Optical Absorption Properties of Vanadate GlassesGordon Wood Anderson and W. Dale Compton Citation: The Journal of Chemical Physics 52, 6166 (1970); doi: 10.1063/1.1672922 View online: http://dx.doi.org/10.1063/1.1672922 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/52/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Optical and other physical properties of semiconducting cadmium vanadate glasses J. Appl. Phys. 101, 083511 (2007); 10.1063/1.2718285 Electrical properties of semiconducting barium vanadate glasses J. Appl. Phys. 87, 3355 (2000); 10.1063/1.372349 Semiconducting properties of magnesium vanadate glasses J. Appl. Phys. 86, 2078 (1999); 10.1063/1.371012 Transport properties of semiconducting ternary vanadate glasses J. Chem. Phys. 102, 1385 (1995); 10.1063/1.468924 Erratum: Optical Absorption Properties of Vanadate Glasses J. Chem. Phys. 54, 3247 (1971); 10.1063/1.1675334

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 52, NUMBER 12 15 JUNE 1970

Optical Absorption Properties of Vanadate Glasses*

GORDON WOOD ANDERSONt AND W. DALE COMPTON

Department of Physics and Materials Research Laboratory, University of Illinois, Urb.:na, Illinois 61801

(Received 13 October 1969)

The optical absorption of vanadate glasses based on the system V20.-P20. was measured in the range 20 cm-I to 25 000 cm-I at room and liquid-nitrogen temperatures. The samples were blown films of thickness about 1-2 J.I and of composition 70.0, 80.0, and 87.5 mole % V20 •. Vibrational absorption peaks were observed at about 360, 420, 680, 1010, and 1100 cm-I with additional structure likely at about 900 cm-I in the 70.0 mole% V20. films. Peaks were observed at about 330, 435,635,810,1007, and 1085 cm-I in the 87.5 mole % films. Absorption tails were observed extending from the lowest-energy peaks to 20 and 33 cm-I in the 70.0 and 87.5 mole % V20. samples, respectively. No noticeable temperature effects on spectra shape and peak positions were observed. Absorption peaks were also observed at 1038 and 1277 cm-I in crystalline V20. at room temperature and at 915, 1040, and 1274 cm-I and possibly at 1256 cm-I at liquid-nitrogen temperature. The peaks at about 1010 cm-I in the glasses are thought to be the V-Q stretching vibrations, and the peaks at about 1090 cm-I are assigned to a phosphorous---{)xygen vibration. Other peaks are un­assigned. A broad absorption tail which is responsible for the dark black color of bulk samples was observed between the apparent fundamental absorption edge of the glasses in the short-wavelength region of the visible and about 4000 em-I. The cause of this absorption is not definitely ascertained, though V4+ ions may contribute. The absorption edge of both the 70.0 and 87.5 mole % V20. glasses fits the condition for direct forbidden transitions as does the edge of crystalline V20 •. Eg values were determined to be 2.38 and 2.41 eV for 87.5 mole % V20. films at room and liquid-nitrogen temperatures, respectively, and 2.47 and 2.51 eV for the 70.0 mole % ViO. films at room and liquid-nitrogen temperatures, respectively.

I. INTRODUCTION for samples of thickness greater than 1.5 mm.2 Russian investigators also state that glasses in the V205-P205-

The properties of semiconducting glasses have been ROx system are reasonably transparent in the wave­of increasing interest in the last 20 years with much of length range between 2 and 5 J.I. but are opaque in the the work being done on glasses based on the V20 5-P205 visible.17 More recently, Janakirama-Rao has studied system. Although these glasses were first reported to be the transmission of numerous compositions of the sys­prepared by Roscoe over 100 years ago,! it was not tem V20 5-P20 5-Ge02 in the range 2-15 J.I. by the powder until 1954 that Denton, Rawson, and Stanworth technique.16 He observed the V-O vibration at about suggested that they are n-type semiconductors.2 Since 9.95 J.I. in glasses containing both VH and pH and at then, other studies have been done on the electrical 9.85 J.I. in glasses without p5+. He also observed absorp­properties of the vanadate glasses which have confirmed tions at 9.17 and 7.90 J.I. which he attributed to p-o that they are indeed n-type semiconducting glasses vibrations. Nester and Kingery have reported that the with an activation energy for conduction that varies fundamental absorption edge of V20 5-P20 5 glass films between 0.20 and 0.40 eV depending on composition.2-12 varies from 455 to 550 mJ.l. as the V205 concentration In addition, a knee or bend in the curve of logO" versus increases from 50% to 90%.5 liT has been reported, suggesting that two processes Optical measurements have recently been reported for conduction may exist.5.6.9 It is still the case, though, for single crystals of V20 5 in the range 0.4-8 J.I., with that a detailed understanding of the electronic energy emphasis being given to the apparent intrinsic absorp­levels and the electrical conduction mechanisms is not tion edge and to the near-infrared properties.18- 20

