crown_glass material model

1. Introduction

This page contains the OghmaNano material model for crown_glass (SiO2-B2O3-Na2O-K2O (borosilicate crown)).

Crown glass (low-dispersion borosilicate crown, N-BK7 archetype), passive optical medium

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

Supporting definitions

-- See end of file for copyright, licensing and documentation links.

local material = {}

-- ---------------------------------------------------------------------
-- Crown glass is a PASSIVE OPTICAL DIELECTRIC, not a semiconductor.
-- The electronic/transport entries used for the semiconductor and
-- absorber material files (band gap, electron affinity, Nc/Nv, carrier
-- mobilities, radiative/Auger/SRH recombination) have NO physical
-- meaning for an insulating optical glass with no free carriers, and
-- have therefore been removed. The amorphous glass also has no
-- crystalline lattice constant, so that entry is removed too.
--
-- What remains are the properties that actually define an optical
-- glass: refractive index, dispersion (Abbe number), the optical
-- permittivity (n^2), and bulk thermal/mechanical properties.
-- ---------------------------------------------------------------------

function material.name()
	local enabled = true

	return "crown_glass", enabled
end

function material.description()
	local enabled = true

	return "Crown glass (low-dispersion borosilicate crown, N-BK7 archetype), passive optical medium", enabled
end

function material.formula()
	local enabled = true

	-- Glasses are amorphous mixtures with no stoichiometric formula;
	-- crown glasses are broadly SiO2-B2O3 borosilicates with alkali
	-- (Na2O/K2O) modifiers.
	return "SiO2-B2O3-Na2O-K2O (borosilicate crown)", enabled
end

function material.epsilonr(state)
	-- Relative permittivity (OPTICAL)
	-- Dimensionless
	--
	-- Reference:
	-- Optical value epsilon = n_d^2 = 1.5168^2 ~ 2.301, i.e. the
	-- high-frequency permittivity relevant to electromagnetic (FDTD /
	-- ray-tracing) propagation through the glass.
	--
	-- Note: the low-frequency / DC permittivity of a borosilicate
	-- crown glass is considerably higher (~7) because of ionic and
	-- dipolar contributions. For a passive optical medium the OPTICAL
	-- value is the operative one and is returned here.

	local enabled = true
	local value = 2.301

	return value, enabled
end

function material.thermal_kl(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- Reference:
	-- SCHOTT N-BK7 datasheet, kappa ~ 1.11 W/m/K at ~300 K.

	local enabled = true
	local value = 1.11

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- SCHOTT N-BK7 datasheet, c_p ~ 858 J/kg/K at ~300 K. Approximate.

	local enabled = true
	local value = 858.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- SCHOTT N-BK7 datasheet, rho = 2.51 g/cm^3.

	local enabled = true
	local value = 2510.0

	return value, enabled
end

function material.thermal_tau_e(state)
	-- Electron energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Numerical fallback
	-- Confidence: Low
	--
	-- Reference:
	-- No specific reference supplied.
	--
	-- Comments:
	-- Passive insulator/optical layer. No mobile-carrier hydrodynamic equation
	-- should normally be solved; fast fallback only.

	local enabled = false
	local value = 1.000000e-14

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Numerical fallback
	-- Confidence: Low
	--
	-- Reference:
	-- No specific reference supplied.
	--
	-- Comments:
	-- Passive insulator/optical layer. No mobile-carrier hydrodynamic equation
	-- should normally be solved; fast fallback only.

	local enabled = false
	local value = 1.000000e-14

	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("Optical permittivity:   %.6f", material.epsilonr(state)))

	print(string.format("Electron energy relax.:  %.6e s", material.thermal_tau_e(state)))
	print(string.format("Hole energy relax.:      %.6e s", material.thermal_tau_h(state)))

	print(string.format("Thermal conductivity:   %.6e W/m/K", material.thermal_kl(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

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-- This file is part of the OghmaNano Materials Model Library.
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