Far infrared optical properties of polycrystalline NaClO3, KClO3, NaBrO3 and KBrO3

J. Phys. Chem. Solids, 1973,Vol. 34, pp. 1993-201)2. PergamonPress. Printedin Great Britain

FAR INFRARED OPTICAL PROPERTIES OF POLYCRYSTALLINE NaCIO3, KC103, NaBrO3 AND KBrO3* J. D. NEUFELDt and G. ANDERMANN Chemistry Department and Hawaii Institute of Geophysics, University of Hawaii, Honolulu, Hawaii 96822, U.S.A. (Received 27 N o v e m b e r 1972; in revised form 12 April 1973)

Abstract--The resonant frequencies, damping constants and oscillator strengths of far infrared lattice vibrations of polycrystalline NaC103, KC103, NaBrO~ and KBrO3 have been obtained through classical dispersion (CD) analysis of transmission data. Space group analysis has been applied for attribution assignments and to ascertain the translational and rotational character of the respective lattice bands. The damping constants were found to be unusually large indicating short lifetimes of the excited states in spite of an apparent absence of phonon-phonon coupling. The CD analysis of the spectra also provide reliable values of oscillator strength and resonant frequency. 1. INTRODUCTION

RECENT technological advances in far i.r. spectrometry have provided for a quantitative evaluation of the optical properties of lattice modes of polyatomic ionic solids. Far i.r. and Raman spectra of NaC103 have been obtained [1, 2] by utilizing single crystal techniques. The experimental data published by Hartwig et a/.[1] is somewhat incomplete due to their non-observance of an i.r. active mode at ca. 126cm -t as reported by other workers [2] and as found in this work. Hartwig et a/.[1] have obtained transition strength ($3, resonance frequency (v3 and damping constant (,/j) values from the transverse-longitudinal frequency splitting. Since Hartwig's method for these dispersion parameter values employs a 'best fit' procedure at only the spectral maximal and minimal values, we feel it is inadequate for a complete and quantitative description of optical properties. The attribution assignments made by Montaner and Galtier [2] may be considered as incomplete also as they have been carried out on only four i.r. active translational modes,

whereas space group theory predicts the existence of five modes [1]. The far i.r reflectance spectrum of NaBrO3 has been reported in the literature[3]; however, the evaluation of optical properties has been limited to a graphic representation of the real and imaginary dielectric index curves [3], as obtained by a relatively crude Kramers-Kr6nig dispersion analysis. Reflectance spectra of KC103 and KBrO3 have not been obtained due to the general unavailability of large single crystals of these salts [19]. Consequently, we have been forced to develop the technology of obtaining reliable transmission spectra of polycrystalline NaC103, NaBrO3, KC103 and KBrO3 from thin films[4, 5] in order to obtain reliable optical data for these materials. The purpose of this paper is to discuss the number, symmetry assignments, and attribution assignments of the respective lattice modes for each salt and to report detailed information on the optical properties for each substance. 2. EXPERIMENTAL METHOD

*Hawaii Institute of Geophysics Contribution No. 528. tPresent Address: University of North Carolina, Chapel Hill, N.C. 27514, U.S.A.

The far i.r. transmission spectra were obtained from polycrystalline thin films that

1993

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J . D . N E U F E L D and G. ANDERMANN

corrected for phase errors, appodised, and averaged before the Fourier transformation was performed on them. A complete description of the computer program is given in the appendix of Ref. [5]. This procedure provided transmission spectra with a precision of approximately 0.5 per cent in the individual transmission values. The individual experimental spectra are illustrated in Figs. 1-4.

were deposited on a high density polyethylene substrate[4]. These films ranged from 0.8 to 1.2/~ in thickness and were found to be uniform[4]; i.e. the films exhibited a variation in transmission values at v~ of approximately 1.0 per cent when measured at six independent areas of the film. The respective spectrum of each sample was calculated from a set of interferograms that was obtained from an R.I.I.C. FS 720 interferometer. Generally, five sample interferograms were obtained alternatively with the same number of substrate interferograms. The respective sets of interferograms were I

3. METHOD OF CALCULATING OPTICAL PROPERTIES

A self-bracketing-search (SBS) classical dispersion analysis technique was used to

i

I

I

I

,

r

I

.~

S

9(3

8O oe

7O --To 60

eooeo

Tx

I

L

I

60

100

140

I

180

220 260 ~,(c~"1)

300

I

I

I

460

480

500

Fig. 1. Transmission spectrum of NaC103. Tx = experimental and T,, is calculated from averaged DHO dispersion parameter values.

