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[Display omitted] • Dispersion analysis was extended to include isotropic chiral materials. • We applied extended dispersion analysis to the VCD spectra of α-Pinene. • We applied extended dispersion analysis to the VCD spectra of Propylene oxide. • The area of a couplet divided by wavenumber is the same above and below zero. Classical electromagnetic theory applied to infrared (IR) and vibrational circular dichroism (VCD) spectra of chiral compounds can provide useful insights, such as the fact that the area of all bands of wavenumber-normalized absorbance above zero must be the same as the area below zero. Additionally, dispersion analysis based on wave optics and dispersion theory, which was extended by Born and Kuhn to include chiral substances, can be used to quantitatively describe the dielectric function and the chiral admittance functions that shape IR and VCD spectra. For dispersion analysis, pairs of coupled oscillators, with five different kinds of parameters, namely oscillator strength, damping, oscillator position, vertical distance between coupled oscillators, and the coupling constant are used to model the dielectric functions and chiral admittance functions. We report the results of such an analysis for α-Pinene and Propylene oxide. For most bands, the oscillator model using two coupled oscillators is sufficient to achieve a good correspondence between experimental and modelled data. [ABSTRACT FROM AUTHOR]

[Display omitted] • Wave optics is needed to explain the infrared 2D-COS spectra of oriented materials. • Wave optics allows to determine orientation to a much higher degree than LDT. • Two-trace 2D-COS can uniquely identify the orientation distribution of a sample. On the level of the Bouguer-Beer-Lambert approximation, the effects introduced by linear dichroism into absorbance spectra can be simulated by classic linear dichroism theory. If wave optics and dispersion theory are employed, linear dichroism can be modelled with a 4x4 matrix formalism. For linear dichroism theory, the angle between polarization direction and transition moment can be seen as a perturbation which allows to calculate corresponding infrared 2D correlation spectra. Similarly, with help of an orientation representation based on Euler's angles, varying the latter allows the same if electromagnetic theory is employed. Correspondingly, we compare the substantially different footprints of linear dichroism according to both theories in infrared 2D correlation spectra and show that only those based on wave optics and dispersion theory are in accordance with experimental results. Accordingly, in particular asynchronous 2D correlation spectra allow to detect orientation with a sensitivity that is unparalleled in case of conventional spectra, even if they are recorded with help of a polarizer and an analyzer. [ABSTRACT FROM AUTHOR]

[Display omitted] • A formalism to determine the chirality admittance functions was developed. • The corresponding functions were determined for α-Pinene and Propylene oxide. • For VCD spectra the Bouguer-Lambert approximation holds strictly. • The area of a VCD signal divided by wavenumber is the same above and below zero. Optical constants functions of analytes are indispensable for the effective design of plasmonic sensors. Such sensors are potentially able to enhance the sensitivity by several order of magnitudes which can greatly facilitate the determination of the generally weak spectral signals caused by vibrational circular dichroism. Accordingly, to demonstrate how to obtain these functions, we have determined the dielectric and chirality admittance functions of α-Pinene and Propylene oxide in the mid-infrared spectral range using attenuated total reflection and vibrational circular dichroism spectroscopy. Our iterative formalism starts with an estimation of the absorption index function, followed by the calculation of the refractive index function using the Kramers-Kronig relation and a modelled spectrum based on Fresnel's equations. By comparing the experimental and modelled spectra, we improve the absorption index function. To determine the chirality admittance function, we use the same iterative formalism, but with a modified 4x4 matrix formalism formulated by Berreman. Our results show that the experimental absorbance difference is independent of the dielectric function of the chiral substance and depends linearly on the cuvette thickness. Additionally, we provide a sum rule that can be used to assess the quality of VCD spectra and determine the position of the baseline. Our findings provide crucial insights into the optical properties of chiral substances in the mid-infrared spectral range, which have important implications for a range of applications in fields such as analytical chemistry and materials science. [ABSTRACT FROM AUTHOR]

