Diamond Optics
n(λ) from Peter's Sellmeier formula to 644 nm and Palik's tabulated values beyond; an uncoated, non-absorbing plate transmits at most 2n/(n² + 1) (reflections added incoherently).
n at 589 nm
2.4173
Peter's Sellmeier formula
Reflectance per surface
17.20 %
((n − 1)/(n + 1))², normal incidence
Fresnel-limited transmission
70.6 %
2n/(n² + 1): uncoated plate, both surfaces, no absorption
Refractive index
Properties
| Indirect band gap | 5.47 eV (absorption edge ≈ 227 nm) |
| Thermal conductivity | 2600 W/(m·K) at 273 K |
| dn/dT | +9.6 ×10⁻⁶/K |
| Thermal expansion | 1 ×10⁻⁶/K at 293 K |
| Knoop hardness | 5700–10400 kg/mm² (with orientation) |
| Young's modulus | 1050 GPa |
| Density | 3.51 g/cm³ |
| Specific heat | ≈ 502 J/(kg·K) near room temperature |
| Melting point | 3497 °C, only at GPa pressures. At 1 atm diamond does not melt: it graphitizes above ≈ 1500 °C in vacuum or inert gas and oxidizes in air from ≈ 700 °C |
Crystran data sheet (type IIa); band gap from Clark, Dean & Harris (1964).
Transmission bands
Type IIa, Crystran: 0.3–2.5 µm and 7 to beyond 100 µm. Poorer samples may cut off at 350 nm.
Model
n² = 1 + 0.3306 λ²/(λ² − 0.175²) + 4.3356 λ²/(λ² − 0.106²) (λ in µm, 226–644 nm), T_max = 2n/(n² + 1)
Below 644 nm the index is Peter's Sellmeier formula, fitted to his own measurements; beyond it, Palik's tabulated values (0.656–20 µm) interpolated linearly in wavelength. Diamond is cubic, so it has one index. An uncoated, non-absorbing plate with both surfaces' multiple reflections added in intensity transmits at most T = 2n/(n² + 1) (incoherent: no interference between the surfaces): about 71 % in the visible. Absorption in the two- and three-phonon band (2.5–7 µm), near the UV edge and from nitrogen impurities (type I diamond) lowers it.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Peter's Sellmeier fit is exact for the fit over his 226–644 nm; beyond that the index is interpolated linearly in 1/λ² between Palik's values to 20 µm (on a smooth dispersion curve this adds under 1e-4; linear in λ it was up to 3e-3 between 0.66 and 2 µm). Transmission is the lossless two-surface Fresnel limit; the 2.5–7 µm multiphonon band and impurities lower it. Properties are room-temperature data-sheet values.
- Peter F. (1923). Über Brechungsindizes und Absorptionskonstanten des Diamanten zwischen 644 und 226 mμ. Z. Phys. 15, 358–368. doi:10.1007/BF01330487
- Palik E. D. (ed.) (1985). Handbook of Optical Constants of Solids, vol. 1. Academic Press. Diamond, as tabulated by Crystran.
- Clark C. D., Dean P. J., Harris P. V. (1964). Intrinsic edge absorption in diamond. Proc. R. Soc. A 277, 312–329. Indirect band gap. doi:10.1098/rspa.1964.0025
- Crystran. Handbook of Infrared and Ultraviolet Optical Materials, data sheets: diamond: transmission range, dn/dT, thermal conductivity and expansion, Knoop hardness, density, specific heat, Young's modulus. crystran.com
- Born M., Wolf E. (1999). Principles of Optics, 7th ed. Cambridge University Press. Fresnel formulae at normal incidence.