# ASTM E573-01 (Reapproved 2013)

Designation: E573 − 01 (Reapproved 2013)Standard Practices forInternal Reflection Spectroscopy1This standard is issued under the fixed designation E573; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 These practices provide general recommendations cov-ering the various techniques commonly used in obtaininginternal reflection spectra.2,3Discussion is limited to theinfrared region of the electromagnetic spectrum and includes asummary of fundamental theory, a description of parametersthat determine the results obtained, instrumentation mostwidely used, practical guidelines for sampling and obtaininguseful spectra, and interpretation features specific for internalreflection.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.2. Referenced Documents2.1 ASTM Standards:4E131 Terminology Relating to Molecular SpectroscopyE168 Practices for General Techniques of Infrared Quanti-tative Analysis (Withdrawn 2015)5E284 Terminology of Appearance3. Terminology3.1 Definitions of Terms and Symbols—For definitions ofterms and symbols, refer to Terminologies E131 and E284, andto Appendix X1.4. Significance and Use4.1 These practices provide general guidelines for the goodpractice of internal reflection infrared spectroscopy.5. Theory5.1 In his studies of total reflection at the interface betweentwo media of different refractive indices, Newton (1)6discov-ered that light extends into the rarer medium beyond thereflecting surface (see Fig. 1). In internal reflectionspectroscopy, IRS, this phenomenon is applied to obtainabsorption spectra by measuring the interaction of the penetrat-ing radiation with an external medium, which will be called thesample (2,3). Theoretical explanation for the interactionmechanisms for both absorbing and nonabsorbing samples isprovided by Snell’s law, the Fresnel equations (4), and theMaxwell relationships (5).NOTE 1—To provide a basic understanding of internal reflectionphenomena applied to spectroscopy, a brief description of the theoryappears in Appendix X2. For a detailed theoretical discussion of thesubject, see (4).6. Parameters of Reflectance Measurements6.1 Practical application of IRS depends on many preciselycontrolled variables. Since an understanding of these variablesis necessary for proper utilization of the technique, descriptionsof essential parameters are presented.6.2 Angle of Incidence, θ—When θ is greater than thecritical angle, θc, total internal reflection occurs at the interfacebetween the sample and the internal reflection element, IRE.When θ is appreciably greater than θc, the reflection spectramost closely resemble transmission spectra. When θ is lessthan θc, radiation is both refracted and internally reflected,generally leading to spectral distortions. θ should be selectedfar enough away from the average critical angle of thesample—IRE combination that the change of θcthrough theregion of changing index (which is related to the presence ofthe absorption band of the sample) has a minimal effect on theshape of the internal reflection band. Increasing θ decreases thenumber of reflections, and reduces penetration. In practice,1These practices are under the jurisdiction of ASTM Committee E13 onMolecular Spectroscopy and Separation Science and are the direct responsibility ofSubcommittee E13.03 on Infrared and Near Infrared Spectroscopy.Current edition approved Jan. 1, 2013. Published January 2013. Originallyapproved in 1976. Last previous edition approved in 2007 as E573 – 01 (2007).DOI: 10.1520/E0573-01R13.2Internal Reflection Spectroscopy, IRS, is the accepted nomenclature for thetechnique described in these practices. Other terms are sometimes used whichinclude: Attenuated Total Reflection, ATR; Frustrated Total Reflection, FTR;Multiple Internal Reflection, MIR; and other less commonly used terms. In olderliterature, one may find references to Frustrated Total Internal Reflection, FTIR.This should not be confused with Fourier Transform Infrared Spectroscopy FT-IR.3Other terms sometimes used for referring to the internal reflection element are:ATR crystal, MIR plate, or sample plate.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.5The last approved version of this historical standard is referenced onwww.astm.org.6The boldface numbers in parentheses refer to the list of references at the end ofthese practices.