ISSN 0030400X, Optics and Spectroscopy, 2009, Vol. 107, No. 5, pp. 754–767. © Pleiades Publishing, Ltd., 2009. Original Russian Text © V.M. Zolotarev, 2009, published in Optika i Spektroskopiya, 2009, Vol. 107, No. 5, pp. 794–807.

PHYSICAL OPTICS

Study of Quartz Glass by Differential Fourier Transform IR Reflection Spectroscopy: Bulk and Surface Properties V. M. Zolotarev St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101 Russia email: [email protected] Received May 26, 2009

Abstract—The optical characteristics of quartz glass are studied in the bulk and on the surface by the method of differential Fourier transform IR reflection spectroscopy. Tabular values of the optical constants that char acterize the bulk properties of quartz glass in the range 3.5–2000 μm are obtained. Particular features of the dielectric function are estimated, which make it possible to describe the properties of the surface of polished quartz glass in the IR range. PACS numbers: 42.72.Ai DOI: 10.1134/S0030400X09110113

INTRODUCTION Rayleigh was the first who noticed that the optical properties of polished surface of quartz glass differ from the bulk properties of this material [1]. Later, mechanisms of the formation of physicochemical properties of surface layers formed upon polishing of glass have been actively studied by Grebenshchikov [2] and his students [3–9], as well as by foreign research ers [10–14]. Various aspects of the physicochemical process of polishing glass obtained from studies by predominantly traditional visible optical microscopy methods were actively discussed in a number of meet ings [4–8]. These discussions were generalized in review [9], were it was concluded that three main fac tors, mechanical, chemical, and physicochemical, are important for the polishing process. In [1–10], it was shown that, under the action of these factors, a film of hydrolyzed silica 50–1200 Å thick is formed on a pol ished glass surface. At present, new tasks that face hightech fields, such as microelectronics, optoelec tronics, and fiber optics, increased the importance of surface studies. The creation of modern planar ele ments has raised the standards in surface characteris tics. In particular, in handbook [15], attention is paid to the importance of studying these questions as applied to quartz glass. The objective of this work is to study factors that affect the reflection coefficient in the range of funda mental IR bands and, using this information, to obtain optical constants of quartz glass that describe its prop erties in the bulk and surface layers. The effect of surface layers of quartz glass in the IR range has not been taken into account for a long time [15–19]; since their thickness is small, it was assumed that they only insignificantly affect the reflection coef

ficient R. To take into account the effect of surface lay ers on the measurement results of the optical constants of quartz glass in the IR range, in [20–24], in terms of the technique of attenuated total reflection (ATR), theoretical and experimental methods were developed that make it possible to separate the characteristics of the bulk and surface layers. The effects of adsorption water and hydrocarbon films, as well as technological surface layers, on the reflection spectra of various glasses were also estimated in terms of the external reflection method [15, 25]. In particular, the authors of [25] studied the effect of technological peculiarities of polishing on R in the range of maxima of the funda mental IR bands of relatively soft borate and phos phate glasses near 1100 and 450 cm–1. For different polishing regimes, R of different glasses was varied within ΔR = 5–7%, which led to errors in n and κ to 10–15%. These results show that the optical constants obtained without taking into account surface layers have systematic errors. In other words, these data are of an effective character, since they are averaged values of n and κ, whose values depend on the properties of the substrate and surface layers, as well as on the method of measurements. Indeed, an analysis of the data on the optical con stants of more hard quartz glass published in [15–19, 25, 26] shows that the real and, especially, imaginary part of the complex refractive index ( n = n – iκ) sys tematically differ in value (Fig. 1). Since the values of R were determined by the methods of external reflec tion [15–19, 26] and ATR [16, 20–24], and the data were processed predominantly by the Kramers–Kro nig method, this makes it possible to single out a com mon reason for the differences between collated values of n and κ. It seems that the reason for this lies in the

754

STUDY OF QUARTZ GLASS

755

κ 3

A

B

2 1 2 3 1

4

A B

5 6 7

0 1300

1200

1100

1000

900 ν, cm−1

Fig. 1. The absorption index κ of quartz glass; the band at 1100 cm–1. References: (1) [15], (2) [18], (3) [23], (4) [24], (5) [26], (6) [17], and (7) [16].

particular features of the physicochemical structure of the surface of samples, which depends on particular features of the technology of polishing. Figure 1 shows that the spectrum of κ varies systematically, which manifests itself in a shift of the center of the absorption band at 1122 cm–1 and the continuous deformation of the wings of the band contour. For clarity, these differ ences in the wings of the 1122 cm–1 band are shown scaledup in the ordinate on the left and top right. In the literature, the errors Δn and Δκ are com monly assumed to be caused mainly by the mathemat ical processing of the reflection spectra of R with the Kramers–Kronig method [15, 19]. It was noted in these works that Δn and Δκ strongly depend on the application conditions of this method (peculiarities of extrapolation, integration range, procedures by which parts of the spectrum beyond the measurement range are taken into account, etc.). The highest relative error Δκ upon processing the spectra of R by the Kramers– Kronig method is obtained for the absorption coeffi cient κ ≤ 0.5; therefore, in this range, κ is determined by the transmission method. However, the measure ment of κ ≈ 0.1 by the transmission method is also dif ficult, since it requires the preparation of thin samples of different thicknesses and makes it possible to calcu late only the imaginary part of the complex refractive index. These particular features of the two basic exper OPTICS AND SPECTROSCOPY

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imental methods led to the situation that the reference data obtained by these methods for quartz glass in the range 2.5–7 μm are available in the literature as sepa rate tables for the refractive index n and absorption coefficient κ [15]. Significant variations in the data on n and κ presented in [15–19] were also noted in [26, 27], where reasons for the reduced determination accuracy of these quantities were analyzed. In view of the above discussion, further investigations aimed at increasing the measurement accuracy of the charac teristics of quartz glass in the mid IR range are neces sary [15]. Therefore, it becomes evident from the abovesaid that, along with the determination errors of n and κ, which are related to the methods of mathematical pro cessing of IR spectrum of R, it is necessary to analyze errors that arise because of the occurrence of surface layers. Traditionally, these differences for samples in the strong absorption range are attributed to peculiar ities of the structure of the surface, related to the pro cessing technology of samples, since the measured reflection spectra in the range of fundamental vibra tional bands are significantly affected by the properties of thin surface layers [28]. However, in practice, it is difficult to take into account the effect of surface layers because of the fact that the physicochemical proper

