Physicochemical properties and catalytic behavior of manganese oxides

Physicochemical properties and catalytic behavior of manganese oxides

Physicochemical Properties and Catalytic Behavior of Manganese Oxides L. D. AHUJA,* D. RAJESHWER,* AND K. C. N A G P A L t *Department of Chemistry, I...

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Physicochemical Properties and Catalytic Behavior of Manganese Oxides L. D. AHUJA,* D. RAJESHWER,* AND K. C. N A G P A L t *Department of Chemistry, Indian Institute of Technology, New DelhL 110 016, India; and ~fX-Ray Division, National Physical Laboratory, Hillside Road, New Delhi-110 012, India Received August 15, 1986; accepted November 11, 1986 Two series of manganese oxides have been prepared by the thermal decomposition of manganese carbonate and oxalate under v a c u u m (300-900°C temperature). The kinetics of aqueous H202 decomposition on these oxide surfaces have been studied. The reaction was found to be first order with respect to [H202]. Catalytic activities were found to be decreasing with the increasing temperature of decomposition. X-ray diffraction studies of the powdered samples show that the samples contain mainly two types of structures. NaCI(MnO) and calcinite (Mn304). Infrared spectra show a characteristic band at 796 c m -~ for the sample obtained by the decomposition of both M n oxalate and M n carbonate at 750 and 900°C. Samples prepared at other temperatures show similar characteristic bands, i.e., at 1124, 604, and 484 cm -1, etc. Surface areas vary from 112 to 4 m2]g. Pores are mainly o f cylindrical shape. There is an agglomeration o f the particles as the temperature of decomposition is increased. Conductivity measurements indicate that most of the samples show p-type semiconductivity. © 1987AcademicPress,Inc.

EXPERIMENTAL

INTRODUCTION

In an earlier work done in our laboratories (1) with cobalt chalcogenides, it was found that the physicochemical characteristics and catalytic properties o f a solid depend mostly on its method of preparation. An attempt was made (1) to correlate these characteristics with chemical composition and other physical properties. But in those chalcogenides, the crystal structures of various samples differed greatly and hence no firm conclusion could be derived. A perusal of the literature showed that the crystal structure of manganese chalcogenides does not differ to a large extent. It falls broadly into two categories, i.e., NaC1 structure or the calicite structure. It was thought that a study of the physicochemical characteristics of manganese chalcogenides and their catalytic properties may enable us to distinguish the relative roles played by the textural and structural factors. With this idea in mind, a detailed study of the oxides was undertaken. Studies for sulfides, selenides, and tellurides have also been made and the results will be communicated in a subsequent publication.

Catalyst Preparation Manganese oxalate (BDH) or manganese carbonate (BDH) was taken in a quartz tube closed at one end while the other side of the tube was connected to a vacuum system (~<10 -2 m m Hg), which was fitted with K O H and with fused CaCI2 traps to absorb carbon dioxide and moisture, respectively. The quartz tube was heated in a horizontal tubular electrical furnace with temperature indicator and controller. The rate of heating was programmed to 4°C per minute. The samples were maintained at the desired temperature for 6 h, cooled to room temperature under vacuum, and exposed to N2 gas before being taken out. All the samples were ground in a pestle and mortar, seived to - 100 (BSS) mesh, and stored in a vacuum desiccator over fused CaCI> The samples prepared from manganese oxalate were labeled as M O X - T ° C and those from the manganese carbonate as MC-T°C, where T is the decomposition temperature in degrees Celsius. 481

Journalof Colloidandlnterface Science,Vol. 119,No. 2, October 1987

0021-9797/87 $3.00 Copyright© 1987by AcademicPress,Inc. All rightsof reproductionin any formreserved.

482

AHUJA, RAJESHWER, A N D N A G P A L

He02 Decomposition Reaction of HzO2 decomposition was studied according to the procedure laid down in (2), which was a modification of the procedure described by Deren et aL (3) and Cota et al. (4). This heterogeneous gasometric reaction was studied at different temperatures to enable us to calculate kinetic parameters such as specific rate constant, apparent energy of activation, and preexponential factor. The optim u m concentration of HzO2 chosen was 0.5% w/v.

Measurement of Electrical Conductivity The electrical conductivities (or)of powdered samples were measured by a technique adopted by Kramorz and Zajecki (5) in which the powdered sample was compressed into a pellet at a constant pressure (9 tons/in.Z); the electrical resistance across the pellet was measured with multimeter. Temperature of the cell was controlled by a programmable temperature indicator. A chromel-alumel thermocouple was used as a temperature probe.