In contrast to the extensive molecular and crystal structure investigations on oxalic acid dihydrate (C 2 H 2 O 4 ·2H 2 O, α-POX) and its deuterated analogues (α-DOX), stands the absence of a complete vibrational spectra analysis. Such analysis is desirable in view of the proton dynamics in α-POX crystals. In this communication we report the room temperature polarized IR reflectance spectra of a single crystal of α-POX recorded from the ac crystal plane, and from the plane containing the b -crystallographic axis, with polarization along the axis. Dispersion analysis of the reflectance spectra of both B u and A u symmetry type modes, using model dielectric and reflectance function valid for the monoclinic case, have been performed and the results are discussed. Some aspects of the obtained fit results for some of the spectral regions and the peculiar change of the reflectance function with polarization angle are also discussed in this work. A correlation between the crystal structure and measured spectra, together with the results of the performed dispersion analysis, gave answers to some of the problems concerned with the orientation of the transition dipole moments of the IR active modes. The assignment of modes is assisted by DFT calculations. Another aspect covered in this work is the model reflectance functions using different averaging theories that have been applied in obtaining the reflectance spectrum of a polycrystalline sample. The results of the comparison between these spectra and the recorded reflectance spectra from a polycrystalline sample were further discussed. Unlabelled Image • The RT polarized reflectance spectra of a single crystal of α-POX recorded from the ac crystal plane are presented. • Dispersion analysis of the reflectance spectra, have been performed and the results are discussed. • The assignment of modes was assisted by DFT calculations. [ABSTRACT FROM AUTHOR]

Abstract We report a considerable improvement of Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis. Whereas the first method is an alternative to the well-established conventional Kramers-Kronig analysis, but fully analytical, the second method allows to capture subtle spectral features that might get lost by conventional dispersion analysis using oscillator models. Since both methods share the same physical foundation, an improvement in the Kramers-Kronig conformity will be a benefit for either. The corresponding improvement that we report decreases the average errors and increases conformity by about three orders of magnitude. This puts Poor Man's Kramers-Kronig analysis in the range of Maclaurin's method, which is still one of the numerical benchmarks. Kramers-Kronig constrained variational analysis on the other hand can now unleash its full potential and is able to correctly model even spectra of inorganic materials with their strong absorption bands without being supported by conventional oscillators. Graphical abstract Unlabelled Image Highlights • Increase of the accuracy of Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis by three orders of magnitude. • Kramers-Kronig constrained variational analysis can now be employed without support from damped harmonic oscillators, also for materials with very strong absorption. • Kramers-Kronig conformity of Poor Man's Kramers-Kronig analysis is henceforth in the range of Maclaurin's method. [ABSTRACT FROM AUTHOR]

We show that an electric field standing wave effect is responsible for the oscillations and the non-linear dependence of the absorbance on the layer thickness in thin layers on a reflective surface. This effect is connected to the occurrence of interference inside these layers. Consequently, the absorptance undergoes a maximum electric field intensity enhancement at spectral positions close to those where corresponding non-absorbing layers on a metal show minima in the reflectance. The effect leads to changes of peak maxima ratios with layer thickness and shows the same periodicity as oscillations in the peak positions. These peculiarities are fully based on and described by Maxwell's equations but cannot be understood and described if the strongly simplifying model centered on reflectance absorbance is employed. [ABSTRACT FROM AUTHOR]

We investigate electric field standing wave effects in the system semiinfinite incidence medium with high index of refraction/layer/vacuum, the latter being the semiinfinite exit medium. If the layer has a lower index of refraction than the incidence medium, then very strong resonances occur between the two critical angles of the system defined by the systems incidence medium/layer and incidence medium/vacuum, as the layer is then a cavity. In particular close to the lower critical angles, the evanescent fields extend strongly into the exit medium. Based on this effect we suggest two new spectroscopic modalities, namely interference-enhanced internal reflection Raman spectroscopy and interference-enhanced attenuated total reflection infrared spectroscopy. [ABSTRACT FROM AUTHOR]

