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Properties of Ray Tracing Materials

This topic lists properties of the materials supported by these ray tracing objects and functions: siteviewer, RayTracing, raytrace, sigstrength, coverage, sinr, link, and pathloss.

For all supported materials:

  • The relative permeability is 1.

  • Surface roughness is calculated using a Gaussian model.

  • The reference density for specific gravity is 999.97 kg/m3.

Note that the constitutive electromagnetic properties are permittivity, permeability, and conductivity. Depending on the material, the software uses parameters and methods from different electromagnetic models, which can make assumptions about the constitutive properties or use alternate properties. For example:

  • Some models specify the refractive index, which is related to permittivity and permeability.

  • In the frequency domain, permittivity and permeability are typically complex-valued, while conductivity is assumed to be real-valued.

  • Models often specify permittivity and permeability using values that are relative to the absolute values of vacuum.

  • Models can use property values that vary depending on the material, the frequency, or the wavelength. In addition, models can use varying strategies to determine the real and imaginary parts of complex values.

  • Models can specify permittivity or the refractive index using an effective value that includes the effect of conductivity.

Functions that accept ray tracing models as input use the fundamental electromagnetic constant values that are recommended by the 2022 Committee on Data of the International Science Council (CODATA) adjustment of fundamental constants [29].

Note that the thermal property linear expansion can also be known as coefficient of linear thermal expansion.

Common Building Materials

This table lists the electromagnetic, mechanical, and thermal properties for supported common building materials.

MaterialElectromagnetic PropertiesMechanical PropertiesThermal Properties

"acrylic" — Acrylic

  • Conductivity: 5 × 10–14 S/m

  • Relative permittivity: Calculated using Havriliak-Negami model [54]

  • Damping ratio: 0.01

  • Poisson's ratio: 0.4

  • Specific gravity: 1.18

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 0.0002 m

  • Young's modulus: 3 × 109 Pa

  • Conductivity: 0.21 W/(m·K)

  • Linear expansion: 8.1 × 10–6 1/K

  • Specific heat capacity: 4200 J/(kg·K)

"brick" — Brick

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 0.0003 S/m

  • Damping ratio: 0.01

  • Density: 2000 kg/m3

  • Poisson's ratio: 0.2

  • Surface roughness:

    • Correlation length: 0.0008 m

    • Height standard deviation: 0.016 m

  • Young's modulus: 1 × 1010 Pa

  • Conductivity: 1 W/(m·K)

  • Linear expansion: 6 × 10–6 1/K

  • Specific heat capacity: 900 J/(kg·K)

"ceiling-board" — Ceiling board

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 1 × 10–6 S/m

  • Damping ratio: 0.01

  • Density: 800 kg/m3

  • Poisson's ratio: 0.26

  • Surface roughness:

    • Correlation length: 0.00025 m

    • Height standard deviation: 0.0005 m

  • Young's modulus: 2 × 109 Pa

  • Conductivity: 0.27 W/(m·K)

  • Linear expansion: 1.44 × 10–5 1/K

  • Specific heat capacity: 1000 J/(kg·K)

"chipboard" — Chipboard

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 1 × 10–6 S/m

  • Damping ratio: 0.01

  • Poisson's ratio: 0.2

  • Specific gravity: 0.7

  • Surface roughness:

    • Correlation length: 0.0001

    • Height standard deviation: 0.0005 m

  • Young's modulus: 3 × 109 Pa

  • Conductivity: 0.1 W/(m·K)

  • Linear expansion: 1.62 × 10–5 1/K

  • Specific heat capacity: 1400 J/(kg·K)

"concrete" — Concrete

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 0.001 S/m

  • Damping ratio: 0.01

  • Density: 2400 kg/m3

  • Poisson's ratio: 0.2

  • Surface roughness:

    • Correlation length: 0.01 m

    • Height standard deviation: 0.0001 m

  • Young's modulus: 3 × 1010 Pa

  • Conductivity: 1 W/(m·K)

  • Linear expansion: 1 × 10–5 1/K

  • Specific heat capacity: 900 J/(kg·K)

"floorboard" — Floorboard

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 1 × 10–10 S/m

  • Damping ratio: 0.01

  • Density: 600 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 0.00015 m

    • Height standard deviation: 0.0001 m

  • Young's modulus: 1 × 1010 Pa

  • Conductivity: 0.2 W/(m·K)

  • Linear expansion: 2 × 10–5 1/K

  • Specific heat capacity: 2000 J/(kg·K)

