Vibrational Spectrum of Cesium Azide CrystalsJames I. Bryant Citation: J. Chem. Phys. 45, 689 (1966); doi: 10.1063/1.1727629 View online: http://dx.doi.org/10.1063/1.1727629 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v45/i2 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 45. NUMBER 2 15 JULY 1966

Vibrational Spectrum of Cesium Azide Crystals*

JAMES I. BRYANT

Basic Research Laboratory, U.S. AERDL, Fort Belvoir, Virginia

(Received 3 February 1966)

The infrared and Raman spectra of CsN3 crystals have been investigated over the frequency region from 30 to 4000 cm-I by using grating photoelectric recording spectrometers. The selection rules for the k"-'O modes of the crystals, determined by the method of Bhagvantam and Venkatarayudu, were used for the vibrational analysis. By making use of frequencies observed in the infrared and Raman lattice frequency regions, assignments were made by species of numerous absorptions constituting fine structure about the fundamental absorptions in the medium infrared. In most cases, because of the wealth of spectral data, numerical checks were provided for assignments of lattice combinations and for combinations due to internal mixing. Several observations, believed to represent violations of the k~ selection rules, are mentioned. A previously reported discrepancy related to the symmetry of N3- in CsN3 crystals is cleared up.

INTRODUCTION

I NFRARED spectra of alkali-metal azides were measured as early as 1934 by Lanseth and co­

workers. l Extensive subsequent studies of infrared and Raman spectra were carried out by a number of inves­tigators,2-6 providing sufficient data for Gray and Waddington7 in 1957 to report the fundamental fre­quencies and force constants of all five alkali-met~l azides. With recent improvements in spectroscopIc instrumenth.tion and techniques, interest has turned to the investigation of single crystals of the inorganic azide.8•9 These samples produce spectra with a wealth for fine structure which provides excellent opportunities of correlations with theoretical models. If the correla­tions can be made effectively, the observation of the complete vibrational spectrum (including infrared, Raman, and far infrared) of azide single crystals should provide valuable information concerning the vibratory motions and energies of these materials in their natural states. It is for these reasons primarily that we are interested in the vibrational spectrum of CsNa crystals.

Another cause for interest in CsNa is the observation by Papazian8 of a prominent band in the infrared spec-

* Presented in part at the 8th European Congress on Molecular Spectroscopy, Copenhagen, Denmark, August 1965.

1 A. Lanseth, J. R. Nielson, and J. Soresen, Z. Physik. Chern. 27, 100 (1934).

2 G. B. Sutherland and W. G. Penny, Proc. Roy. Soc. (London) A156, 678 (1936).

3 B. Venkateswaran, Proc. Indian Acad. Sci. 7A! 144 (1938). 4 M. Bassiere, Compt. Rend. 208, (1939); J. Chlm. Phys. 36,

71 (1939); Mem. Servo Chim. Etat (Paris) 30,33 (1943). 6 A. Delay, C. Duval, and J. Lecompt, Bull. Soc. Chim. France

12, 581 (1945). 6 L. Kohavec and K. Kohlrausch, Monatsh. Chern. 77, 180

(1947). 7 P. Gray and T. Waddington, Trans. Faraday Soc. 53, 901

(1957) . 8H. A. Papazian, J. Chern. Phys. 34, 1614 (1961). 9 J. I. Bryant, J. Chern. Phys. 38, 2845 (1963); 40,3195 (1964);

43, 880 (1965).

trum at 1365 cm-1• The 1365-cm-1 band was tentatively assigned as the symmetric stretching fundamental of Na-, presumably induced by strain generated in the crystal during the growth process. If the 1365-cm-l band is indeed JlI, then the azide ions of CsNa crystals can be other than linear and symmetric. The availability of the complete vibrational spectrum of CsN a in addi­tion to allowing the classification and assignmen t of the internal and external modes for the crystal, permit a more definitive characterization of the 1365-cm-l band.

SYMMETRY AND VIBRATIONS CONSIDERATIONS

The crystal structure of CsNa has been investigated by WaddingtonlO and is reported to be body centered tetragonal belonging to the space group 5)41&18- 14/mcm (Fig. 1). The lattice dimensions are a=b=6.72 and c=7.41 A. The azide ions are situated in planes parallel to (001) and inclined at an angle of 45° to the (100) plane. No structural evidence has been reported for the deviation of the ion symmetry in the crystal from that of a linear symmetric group. Since the crystal structure of CsNa is reported to be isomorphous with that of KNa, the vibrational selection rules which have been previously reported5 for the latter are applicable here. These selection rules (Table I) for the k~ spectrum (where k is the wave vector of the phonon) were deter­mined by application of the "unit-cell" (factor-group) method of Bhagavantam and Venkatarayudu.ll

Representations of Na-(5)roh) as a hypothetical free ion and in the 5)4,,18 lattice are presented in Table II.

10 T. C. Waddington, Doctoral dissertation, Cambridge Univer­sity. 1955.

11 S. Bhagavantam and t. Venkatarayudu, The~ry 0/ Groups and Its Application to Phystcal Problems (Andra Urnvemty Press, Waltair, India, 1951), pp. 127-140.