[

I

I

I

I

I

I

I ~'

I

I

lee

e~/

9C

8O

m T

6O

c

oeooo Tx

I 100

120

140

160

180 200 ,,(cm-] )

220

240" 470

Fig. 2. Transmission spectrum of KCIO3.

490

FAR INFRARED OPTICAL PROPERTIES OF POLYCRYSTAI.LINE l

i

1995

i

f 8O

Na BrO 3

70

60 ~T~

5G

aeeoo'rx

60

140 ]

I00

180

220

360

v(cm"1}

400

440

480

Fig. 3. Transmission spectrum of NaBrO3.

bands in the spectrum. The final constant value of Q may be attributed to random or nonrandom errors in the experimental spectrum, or to failure of the experimental spectrum to match the calculated uncoupled DHO spectrum, due to harmonic [7] or anharmonic[8] coupling of the oscillators. By evaluating the precision of the experimental spectrum, it is possible to estimate the total random error here defined as Q*. Serious efforts were carried out to eliminate or minimize the nonrandom errors in the experimental spectrum. By subtracting the Q* value from the Q value, i.e. AQ = Q - Q* and dividing the remainder by Q*, we have obtained a

minimize the deviation between the experimental transmission spectrum and a spectrum calculated by employing an isolated, (uncoupled) damped harmonic oscillator, DHO, model [6]. The deviation or error function is expressed by the equation Q=

f

(1)

( Tc-Tx)2dv

Region

where Tc is the calculated transmission spectrum, T~ is the experimental transmission spectrum, and v is the frequency in wavenumbers. Q is minimized by systematically adjusting the vj, 7i and Sj values [6] for each of the i

i

i

i

~

i

t

KBrO 3

60 hT~ 50

i

f--

80

7, 70

i

Tx

60

100

140

180

v(cm "I)

3 0

3 0

Fig. 4. Transmission spectrum of KBrO3.

460

1996

J.D.

NEUFELD

and G. A N D E R M A N N

AQ/Q* value that is normalized according to the range of the integral in equation (1). This normalized AQ/Q* value is useful in comparing the magnitude of deviation between the respective experimental sets of data and those of the uncoupled DHO model. Upon application of this method on the far i.r. transmission spectra of NaCIO3, NaBrO3, KCIO3 and KBrO3, an unusually small value of AQ/Q* was found to exist for these substances, e.g.

tallography [10]. NaCIO3 and NaBrO3 contain cubic 7"4 space symmetry; KCIO3 contains monoclinic C~h space symmetry, and KBrO3 contains rhombohedral C~o space symmetry. By employing correlation diagrams and the Fateley method[9] of making use of space symmetry, the number of theoretically allowed external fundamental vibrational modes was determined for the translational and rotational motion of the ions in the lattice. A sum, mary of the results as applied to these salts is AQ/Q*(NaC103) = 0-21, shown in Table 2. AQ/Q* (NaBrO3) = 0"0, The problem of frequency assignments, i.e. associating an observed resonant frequency AQ/Q* (KC103) = 0.04 with a theoretically derived irreducible repand resentation, is rather complicated in the case AQ/Q* (KBr03) = 0-6. of NaC103 and NaBrO3 where each lattice As indicated by Kachare et a/.[8] the S~ and vj contains a total of 57 optical modes of vibradispersion parameter values obtained by this tion. With laser Raman spectroscopy the varimethod may be considered to be reliable even ous orientations of the crystal through polarin the presence of strong anharmonic ization measurements have been used to idenphonon-phonon coupling where AQ/Q* val- tify many of the vibrations that are Raman ues are high, i.e. for LiF, AQ/Q* = 216.0 and active[l 1]. This information has been correfor MgO, AQ/Q*=26.0. Since the present lated with i.r. data to make the separate asstudy AQ/Q* values approach zero, the dis- signments of the fundamental modes. This persion parameter values can be considered to section is divided into three parts in order to be highly reliable, including the ~/j values [8]. discuss the different types of space groups The final calculated transmission lattice represented in the alkali halogenate crystal, as spectra of the individual alkali halogenate sol- shown in Table 2. ids are shown in Figs 1-4. The spectra were calculated by averaging the final parameter 4.1 NaCl03 and NaBr03 Correlation of theoretically derived symvalues from three or four different samples from each substance[5]. As shown in Figs. metry types with observed vibrational modes 1-4 there is very close agreement between T~ in the Raman and i.r. spectra of NaC103 has and Tx for all of the substances. The averaged been accomplished by Hartwig et a/.[1] The values used in calculating these spectra are attribution of these modes, i.e. whether or not summarized in Table 1. The respective values they are translational or rotational in nature, published by Hartwig et al.[1] for NaC103 has been performed by Montaner and have been included for comparison purposes. Galtier[2]. A summary of the NaC103 assignments along with our assignments for the 4. SYMMETRY ASSIGNMENTS NaBrO3 lattice modes has been included in Space group analysis [9] was used to deter- Table 3. We have also included in Table 3 a mine theoretically the number and group sym- comparison of our v~ values with those that metry of the respective fundamental lattice have been reported in the first two references. modes that are Raman and/or i.r. active. The Hartwig et a/.[1] have observed an F-type space group symnetry of each of these salts mode at 183 cm -~, that Montaner et a/.[2] have has been determined by X-ray _crys- not taken into consideration thereby making