"foam" — Foam

  • Dielectric constant: 1.03

  • Dielectric loss tangent: 0.0001

  • Static conductivity: 1 × 10–16 S/m

  • Damping ratio: 0.05

  • Density: 20 kg/m3

  • Poisson's ratio: 0.1

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 0.0002 m

  • Young's modulus: 2 × 106 Pa

  • Conductivity: 0.04 W/(m·K)

  • Linear expansion: 7 × 10–5 1/K

  • Specific heat capacity: 1200 J/(kg·K)

"FR4" — FR-4 (fiberglass)

  • Conductivity: 8 × 10–11 S/m

  • Relative permittivity: Calculated using Djordjevic-Sarkar model [8]

  • Damping ratio: 0.01

  • Density: 1600 kg/m3

  • Poisson's ratio: 0.16

  • Surface roughness:

    • Correlation length: 6 × 10–5 m

    • Height standard deviation: 6 × 10–6 m

  • Young's modulus: 2.5 × 1010 Pa

  • Conductivity: 0.2 W/(m·K)

  • Linear expansion: 2 × 10–5 1/K

  • Specific heat capacity: 600 J/(kg·K)

"glass" — Glass

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 1 × 10–3 S/m

  • Damping ratio: 0.0001

  • Density: 2200 kg/m3

  • Poisson's ratio: 0.2

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 0.0002 m

  • Young's modulus: 7 × 1010 Pa

  • Conductivity: 1 W/(m·K)

  • Linear expansion: 1 × 10–6 1/K

  • Specific heat capacity: 800 J/(kg·K)

"marble" — Marble

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 1 × 10–6 S/m

  • Damping ratio: 0.01

  • Density: 2700 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 0.0013 m

    • Height standard deviation: 0.0005 m

  • Young's modulus: 3 × 1010 Pa

  • Conductivity: 2 W/(m·K)

  • Linear expansion: 6 × 10–6 1/K

  • Specific heat capacity: 800 J/(kg·K)

"metal" — Metal

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 1 × 107 S/m

  • Damping ratio: 0.001

  • Density: 10000 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 1.5 × 1011 Pa

  • Conductivity: 100 W/(m·K)

  • Linear expansion: 2 × 10–5 1/K

  • Specific heat capacity: 400 J/(kg·K)

"plasterboard" — Plasterboard

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 4.621 × 10–5 S/m

  • Damping ratio: 0.01

  • Density: 800 kg/m3

  • Poisson's ratio: 0.26

  • Surface roughness:

    • Correlation length: 0.00015 m

    • Height standard deviation: 1 × 10–5 m

  • Young's modulus: 2 × 109 Pa

  • Conductivity: 0.27 W/(m·K)

  • Linear expansion: 1.44 × 10–5 1/K

  • Specific heat capacity: 1000 J/(kg·K)

"plywood" — Plywood

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 0.33 S/m

  • Damping ratio: 0.01

  • Poisson's ratio: 0.3

  • Specific gravity: 0.5

  • Surface roughness:

    • Correlation length: 0.00015

    • Height standard deviation: 0.0001 m

  • Young's modulus: 8 × 109 Pa

  • Conductivity: 0.1 W/(m·K)

  • Linear expansion: 4 × 10–6 1/K

  • Specific heat capacity: 1400 J/(kg·K)

"polystyrene" — Polystyrene

  • Conductivity: 1.42 × 10–5 S/m

  • Relative permittivity: Calculated using Havriliak-Negami model [54]

  • Damping ratio: 0.01

  • Poisson's ratio: 0.33

  • Specific gravity: 1.04

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 3 × 109 Pa

  • Conductivity: 0.1 W/(m·K)

  • Linear expansion: 7.2 × 10–7 1/K

  • Specific heat capacity: 1300 J/(kg·K)

"Teflon" — Teflon® (PTFE)

  • Conductivity: 8.457 × 10–5 S/m

  • Relative permittivity: Calculated using Havriliak-Negami model [54]

  • Damping ratio: 0.01

  • Poisson's ratio: 0.46

  • Specific gravity: 2.2

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 0.0002 m

  • Young's modulus: 5 × 108 Pa

  • Conductivity: 0.24 W/(m·K)

  • Linear expansion: 0.00099 1/K

  • Specific heat capacity: 1050 J/(kg·K)

"wood" — Wood

  • Effective relative permittivity: Calculated using power-fit model [17]

  • Static conductivity: 0.001 S/m

  • Damping ratio: 0.01

  • Density: 500 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 0.001 m

    • Height standard deviation: 0.03 m

  • Young's modulus: 1 × 1010 Pa

  • Conductivity: 0.2 W/(m·K)

  • Linear expansion: 2 × 10–5 1/K

  • Specific heat capacity: 2900 J/(kg·K)

Metals

This table lists the electromagnetic, mechanical, and thermal properties for supported metal materials.