[Display omitted] • That the refractive index function squared equals the dielectric function, is one cause of coupling effects in IR spectra. • Another cause are local field effects like those represented by the Lorentz-Lorenz or Clausius-Mossotti-relation. • Coupling effects are important for band fitting and for understanding the results of quantum mechanical calculations. We discuss coupling effects in infrared spectra which are caused by dispersion and local field effects. The first effect is instigated by changes of the refractive index due to absorption which have an impact on the strength of adjacent absorptions. The second effect is a consequence of the light-induced polarization of one molecule affecting neighboring ones. These coupling effects do not only effect band positions, but also influence relative intensities. They are particularly strong in case of overlapping bands and complicate their deconvolution by band fitting. We investigated the corresponding challenges for the HO-stretching vibrations in water and the Amide I band in proteins. Our findings show that the effects are significant and of high interest for protein and water structure determination. Especially, for the water stretching vibrations we conclude that it is of utmost importance to consider such coupling effects in quantum mechanical calculations of water spectra. Otherwise, progress in understanding band positions and profiles is likely to be hampered. Also, in case of the Amide I band we found a distinct impact of such coupling effects. Accordingly, we strongly recommend consideration of dispersion and local field effects to ensure the possibility of an accurate, quantitative determination of α-helix and β-sheet structures. [ABSTRACT FROM AUTHOR]

Several samples of flat soda-lime silicate glass were investigated by the Infrared Attenuated Total Reflection (IR-ATR) spectroscopy technique. The specular reflectance spectra together with the results of the performed dispersion analysis and the generated reflectance spectra, using Fresnel equations, suggest that the samples are isotropic. In contrast, spectra recorded by the ATR technique suggest an anisotropic structure on the surface of the specimen different from that in the bulk. This is established through differences in the s- and p-polarized IR-ATR spectra, which cannot be simply transformed into one another employing Fresnel formula for an isotropic case. It appears that this thin film having a structure different from the bulk is larger than the ATR effective penetration depth of the evanescent ray for each incidence angle above the critical one. The investigation suggests C 2 symmetry of the SiO 4 unit. [ABSTRACT FROM AUTHOR]

We investigate how dispersion analysis can profit from the use of a Lorentz-type description of the inverse dielectric function. In particular at higher angles of incidence, reflectance spectra using p -polarized light are dominated by bands from modes that have their transition moments perpendicular to the surface. Accordingly, the spectra increasingly resemble inverse dielectric functions. A corresponding description can therefore eliminate the complex dependencies of the dispersion parameters, allow their determination and facilitate a more accurate description of the optical properties of single crystals. [ABSTRACT FROM AUTHOR]

[Display omitted] • Classical chemometric methods are based on Beer's approximation, which does not hold for ideal liquid mixtures. • Multivariate Classical Least Squares (CLS) regression is found to be inferior to Univariate CLS if peak values of a band with a comparably weak oscillator is selected. • Inverse Least Squares (ILS) Regression should therefore also be based on bands of comparably weak oscillators. • Principle Component Regression is superior to CLS and ILS if all available components are used. A considerable reduction of components is not advisable. We have recorded ATR-IR spectra of binary mixtures in the (quasi-)ideal systems Benzene-Toluene, Benzene-Carbon tetrachloride and Benzene-Cyclohexane and performed classical least squares, inverse least squares and principal component regression on the resulting spectra. In contrast to the general expectation, the spectra of ideal mixtures follow only roughly Beer's approximation, in particular stronger bands show shifts and increased intensities for intermediary compositions since the polarization of matter by light cannot be neglected. As a consequence, these conventional regression techniques lead to principle and unavoidable errors, even though some of the classical regression techniques are assumed to be able to cope with nonlinearities. In particular in the system Benzene-Carbon tetrachloride large errors result and the relative average error of the volume fraction determination is about 10 % for all three methods. Especially remarkable is that the multivariate regression methods do not perform better than the classical univariate calibration if for the latter a peak due to an oscillator with comparably low oscillator strength is selected, since for such bands polarization effects are weak and Beer's approximation holds comparably well. [ABSTRACT FROM AUTHOR]

Abstract We present a rigorous derivation of Beer's law from electromagnetic theory which allows to establish the connection of wave optics and Maxwell's equations with quantitative UV/VIS and infrared spectroscopy. As a result of this derivation, the attenuation constant is shown to be a function of the index of refraction. For small concentrations and an index of refraction not very different from unity, however, the empirical law is retrieved. Only for very strong absorptions with attenuation constants beyond 103 l/(mol·cm) and high concentrations, noticeable deviations from the empirical law and its linear concentration dependence are predicted to occur. The derivation is presented in a form, which is not only similar to that leading to the Clausius-Mossotti equation, but also shares the same starting point. Accordingly, it can easily be included in the curricula of physical chemistry. Graphical abstract Unlabelled Image Highlights • Derivation of Beer's law from simple electromagnetic Theory • Result of the derivation shows that the molar attenuation constant depends on the index of refraction. • This dependency can be neglected except for high molar attenuation constants and concentrations. [ABSTRACT FROM AUTHOR]