known. Recent nuclear magnetic resonance and electron Earlier transmission measurements covered the range spin resonance studies indicate that the coordination between 0.2 and 25 J.I..21- 23 Accurate values of the index number of the vanadium ions in the glass is the same as of refraction at two wavelengths in the visible have for the vanadium ions in crystalline V20 5 and that their been reported,24 and measurements have been made of site symmetry is similar to that in the crystal.13•14 These the diffuse reflectance from powders at room tempera­resonance studies further indicate that the concentration ture.25 It has also been noted that the structure of of V4+ ions in the glasses increases with increasing P20 5 crystalline V20 5 is orthorhombic26-28 and that the optical content, confirming the earlier analytical results using absorption is dependent on the polarization of the wet chemical techniques.5.9 incident light,18-20

The optical properties of vanadate glasses have Recent investigationsl 8-20 of the absorption coefficient received considerably less attention than the electrical in the long-wavelength tail of the absorption edge of properties, though some work has been done in the V20 5 show that it depends exponentially on both infrared2.4.15-17 and one study of the absorption edge in photon energy hv and reciprocal temperature liT the visible has been reported.5 An early paper notes that between 293 and 6S3°K for E II a and Ell c, where some of the glasses are transparent in the infrared be- a, b, and c are the three crystallographic axes. Thus the tween 1.S and S J.I. but that all are opaque in the visible absorption coefficient follows Urbach's rule.29 In addi-

6166

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OPTICAL ABSORPTION OF VANADATE GLASSES 6167

(a) (b) (c)

FIG. 1. V205-P205 glass thin films. (a) 87.5 mole % V,05, unannealed, bright field; (b) 87.5 mole % V,O., unannealed, bright field; (c) 70.0 mole % V,O., annealed, bright field. Electron microscope magnification of (a) and (b) X40 000; enlarged X3; shown here X 120 000. Electron microscope magnification of (c) X38 500; enlarged X3; shown here X115 500.

tion, it was found that the absorption coefficient fits the condition for direct forbidden transitions,30

( 1)

much better than it fits the condition for direct allowed transitions,30

(2)

The bandgap energy Ey was found to be about 2.4 eV at room temperature and depended on temperature and the polarization of the exciting light. Absorption peaks were found at 0.83 and 1.0 p. for E II a but not for E II b of E II c, and crystals grown in air rather than oxygen had enhanced absorption at these wavelengths. At wavelengths greater than 5 p. the absorption coefficient was found to increase sharply.

Work on other vanadium oxides has been done but will not be discussed in detail here. The optical prop­erties of V02, for example, differ markedly from those of V20. because of the presence of d electrons and the metal-semiconductor transition.31 .32 It is significant to note, also, that below the metal-semiconductor transi­tion temperature the absorption edge in V02 occurs at about 0.4 eV or at lower energy than in V20 6•

The present study was undertaken in order to thor­oughly examine the dependence of the infrared absorp­tion properties of the V20 5-P20. glasses over a larger range of temperature for a wide range of wavelengths and for various compositions of materials. A correlation of the observed absorption bands in the glasses with known molecular vibrations is made wherever possible. A study of the apparent fundamental absorption edge as a function of temperature and of composition was also undertaken. A correlation of these observations is made with the properties of single-crystal V20 5.

Finally, where possible, the relationship of these observations to the more thoroughly studied transport and magnetic properties of these materials is given.

II. SAMPLE PREPARATION AND CHARACTERIZATION

Glass samples used in the optical experiments were blown films having thicknesses between 1 and 2 p..

Because detailed descriptions of the sample preparation techniques have been given elsewhere,9,33,34 only a few critical points will be given here. Fifty-gram batches were made by mixing reagent grades of V20 5 and P20 5 in an atmosphere of dry nitrogen having a dew point below -43°C. The initial compositions contained 70.0, 80.0, and 87.5 mole % V205. The batches were melted in platinum or high-purity silica (Corning 7941) crucibles in an air atmosphere at 900°C for 3 h. Films were blown from a small amount of semimolten material gathered on the end of a refractory tube.

Sample characterization by transmission electron microscope was carried out for thinner (<: 0.1 p.) films of each composition.33- 35 All films examined were found to be amorphous with no crystals larger than 20--40 A observed in bright-field, dark-field, and diffraction­electron microscopy. The unannealed 70.0 and 80.0 mole % V205 films were generally uniform and homo­geneous. Approximately half of the unannealed 87.5 mole % V20. films exhibited phase separation [Fig. 1 ( a)]. The shape of the minor phase regions appeared similar to the shape of the minor phase regions theoreti­cally derived by Cahn for the spinodal phase separation mechanism in glass.36 ,37 Unannealed films of each composition very occasionally exhibited relatively large, nearly opaque inhomogeneities [Fig. 1 (b) ] of about

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6168 G. W. ANDERSON AND W. D. COMPTON

0.1-0.2-/L dimension and thus often of dimension greater than the film thickness. These large inhomogeneities never demonstrated crystalline characteristics in dif­fraction or in dark field and were most likely thick sections of the films with properties approaching bulk glass.

