ASTM E573-01(2007)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation:E573 −01(Reapproved2007)
Standard Practices for
Internal Reflection Spectroscopy
This standard is issued under the fixed designation E573; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 5. Theory
1.1 These practices provide general recommendations cov- 5.1 In his studies of total reflection at the interface between
ering the various techniques commonly used in obtaining two media of different refractive indices, Newton (1) discov-
2,3
ered that light extends into the rarer medium beyond the
internal reflection spectra. Discussion is limited to the
infrared region of the electromagnetic spectrum and includes a reflecting surface (see Fig. 1). In internal reflection
spectroscopy, IRS, this phenomenon is applied to obtain
summary of fundamental theory, a description of parameters
that determine the results obtained, instrumentation most absorptionspectrabymeasuringtheinteractionofthepenetrat-
ingradiationwithanexternalmedium,whichwillbecalledthe
widely used, practical guidelines for sampling and obtaining
useful spectra, and interpretation features specific for internal sample (2,3). Theoretical explanation for the interaction
mechanisms for both absorbing and nonabsorbing samples is
reflection.
provided by Snell’s law, the Fresnel equations (4), and the
Maxwell relationships (5).
2. Referenced Documents
2.1 ASTM Standards: NOTE 1—To provide a basic understanding of internal reflection
phenomena applied to spectroscopy, a brief description of the theory
E131Terminology Relating to Molecular Spectroscopy
appears in Appendix X2. For a detailed theoretical discussion of the
E168Practices for General Techniques of Infrared Quanti-
subject, see (4).
tative Analysis
E284Terminology of Appearance
6. Parameters of Reflectance Measurements
6.1 Practical application of IRS depends on many precisely
3. Terminology
controlled variables. Since an understanding of these variables
3.1 Definitions of Terms and Symbols—For definitions of
isnecessaryforproperutilizationofthetechnique,descriptions
termsandsymbols,refertoTerminologiesE131andE284,and
of essential parameters are presented.
to Appendix X1.
6.2 Angle of Incidence, θ—When θ is greater than the
criticalangle, θ ,totalinternalreflectionoccursattheinterface
c
4. Significance and Use
between the sample and the internal reflection element, IRE.
4.1 These practices provide general guidelines for the good
When θ is appreciably greater than θ , the reflection spectra
c
practice of internal reflection infrared spectroscopy.
most closely resemble transmission spectra. When θ is less
than θ , radiation is both refracted and internally reflected,
c
generally leading to spectral distortions. θ should be selected
far enough away from the average critical angle of the
These practices are under the jurisdiction of ASTM Committee E13 on
sample—IRE combination that the change of θ through the
Molecular Spectroscopy and Separation Science and are the direct responsibility of
c
Subcommittee E13.03 on Infrared and Near Infrared Spectroscopy.
region of changing index (which is related to the presence of
Current edition approved March 1, 2007. Published March 2007. Originally
the absorption band of the sample) has a minimal effect on the
approved in 1976. Last previous edition approved in 2001 as E573–01. DOI:
shapeoftheinternalreflectionband.Increasing θdecreasesthe
10.1520/E0573-01R07.
Internal Reflection Spectroscopy, IRS, is the accepted nomenclature for the number of reflections, and reduces penetration. In practice,
technique described in these practices. Other terms are sometimes used which
there is some angular spread in a focused beam. For instru-
include: Attenuated Total Reflection, ATR; Frustrated Total Reflection, FTR;
ments that utilize f4.5 optics in the sample compartment, there
Multiple Internal Reflection, MIR; and other less commonly used terms. In older
is a beam spread of 6 5°, but the beam spread in the IRE is
literature, one may find references to Frustrated Total Internal Reflection, FTIR.
This should not be confused with Fourier Transform Infrared Spectroscopy FT-IR.
smaller because of its refractive index.The value will increase
Other terms sometimes used for referring to the internal reflection element are:
as lower f-number optics are utilized. This beam spread
ATR crystal, MIR plate, or sample plate.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
the ASTM website. these practices.
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E573−01(2007)
NOTE 1—The ray penetrates a fraction of a wavelength (d ) beyond the
p
reflecting surface into the rarer medium of refractive index n (the
sample), and there is a certain displacement (D) upon reflection. θ is the
angleofincidenceoftherayinthedensermedium,ofrefractiveindex, n ,
at the interface between the two media.
FIG. 1Schematic Representation of Path of a Ray of Light for
Total Internal Reflection
Solid Line—Refractive index of sample.