689

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690 JAMES 1. BRYANT

PERSPECTIVE VIEW

PROJECTION DOWN [001]

• NITROGEN ATOMS

CESIUM ATOMS

D~~ - I 4/mcDI

FIG. 1. Model of the structure of CsNa crystals.

Vibrations of species Azu and Eu are infrared active for the ~4h space group. The infrared spectrum of a CsNa crystal should thus consist of three fundamental modes [vz(Azu+Eu) and va(Eu)] and three lattice modes [T'(A zu+2Eu )]. Vibrations of Species A lg, B2g,

and Eg can undergo a change of polarizability and are hence Raman active. Therefore, two fundamental species [VI (Alg+Bzg )], a translatory lattice mode [T' (Eg)] and two rotatory lattice modes [R' (Blg+ Eg)] should constitute the Raman spectrum for the crystal. In addition, the infrared spectrum should include

TABLE I. Vibrational species of crystalline CsNa.&

:D'h ~ni T T' R' n/ Activity

Alo 0 0 0 R VI

A20 2 0 1 0 Blo 0 0 0 R B20 0 0 0 1 R VI

Eo 2 0 1 1 0 R Alu 0 0 0 0 0 A 2u 3 1 0 ir V2

B lu 2 0 1 0 V2

B 2u 0 0 0 0 0 Eu 5 1 2 0 2 ir 1I2, va

numerous combinational modes resulting from the mixing of internal modes and of internal and external mixing. Although arguments have been proposed to the effect that factor-group selection rules are not rigorously obeyed by combination transitions, it is generally accepted that they may serve as a guide for their classi­fication. Combinational features, although theoretically allowed in the Raman spectrum, are not expected to be observed because of their extremely weak intensities. Finally, approximations of the unit-cell modes for a

TABLE II. Relation between the molecular symmetry of Na- and the symmetry of the unit cell containing two molecules.

Vibrational mode :D4h

CsNa crystal have been constructed and are presented in Figs. 2 and 3.

EXPERIMENTAL

Although CsN3 is available from commercial sources, for reasons which are explained later, crystals obtained from various lots of such materials were found to be unsuited for use in this study. The CsNa used in this work was prepared by dissolving high-purity (99.9%) CsOH in a 10% aqueous solution of hydrazoic acid. The acid, which was prepared by the ion-exchange technique12 was re-eluted through the resin several times to ensure a high purity. The resulting CsNa

& ~ni, total number of modes; T, acoustic modes; T', optical modes; ni', 12 J. Bryant and H. Rosenwasser, J. Chern. Educ. 39, 296 internal modes. (1962) .

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V I BRA T ION A L S PEe T RUM 0 FeE S I U M A Z IDE CRY S TAL S 691

1)

solution was evaporated to near crystallization and reacidified. Crystals for spectroscopic use were grown by a very slow evaporation of the acidified solutions in a carbon-dioxide-free atmosphere. Growth solutions were contained in covered polyethylene cups with appropriate holes in the tops to control the evaporation rate. By this method, clear flat single crystals approxi­imately 1.5X 1.5 cm2 in area were easily obtained within a period of one to three days. The crystals, which ranged in thickness from 0.5 to 1.0 mm, were ideally suited for infrared spectra, but produced Raman spectra of poor quality. Thicker but somewhat irregular-shaped clear crystals were obtained by extremely slow evapora­tion over a period fo several weeks. These samples allowed measurement of the most useful Raman spectra.

6)~ {~ 8

VitAl 9)

I ~ }~ VI IB29) V2(Ep.l

:~ ()-(}-{) ~ 0-0---0-- + -

V2IA 2P.)

:~ ()-(}-{) 1~ + - +

11'2 (BI.,.,) Va(EJd

Medium infrared spectra were measured over the frequency region from 4000 to 400 cm-1 using a Model 421 Perkin-Elmer grating spectrometer. Spectra were recorded at 2980 and 77°K with the crystals mounted in an evacuated low-temperature Dewar during both measurements. The accuracy of the frequencies of the sharp bands reported is of the order of 0.8 cm-I and that of the broad bands, 2.0 cm-I • Samples for far­infrared spectra were in the form of CsNa crystallites dispersed in a polyethylene film. The far-infrared spec­trum from 600 to 33 cm-I was recorded using a Beckman IR-ll infrared spectrometer at the Beckman Instru­ment Company, Fullerton, California. FrG. 2. Internal unit-cell modes constructed for CsN3 crystals.

FIG. 3. External unit-cell modes constructed for CsNa crystals.

8 8 + F +

®---. ---@ + I + +

• + TIA211)

0- cr ~-f~

6 6 &_t-~

TIEJI,)

0 0 + F -().... ---0

- - + -+ T/(A2111

0- -0

.o-f~ 6 9 (

6--~ )---6 T'(EOI

0 0 -r-0-- --() + + +

+ T'(A21l'

0 0 + 1 -

0--- ----{) -t -t- T

- T'(BI Jl'

0- cr ~l-O

9f9 0 0

tr- -~ &-11 T'IEJI,I R(Azgl

0 0 0 0

"---F<> »-t-~ + -+ RIB I">

0 0 o . CESIUM ATOMS

"--F<> o • NITROGEN ATOMS

- + + R(E,1

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692 JAMES I. BRYANT

300 200 120 80 78 63 48 33

FREQUENCY (CM-I)

FIG. 4. Far-infrared spectra of crystalline CsN3 in polyethylene film. Solid line spectrum, concentrated sample; broken line spec­trum, dilute sample.

