Spectrochlmica A&%, Vol. 27A, pp. 2019 to 2026. Pergaman Press 1971. Printed In Northern Ireland

I&axed spectra of KBr crystals doped with CrOdpr- and some dipositive ions*

P. J. MILLER, C. L. CESSAC and R. K. KEIANNA Department of Chemistry and The Center of Mater&s Research, Umversity of Maryland

College Park, Maryland 20742

(Recezved 10 December 1970)

Al&r&-The 1.1. spectra of single crystals of KBr grown with minute amounts of CrOd2- and MB+ (&f = Mg, Ce, Sr, Be, and Pb) ions have been obtsmed. Small but definite shifts m the absorption maxima of the five crystals mdicate ion pair formation (MB+ - CrOl*). Anal- ysis of the speotra has enabled us to correlate the bands m the spectral region 100~800 cm-l to the stretchmg modes of CrG4* ions occupying at least three distinct symmetry sites. A simph- fied normal ooordmate analysis hss led to the assignment of the most intense bands m the spectra to the C,, site symmetry of the CrO,* ion paired with the divalent cation.

INTRODUCTION

THE TECHNIQUE of employing solid solutions for the determination of the vibrational frequencies of polyatomio ions was tist introduced by &&%AKOWEZ [l] who reported the i.r. spectrum of NO, ion in KCl lattice. Since then a number of reports on the i.r. spectra of several ions as substitutional solid solutions in alkali halides have appeared in the literature. In particulsr, MOROAN and STAATS [2] investigated the i.r. spectra of KBr and KC1 crystals doped with COs2- and some dipositive ions like Ca2+, Ba2+, and Pb2+ which gave evidence of ion pairing of the type C0,2--X2+ (X = Ca, Ba and Pb). COKER et al. [3] investigated the i.r. spectra of KC1 crystals doped with SO,2- and Ma+ ions and found evidence of similar ion pairing. Sub- sequently, DECIUS et a,?. [4] interpreted the spectra of the SOd2- and M2+ doped alkali halides on the basis of O,, site symmetry of the SOd2- substituting for the halide ion and paired with a Ms+ ion occupying the nearest neighbor alksli ion site. DECIUS

[5] treated the observed splitting of the triply degenerate fundamental modes of SOpa- on the basis of a vibrational Stark effect arising from an electric field due to an excess charge on the 111’6+ ion.

The CrO,s- ion like the SOd2- ion is tetrahedml and the CrO bond length in CrOd2- ion (~1.60 A) is only slightly larger than the SO bond length in SO,%- (1.49 8) [4]. In an effort to obtain evidence of (a) solid solution form&ion and (b) ion pairing with some d&positive ions, we have investigated the i.r. spectra of single crystals of KBr grown with minute amounts of CrOd2- and MB+ (M = Mg, Ca, Sr, Ba and Pb) ions. The analysis of the spectra give evidence of both the features, namely (a) and (b). Also, the solid solution bands being extremely sharp (half width ~1 cm-l)

* Supported m pert by a grant from the Advanced Research Projects Agency, Department of Defense.

[l] I. IcIBs~~~owuz, 2. Phyeik 61, 096 (1928). [2] H. W. MO~QAN and P. A. STMTS, J. A&. Phye. 33, 364 (1962). [3] E. H. COKER, J. C. DECIUS and A. B. SCOTT, J. Chem. Phye. 86, 745 (1961). [4] J. C. DECIUS, E. H. COKER end G. L. BRENNA, Spctrochim. Acta 19, 1281 (1963). [5] J. C. DEOITJS, Spectrochim. Acta 21, 16 (1966).

1 2019

2020 P. J. Mm-, G. L. CESSAC and R. K. KHANNA

the absorption peaks due to the stretching modes of CrO,s- ion in solid solution provide solid state calibration standards in the region 1000-800 cm-l.

EXPERIMENTAL PROCEDURE

Single crystals of doped KBr were grown from the melt by the BRID~EMAN’S technique [6]. The Cr0,2- ion was introduced as K,CrO, crystal and appropriate quantity of &f2+ ion was supplied by MBr,. Due to rejection process during crystal growth the concentration of the CrO,2- ions varied along the length of the crystal. Suitable sections of the crystals (~0.5 to 1 cm long and ~3 cm2 cross section) were chosen for the investigation of the absorption spectra. The spectra were re- corded in the region 1000-350 cm-l on a Perk&Elmer 225 i.r. spectrophotometer, at room temperature snd at liquid N, temperature. Spectral slit width of ~1 cm-l was employed throughout the range of the spectra investigated.