Because of the interesting observations of phase separation/a- a5 annealing and heat treatments of the glass films were subsequently initiated to bring about phase separation in the lower vanadium content glasses in order to learn if, on further heat treatment, the induced phase separation would proceed to devitrifica­tion. The annealing and heat treatments were carried out on the 87.5 and 70.0 mole % V20 5 compositions only.

It was found that phase separation and growth were induced in the 70.0 mole% V20 5 films after annealing at about 290°C [Fig. 1 (c) ] but not at lower tempera­tures for annealing times as long as 15 h. Devitrification was induced after heating to about 400°C for approxi­mately 10 min but not at lower temperatures. In the 87.5 mole % V20 5 films, phase separation was apparently induced after annealing at about 240°C for some 6 h, and devitrification was definitely induced after heating to about 245°C. Annealing at temperatures lower than those which produced the phase separation apparently resulted in the growth of many more large, round, nearly opaque, amorphous inhomogeneities than occurred in unannealed films. These are thought to be thick sections of the films similar to those of Fig. 1 (b). It was not possible in this sequence of measurements to ascertain whether or not crystallization in heated films was induced directly from amorphous phase separation.

III. OPTICAL ABSORPTION RESULTS

A. Experimental Procedure

Optical absorption measurements of 70.0 and 87.5 mole % V20 5 glass films were made in the range 33-25000 cm-I (300-0.4/L) at room and at liquid-nitrogen temperatures. Experiments were done using different spectrophotometers for the different wavelength ranges: a Beckman Model IR-ll in the range 33-800 cm-I

(300-12.5 /L), a Beckman Model IR-9 in the range 400-4000 cm-I (25-2.5 /L), and a Cary Model 14 in the range 3850-25000 cm-I (2.6-0.4 /L). Each instrument was operated in the double beam mode and was con­tinuously flushed with dry air or nitrogen. Samples were mounted on identical, interchangeable OFHC copper sample mounting pieces which contained (5/32)­in. holes for light transmission. These sample mounting pieces were attached to the copper sample holder of a nitrogen temperature optical Dewar. A reflectance attachment for the Cary 14 was used to determine the reflectance of two bulk samples in the range 2850-50000 em-I.

A beam condensera8 was used on both the IR-ll and IR-9. Wavenumber resolution of the IR-11 at the peak of the absorption bands was about 3.5 em-lor better except at 335 cm-I, where it was slightly better than 5 em-I, and for the IR-9 it was better than 2 cm-I at all photon energies except those less than 700 cm-I , for which it was about 3 cm-I. The film samples were attached to the copper sample holder with vacuum grease. Although the actual temperature of the film samples could not be ascertained when the samples were in the light path, it is reasonable to expect that good conduction cooling occurred. A heat shield was attached to the sample block. Four different tail pieces having polyethylene, KBr, CsI, or sapphire windows were used depending on the measuring wavelength. Room-temperature measurements were made without windows. For measurements at liquid-nitrogen tem­perature with both the IR-ll and IR-9, the chopper between the sample and the detector was stopped so that the net modulated incident energy at the detector at a given wavelength was not affected by blackbody radiation from the sample and detector.

For one experiment an FS-720 Module interferometer Fourier spectrometer made by the Research and Industrial Instruments Company, England, was used. This instrument extended the long-wavelength range of observation to 20 cm-I and provided a comparison with the Beckman IR-ll results for the range 33-300 cm-I.

Thicknesses of all samples were measured mechani­cally with a DoAll Model TH-18 Trans-Chek gauge which has a sensitivity to changes in thickness as small as 5X 10-6 in. These results were compared with thick­nesses determined optically from interference fringes.