Raman spectra were recorded using a Cary Model 81 Raman spectrometer. A quartz tube approximately 6 ern in length and 1 ern in diameter with a quartz window on one end was filled with the irregular-shaped crystals. Spectra were measured at 40°C, making use of the 19-mm optics of the spectrometer. A modified low-temperature Dewar of the Ferraro design13 was used to obtain low temperature down to -70°C. Although the irregular-shaped crystals grown from aqueous media produced the most intense and hence the most useful spectra, measurements could be made using other types of samples. CsNa slowly crystallized from the melt in a quartz tube produced a mosaic mass of clear and cloudy crystallites whose spectra could be recorded directly in the tube. Although the convenience of preparation of this method is advantageous, a greater degree of scattering of the incident light made the samples somewhat less desirable than the crystals. Pressed disks of CsNs were quite whitish in appearance and the resultant Rayleigh scattering made these sam­ples the least desirable of the three.

The depolarization of the Raman peaks was deter­mined by surrounding tbe tube containing the crystals wi th Polaroid cylinders capable of polarizing the incident light either parallel or perpendicular to tbe axis of the Toronto arc source. Polarization assignments were made on the basis of the two relative intensities pro­duced by the scattered Raman light with the spectrom­eter counter set at the frequency of the center of the peak concerned.

RESULTS AND DISCUSSION

The observed vibrational spectrum of CsNs crystals can be separated into the following parts for convenience of discussion: (1) the far-infrared and Raman lattice frequency regions (30 to 200 cm-1); (2) the infrared bending frequency region (500 to 850 cm-1 region), the infrared and Raman symmetric stretching frequency regions (1200 to 1500 cm-l ), the infrared asymmetric stretching frequency region (1800 to 2300 cm-I), and the infrared combination frequency region near 3300 em-I. Using the unit-cell selection rules as a guide throughout, assignments Were made for all the bands observed in the above regions.

The observed vibrational spectrum of CsNs crystals is shown in Figs. 4 through 11. The complete list of vibrational assignments is presented in Table III. Beginning with the low- and proceeding to the higher­frequency regions, the spectrum of the far-infrared lattice frequency region is shown in Fig. 4. The k~O selection rules allow infrared activity for three trans­latory lattice modes in this region: T' (A 2u ), T' (E .. ) , and T' (Eu)'. Three bands can be clearly observed in the frequency region below 300 cm-I. Tentative assign­ments were made of the weak band at 38 cm-1 and:the strong one at 89 cm-I as the two T' (Eu) modes and

/r A I I \ I

_ .... ''''''''' /

200

t

I f

f

/ t

I I

t

" / I

170

, \ I I \ I , \ I

: \ I I \ / I \ I 1 \ /

: \ 0/ f \ l

f \ I

/', ;// b / '... .....""

/1//1' -------

/\ f

I \ " ... ",1"-',,/ \.,,/

140 50 60

13 J. Ferraro, J. Ziomek, and K. Puckett, Rev. Sci. Instr. 35, 754 (l964).

30

FIG. 5. Raman spectrum of CsNa crystal in the lattice frequency re­gion: a, -70°C; h, 40°C.

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VIBRATIONAL SPECTRUM OF CESIUM AZIDE CRYSTALS 693

" i i i ~ I'~:' .' I:

'i 11 ii ; i

; ; >-

FIG. 6. Raman spectrum of CsNa 55 crystal in the symmetric stretching r5 frequency region: a, no polarizer; b, !z axial polarizer; c, cross polarizer.

i. Ii r

" i i Ii i ! i ;, ! i j 'i j,

,i i i, . I

j !'J j

-_.----_."",. __ ,I Q_--.- -b / -c-------

1360 1350

the broad band at 118 cm-1 as T' (A2u). As is shown later, the principal justifications for the mode of indi­vidual assignments in this region are the satisfactory agreement of the frequencies of the bands observed with the separations of a number of medium to weak strength absorptions about the symmetric stretching funda­mental. A very weak absorption is observed at S9 cm-1

which could not be explained in terms of the ~o selection rules. Doped samples indicate that it is not due to any of the principal impurities expected to be found in CsNa• This absorption is assigned as the T' (B1u ) mode which is not infrared active by the factor­group selection rules, but might be allowed in a more general approximation. The Raman lattice frequency region is shown in Fig. S. Three Raman-active lattice

fi:l t­t: ~ z « a: t-

~ W Z W

90IinO-----..·i<oon----roo----'---sQ\no-----.<kn------.!v.

FREQUENCY (CM-')

FIG. 7. Infrared spectra of CsN 3 crystals in the bending frequency region: a, O.S-mm-thick crystal; b, O.t-mm-thick crystal. Solid line spectra, 298°K; broken line spectra, 77°K.

r' i . I i I • :i i ! :i ; \ '" " . , / :\ 1 i i \,_/-.-------.-i\ .-. ! "\;" 1 ....... • ..... /~ ...... /\ • ./,\ ----------" """ / \ I ,

I \

\:-----------------------~/ '---------------------

1320 1290

AV (eM-I)

1260 1230 1200

modes as predicted by the selection rules, and assign­ments were made for three peaks in this region due to CsNa_ The feature at 14S cm-1 is due to the lamp back­ground and is frequently observed with the instrument used for these studies. Spectra in this region, with the exception of the sharp peak at 42 em-I, were recorded at 40° and -70°C. At the lower temperature, con­siderable sharpening of the peaks with the expected improvement in resolution is noted. Small shifts to

SPECTROMETER SOURCE

FIG. 8. Diagram showing relationship between the orientation of the electric vectors (E) to the internal crystal structure when fiat single crystals are mounted in the spectrometer beam.

