiber_load_fraction = 0.9311740891, E_long = 2.964e+10 Pa, E_trans = 5486435921 PaBurgers vector: structure = FCC, a = 0.3615 nm
structure = FCC, a = 0.3615 nmb = 2.556191014e-10 m, b_nm = 0.2556191014, direction = a/2<110>Every snippet was run as shown; the output under it is what it printed.
import materials_science_ai999x as m
a = m.ask("Theoretical density: structure = FCC, A = 63.55 g/mol, R = 0.128 nm")
print(a.outcome)
print(a.values)
for step in a.steps:
print(step["name"])SOLVED
{'rho': 8895.2826897, 'rho_gcc': 8.8952826897, 'a_nm': 0.362038671968}
Theoretical density of a metal
import materials_science_ai999x as m
a = m.solve("planar_density", structure="BCC", h=1, k=1, l=0, a="0.2866 nm")
print(a.outcome)
print(a.values)SOLVED
{'PD_per_nm2': 17.2172040168, 'PD': 1.72172040168e+19, 'PPF': 0.833040550905}
import materials_science_ai999x as m
# an input is missing: the answer says what it needs instead of guessing
a = m.solve("planar_density")
print(a.outcome)
print(a.message)NEEDS_INPUT
planar_density needs structure, h, k, l, a (crystal structure (SC, BCC, FCC); Miller index h; Miller index k; Miller index l; lattice parameter). Example: solve('planar_density', structure='FCC', h=1, k=0, l=0, a='4e-10 m').
materials-science-ai999x "Theoretical density: structure = FCC, A = 63.55 g/mol, R = 0.128 nm"
rho = 8895.28 kg/m^3, rho_gcc = 8.89528, a_nm = 0.362039 1. Theoretical density of a metal: a from R (hard spheres), V_cell = a^3 (HCP: (3 sqrt(3)/2) a^2 c with c = sqrt(8/3) a), rho = n A/(V_cell N_A) with structure = FCC, A = 63.55 g/mol, R = 0.128 nm -> rho = 8895.28 kg/m^3, rho_gcc = 8.89528, a_nm = 0.362039 Assumptions: A > 0; R > 0 …
Every value in these figures was computed by the package, each point a run of solve(); in a notebook, plot() and plot_relation() draw a capability's curves the same way.
12 of its 87 formulas; every one is in the capability browser below.
Search by name, formula, input or topic. Each capability opens to show what it takes, what it returns, when it applies, and a question it answered.
radius_ratio_coordinationThe expected coordination number and polyhedron of a cation from the ratio of the cation and anion radii (Pauling's radius-ratio rule).
rc cation radius [m]ra anion radius [m]ratio rc/raCN coordination numbergeometry coordination polyhedronceramic_densityThe cubic lattice parameter and theoretical density of a rock-salt, cesium-chloride, zinc-blende or fluorite crystal from its ionic radii and molar masses.
prototype crystal structure (rocksalt, CsCl, zincblende, fluorite) choicerc cation radius [m]ra anion radius [m]Ac molar mass of the cation element [kg/mol]Aa molar mass of the anion element [kg/mol]a lattice parameter [m]a_nm lattice parameter in nmrho density [kg/m^3]rho_gcc density in g/cm^3critical_fiber_lengthThe critical length l_c = sigma_f d / (2 tau_c) a fibre needs to be loaded to its strength through the fibre-matrix interface.
sigma_f fibre tensile strength [Pa]d fibre diameter [m]tau_c fibre-matrix bond strength (or matrix shear yield strength) [Pa]lc critical fibre length [m]lc_mm critical length in mmaspect_ratio l_c/dcomposite_rule_of_mixturesThe longitudinal (isostrain) and transverse (isostress) moduli of an aligned continuous-fibre composite and the fraction of the load carried by the fibres.
Ef fibre modulus [Pa]Em matrix modulus [Pa]Vf fibre volume fraction (0 to 1)E_long_GPa longitudinal modulus in GPaE_trans_GPa transverse modulus in GPafiber_load_fraction fraction of a longitudinal load carried by the fibresE_long longitudinal modulus [Pa]E_trans transverse modulus [Pa]angle_between_directions_cubicThe angle between the directions [u1 v1 w1] and [u2 v2 w2] of a cubic crystal (also the angle between the planes with those indices).
u1 index u of direction 1 integerv1 index v of direction 1 integerw1 index w of direction 1 integeru2 index u of direction 2 integerv2 index v of direction 2 integerw2 index w of direction 2 integerangle_deg angle in degreesangle_between_directionsThe angle between the directions [u1 v1 w1] and [u2 v2 w2] of a crystal with any cell (a, b, c, alpha, beta, gamma).
a cell edge a [m]b cell edge b [m]c cell edge c [m]alpha cell angle alpha in degrees (between b and c)beta cell angle beta in degrees (between a and c)gamma cell angle gamma in degrees (between a and b)u1 index u of direction 1 integerv1 index v of direction 1 integerw1 index w of direction 1 integeru2 index u of direction 2 integerv2 index v of direction 2 integerw2 index w of direction 2 integerangle_deg angle in degreesangle_between_planesThe angle between the normals of the planes (h1 k1 l1) and (h2 k2 l2) of a crystal with any cell.