756

ZOLOTAREV ΔR 0.1 R 0.8 0

3 5 6

0.6

−0.1

0.4

−0.2 1300

1200 1100 ν, сm−1

0.2

0 1300

1200

1100

1000

1000 1 2 3 4 5 6 7

900 ν, сm−1

Fig. 2. The external reflection coefficient R of quartz glass; the band at 1122 cm–1. Calculation: (1) [15], (2) [18], (3) [23], (4) [24], (5) [26], (6) [17], and (7) [16]. At the top right, the differential spectra of ΔR. As R0, the data from [24] for a cleavage are used; curves 3, 5, and 6 refer to the references indicated above.

ties and thickness of layers formed during polishing are affected by many technological factors. To analyze in detail the results of [15–19, 23, 26], it is convenient to transform the values of n and κ pre sented in these works into the data of primary mea surements of the reflection coefficient R (for the angle of incidence near the normal), which can be done with the help of the Fresnel equations. It is noted in the lit erature that the spread of values of R in the IR bands 1122 cm–1 of fused quartz is in the range 60–80%, which considerably exceeds random measurement errors of R. It can be seen from Fig. 2 that the calcu lated curves of R correlate with the corresponding curves of κ (Fig. 1). Therefore, the largest differences in the shape of the R and κ bands are observed not only at the maximum 1122 cm–1, but also on the wings in the vicinity of 1000 and 1250 cm–1. The differences in the values of R in the range of 1250 cm–1 calculated based on n and κ obtained by the ATR method at graz ing angles of incidence are the most noticeable [23, 24]. It should be noted that, in [15–26], quartz glasses of different types were studied, and, although no noticeable spectral differences were observed for the mid IR range, nevertheless, these differences can be revealed upon an increase in the measurement sensi tivity, especially because the values of κ in the range 0.2–3.4 μm for the glasses of the type Sh (KI grade) and type III (KU1 grade) are substantially different [29–31]. In recent work [32], the range of 2–7 μm was

analyzed for glasses of types I and III by the dispersion method, and it was also noted that the number and shape of overtone bands of these objects in this range are different. The total systematic determination error of n and κ for the bulk of quartz glass in the midIR range can conventionally be divided into the four following com ponents: (i) instrumental errors (angular, aperture, polarization, photometric); (ii) methodical errors related to the particular method of calculation of n and κ (for example, the Fresnel or Kramers–Kronig [15] methods); (iii) errors related to the influence of the surface processing technology on the spectrum of R, since the effect of surface layers is not commonly taken into account in calculations; and (iv) errors related to the differences in the bulk properties of quartz glasses of different types obtained using strongly different technologies [30, 31]. The latter two groups can only conventionally be related to measurement errors. Fur thermore it is assumed that they, as a rule, make a rel atively small contribution into the measured value of R. In certain variants of the reflection method, the effect of the absorbing surface layer on the reflection coefficient of the absorbing substrate can be estimated analytically. These solutions were obtained for the ATR method, whereas, in the case of external reflec tion, one is more frequently forced to use numerical methods. OPTICS AND SPECTROSCOPY

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THIN ABSORBING FILM ON THE ABSORBING SUBSTRATE For the ATR method, the direct solution of the problem of finding the effect of a thin absorbing sur face layer on the absorbing substrate in the case of s polarized radiation has the form [33] 4n 21 d cos θ A s = 1 – R s ≈ α 2   2 1 – n 31

(1)

n 31 λ 1 cos θ + α 3   , 2 2 1/2 2 π ( 1 – n 31 ) ( sin θ – n 31 )

where Аs is the attenuation of the reflected beam caused by the absorption of the radiation in the surface layer and substrate, α2 = 4πκ2/λ, α3 = 4πκ3/λ, d  λ is the thickness of the surface layer, n21 = n2/n1, n31 = n3/n1, λ1 = λ/n1, and θ is the angle of incidence. The indices j = 1, 2, and 3 denote the medium transmitted by the beam, i.e., the ATR prism, the film (surface layer), and the substrate, respectively. It follows from Eq. (1) that, to obtain more contrast spectra of the sur face layer, it is necessary to choose large values of n1. The solution to the inverse problem related to the determination of the parameters α2 and d of the surface layer with the help of the ATR method in terms of the theory of small perturbations was given in [20–22]. In 2 this case, for the system 1(ε1 = n 1 )–2(surface layer, ε 2 )–3(substrate, ε 3 ), assuming that the thickness of the surface layer d  λ, the dielectric permittivity of this layer can be represented as ε 2 ( z ) = ε 3 + Δε ( z ),

(2)

where ε3 = ε 3' – iε 3'' is the dielectric permittivity of the substrate, Δε(z) is the deviation from the ε 3 (z) at the interface between the two media, and z is the coordi nate that is counted from the interface between media 1 and 2 in the direction of the second medium (the sur face layer). For several typical forms of the function Δε (z) (constant, linear, and exponential), a solution was obtained in terms of the ATR method, which makes it possible to find ε 2' , ε 2'' , and d, from three measurements of R under the condition that ε 3' and ε 3'' should be known or be determined from indepen dent measurements. The effect of the surface layer on the reflection coef ficient R near the normal angle of incidence (θ = 0) has a more complex character compared to that in the case of the ATR method, since ε 3' changes its sign in the frequency interval of strong bands because of an anomalous dispersion and, in the vicinity of this change, R depends on ε 2'' in a complex way. Therefore, in the general case, particular features of the spectrum OPTICS AND SPECTROSCOPY

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of an absorbing film on an absorbing substrate is numerically analyzed. However, these peculiarities can be qualitatively analyzed using Eq. (2), from 2 2 which it follows that, when ε 3' = ( n 3 – κ 3 ) < 0, a so called metal reflection is observed. For this substrate, a surface layer with positive Δε' manifests itself as an increase in the effective value of ε 3' . For this case, this increase is related to the inequality ε 2' > ε 3' , which results in a decrease in R. The reflection attenuation A = 1 – R for the s polarization is linear in a rather large range of variations of d ε 2'' = 2n2κ2d. Thus, for example, thin organic films on metal substrates behave. In this case, the shape of bands resembles ordinary absorption spectra; therefore, these spectra are frequently called the “reflection–absorption” spectra [33–36]. 2