B. Experimental Results

1. Intermediate and Far-Infrared Range

Several vibrational absorption peaks were observed in the V205-P205 glasses between 33 and 1300 cm-I. These are shown in Figs. 2 and 3, which present reduced data from room-temperature experiments on samples 70.0.3-2 and 87.5.2-1. These samples were prepared from melts initially containing 70.0 and 87.5 mole % V20 5, respectively. Vibrational absorption peaks in the 70.0 mole % V205 glass films occur at about 360, 420, 680, and 1010 cm-I with additional structure likely at about 900 and 1100 em-I. In the 87.5 mole % V20 6 glasses the peaks occur at about 330,435,635,810, 1007, and 1085 em-I. For each composition an absorp­tion tail extends to 33 em-I. It should be noted that, with the exception of the peaks at about 1010 em-I, these peaks are quite broad and overlap considerably, so that locating them more accurately than at best within ± 10 cm-I is not possible. The values listed are averages of several experiments on more than one sample for each composition. It may be the case that

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OPTICAL ABSORPTION OF VANADATE GLASSES 6169

0.8

0.7

>-0.6 I--V>

~0.5 o -' ;30.4 ;:: a. °0.3

0.2

0.1

WAVELENGTH (microns) :300 100 50 30 20

---- 87.5.2-1 --70.0.3-2

I"" ........ ', .. -- ,/

// ',-/ "\-,/

I

, ,/

,/ /1

I

I I

I

I , I

I I

I I

I

15

, , , ' , ' , " " ...... I

12.5

%~~1~00~~20~0~~3~0~0--~40~0~~5~0~0--~6~00~~70~0--~8~00 WAVENUMBER (em-I)

FIG. 2. Room-temperature optical absorption spectra of 70.0 and 87.5 mole % V,05 films in range 33-800 em-I. Thickness of each sample determined mechanically to be about 1.15 /1-.

two broad peaks rather than one occur between 680 and 1010 em-I. It appears, however, that the observed vibrational absorption peaks have a one-to-one corre­spondence between the two glass compositions studied.

Samples of 87.5 and 70.0 mole % V20 5 films were tested in the ranges 33-1100 and 400-4000 cm-r, respectively, at liquid-nitrogen temperature. No notice­able effects on spectra shape or peak positions were observed at the lower sample temperature. In addition, the sample thickness and the crucible materials, plat­inum or silica, used for melting had no effect on spectra shape or peak positions for either composition.

The absorption of one 70.0 mole % V20 5 sample, 70.0.3-3, was measured in the range 20-300 cm-I on an in terferometer spectrophotometer. No new absorption peaks appeared at longer wavelengths, indicating that the long-wavelength tail extends to at least 20 cm-I and that the absorption steadily increases from 20 to 300 cm-r, similar to the results cited above.

A limited number of measurements was made on

WAVELENGTH ~icrons) 25 20 15 12.5 10 8

o.a -70.0.3-2 ---87.5.2-1

02

500 600 700 800 900 1000 1100 1200 1300 WAVENUMBER Icm-I)

FIG. 3. Room-temperature optical absorption spectra of 70.0 and 87.5 mole % V20 5 films in range 400-1300 em-I. Thickness of each sample determined mechanically to be about 1.15/1-.

WAVELENGTH (microns)

6.0 5.0 4.0 3.0 2.5

V2 0, -2 Uguid Nitrogen Temperature

O~~_-L ___ L-__ ~ ____ ~~~~~~~~~~

1000 1400 1800 2200 2600 3000 3400 3800

WAVENUMBER (em-I)

FIG. 4. Liquid-nitrogen temperature optical absorption spectra of crystalline V20 5 sample V20 5-2 in range 880-4000 em-I. Dis­continuity at 1200 em-I occurs at change of spectrophotometer gratings. Thickness about 25 /1-.

single crystals of V20 5• Samples were cleaved to about 25-~ thickness. The light was incident along the y or b crystal direction. Typical results for a measurement at liquid-nitrogen temperature are shown in Fig. 4, in which interference fringes are shown between 1400 and 4000 cm-r, the amplitude modulation occurring because the light was unpolarized. Absorption peaks are seen at 915, 1040, 1274, and possibly at 1256 cm-I. At room temperature, definite absorption peaks were observed at 1038 and 1277 cm-I. Other structures may be present,

WAVELENGTH (microns) )0.0 2.5 1.0 O.S 0.6 0.5

5.0

---------- Room Temperature ------ Liquid Nitrogen Temperature

>­)--

4.0

~3.0 w o --1 <{ u i=2.0 c-o

" 1.0 I

~l 1 l ~. /'\

o 4000

~.-

16000 20000 24000 WAVENUMBER (em-I)

FIG. 5. Liquid-nitrogen temperature optical absorption spec­trum of 70.0 mole % V20. glass film, sample 70.0 3-3, in range 3850--25 000 cm-I and room-temperature spectrum in range 400--25000 em-I. Thickness mechanically determined to be between 1.0 and 1.7 /1-.

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6170 G. W. ANDERSON AND W. D. COMPTON

although the noise level and interference fringes made it difficult to observe with certainty.

