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Principles of quantitative absorbance measurements in anisotropic crystals

Abstract

The accurate measurement of absorbance (A=-log T; T=I/I 0) in anisotropic materials like crystals is highly important for the determination of the concentration and orientation of the oscillator (absorber) under investigation.

The absorbance in isotropic material is linearly dependent on the concentration of the absorber and on the thickness of the sample (A=ɛ·c·t). Measurement of absorbance in anisotropic media is more complicated, but it can be obtained from polarized spectra (i) on three random, but orthogonal sections of a crystal, or (ii) preferably on two orthogonal sections oriented parallel to each of two axes of the indicatrix ellipsoid. To compare among different crystal classes (including cubic symmetry) it is useful to convert measured absorbance values to one common basis (the total absorbance A tot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (a tot=A tot/t) is calculated by

$$\left( {\text{i}} \right)a_{{\text{tot}}} = \sum\limits_{i = 1}^3 {(a_{\max ,i} + a_{\min ,i} )} /2, {\text{or}} {\text{by}} {\text{(ii) }}a_{{\text{tot}}} = a_x + a_y + a_z .$$

Only in special circumstances will unpolarized measurements of absorbance provide data useful for quantitative studies of anisotropic material.

The orientation of the absorber with respect to the axes of the indicatrix ellipsoid is calculated according to A x/A tot=cos2 (x < absorber), and analogously for A yand A z. In this way, correct angles are obtained for all cases of symmetry.

The extinction ratio of the polarizer (Pe=I crossed/I parallel) has considerable influence on the measured amplitude of absorption bands, especially in cases of strong anisotropic absorbance. However, if Pe is known, the true absorbance values can be calculated even with polarizers of low extinction ratio, according to A max=−log[(T max,obs−0.5·Pe·T min,obs)/(1−0.5·Pe)], and similar for A min.

The theoretical approach is confirmed by measurements on calcite and topaz.

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References

  • Beran A (1991) Trace hydrogen in Verneuil-grown corundum and its color varieties — an IR spectroscopic study. Eur J Mineral 3:971–975

    Google Scholar 

  • Beran A, Langer K, Andrut M (1993) Single crystal infrared spectra in the range of OH fundamentals of paragenetic garnet, omphacite and kyanite in an eclogitic mantle xenolith. Mineral Petrol 48:257–268

    Google Scholar 

  • Dowty E (1978) Absorption optics of low-symmetry crystals — Application to titanian clinopyroxene spectra. Phys Chem Minerals 3:173–181

    Google Scholar 

  • Goldman DS, Rossman GR (1979) Determination of quantitative cation distribution in orthopyroxenes from electronic absorption spectra. Phys Chem Minerals 4:43–53

    Google Scholar 

  • Gonzalez-Carreño T, Fernández M, Sanz J (1988) Infrared and electron microprobe analysis of tourmalines. Phys Chem Minerals 15:452–460

    Google Scholar 

  • Griffiths PR, de Haseth J (1986) Fourier transform infrared spectrometry. John Wiley and Sons, New York, Chichester, Brisbane, Toronto, Singapore

    Google Scholar 

  • Kliger DS, Lewis JW, Randall CE (1990) Polarized light in optics and spectroscopy. Academic Press, Boston, San Diego, New York, London, Sydney, Tokyo, Toronto

    Google Scholar 

  • Labotka TC, Rossman GR (1974) The infrared pleochroism of lawsonite: The orientation of the water and hydroxide groups. Am Mineral 59:799–806

    Google Scholar 

  • Libowitzky E, Beran A (1995) OH defects in forsterite. Phys Chem Minerals 22:387–392

    Google Scholar 

  • Nesse WD (1986) Introduction to optical mineralogy. Oxford University Press, New York, Oxford

    Google Scholar 

  • Paterson MS (1982) The determination of hydroxyl by infrared absorption in quartz, silicate glass and similar materials. Bull Mineral 105:20–29

    Google Scholar 

  • Rouxhet PG (1970) Hydroxyl stretching bands in micas: a quantitative interpretation. Clay Minerals 8:375–388

    Google Scholar 

  • Shinoda K, Aikawa N (1993) Polarized infrared absorbance spectra of an optically anisotropic crystal: application to the orientation of the OH dipole in quartz. Phys Chem Minerals 20:308–314

    Google Scholar 

  • Shinoda K, Aikawa N (1994) The orientation of the OH dipole in an optically anisotropic crystal: an application to the OH dipole in topaz. Phys Chem Minerals 21:24–28

    Google Scholar 

  • Smakula A (1962) Einkristalle. Wachstum, Herstellung und Anwendung. Springer, Berlin, Göttingen, Heidelberg

    Google Scholar 

  • Strens RGJ, Mao HK, Bell PM (1982) Quantitative spectra and optics of some meteoritic and terrestrial titanian clinopyroxenes. In: Saxena SK (ed.) Advances in physical geochemistry, vol. 2, Springer, New York, Heidelberg, Berlin, pp. 327–346

    Google Scholar 

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Libowitzky, E., Rossman, G.R. Principles of quantitative absorbance measurements in anisotropic crystals. Phys Chem Minerals 23, 319–327 (1996). https://doi.org/10.1007/BF00199497

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  • DOI: https://doi.org/10.1007/BF00199497

Keywords

  • Calcite
  • Isotropic Material
  • Anisotropic Material
  • Absorbance Measurement
  • Anisotropic Medium