2

When ε 3' = ( n 3 – κ 3 )  0, the presence of a surface layer leads to an increase in the selective reflection in the absorption band (for κ2  κ3) due to the addition Δε''. This differently directed behavior of R in the spectrum of external reflection is observed in the vicinity of fundamental vibrational absorption bands of dielectrics because of an anomalous dispersion. Figure 3 compares the ATR and external reflection spectra of a thin absorbing film under the conditions ε 3'  0 and ε 3'  0 and with the properties of the film being modeled with the help of two pairs of oscillators whose amplitudes are approximately equal to 2n2κ2. The frequencies of the first pair of oscillators are 950 and 1050 cm–1, and their substrate satisfies the condi tion ε 3'  0, while the frequencies of the second pair are 1150 and 1250 cm–1, and, for their substrate, ε 3' < 0. The chosen values of ε 3' correspond to typical values of ε 3' (υ) on the left and on the right from the center of the band 1122 cm–1 of fused quartz. It can be seen from this figure that the ATR spectra for these two cases are similar to each other; i.e., the frequencies in the ATR spectrum coincide with the frequencies of the maxima of ε 2'' , and the intensities of the bands are pro portional to ε 2'' . The cases under comparison differ only in the band intensities. For the external reflection spectra, these differences are cardinal; namely, for the substrate with ε 3' < 0, the minimum in both the R and in ATR spectrum corresponds to every maximum in the spectrum of ε 2'' = 2n2κ2. In contrast, when ε 3' > 0, the maxima in ε 2'' = 2n2κ2 correspond to maxima in the spectrum of R, and their contrast is noticeably lower than in the ATR spectrum. Modeling in the in the transition range, where 0 ≥ ε 3' ≥ 0, shows that the shape of the R spectrum strongly depends on particular val

758

ZOLOTAREV ε'' = 2nk

Rs 1.0

20 3 16

12 ~ ~

0.5 1

1.5

2

1.0 0.5 0 1400

1300

1200

1100

n = 0.4−i0.6

1000

900

ν,

cm−1

0 800

n = 2.0−i0.6

Fig. 3. ATR and external reflection spectra for a thin film (d  λ) on an absorbing substrate. The properties of the film are modeled by a system of two pairs of oscillators; the values of the imaginary part of the dielectric permittivity of the film, ε 2'' = 2n2κ2, are given on the left ordinate. The properties of the substrate for each pair of oscillators are listed below the abscissa axis. The reflec tion properties of the substrate n3 = 0.4–i0.6 and n3 = 2.0–i0.06 are characteristic of metals and dielectrics, respectively.

ues of ε 3 . Therefore, to study the surface layer based on external reflection spectra, as well as in the case of ATR, it is necessary to have reliable data for ε 3 . DIFFERENTIAL REFLECTION SPECTROSCOPY Since ultrathin films weakly affect the external reflection spectrum of R, to analyze the surface layer, a specialized experimental method and highprecision equipment are needed. For this reason, until now, it was difficult to study the effects of technological fac tors on the optical properties of quartz glass because of instrumental limitations of classical dispersion spec trophotometers with an analog output. The appearance of modern IR Fouriertransform spectrophotometers with a digital output, high wave number and photometric reproducibilities, and a high signaltonoise ratio makes it possible to increase the measurement sensitivity of small changes in the reflec tion coefficient. In turn, these instrumental possibili ties allow one to study the optical properties of quartz glass on a new basis and refine available values of the

optical constants, characterizing the bulk properties of this material. It is convenient to study thin surface layers by dif ferential reflection spectroscopy [35–37], where the results of measurements are frequently represented as a difference between the external reflection coeffi cients R of an object under study and of a reference sample (standard) R0, ΔR = R – R0,

(3)

where R0 is determined experimentally or is taken from the literature. In essence, this method is analo gous to the difference method, where the ratio of ΔR and R0 is compared. This method can be easily used on classical dispersion spectrophotometers, where the measured signal A is the ratio R – R0 A = . R0

(4)

The differential method is traditionally used in studies of the effect of external physical fields (thermal, elec tromagnetic, etc.) on the object [36]. In experiments on modern IR Fouriertransform spectrophotome OPTICS AND SPECTROSCOPY

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ters, results can be represented in any form, since the output signal is digital. If thin layers formed during polishing are studied by the method of differential reflection spectroscopy, one can use as a reference sample the data for R0 obtained for polished samples whose surface layers are defi nitely thinner than those of objects under investigation or use the data for cleavages [24]. Since R and R0 of ultrathin films are close to each other under external reflection conditions, the representation of the mea surements results in the form of the difference ΔR makes it possible to achieve a higher contrast, which simplifies the analysis is small deviations of R from R0. As an example, Fig. 2 shows the ordinary spectra of the reflection coefficient R of a polished surface of quartz glass for the 1122 cm–1 band that were calculated from the data on n and κ from different authors [15–19, 23–26] and (at the top right) the differential spectra of ΔR. As a reference sample R0, the data of [24] for a cleavage of quartz glass of the KI grade were used. It is seen from this figure that the spectrum of ΔR is somewhat more contrasting than that of R. It is signif icant that the character of the spectral dependence of ΔR for the data of [15–19, 23, 24] hardly varies at all, except for the data of [25]. This is related to the fact that, in this case, the surface of quartz glass was pol ished according to socalled “dry” technology, where water in a polishing emulsion was replaced by ethylene glycol [25], which, as can be judged from the spectrum in Fig. 2, changed the properties of the surface layer and decreased its thickness. The structural and chem ical interpretation of extrema in the spectrum of ΔR requires a more thorough analysis of the spectrum of R, which takes into account the effect of the dielectric characteristics of surface layers and substrate. To reduce the errors in the systematic determination of the reflection coefficients of the object (R) and stan dard (R0) for different experimental conditions in dif ferent studies [15–19, 23, 24], we decided to perform these measurements in the course of a single experi ment. POLISHED SAMPLES AND CLEAVAGES OF QUARTZ GLASS We studied samples of quartz glass KITM (type I), KVTM (type II), and KU1TM (type III). Glasses of type I are obtained by melting silica grist in a vacuum. These glasses do not have a band of water near 2.7 μm and, therefore, they are transparent in the near IR and UV ranges. TypeII glasses are obtained by melting grist of nat ural or synthetic quartz in a hydrogen–oxygen flame. Unlike typeI glasses, they exhibit a water absorption band at 2.7 μm; in addition, they absorb in the UV range. TypeIII glasses are highpurity hydroxylcontain ing media, which are obtained by hightemperature OPTICS AND SPECTROSCOPY