a cell edge a [m]b cell edge b [m]c cell edge c [m]alpha cell angle alpha in degrees (between b and c)beta cell angle beta in degrees (between a and c)gamma cell angle gamma in degrees (between a and b)h1 Miller index h of plane 1 integerk1 Miller index k of plane 1 integerl1 Miller index l of plane 1 integerh2 Miller index h of plane 2 integerk2 Miller index k of plane 2 integerl2 Miller index l of plane 2 integerangle_deg angle between the plane normals in degreesatomic_packing_factorThe fraction of a crystal's volume filled by hard-sphere atoms, the coordination number and the atoms per conventional cell of SC, BCC, FCC, HCP or diamond cubic.
structure crystal structure (SC, BCC, FCC, HCP, diamond) choiceapf atomic packing factorcoordination coordination numberatoms_per_cell atoms per conventional cell (HCP: the hexagonal prism)miller_bravais_to_three_indexConvert a Miller-Bravais direction [u v t w] of a hexagonal crystal to the three-index form [U V W].
u index along a1 integerv index along a2 integert index along a3 (= -(u + v)) integerw index along c integerU three-index component UV three-index component VW three-index component Windices [U V W]lattice_parameter_from_densityThe lattice parameter a and hard-sphere atomic radius R of a crystal of known structure, density and molar mass.
structure crystal structure (SC, BCC, FCC, HCP, diamond) choicerho measured density [kg/m^3]A molar mass [kg/mol]a lattice parameter a [m]a_nm lattice parameter a in nmR_nm atomic radius in nmcubic_lattice_parameterThe cubic lattice parameter a of an SC, BCC, FCC or diamond-cubic crystal of hard-sphere atoms of radius R.
structure crystal structure (SC, BCC, FCC, diamond) choiceR atomic radius [m]a lattice parameter [m]a_nm lattice parameter in nmnearest_neighbour_nm nearest-neighbour distance 2R in nmlinear_densityThe number of atoms per unit length along the [u v w] direction of an SC, BCC or FCC crystal, and the linear packing fraction.
structure crystal structure (SC, BCC, FCC) choiceu direction index u integerv direction index v integerw direction index w integera lattice parameter [m]LD_per_nm atoms per nm along [uvw]LD atoms per metre along [uvw] [1/m]repeat_nm repeat distance along [uvw] in nmLPF linear packing fraction (hard spheres)miller_indices_from_interceptsThe Miller indices (h k l) of a plane cutting the axes at x, y, z (in units of the cell edges; inf for a plane parallel to an axis).
x intercept on the a axis (number, fraction or inf) texty intercept on the b axis textz intercept on the c axis texth Miller index hk Miller index kl Miller index lindices (h k l)planar_densityThe number of atoms per unit area on the (h k l) plane of an SC, BCC or FCC crystal, and the planar packing fraction.
structure crystal structure (SC, BCC, FCC) choiceh Miller index h integerk Miller index k integerl Miller index l integera lattice parameter [m]PD_per_nm2 atoms per nm^2 on the planePD atoms per m^2 on the plane [1/m^2]PPF planar packing fraction (hard spheres)space_groupThe space-group number, Hermann-Mauguin symbol and crystal system of a common metallic or ionic structure.
structure structure (SC, BCC, FCC, HCP, diamond, rocksalt, CsCl, zincblende, fluorite) choicenumber space-group number (International Tables)symbol Hermann-Mauguin symbolcrystal_system crystal systemtheoretical_densityThe density of a crystal from its structure, the atomic radius and the molar mass: rho = n A / (V_cell N_A).
structure crystal structure (SC, BCC, FCC, HCP, diamond) choiceA molar mass (atomic weight) [kg/mol]R atomic radius [m]rho theoretical density [kg/m^3]rho_gcc density in g/cm^3a_nm lattice parameter a in nmmiller_bravais_directionConvert a hexagonal direction [U V W] (axes a1, a2, c) to the Miller-Bravais form [u v t w] (axes a1, a2, a3, c).
U index along a1 integerV index along a2 integerW index along c integeru Miller-Bravais index uv Miller-Bravais index vt Miller-Bravais index tw Miller-Bravais index windices [u v t w]hcp_cell_densityThe volume of the HCP hexagonal prism (6 atoms), the density and the c/a ratio from a, c and the molar mass.
a lattice parameter a [m]c lattice parameter c [m]A molar mass [kg/mol]V volume of the hexagonal prism (6 atoms) [m^3]V_nm3 prism volume in nm^3rho density [kg/m^3]rho_gcc density in g/cm^3c_over_a c/a ratiopolymorphic_volume_changeThe percentage volume change when a metal transforms from BCC to FCC (as iron at 912 C), from the atomic radius in each structure.