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1there is some angular spread in a focused beam. For instru-ments that utilize f4.5 optics in the sample compartment, thereis a beam spread of 6 5°, but the beam spread in the IRE issmaller because of its refractive index. The value will increaseas lower f-number optics are utilized. This beam spreadproduces a corresponding distribution of effective paths andeffective depth of penetrations.6.3 Number of Reflections, N—N is an important factor indetermining the sensitivity of the IRE. Where multiple reflec-tions are employed, internal reflection occurs a number oftimes along the length of the IRE depending on its length, l,thickness, t, and on the angle of incidence, θ, of the radiantbeam.NOTE 2—The length of an IRE is defined as the distance between thecenters of the entrance and exit apertures.6.3.1 Absorption occurs with each reflection (see Fig. 2),giving rise to an absorption spectrum, the intensity of whichdepends on N. For single-pass IREs, N can be calculated usingthe following relationship:N 5SltDcotθ (1)For double-pass IREs:N 5 2SltDcotθ (2)Many single-pass IREs employ approximately 25 reflec-tions.NOTE 3—N must be an odd integer for IREs in the shape of a trapezoid,and an even integer for IREs in the shape of a parallelogram.6.4 Relative Refractive Index, n21, of the Sample, n2, andIRE, n1;(n21=n2/n1)—Refractive index matching controls thespectral contrast. If the indexes of the sample and the IREapproach each other, band distortions can occur. Therefore, it isnecessary to select an IRE with a refractive index considerablygreater than the mean index of the sample.6.4.1 The refractive index of a material undergoes abruptchanges in the region of an absorption band. Fig. 3 (6) showsthe change in refractive index of a sample across an absorptionband as a function of wavelength. When an IRE of index nAisselected, there may be a point at which the index of the sampleis greater than that of the IRE. At this wavelength, there is noθ at which total internal reflection can take place, and nearly allof the energy passes into the sample. The absorption bandresulting in this case will be broadened toward longerwavelengths, and hence appear distorted. When an IRE ofindex nBis selected, there is no point at which the index of thesample exceeds it. On the long wavelength side, however, therefractive indexes approach each other. This results in anabsorption band that is less distorted, but that is still broadenedon the long wavelength side. With an IRE of index nC,aconsiderably higher refractive index than that of the sample,the index variation of the sample causes no obvious distortionof the absorption band.6.5 Depth of Penetration, dp—The distance into the rarermedium at which the amplitude of the penetrating radiationfalls to e−1of its value at the surface is a function of thewavelength of the radiation, the refractive indexes of both theIRE and the sample, and the angle of incidence of the radiationat the interface.6.5.1 The depth of penetration, dp, can be calculated asfollows:dp5λ12 π~sin2θ 2 n212!½(3)where: λ15λn15wavelength of radiation in the IRE.The depth of penetration increases as the angle of incidencedecreases, and becomes infinitely large as θ approaches thecritical angle (see Figs. 4 and 5) (7).NOTE 1—The ray penetrates a fraction of a wavelength (dp) beyond thereflecting surface into the rarer medium of refractive index n2(thesample), and there is a certain displacement (D) upon reflection. θ is theangle of incidence of the ray in the denser medium, of refractive index, n1,at the interface between the two media.FIG. 1 Schematic Representation of Path of a Ray of Light forTotal Internal ReflectionFIG. 2 Multiple Internal Reflection EffectSolid Line—Refractive index of sample.Dotted Line—Absorption band of sample.Dashed Lines—Refractive indices of reflector plates.FIG. 3 Refractive Index Versus WavelengthE573 − 01 (2013)26.6 Effective Path Length, de—The effective pathlength, orrelative effective thickness, de, for the beam for each reflectionis defined by Harrick (4) in detail, and is different for -polarized than for i-polarized radiation. For bulk materials,when θ = 45°, de =1⁄2 dei, and the average effective thicknessis about equal to the penetration depth, dp. For larger angles, deis smaller than dpand for smaller angles, deis larger than dp.The total effective pathlength is equal to N times the effectivepathlength, de. An example of the effect of θ on N· deis shownin Fig. 6.6.7 Absorption Coeffıcient, α—As in transmissionspectroscopy, the absorptivity of a material affects the fractionof the incident radiation that is absorbed, and hence the spectralcontrast. The internal reflectance of bulk materials and thinfilms, for small abosrptivities, is as follows:R 5 1 2 α de(4)The reflectance for N reflections is:RN5~1 2 αde!N(5)6.7.1 If αdeθc. The Fresnel reflectionequations become:r 5cos θ 2 i ~ sin2θ 2 n212!½cos θ1i ~ sin2θ 2 n212!½(X2.8)ri5n212cosθ 2 i ~ sin2θ 2 n212!½n212cosθ1i ~ sin2θ 2 n212!