Qualitative Analysis The far infrared absorption spectra of all samples were recorded on Nicolet 5 D X FTIR spectrometer--with KBr as a binder. For phase analysis, the oxide samples were subjected to the X-ray powder diffraction technique (XRD). The work was carried out on a Philips (Holland) X-ray diffractometer with a scintillation counter and pulse height analyzer at 35 kV, 14 mA, using CuK~ (1.5405 ~,) radiation. The scanning speed was 1 °/min at 2 × 102 Cps. From the two values on the diffractogram, we calculated interplanar spacings (d-lines). These d-fines and their relative intensities were compared with those in ASTM literature, in order to determine the phases present.

absorption spectrometer (AAS) (Pyeunicam, Model SP 191). Solutions for AAS analysis were prepared by decomposing the samples in 5 ml of concentrated H2SO4 (A.R.) + 5 ml of concentrated HC1 (A.R.). For analyzing M n 2+ concentration, we used the eolorimetric method of Aimassy and Wezso (6). This method depends on the catalytic effect o f Mn z+ on the reaction of C20]- with CrzO~-. A mixture of 0.5 ml 10% NazCO3, 0.3 ml saturated NazCzO4, 0.3 ml H3PO4, and 0.2 ml 1% KzCr207 was added to the sample analyzed and the contents were placed in boiling water for 10 rain. The intensity of the green color at 470 #m was measured. As will be shown later, our samples have only Mn 2+ and M n 3+ ions at the surface. We can calculate the concentration of M n 3+ from the total manganese and Mn z+ concentrations, respectively. These results have been further confirmed by iodometric analysis (7).

Textural Studies Specific surface areas (SBET) of manganese oxides were determined by the conventional BET apparatus with small modifications, which enable us to study complete adsorption and desorption isotherms. Dry nitrogen was used as the adsorbate at liquid nitrogen temperature, on initially degassed samples at 200°C for 2 h. The area o f cross section for an Nz molecule was taken to be 16.4 ~z. Specific surface areas (Smo,o) of manganese oxides were also measured by a rapid surface area analyzer, Model 2200 A (Micrometrics). Average particle size was calculated from micrographs taken on a scanning electron microscope (Cambridge, Model Stereoscan $410). The surface acidity (Brfnsted) of these oxides was measured with the n-butyl amine titration method (8), using p-dimethyl aminobenzene as indicator.

Quantitative Analysis

RESULTS A N D DISCUSSION

Total manganese concentration in our samples was determined by using an atomic

X R D patterns of oxides prepared from manganese oxalate are shown in Fig. 1. From

Journal of Colloid and Interface Science, Vol. 119,No. 2, October 1987

483

PROPERTIES AND BEHAVIOR OF MANGANESE OXIDES

~6 ~

~1',~',,,,,,,~',,~

"~*5

I-z LU I-Z

sharp as the temperature of decomposition is increased, thus showing that the degree of crystallinity is increasing with the temperature of decomposition. XRD patterns of manganese oxides prepared from carbonates are also given for comparison (Fig. 2). Far infrared spectra of MOX- T°C samples are shown in Fig. 3. Spectra of MOX-300 show the presence of Mn304 and no MnO. A spectrum of Mn304 is very complicated. This may be due to its tetragonal symmetry. Characteristic absorption bands at 1112- and 604-cm -1 broad bands and 484-, 404, and 328-cm -1 bands are due to lattice vibrations of Mn304 (9). Infrared spectra ofMOX-500, MOX-750, and MOX-900 samples showed a 796-cm -1 absorption band indicating the presence of MnO. The increasing sharpness of this band with the temperature of preparation shows the increasing phase concentration of MnO. The absorption band at 1124 cm -1 is common in

~

¢o 6'5

6'0 5'5

6

5'0 4'5 4'0 3'5 3'0 2~

FIG. 1. X-ray diffraction spectra of manganese oxide prepared at different temperatures from manganeseoxalate at (°C) (1) 300, (2) 400, (3) 500 (4) 600, (5) 750, (6) 900.

the d-lines at 2.49, 2.77, and 1.54 ~, with respective relative intensifies of 100, 85, and 50, we infer the presence of calicite crystal structured Mn304 (hausmanite), while from the dlines at 2.22, 2.57, 1.57, and 2.568 A with respective relative intensities 100, 62, 58, and 62, we infer the presence of NaC1 crystal structured MnO (manganosite). It is also seen from the XRD pattern that the peaks are broad at low temperatures and gradually become

~ 4

8'o

7'o

6'o'

4o-'

4o

2(~ DEGREE

~o

2'o

FIG. 2. X-ray diffraction spectra of manganese oxide prepared at different temperatures from manganese carbonate at (°C) (1) 300, (2) 400, (3) 500, (4) 600, (5) 750,

(6) 900. Journal of Colloid and Interface Science.