R_bcc atomic radius in the BCC form [m]R_fcc atomic radius in the FCC form [m]volume_change_percent volume change BCC -> FCC in percent (negative = contraction)V_atom_bcc_nm3 volume per atom in BCC, nm^3V_atom_fcc_nm3 volume per atom in FCC, nm^3unit_cell_volumeThe volume of a unit cell from its six lattice parameters a, b, c, alpha, beta, gamma.
a cell edge a [m]b cell edge b [m]c cell edge c [m]alpha cell angle alpha in degrees (between b and c)beta cell angle beta in degrees (between a and c)gamma cell angle gamma in degrees (between a and b)V cell volume [m^3]V_nm3 cell volume in nm^3burgers_vectorThe magnitude of the shortest lattice translation (the Burgers vector of a perfect dislocation) in an SC, BCC or FCC metal.
structure crystal structure (SC, BCC, FCC) choicea lattice parameter [m]b Burgers vector magnitude [m]b_nm Burgers vector in nmdirection Burgers vector familyvacancy_concentrationThe number of atomic sites per volume and the equilibrium number of vacancies N_v = N exp(-Q_v/kT) of a metal.
rho density [kg/m^3]A molar mass [kg/mol]Qv vacancy formation energy (per vacancy, e.g. eV) [J]T temperature [K]N atomic sites per volume [1/m^3]Nv vacancies per volume [1/m^3]fraction vacancy fraction Nv/Nlog10_Nv log10 of Nv in m^-3N_per_cm3 atomic sites per cm^3interstitial_site_sizeThe radius of the largest sphere that fits the octahedral or tetrahedral interstitial site of an FCC or BCC lattice of host atoms of radius R.
structure crystal structure (FCC, BCC) choicesite interstitial site (octahedral, tetrahedral) choiceR radius of the host atoms [m]r radius of the interstitial sphere [m]r_nm interstitial radius in nmratio r/Rvacancy_formation_energy_fitThe vacancy formation energy Q_v and prefactor from vacancy fractions measured at two or more temperatures (least-squares Arrhenius line).
T temperatures in kelvin vectorfraction vacancy fractions N_v/N at those temperatures vectorQv_eV vacancy formation energy in eVQv vacancy formation energy [J]prefactor prefactor C of N_v/N = C exp(-Q_v/kT)r_squared r^2 of the fitbragg_angleThe diffraction angle theta (and 2-theta) of planes of spacing d for X-rays of wavelength lambda: n lambda = 2 d sin(theta).
d interplanar spacing [m]lam X-ray wavelength [m]n order of the reflection (default 1) integer optionaltheta_deg Bragg angle theta in degreestwo_theta_deg diffraction angle 2-theta in degreescubic_reflection_angleThe interplanar spacing and the diffraction angle 2-theta of the (h k l) reflection of a cubic crystal of lattice parameter a at wavelength lambda.
a lattice parameter [m]h Miller index h integerk Miller index k integerl Miller index l integerlam X-ray wavelength [m]d_nm interplanar spacing in nmtheta_deg Bragg angle in degreestwo_theta_deg diffraction angle 2-theta in degreesallowed_reflections_cubicThe values of h^2 + k^2 + l^2 of the first allowed X-ray reflections of a monatomic SC, BCC, FCC or diamond-cubic crystal, in order of increasing angle.
structure crystal structure (SC, BCC, FCC, diamond) choicecount how many reflections (1 to 15, default 6) integer optionalN_values h^2 + k^2 + l^2 of the allowed reflections, ascendingN_last the last of themN_first the first allowed reflectionbragg_spacingThe interplanar spacing d of planes that reflect X-rays of wavelength lambda at the Bragg angle theta in order n.
lam X-ray wavelength [m]theta Bragg angle theta in degrees (half of 2-theta)n order of the reflection (default 1) integer optionald interplanar spacing [m]d_nm interplanar spacing in nmd_spacing_cubicThe spacing of the (h k l) planes of a cubic lattice: d = a / sqrt(h^2 + k^2 + l^2).
a lattice parameter [m]h Miller index h integerk Miller index k integerl Miller index l integerd interplanar spacing [m]d_nm interplanar spacing in nmd_spacing_triclinicThe spacing of the (h k l) planes of any lattice from its six cell parameters, through the reciprocal metric tensor.
a cell edge a [m]b cell edge b [m]c cell edge c [m]alpha cell angle alpha in degrees (between b and c)beta cell angle beta in degrees (between a and c)gamma cell angle gamma in degrees (between a and b)h Miller index h integerk Miller index k integerl Miller index l integerd interplanar spacing [m]d_nm interplanar spacing in nmd_spacing_hexagonalThe spacing of the (h k l) planes of a hexagonal lattice: 1/d^2 = 4(h^2 + hk + k^2)/(3a^2) + l^2/c^2.
a lattice parameter a [m]c lattice parameter c [m]h Miller index h integerk Miller index k integerl Miller index l integeri Miller-Bravais index i = -(h + k) (optional, checked) integer optionald interplanar spacing [m]d_nm interplanar spacing in nmd_spacing_tetragonalThe spacing of the (h k l) planes of a tetragonal lattice: 1/d^2 = (h^2 + k^2)/a^2 + l^2/c^2.
a lattice parameter a [m]c lattice parameter c [m]h Miller index h integerk Miller index k integerl Miller index l integerd interplanar spacing [m]d_nm interplanar spacing in nmd_spacing_orthorhombicThe spacing of the (h k l) planes of an orthorhombic lattice: 1/d^2 = h^2/a^2 + k^2/b^2 + l^2/c^2.
