matminer.models package¶
Submodules¶
matminer.models.mechanical_properties module¶
matminer.models.sound_velocity module¶
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class
matminer.models.sound_velocity.
SoundVelocityModel
¶ This is an example model
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__init__
()¶
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citation
()¶
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compute
(*args, **kwargs)¶
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matminer.models.sound_velocity.
effective_cubic_elasticconstant
(direction, mode, C_11=None, C_12=None, C_44=None)¶ Calculate effective elastic constant (C_eff) for a cubic material.
- References:
- http://unlcms.unl.edu/cas/physics/tsymbal/teaching/SSP-927/Section%2004_Elastic_Properties.pdf
- Args:
- direction: (str) direction of sound velocity. Choose from Choose from “100”, “110”, and “111”. mode: (str) wave mode. Choose from “longitudinal”, “transverse1”, and “transverse2”. C_11: elastic constant C_xxxx (N/m^2) C_12: elastic constant C_xxyy (N/m^2) C_44: elastic constant C_yzyz (N/m^2)
Returns: (float) effective elastic constant (C_eff) for a cubic material (N/m^2).
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matminer.models.sound_velocity.
sound_velocity
(C_eff, rho)¶ Calculate sound velocity (v) in a material from elastic constant.
- Args:
- C_eff: (float) effective elastic constant (N/m^2) rho: (float) material density (kg/m^3)
Returns: (float) velocity of sound (m/s) in the material
matminer.models.thermal_conductivity module¶
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class
matminer.models.thermal_conductivity.
CahillSimpleModel
(*values, **kw)¶ Calculate Cahill thermal conductivity.
- References:
- DOI: 10.1016/j.jallcom.2014.09.022 (Title: “Electronic structure, elastic anisotropy,
thermal conductivity and optical properties of calcium apatite Ca5(PO4)3X (X = F, Cl or Br)”) - DOI: 10.1016/j.commatsci.2015.07.029 (Title: “Electronic structure, mechanical properties and anisotropy of thermal conductivity of Y-Si-O-N quaternary crystals”) - DOI: 10.1002/adma.201400515 (Title: “High Thermoelectric Performance in Non-Toxic Earth-Abundant Copper Sulfide”)
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__init__
(*values, **kw)¶ - Args:
- n: (int) number of atoms in unit cell V: (float) unit cell volume (in SI units, i.e. m^(3)) v_l: (float) longitudinal sound velocity (in SI units, i.e. m/s) v_t1: (float) transverse sound velocity in direction 1 (in SI units, i.e. m/s) v_t2: (float) transverse sound velocity in direction 2 (in SI units, i.e. m/s)
Returns: None
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calculate
(*values, **kw)¶ Returns: (float) Cahill thermal conductivity (in SI units, i.e. joule/(m*s*kelvin))
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matminer.models.thermal_conductivity.
cahill_integrand
(x)¶ Integrand function to calculate Cahill thermal conductivity.
- Args:
- x: (hbar * omega)/(k * T) # hbar: reduced Planck’s constant, omega = phonon frequency
Returns: (float) integral value
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matminer.models.thermal_conductivity.
cahill_integrand_model
(n, V, cahill_integrand_sum)¶ Calculate Cahill thermal conductivity using the intergrand model.
- References:
- DOI: 10.1002/adfm.201600718 (Title: “Minimum Thermal Conductivity in Weak Topological Insulators with
Bismuth-Based Stack Structure”) - DOI: 10.1038/nature13184 (Title: “Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals”) (full formula)
- Args:
- n: (int) number of atoms in primitive cell V: (float) unit cell volume (in SI units, i.e. m^(3)) cahill_integrand_sum: (float) sum of the term calculate using the above function “cahill_integrand_summation”
Returns: (float) Cahill thermal conductivity (in SI units, i.e. W(mK)^(-1))
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matminer.models.thermal_conductivity.
cahill_integrand_summation
(v_i, T, theta)¶ Calculate the summation term for the Cahill thermal conductivity integrand model. Use this function repeatedly to calculate the total sum over all acoustic modes.
- References:
- DOI: 10.1002/adfm.201600718 (Title: “Minimum Thermal Conductivity in Weak Topological Insulators with
Bismuth-Based Stack Structure”) - DOI: 10.1038/nature13184 (Title: “Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals”) (full formula)
- Args:
- v_i: (float) sound velocity for the acoustic mode i (in SI units, i.e. m(s)^(-1)) T: (float) absolute temperature (in K) theta: (float) Debye temperature (in K)
Returns: (float) summation term for only one acoustic mode i
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matminer.models.thermal_conductivity.
callaway_integrand
(x, t_ph)¶ Integrand function to calculate Callaway thermal conductivity.