Vol.119,No.2, October1987

484

AHUJA, RAJESHWER, AND NAGPAL

z <

z n-. I-

1000.0

800.0 600.0 400.0 WAVENUMBER (CM -1)

200.0

FIG. 3. Infrared absorption spectra of manganese oxide prepared from its oxalateat temperatures (°C) (I) 300, (2) 400, (3) 500, (4) 600, (5) 750, (6) 900.

all samples and can be attributed to m e t a l oxygen band vibration in manganese oxides. Table I lists the qualitative and quantitative

analysis results of manganese oxides prepared from manganese carbonate and oxalate decomposition, respectively. Kinetic parameters for the decomposition of H202 on manganese oxide surfaces are given in Table II. It is found that in both series, there is a linear relation between the specific rate constant (K) and the M n 3+ concentration. HzO2 decomposition follows first-order kinetics on all manganese oxide surfaces (Fig. 4). During the reaction, the p H of the solution changes from 5.2 to 8.5. The activation energies for this reaction vary from 3.2 to 19.8 kcal mole -1 in the carbonate series and from 8.7 to 19.2 kcal mole -l in the oxalate series. To find out how the surface morphology changes with the increasing temperature of decomposition, we studied the complete N2 adsorption and desorption isotherms of MC400, MC-900 and MOX-300, MOX-900 as representative samples from the two series. Figures 5a and 5b show the adsorption and desorption isotherms of N: at liquid N2 temperatures for the samples MC-400, MOX-300 and MC-900, MOX-900 respectively evacuated at 200°C temperature. MC-400 and MOX-300 gave Type IV adsorption isotherms having hysteresis at the higher pressure range, which m a y be ascribed to the pressure of me-

TABLE I Quantitative and Qualitative Analysesof Manganese Oxide Samples Volumetric and colorimetric analyses

Catalyst

Phases present (XRD)

O/Mn ratio (AAS)

MC-300 MC-400 MC-500 MC-600 MC-750 MC-900

Undecomposed MnCO3 Mn304, MnCO3 traces MnO, Mn304, MnzO3traces MnO, Mn304 MnO, Mn304 traces MnO

-1.56 1.28 1.18 1.02 0.99

MOX-300 MOX-400 MOX-400 MOX-600 MOX-750 MOX-900

Mn304 Mn304,MnO MnO, Mn304 traces MnO, Mn304 traces MnO MnO

1.402 1.33 1.24 1.07 1.02 0.998

Journal of Colloid and Interface Science, VoL 119, No. 2, October 1987

Weight percent Mn304

3.203 57.65 19.60 13.39 1.53 1.57 100 95.22 18.21 1.08 0.61 --

Weight percent MnO

Percentage Mn+3

Percentage Mn+2

-42.35 80.40 86.61 98.47 98.43

4.4 39.76 13.53 9.24 1.07 1.08

95.6 60.24 86.47 90.76 98.93 98.92

-4.78 81.79 98.9 99.39 100

68.9 65.66 12.56 0.75 0.43

31.1 34.34 87.44 99.25 99.57 100

-

-

485

PROPERTIES AND BEHAVIOR OF MANGANESE OXIDES TABLE II Kinetic Parameters for the Decompositionof Aqueous H202 (0.5%) on the Manganese Oxide Surfaces Rate constant (K) × - 1 6 +2 (rain ~) 50°C