a lattice parameter a [m]b lattice parameter b [m]c lattice parameter c [m]h Miller index h integerk Miller index k integerl Miller index l integerd interplanar spacing [m]d_nm interplanar spacing in nmstructure_factor_cubicThe structure factor |F|/f of the (h k l) reflection of a monatomic SC, BCC, FCC or diamond-cubic crystal, and whether the reflection is allowed.
structure crystal structure (SC, BCC, FCC, diamond) choiceh Miller index h integerk Miller index k integerl Miller index l integerF_over_f |F| in units of the atomic scattering factor fF2_over_f2 |F|^2 / f^2 (proportional to intensity)allowed whether the reflection appearsbragg_wavelengthThe wavelength that reflects from planes of spacing d at the Bragg angle theta in order n.
d interplanar spacing [m]theta Bragg angle theta in degrees (half of 2-theta)n order of the reflection (default 1) integer optionallam wavelength [m]lam_nm wavelength in nmdiffusion_arrhenius_fitQ_d and D_0 of D = D_0 exp(-Q_d/RT) from diffusion coefficients at two or more temperatures, and D at another temperature.
T temperatures in kelvin vectorD diffusion coefficients in m^2/s at those temperatures vectorT_target temperature at which D is wanted (optional) [K] optionalQ activation energy [J/mol]Q_kJmol activation energy in kJ/molD0 pre-exponential factor [m^2/s]log10_D0 log10 of D0 in m^2/sr_squared r^2 of the fitD_target D at T_target [m^2/s]log10_D_target log10 of D at T_targetfick_second_law_concentrationThe concentration at depth x after time t in a semi-infinite solid with a constant surface concentration (carburizing, doping): C_x = C_s - (C_s - C_0) erf(x / 2 sqrt(Dt)).
C0 initial (bulk) concentration (wt%, at% or any one unit)Cs surface concentration (same unit)x depth below the surface [m]D diffusion coefficient [m^2/s]t diffusion time [s]Cx concentration at depth x (unit of C0, Cs)z erf argument x / (2 sqrt(D t))ratio (Cx - C0)/(Cs - C0)diffusion_depth_of_concentrationThe depth at which the concentration equals C_x after diffusion time t in a semi-infinite solid with constant surface concentration (case depth).
C0 initial concentrationCs surface concentrationCx target concentrationD diffusion coefficient [m^2/s]t diffusion time [s]x depth [m]x_mm depth in mmz erf argumentarrhenius_diffusivityThe diffusion coefficient D = D0 exp(-Q_d/RT) at temperature T from the pre-exponential factor and the activation energy.
D0 pre-exponential factor [m^2/s]Q activation energy per mole [J/mol]T absolute temperature [K]D diffusion coefficient [m^2/s]log10_D log10 of D in m^2/sQ_over_RT Q_d/(R T)fick_first_law_fluxThe steady-state diffusion flux between two positions with known concentrations: J = -D (C2 - C1)/(x2 - x1).
D diffusion coefficient [m^2/s]C1 concentration at x1 [kg/m^3]C2 concentration at x2 [kg/m^3]x1 first position [m]x2 second position [m]J diffusion flux (positive towards increasing x) [kg/(m^2*s)]J_per_hour flux in kg/(m^2 h)diffusion_time_to_concentrationThe diffusion time for the concentration at depth x to reach C_x in a semi-infinite solid with constant surface concentration (carburizing time).
C0 initial concentrationCs surface concentrationCx target concentration at depth xx depth [m]D diffusion coefficient [m^2/s]t diffusion time [s]t_hours diffusion time in hoursz erf argumentband_gap_from_conductivityThe band gap of an intrinsic semiconductor from its conductivity at two or more temperatures, with sigma = C exp(-Eg/2kT) (the weak temperature dependence of the prefactor neglected).
T temperatures in kelvin vectorsigma conductivities (any one unit) at those temperatures vectorEg_eV band gap in eVprefactor prefactor C (unit of sigma)r_squared r^2 of the fitpn_junction_built_in_potentialThe built-in potential V_bi = (kT/q) ln(n_n p_p/ni^2) of an abrupt p-n junction (majority concentrations from charge neutrality; V_bi ~ (kT/q) ln(Na Nd/ni^2) when Na, Nd >> ni), and with a permittivity the zero-bias depletion width.
Na acceptor concentration on the p side [1/m^3]Nd donor concentration on the n side [1/m^3]ni intrinsic carrier concentration [1/m^3]T temperature [K]eps_r relative permittivity of the semiconductor (optional, for the depletion width) optionalV_bi built-in potential [V]V_bi_approx (kT/q) ln(Na Nd/ni^2) [V]thermal_voltage kT/q [V]W zero-bias depletion width [m]W_um depletion width in umx_n_um depletion width on the n side in umx_p_um depletion width on the p side in umextrinsic_carrier_concentrationThe electron and hole concentrations of a semiconductor with donor and acceptor concentrations Nd and Na (complete ionisation), from charge neutrality and n p = ni^2, and the Fermi level relative to the intrinsic level.