MaterialElectromagnetic PropertiesMechanical PropertiesThermal Properties

"aluminum" — Aluminum

  • Conductivity: 3.77 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 2700 kg/m3

  • Poisson's ratio: 0.345

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 6.7 × 1010 Pa

  • Conductivity: 237 W/(m·K)

  • Linear expansion: 2.36 × 10–5 1/K

  • Specific heat capacity: 900 J/(kg·K)

"brass" — Brass

  • Conductivity: 1.7 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 8500 kg/m3

  • Poisson's ratio: 0.34

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 9.7 × 1010 Pa

  • Conductivity: 120 W/(m·K)

  • Linear expansion: 2 × 10–5 1/K

  • Specific heat capacity: 380 J/(kg·K)

"copper" — Copper

  • Conductivity: 5.98 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 8960 kg/m3

  • Poisson's ratio: 0.308

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 1.28 × 1011 Pa

  • Conductivity: 398 W/(m·K)

  • Linear expansion: 1.65 × 10–5 1/K

  • Specific heat capacity: 380 J/(kg·K)

"gold" — Gold

  • Conductivity: 4.35 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 19320 kg/m3

  • Poisson's ratio: 0.4498

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 7.8 × 1010 Pa

  • Conductivity: 315 W/(m·K)

  • Linear expansion: 1.42 × 10–5 1/K

  • Specific heat capacity: 129 J/(kg·K)

"Invar" — Invar

  • Conductivity: 1.2 × 106 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 8000 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 1.5 × 1011 Pa

  • Conductivity: 11 W/(m·K)

  • Linear expansion: 1 × 10–6 1/K

  • Specific heat capacity: 515 J/(kg·K)

"iron" — Iron

  • Conductivity: 1.03 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 7870 kg/m3

  • Poisson's ratio: 0.291

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 2.082 × 1011 Pa

  • Conductivity: 80.3 W/(m·K)

  • Linear expansion: 1.17 × 10–5 1/K

  • Specific heat capacity: 444 J/(kg·K)

"lead" — Lead

  • Conductivity: 4.8443 × 106 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 11340 kg/m3

  • Poisson's ratio: 0.44

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 2.61 × 1010 Pa

  • Conductivity: 35.2 W/(m·K)

  • Linear expansion: 2.93 × 10–5 1/K

  • Specific heat capacity: 160 J/(kg·K)

"silver" — Silver

  • Conductivity: 6.15 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 10490 kg/m3

  • Poisson's ratio: 0.37

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 7.1 × 1010 Pa

  • Conductivity: 427 W/(m·K)

  • Linear expansion: 1.968 × 10–5 1/K

  • Specific heat capacity: 237 J/(kg·K)

"steel" — Steel

  • Conductivity: 5.8 × 106 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 8000 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 2 × 1011 Pa

  • Conductivity: 40 W/(m·K)

  • Linear expansion: 1 × 10–5 1/K

  • Specific heat capacity: 500 J/(kg·K)

"tungsten" — Tungsten

  • Conductivity: 1.7 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Poisson's ratio: 0.283

  • Specific gravity: 19.251

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 3.45 × 1011 Pa

  • Conductivity: 178 W/(m·K)

  • Linear expansion: 4.6 × 10–6 1/K

  • Specific heat capacity: 133 J/(kg·K)

"zinc" — Zinc

  • Conductivity: 1.69 × 107 S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 7130 kg/m3

  • Poisson's ratio: 0.25

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 1.045 × 1011 Pa

  • Conductivity: 121 W/(m·K)

  • Linear expansion: 3.97 × 10–5 1/K

  • Specific heat capacity: 388 J/(kg·K)

Terrestrial Materials

This table lists the chemical, electromagnetic, mechanical, and thermal properties for supported terrestrial materials.