40°C

36°C

Energy of activation E~ (kcal/mole)

logwa

MC-300 MC-400 MC-500 MC-600 MC-750 MC-900

7.02 42.16 17.53 13.71 10.4 4.34

2.82 34.02 9.04 9.41 5.70 2.53

1.56 31.23 6.35 9.36 3.22 1.95

19.79 3.27 13.32 10.0 11.35 10.82

12.18 1.81 8.20 7.95 6.63 5.91

MOX-300 MOX-400 MOX-500 MOX-600 MOX-750 MOX-900

57.98 8.29 2.82 2.81 2.51 1.44

33.11 5.78 1.32 1.38 1.14 0.55

19.61 3.57 0.58 0.64 0.501 0.20

10.75 8.70 15.10 14.42 12.36 19.22

7.02 4.84 8.66 8.05 6.69 11.16

Catalyst

sopores in the sample, while MC-900 and MOX-900 gave Type III adsorption isotherms with small hysteresis at the higher pressure range. With reference to de Boer (10) classi-

24

t1

20

18

T 16

+~ 14 ×

12

'J

2

4

6

8 10 12 Time (min) ......

14

16

18

FIG. 4. First-order plots for decomposition of H202 on manganese oxides prepared from oxalate at temperatures (°C) (1) 300, (2) 400, (3) 500, (4) 600, (5) 750, (6) 900.

fication, we can say that both samples are macroporous. However, it will be reasonable to opine that the pores may be formed by nonparallel plates. Surface acidities of these samples as a function of decomposition temperature are given in Table III. Figure 6 shows the relation between the specific rate constant for H202 decomposition (kmin -1 M -2) and the surface acidity (#eq/M 2 cat.). As already indicated, the oxides fall under two categories and there is an inverse relation. However, this inverse relation is obeyed by the M C - T ° C series but not by the M O X - T ° C series. To measure the average particle size o f our samples, we recorded the number of scanning electron micrographs for each sample enabling us to average over a large number of particles. The results are shown in Table II. In the M C - T ° C series particles are spherical in shape and increase in size from 2416 to 3442 ~, with the increasing temperature of their preparation. In MC-900, particles are agglomerating leaving broad voids. These results are in good agreement with the data shown from adsorption isotherms. It is interesting to note that particles in the case of MOX-300 and MOX-900 have regular spherical shapes while others have irregular flakes. Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

486

AHUJA, RAJESHWER, AND NAGPAL

z,.O O-MC-400 &-MOX-300

o_ 3.0

Q

~ 2.0 <

>o 1.0

0,~

oJ

0J

o.~

oA

o.~

oJ

o.~

o.6

~o

o.~

o.g

1~o

PI~ b

~lOi~

o'MC--900

~-MOX-900

"7 3.0 m [3_

u

c3

~o

2.0

P~ 3

o> 1.0

o.~

0.2

o.'3

o.'~

o.'s

o~

o~z

PIPo

FIG. 5. Adsorption isotherms of N2 on (a) MC-400 and MOX-300 and (b) MC-900 and MOX-900. (Solid line, absorption isotherm; broken line, desorption isotherm.)

Journal of Colloid and Interface Science, Vol. 119, No. 2, October t987

PROPERTIES AND BEHAVIOR OF MANGANESE OXIDES

487

TABLE III Surface Morphological Studies of Manganese Oxide Catalysts Specific surface area Catalyst

SBzr (m2/g)

MC-300 MC-400 MC-500 MC-600 MC-750 MC-900 MOX-300 MOX-400 MOX-500 MOX-600 MOX-750 MOX-900

S~

Particle size (SEM) (A)

(m2/g)

11.0 26.5 18.2 17.8 10.4 6.5

12.3 28.2 19.0 18.3 11.0 7.8

112.2 29.8 11.8 13.2 14.0 4.0

119.5 31.5 12.5 13.6 14.1 4.2

2660 2416 2681 2695 3080 3442

Electrical Conductivity Measurements As o u r samples were prepared above a temperature o f 300°C, their electrical conductiv3k16 ~ C-750

'1~ C-900

Surface acidity (#eq/m 2 cat.)

Rate constant (K) at 40°C (min -1 m -2) × 10-~

40.16 22.27 18.35 14.38 15.07 23.66

2.56 6.42 4.97 5.29 27.4 19.46

3.42 11.27 23.53 15.31 40.69 108.87

2.95 1.94 1.12 1.05 0.82 1.37

ities were m e a s u r e d between 40 and 2 5 0 ° C to find out the energy o f activation for c o n d u c tivity. In Fig. 7, lOgloa values o f various samples o f manganese oxide f r o m oxalate d e c o m position are plotted as a function o f the reciprocal o f absolute temperature. Each o f the curves is linear a n d shows a negative slope, but exhibits a discontinuity in the temperature region 85-150°C. The data can be represented by the general expression

9XI06

~- MC-400

E ~c

MC-600 M C-500

MOX-300

IXI~

MC-300

MOX-SO0Oo0M~

,'0 MOX-~.OO • MOX-750

i'o

2~

3'0

SurYace

acidity / d E q / m 2

~o

sb

6'o

FIG. 6. A plot to correlate surface acidities and specific rate constants of manganese oxides.