Nd donor concentration [1/m^3]Na acceptor concentration [1/m^3]ni intrinsic carrier concentration [1/m^3]T temperature (optional, for the Fermi level) [K] optionaln electron concentration [1/m^3]p hole concentration [1/m^3]log10_n log10 of n in m^-3log10_p log10 of p in m^-3carrier_type n-type, p-type or intrinsicEF_minus_Ei_eV Fermi level above the intrinsic level in eV (when T is given)fermi_energy_free_electronThe conduction-electron density, Fermi energy, Fermi temperature and Fermi velocity of a metal from its density, molar mass and number of valence electrons per atom.
rho density [kg/m^3]A molar mass [kg/mol]valence valence electrons per atomn conduction-electron density [1/m^3]log10_n log10 of n in m^-3EF Fermi energy [J]EF_eV Fermi energy in eVTF Fermi temperature [K]vF Fermi velocity [m/s]intrinsic_carrier_concentrationThe effective densities of states Nc and Nv and the intrinsic carrier concentration ni = sqrt(Nc Nv) exp(-Eg/2kT) from the band gap, temperature and effective masses.
Eg band gap [J]T temperature [K]me electron density-of-states effective mass / m0 (default 1) optionalmh hole density-of-states effective mass / m0 (default 1) optionalNc effective density of states, conduction band [1/m^3]Nv effective density of states, valence band [1/m^3]ni intrinsic carrier concentration [1/m^3]log10_ni log10 of ni in m^-3log10_Nc log10 of Nc in m^-3Ei_offset_meV intrinsic Fermi level above midgap in meVcritical_crack_lengthThe largest crack a part can carry at stress sigma without fracture: a_c = (K_IC / (Y sigma))^2 / pi.
K_IC plane-strain fracture toughness [Pa*m^0.5]sigma applied stress [Pa]Y geometry factor Y (default 1) optionala_c critical crack length [m]a_c_mm critical crack length in mmweibull_design_stressThe stress at which a brittle part reaches a given failure probability, from the Weibull modulus and characteristic strength (and V/V0).
P_failure allowed probability of failure (0 to 1)sigma0 characteristic strength [Pa]m Weibull modulusV_ratio V/V0 (default 1) optionalsigma design stress [Pa]sigma_MPa design stress in MPafracture_critical_stressThe stress at which a crack of length a fails in a material of plane-strain fracture toughness K_IC: sigma_c = K_IC / (Y sqrt(pi a)).
K_IC plane-strain fracture toughness [Pa*m^0.5]a crack length (surface) or half-length (internal) [m]Y geometry factor Y (default 1) optionalsigma_c critical stress [Pa]sigma_c_MPa critical stress in MPagriffith_critical_stressThe stress at which a crack of length 2a (internal) or a (surface) propagates in a brittle solid: sigma_c = sqrt(2 E gamma_s / (pi a)).
E Young's modulus [Pa]gamma_s specific surface energy [J/m^2]a half-length of an internal crack (or length of a surface crack) [m]sigma_c critical stress [Pa]sigma_c_MPa critical stress in MPaweibull_modulus_fitThe Weibull modulus m and characteristic strength sigma_0 from measured fracture strengths, by median-rank regression (Bernard's ranks).
strengths fracture strengths (any one unit, e.g. MPa) vectorm Weibull modulussigma0 characteristic strength (unit of the data)r_squared r^2 of the fitweibull_failure_probabilityThe probability that a brittle (ceramic) part fails at stress sigma, from the Weibull modulus m and characteristic strength sigma_0, with an optional volume ratio V/V0.
sigma applied stress [Pa]sigma0 characteristic strength (63.2 % failure at V0) [Pa]m Weibull modulusV_ratio stressed volume over the reference volume V/V0 (default 1) optionalP_failure probability of failureP_survival probability of survivaloffset_yield_strengthThe yield strength where the stress-strain curve (piecewise linear through the data) meets a line of slope E offset by 0.2 % strain (or another offset).
strain engineering strains, increasing vectorstress engineering stresses in MPa vectorE Young's modulus [Pa]offset strain offset (default 0.002) optionalyield_MPa offset yield strength in MPayield_strain strain at the intersectionelastic_deformation_of_a_rodStress, axial strain, elongation, lateral strain and diameter change of a cylindrical rod under an axial force (Hooke's law and Poisson's ratio).
F axial force (tension positive) [N]d0 original diameter [m]l0 original length [m]E Young's modulus [Pa]nu Poisson's ratiostress_MPa axial stress in MPaaxial_strain axial strainelongation_mm elongation in mmlateral_strain lateral straindiameter_change_um change of diameter in micrometres (negative = contraction)hall_petchsigma_0 and k of sigma_y = sigma_0 + k d^(-1/2) from yield strengths at two or more grain sizes, and the yield strength at another grain size.
d_um grain diameters in micrometres vectoryield_MPa yield strengths in MPa vectord_target_um grain diameter in micrometres at which the yield strength is wanted (optional) optionalsigma0_MPa friction stress sigma_0 in MPak_MPa_sqrt_um k in MPa um^0.5k_MPa_sqrt_m k in MPa m^0.5r_squared r^2 of the fityield_target_MPa yield strength at the target grain size in MPalarson_miller_parameterThe Larson-Miller parameter LMP = T (C + log10 t_r) from a rupture time at a temperature, and the rupture time at another temperature for the same parameter (same stress).