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694 JAMES I. BRYANT

TABLE III. Vibrational spectrum of CsNa crystals.

Frequency observed

(cm-l ) Strength- Assignment Remark

38 w T'(E,,)

42 s T'(E.) Observed in Raman spectrum, depolarized

59 vw? T'(BI,,) Not ir active by factor-group selection rules

89 s [T'(E,,}'

108 s R(E.) Observed in Raman spectrum, depolarized

118 5 T'(A.,,)

153 m R(BI.) Observed in Raman spectrum, polarized

480 vw? v.(E .. ) -R' (Bl .) Calc, 483 cm-l

568 w JI.(E,,) - T' (A •• ) T'(A •• ) "",68 cm-l

594 w 112 (A ... ) - T' (E.) Calc, 592 cm-l

607 w 2112 (AI.) -112 (E .. ) Calc, 606 cm-l

618 w 2J1. (B •• ) -Jl. (E,,) Calc, 617 cm-l

634 sh JI.(A.,,) Observed only at low temperatures

636 5 JI.(E,,)

647 w [21'. (AI.) J"-Jl.(E,,) Calc, 644 cm-l

668 w Jl2(Bl .. )+T'(E.) JI.(BI,,) "",626 cm-l

680 w I12(A2,,)+T'(E.) Calc, 676 cm-l

689 m JIJ, (B2g) -Jl.(E .. ) Calc, 689 cm-l

699 w JIJ,(A l.) -Jl.(E,,) Calc, 700 cm-l

704 m Jl2(E .. )+T'(A •• ) T'(A •• ) "",68 cm-I

736 w I12(B1,,)+R'(E.) Calc, 734 cm-l

748 m JI.(A.,,)+R'(E.) Calc, 742 cm-l

773 w JI.(E,,) +R' (A •• ) R'(A •• ) "",137 cm-I

790 m JI.(E,,)+R'(Bl.) Calc, 789 em-I

1194 w 21'. (B •• ) - T' (Btu) T'(BI,,) "",61 cm-l

1207 w 2J1.(B •• ) - T'(E,,) Calc, 1215 cm-l

1236 m JIJ,(B •• ) -[T' (E,,)], Calc, 1236 cm-l

1242 w 2112 (AI.) Observed in Raman spectrum, polarized

1253 s 2J1.(B •• ) Observed in Raman spectrum, depolarized

1264 w VI (B •• ) - T' (B l ,,) T' (B l ,,) ""'61 cm-l

1266 w [2112 (AI.) ]' Observed in Raman spectrum, polarized

1280 w [21'. (AI.)]" Observed in Raman spectrum, polarized

1286 m VI (B •• ) - T' (E,,) Calc, 1286 cm-l

1289 w 2v.(B •• )+T'(E,,) Calc, 1291 cm-l

1314 w 21'. (B •• ) + T' (B l ,,) Calc, 1314 cm-l

1325 s VI (B •• ) Observed in Raman spectrum, depolarized

1336 w 1'1 (AI.) Observed in Raman spectrum, depolarized

1362 s VI (B •• ) + T' (E,,) Calc, 1363 cm-I

1384 m JIJ, (B •• ) + T' (B lu) Calc, 1386 cm-l

1412 m JlI(B •• )+T'(E,,) Calc, 1414 cm-l

1869 s I'2(E,,)-R'(B l .) Calc, 1869 cm-l

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VIBRATIONAL SPECTRUM OF CESIUM AZIDE CRYSTALS 695

TABLE III (Continued)

Frequency observed

(cm-I) Strength- Assignment

1914 w IIa(E,,)-R'(Eg)

1950 w v.(E .. ) - T'(A 2g )

1969 w VI (B •• ) +V2 (E,,)

2022 vs 113 (Eu)

2062 w Va (Eu) - T' (Eg)

2172 s Va (Eu) + R' (BIg)

3165 vw (VI+IIa) -R'(Blg)

3203 w (1IJ.+1Ia)'-R'(Blg)

3225 m (211a+va) (E,,)

3249 s (2v2+va)' (Eu)

3273 w (2V2+1Ia) " (Eu)

3297 w (2V2+113)'" (Eu)

3319 s (vl+va) (Eu)

3343 s (111+113)' (Eu)

3474 w (vl+va) (Eu)+R'(B,.)

3482 w (VI+IIa)' (Eu) + R' (A.g)

a 5, rtrongj m, mediwn; w, weakj sh, shoulder.

higher frequencies are also noted at -70°C. It is only at the lower temperature that the Raman band at 153 em-I can be effectively distinguished from the lamp background.