2. Near-Infrared and Visible Range

The optical absorption spectra of glass film samples of initial composition 70.0 and 89.5 mole % V20 5 and of V20 5 crystalline samples were measured in the range 3850-25000 cm-I at room temperature and at liquid­nitrogen temperature. Results are shown in Figs. 5 and 6 for the glass samples. In each case the apparent funda­mental absorption edge occurs between 18 000 and 25000 em-lor in the short-wavelength region of the visible. Samples of each glass composition have a broad absorption tail between about 4000 cm-I and the ab­sorption edge which was not observed in the crystals.I8 ,34 It is this absorption that is responsible for the black color of bulk glass samples. No sharp line absorption was seen in this range. The fundamental absorption edge shifts to higher energy with cooling to liquid­nitrogen temperature.

The reflectivity of the two 87.5 mole % V20 5 bulk glass samples was measured at room temperature in the range 3850-40000 em-I. It was found to be quite con­stant in the range 3850-16 670 cm-I and to increase by about 25% between 16670 and 25000 em-I. At higher energies the reflectivity gradually decreased. Thus the change in the reflectivity of the bulk samples in the region of the absorption edge is fairly small.

C. Discussion of Results

1. Intermediate and Far-Infrared Range

The vibrational absorption bands in the range 33-1300 cm-I may arise from any of a large number of modes and may be due to both bridging and nonbridging oxygen ions which are doubly and singly bonded oxygen ions, respectively, to phosphorous ions possibly only of +5 valence, and to vanadium ions of +4 and +5 valences. In addition, it may be that still other valence states of vanadium exist, and that more than one general type of cation site occurs for a given type ion. Although it is difficult to conclusively assign the ob­served absorption peaks to particular modes of vibra­tion, some suggestions can be made about their source.

Many compounds containing vanadium and oxygen are reported to have V-O stretching vibrations at energies between 900 and 1050 cm-I.15 ,16,3!l-42 In several halogen compounds such as OVF3 with vanadium in the +5 state, the stretching frequency is reported to occur between 1025 and 1050 cm-I.40,42 In compounds with reduced vanadium the stretching frequency often occurs at slightly lower energies.39- 4I

The present measurements on crystalline V20 5

(Fig. 4) seem particularly critical here. A sharp absorption occurs at 1038 cm-I at room temperature and

1040 cm-I at liquid-nitrogen temperature. It is suggested that this absorption involves vanadium in the +5 valence state. Janakirama-RaoI6 apparently failed to observe this peak at this energy in V20 5, perhaps because the pulverizing which was done to produce the powdered samples resulted in a modification of the crystalline properties.

The origin of the two absorption bands in both compositions of the vanadate glasses at about 1010 and 1090 cm-I is less clear, though one of them is thought to arise from vanadium-oxygen stretching vibrations. It is suggested that the peaks at about 1010 cm-I are V-O vibrational peaks, mainly involving V5+ in corre­spondence to the single-crystal absorption at 1038 cm-I. This assignment corresponds to that of Jana­kirama-RaoI6 and is not inconsistent with the suggestion made in the recent magnetic resonance studiesI3 ,I4 that in this glass system the coordination number of the vanadium ions is the same as and their site sym­metry is similar to those of the cations in crystalline V20 S•

Phosphate ions have been reported to introduce weak vibrational absorption in some phosphate glasses in the range 1020-1100 cm-I 43-46 and in many crystalline phosphate materials in the range 1150-1400 cm-I.I5 ,I6,43-5I It is suggested, therefore, that the broad shoulder that occurs between 1085 and 1100 cm-I is due to a phos­phorous-oxygen vibration. This is at a somewhat lower energy than would be predicted from a simple scaling of the masses of the phosphorous and vanadium ions, therefore suggesting that the force constants are different for the two ions.

5.0

4.0

>-~3.0 z w o

1.0

10.0

~\

WAVELENGTH (microns) 2.5 1.0 0.8 0.6 0.5 0.4

--------- Room Temperature --- Liquid Nitrogen Temperature

-" '" .'

O~\~~~'~~~~~~~~~~~~~~~ o 16000 20000 24000 (cm-I )

FIG. 6. Liquid-nitrogen temperature optical absorpti<?n spec­trum of 87.5 mole % VZ05 glass film, sample 87.5.2-1, In range 3850--24000 cm-I and room-temperature spectrum in range 400-24000 em-I, Thickness mechanically determined to be 1.15 Jl..