MaterialChemical PropertiesElectromagnetic PropertiesMechanical PropertiesThermal Properties

"air" — Air

Not applicable
  • Extinction coefficient: 0

  • Real refractive index: 1.0003

  • Static conductivity: 0 S/m

  • Damping ratio: 0

  • Density: 1.229 kg/m3

  • Surface roughness:

    • Correlation length: Inf m

    • Height standard deviation: 0 m

  • Conductivity: 0.025 W/(m·K)

  • Linear expansion: 0.0034 1/K

  • Specific heat capacity: 715 J/(kg·K)

"ice" — Ice

Not applicable
  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.001

  • Density: 916 kg/m3

  • Poisson's ratio: 0.35

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 4 × 109 Pa

  • Conductivity: 2.2 W/(m·K)

  • Linear expansion: 5 × 10–5 1/K

  • Specific heat capacity: 2100 J/(kg·K)

"loam" — Loam

  • Bulk density: 1578.1 kg/m3

  • Percent clay: 8.53 % m3/m3

  • Percent sand: 41.96% m3/m3

  • Volumetric water content: 0.5% kg/kg

  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.1

  • Poisson's ratio: 0.3

  • Specific gravity: 2.7

  • Surface roughness:

    • Correlation length: 0.15 m

    • Height standard deviation: 0.02 m

  • Young's modulus: 1 × 107 Pa

  • Conductivity: 1 W/(m·K)

  • Linear expansion: 1 × 10–5 1/K

  • Specific heat capacity: 1500 J/(kg·K)

"seawater" — Seawater

  • Salinity: 35 g/kg

  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.1

  • Density: 1030 kg/m3

  • Poisson's ratio: 0.5

  • Surface roughness:

    • Correlation length: 0.5 m

    • Height standard deviation: 0.05 m

  • Conductivity: 0.6 W/(m·K)

  • Linear expansion: 0.0003 1/K

  • Specific heat capacity: 4000 J/(kg·K)

"snow" — Snow

  • Dry snow density: 300 kg/m3

  • Liquid water content: 0 m3/m3

  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.1

  • Density: 300 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 0.001 m

    • Height standard deviation: 0.001 m

  • Young's modulus: 1 × 107 Pa

  • Conductivity: 0.2 W/(m·K)

  • Linear expansion: 5 × 10–5 1/K

  • Specific heat capacity: 2000 J/(kg·K)

"tree" — Tree

  • Gravimetric water content: 0.5 kg/kg

  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.1

  • Density: 800 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 0.01 m

    • Height standard deviation: 0.001 m

  • Young's modulus: 1 × 1010 Pa

  • Conductivity: 0.31 W/(m·K)

  • Linear expansion: 0 1/K

  • Specific heat capacity: 2600 J/(kg·K)

"vegetation" — Vegetation

  • Gravimetric water content: 0.5 kg/kg

  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.1

  • Density: 800 kg/m3

  • Poisson's ratio: 0.3

  • Surface roughness:

    • Correlation length: 0.001 m

    • Height standard deviation: 0.5 m

  • Young's modulus: 1 × 1010 Pa

  • Conductivity: 0.31 W/(m·K)

  • Linear expansion: 0 1/K

  • Specific heat capacity: 2600 J/(kg·K)

"water" — Water

  • Salinity: 0 g/kg

  • Effective relative permittivity: Calculated using methods in [18]

  • Conductivity: Calculated using methods in [18]

  • Damping ratio: 0.1

  • Density: 998 kg/m3

  • Poisson's ratio: 0.5

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Conductivity: 0.598 W/(m·K)

  • Linear expansion: 0.0002 1/K

  • Specific heat capacity: 4170 J/(kg·K)

Theoretical Materials

This table lists the electromagnetic, mechanical, and thermal properties for supported theoretical materials.

MaterialElectromagnetic PropertiesMechanical PropertiesThermal Properties

"PEC" — Perfect electrical conductor

  • Conductivity: Inf S/m

  • Dielectric constant: 1

  • Damping ratio: 0.001

  • Density: 10000 kg/m3

  • Surface roughness:

    • Correlation length: 1 × 10–5 m

    • Height standard deviation: 1 × 10–6 m

  • Young's modulus: 1.5 × 1011 Pa

  • Conductivity: 100 W/(m·K)

  • Linear expansion: 2 × 10–5 1/K

  • Specific heat capacity: 400 J/(kg·K)

"vacuum" — Vacuum (free space)

  • Conductivity: 0 S/m

  • Relative permittivity: 1

  • Damping ratio: 0

  • Density: 0 kg/m3

  • Surface roughness:

    • Correlation length: Inf m

    • Height standard deviation: 0 m

  • Conductivity: 0 W/(m·K)

References

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[2] Butkovich, T. R. "Linear Thermal Expansion of Ice." Research Report 40. Wilmette, Illinois: US Army Snow Ice and Permafrost Research Establishment, 1957.