½(X2.9)When n21is real (both media nonabsorbing), |r |=|ri|=1,and internal reflection is total for θc≤θ= 90°.7The Symbols provided in Appendix X1 are not to be considered standardnomenclature. These are under advisement by Subcommittee E13.04 on Nomen-clature and must be further approved by ASTM Committee E13 on MolecularSpectroscopy.FIG. X2.1 Refraction and Internal Reflection of Rays of LightNOTE 1—Reflectance versus angle of incidence for an interface betweenmedia with indices, n1= 4 and n2= 1.33, for light polarized perpendicular,R , and parallel, Ri, to plane of incidence for external reflection (solidlines) and internal reflection (dashed lines). θc, θB, and θpare the critical,Brewster’s, and principal angles, respectively.FIG. X2.2 Reflectance Versus Angle of IncidenceE573 − 01 (2013)14X2.2 Absorbing Rarer MediumX2.2.1 When the rarer medium is absorbing, its complexrefractive indexnˆ25 n2~11iκ2! (X2.10)replaces n2in the Fresnel Eq X2.8 and Eq X2.9 (Note X2.1).The attenuation index, κ, is related to the absorptioncoefficient, α, and the absorptivity, α, of the Bouguer-Beer lawby:nκ 5 αco/4πν (X2.11)P/Po5 e2ab5 102abc(X2.12)α 5 M·a·c (X2.13)Here, cois the velocity of light in vacuo, and ν its frequency.M is the natural logarithm of 10, M = 2.303; b is samplethickness, and c is the concentration of the absorbing species inthe sample.NOTE X2.1—The complex refractive index is written n2= n2+ iκ2byIUPAC, and κ2is called the absorption index.X2.2.2 Internal reflection is affected by an absorbing rarermedium as illustrated in Fig. X2.3. For radiation incidentbetween θ = 0 and θ≈θp, internal reflectance is ratherinsensitive to absorption coefficient, until it becomes verylarge. For angles of incidence greater than the critical angle,however, internal reflectance can be highly sensitive to theabsorption coefficient, and the parallel component of polariza-tion is more sensitive than the perpendicular.X2.3 Attenuated Total ReflectionX2.3.1 Maxwell’s equations predict the evanescent wavethat extends into the medium of lower refractive index, beyondthe reflecting interface. The frequency of this wave is that ofthe incident radiation, and its amplitude diminishes exponen-tially with distance from the interface. It is possible to couplewith this evanescent wave and extract energy from it, therebymaking the reflection less than total. The strength of thecoupling depends (in part) on the amplitude (electric fieldstrength) of the evanescent wave. Frustrated total reflectionoccurs when the coupled medium does not absorb the energy,but conducts it away from the interface. Attenuated totalreflection occurs when the coupled medium absorbs the energyextracted from the evanescent wave.X2.3.2 Attenuated total reflection is observed when theangle of incidence is maintained greater than the critical anglewhile wavelength is scanned across an absorption band. Theamount by which internal reflection is diminished from beingtotal, because of absorption of energy from the evanescentwave, that is, the reflectance loss per reflection, is the absorp-tion parameter, a:a 5 1 2 R (X2.14)The absorption parameter is greater near the critical anglethan at larger angles, and is also greater for i-polarization thanfor -polarization.X2.3.3 The relationship between attenuated internal reflec-tance and the absorption coefficient of Beer’s law can beexpressed in simplified form if absorption is small, forexample, αb 0.1. Then Beer’s law can be approximated by:P/Po 1 2 αb (X2.15)where αb is the fraction absorbed for transmission through asample of thickness, b. The corresponding quantity for internalreflection is the absorption parameter, so that the internalreflectance of a single reflection can be expressed by:R 5 1 2 a 5 1 2 αde(X2.16)Here deis an effective pathlength, or effective thickness of athin film, and is defined by:de5 a/α (X2.17)NOTE 1—Internal reflectance at an interface versus angle of incidence atλ = 0.4 µm for n21= 0.333 and various values of absorption coefficientα2. Note that the curves tend to resemble those for external reflection whenα2becomes high.FIG. X2.3 Internal Reflectance at an Interface Versus Angle ofIncidenceE573 − 01 (2013)15X3. INTERNAL REFLECTION ELEMENTSX3.1 Various transparent optical elements used in internalreflection spectroscopy for establishing the conditionnecessaryto obtain the internal reflection spectra of materials are shownin Fig. X3.1.REFERENCES(1) Newton, Opticks II, Book 8, 1917 p. 97.(2) Fahrenfort, J., “Attenuated Total Reflectance—A New Principle forProduction of Useful Spectra of Organic Compounds,” MolecularSpectroscopy, 1962, p. 701.(3) Harrick, N. J., Discussion of December 1959, p. B.D.-4, followingpaper presented by Eischens, R. P., “Infrared Methods Applied toSurface Phenomena in Semiconductor Surfaces,” (Proceedings ofSecond Conference), Pergamon Press, London, 1960, p. 56.(4) Mirabella, F. M., and Harrick, N. J., Internal Reflection SpectroscopyReview and Supplement, Harrick Scientific Corp., Ossining, NY,1985.(5) Born, M