Dotted Line—Absorption band of sample.
produces a corresponding distribution of effective paths and
Dashed Lines—Refractive indices of reflector plates.
effective depth of penetrations.
FIG. 3 Refractive Index Versus Wavelength
6.3 Number of Reflections, N—N is an important factor in
determining the sensitivity of the IRE. Where multiple reflec-
tions are employed, internal reflection occurs a number of
band as a function of wavelength. When an IRE of index n is
A
times along the length of the IRE depending on its length, l,
selected,theremaybeapointatwhichtheindexofthesample
thickness, t, and on the angle of incidence, θ, of the radiant
is greater than that of the IRE.At this wavelength, there is no
beam.
θatwhichtotalinternalreflectioncantakeplace,andnearlyall
of the energy passes into the sample. The absorption band
NOTE 2—The length of an IRE is defined as the distance between the
resulting in this case will be broadened toward longer
centers of the entrance and exit apertures.
wavelengths, and hence appear distorted. When an IRE of
6.3.1 Absorption occurs with each reflection (see Fig. 2),
index n is selected, there is no point at which the index of the
B
giving rise to an absorption spectrum, the intensity of which
sample exceeds it. On the long wavelength side, however, the
depends on N. For single-pass IREs, N can be calculated using
refractive indexes approach each other. This results in an
the following relationship:
absorptionbandthatislessdistorted,butthatisstillbroadened
l
on the long wavelength side. With an IRE of index n,a
C
N 5 cotθ (1)
S D
t
considerably higher refractive index than that of the sample,
the index variation of the sample causes no obvious distortion
For double-pass IREs:
of the absorption band.
l
N 5 2 cotθ (2)
S D
6.5 Depth of Penetration, d —The distance into the rarer
p
t
medium at which the amplitude of the penetrating radiation
−1
Many single-pass IREs employ approximately 25 reflec-
falls to e of its value at the surface is a function of the
tions.
wavelength of the radiation, the refractive indexes of both the
IREandthesample,andtheangleofincidenceoftheradiation
NOTE3—NmustbeanoddintegerforIREsintheshapeofatrapezoid,
and an even integer for IREs in the shape of a parallelogram. at the interface.
6.5.1 The depth of penetration, d , can be calculated as
p
6.4 Relative Refractive Index, n , of the Sample, n , and
21 2
follows:
IRE, n;(n =n /n )—Refractive index matching controls the
1 21 2 1
spectral contrast. If the indexes of the sample and the IRE λ
d 5 (3)
p 2 2 ½
approacheachother,banddistortionscanoccur.Therefore,itis
2 π sin θ 2 n
~ !
necessary to select an IRE with a refractive index considerably
λ
greater than the mean index of the sample.
where: λ 5 5wavelengthofradiationintheIRE.
n
6.4.1 The refractive index of a material undergoes abrupt
The depth of penetration increases as the angle of incidence
changes in the region of an absorption band. Fig. 3 (6) shows
decreases, and becomes infinitely large as θ approaches the
thechangeinrefractiveindexofasampleacrossanabsorption
critical angle (see Figs. 4 and 5) (7).
6.6 Effective Path Length, d —The effective pathlength, or
e
relative effective thickness, d , for the beam for each reflection
e
is defined by Harrick (4) in detail, and is different for
'-polarized than for i-polarized radiation. For bulk materials,
when θ=45°, d = ⁄2 d ,andtheaverageeffectivethickness
e' ei
FIG. 2 Multiple Internal Reflection Effect isaboutequaltothepenetrationdepth, d .Forlargerangles, d
p e
E573−01(2007)
NOTE 1—Total effective pathlength versus angle of incidence for
polystyrene stain on silicon surface. The sharp drop with angle of
incidence is largely, although not entirely, due to decrease of N with θ.
NOTE 1—Fractional penetration depth of electromagnetic field in rarer
Points represent experimental measurements and solid curves are theo-
bulk medium for total internal reflection versus angle of incidence for a
retical calculations (4).
number of interfaces. The penetration depth is infinitely large at the
critical angle and is about one tenth the wavelength at grazing incidence
FIG. 6Total Effective Pathlength Versus Angle of Incidence
for relatively high index media. λ = λ/ n is the wavelength in the denser
1 1
medium.
N N
R 5 1 2 αd (5)
FIG. 4Relative Penetration Depth Versus Angle of Incidence ~ !
e
N
6.7.1 If αd << 1, R ≈1− N · α· d , that is, the reflection
e e
lossisincreasedbyafactorofN.Therelationshipsbetweenthe
absorption coefficient, α, and the absorptivity, a, are given by
Eq X2.13 and Eq X2.14.