FAR INFRARED OPTICAL PROPERTIES OF POLYCRYSTALLINE

1997

Table 1. Averaged DHO parameter values for lattice modes of NaCl03, KCI03, NaBr03 and KBr03 Band No. L,

L~

L3

/.4

Ls

L6

/-.

Ls

Hartwig et al.[1] NaCIO3

Parameter S c m -z 3' c m -~ v c m -1 S c m -~ 3,cm i v cm-' S cm 2 3' c m - ' u cm ' S c m -~ 3,cm vcm 1 Scm ~ 3' c m - ' v cm ' S c m -2 3" c m ' v c m -~ Scm ~ 3"cm 1 vcm S c m -z 3' c m -~ v c m -~

5170 5 72

NaC103 2584,0 7,0 74.2

3442.0 12.5 125.7

13800 12 142 15000 20 176

13500.0 14.0 143.7 9190.0 14.9 180.2

7690 15 202

20589.0 29.3 208-0

their attributions questionable. Since the analogous mr,de has been observed in the i.r. spectrum of NaBrO3, it appears that this mode should be rotational, producing more rotational modes than are allowed by theory, as

KC103

NaBrO~

KBrO3

391-8 7.2 80.9 530.0 5'9 121.6 16888.0 31.4 131.0 16005.0 50-9 157.1

1795-0 5.3 76.8 310.0 9.3 98.2 3058.0 11-7 129-9

5813.0 21.8 97.1 14694.0 33.3 124-0 2015.0 20.1 169.2

8818.0 16.5 152.7 4468.0 12.8 178.1 2021.0 19-8 191.7 4673.6 20.0 214-7

shown in Table 2. Only four translational modes have been assigned by Montaner et al.[2] instead of the theoretically derived five. Because the i.r. intensity of the L3 mode in NaC103 and NaBrO3 is medium, it is likely that

Table 2. Summary of external fundamental modes Substance NaCIO3 and NaBrO3 KC103

Irred. Repr.

(T)

3A 5 E 5 F 15 A~ 9 A~ 6 B~ 6 B~ 9 KBrO3 A~ 4 A2 1 E 5 T total number of lattice modes A--acoustic modes T'--translational modes R'--rotational modes

JPCS Vol. 34, No. 11- P

(A)

(T')

(R l)

i.r.