Glockerl4 has pointed out that while translatory lattice modes tend to have relatively low frequencies and intensities, rotatory modes exhibit high frequencies and frequently have appreciable intensities. On this basis, the weak sharp peak very close to the exciting line at 42 cm-1 is assigned as the translatory lattice mode, T' (Eg ). This mode is the only translatory lattice mode allowed Raman activity by the unit-cell selection rules. The intense peak at 108 cm-l and the medium strength one at 153 cm-l are both depolarized and the species therefore cannot be distinguished on the basis of polarization. They are assigned as R' (BIg) and R' (Eg), respectively, also because such assignments are the most compatible with the possible lattice species which can combine with various fundamentals in the medium infrared. As is seen later, absorptions with separations of 108 and 153 cm-l appear about the various fundamentals. By knowing the symmetry species of the fundamental and that of the lattice com­bination, the species of the lattice mode involved can often be discerned.

The Raman spectrum of the symmetric stretching frequency regions is shown in Fig. 6. Two intense peaks in this region appear at 1253 and 1325 cm-l and are

14 G. Glocker, Rev. Mod. Phys. 15, 111 (1943).

Calc, 1914 cm-I

Calc, 1954 cm-I

Remark

Calc, 1961, observed only at low temperature

Calc, 2064 em-I

Calc, 2175 em-I

Calc, 3166 cm-I

Calc, 3206 cm-I

2V2(AI.)

2V2(B2.)

2v2IA,.;

2V2IA,.:

v, (B,.'

vl{A 1.)

Calc, 3472 cm-:

Calc, 3480 em-I

assigned as components of 21'2 and 1'1, respectively. The apparent small degree of intensity borrowing indicates that Fermi resonance perturbation between the two levels is only slight. The weaker features occurring with the above two intense peaks are additional components of 21'2 and 1'1 arising as a result of the crystal structure. Raman activity is allowed for five species of the first overtone of the bending mode [21'2(3Alo+Blo+B20)] by the unit-cell selection rules. Two species of the 1'1

fundamental are predicted, i.e., 1'1 (AIg) and 1'1 (B2g). Four of the above components of 21'2, being of the same symmetry species as VI, can undergo Fermi resonance with this mode. These resonating species, because of their capability to borrow intensity, have the greater

~ I '/ ........ oooooo '000

0:: ...

~ 1600 1500 1400 1300

FREQUENCY (CMOI

)

: /---"~'-~-~' r J\ t "",,:\ f

I ~ I I" : IV I 1"'-1'>', I

i I I I

I I I

1200

FIG. 9. Infrared spectrum of CsNs crystals in the symmetric stretching frequency region. Solid line, 298°K; broken line, 77°K.

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696 JAMES I. BRYANT

probability of producing observable peaks in the Raman spectrum.

Individual assignments can be made of the compo­nents of VI and 2V2 by considering their polarization properties and relative intensities. Both of the intense peaks at 1253 and 1325 cm-1 are depolarized and there­fore cannot be totally symmetric Ala species. The only other possibility for the VI component is the assignment as vl(B2a ). By elimination, the remaining weaker component at 1336 cm-1 must be vl(A 1a ). If the above assumption concerning intensity borrowing of 2V2 com­ponents is correct, the four observed species can now be classified as either Ala or B2a modes. Since all of the weak components of 2V2 are polarized, they must be classified as totally symmetric Ala species. The intense peak at 1253 cm-1 is 2v2(B2a). Finally, the fifth com­ponent of 2V2 allowed by the selection rules [2V2 (BIg)], which cannot resonate with either species of VI, is assumed to be too weak to be observed.

Infrared spectra in the bending frequency region are presented in Fig. 7. Spectra in this region, as well as in the remaining regions of the medium infrared, were measured using single crystals and hence exhibit con­siderable amounts of structure. This structure arises from two sources. First, the various individual com­ponents of the fundamental modes combine to produce absorptions, and secondly the individual components

-------... _----=------... ,'\

\ Ii

FREQUENCY (CM-I)

FIG. 11. Infrared spectra of CsNa crystals in the 3300-cm-1

combination frequency region: a, O.l-mm-thick crystal; b, 0.5-mm-thick crystal. Solid line spectra, 298°K; broken line spectra, 77°K.

FIG. 10. Infrared spectrum of CsNa crystal in the asymmetric stretching frequency region. Solid line, 298°K; broken line, 77°K,

can mix with the lattice modes to produce lattice combinations. The totality of bands thus made possible is therefore generally large. The assignment of the fundamental modes of the single crystals is more or less straightforward and can be made on the basis of the relative intensity of the observed peaks. The pat­terns of fine structure, however, are fairly complex, since the two types of combinations are generally intermingled. The over-all pattern is therefore one of randomly varying intensities showing little or no distinguishable order.

A major key to the making of assignments in the medium infrared regions is the relationship of the orien­tation of the electric vector of the incident beam to that of the various unit-cell modes during spectral measure­ments. It is shown by x-ray Laue photographs that when the flat CsNa crystals are mounted in the spec­trometer beam, the c axis of the crystal is perpendicular to the plane of the E vectors (Fig. 8). For a CsNa crystal (Space Group :D4h), infrared activity is confined to vibrations of species A 2u and Eu. Since the A 2u modes have symmetry about (parallel to) the c axis of the crystal, and therefore perpendicular to the plane of the E vectors, these cannot be active in the infrared. On the other hand, the E" modes are parallel to the plane of the E vectors and thus can become vibration ally excited. In reality, the A 2u modes can appear weakly due to such factors as beam convergence, discrepancies in alignment, crystal imperfection, and the like. In spite of this fact, the orientation factor is found to have a dominant effect in determining the relative intensities of the absorptions and restricts the exhibition of any appreciable intensity to the Eu species modes.