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OPTICAL ABSORPTION OF VANADATE GLASSES 6171

2. Near-Infrared and Visible Range

Two general regions of absorption are of interest in the glasses. First, there is the broad absorption tail that extends to about 4000 cm-I, and second, the absorption edge near 20 000 cm-I • The broad absorption tail in the glasses extends from about 4000 to 20000 cm-I (Figs. 5 and 6) and for samples of comparable thickness is much stronger than the absorption tail observed in crystalline V20 5. This absorption may arise for a number of reasons: the phosphorous content, reduced valence states of vanadium ions, reduced valence states of the phosphorous ions, a charge transfer absorption that does not occur in the crystal, an electronic effect introduced due to nonbridging oxygen ions, disorder of the material, or some combination of these possible causes. Although additional studies will be needed to clarify the origin of this absorption, particular effort was made here to determine the influence of the phos­phorous content of these glasses upon this absorption. In order to do this it was necessary to correct the trans­mission data for reflection losses and to determine accurately the thickness of the samples. The methods used by Hevesi20 can be used to determine the real part n of the index of refraction and the thickness d and thus the imaginary part k of the index and the absorp­tion coefficient K, where K = 47rk/r.., from the magnitude of the transmission and the separation of adjacent maximum and minimum values of transmission in the energy range in which interference fringes occur. Al­though the background absorption complicated these determinations, typical values of n, calculated at different wavelengths, varied between 1.75 and 1.9 for sample 70.0.3-3 and between 1.75 and 2.1 for sample 87.5.2-1 in this energy range. Calculated values of d varied between 1.95 and 2.35 J.L for sample 70.0.3-3 and between 1.3 and 1.85 J.L for sample 87.5.2-1. In each case two values of n were calculated and then averaged from either one T max value and the adjacent two T min values or one T min value and the adjacent two T max values. The calculated values of thickness are moderately consistent and compare reasonably favorably with the values determined mechanically.

Because this method of calculating K in the region of the broad tail was accurate only within about 35%, an attempt was made to calculate K by an iterative process from the usual expression for transmission as a function of K, reflectivity, and thickness for a sample of two parallel faces with normal incident light. Using typical values of nand d as calculated above, K was determined to be 3.8X103 and 4.7X103 cm-I at 5865 A ("-'17050 cm-I ) for samples 87.5.2-1 and 70.0.3-3, respectively.

These numbers in themselves are too similar to offer a valid comparison of K for the 70.0 and 87.5 mole % V20 5 films, particularly when the calculated values of n are not extremely reliable. It is only valid to remark

with certainty that at the high-energy region of the broad absorption tail, the absorption coefficients of the 70.0 and 87.5 mole % glasses are of the same order of magnitude. It is interesting to note, though, that the absorption edge of V02 for temperatures less than the metal-semiconductor transition temperature occurs at a considerably lower energy, about 0.4 eV,32 than the edge of V20 5. Thus, the V4+ ions in the vanadate glasses may contribute significantly to this broad absorption tail. Further optical and electrical experiments are needed on vanadate glasses to test the recent specula­tions about band theory of glasses for this materia1.52- 54

Consider now the absorption edge of the glasses. As discussed above, the lower-energy region of the edge in crystalline V20 5 has been shown to obey Urbach's rule.18- 20 Further, the absorption edge best fits the con­dition for direct forbidden transitions [Eq. (1) J.

The fundamental absorption edge of the 87.5 and 70.0 mole % V20 5 glass films appears to occur in the short­wavelength part of the visible, as shown in Figs. 5 and 6. The existence of the broad absorption tail, the inter­ference fringes, and the present uncertainty in n make it difficult to carefully analyze the low-energy portion of the fundamental edge to ascertain whether the glasses obey Urbach's rule.

lt is possible, however, to examine whether or not the vanadate glasses give evidence of direct for­bidden transitions. lt was first necessary to correct the optical density in order to separate out the effects of the broad absorption tail and of reflection losses in the visible and near infrared. In view of the uncertainty in the calculations of the index of refraction and thick­ness, it was thought more reliable to draw a straight line through the mean points of the optical density maxima and minima in the tail (Figs. 5 and 6), extend this line into the region of fundamental absorption, and subtract it from the measured optical density to obtain a corrected optical density. Because the measured reflectivity of two bulk samples changed only slightly in the region of the fundamental absorption, this process, which assumes little change in reflectivity in the region of the absorption edge, seemed reasonable in the case of the films. Account was taken of the discontinuity of the optical density curves at about 16000 cm-l •

The results of this analysis are shown in Fig. 7 for samples 70.0.3-3 and 87.5.2-1. Straight lines are drawn through four of the curves, illustrating the good fit of the data for each sample to the condition for direct forbidden transitions at room and liquid-nitrogen tem­peratures. In each case the absorption edge fits the condition for direct forbidden transitions much better than the condition for direct allowed transitions, as is shown by the points at the far right in Fig. 7. The uncorrected absorption edge also fits the condition for direct forbidden transitions very well and much better than it fits the condition for direct allowed transitions. It should be mentioned, though, that the data have not

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6172 G. W. ANDERSON AND W. D. COMPTON

TABLE 1. Comparison of fundamental absorption edge analyses of vanadate glasses and V.O •.