F r o m the equation [1] the activation energy (Ea) can be obtained. Results are given in Table IV. To correlate the conductivity with other parameters, we choose the conductivity value o f each sample measured at 100°C. M n O differs f r o m other oxides o f m a n ganese in that it can exist either as an n-type or as a p-type semiconductor, whereas others exhibit p-type semiconductivity (11, 12). In this temperature range, the conductivity m a y be due to the mobility o f the charge carriers. Activation energies for conductivity were f o u n d to be in agreement with the values o f Z i m a n (13) f o u n d in the temperature range 100-1 15°C, i.e., 1.37 eV. It is observed that Ea for electrical c o n d u c tivity follows a parallel relation with Ea for Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

488

AHUJA, RAJESHWER, AND NAGPAL

catalytic decomposition of H202 , thereby showing that the species which are responsible for the conductivity are also the ones which constitute the active sites for the decomposition reaction.

The Enthalpy of Chemisorption of Oxygen on Manganese Oxide

-7.C t~

\

-g.0

1.~

2J8

22

i

I 2.~

A

218

3!0

112

l I T × ~o3

FIG. 7. Electrical conductivity as a function of inverse temperature for manganese oxides prepared from oxalate at temperatures (°C) (A) 300, (×) 400, (O) 500, ([3) 600, (O) 750, (A) 900.

When the sample of manganese oxide, after the carbonate was heated under v a c u u m at a temperature of 400°C, was exposed to the atmosphere, a fast reaction liberating an enormous a m o u n t of heat occurred. The reaction was so fast that the color of the sample changed from gray to brownish black in a few seconds. This liberation of heat m a y be due to a reaction with either atmospheric oxygen or moisture. To decide which of these two possibilities is the actual cause of the liberation of heat, another sample was decomposed in two thinwalled glass bulbs, which were sealed after the decomposition. The sealed bulb was broken in a calorimeter containing distilled water maintained at a constant temperature. The rise in the temperature of water in the calorimeter was negligible. It thus appeared that the cause of liberation of heat was probably the rapid oxidation of lower oxide of manganese to

TABLE IV The Values of Electrical Conductivity and Energy of Activation in Manganese Oxide Samples

Catalyst

Electrical conductivity (a) at 373 K (ohm-' - cm -2) × 10-~

Activation energy for conductivity Ea (eV)

Forbidden energy gap calculated E B(eV)

MC-300 MC-400 MC-500 MC-600 MC-750 MC-900

-9.62 5.96 1.26 4.70 7.93

-1.597 1.224 1.184 1.454 1.227

-2.764 2.018 1.938 2.478 2.023

MOX-300 MOX-400 MOX-500 MOX-600 MOX-750 MOX-900

5.71 2.38 1.63 0.969 0.965 0.804

1.151 0.873 0.912 1.112 1.271 1.428

1.872 1.316 1.394 1.794 2.110 2.430

Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

489

PROPERTIES AND BEHAVIOR OF MANGANESE OXIDES TABLE V Effect of pH on the Decomposition of Aqueous H202 at 40°C on Manganese Oxide Samples Rate constant (K) X 10-2 (min t) at p H Active catalyst in series

2.0

4.0

7.0

9.2

K without buffer (min) -j X 10-2

MC-400 MOX-300

3.75 2.26

0.278 0.183

0.979 0.279

50.7 71.1

3.40 3.31

maintained at constant values of p H by using standard buffer solutions. It was found that rates of decomposition were considerably higher at higher p H as compared to those at lower pH, for samples obtained from both M n carbonate and M n oxalate. However, beyond a p H of 9, autodecomposition of ricO2 started and the rate became too fast to be controlled. The values of K on MC-400 and MOX-300 representative samples at different p H are given in Table V.

higher oxides on exposure to the atmosphere. To confirm this, the sample in the second bulb was exposed to oxygen. An appreciable volu m e of oxygen gas absorbed and the color of the sample changed from grey to brownish black. A perusal of the literature showed that the gray sample corresponded to approximately MnO, while the brownish sample m a y be Mn304. This type of behavior was not observed with manganese oxide prepared from oxalate decomposition.