T absolute temperature [K]t_r rupture time (hours, h ...) [s]C Larson-Miller constant (default 20, with t_r in hours) optionalT2 another temperature at the same stress (optional) [K] optionalLMP Larson-Miller parameter (K, t in hours)LMP_thousands LMP / 1000log10_t_hours log10 of the rupture time in hourst_r2_hours rupture time at T2 in hourslog10_t2_hours log10 of the rupture time at T2modulus_of_resilienceThe elastic strain energy per unit volume stored up to yielding: U_r = sigma_y^2/(2E).
sy yield strength [Pa]E Young's modulus [Pa]Ur modulus of resilience [J/m^3]Ur_MJ_m3 modulus of resilience in MJ/m^3 (= MPa)yield_strain strain at yieldmax_schmid_factorThe largest Schmid factor over the 12 {111}<110> (FCC) or {110}<111> (BCC) slip systems for a tensile load direction, how many systems share it, and the yield stress from the CRSS.
structure crystal structure (FCC, BCC) choiceload loading direction [u v w] vectortau_crss critical resolved shear stress (optional) [Pa] optionalmax_schmid_factor largest Schmid factoractive_systems number of systems with that factorsystems slip systems consideredyield_MPa tensile yield stress in MPaschmid_factorThe Schmid factor cos(phi) cos(lambda) of a slip system (plane normal and slip direction) for a tensile load along a direction of a cubic crystal, the resolved shear stress and the stress to start slip.
load loading direction [u v w] vectorplane slip-plane normal (h k l) vectordirection slip direction [u v w] vectorsigma applied tensile stress (optional) [Pa] optionaltau_crss critical resolved shear stress (optional) [Pa] optionalschmid_factor |cos(phi) cos(lambda)|phi_deg angle between load and plane normallambda_deg angle between load and slip directiontau_R_MPa resolved shear stress in MPayield_MPa tensile stress at which slip starts, in MPaisotropic_elastic_constantsThe shear modulus G, bulk modulus K and Lame constant lambda of an isotropic material from Young's modulus E and Poisson's ratio nu.
E Young's modulus [Pa]nu Poisson's ratioG shear modulus [Pa]G_GPa shear modulus in GPaK bulk modulus [Pa]K_GPa bulk modulus in GPalame_GPa Lame's first constant in GPastrain_hardening_exponentThe strain-hardening exponent n and strength coefficient K of sigma_T = K epsilon_T^n from true stress-strain points of the plastic region, and the stress at another strain.
true_strain true plastic strains vectortrue_stress true stresses in MPa vectorstrain_target true strain at which the stress is wanted (optional) optionaln strain-hardening exponentK_MPa strength coefficient in MPar_squared r^2 of the log-log fitstress_target_MPa true stress at the target strain in MPacreep_parameters_fitn and Q_c of the power-law creep model rate = A sigma^n exp(-Q_c/RT) from steady-state creep rates at several stresses and temperatures (least squares).
stress_MPa stresses in MPa vectorT temperatures in kelvin vectorrate steady-state creep rates in 1/s vectorn stress exponentQ_kJmol creep activation energy in kJ/molthermal_stressThe stress from a temperature change in a body held in one direction (rod between walls), two (thin film or plate) or three (fully constrained).
E Young's modulus [Pa]alpha linear thermal expansion coefficient [1/K]dT temperature change (positive = heating) [K]constraint constraint (uniaxial, biaxial, triaxial; default uniaxial) choice optionalnu Poisson's ratio (needed for biaxial and triaxial) optionalstress thermal stress (negative = compression) [Pa]stress_MPa thermal stress in MPatensile_toughnessThe energy absorbed per unit volume up to fracture (trapezoidal area under the stress-strain data), the tensile strength and the fracture strain.
strain engineering strains, non-decreasing vectorstress engineering stresses in MPa vectortoughness_MJ_m3 toughness in MJ/m^3toughness toughness [J/m^3]uts_MPa tensile strength (largest stress) in MPafracture_strain strain at the last pointtrue_stress_and_strainTrue stress and true strain from the engineering stress and strain of a tensile test before necking (volume conserved).
stress engineering stress [Pa]strain engineering strain (dimensionless)true_stress true stress [Pa]true_stress_MPa true stress in MPatrue_strain true strainyoungs_modulus_from_dataYoung's modulus as the slope of the least-squares line through stress-strain points of the elastic region.
strain engineering strains (dimensionless) vectorstress engineering stresses in MPa vectorE_GPa Young's modulus in GPaE Young's modulus [Pa]intercept_MPa intercept of the line in MPar_squared r^2 of the fitatomic_to_weight_percentConvert the composition of a binary alloy from atomic percent to weight percent.
element1 symbol of element 1 textelement2 symbol of element 2 textat1 atomic percent of element 1wt1 weight percent of element 1wt2 weight percent of element 2gibbs_phase_ruleThe number of degrees of freedom F = C - P + 2 (or + 1 at fixed pressure) of a system of C components and P phases in equilibrium.