Raman

0 0 1 0 1 0 2 1 0 1

2 2 5 4 1 2 2 1 0 1

1 1 3 1 2 2 1 0 1 1

0 0 8 0 3 0 3 1 0 2

3 3 8 5 0 4 0 1 0 2

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J . D . N E U F E L D and G. A N D E R M A N N

e2

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Q

e-,

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FAR INFRARED OPTICAL PROPERTIES OF POLYCRYSTALLINE this m o d e is translational. This assignment is based on the assertion that the rotational modes h a v e greater R a m a n intensity than i.r. intensity and that the translational m o d e s h a v e the opposite characteristics[12]. Since the L~ and L3 modes display a considerable a m o u n t of intensity in both spectra, it is possible that they are translational with some rotational character. The L2 and L4 m o d e s are attributed to rotations since their R a m a n intensity is large, their i.r. intensity is minimal and they have not been o b s e r v e d in our experiment. It should be noted that Montaner et al.[2] h a v e reported a shoulder at 90 c m -~ (the L2 mode) on their reflection spectrum. The (131) c m -1 rotational band for NaBrO3 was included for completeness in Table 3, h o w e v e r it was not o b s e r v e d in our i.r. data. R a m a n data, which is presently not available, is needed to verify this assignment. 4.2 KCi03 The analysis of the far i.r. spectra of KC103 involves the o b s e r v e d spectra of two w e a k modes at 81 and 122 cm -~ and two v e r y strong modes at 131 and 157 cm -~. Since the C2h unit cell s y m m e t r y of KC103 contains a center of s y m m e t r y , the R a m a n and i.r. spectral assignments do not overlap as f o r NaC103, therefore, essentially independent analysis is required. According to B a t e s [ l 1], the external motions of the C103- ions cannot be simply described as rotational or translational due to allowed mixing of translation and rotation at the acentric cite, C~. Therefore, the m o d e s that retain the largest a m o u n t of rotational character

1999

should still exhibit s o m e intensity in the i.r. With this rationale, it seems reasonable to attribute the two w e a k i.r. modes to the rotation of C103-. Since these modes differ appreciably in frequencies, it seems logical to assign the antisymmetrical B, representation to the higher energy vibrational 122 c m 1 mode and the symmetrical A, representation to the lower energy vibrational 81 cm 1 mode. This leaves one B, rotational mode unaccounted for; however, it would not be detected if it were located b e t w e e n the two v e r y strong i.r. bands. The two strong bands in the lattice region are attributed to translational vibration between the K + sublattice and the C103- sublattice. Since F ( T ) = A , + 2 B , , it is extremely difficult to justify a unique assignment of these two strong modes. Although the intensities of these modes are v e r y similar, the band width of the 157 c m ' b a n d is 1-6 times as large as the 1 2 2 c m - ' , thus raising the possibility of two similar types bands existing in the upper frequency band. With this possibility, the 131 c m -I band would h a v e A. s y m m e t r y and the 157cm -1 band would have B. symmetry. A s u m m a r y of the assignments is given in Table 4. 4.3 KBr03 T h e far i.r. transmission spectrum contains three bands at frequencies of 97, 124 and 169 c m -1 which display relative intensities of medium, very strong and weak, respectively. Since the theoretically derived s y m m e t r y representations of these modes can be expressed as (lattice)= lA(T~)+ E(T')+ E(R 1)

Table 4. Summary of external vibrational mode assignments for KCIO~ and KBr03 KCIO3

KBrO3

cm-'

Sym. type

Attribution

cm-'

Sym.type

Attribution

81 122 131 157

A. B. A. B.

R1 R' T~ T'

97.1

A,

T'

124-0 169.2

E E

T' R'

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N E U F E L D and G. A N D E R M A N N

(see Table 2), the frequency assignments and attributions are straightforward. The two strongest modes are attributed to translations of the K + and the BrO3 sublattices, therefore the stronger, higher energy 124 cm ~mode can be represented by the doubly degenerate E symmetry, and the weaker, lower frequency mode, 97 cm -J, can be represented by A1 symmetry. The weak band at 169 cm -1 is attributed to rotation of the BrO~ ion and is represented by E symmetry. This mode could possibly correspond to the 191.7 cm i rotational mode of NaBrO3, e.g. see Table 3. The fact that the KBrO3 band is at a lower frequency is consistent with the fact that all the internal vibrational resonant frequencies are less in the KBrO3 lattice than in the NaBrO3 lattice[13]. A summary of these assignments is given in Table 4. 5. ABSOLUTE INTENSITY OF RESPECTIVE LATTICE MODES