Consideration of the k~ selection rules for the bending frequency region (Table I) indicates that three different species of the V2 fundamental are pre­dicted: v2(E,.), v2(A 2u ), and v2(Blu ). These fundamental modes can combine with the five different g species lattice modes to produce nine infrared-active lattice combinations. Of the nine combinations, seven are E" species and are hence expected to be observed. In addition, several combinations due to internal mixing are expected to be observed in this region. The most intense band in this region at 636 cm-1 can be assigned in a straightforward manner as the fundamental, V2 (E,,). A weak shoulder is observed at 634 cm-1 only in the

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VIBRATIONAL SPECTRUM OF CESIUM AZIDE CRYSTALS 697

thin-crystal spectra measured at 77°K. This absorption is assigned as 112 (A 2,.) appearing weakly because of the above-mentioned experimental discrepancies. If the temperature shift of the A 2u component is equivalent to that displayed by 112 (Eu ), the room-temperature frequency of 112 (A 2,,) can be taken as 634 cm-l . In close proximity to the 112 fundamentals are three difference bands (607,618, and 647 em-I) which can be identified by their strong temperature dependence. These bands are assigned as differences of three of the individual components of 2112 (observed in the Raman spectrum) and 112 (E,.). Similar difference bands with strong tem­perature dependence, located at 689 and 699 cm-l, are assigned as the differences of the two components of III and 112 (Eu).

The remaining absorptions in this region exhibit a temperature dependence quite different from that shown by the difference bands. At 77°K, these absorp­tions become more highly resolved and exhibit slight temperature shifts to higher frequencies. These bands are due to combinations of the various components of 112 with g species lattice modes. Since most of these lattice modes were observed in the Raman spectrum, individual assignments can be made for the lattice combinations. To begin, the medium strength absorp­tion at 790 cm-1 exhibits a separation of approximately 153 cm-1 from the 112 (Eu) fundamental at 636 cm-l •

This observation permits two conclusions to be drawn. First, the 790-cm-l absorption is identified as a lattice combination with the 112 (Eu) component, and second the rotatory lattice mode observed in the Raman spectrum at 153 cm-1 must be identified as the (BIg) species. The latter conclusion is the result of the follow­ing. Assuming that the 790-cm-l band is an Eu species (because of the above arguments concerning orienta­tion), the combining lattice mode must be either of A20 or Blo species in order to combine with 112(Eu) to produce the resulting Eu species lattice combination. The A20 species cannot be Raman active by the k~ selection rules, leaving only the Blo assignment. A very weak absorption was observed with some of best quality thin crystals at 480 cm-l when the spectrum was meas­ured at 77°K. This absorption, if real, would be in agreement with the frequency expected for

Because of the small separation from the fundamental modes, the weak absorptions at 669 and 680 cm-l are assigned as combinations with the translatory lattice mode, T' (Eg), observed in the Raman spectrum at cm-l • The 680-em-1 absorption is assigned as [112 (A 2u ) + T'(Eo)] and 668-cm-1 band as [1I2(Blu )+T'(Eo)]. The fundamental component 112 (Blu ) is not infrared active, but an inferred frequency of 626 cm-1 is obtained from the above latter assignment. The weak shoulder at 594 cm-l is assigned as the corresponding difference band [1I2(A 2u )-T'(Eo)]. The difference band

[1I2(Blu )-T'(Eg)] which should appear at 584 cm-l, could not be confidently identified although a weak doubtful absorption was observed at times in 580-cm-1

region. The lack of numerical agreement prevents the assign­

ment of the medium strength 704-cm-1 absorption as a combination involving a component of 112 and any of the three observed lattice modes. The remaining possi­bility is the assignment of this absorption as a lattice combination involving either T' (A2g) or R' (A2g) which are neither infrared nor Raman active. Only the E" fundamental species can produce a resulting Eu lattice combination with the A20 lattice mode. Because of the tendency of translatory lattice modes to exhibit lower frequencies than rotatory, the logical choice is the assignment [1I2(Eu)+T' (A2o)]. An inferred value of 68 cm-l is thus obtained for T' (A2g) which was not observed experimentally. A very weak band, which consistently appeared at 568 cm-l is taken as the corre­sponding difference band [v2(Eu)T'(A2o )]. This latter assignment also supports the assignment of an inferred frequency of 68 cm-l for T'(A 2o )'

The weak absorption at 736 cm-l and the strong one at 748 cm-l are assigned as lattice combinations with the rotatory lattice mode, R' (Eo), observed at 108 cm-l in the Raman spectrum. The 736-cm-l band exhibits satisfactory numerical agreement with that calculated for 112(Blu )+R'(Eo) when the previously inferred value of 626 cm-l is used for 112 (Blu), The 748-cm-l absorption is assigned as 112 (A 2u ) + R' (Eo).