[Display omitted] • The upper limit of the Kramers-Kronig integrals can generally be adapted to the upper measurement range by the use of the (square root of the) dielectric background. • For the calculation of the absorption index or the phase function of reflectance, setting all values below the measured region to the value at the limit of the measurement range marginalizes the errors of the KKA. • A further error reduction can be achieved if a two stage Kramers-Kronig analysis is employed or if a slope is introduced by a fit procedure. • All suggested methods are reliable, fast and, in particular, simple. Therefore, existing KKR programs can be easily adapted and even conventional spreadsheet software can be used. Since about 60 years, it is possible to determine the set of optical constants from reflectance measurements by the Kramers-Kronig relations. Unfortunately, the potential of the method seems to be limited in practice by the need to extend measured data into unknown regions by extrapolation, which is prone to error and leads to deviations from the true values in the known region depending on the method of extension. With the advent of infrared refraction spectroscopy, which uses reflectance measurements at normal or near normal incidence, the development of a fast method to determine the complex index of refraction function reliably for these cases has become an even more interesting goal. In this work, we introduce a way to perform a Kramers-Kronig analysis of such reflectance spectra without the need to extrapolate the measured data for higher wavenumbers beyond the measurement range. Furthermore, we introduce and compare very simple and reliable material-independent ways to extrapolate the measured data for lower wavenumbers. As a result, we devise fast and sufficiently accurate methods, which are easily implementable into existing spectrometer software, to extract quantitative spectral information from reflectance measurements at near normal incidence. [ABSTRACT FROM AUTHOR]

Highlights: [•] Complete dispersion analysis of polarized IR reflectance spectra was performed. [•] A technique for discriminating between anion vibrations and water librations was proposed. [•] The HOH stretching transition dipole directions were discussed. [•] The reason for the isolated ion stretching vibration red shift was discussed. [ABSTRACT FROM AUTHOR]

We reply to a comment made in [E. Rousseau, N. Izard, J.-L. Bantignies, D. Felbacq, Comment on the paper "Improving Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis", Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, (2021) 119849]. [ABSTRACT FROM AUTHOR]

Abstract: Polarized IR reflectance spectra of K2Ni(SO4)2·6H2O single crystal (belonging to the group of Tutton salts) were recorded at near-normal incidence. From the dispersion analysis performed on the spectra recorded from the ac crystal plane, mode parameters: transversal frequency, oscillator strength, attenuation constant and the orientation of the transition moment were determined. The polarized spectrum along the b crystallographic axis was also recorded and a dispersion analysis performed. Comparison between the spectroscopically obtained transition moment directions with those obtained from the structure data for various modes is discussed. All dielectric tensor component values were obtained for the whole mid-IR frequency range. Also, the real and the imaginary parts of the complex indexes of refraction for the waves with wave vector in the direction of the b crystallographic axis and in the ac plane (when the direction of the electric vector is oriented along the b axis) were found as functions of frequency. [Copyright &y& Elsevier]

Abstract: If two overlapping bands originate from transition moments that are perpendicular and lie along the principal axes of the infinity frequency dielectric tensor, an isosbestic-like point (ILP) appears in the overlaid polarized IR reflectance spectra of single crystals. These conditions can also be met in principle in case of the reflectance from the ac-plane of a monoclinic crystal despite of the crystal''s low symmetry. In order to determine the transition moment directions, diagonalization of the infinity frequency dielectric tensor should be performed. It is shown that a critical magnitude for the appearance of ILP is the angle of incidence. An increase of this angle leads to a transformation of the ILP to an isosbestic-like region, which eventually vanishes at higher incidence angles. Polarized reflectance spectra of gypsum (CaSO4·2H2O), recorded from the ac crystal face, were used to verify the theoretical results. [Copyright &y& Elsevier]