- Args:
- x: (hbar * omega)/(k * T) # hbar: reduced Planck’s constant, omega = phonon frequency t_ph: (float) phonon relaxation time (in SI units, s^(-1))
Returns: (float) integral value
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matminer.models.thermal_conductivity.
callaway_model
(v_m, T, theta, t_ph)¶ Calculate Callaway thermal conductivity (In some circumstances, a second term may be required as seen in http://link.springer.com/chapter/10.1007%2F0-387-25100-6_2#page-1)
- References:
- DOI: 10.1002/adfm.201600718 (Title: “Minimum Thermal Conductivity in Weak Topological Insulators with
Bismuth-Based Stack Structure”) - DOI: 10.1063/1.4906225 (Title: “Critical analysis of lattice thermal conductivity of half-Heusler alloys using variations of Callaway model”) - DOI: 10.1103/PhysRev.134.A1058 (Title: “Thermal Conductivity of Silicon and Germanium from 3 K to the Melting
Point”)- Args:
- v_m: (float) speed of sound in the material (in SI units, i.e. m(s)^(-1)) T: (float) absolute temperature (in K) theta: (float) Debye temperature (in K) t_ph: (float) phonon relaxation time (in SI units, s^(-1))
Returns: (float) Callaway thermal conductivity (in SI units, i.e. W(mK)^(-1))
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matminer.models.thermal_conductivity.
clarke_model
(n, E, m, V)¶ Calculate Clarke thermal conductivity.
- References:
- DOI: 10.1016/j.jallcom.2014.09.022 (Title: “Electronic structure, elastic anisotropy,
thermal conductivity and optical properties of calcium apatite Ca5(PO4)3X (X = F, Cl or Br)”) - DOI: 10.1016/j.commatsci.2015.07.029 (Title: “Electronic structure, mechanical properties and anisotropy of thermal conductivity of Y-Si-O-N quaternary crystals”)
- Args:
- n: (int) number of atoms in primitive cell E: (float) Young’s modules (in SI units, i.e. Kgm(s)^(-2)) m: (float) total mass per unit cell (in SI units, i.e. Kg) V: (float) unit cell volume (in SI units, i.e. m^(3))
Returns: (float) Clarke thermal conductivity (in SI units, i.e. W(mK)^(-1))
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matminer.models.thermal_conductivity.
debye_model
(M, E, m, V)¶ Calculate Debye thermal conductivity.
- Args:
- M: (float) molecular mass E: (float) Young’s modules (in SI units, i.e. Kgm(s)^(-2)) m: (float) total mass (in SI units, i.e. Kg) V: (float) unit cell volume (in SI units, i.e. m^(3))
Returns: (float) Debye thermal conductivity (in SI units, i.e. W(mK)^(-1))
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matminer.models.thermal_conductivity.
keyes_model
(gamma, e_m, T_m, m, V, T, A)¶ Calculate Keyes thermal conductivity
- References:
- DOI: 10.1103/PhysRev.115.564 (Title: “High-Temperature Thermal Conductivity of Insulating Crystals:
Relationship to the Melting Point”)
- Args:
- gamma: (float) Gruneisen parameter e_m: (float) amplitude of atomic vibrations as fraction of lattice constant at which melting takes place T_m: (float) melting temperature (K) m: (float) total mass (in SI units, i.e. Kg) V: (float) unit cell volume (in SI units, i.e. m^(3)) T: (float) absolute temperature (in K) A: (float) average atomic weight
Returns: (float) Keyes thermal conductivity (in SI units, i.e. W(mK)^(-1))
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matminer.models.thermal_conductivity.
slack_integrand
(x, t_c)¶ Integrand function to calculate Callaway thermal conductivity.
- Args:
- x: (hbar * omega)/(k * T) # hbar: reduced Planck’s constant, omega = phonon frequency t_c: (float) phonon relaxation time (in SI units, s^(-1))
Returns: (float) integral value
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matminer.models.thermal_conductivity.
slack_integrand_model
(v_m, T, theta, t_c)¶ Calculate Slack thermal conductivity using the integral model. (In high temperature regions, those higher than that of the Debye temperature of the material, the Callaway model is insufficient at predicting the lattice thermal conductivity. This shortfall must be addressed as many thermoelectric materials are designed to be used in conditions beyond the Debye temperature of the alloys and accurate predictions are required. At high temperatures, a modification suggested by Glassbrenner and Slack is made to model thermal conductivity as shown here.)
- References:
- DOI: 10.1103/PhysRev.134.A1058 (Title: “Thermal Conductivity of Silicon and Germanium from 3 K to the Melting
Point”)- DOI: 10.1063/1.4906225 (Title: “Critical analysis of lattice thermal conductivity of half-Heusler alloys
using variations of Callaway model”)
- Args:
v_m: (float) speed of sound in the material (in SI units, i.e. m(s)^(-1)) T: (float) absolute temperature (in K) theta: (float) Debye temperature (in K) t_c: (float) combined phonon relaxation time that includes higher-order processes (in SI units, s^(-1))
(see Ref:- DOI: 10.1103/PhysRev.134.A1058)
Returns: (float) Slack thermal conductivity (in SI units, i.e. W(mK)^(-1))
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matminer.models.thermal_conductivity.
slack_simple_model
(M, theta, v_a, gamma, n, T)¶ Calculate the simple Slack thermal conductivity
- References
- DOI: 10.1007/0-387-25100-6_2 (Title: “High Lattice Thermal Conductivity Solids”)
- DOI: 10.1002/adfm.201600718 (Title: “Minimum Thermal Conductivity in Weak Topological Insulators with
Bismuth-Based Stack Structure”)
- Args:
- M: (float) average atomic mass theta: (float) Debye temperature (K) v_a: (float) (v_a)**3 is the volume per atom (Angstroms) gamma: (float) Gruneisen parameter n: (int) number of atoms in primitive cell T: (float) absolute temperature (K)
Returns: (float) Slack thermal conductivity (in SI units, i.e. W(mK)^(-1))