6.8 Sampling Area—Whenmultiplereflectionsareused,the
sampling area is somewhat analogous to the pathlength in
transmission spectroscopy. The amount of absorption by a
sampleincontactwithamultiple-reflectionIREisproportional
totheareaofcontactwithinthesensitiveregion.Samplingarea
is proportional to 1/cos θ and increases with increasing θ.
FIG. 5 Variation of Penetration Depth with Wavelength of Radia-
6.8.1 The sensitive region of an IRE sampling face varies,
tion in Sample (7)
depending on the IRS system in which it is used. A small
regionortheentireareaofthesamplingfacescanbesensitive,
as seen for the dispersive systems shown in Fig. 7. It must be
is smaller than d and for smaller angles, d is larger than d .
p e p
emphasized that, in general, there is no relationship between
The total effective pathlength is equal to N times the effective
thesizeofthesensitivesamplingareaandtheopticalefficiency
pathlength, d .An example of the effect of θ on N· d is shown
e e
oftheIRSsystem,providedthattheslitheightofthedispersive
in Fig. 6.
spectrophotometer is filled. In fact, it is preferred that an IRE
6.7 Absorption Coeffıcient, α—As in transmission
spectroscopy, the absorptivity of a material affects the fraction
oftheincidentradiationthatisabsorbed,andhencethespectral
contrast. The internal reflectance of bulk materials and thin
films, for small abosrptivities, is as follows:
R 5 1 2 α d (4)
e
The reflectance for N reflections is: FIG. 7 Sensitive Sampling Areas of IRE Plates
E573−01(2007)
have insensitive edges so that gasket materials or sample
holders do not cause spectral interference. It is important that
samples be positioned so that they lie completely across the
width of the sensitive area. For accessories utilizing single-
reflection prisms and hemicylinders, the entire sample face
shouldbecovered.Ifthisareaisnotcompletelycoveredbythe
sample, radiation bypasses the sample and the effect will be
similar to a transmission cell with an air bubble in it. Knowing
(a)(b)
the sensitive sampling area on an IRE is important when the
sample is limited and it is desirable to place the sample on the
NOTE 1—(a) utilizes trapezoid IREs, and (b) utilizes parallelepiped
IREinthemostefficientmanner (8).Thesensitiveregionofan
IREs.
IRE sampling face may differ quite radically when used in an
FIG. 8Fixed-Angle Multiple-Reflection Internal Reflection Attach-
interferometer. The focused image is nearly circular and may ments
not fill the vertical dimension of the crystal but often will
the crystal. Very careful cleaning and sampling procedures
overfillthewidthoftheIREface.Thisresultsinvignettingand
(more than usual) are required here. Spectral verification of
introduces small wavenumber errors in Fourier Transform
IRE cleanliness is essential. Internal reflection equipment
spectroscopy. The problem of overfilling the entrance aperture
includes the following:
canbeminimizedbyutilizingbeamcondensingoptics,butthis
7.1.1 The IRAs designed to be placed into the sampling
will increase the angular spread of the incident rays.
compartment of a spectrophotometer. These are of the follow-
NOTE4—ItisrecommendedthatanIREwithaverticaldimensiononly
ing types: (a) variable-angle single internal reflection; (b)
slightly larger than the focused beam diameter be used. This ensures that
fixed-angle multiple internal reflection (θ usually set at 45°),
the sensitive area encompasses the full crystal face.
and (c) variable-angle multiple internal reflection (θ is either
6.9 Effıciency of Contact—In order to obtain an internal
continuously variable, usually between 30 and 60°, or a choice
reflection spectrum, it is necessary to bring the sample to a
of angles is preset by the manufacturer, usually at 30, 45, and
distance within the penetration depth, d . Physical contact of
p
60°. In order to have the θ that is specified on the attachment,
the sample with the IRE may be sufficient to obtain a
an IRE for that same θ must be used.) (d) platforms for
qualitative spectrum. However, if the exact contact conditions
supporting fixed-angle plates in a horizontal position, and (e)
are not reproduced, a source of error may result, particularly
IRAs for supporting prism IREs of various geometry.
wheninterpretationrequiresadirectcomparisonwithsimilarly
7.1.2 Goniometers—Goniometers are essential for absolute
obtainedspectra,orwhenquantitativemeasurementsaremade.
intensity measurements.
6.10 Electric Field Strength—Spectral contrast is affected
7.1.3 Horizontal ATR Attachments—Thisfamilyofaccesso-
bythestrengthoftheelectricfield,thatis,theamplitudeofthe
ries is based on single-pass IRE geo
...