Heterogeneous or Homogeneous Reaction Effect of pH on the Decomposition of HeOe

It is just possible that decomposition of H202 m a y be partly homogeneous and partly heterogeneous. In order to verify this, 10 mg of each of the MC-400 and MOX-300 catalysts

To study the effect of the p H of the m e d i u m on the rate of H202 decomposition in the presence of oxide samples, the m e d i u m was

2 1

f

10

<

8. 0

2

q

5

8

10

o.



12

1L,

16

16'

20

22

E a { Kcet/'mote ) LOG10 A AS A FUNCTION OF ACTIVATION ENERGY E a

FIG. 8.

Logl~l as a function of activation energy. (1) -MOX-T°C, (2) -MC-T°C. Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

490

AHUJA, RAJESHWER, AND NAGPAL

was added to separate flasks containing 20 ml of 0.5% H202 solution and the reaction was allowed to proceed for 5 h, after which the solutions were filtered. To 10 ml of each filtrate was added another 10 ml of the fresh H202 (0.5%) solution. It was found in both cases that the activity of the filtrate was almost negligible as compared to that in the presence of the solid sample, thereby showing that the entire reaction was heterogeneous. A comparison of the (CSFE) crystal field stabilization energy of M n 2+ and M n 3+ shows that the M n 2+ state is favored with a weak field ligand and the M n 3+ state is favored with a strong field ligand like the d 7 and d 6 systems of Co 2+ and Co 3+, respectively (14). This means that the M n 3+ state will be more stable in an alkaline m e d i u m than in a neutral me-

_1.2

dium. I f M n 3+ is mostly responsible for H202 decomposition, the rate of the reaction should be high in alkaline medium. This point has been established by the results K a t 4 0 ° C in N H 4 O H solution = 52.7 × 10-3min - ' K a t 40°C in aqueous solution = 34.02 × 10 -3 m i n -1.

Compensation Effect A linear reaction between the preexponential factor and the energy of activities has been observed as shown in Fig. 8. The parallel nature of the curves logA vs 1/Tis shown in Fig. 9, which shows that there is no progressive decrease in the energy of various active sites obtained by the increasing temperature of decomposition. At this stage, it is not possible for us to address anything beyond that. REFERENCES

3.G

3.8

3.o

~'

+ ~ lo~._-~ 3~

I

3.~

FIG. 9. Arrhenius plots for H202 decomposition on Mn oxides prepared from oxalates at temperatures (°C) (©) -300, (A) -400, (O) -500, (El) -600, (A) -750, (m) -900. Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

1. Ahuja, L. D., and Brar, A. S., J. Colloid Interface Sci. 50, 197 (1975). 2. Ahuja, L. D., Rajeshwar, D., and Nagpal, K. C., in "Advances in Catalysis Sciences & Technology" (T. S. R. Prasada Rao, Ed.), p. 563. Wiley, India, 1985. 3. Deren, J., Hasu, J., Podgorecka, A., and Burzyk, V. J., J. Catal. 2, 161 (1963). 4. Cota, H. M., Katan, J., Chin, M., and Schoenweis, F. J., Nature (London) 203, 1281 (1964). 5. Kramorz, W., and Zajecki, J., Pol. J. Chem. 54, 2075 (1980). 6. Almassy, Gy., and Wezso, I., Magy. Kem. Foly. 60, 249 (1954). 7. Vogel, A. I., "A Textbook of Quantitative Inorganic Analysis," p. 356. Longmans, Green, London, 1978. 8. Johnson, 0., J. Phys. Chem. 59, 827 (1955). 9. R. A. Nyquist, and R. O. Kagel, "Infrared Spectra of Inorganic Compounds," Spectra No. 337. Academic Press, New York, 1971. 10. De Boer, J. H., "The Structure and Properties of Porous Materials" (D. H. Everett and F. S. Stone, Eds.), p. 68, Butterworths, London, 1958. 11. Eror, N., Ph.D. thesis, Northwestern University, 1965. 12. Becker, J. H., and Frederikse, H. P. R., J. AppL Phys. Suppl. 33, 447 (1962). 13. Ziman, J. M., "Electrons and Phonons," p. 437. Oxford Univ. Press (Clarenden), 1962. 14. Carra, S., Egtratto dalla Ravista Lachemical E L'Industria 53, 366 (1971).