Finally, by making use of an argument essentially identical with that used to assign the 704-cm-1 absorp­tion, the 773-cm-l absorption is assigned as the lattice combination 112 (E,.)+R' (A2g). The inferred frequency of 137 cm-l is subsequently obtained for the unobserved mode, R' (A2g).

The spectrum of the infrared symmetric stretching frequency region is shown in Fig. 9. Infrared-active fundamental absorptions are not allowed in this region by the k~ selection rules. As shown earlier, the sym­metric stretching fundamental is observed in the Raman spectrum where it undergoes Fermi resonance with the 2112 overtone. The absorptions shown in Fig. 9 are due to combinations of the translatory lattice modes ob­served in the far-infrared spectrum with the B2g species of III and 2112. Thus the effective assignment of the spec­trum in the symmetric stretching frequency region is dependent upon the correlation of data from three spectral regions: the lattice combinations in the medium infrared spectrum, the fundamental modes in the Raman spectrum, and finally the lattice modes in the far-infrared region. With the availability of these data, individual assignments with numerical checks can be made for the combinations which produce the observa­ble absorptions in the single-crystal infrared spectrum. As can be seen from Table III, the agreement between the observed and calculated values is satisfactory. A key to the assignments of individual absorptions in the

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698 JAMES 1. BRYANT

1200- to 1500-cm-1 infrared region was the observation of the symmetrical arrangement of bands about the frequencies of the B2g species of III and 2112 indicated by the broken vertical lines in Fig. 9.

The absorptions at 1314 and 1264 cm-l are assigned as lattice combinations with 111 (B2g) and 2112 (B2g ), respectively, and the infrared-inactive lattice mode, T' (Blu ). From these assignments, an inferred frequency of 61 cm-I is obtained for T' (Blu). The agreement of the 61-cm-l value with the frequency of the previously mentioned weak absorption observed at 59 cm-I in the far-infrared spectrum supports the assignment of the 59-cm-l absorption as T' (Blu). The appearance of T' (Blu ) in the infrared spectrum is in violation of the k~ selection rules.

The most intense absorptions in the medium infrared spectrum occur in the region of the asymmetric stretch­ing fundamental lIa(Eu), near 2000 cm-l (Fig. 10). Besides the fundamental, additional E" modes can appear in this region due to the combination of the fundamental with the three nondegenerate g species lattice modes, T'(A 2g ), R'(A2g ), and R'(BIg). Finally, the E .. species of the (111+112) and (2112+112) combina­tions can produce absorptions in this region.

Due to the extremely intense nature of the absorption produced in this region even by the thinnest crystals, only a moderate amount of structural detail could be observed. Because of the symmetrical arrangement of two strong absorptions about the 2022-cm-l frequency, the 2022-cm-l value is assigned as the center of the intense lIa (Eu) fundamental. The two surrounding bands, centered at 1869 and 2175 cm-t, exhibit separa­tions of 153 cm-l from the fundamental. These bands can be assigned confidently as the difference and sum, respectively, of lIa (Eu) and the lattice mode, R' (Big), since the latter mode was observed in the Raman spectrum. A weak shoulder is observed in the 77°K spectrum at 1950 cm-l. By using the inferred value of 68 cm-I for T' (A 2g ) (see 112 region assignments), the 1950-cm-l absorption can be assigned as [lla (Eu) -T' (A2g)]. The corresponding difference band probably falls beneath the intense central envelope and is not observed. Absorptions due to the combination of Va (E .. ) with R' (A2g) cannot be identified. The frequency of R' (A 2g ), which is neither infrared nor Raman active, is not observed. It is not unreasonable that the strong absorptions in the 1969- and 2172-cm-1 regions may be due partly to [113 (Eu)±R' (A2g)].

The intense nature of the lIa fundamental apparently also permits the observation of A 2u species combinations in spite of the previously discussed effects of crystal orientation. Absorptions are observed at 1914 and 2175 cm-l which can be assigned best as combinations of lIa(E .. ) with the R' (Eu) and T' (Eg) lattice modes, respectively. Of the four resulting species of the com­binations, only the A 2u modes can be infrared active by the k~ selection rules. Finally in this region at 1969 cm-l, a weak sharp absorption is observed super-

posed on the broad lIa(Eu) envelope. This sharp feature is assigned as the combination, [lIl(B2g )+1I2(Eu)].

The final region of the medium-infrared spectrum of CsNa crystals is the combination frequency region near 3300 cm-l (Fig. 11). Summations of lIa(Eu) and the six components of III and 2112 can produce infrared-active absorptions in this region. All the resulting combinations are of species Eu and, by virtue of the previously dis­cussed orientation considerations, should be observable. Assignments of individual absorptions can be made by comparing the infrared spectral pattern with that of the Raman symmetric stretching frequency region. The resemblance of the two spectral patterns can be recognized most easily by an identification of individual bands in the 77°K infrared spectrum of the thinner crystal with the corresponding bands in the unpolarized Raman spectrum. By doing so, it can be seen that the Fermi resonance of the components of III and 2112 is repeated between the components of (lIl+lIa) and (2112+113)' The individual assignments are presented in Table III.