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hydrolysis of SiCl4 vapor in a hydrogen–oxygen flame. These glasses are transparent in the UV range; how ever, unlike typeI glasses, they have a band at 2.7 μm. Samples were polished using different technologi cal polishing regimes, including deep grinding–pol ishing. Water was used as an emulsion liquid. The obtained data for R were compared to external reflec tion measurements of cleavages, which were prepared from 25 × 50 × 5mm quartz glass plates applying a special technology where the cleavage plane was set by a notch made by a diamond cutter. Cleaving was per formed on a special setup where the pressure along the cleavage line was provided by a metal prism whose face was directed along the cleavage. This procedure made it possible to obtain flat, smooth cleavages with high reflection coefficients. Depending on the polishing regime (the type and size of a powder, the rate of a polisher, the pressure on the polisher, etc.), the values of R for the bands 1122/480 cm–1 for samples of typeI and III glasses were varied within the limits of 0.64–0.76/0.48–0.61. Deep grinding–polishing made it possible to achieve high reflection coefficients, whose values at the max ima of the bands 1122/480 cm–1 were 0.78/0.63, respectively (Fig. 4). Similar high reflection coeffi cients were also obtained for some samples of cleav ages. The highest values of R were obtained for sam ples whose reflection coefficient tended to zero at the minimum 1375 cm–1, which, as calculations showed, indicates that these samples do not have surface layers. It is significant that, for samples polished under stan dard regimes, the ratio ΔR/Δν, which characterizes the slope of R in the vicinity of the minimum at 1375 cm–1, was, as a rule, smaller than that of cleav ages or samples obtained with the help of deep grind ing–polishing deep (Fig. 5). Along with the value of R at the minimum at 1375 cm–1, the parameter ΔR/Δν significantly affects the results of calculation of ε 2'' = 2n2κ2 in the range 1400–2800 cm–1, where the main overtones and combination vibrations of the Si–O–Si bond are located. Since, at the minimum at 1375 cm–1, κ2  0.1 and n2 ≈ 1, then, for the air–medium inter 2

face, the equality n 1 ≈ ε 2' = n2 – κ2 holds true in this narrow frequency range. Taking this into account, the Fresnel formula for the normal incidence yields that ε 2'' ≈ 4 R . From this, by measuring R, ε 2'' can be determined. For cleavages of quartz glass, the reflec tion coefficient at the minimum at 1375 cm–1 was R = 0.00004 ± 0.000005, and the calculated value R = 0.000049 was obtained based on the tabular data for n and κ. The fact that the calculated and experimental values of R nearly coincide indicates that there is no appreciable surface layer at the air–cleavage interface. Corresponding values of R for polished samples of glasses were in the interval R = 0.00001–0.00008 (Fig. 5).

760

ZOLOTAREV R 0.8

0.6

R 0.60

A R 0.8 0.7

A 1 B

4

4

0.54

0.48

0.6 0.4

3

2

0.51

2 1120

1

0.57

3

1140

B

1100 ν, cm−1

490

480 470 ν, cm−1

0.2

0

10000

1000

100

ν, сm−1

Fig. 4. Reflection spectrum of quartz glass. The insets А and В show scaledup parts A and B of the spectrum for samples: (1) cleav age (KI), (2) KI, (3) KU1, and (4) KV. Curves 2 and 4 were obtained at standard polishing and curve 3, at deep grinding–pol ishing.

R 0.03 1 1

2

3

3

2 4

4

0.02 5 R 0.002

1 6

4 0.01 0.001

0 1420 0

2400

6

3

2

5

5

6

1380

ν, cm−1

1340 2000

1600

ν, сm−1

Fig. 5. External reflection spectra of quartz glass in the vicinity of the minimum at 1375 cm–1: (1) cleavage (KI); (2, 3) KU1 glass, and (4–6) KI glass. OPTICS AND SPECTROSCOPY

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EXPERIMENT External reflection in the range 14 × 103–450 cm–1 was measured with respect to an aluminum mirror on a PerkinElmer Spectrum100 IR Fouriertransform spectrophotometer using a VASR accessory; the angle of incidence was 10°. The internal reflection spectra were measured in the range of angles 30°–70° using an ATR3 accessory. The elements of the ATR had the configuration of an Abbe prism and were prepared from an IKS35 thermoplastic glass, which ensured a necessary optical contact of the ATR element and the object under study [24, 37]. In the range below 450 cm–1, the external reflection was measured on a Bruker VERTEX70 IR Fouriertransform spectro photometer. As a polarizer, we used a semitransparent KRS5 diffraction grating with 1200 grooves/mm. The spectra were recorded with a resolution of 1 and 4 cm–1. The signaltonoise ratio in the range of 1000 cm–1 was 140 000, which ensured the measurement sensitiv ity of R at a level of 0.00005. Upon the calculation of n and κ, the spectra of R were processed by the Kram ers–Kronig method using an OPUS standard software and compensating the atmosphere absorption, which was especially important for the range 1300–2800 cm–1. The phase angle of the reflected wave was calculated by the formula ∞

ν ln R ( ν ) ϕ ( ν 0 ) = – 0   dν, π ν2 – ν 2 0 0

∫

(5)

where ϕ(ν0) is the phase shift for the fixed frequency ν0, ν is the current frequency of the spectrum, ˆr (ν) = reiϕ(ν) is the amplitude reflection coefficient, and R = ˆr 2 is the reflection coefficient to be measured near the normal. Calculating the phase shift ϕ(ν0) by for mula (5) and, thus, determining the quantity ˆr (ν0), we can determine n and κ from the Fresnel formula for the normal angle of incidence, 1–R n =  , 1 + R – 2 R cos ϕ

(6)

– 2 R sin ϕ κ =  . 1 + R – 2 R cos ϕ

The quantity ϕ(ν0) was calculated in a wide frequency range of 1–5 × 105 cm–1 by the Kramers–Kronig method with allowance for the integration conditions (see Eq. (5)), which made it possible to take into account the effect of electronic transitions in the UV range and relaxation vibrations of quartz glass in the range below 20 cm–1. Extrapolations of R to the ranges υ ∞ and υ 0, necessary for these calculations, were performed taking into account the dielectric per mittivities ε∞ and ε0 for the UV and radiofrequency ranges, respectively [15, 38]. Then these data were OPTICS AND SPECTROSCOPY

