Method to derive the infrared complex refractive indices n(λ) and k(λ) for organic solids from KBr pellet absorption measurements

Kelly A. Peterson; Ryan M. Francis; Catherine A. Banach; Ashley M. Bradley; Sarah D. Burton; Jeremy D. Erickson; Schuyler P. Lockwood; Karissa L. Jensen; Michael O. Yokosuk; Timothy J. Johnson; Tanya L. Myers

doi:10.1364/AO.514661

Applied Optics
Vol. 63,
Issue 6,
pp. 1553-1565
(2024)
•https://doi.org/10.1364/AO.514661

Method to derive the infrared complex refractive indices n(λ) and k(λ) for organic solids from KBr pellet absorption measurements

Kelly A. Peterson, Ryan M. Francis, Catherine A. Banach, Ashley M. Bradley, Sarah D. Burton, Jeremy D. Erickson, Schuyler P. Lockwood, Karissa L. Jensen, Michael O. Yokosuk, Timothy J. Johnson, and Tanya L. Myers

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Kelly A. Peterson, Ryan M. Francis, Catherine A. Banach, Ashley M. Bradley, Sarah D. Burton, Jeremy D. Erickson, Schuyler P. Lockwood, Karissa L. Jensen, Michael O. Yokosuk, Timothy J. Johnson, and Tanya L. Myers, "Method to derive the infrared complex refractive indices n(λ) and k(λ) for organic solids from KBr pellet absorption measurements," Appl. Opt. 63, 1553-1565 (2024)

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Abstract

Obtaining the complex refractive index vectors $n({\tilde \nu})$ and $k({\tilde \nu})$ allows calculation of the (infrared) reflectance spectrum that is obtained from a solid in any of its many morphological forms. We report an adaptation to the KBr pellet technique using two gravimetric dilutions to derive quantitative $n({\tilde \nu})$/$k({\tilde \nu})$ for dozens of powders with greater repeatability. The optical constants of bisphenol A and sucrose are compared to those derived by other methods, particularly for powdered materials. The variability of the $k$ values for bisphenol A was examined by 10 individual measurements, showing an average coefficient of variation for $k$ peak heights of 5.6%. Though no established standards exist, the pellet-derived $k$ peak values of bisphenol A differ by 11% and 31% from their single-angle- and ellipsometry-derived values, respectively. These values provide an initial estimate of the precision and accuracy of complex refractive indices that can be derived using this method. Limitations and advantages of the method are discussed, the salient advantage being a more rapid method to derive $n/k$ for those species that do not readily form crystals or specular pellets.

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Supplementary Material (2)

Name	Description
Data File 1	The n(v) and k(v) data for four solids reported from 4000 to 400 cm-1: Bisphenol A, avobenzone, benzoyl peroxide and loratadine. The k(v) data are derived from quantitative absorbance measurements using KBr pellets.
Supplement 1	Table S1

Data availability

The average $n$ n and $k$ k data for bisphenol A, avobenzone, benzoyl peroxide, and loratadine presented in this paper are available in Data File 1. Other data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Peak ( ${c m}^{- 1}$ )	KBr $k$	KBr $k$ COV	KBr $k$ PRR
3363	$0.084 \pm 0.005$	5.7%	20%
2966	$0.0436 \pm 0.0009$	2.1%	7.5%
1612	$0.099 \pm 0.004$	4.5%	13%
1599	$0.101 \pm 0.004$	3.6%	12%
1510	$0.353 \pm 0.008$	2.3%	8.5%
1447	$0.097 \pm 0.005$	5.4%	20%
1363	$0.089 \pm 0.005$	5.3%	18%
1239	$0.30 \pm 0.01$	4.0%	15%
1178	$0.228 \pm 0.007$	3.3%	11%
1084	$0.069 \pm 0.006$	8.9%	28%
1013	$0.062 \pm 0.006$	10%	32%
828	$0.39 \pm 0.02$	4.2%	15%
759	$0.09 \pm 0.01$	12%	32%
565	$0.28 \pm 0.02$	6.6%	24%
553	$0.33 \pm 0.02$	5.8%	22%
Average:		5.6%	19%

