Principles of quantitative absorbance measurements in anisotropic crystals
Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Libowitzky, Eugen [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1996 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1996 |
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| Übergeordnetes Werk: |
Enthalten in: Physics and chemistry of minerals - Springer-Verlag, 1977, 23(1996), 6 vom: Aug., Seite 319-327 |
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| Übergeordnetes Werk: |
volume:23 ; year:1996 ; number:6 ; month:08 ; pages:319-327 |
| Links: |
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| DOI / URN: |
10.1007/BF00199497 |
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| 520 | |a Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. | ||
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| 650 | 4 | |a Anisotropic Material | |
| 650 | 4 | |a Absorbance Measurement | |
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| 700 | 1 | |a Rossman, George R. |4 aut | |
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10.1007/BF00199497 doi (DE-627)OLC2072359406 (DE-He213)BF00199497-p DE-627 ger DE-627 rakwb eng 550 540 530 VZ BIODIV DE-30 fid Libowitzky, Eugen verfasserin aut Principles of quantitative absorbance measurements in anisotropic crystals 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. Calcite Isotropic Material Anisotropic Material Absorbance Measurement Anisotropic Medium Rossman, George R. aut Enthalten in Physics and chemistry of minerals Springer-Verlag, 1977 23(1996), 6 vom: Aug., Seite 319-327 (DE-627)129323039 (DE-600)131393-9 (DE-576)014557398 0342-1791 nnns volume:23 year:1996 number:6 month:08 pages:319-327 https://doi.org/10.1007/BF00199497 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-GEO SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-GGO GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2027 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4112 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 AR 23 1996 6 08 319-327 |
| spelling |
10.1007/BF00199497 doi (DE-627)OLC2072359406 (DE-He213)BF00199497-p DE-627 ger DE-627 rakwb eng 550 540 530 VZ BIODIV DE-30 fid Libowitzky, Eugen verfasserin aut Principles of quantitative absorbance measurements in anisotropic crystals 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. Calcite Isotropic Material Anisotropic Material Absorbance Measurement Anisotropic Medium Rossman, George R. aut Enthalten in Physics and chemistry of minerals Springer-Verlag, 1977 23(1996), 6 vom: Aug., Seite 319-327 (DE-627)129323039 (DE-600)131393-9 (DE-576)014557398 0342-1791 nnns volume:23 year:1996 number:6 month:08 pages:319-327 https://doi.org/10.1007/BF00199497 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-GEO SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-GGO GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2027 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4112 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 AR 23 1996 6 08 319-327 |
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10.1007/BF00199497 doi (DE-627)OLC2072359406 (DE-He213)BF00199497-p DE-627 ger DE-627 rakwb eng 550 540 530 VZ BIODIV DE-30 fid Libowitzky, Eugen verfasserin aut Principles of quantitative absorbance measurements in anisotropic crystals 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. Calcite Isotropic Material Anisotropic Material Absorbance Measurement Anisotropic Medium Rossman, George R. aut Enthalten in Physics and chemistry of minerals Springer-Verlag, 1977 23(1996), 6 vom: Aug., Seite 319-327 (DE-627)129323039 (DE-600)131393-9 (DE-576)014557398 0342-1791 nnns volume:23 year:1996 number:6 month:08 pages:319-327 https://doi.org/10.1007/BF00199497 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-GEO SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-GGO GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2027 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4112 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 AR 23 1996 6 08 319-327 |
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10.1007/BF00199497 doi (DE-627)OLC2072359406 (DE-He213)BF00199497-p DE-627 ger DE-627 rakwb eng 550 540 530 VZ BIODIV DE-30 fid Libowitzky, Eugen verfasserin aut Principles of quantitative absorbance measurements in anisotropic crystals 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. Calcite Isotropic Material Anisotropic Material Absorbance Measurement Anisotropic Medium Rossman, George R. aut Enthalten in Physics and chemistry of minerals Springer-Verlag, 1977 23(1996), 6 vom: Aug., Seite 319-327 (DE-627)129323039 (DE-600)131393-9 (DE-576)014557398 0342-1791 nnns volume:23 year:1996 number:6 month:08 pages:319-327 https://doi.org/10.1007/BF00199497 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-GEO SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-GGO GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2027 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4112 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 AR 23 1996 6 08 319-327 |
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10.1007/BF00199497 doi (DE-627)OLC2072359406 (DE-He213)BF00199497-p DE-627 ger DE-627 rakwb eng 550 540 530 VZ BIODIV DE-30 fid Libowitzky, Eugen verfasserin aut Principles of quantitative absorbance measurements in anisotropic crystals 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. Calcite Isotropic Material Anisotropic Material Absorbance Measurement Anisotropic Medium Rossman, George R. aut Enthalten in Physics and chemistry of minerals Springer-Verlag, 1977 23(1996), 6 vom: Aug., Seite 319-327 (DE-627)129323039 (DE-600)131393-9 (DE-576)014557398 0342-1791 nnns volume:23 year:1996 number:6 month:08 pages:319-327 https://doi.org/10.1007/BF00199497 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-GEO SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-GGO GBV_ILN_11 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2027 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4112 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4319 GBV_ILN_4323 AR 23 1996 6 08 319-327 |
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Enthalten in Physics and chemistry of minerals 23(1996), 6 vom: Aug., Seite 319-327 volume:23 year:1996 number:6 month:08 pages:319-327 |
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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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. 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principles of quantitative absorbance measurements in anisotropic crystals |
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Principles of quantitative absorbance measurements in anisotropic crystals |
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Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. © Springer-Verlag 1996 |
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Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. © Springer-Verlag 1996 |
| abstract_unstemmed |
Abstract The accurate measurement of absorbance (A=-log T; T=I/I0) 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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz. © Springer-Verlag 1996 |
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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 Atot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (atot=Atot/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 Ax/Atot=$ cos^{2} $ (x < absorber), and analogously for Ayand Az. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=Icrossed/Iparallel) 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 Amax=−log[(Tmax,obs−0.5·Pe·Tmin,obs)/(1−0.5·Pe)], and similar for Amin. The theoretical approach is confirmed by measurements on calcite and topaz.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Calcite</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Isotropic Material</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anisotropic Material</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Absorbance Measurement</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anisotropic Medium</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rossman, George R.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Physics and chemistry of minerals</subfield><subfield code="d">Springer-Verlag, 1977</subfield><subfield code="g">23(1996), 6 vom: Aug., Seite 319-327</subfield><subfield code="w">(DE-627)129323039</subfield><subfield code="w">(DE-600)131393-9</subfield><subfield code="w">(DE-576)014557398</subfield><subfield code="x">0342-1791</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:23</subfield><subfield code="g">year:1996</subfield><subfield code="g">number:6</subfield><subfield code="g">month:08</subfield><subfield code="g">pages:319-327</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/BF00199497</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-CHE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-GEO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-DE-84</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-GGO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_130</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2279</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4103</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4319</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">23</subfield><subfield code="j">1996</subfield><subfield code="e">6</subfield><subfield code="c">08</subfield><subfield code="h">319-327</subfield></datafield></record></collection>
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