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transformed into the spectra of R with the help of the equations of the classical dispersion analysis. The thus calculated spectra of R (on the left and right of the range of experimental values of R) were joined with the experimental data in the ranges above 104 and below 400 cm–1. After that, the spectra were extrapolated to the ends of the integration interval such that this inter val, due to the extrapolation performed, would cover the wings of electronic and relaxation absorption bands. All joinings of spectra for different samples and extrapolation were performed according to the same method. The values of κ ≤ 0.1 obtained by the Kramers– Kronig method in the range 1400–2800 cm–1 from the external reflection spectra were refined by the ATR method, which made it possible to obtain contrast spectra for this frequency range (Fig. 6). The ATR spectra were processed by the Fresnel formulas for one angle of incidence and two polarization states (s and p) [33]. To reduce the effect of surface layers, according to Eq. (1), the ATR spectra were obtained for an angle of incidence that somewhat exceeds the critical angle. The values κ  0.1 were refined by the transmission method (Т). To do this, the transmission spectra of thin plates with a thickness of 64, 100, 180, 510, and 760 μm were processed [37]. The values of κ were cal culated by formula (7), which made it possible to take into account multiple reflections under the condition of averaging interference fringes in the planeparallel plate with the thickness d as follows: 2

( 1 – R ) exp ( – αd ) T =  , 2 1 – R exp ( – 2αd )

(7)

where α = 4πκ/λ. The denominator in this expression makes it possible to take into account losses related to the absorption of the component of the reflected radi ation upon its double passage through the sample, while the numerator determines losses for the Fresnel reflection from the two surfaces and the absorption of the component of the radiation transmitted through the sample. DISCUSSION OF RESULTS The typical spectra of ΔR of typeI and III quartz glass obtained using standard polishing technology (an aqueous emulsion, polirit abrasive powder) are com pared in Fig. 7a with the spectrum of a cleavage, for which R0 was obtained in the course of a single exper iment. Comparison of the experiment with the calcu lation performed using the data from [15–19, 23, 24] shows that the experimental spectra of ΔR are simpler in structure (Fig. 7a) than the calculated spectra (Fig. 2). At the same time, the main extrema at 1000 and 1150–1250 cm–1 are present in both spectra. Analysis of the spectra of ΔR showed that the posi tion of the fundamental band 1122 cm–1 in the spec

762

ZOLOTAREV R 1.0

2 1

0.5

0 2500

~ ~

3

2000

1400

1200

1000

800

600

400 ν, сm−1

Fig. 6. Reflection spectra of KI quartz glass. ATR (n1 = 2.4): (1) Rp at an angle of 34°, (2) Rs at an angle of 70°, and (3) external reflection, Rs, at an angle of 10°.

trum of R primarily depends on the technological pol ishing regime and weakly depends on the type of glass. It can be seen from Fig. 7a that stable differences in the position, shape, and relative intensity of these bands are observed for the samples of typeI and III glasses. At the same time, in both cases, the intensities of the bands 1122 and 480 cm–1 are lower compared to the cleavage. This makes it possible to assume that the main reason for the decrease in the reflection coeffi cient compared to the cleavage is the occurrence of surface layers, which, at the same polishing condi tions, differ in properties for typeI and III glasses. To verify this assumption, model calculations of the reflection coefficients of ultrathin surface layers on quartz glass were performed (Fig. 7b). The spectro scopic parameters of surface layers were modeled tak ing into account the hydrolytic mechanism of the for mation of these layers based on the breakage of Si–O– Si bonds in SiO4 tetrahedra upon the mechanical action of abrasive particles on the surface of glasses under conditions of a moist medium. Under these conditions, water facilitates the breakage of the strained Si–O–Si bond, as a result of which Si–OH groups are formed in the surface layer of glass [39]. Vibrationally, the properties of this group in the mid IR range can be collated to a first approximation with the properties of silicon oxide SiO. Variation in the concentration of SiO in the surface layers of glasses was taken into account with the help of the Lorentz– Lorenz equation. The calculated values of n and κ characterize the system SiOx(SiO2)(1 – x) for different

values of the volume fraction x (Fig. 8). The values of n and κ calculated in this way were used to determine the difference coefficients ΔR of ultrathin surface lay ers (Fig. 7b). A comparison of Figs. 7a and 7b shows that the main features of the experimental and calcu lated spectra are similar. The positions of the main extrema coincide and agree well with the calculated maxima of ε 2'' of surface layers. It can be seen that the band near 1000 cm–1, which is attributed to the vibra tion of the Si–O bond in the SiO group is more pro nounced for typeIII glasses. A highfrequency shift in the 1122 and 480 cm–1 bands of typeIII glasses com pared to typeI glasses points to a higher concentra tion of SiO groups in surface layers of glasses of type III. These peculiarities, which are related to the shift in the 1122 and 480 cm–1 bands (Fig. 7a), correlate well with the data of calculations of ε 2'' = 2nκ for sur face layers in relation to the concentration of SiO groups (Fig. 8). It can be seen from Fig. 8 that, as the concentration of SiO in the system SiOx(SiO2)(1 – x) increase, the bands 1122 and 480 cm–1 are shifted to higher frequencies. The occurrence of the intense band 1000 cm–1 in the spectrum of ΔR and the shift of the bands 1122 and 480 cm–1 in typeIII glass indicate that the process of hydrolysis in surface layers of these glasses during polishing compared to typeI glass. The shape in the contour of IR bands in the spectrum of R for typeII glasses is closer to that of typeIII glasses; this is especially clearly seen in the spectra of the sec ond derivative of R in the vicinity of the band at OPTICS AND SPECTROSCOPY

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763

d2R/dν2 4 5 6 7

0.001

R 0.8

0.6 0 0.4

4

−0. 001

7

0.2

5 ~ ~

6

ΔR 0

ΔR 0 1

0.05

−0.005 3 −0.010

0.10 2

−0.015 (а) ~ ~

0.15 1280 ΔR 0.05

1120

960

650 600 ν, сm− 1 3

0

(b)