Peak ( ${c m}^{- 1}$ )	KBr $k$	SA $k$	KBr-SA	IRSE $k$	KBr-IRSE
3363	$0.084 \pm 0.005$	0.078	−7.5%	0.12	$+$ 37%
2966	$0.0436 \pm 0.0009$	0.048	$+$ 11%	0.051	$+$ 15%
1612	$0.099 \pm 0.004$	0.10	$+$ 2.7%	0.16	$+$ 46%
1599	$0.101 \pm 0.004$	0.11	$+$ 6.4%	0.16	$+$ 47%
1510	$0.353 \pm 0.008$	0.37	$+$ 4.1%	0.58	$+$ 48%
1447	$0.097 \pm 0.005$	0.11	$+$ 11%	0.15	$+$ 45%
1363	$0.089 \pm 0.005$	0.098	$+$ 9.4%	0.13	$+$ 39%
1239	$0.30 \pm 0.01$	0.29	−1.1%	0.42	$+$ 34%
1178	$0.228 \pm 0.007$	0.22	−1.7%	0.28	$+$ 21%
1084	$0.069 \pm 0.006$	0.099	$+$ 36%	0.099	$+$ 36%
1013	$0.062 \pm 0.006$	0.085	$+$ 32%	0.087	$+$ 35%
828	$0.39 \pm 0.02$	0.36	−8.9%	0.41	$+$ 6.5%
759	$0.09 \pm 0.01$	0.12	$+$ 24%	0.12	$+$ 25%
565	$0.28 \pm 0.02$	0.26	−6.2%	0.23	−20%
553	$0.33 \pm 0.02$	0.34	$+$ 3.3%	0.35	$+$ 4.1%
Average of absolute percent differences:			$11 \pm 10 %$		$31 \pm 14 %$

Peak ( ${c m}^{- 1}$ )	KBr $k$	KBr $k$ COV	KBr $k$ PRR
3363	$0.084 \pm 0.005$	5.7%	20%
2966	$0.0436 \pm 0.0009$	2.1%	7.5%
1612	$0.099 \pm 0.004$	4.5%	13%
1599	$0.101 \pm 0.004$	3.6%	12%
1510	$0.353 \pm 0.008$	2.3%	8.5%
1447	$0.097 \pm 0.005$	5.4%	20%
1363	$0.089 \pm 0.005$	5.3%	18%
1239	$0.30 \pm 0.01$	4.0%	15%
1178	$0.228 \pm 0.007$	3.3%	11%
1084	$0.069 \pm 0.006$	8.9%	28%
1013	$0.062 \pm 0.006$	10%	32%
828	$0.39 \pm 0.02$	4.2%	15%
759	$0.09 \pm 0.01$	12%	32%
565	$0.28 \pm 0.02$	6.6%	24%
553	$0.33 \pm 0.02$	5.8%	22%
Average:		5.6%	19%

Peak ( ${c m}^{- 1}$ )	KBr $k$	SA $k$	KBr-SA	IRSE $k$	KBr-IRSE
3363	$0.084 \pm 0.005$	0.078	−7.5%	0.12	$+$ 37%
2966	$0.0436 \pm 0.0009$	0.048	$+$ 11%	0.051	$+$ 15%
1612	$0.099 \pm 0.004$	0.10	$+$ 2.7%	0.16	$+$ 46%
1599	$0.101 \pm 0.004$	0.11	$+$ 6.4%	0.16	$+$ 47%
1510	$0.353 \pm 0.008$	0.37	$+$ 4.1%	0.58	$+$ 48%
1447	$0.097 \pm 0.005$	0.11	$+$ 11%	0.15	$+$ 45%
1363	$0.089 \pm 0.005$	0.098	$+$ 9.4%	0.13	$+$ 39%
1239	$0.30 \pm 0.01$	0.29	−1.1%	0.42	$+$ 34%
1178	$0.228 \pm 0.007$	0.22	−1.7%	0.28	$+$ 21%
1084	$0.069 \pm 0.006$	0.099	$+$ 36%	0.099	$+$ 36%
1013	$0.062 \pm 0.006$	0.085	$+$ 32%	0.087	$+$ 35%
828	$0.39 \pm 0.02$	0.36	−8.9%	0.41	$+$ 6.5%
759	$0.09 \pm 0.01$	0.12	$+$ 24%	0.12	$+$ 25%
565	$0.28 \pm 0.02$	0.26	−6.2%	0.23	−20%
553	$0.33 \pm 0.02$	0.34	$+$ 3.3%	0.35	$+$ 4.1%
Average of absolute percent differences:			$11 \pm 10 %$		$31 \pm 14 %$

Kelly A. Peterson	https://orcid.org/0000-0002-7355-6611
Ryan M. Francis	https://orcid.org/0000-0002-3964-6090
Ashley M. Bradley	https://orcid.org/0000-0001-7344-9640
Jeremy D. Erickson	https://orcid.org/0000-0002-2335-1159
Schuyler P. Lockwood	https://orcid.org/0000-0003-3582-5179
Karissa L. Jensen	https://orcid.org/0000-0003-4900-0194
Michael O. Yokosuk	https://orcid.org/0000-0003-3981-7715
Timothy J. Johnson	https://orcid.org/0000-0001-9514-6288
Tanya L. Myers	https://orcid.org/0000-0001-8995-7033

Abstract

Supplementary Material (2)

Data availability

Cited By

Figures (9)

Tables (2)

Equations (4)

Applied Optics