The total quantity of energy dissipation associated with a specific solid state vibrational mode may be obtained accurately by integrating the frequency dependent imaginary dielectric index band. With overlapping bands, such as in this study, highly reliable oscillator strength values can be obtained through using a physical model such as a DHO, especially for vibrational modes which yield low AQ/Q* values [6, 8, 20, 21]. The Sj results for the respective lattice bands of these alkali halogenates are given in Table 1. These were obtained by averaging the results from a number of different polycrystalline samples of each substance. Generally, the low frequency, low oscillator strength bands exhibited an approximate error of 20 per cent, e.g. the L1 and L2 bands of KC103 and NaBrO3, whereas the average deviation was 6.8 per cent for the remaining bands. The larger errors may be attributed to nonuniformity in the polycrystalline films and to errors in film thickness measurements. In examining the Sj values given in Table 1, the vibrational modes that are attributed to

translational motion between the respective ions (see Tables 3 and 4) have smaller absolute intensities for the bromate ion than for the cholarate ion. Since the motion of the ion is dependent upon its mass and its freedom to move, the bromate ion is expected to show less change in the charge distribution, a quantity which is directly related to the absolute intensity [ 14], than the chlorate ion in a similar type of translational motion in a similar lattice. Another factor that could be considered in explaining these differences in intensities is found in the 'flatness' of the trigonal pyramid associated with the halogenate ion. X-ray data show that the perpendicular distance from the halogenatom to the plane of the oxygen atoms is 0.48 A in the NaC103 crystal, whereas it is 0.585 A in the NaBrO3 crystal [10]. Along with the difference in 'flatness', the interatomic distance of N a - O is 0-25 A greater in the NaBrO3 lattice than in NaC103[10]. Therefore, with these observable differences in the environment around the ions, a translational motion would tend to produce a greater distortion in the charge distribution around the respective ions, which also effects the absolute intensities, when the ion is 'flatter' and the respective interatomic distances are less. Since the KC103 and KBrO~ lattices have different symmetries, the respective translational modes cannot be compared as in the sodium case.

6. LIFETIMES OF EXCITED STATES

Since the lifetime of an excited state is inversely proportional to the damping constant[15], one can experimentally determine the relative values of the lifetimes associated with the respective lattice modes of these alkali halogenates. In order to compare the relative magnitude of the respective modes, reduced values are used,, namely 3'* [16], i.e. 3'* = 3"J/vJ~ Table 5 summarizes the results found in this work along with the 3'* values for LiF and MgO. These diatomics have been included since they have been

FAR INFRARED OPTICAL PROPERTIES OF POLYCRYSTAI.I.INE

2001

Table 5. 3'* values for alkali halogenates Substance

Band

3'*

Substance

Band

v*

NaCIO3

L, L3 L5 /_6 L~

0.094 0.096 0-098 0.083 0.139

NaBrO3

KCIO3

L, La L~ L~

0.089 0.049 0.236 0.056

KBrO~

L~ La L~ L5 L6 /~ L~ L~ La L3 La

0.069 0.095 0.090 0.108 0.067 0.103 0.093 0.222 0.270 0.118 0.019

LiF*

MgO*

*Ref. [17].

shown to contain the shortest lifetimes found in diatomic lattices[16]. The anomaly of these alkali halogenate results lies in the unusually short lifetimes, i.e. large 3"* values of their lattice (external) modes. In the case of short lifetimes found in diatomic lattices, the large 3'* values may be attributed to the dissipation of energy through the crystal due to anharmonic coupling of the phonons, as exhibited, for example, in the assymetric broadening of the main band and in the phonon sum bands that appear in the LiF spectra [17]. Since the alkali halogenate lattice mode spectra can be represented by the uncoupled DHO model whereas the alkali halide spectra cannot be, these large 3"* values cannot be attributed to anharmonic coupling of phonons. In searching for a plausible explanation for this anomaly, one may argue that the large 3'* values may be due to several close-lying, overlapping transitions, rather than a single transition. For example, in the case of KC103, group theory predicts the existence of six lattice modes and only four are observed. The two modes that are not observed may be overlapping the ones that are observed, causing large bandwidths. This argument is weakened in the case of NaC103 and NaBrO~ where the 'unobserved modes' are attributed to rotational character, due to their appearance in the Raman spectrum and their low intensity in the i.r. spectrum. Therefore, for these substances