C number of components integerP number of phases integerpressure pressure variable or held constant (default variable) choice optionalF degrees of freedomlever_ruleThe mass fractions (and masses) of the two phases of an alloy of overall composition C0 in a two-phase region whose tie line ends at C1 and C2.
C0 overall composition (wt%)C1 composition of phase 1 (wt%)C2 composition of phase 2 (wt%)mass total mass of the alloy (optional) [kg] optionalW1 mass fraction of phase 1W2 mass fraction of phase 2m1 mass of phase 1 [kg]m2 mass of phase 2 [kg]eutectic_microconstituentsThe fractions of primary phase and eutectic microconstituent, and of total alpha and beta, in a binary eutectic alloy cooled just below the eutectic temperature.
C0 alloy composition (wt%)C_alpha composition of alpha at the eutectic temperatureC_E eutectic compositionC_beta composition of beta at the eutectic temperatureW_primary fraction of primary (proeutectic) phaseW_eutectic fraction of eutectic microconstituentW_alpha_total total fraction of alphaW_beta_total total fraction of betaprimary_phase the primary phase (alpha for hypoeutectic, beta for hypereutectic)iron_carbon_microconstituentsThe fractions of proeutectoid ferrite or cementite and of pearlite, and of total ferrite and cementite, in a steel cooled slowly just below the eutectoid temperature.
C0 carbon content in wt% (0.022 to 2.14)W_proeutectoid fraction of proeutectoid ferrite or cementiteW_pearlite fraction of pearliteW_ferrite_total total fraction of ferriteW_cementite_total total fraction of cementiteproeutectoid_phase ferrite (hypoeutectoid) or cementite (hypereutectoid)weight_to_atomic_percentConvert the composition of a binary alloy from weight percent to atomic percent.
element1 symbol of element 1 textelement2 symbol of element 2 textwt1 weight percent of element 1at1 atomic percent of element 1at2 atomic percent of element 2avrami_kineticsThe Avrami exponent n and rate constant k of y = 1 - exp(-k t^n) from transformed fractions at two or more times, the half-transformation time and the time for a target fraction.
t times (any one unit, e.g. s) vectory transformed fractions (0 to 1) vectory_target fraction whose time is wanted (optional) optionaln Avrami exponentk rate constant (time unit^-n)log10_k log10 of kt_half time to 50 % transformation (time unit of t)r_squared r^2 of the fitt_target time to the target fractionhomogeneous_nucleationThe critical radius r* and the energy barrier dG* for homogeneous nucleation of a solid from its undercooled melt.
gamma solid-liquid interfacial energy [J/m^2]dHf latent heat of fusion per volume [J/m^3]Tm melting temperature [K]T temperature of the undercooled liquid [K]undercooling undercooling Tm - T [K]dGv_MJ_m3 volume free-energy change in MJ/m^3r_star critical radius [m]r_star_nm critical radius in nmdG_star activation free energy [J]dG_star_eV activation free energy in eVcopolymer_degree_of_polymerizationThe average repeat-unit molecular weight of a copolymer from the two repeat-unit formulas and the mole fraction of the first, and its degree of polymerization.
formula1 formula of repeat unit 1 textformula2 formula of repeat unit 2 textf1 mole fraction of repeat unit 1 (0 to 1)Mn number-average molecular weight [kg/mol]m_avg_g_mol average repeat-unit molecular weight in g/molDP degree of polymerizationkelvin_voigt_creepThe strain after time t under constant stress for a Kelvin-Voigt (spring and dashpot in parallel) material: eps(t) = (sigma_0/E)(1 - exp(-t E/eta)).
sigma0 applied stress [Pa]E spring modulus [Pa]eta dashpot viscosity [Pa*s]t time under load [s]strain creep strain at time tfraction_of_elastic strain over the final strain sigma_0/Etau retardation time eta/E [s]polymer_chain_dimensionsThe root-mean-square end-to-end distance and characteristic ratio of a polymer chain of n bonds of length l with fixed bond angle and free rotation, and its all-trans contour length.
n number of backbone bonds integerl bond length [m]theta bond angle in degrees (default 109.47, tetrahedral) optionalr_rms rms end-to-end distance [m]r_rms_nm rms end-to-end distance in nmC_n characteristic ratio <r^2>/(n l^2)contour_nm all-trans contour length in nmmolecular_weight_averagesMn, Mw and the dispersity Mw/Mn of a polymer from a molecular-weight distribution given as number fractions or weight fractions per size range.