550

500

450 400 ε2'' = 2n2κ2 8

2 6

−0.05

4

1

−0.10

2

−0.15

OPTICS AND SPECTROSCOPY

~ ~

0 650 600 550 500 450 400 ν, cm− 1 Fig. 7. (a, bottom) Experimental differential reflection spectra (ΔR) of samples of (1) type I and (2) type III. Curve 3 is the spectrum of a sample of type III subjected to heat treatment at 800°С within 1 h. (a, top) Dependence d2R/dν2 for samples: (4) type I, (5) type II, and (6) type III. Curve 7 is the spectrum of R of the sample of type I. (b) Calculation: (1) dielectric function ε 2'' = 2n2κ2 of a SiOx(SiO2)(1 – x) film (x = 0.5); (2, 3) spectra of ΔR of films with x = 0.25 and 0.5, respectively. The thickness of the film is d = 1200 Å; the values of ε 3' and ε 3'' of the SiO2 substrate were calculated from the table. 1280

1120

960

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ZOLOTAREV

Optical constants of the cleavage of KI quartz glass ν, cm–1

λ, µm

n

κ

ν, cm–1

10 20 50 100 150 200 250 300 350 400 410 420 430 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 540 560 580 600 620 630 640 660 680 700 720 740 760 770 780 790 800 810 820 830 840 850 860

1000 500 200 100 66.67 50.0 40.0 33.33 28.57 25.00 24.39 23.81 23.26 22.73 22.47 22.22 21.98 21.74 21.51 21.28 21.05 20.83 20.62 20.41 20.20 20.00 19.80 19.61 19.42 19.23 18.52 17.86 17.24 16.67 16.13 15.87 15.63 15.15 14.71 14.28 13.89 13.51 13.16 12.99 12.82 12.66 12.50 12.35 12.20 12.05 11.90 11.76 11.63

1.9459 1.9472 1.9533 1.9695 1.9837 2.0289 2.1003 2.2044 2.3257 2.5844 2.6666 2.7675 2.8533 2.9143 2.8924 2.7934 2.6169 2.3047 1.8851 1.4249 1.0080 0.7304 0.5910 0.5281 0.5224 0.5606 0.6341 0.7209 0.8139 0.9024 1.1427 1.2562 1.3251 1.3835 1.4394 1.4652 1.4892 1.5367 1.5794 1.6206 1.6633 1.7059 1.7688 1.8269 1.8533 1.8239 1.7680 1.7028 1.6479 1.6142 1.6069 1.6238 1.6661

0.007 0.008 0.011 0.0159 0.0220 0.0337 0.0475 0.0838 0.1948 0.4196 0.5369 0.6771 0.8735 1.2286 1.4692 1.7347 2.0132 2.2739 2.4104 2.3889 2.1977 1.8910 1.5830 1.3074 1.0582 0.8426 0.6676 0.5339 0.4365 0.3695 0.2656 0.2272 0.1892 0.1513 0.1230 0.1121 0.1042 0.0912 0.0855 0.0820 0.0814 0.0859 0.0912 0.1197 0.2004 0.2714 0.3111 0.3161 0.2872 0.2369 0.1763 0.1172 0.0661

880 900 920 940 960 980 1000 1020 1030 1040 1050 1060 1070 1080 1085 1090 1095 1100 1105 1110 1115 1120 1130 1140 1150 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700

λ, µm 11.36 11.11 10.87 10.64 10.42 10.2 10.0 9.80 9.71 9.62 9.52 9.43 9.35 9.26 9.22 9.17 9.13 9.09 9.05 9.01 8.97 8.93 8.85 8.77 8.70 8.62 8.47 8.33 8.20 8.06 7.94 7.81 7.69 7.58 7.46 7.35 7.25 7.14 7.04 6.94 6.85 6.76 6.67 6.58 6.494 6.410 6.329 6.250 6.173 6.098 6.024 5.952 5.882

n

κ

ν, cm–1

λ, µm

n

κ

1.7707 1.8544 1.9399 2.0397 2.1645 2.3348 2.5997 2.9637 3.1001 3.1577 3.1275 2.9947 2.7574 2.4105 2.1975 1.9529 1.6860 1.3949 1.0989 0.8193 0.5954 0.4491 0.3481 0.3622 0.4004 0.4318 0.4614 0.4567 0.4189 0.3750 0.4003 0.6005 0.7473 0.8449 0.9124 0.9697 1.0064 1.0473 1.0774 1.1029 1.1256 1.1453 1.1631 1.1797 1.1953 1.2086 1.2203 1.2376 1.2457 1.2548 1.2615 1.2692 1.2757

0.0331 0.0298 0.0291 0.0341 0.0455 0.0719 0.1509 0.4466 0.7247 1.0598 1.4272 1.8041 2.1592 2.4677 2.5927 2.6887 2.7481 2.7556 2.7003 2.5691 2.3747 2.1479 1.7452 1.4654 1.2791 1.1486 0.9650 0.8253 0.6869 0.5024 0.2416 0.0698 0.0346 0.0217 0.0158 0.0140 0.0122 0.0112 0.0105 0.0098 0.0091 0.0084 0.0078 0.0075 0.0072 0.0069 0.0072 0.0081 0.0088 0.0091 0.0090 0.0075 0.0060

1720 1730 1740 1745 1750 1760 1770 1780 1800 1820 1840 1860 1865 1880 1900 1920 1940 1960 1970 1980 1990 2000 2010 2020 2030 2040 2060 2080 2100 2120 2140 2160 2180 2200 2220 2240 2260 2280 2300 2320 2340 2360 2380 2400 2450 2500 2550 2600 2650 2670 2700 2750 2800

5.814 5.780 5.747 5.731 5.714 5.682 5.650 5.618 5.556 5.494 5.435 5.376 5.362 5.319 5.263 5.208 5.155 5.102 5.076 5.050 5.025 5.000 4.975 4.950 4.926 4.902 4.854 4.808 4.762 4.717 4.673 4.630 4.587 4.545 4.504 4.464 4.424 4.386 4.348 4.310 4.274 4.237 4.202 4.167 4.082 4.000 3.922 3.846 3.774 3.745 3.704 3.636 3.571