Abstract: A new kind of orientation representation called symmetric Euler orientation representation (SEOR) is presented. It is based on a combination of the conventional Euler orientation representations (Euler angles) and Hamilton''s quaternions. The properties of the SEORs concerning orientational averaging are explored and compared to those of averaging schemes that are based on conventional Euler orientation representations. To that aim, the reflectance of a hypothetical polycrystalline material with orthorhombic crystal symmetry was calculated. The calculation was carried out according to the average refractive index theory (ARIT [T.G. Mayerhöfer, Appl. Spectrosc. 56 (2002) 1194]). It is shown that the use of averaging schemes based on conventional Euler orientation representations leads to a dependence of the result from the specific Euler orientation representation that was utilized and from the initial position of the crystal. The latter problem can be overcome partly by the introduction of a weighing factor, but only for two-axes-type Euler orientation representations. In case of a numerical evaluation of the average, a residual difference remains also if a two-axes type Euler orientation representation is used despite of the utilization of a weighing factor. In contrast, this problem does not occur if a symmetric Euler orientation representation is used as a matter of principle, while the result of the averaging for both types of orientation representations converges with increasing number of orientations considered in the numerical evaluation. Additionally, the use of a weighing factor and/or non-equally spaced steps in the numerical evaluation of the average is not necessary. The symmetrical Euler orientation representations are therefore ideally suited for the use in orientational averaging procedures. [Copyright &y& Elsevier]

• Overview of the use of infrared spectroscopy for point-of-care applications. • Recent technological and scientific developments. • Easy to read and tailored for readers less familiar with infrared spectroscopy. In this contribution we review selected point-of-care applications of infrared spectroscopy and the technological innovations they are based on. After a short introduction summarizing the general idea behind point-of-care applications we introduce the reader to important infrared spectroscopy sensing principles on a very basic level. We discuss the role of optical components like quantum cascade lasers, supercontinuum sources, waveguides and how they are potentially going to revolutionize point-of-care applications. First, we focus on the technological solutions of some principal problems like increasing the pathlength in a transmission cell to enhance the sensitivity for solutes in aqueous solutions and discuss indirect methods which circumvent the problem of low transmittance. In the second part we show how the technological progress of the last decades enabled scientific progress leading to selected concrete and outstanding point-of-care solutions and applications based on infrared spectroscopy. These include the detection and quantification of malaria parasitemia, early recognition of Alzheimer's disease long before the onset of clinical symptoms and a non-invasive method for testing the blood glucose content. The selected examples demonstrate and showcase that infrared spectroscopy is on the way to become an indispensable technique for point-of-care applications. [ABSTRACT FROM AUTHOR]

Abstract With generalized dispersion analysis it is possible to gain the dispersion parameters and dielectric tensor function of crystals with not only unknown orientation of the symmetry elements in within the sample but with also unknown crystal symmetry. The developed procedure is applied to two spectra sets of each crystal symmetry type to cover various levels of difficulty in the evaluation with generalized dispersion analysis. Graphical Abstract Unlabelled Image Highlights • Dielectric tensor function of a crystal is gained by dispersion analysis. • A priori knowledge of crystal symmetry and orientation not necessary any more • New evaluation scheme of a set of reflection spectra gives dielectric tensor function. • Crystal symmetry, orientation and oscillator parameters gained as by-product during evaluation [ABSTRACT FROM AUTHOR]

Abstract A single crystal of monoclinic sodium dichromate dihydrate was investigated by FTIR-spectroscopy in the spectral region of 4000–80 cm−1. On the measured reflection spectra dispersion analysis was performed to gain the oscillator parameters of the transition dipole moments of Na 2 Cr 2 O 7 ·2H 2 O and by that the dielectric tensor function. The gained oscillator parameters were verified by forward-calculation of spectra using different crystal faces. Graphical Abstract Unlabelled Image Highlights • Full dispersion analysis of Na 2 Cr 2 O 7 ·2H 2 O for the MIR and FIR spectral region • Complement information to the dichromate ion in addition to K 2 Cr 2 O 7 , Cs 2 Cr 2 O 7 and Rb 2 Cr 2 O 7 • Dispersion parameters confirmed by forward-calculation of spectra of different faces [ABSTRACT FROM AUTHOR]

Abstract We present the first complete dispersion analysis of the organic ethylenediamine- d -tartrate (EDDt) in single crystal form in the spectral range of 5000–100 cm−1. The obtained oscillator parameters were used to generate the polarized and the cross-polarized spectra of randomly oriented polycrystalline EDDt. The comparison of the generated with the experimental spectra confirms the value of obtained oscillator parameters and dielectric tensor function. Graphical Abstract Unlabelled Image Highlights • Only three correct dispersion analyses of organic monoclinic crystals exist by now. • First complete dispersion analysis of monoclinic organic EDDt single crystal • Verification of oscillator parameters with spectrum of polycrystalline sample [ABSTRACT FROM AUTHOR]