Slope of curve Temperature Eg (Khv)·/3 vs hv

Samples Study (OK) (eV) (cm'.eV)-l/3

70.0.3-3 Present Room 2.47 5.12X103b

70.0.3-3 Present Liquid nitrogen 2.51 5.32X103 b 87.5.2-1 Present Room 2.38 7 .12X103 c

87.5.2-1 Present Liquid nitrogen 2.41 7.41X10· c

V,O. (E II c) Kenneyet aI. Room 2.34 7.14X103

V,O. (ll- II c) Hevesi 293 2.30 5.00X1Q3 V,O. (E II a) Kenney et aI. Room 2.36 11. 6X 103

V,O. (E II a) Hevesi 293 2.32 8.58X1Q3

V.O. (E II c) Hevesi 473 2.20 4.62XIQ3 V.O. (E II a) Hevesi 473 2.19 6.00XIQ3 V,O. (E II c) Hevesi 653 2.09 4.45X103

V20. (R I! a) Hevesi 653 2.06 4.80X103

V20. (E II c) Hevesi 78 2.44d V.O. (E II a) Hevesi 78 2.48d

c Thickness taken to be 1.2 p.. s Starting mole % V20, for samples 70.0.3-3 and 87.5.2-1 was 70.0 and 87.5, respectively.

b Thickness taken to be 2.0 p.. d BudD and Hevesi's linear relationships between E2 and temperature

extended to 78°K.

been uniquely fitted to Eq. (1) as it has not been shown that the data fit no other equations. The values of band­gap energy Eg and the slopes of the lines giving the Eg values obtained from this analysis can be compared with the values obtained from previous studies of crys­talline V20 5• This information is given in Table I. The Eg values are taken to be the intercepts of the straight lines with the horizontal axis. Thickness values of 2.0 and 1.3 J.I. were used to obtain the slope in terms of K from the corrected optical density curves for samples 70.0.3-3 and 87.5.2-1, respectively.

It is seen from Table I that Eg increases with an increase of P205 content from crystalline V20 5 to the 70.0 mole % V20 5 glasses at room temperature. It is also observed that the slopes of the curves representing direct forbidden transitions increase slightly with decreasing temperature for each glass sample and also for the V20 5 data of Hevesi. The absolute values of the slopes are also only approximate in the cases of the glass samples as the thicknesses used to determine K could not be accurately determined. Because the values of the slopes of the curves for the glasses (Fig. 7) com­pare reasonably well with those for crystalline V20 5

and because the glass data show a reasonable fit to the same optical transition mechanism as the crystalline V20 5 data, it is thought that the fundamental absorp­tion is the same for the vanadate glasses as for crystal­line V20 5•

It is possible that the transitions occur due to excita­tion of oxygen 2p-like electrons. Moreover, the percent oxygen content must decrease from the crystalline V20 5 through the 70.0 mole % V20 5 glasses because of the increasing percent concentration of reduced vana­dium which occurs as the P20 5 content is increased.5 ,9,13,14

The separation distance between oxygen ions in the

films is expected to increase with increasing P20 5 content for two reasons: First, the oxygen content decreases, and second, the density of bulk V20 5-P20 5 glasses is less than that of V20 5 and also decreases with increasing P20 5 content.4 Because of the disorder in the glass and because of the manner in which the oxygen volume

y IE 3

No(' 2000 '= 20.0 >-~ Vi N Z ........, W >-0 1600 16.0 ~ ....I Vi <C Z U w i=

0

Cl. ....I 0 1200 12.0 <C 0 U

w i= ~ Cl. U 0 w a: 0 a:

800 8.0 w

0 I-~ U

W )( a: ~

a: 0

w ~ ro 400 ~ 4.0 ::::> z w ~ ~

=...

FIG. 7. Analysis of fundamental absorption edge of vanadate glass films. Straight lines drawn through points fitting. condition for direct forbidden transitions. Sample 87.5.2-1: CIrcles and diamonds at room and liquid-nitrogen temperatures, r~sp~cth:ely. Sample 70.0.3-3: triangles and squares at room and IIqmd-mtro­gen temperatures, respectively. Rightmost curve attempts t.o. fit liquid-nitrogen temperature data of sample 70.0.3-3 to condition for direct allowed transitions on right-hand vertical axis.

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OPTICAL ABSORPTION OF VANADATE GLASSES 6173

density varies, the p-like electrons on the oxygen ions may be more localized in the material with greater amounts of P20 5, and this localization may cause the intrinsic absorption to occur at higher energies. The expected decrease in concentration of nonbridging oxygen ions with increasing P20 5 content also may have a significant effect on E g , that is, charged nonbridging energy levels, thus decreasing Eg. Thus, a decrease of Eg with decreasing P20 5 content or increasing nonbridg­ing oxygen ion content would be expected. This increase in 2p electronic energy levels should affect the whole band rather than be localized due to the high per­centage of nonbridging oxygen ions expected because of the high concentration of reduced vanadium ions,o·9.13.14 The trend of Eg in the glasses is toward higher energies with decreasing temperature as it is in V20 5•

The analysis of the apparent fundamental absorption edge of the V20 5-P20 5 glasses suggests that the absorp­tion occurs due to direct forbidden transitions as has been proposed for V20 5.18-20 The analysis also establishes reasonably well that, whatever the mechanism, this absorption in the glasses occurs in the same manner as in V20 5• It is probable that the disordered glass network inhibits expansion and contraction in the glasses as compared to the crystalline V20 5• Thus, the edge would be expected to shift less in the glasses than in the crystals as is shown by the experimental results.