[3] Callister, William D., and David G. Rethwisch. Materials Science and Engineering: An Introduction. 10th edition. Hoboken, NJ: John Wiley & Sons, 2018.

[4] Cramer, S.M., O.M. Friday, R.H. White, and G. Sriprutkiat. "Mechanical Properties of Gypsum Board at Elevated Temperatures." In Fire and Materials 2003, 33–42. San Francisco, CA. London: Interscience Communications Limited, 2003.

[5] Cui, Yiran, Murali Krishna Immadisetty, and Georgios C. Trichopoulos. "Evaluating the Properties of Millimeter- and THz Wave Scattering from Common Rough Surfaces." In 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, 1117–1118. Virtually, Toronto, Canada: IEEE, 2020. https://doi.org/10.1109/IEEECONF35879.2020.9329367.

[6] Czajkowski, Łukasz, Wiesław Olek, Jerzy Weres, and Ryszard Guzenda. "Thermal Properties of Wood-Based Panels: Specific Heat Determination." Wood Science and Technology 50, no. 3 (May 2016): 537–545. https://doi.org/10.1007/s00226-016-0803-7.

[7] Davies, Nicholas T., Clemens M. Altaner, and Luis A. Apiolaza. "Elastic Constants of Green Pinus Radiata Wood." New Zealand Journal of Forestry Science 46, no. 1 (2016): 19. https://doi.org/10.1186/s40490-016-0075-x.

[8] Djordjevic, A.R., R.M. Biljie, V.D. Likar-Smiljanic, and T.K. Sarkar. "Wideband Frequency-Domain Characterization of FR-4 and Time-Domain Causality." IEEE Transactions on Electromagnetic Compatibility 43, no. 4 (November 2001): 662–667. https://doi.org/10.1109/15.974647.

[9] Edwards, Terence C., and Michael B. Steer. Foundations for Microstrip Circuit Design. 4th edition. Chichester, West Sussex: Wiley, IEEE Press, 2016.

[10] Fofonoff, N.P., and R.C. Millard Jr. "Algorithms for the Computation of Fundamental Properties of Seawater." UNESCO, 1983. https://doi.org/10.25607/OBP-1450.

[11] Ross, Robert. Wood Handbook: Wood as an Engineering Material. Madison, WI: US Department of Agriculture, Forest Service, Forest Products Laboratory, 2021.

[12] Geotechdata.info. “Soil Young’s Modulus.” Accessed April 16, 2025. https://www.geotechdata.info/parameter/soil-young-s-modulus.

[13] Goli, Giacomo, Francesca Becherini, Maria Concetta Di Tuccio, Adriana Bernardi, and Marco Fioravanti. "Thermal Expansion of Wood at Different Equilibrium Moisture Contents." Journal of Wood Science 65, no. 1 (2019): 4. https://doi.org/10.1186/s10086-019-1781-9.

[14] Grossman, E. N., M. Gould, and N. P. Mujica-Schwann. "Robust Evaluation of Statistical Surface Topography Parameters Using Focus-Variation Microscopy." Surface Topography: Metrology and Properties 4, no. 3 (2016): 035003. https://doi.org/10.1088/2051-672X/4/3/035003.

[15] Hamdhan, Indra Noer, and Barry G. Clarke. "Determination of Thermal Conductivity of Coarse and Fine Sand Soils." In World Geothermal Congress 2010. Bali, Indonesia: 2010.

[16] Harvey, A. "Properties of Ice and Supercooled Water." In CRC Handbook of Chemistry and Physics 97th edition, edited by William M. Haynes. Boca Raton, FL: CRC Press, 2017.

[17] International Telecommunications Union Radiocommunication Sector. Effects of Building Materials and Structures on Radiowave Propagation Above About 100MHz. Recommendation P.2040. ITU-R, approved August 23, 2023. https://www.itu.int/rec/R-REC-P.2040/en.

[18] International Telecommunications Union Radiocommunication Sector. Electrical Characteristics of the Surface of the Earth. Recommendation P.527. ITU-R, approved September 27, 2021. https://www.itu.int/rec/R-REC-P.527/en.

[19] Gray, Jack. "Thermal Expansion Calculator & Table for Building Materials." Accessed April 18, 2025. https://roofobservations.com/thermal-expansion-building-materials/.

[20] Stephan, K., and A. Laesecke. "The Thermal Conductivity of Fluid Air." Journal of Physical and Chemical Reference Data 14, no. 1 (1985): 227–234. https://doi.org/10.1063/1.555749.

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