1.2831 1.2871 1.2904 1.2915 1.2935 1.2966 1.2997 1.3026 1.3077 1.3136 1.3184 1.3203 1.3212 1.3222 1.3242 1.3282 1.3321 1.3359 1.3377 1.3387 1.3397 1.3415 1.3424 1.3434 1.3453 1.3462 1.3491 1.3519 1.3556 1.3583 1.3611 1.3629 1.3647 1.3674 1.3692 1.3711 1.3728 1.3755 1.3764 1.3799 1.3791 1.3808 1.3844 1.3853 1.3887 1.3913 1.3941 1.3957 1.3992 1.4001 1.4018 1.4035 1.4052

0.0056 0.0056 0.0061 0.0063 0.0062 0.0056 0.0057 0.0056 0.0062 0.0071 0.0082 0.0099 0.0102 0.0098 0.0086 0.0070 0.0064 0.0061 0.0060 0.0062 0.0063 0.0062 0.0058 0.0053 0.0047 0.0042 0.0027 0.0013 5.19Е–4 3.54Е–4 2.81Е–4 2.42Е–4 2.23Е–4 2.25Е–4 2.45Е–4 2.7Е–4 2.82Е–4 2.76Е–4 2.38Е–4 1.98Е–4 1.62Е–4 1.4Е–4 1.28Е–4 1.2Е–4 9.17Е–5 6.98Е–5 6.3Е–5 6.09Е–5 6.2Е–5 6.2Е–5 5.3Е–5 3.75Е–5 2.98Е–5

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480 cm–1 (Fig. 7a). In this range, the function d2R/dν2 exhibits a doublet at 480/490 cm–1. The intensity ratio of the components of this doublet is redistributed upon passage from type I to type III. The intensities of these bands for type II correspond to those of type III. Tak ing into account the classification of glasses with respect to the nature of impurities [30, 31], these observations show that water plays an important role in the formation of the vibrational spectrum of quartz glass.

2nκ 12

These data are consistent with the notion of the role played by hydrolysis in breaking of Si–O–Si bonds in the course of glass polishing [39]. The spec trum obtained upon the heating of samples of typeIII quartz glass (Fig. 7a, curve 3) additionally supports this consistency. It can be seen that the heat treatment of KU1 glass at 800 °С within 1 h leads to an increase in the intensity of the 1122 and 480 cm–1 bands. In this case, the shape and position of the bands still are char acteristic of type III; however, additional features appear in the spectrum, namely, inflection points on band contours. Another characteristic feature is that the spectrum of typeIII glass exhibits bands in the 550–620 cm–1 range, which are not observed for type I samples. After heat treatment, the intensity of this group of bands increased noticeably. Taking into account the characteristicity of IR bands in this spec tral range [40], we can state that, during polishing of glasses of type III, centers (nuclei) of a microdisperse correlation phase are formed in surface layers, whose volume increases upon heat treatment. An increase in the heat treatment time to 3 h (at 800 °С) leads to an increase in the intensity of bands in the range 550– 620 cm–1 and, furthermore, a band appears at 619 cm–1, which is characteristic of cristobalite. The possibility of structural transformations in surface layers of glasses upon polishing was pointed out in [9, 11, 40].

4

To study the surface layer of quartz glass in terms of a homogeneous singlelayer model, we calculated the values of ε 3' and ε 3'' of the substrate, and, using the ATR method and the computational algorithm of [20, 21], determined the form of the function Δε'' and the thickness of the surface layer for polished KU1 glass (Fig. 10). It can be seen from this figure that, in the surface layer, the absorption at the maximum of the band νas = 1122 cm–1 decreases and, in its wings, increases. Since SiO4 tetrahedra in the surface layer of polished quartz glass are deformed, this removes the degeneracy of the vibration νδ; as a result, the shape of the contour of the band νδ changes and its center of gravity is shifted to the highfrequency range (Fig. 7a).

Of all the objects considered, the investigations performed allowed us to select standard samples of typeI and III glasses whose surface layer was very thin and, therefore, hardly affects the value of R at all. The selection criteria of these samples were the follow ing three characteristics: high values of R for the 1122/480 cm–1 bands, small R at the minimum at 1375 cm–1, and coincidence between the experimen tal and calculated values of R in the range 1–3.4 μm. For this range, there are data of refractometric mea surements of the refractive index [29], which make it possible to calculate values of R. We used these calcu lated values as standard values of R0 in obtaining dif ferential spectra (Fig. 7a), and in Kramers–Kronig calculations of the optical constants of quartz glass (Fig. 9 and table). The obtained data refine the values of n and κ in the range 3.4–8.0 μm and in the vicinities of two fundamental IR bands (νas, νδ) of typeI quartz glass. The estimated errors of and κ were 5–8% and 2– 5%, respectively.

An additional absorption of the function Δε'' man ifests itself in the spectra of ΔR as a maximum at 1000 cm–1 and minima near 1250 and 1120 cm–1, which is determined by the dielectric properties of the substrate ( ε 3' ). In the vicinity of 1000 cm–1, ε 3' ≤ 0, while in the range 1250–1120 cm–1 ε 3' > 1 (Fig. 10), which is well consistent with the analysis performed based on the calculations presented in Fig. 3. The functions Δε'' for typeI and III glasses differ in that the maximum at 1100 cm–1 for typeI glass is shifted by ≈5 cm–1 toward higher frequencies. The main fea tures of the spectra of ΔR (Fig. 10) calculated taking into account the properties of the surface layer ( ε 2' , ε 2'' , d) obtained from the ATR spectra [20, 21] coin cide with the main features of the experimental spectra of ΔR (Fig. 7a). This confirms the objectivity of the obtained data on the properties of quartz glass in the bulk and on the surface layer of polished samples.

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2 8 3 4

0

5

~ ~

OPTICS AND SPECTROSCOPY

1

1200

1000

800

600 500

400 ν, сm−1

Fig. 8. Dielectric function ε'' = 2nκ of a system SiOx(SiO2)(1 – x). The volume fractions (SiO): (1) x = 0.0, (2) x = 0.1, (3) x = 0.25, (4) x = 0.5, and (5) x = 1.0.

766

ZOLOTAREV κ

n

1 κ 0.1 0.01

3 n

1E–3

2

1E–4

1

3

4

5

6

~ ~

~ ~

1E–5

10

20

30

40

50

0 500 1500 1000 2000 λ, μm

Fig. 9. Optical constants of KI quartz glass in the range of 3–2000 μm.