Dispersion analysis is applicable to arbitrarily cut monoclinic crystals of unknown orientation in order to find the symmetry axis. By this it is possible to differentiate between the transition moments oriented parallel and normal to the b -axis and to determine the dielectric tensor functions of those two principal directions. Dispersion analysis of arbitrarily cut monoclinic crystals is based on an extension of the evaluation scheme developed for arbitrarily cut orthorhombic crystals. We present dispersion analysis of monoclinic crystals exemplarily on spodumene (LiAl(SiO 3 ) 2 ) and yttrium orthosilicate (Y 2 SiO 5 ). [ABSTRACT FROM AUTHOR]

We developed a measurement and evaluation scheme to perform dispersion analysis on arbitrarily cut orthorhombic crystals based on the schemes developed for triclinic and uniaxial crystals. As byproduct of dispersion analysis the orientations of the crystal axes are found. In contrast to the spectra of arbitrarily cut uniaxial crystals, where the fit routine has to separate two independent principal spectra, the spectra of arbitrarily cut orthorhombic crystals are a combination of three independent spectra and the evaluation scheme gets more complex. Dispersion analysis is exemplary performed on two different crystals, which show different spectral features and different levels of difficulties to evaluate. Neodymium gallate (NdGaO 3 ) has broad overlapping reflections bands while topaz (Al 2 SiO 4 [F, OH] 2 ) has a quite high total number of infrared active bands. [ABSTRACT FROM AUTHOR]

[Display omitted] • New method for thin-film investigation using IR-reflectance spectra was developed. • Correlation between IR ratio-reflectance spectra and film structure was proposed. • Properties of organo-silane films on glass discussed using ratio-reflectance spectra. • IR ratio-reflectance spectra correlation with morphology of the coating proposed. In case of thin films of siloxane obtained from different organo-silane derivatives (alkoxy and chloro) on soda lime silica glass substrates, IR-ATR and IR-SR could not detect the organic functional groups of the coating. This becomes even more problematic for the case of tetraethoxysilane (when fully hydrolyzed), the coating of which possesses the same functional groups as the glass substrate. In this work we propose to employ the so-called ratio-reflectance spectra in the v(Si-O) wavenumber region, where both glass and the siloxane coating give most prominent bands, important for the evaluation of the quality of coating formation and qualitative knowledge on its structure. We show that the reflectance-absorbance spectra obtained from the ratio-reflectance spectra are in direct connection to the structure of the siloxane network which depends not only on the chemical nature of the parent silane, but also on the dipping time and the solvent composition. Some characteristics of the reflectance-absorbance spectra, like the appearance of a two well defined bands at 1110 and 975 cm−1, can be correlated to the film morphology and bridging oxygen number. We support our conclusions using principal component analysis of reflectance spectra, contact angle, AFM and SEM measurements. [ABSTRACT FROM AUTHOR]

We present a dispersion analysis of the orthorhombic peptide single crystal Z -Aib-Aib-Aib-L-Ala-OtBu (N-benzyloxycarbonyl-α-aminoisobutyryl-α-aminoisobutyryl-α-aminoisobutyryl-L-alanine tert-butyl ester, C 27 H 42 N 4 O 7), where Z is benzyloxycarbonyl and OtBu is the tert-butylester) in the MIR spectral region by means of adapted generalized dispersion analysis, employing the naturally grown crystal faces. Based on the results we identify the orientation of the crystal axes a , b , c within the sample, and supported by a stereographic projection of the crystal, we assign the individual axes. The gained dielectric tensor function and the oscillator parameters were confirmed by forward calculation of reflection spectra of different orientations. The orientation of the crystal axes was verified by a second stereographic projection with another crystal face in the center. Unlabelled Image • First dispersion analysis of a peptide crystal. • Determination of the orientation of the molecule helices in the crystal. • Dispersion parameters confirmed by forward-calculation of different faces. • Orientation of the crystal axes and molecule helices confirmed by stereographic projection. [ABSTRACT FROM AUTHOR]