EXPERIMENTAL RESTIXTS The traces of the spectra at liquid N, temperature are reproduced in Figs. 1 and

2. The room temperature spectra (not shown) reveal three strong peaks with some unresolved structure on their shoulders. Cooling the sample to liquid N, tempera- ture results in a dramatic sharpening and, consequently, excellent resolution of the weak absorption peaks. In some spectra the absorption due to minor isotope species (soCr-4.410/o, 5sCr-9.540/o and 54Cr-2.610/o) can be separated from the peaks due to 52Cr(83.46%) species. The relative intensities of these isotopic bands corresponded to their relative abundances, and furthermore, the observed splittings were in accord with calculated isotopic splittings (~2.5 cm-i per mass unit) within experimental error. For crystals containing different concentrations of the same doped ions, the frequencies of the absorption maxima were reproducible, but changes in relative intensities were observed for some of the bands. This enabled us to group the bands into different site species. Table 1 gives the frequencies of the absorption maxima in the spectra of the five crystals.

DISCUSSION Small but definite differences in the spectra of the five crystals indicate the effect

of ills+ ion on the vibrational modes of Cr042- ion. The interpretation is, thus, based on possible substitutional arrangements of the Cr042- and Ha+ ions in the KBr lattice. Consider a CrO42- ion substituting for a Br- ion at the center of the cubic unit cell of KBr, with its oxygens pointing towards four of the eight corners of the cell. If Illa+ pairs with the Cr042- it must replace the K+ ion either at a face center or at a corner of the cell, resulting in a C,, or C,, site symmetry respectively of the CrO,” ion. A site symmetry lower than C,, would result only if the lattice has vacancies. Other sites sre possible for aggregate formations, but this is unlikely due to the concentration of N one Cr042- ion per 1000 unit cells of KBr.

The analysis of the spectra has enabled us to correlate the bands in the region 1000-800 cm-i to the stretching modes of Cr042- ions occupying et least three dis- tinct symmetry sites. Thus, the three strongest peaks in the spectra of all the five

[6] P. W. BRIDOXAN, Proc. Am. Acud. Arts Sci. 60, 303 (1925).

Infrared spectra of KBr crystals doped with Cr04b- end some dipositive ione 2021

r CaCrQ

900

CM-’

8 10

Fig. 1. The low temperature 1.r. spectra of CrO,* and Mz+ ion doped KBr crystals.

crystals appear to be due to vs split into three components due to a reduced site symmetry. The two high frequency components show a blue shift and the low frequency component shows a red shift with increasing size of the Ha+ ion. This feature is similar to the one reported in the spectra of MB+-SO,“- doped alkali halides [a]. We, therefore, believe that these bands are due to v, of a CrOd2- ion occupying a site C,,(I) resulting due to its pairing with a Ma+ ion occupying a nearest neighbor alkali ion site. A weak band at 4350 cm-l [~837 cm-r in the ease of Pb2+-Cr0,2- doped KBr] is assigned to vi. Three weak bands in the region -400

cm-i are assigned to vq. v2 which is inactive for Td symmetry becomes active under the lower symmetry C,,. This mode, however, is not observed in any of the spectra partly due to its expected weak intensity and partly due to background absorption by KBr below -370 cm-l. The results of a normal coordinate analysis, described later in the section, are also consistent with the above interpretation.

2022 P. J. M-IS, G. L. CESSAO tmd R. K. KEANNA

PbCrQ

900

CM-’ Fig. 2. The low temperature 1.1. spectra of CrO,* and Pba+ doped KBr

crystal.

