Optical constants

Refractive index of Zr (Zirconium)

Windt et al. 1988: n,k 0.0024–0.122 µm

Data: tabulated nk
Range: 0.00236–0.1216 µm
Points: 36
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 0.92122
Extinction coefficient k: 0.021405

Permittivity ε₁: 0.848188
Permittivity ε₂: 0.0394375

Absorption coefficient α: 159162 cm⁻¹
Penetration depth δ = λ/(2πk): 125.658 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -10.0836 µm⁻¹

Group index n_g: 1.09163
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 73.3634 eV

ε = (n + ik)², α = 4πk/λ, n_g = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.

Use it in Lightsmith

Load this data in Python, simulate in one more line

pip install lightsmith

import lightsmith as ls

# Zr (Zirconium): Windt et al. 1988: n,k 0.0024–0.122 µm
zr = ls.fetch_refractiveindex("main", "Zr", "Windt", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(zr.range_nm)  # (2.36, 121.57) nm
eps = zr.eps([16.9])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_03702e98c34c/lightsmith"
zr = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(zr.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (zr/windt-1988).

# ... load zr as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=zr)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=3, stop_nm=121, num=81),
)
res = ls.solve(sim)  # exact Mie for a sphere
print(res.q_ext)     # extinction efficiency at each wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.

References

D. L. Windt, W. C. Cash, M. Scott, P. Arendt, B. Newnam, R. F. Fisher, A. B. Swartzlander. Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å. Appl. Opt. 27, 246-278 (1988)

doi:10.1364/ao.27.000246 Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å, Applied Optics (1988)

Cite

David L. Windt et al.. Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å. Applied Optics, 27, 246 (1988), doi:10.1364/ao.27.000246; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

36 rows as published

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Zr (Zirconium), Windt et al. 1988: n,k 0.0024–0.122 µm: n and k versus wavelength
λ (µm)	n	k
0.00236	0.99783	0.00117
0.00316	0.99781	0.00135
0.00447	0.99536	0.00498
0.00676	0.9922	0.00269
0.0114	0.9694	0.00625
0.01355	0.955	0.0131
0.01714	0.9188	0.022
0.0243	0.808	0.0987
0.02563	0.79	0.119
0.03038	0.757	0.324
0.0327	0.868	0.32
0.03568	0.949	0.373
0.03793	0.963	0.318
0.04059	0.9	0.232
0.04478	0.866	0.314
0.04607	0.829	0.321
0.04895	0.844	0.347
0.05391	0.825	0.337
0.05843	0.838	0.362
0.06163	0.826	0.33
0.06714	0.768	0.332
0.07185	0.807	0.44
0.07359	0.789	0.492
0.07437	0.817	0.533
0.08345	0.817	0.673
0.0878	0.828	0.759
0.09198	0.81	0.858
0.09321	0.804	0.848
0.09888	0.814	0.905
0.10258	0.895	0.99
0.10482	0.952	1.1
0.10667	0.85	1.08
0.10857	0.907	1.11
0.1135	1.15	1.27
0.12007	1.14	1.24
0.12157	1.28	1.31

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Zr (Zirconium): all datasets

About Zr (Zirconium)

Zirconium (Zr) is a lustrous, greyish-white, soft, ductile, malleable metal that is solid at room temperature. It's located in group 4 of the periodic table and resembles hafnium and titanium in many of its properties. Zirconium is resistant to corrosion by alkalis, acids, salt water, and other agents, which makes it ideal for various applications in the chemical industry. Its most significant use is in the ceramic industry to make high-temperature ceramics, primarily in the form of zircon (zirconium silicate) which is derived from zirconium ore. Additionally, due to its low neutron-capture cross-section, zirconium alloys are used in nuclear reactors for cladding fuel elements. The metal also finds use in superconductive magnets. Another critical application of zirconium is in the construction of biocompatible implants for the human body, as it is non-toxic and not rejected by the immune system.

More about Zr (Zirconium) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Zr/nk/Windt.yml
ID: ds_03702e98c34c
API: /v1/datasets/ds_03702e98c34c

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