The two most intense components of (111+113) and (2112+113) at 3319 and 3249 cm-t, respectively, are separated by approximately 70 cm-t, in agreement with the separation of the intense components, IIl(B2g ) and 2112 (B2g). Weak infrared absorptions on either side of the resonating components near 3150 and 3470 cm-l

are observed in the thicker-crystal spectra. The weak absorption at 3165 cm-I and the broad band at 3474 cm-l are assigned as the difference and sum, respectively, of (111+113) and R'(Blg ). A wfak band at 3203 em-I, with a strong temperature dependence, shows numerical agreement with the frequency expected for [(111+113)' + R' (A2g)]. The inferred frequency value of 137 cm-l, obtained from the assignments in the 112 region, is used for R' (A2o). The corresponding summation band

FIG. 12. Survey spectrum of CsN3 crystals grown from commer­cial and doped azide: a, commercial CsNaj h, 0.2% NOa-j c, 2.0% NO,- in the crystal growth solution.

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VIBRATIONAL SPECTRUM OF CESIUM AZIDE CRYSTALS 699

[(1'1+1'3)' + R' (A2g)] should be located at 3480 cm-1

and is probably partly responsible for the broad nature of the absorption in the 3470-cm-1 region.

Finally, Fig. 12 shows a survey spectrum of a CsNs crystal grown from the commercial salt. As mentioned earlier, this material was found to be unsuited for use in this work. It was also mentioned that in a previous studY' a prominent band was reported at 1365 cm-1

which was tentatively assigned as the symmetric stretching fundamental of CsNs presumably induced by strain generated during the growth process. As can be seen by Fig. 12, the 1365-cm-l band can be positively identified as being due to the nitrate-ion impurity. The 1365-cm-1 absorption as well as the weaker absorp­tion at 825 cm-! (va and 1'2 of NOa-, respectively), exhibit increased intensities when the nitrate ion im­purity is added to the CsNa crystal growth solution.

THE JOURNAL OF CHEMICAL PHYSICS

Therefore, the previous conclusion8 suggesting a possible symmetry change of Na- in the CsNa crystal causing VI to become active must be rejected.

In summary, the vibrational spectrum of crystals grown from very pure CsNa was investigated over the frequency region from 30 to 4000 cm-I • By application of the k~O selection rules, assignments were made by species for more than 50 observed absorptions. The observed spectrum is in good agreement with the re­ported crystal structure, :D4h18-14/mcm.

ACKNOWLEDGMENT

The technical assistance of Mr. Robert L. Brooks of the Basic Research Laboratory in carrying out the experimental phases of this work is gratefullyacknowl­edged.

VOLUME 45, NUMBER 2 15 JULY 1966

Low-Frequency Motions of H 20 Molecules in Crystals. U*

HENRY J. PRASKt AND HENRI BOUTIN·

Picatinny Arsenal, Dover, New Jersey (Received 21 February 1966)

Translational and librational motions of H20 molecules in a frequency region lying below 1000 cm-1

have been previously examined for various configurations using the inelastic scattering of low-energy neutrons (0.005 e V). In the present work, H20 motions are studied in cases where neither of the lone electron pairs on the oxygen of the H20 molecule is specifically directed (K2C20,·H20), where the lone pairs are directed toward two monovalent metal ions (KF·2 H20), where the H 20 molecule has a single orientation [Ba(CIOah·H20] or two distinct, equally probable orientations (Li2S0,·H20). The neutron spectrum of K2C20,·H20 typically exhibits torsional peaks at 500, 605, and 700 cm-1 which shift by 1.35 in frequency upon deuteration. They are well separated from a sharp peak at 195 cm-1 which is assigned to the stretching motion of an H20 molecule H bonded to the oxalate ion and does not shift upon deuteration. The neutron spectra are discussed and compared with the results of proton magnetic resonance, Raman, and infrared measurements.

INTRODUCTION

I N a previous paperl it was shown how the inelastic scattering of neutrons can provide information

concerning the intermolecular motions of H20 mole­cules in crystalline salts. These intermolecular motions which consist of hindered translations and rotation of H20 molecules are expected to occur below 1000 cm-1

and are most sensitive to the nature and symmetry of the environment of the H20 molecule and to its binding. In the case of an H20 molecule occupying a site in a nonhydrogenous lattice, the characteristic spectrum

• Work supported in part by the Defense Atomic Support Agency, Washington, D.C.

t Guests at the U.S. Army Materials Research Agency, Water­town, Mass.

1 H. Boutin, G. J. Safford, and H. R. Danner, J. Chem. Phys. 40,2670 (1964).

of intermolecular vibrations of the H20 molecule will be predominant because of the large incoherent scatter­ing cross section of hydrogen. In the polycrystalline samples studied in the present work, the spectrum characteristic of the lattice will contribute as a back­ground. However, vibrations characteristic of the lattice may manifest themselves indirectly in the observed spectrum by exchanging energy with the H20 molecules.

The incident "quasi" monochromatic neutron (Eo = 0.005 eV or 40 cm-I ) undergoes a single scattering event in the sample and gains energy [in a range 0.003 eV (24 cm-I ) to 0.130 eV (1040 cm-I )] from thermally populated levels. Any such transition, therefore, should manifest itself in the neutron spectrum by a peak whose width depends on the phonon lifetime and the instru­mental resolution at that particular frequency. In general, the peak height depends on the energy transfer

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