Table 1. Frequencies (cm-l) of absorption maxIme in the spectra of iH~-Cr04a- doped KBr

MB”+ clG+ sr*+ Ba’+ Pb’+

943 942 937 936 934 934 931 931

926 922

924 922

906 903 890

904

886 880 878 871

866

884 879 5 877 874 871 866 433 416 399

960 963 944 946 947 938 940 941.6 936 937 938.7 932 934 928 927 922 921 920 920 918 918 914

887 880 884 877 878 871.6 844 876 869 873 866

8716 863 849 838 428 427 416

414 391 399 401 378

The spectrum of Mg2+-CrO, 2- doped KBr shows three additional bands (-889 cm-l-sharp, -903 cm-l-broad and -906 cm-l-sharp). A number of site symmetries can account for these bands. For example, a site symmetry C, or C, resulting from a lattice vacancy in addition to a Ms+ ion in the unit cell can cause a splitting of yS and vp into three components. A site symmetry D, which results if the Cr042- ion moves in between two adjacent lattice vacancies can also cause such splitting, however, this arrangement is sterically less probable [5]. Further, the spectra of

Infrared spectra of KBr crystals doped mth CrOIS- and some &podme ions 2023

Caz+-CrO,*- and Ba*+-CrO,*- doped KBr show only one broad band centered around 903 cm-l. It is, therefore, quite likely that the 903 cm-l band in the three spectra is due to v3 of sn undistorted (Td) Crop*- ion. This would then suggest that the 889 cm-l and 906 cm-l bands are due to vs of a Cr04z- ion occupying either a C,, or s, D,, site. The former corresponds to Jf2+ occupying a unit cell corner as described earlier and the latter corresponds to two iP+ ions occupying opposite face centers. Although vl is active for C,, and inrtctive for Daa site it is not possible to distinguish between the two from the i.r. spectra, because of extremely small popu- l&ion of these sites. However, in view of the fact that the Ca?+ and CrO,Yon concentration is about one per thousand unit cells, the Daa site which requires two CW+ in the same unit cells is considered less probable. Therefore, we assign the 889 cm-l and the 906 cm-l bands (the former is about twice as intense as the latter) to the E and A, components respectively of vs of a CrOdZ- ion occupying a C,, site. This interpretation suffers from a serious drawback; namely, the relative shifts of v,(E) and v&4,) components from vso (superscript 0 refers to Td symmetry) do not agree with the theoretical values. The vibrational Stark splitting theory developed by DECIUS [li] predicts that the A, component should be shifted up approximately twice as much and in the opposite direction as the E component from vao. The above assignment is consistent with the sign of the shifts but not with their magnitudes. One reason for this discrepancy may be the coupling of vJA1) with vl(AI), the totally symmetric stretch.

Another set of three bands observed in the spectra of Sra+-CrO,a- and Ba2+- CrO,g- doped KBr reveals a third symmetry site (III) occupied by the CrO,s- ions. These bands are approximate equally intense and also approximately equally spaced. They, apparently, belong to a paired arrangement because of small but definite frequency differences in the two spectra. A site C, or Cl of CrOd2- may result in relatively large (as observed) splitting of vs. Approximately equal spacings of the three components probably results from a random srrangement of two JP+ ions or perhaps one &P+ and one lattice vacancy in a unit cell leading to a low site symmetry of Cr0,2- ion.

A simplified normal coordinate analysis of the stretching modes of CrO,a- ion will now be presented. Starting with vlo and vso of a CrOd2- (TJ ion and neglecting the coupling between vso (stretch) and v40 (bend) the bond stretch and the interaction constsnts fr and f, respectively rare calculated. vsO is chosen to be 903 cm-l as discussed above. v10 is calculated from a plot of observed frequencies (assigned to vl) vs. the polerizability of Af2+ and extrapolating to zero polarizability. The force constants are:

f, = 5.84 md/8.

f, = 0.38 md/A.

Now, for a paired arrangement the stretching modes of a CrO,z- (C,, site) are distri- buted among the symmetry species of C,, as follows

r = 24 + Bl + B,.

2024 P. J. MILLER, G. L. CESSAC and R. K. KEIANNA

Fig. 3. The molecular arrangement of the Ma+ and Cr0,8- Ions for C,, site symmetry m the KBr lattice. The M&t Ion 1s located at one of the face

centers and the CrOd2- ion is located at the body center of the cube.