all the modes have been accounted for and the large 7,* values cannot be attributed to strongly overlapping modes. In the case of KBrO3, where the number of theoretically predicted modes corresponds to the number of experimentally observed ones, the explanation of strongly overlapping transitions again breaks down. Because of the above arguments, we conclude that for alkali halogenates large 3,* values cannot be attributed to overlapping transitions but represent short lifetimes of the transition in the excited state. A plausible argument that may be used to explain these short lifetimes is centered around the possibility of the diffusion of lattice energy through combination modes with internal modes. Since the polyatomic anion contains six internal vibrational modes, a number of possible combinations may exist, i.e. external + internal modes. Direct evidence of this type of coupling has been observed in the transmission spectra of the internal modes of NaCIO3 and NaBrO3[5, 18]. 7. CONCLUSIONS

By employing polycrystalline thin film transmission spectra, it has been possible to compare the optical properties of the lattice vibrational modes of NaCIO3, NaBrO3, KC103 and KBrO3. In most cases unambiguous symmetry and attribution assignments have been made for these lattice spectra. Quantitative evaluation of these spectra via classical dis-

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J . D . N E U F E L D and G. ANDERMANN

persion analysis has revealed unusually large damping constant values for these modes as compared to those observed in the lattice modes of alkali halides which exhibit a considerable amount of anharmonic phonon-phonon coupling. The very short excited state lifetimes are especially puzzling since these lattice modes do not exhibit anharmonic or harmonic phonon-phonon coupling. Acknowledgement--This work was supported by NSF Grant No. 13087. REFERENCES 1. HARTWIG C. M., ROUSSEAU D. L. and PORTO S. P. S., Phys. Rev. 188, 1328 (1969). 2. MONTANER A. and GALTIER M., J. Phys. Chem. Solids 32, 55 (1971). 3. MONTANER A., DUVERNEY R. and GALTIER M., J. Mol. Struct. 4, 326 (1969). 4. N E U F E L D J. and ANDERMANN G., Appl. Spectrosc. 25, 597 (1971). 5. N E U F E L D J., Ph.D. Dissertation, University of Hawaii (1972). 6. N E U F E L D J., BRANTLEY L. R., SAKAMOTO P. and ANDERMANN G., Appl. Spectrosc. (In press). 7. BARKER A. S. and HOPFIELD J. J., Phys. Rev. 135A, 1732 (196,1).

8. KACHARE A., ANDERMANN G. BRANTLEY L. R., J. Phys. Chem. Solids 33, 467 (1972). 9. FATELEY W. G., MCDEVITT N. T. and BENTLEY F. F., Appl. Spectrosc. 20, 190 (1971). 10. WYCKOFF R. W. G., Crystal Structures (2nd edition), Vol. 2, pp. 380-391. Interscience, New York (1971). ll. BATES J. B., J. chem. Phys. 55, 494 (1971). 12. MOLLER K. D. and ROTSCHILD W. G., Far Infrared Spectroscopy, Chapter 13. Wiley-lnterscience, New York (1971). 13. MILLER F. A., CARLSON G. L., BENTLEY F. F. and JONES W. H., Spectrochim. Acta 16, 135 (1960). 14. BROWN T. L., Chem. Rev. 58, 581 (1958). 15. FAHRENFORT J., Infrared Spectroscopy and Molecular Structure (Edited by M. Davies), Chapter II. Elsevier, London (1963). 16. PLENDL J. N., Far Infrared Properties of Solids (Edited by S. Nudleman and S. S. Mitra), pp. 387 ft. Plenum Press, New York, (1970). 17. KACHARE A., Ph.D. Dissertation, University of Hawaii (1972). 18. HOLLENBERG J. L. and DOWS D. A., Spectrochim. Acta 16, 1155 (1960). 19. Recently J. B. Bates obtained polarized spectra on a single crystal of KCIO3 (See Ref. f11]). His study is purely qualitative. 20. ANDERMANN G., Ph.D. Dissertation, University of Southern California (1965). 21. ANDERMANN G. and BRANTLEY L. R., J. Opt. Soc. Am. 58, 171 (1968).