ε3'

ΔR

Δε''3

4

0

12 10 5

3

−0.05

8 8 6

0 −0.10

Δε'' 2

2 4 −8 +

−0.15

+ 1300

−

+ 1200

1100

1 2

1 −16 0

1000

0

900 ν, cm−1

Fig. 10. Spectral dependences of dielectric functions: (1) Δε'', (2) ε 3'' , and (3) ε 3' of polished KU1 quartz glass. (The “+” and “–” signs refer to the function Δε''.) Calculated spectra of ΔR were obtained from the experimental data on Δε'' for surface layers (with a thickness of (4) 600 and (5) 1200 Å) on a quartz substrate ( ε 3' ).

CONCLUSIONS Our studies of quartz glass in the IR range by the method of differential reflection spectroscopy showed that the measured reflection coefficient of this mate rial is substantially affects by the surface layer, whose

properties are determined by characteristic features of the polishing technology of samples. Taking into account these investigations, we refined the optical constants of quartz glass, which characterize its bulk properties, and determined the form of the dielectric OPTICS AND SPECTROSCOPY

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STUDY OF QUARTZ GLASS

function Δε'', which describes the properties of a pol ished surface. ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research, project no. 060800340a. REFERENCES 1. D. W. Rayleigh, Proc. Roy. Soc. (London) 160, 507 (1937). 2. I. V. Grebenshchikov, Izv. AN SSSR, Ser. Tekhn., No. 1, 3 (1937). 3. N. N. Kachalov, Principles of Glass Grinding and Polish ing (Akad. Nauk SSSR, Moscow, 1946) [in Russian]. 4. S. M. Kuznetsov, Opt.Mekhanich. Promyshl., No. 1, 45 (1956). 5. K. G. Kumanin, Opt.Mekhanich. Promyshl., No. 1, 41 (1956). 6. V. M. Vinokurov, Opt.Mekhanich. Promyshl., No. 2, 42 (1956). 7. Yu. A. Brodskiі, Opt.Mekhanich. Promyshl., No. 3, 49 (1956). 8. V. S. Molchanov, Opt.Mekhanich.Promyshl., No. 3, 55 (1956). 9. L. I. Demkina, Opt.Mekhanich.Promyshl., No. 3, 23 (1956). 10. F. Brüche and H. Poppa, Glastechn. Berichte 28, 6 (1955). 11. F. Preston, Trans. Opt. Soc. 18, 181 (1926). 12. H. Sakata, Verres Refract. 27 (2), 58 (1973). 13. J. P. Mariage, Neuv. Rev. Optique 6 (2), 121 (1973). 14. L. L. Hench, J. NonCryst. Solids 25, 343 (1977). 15. H. R. Philipp, in Handbook of Optical Constants, Ed. by E. D. Palik (Academic, New York, 1991), Vol. 1. p. 749. 16. V. M. Zolotarev, Opt. Spektrosk. 29 (1), 66 (1970). 17. T. R. Steyer, K. L. Day, and D. R. Huffman, Appl. Opt. 13, 1586 (1974). 18. S. L. Popova, T. S. Tolstykh, and V. G. Vorob’ev, Opt. Spektrosk. 33, 801 (1972). 19. M. L. Lang and W. L. Wolfe, Appl. Opt. 22, 1267 (1983). 20. N. N. Rozanov and V. M. Zolotarev, Opt. Spektrosk. 49 (5), 925 (1980). 21. G. M. Mansurov, N. N. Rozanov, V. M. Zolotarev, and S. M. Sutovskiі, Opt. Spektrosk. 53, 301 (1982).

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22. G. M. Mansurov, R. K. Mamedov, A. S. Sudarushkin, et al., Opt. Spektrosk. 52, 852 (1982). 23. G. V. Saіdov and O. V. Sverdlova, Fundamentals of Molecular Spectroscopy (NPO Professional, St. Peters burg, 2006) [in Russian]. 24. R. K. Mamedov, G. M. Mansurov, and N. I. Dubovikov, Opt.Mekhanich. Promyshl., No. 4, 56 (1982). 25. A. M. Efimov, V. G. Pogareva, V. N. Parfinskii, et al., Glass Technol. 46 (1), 20 (2005). 26. A. M. Efimov, Optical Constants of Inorganic Glasses (CRC Press, Boca Raton, 1995). 27. V. M. Zolotarev, V. N. Morozov, and E. V. Smirnova, Optical Constants of Natural and Technical Media (Khimiya, Leningrad, 1984) [in Russian]. 28. R. W. Pohl, Optik und Atomphysik (SpringerVerlag, Berlin, 1963; Nauka, Moscow, 1966). 29. GOST (State Standard) 1513079 “Optical Quartz Glass” (Izdvo Standartov, Moscow, 1980) [in Russian]. 30. V. K. Leko and O. V. Mazurin, Properties of Quartz Glass (Nauka, Leningrad, 1985) [in Russian]. 31. R. Brückner, in Encyclopedia of Applied Physics (Wiley, New York, 1997), Vol. 18. 32. A. M. Efimov and V. G. Pogareva, Chem. Geology 229, 198 (2006). 33. N. J. Harrick, Internal Reflection Spectroscopy (Wiley, New York, 1967; Mir, Moscow, 1970). 34. R. G. Greenler, J. Chem. Phys. 50, 1963 (1969). 35. W. G. Golden, Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems, Ed. by J. R. Ferraro and L. J. Basile (Academic, Orlando, 1985), Vol. 4. 36. V. A. Kizel’, Reflection of Light (Nauka, Moscow, 1973) [in Russian]. 37. V. M. Zolotarev, Methods of Investigation of Materials for Photonics (SPbGU ITMO, St. Petersburg, 2008). 38. E. M. Voronkova, B. N. Grechushnikov, G. I. Distler, and I. P. Petrov, Optical Materials for Infrared Technol ogy: Reference Book (Nauka, Moscow, 1965) [in Rus sian]. 39. V. A. Bershteіn, Mechaniical and Hydrolytic Processes and Strength of Solids (Nauka, Leningrad, 1987) [in Russian]. 40. A. G. Vlasov, V. A. Florinskaya, V. N. Morozov, and E. V. Smirnova, IR spectra of Inorganic Glasses and Crystals (Khimiya, Leningrad, 1974) [in Russian].

Translated by V. Rogovoi