The change in the force constants of the CrO bonds due to pairing is calculated from the following considerations. The X2+ ion induces a charge --6 on each of the two oxygens facing H2+ and a charge +6 each on the other two oxygens (Fig. 3). This results in a softening of the two CrO bonds facing H2+ and a stiffening of the other two. The corresponding changes in the stretching force constants are denoted by -A and +A’, respectively. The geometry of the CrOd2- ion is, however, assumed to be altered only slightly, therefore, the interaction constant f, is assumed to be unaffected. Employing the following symmetry coordinates

the symmetrized F and G matrices for the various species of C,, are:

F(4) = fr - A + fw

[

2fw

2fw fr + A’ 1 +fw

G(4) = lu0 + kr(l + 00s a01 2p2 00s a0

2pu, 00s a0 1 rue + PC& + cos a01

(1)

F(4) = fp -fr, - AG(BJ = W&d = p. + ,dl - ~0s a01

W32) = fr -f, + A’. (2)

Infrared spectra of KBr crystals doped with CrO,B- and some &posltwe ions 2025

cc is the reciprocal mass and 01~ is the tetrahedral angle between the CrO bonds. From the calculated values off,, f,, and the observed frequencies assigned to B, and B, species the solution of the secular equation (3)

[FU - Ml = 0 (3)

for each of the species gives values for A and A’. These vsJues are substituted in the secular equstion for the A, species to obtain the frequencies of the two A, modes which are compared with the observed frequencies. An examination of Table 2 shows that the frequencies for .&f = Mg, Ca, Sr and Ba are not unduly different; therefore,

Table 2. Correlation of absorption peaks to different symmetry sites of Cr04

W++ Cd+ SS+ Baa+ Pb

She RT LT RT LT RT LT RT LT RT LT Asf31gnment

933 937 932 936 934 938 937 940 937 941 vs(W

921 925 920 924 919 922 918 921 916 920 +%)

(921) (920)

C 2u 876 880 876 880 876 878 869 972 843 vsW 836

853 866 853 855 851 853 848 849 837 v,(A)

(852) (830) - 431 433 - 428 425 427 412 416

- 414 416 - -- 411 414 388 391 VP

- 397 399 - 399 398 401 375 378

TGi 903 904 - 904 - vs 906 - - - - v&h)

ca 889 - - - - v,(E)

946 960 949 962

C, or C, 917 918 911 914 % 884 887 877 880

RT: Room temperature

LT: Llquld Na temperature.

the data for only Mga+-Cr0,2- and Pbs+-CrO,+ was analysed. The calculated frequencies are given in the psrenthesis. The agreement may be considered remark- able in spite of the approximation made.

We have also made a rough calculation of A based on an electrostatic model presented by DECIUS et al. [a].

Awh’w2 [I ; [fcl=o -for-o1

where f- is the stretching force constant of a pure CrO double bond and for=,, is the corresponding constant for a CrO bond in a, tetrahedral CrO,a- ion. S/e is cdculated from the following equation

2026 P. J. MILLER, G. L. CESSAC and R. K. KEIANNA

where a is the polarizability of the CrO,s- ion, r is the CrO bond length and a is the KBr unit cell dimension. a ia estimated from the Lorenz-Lorentz equation as applied to K,CrO, crystal. The CrO bond length is calculated to be ~1.60 A from the reported data on the crystal structure of K,CrO, [7]. From the reported values of the refractive index and density of K,CrO, [S] and the polarizability of Kf [9] the polarizability of CrO,s- is estimated to be ~3.9 A [3]. The CrO stretching force constant in CrO,Cl, (where CrO is a double bond) is reported to be 7.17 mdyn@ [lo]. A value of A N 0.66 mdyn/A is thus obtained whereas the normal coordinate analysis gives an average of A N 9.35 mdyn/A for Ms+-CrO,s- and MO.69 for Pb2+ CrOd2-.

Lead which has maximum polarizabihty produces maximum shifts in the fre- quencies of the CrOd2- ion. Larger polarizability means stronger non-bonded inter- action between W+ and the oxygens of the CrOh2- and there by more softening of the CrO bonds near Ms+ and, consequently, more hardening of the bonds away from iW+.

Acknowledg~n&--We would hke to thank Professor ELLIS R. LIPPINCOTT for providing us w&h the lrtboratory facihtles upon which this research w&8 carried out.

[7] R. W. G. WYCKOBR, Crystal Structures, Vol 3, p. 38. John Wiley (1966). [S] Handbook of Chemktry and Physics, 8th Ed. Chemical Rubber Company, Cleveland, Ohio

(1967). [Q] J. !I?Ess~N, A. KAHN end W. SHOCKLEY, Whys. Rev. 92, 890 (1963).

[lo] H. STAMMREICH, K. KAWAI and Y. TAVARES, Spectrochm. Acta 16, 438 (1969).