IV. SUMMARY AND CONCLUSIONS

In blown films of vanadate glass based on the system V20 5-P20 5, the optical absorption has been studied in the range 33-25 000 em-I (300-0.40 J.L) as a function of temperature. In the intermediate and far-infrared range (33-1300 em-I) several vibrational absorption peaks have been observed, and the shape of the spectra and peak positions were unaffected by temperature between liquid-nitrogen and room temperatures. One peak in particular, at about 1010 em-I, appears to be the V -0 stretching vibration mode and indicates that the site symmetry of the vanadium cations in the glass may be similar to that in crystalline V20 5• A second absorption peak at about 1090 em-I is thought to be due to a phosphorous-oxygen complex vibration mode.

Between about 4000 em-I and the apparent funda­mental absorption edge of the glasses, which occurs in the short-wavelength region of the visible, a broad absorption tail was observed which is responsible for the dark black color of bulk samples. Although the cause of this absorption is not definitely ascertained, reduced vanadium ions may contribute to it.

The sharp absorption edge of the glasses in the short­wavelength region of the visible is dependent on both temperature and composition. An analysis of these data suggest that the fundamental absorption arises from direct forbidden transitions and occurs at about 2.4 eV. In these respects, with the exception of the dependence of Eg on composition, the absorption edge in this glass

system is the same as that in crystalline V205 and thus is thought to occur from the same mechanism.

ACKNOWLEDGMENTS

The authors are indebted to Professor Miles V. Klein for helpful discussions and for the use of optical equip­ment, to Dr. Hugh Macdonald for many helpful dis­cussions and courteous cooperation, to Dr. Hans Peisl for performing the far-infrared transmission experiment extending the range of observation to 20 em-I, to Professor G. Jacobs for providing the crystalline V20 5

samples, and to Miss Sophie Lau and Mr. David Fong for assistance in the data reduction.

* Work supported in part by the U.S. Atomic Energy Commis­sion and the Advanced Research Projects Agency.

t Current address: U.S. Naval Research Laboratory, Washing­ton, D.C. 20390.

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THE JOURNAL OF CHEMICAL PHYSICS

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VOLUME 52, NUMBER 12 15 JUNE 1970

Calculation of Ion-Molecule Reaction Product Distributions Using the Quasiequilibrium Theory of Mass Spectra

S. E. BUTTRILL, JR.*

Department of Chemistry, Stanford University, Stanford, California 94305

(Received 29 January 1970)

The quasiequilibrium theory of unimolecular reactions is applied to the calculation of ion-molecule reaction product distributions in ethylene and ethylene-acetylene mixtures. The unimolecular decomposition rates of the ion-molecule reaction complex are computed using the continuous approximation of Vestal et al. O. Chern. Phys. 37, 1276 (1962)]' The reactions investigated include

CaH5++CH3, [1J /'

C~++C~ '\0

C4H7+H, [2J

CsHa++CHa, [3J /'

C~++CaH2 '\0

C,H5++H, [4J

as well as analogous reactions of the perdeuterated compounds. The calculated and experimental product distributions are in good agreement. When the reaction complex is formed from only partially deuterated reactants, there is an isotope effect favoring loss of hydrogen over deuterium. The theory accurately predicts this effect. The calculation of isotope effects allows very little freedom in the choice of variables such as activation energy or activated complex configurations. The success of these calculations is therefore strong evidence for the validity of the equilibrium hypothesis.

I. INTRODUCTION

The quasiequilibrium theory of unimolecular reac­tions was first applied to the calculation of mass spectral fragmentation patterns by Rosenstock, Wallenstein, Wahrhaftig, and Eyring.' The general expression for the average reaction rate of a molecule or ion is

(1)

where Eo is the activation energy for the reaction, h is Planck's constant, and p(E)dE is the number of states of the reactant with energy between E and E+dE. The function pt(e) is the density of states obtained by including all of the degrees of freedom of the activated complex except the reaction coordinate. The amount of translational energy in the reaction coordinate is E-Eo-e so that the sum in Eq. (1) is over all of the possible ways of partitioning the excess energy E- Eo between the reaction coordinate and the rest of the

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