Tungsten material model
1. Introduction
This page contains the OghmaNano material model for Tungsten (W).
Bulk tungsten metal
The model is written in Lua and provides simulation-ready material parameterisations for use within OghmaNano. For documentation, licensing, references, and information about the scope and accuracy of these models, see the material scripting documentation.
2. Lua material model
-- See end of file for copyright, licensing and documentation links.
local material = {}
function material.name()
local enabled = true
return "Tungsten", enabled
end
function material.description()
local enabled = true
return "Bulk tungsten metal", enabled
end
function material.formula()
local enabled = true
return "W", enabled
end
function material.Xi(state)
-- Vacuum-referenced electronic energy
-- Units: eV
--
-- For semiconductors:
-- Xi = E_vac - E_C
-- and therefore represents the electron affinity.
--
-- For metals:
-- Xi = E_vac - E_F
-- and therefore represents the metal work function.
--
-- A representative polycrystalline work function for tungsten is
-- approximately 4.55 eV (single-crystal faces range ~4.3-5.2 eV).
-- The value depends on crystal orientation, surface oxidation and
-- contamination.
--
-- Reference: Michaelson, H. B., J. Appl. Phys. 48, 4729 (1977) (polycrystalline).
local enabled = true
local value = 4.55
return value, enabled
end
function material.electrical_conductivity(state)
-- Electrical conductivity
-- Units: S m^-1
--
-- Representative conductivity near 300 K:
-- sigma(300 K) = 1.8e7 S/m
-- (equivalently rho(300 K) ~ 5.6 micro-ohm cm)
--
-- The temperature dependence is calculated from the approximately
-- linear temperature dependence of the electrical resistivity:
--
-- rho(T) = rho(300 K) *
-- [1 + alpha_rho*(T - 300 K)]
--
-- where alpha_rho is approximately 4.5e-3 K^-1.
--
-- Since sigma = 1/rho:
--
-- sigma(T) = sigma(300 K) /
-- [1 + alpha_rho*(T - 300 K)]
--
-- This approximation is intended for temperatures reasonably
-- close to room temperature.
--
-- Note: this is the value for well-annealed bulk tungsten. Thin
-- films and cold-worked material show substantially higher
-- resistivity.
--
-- Reference: Matula, R. A., J. Phys. Chem. Ref. Data 8, 1147 (1979); CRC Handbook of Chemistry and Physics.
local enabled = true
local T = state.T
local sigma_300 = 1.8e7
local alpha_rho = 4.5e-3
local denominator = 1.0 + alpha_rho*(T - 300.0)
-- Prevent an unphysical negative or zero resistivity if the
-- linear approximation is evaluated far outside its valid range.
if denominator <= 0.0 then
return 0.0, false
end
local value = sigma_300/denominator
return value, enabled
end
function material.epsilonr(state)
-- Relative permittivity
-- Dimensionless
--
-- A static scalar relative permittivity does not provide a useful
-- physical description of the electromagnetic response of a metal.
--
-- Electrostatic calculations should normally treat the metal as an
-- equipotential conductor. Optical calculations should use complex,
-- wavelength-dependent optical constants instead.
--
-- This parameter is therefore disabled.
local enabled = false
local value = 1.0
return value, enabled
end
function material.thermal_conductivity(state)
-- Thermal conductivity
-- Units: W m^-1 K^-1
--
-- Representative value for bulk tungsten near 300 K:
-- kappa = 173 W m^-1 K^-1
--
-- The value depends on purity, microstructure and temperature.
--
-- Reference: Ho, Powell & Liley, J. Phys. Chem. Ref. Data 1, 279 (1972); CRC Handbook of Chemistry and Physics.
local enabled = true
local value = 173
return value, enabled
end
function material.heat_capacity(state)
-- Specific heat capacity
-- Units: J kg^-1 K^-1
--
-- Representative constant-pressure value near 300 K:
-- cp = 132 J kg^-1 K^-1
--
-- Reference: CRC Handbook of Chemistry and Physics, 100th ed. (2019).
local enabled = true
local value = 132
return value, enabled
end
function material.density(state)
-- Mass density
-- Units: kg m^-3
--
-- Representative room-temperature density:
-- rho = 19250 kg m^-3
--
-- Reference: CRC Handbook of Chemistry and Physics, 100th ed. (2019).
local enabled = true
local value = 19250
return value, enabled
end
function material.print()
local state = {
T = 300.0,
x = 0.0,
y = 0.0,
z = 0.0,
photon_density = 0.0,
}
print(string.format("Material: %s", material.name()))
print(string.format("Description: %s", material.description()))
print(string.format("Formula: %s", material.formula()))
print(string.format("Temperature: %.2f K", state.T))
print(string.format("Position: %.6e, %.6e, %.6e m", state.x, state.y, state.z))
print(string.format("Photon density: %.6e m^-3", state.photon_density))
print(string.format("Work function (Xi): %.6f eV", material.Xi(state)))
print(string.format("Electrical conductivity: %.6e S/m", material.electrical_conductivity(state)))
print(string.format("Relative permittivity: %.6f", material.epsilonr(state)))
print(string.format("Thermal conductivity: %.6e W/m/K", material.thermal_conductivity(state)))
print(string.format("Heat capacity: %.6e J/kg/K", material.heat_capacity(state)))
print(string.format("Mass density: %.6e kg/m^3", material.density(state)))
end
return material
-- ============================================================================
-- Copyright (C) 2026 The OghmaNano Project
-- All rights reserved.
--
-- This file is part of the OghmaNano Materials Model Library.
--
-- Website:
-- https://www.oghma-nano.com
--
-- Documentation and accuracy statement:
-- https://www.oghma-nano.com/manual/material-scripts.html
--
-- These material models are provided to support scientific research and
-- semiconductor device simulation. If you find them useful, please cite
-- OghmaNano where appropriate. Please do not redistribute these files or
-- incorporate them into other software or databases without permission.
-- ============================================================================