M mean molecular weight of each size range in g/mol vectorfraction number or weight fraction of each range (normalised) vectorbasis whether the fractions are number (x_i) or weight (w_i) fractions (default number) choice optionalMn number-average molecular weight in g/molMw weight-average molecular weight in g/molPDI dispersity (polydispersity index) Mw/Mnpolymer_crystallinityThe mass percent crystallinity of a semicrystalline polymer from its density and the densities of the fully crystalline and fully amorphous polymer.
rho_s density of the sample [kg/m^3]rho_c density of the totally crystalline polymer [kg/m^3]rho_a density of the totally amorphous polymer [kg/m^3]crystallinity_percent percent crystallinity (by mass)degree_of_polymerizationThe molecular weight of a repeat unit from its formula and the number-average degree of polymerization DP = Mn / m.
formula repeat-unit formula, e.g. C2H3Cl textMn number-average molecular weight [kg/mol]repeat_unit_g_mol repeat-unit molecular weight in g/molDP degree of polymerizationrubber_elasticityThe shear modulus G = rho R T / Mc of a crosslinked rubber and its engineering and true stress at a uniaxial stretch ratio lambda.
rho density of the rubber [kg/m^3]Mc molecular weight between crosslinks [kg/mol]T temperature [K]stretch stretch ratio lambda = L/L0G_MPa shear modulus in MPastress_MPa engineering stress in MPatrue_stress_MPa true stress in MPamaxwell_stress_relaxationThe stress remaining after time t in a polymer held at constant strain, modelled as a Maxwell element: sigma(t) = sigma_0 exp(-t E/eta).
sigma0 initial stress [Pa]E spring modulus [Pa]eta dashpot viscosity [Pa*s]t time held [s]sigma_t stress at time t [Pa]sigma_t_MPa stress at time t in MPatau relaxation time eta/E [s]ratio sigma(t)/sigma_0wiedemann_franzThe electronic thermal conductivity kappa = L sigma T of a metal from its electrical conductivity (or resistivity) and temperature, with the Sommerfeld value of the Lorenz number.
T temperature [K]sigma electrical conductivity (or give rho) [1/(ohm*m)] optionalrho electrical resistivity (or give sigma) [ohm*m] optionalkappa thermal conductivity [W/(m*K)]lorenz Lorenz number in W ohm/K^2linear_thermal_expansionThe length change dL = alpha L0 dT and the new length of a bar heated or cooled freely by dT.
alpha linear thermal expansion coefficient [1/K]L0 initial length [m]dT temperature change (positive = heating) [K]dL length change [m]dL_mm length change in mmL new length [m]strain thermal strain alpha dTdebye_heat_capacityThe constant-volume molar heat capacity of a monatomic solid from the Debye model at temperature T.
theta_D Debye temperature [K]T temperature [K]Cv molar heat capacity at constant volume [J/(mol*K)]Cv_over_3R Cv / 3R (1 at high T)einstein_heat_capacityThe constant-volume molar heat capacity of a solid from the Einstein model (all atoms vibrating at one frequency).
theta_E Einstein temperature [K]T temperature [K]Cv molar heat capacity at constant volume [J/(mol*K)]Cv_over_3R Cv / 3Rvolumetric_thermal_expansionThe volume change dV = beta V0 dT of an isotropic solid with beta = 3 alpha (linearised), and the exact change V0((1 + alpha dT)^3 - 1).
alpha LINEAR thermal expansion coefficient [1/K]V0 initial volume [m^3]dT temperature change (positive = heating) [K]beta volumetric coefficient 3 alpha [1/K]dV linearised volume change beta V0 dT [m^3]dV_cm3 linearised volume change in cm^3V new volume (linearised) [m^3]dV_exact exact volume change V0((1 + alpha dT)^3 - 1) [m^3]dV_exact_cm3 exact volume change in cm^315 files, 42.8 MB in total. The largest:
| File | Size |
|---|---|
| model.safetensors | 18.9 MB |
| dist/materials_science_ai999x-1.0.0-py3-none-any.whl | 14.9 MB |
| onnx/search/encoder.int8.onnx | 4.9 MB |
| docs/materials_science_ai999x_capabilities.pdf | 3.1 MB |
| onnx/search/index.json | 403.3 KB |
| docs/materials_science_ai999x_capabilities.html | 241.4 KB |
| docs/materials_science_ai999x_capabilities.md | 177.2 KB |
| onnx/search/tokenizer.json | 176.4 KB |
| README.md | 23.4 KB |
| LICENSE | 11.4 KB |
| evaluation/release_gate.md | 2.3 KB |
| evaluation/KNOWLEDGE_CARD.md | 1.4 KB |
Materials Science answers questions in materials science: crystal structures and diffraction, defects and diffusion, mechanical properties, phase diagrams, polymers, ceramics and composites, and electronic and thermal properties. Each answer gives the value with its unit, the steps and the formula in LaTeX.
With pip: pip install materials-science-ai999x. The same files are on Hugging Face (hf download AI999X/materials-science-ai999x --local-dir materials-science-ai999x) and GitHub.
Yes. It is a Python package that runs on an ordinary CPU without a network connection (Python >=3.10); no GPU and no API key are needed.
87 capabilities in 13 topics, including Crystal structures, Mechanical properties, Diffraction, Polymers, Diffusion.
Field: Physical Sciences. Tasks: Question Answering, Token Classification, Text Classification, Sentence Similarity, Feature Extraction.
Asked "Theoretical density: structure = FCC, A = 63.55 g/mol, R = 0.128 nm", it answers: rho = 8895.28 kg/m^3, rho_gcc = 8.89528, a_nm = 0.362039.
It says so and names what is missing or out of range, instead of guessing a number.