Infrared and Raman spectra and normal coordinate analysis of zirconium diphosphate

05R4_8539/X0/0901--0839$02

Spectrochnmxa Acta, Vol MA, pp X39 to X42 @ Pergmon Press Ltd 1980. Pnnted in Great Bntam

Infrared

and Raman

spectra

and normal coordinate diphospbate

analysis

of zirconium

YOSHIE INOMATA, TADAAKI INOMATA and TAKAO MORIWAKI Department of Chemistry, Faculty of Science and Technology, Sophia University, Chiyoda-ku, Tokyo

(Received

29 January

00/O

102, Japan

1980)

Abstract-The i.r. and Raman spectra of zirconium diphosphate were investigated from 1300 to 200 cm-‘. A normal coordinate analysis was performed assuming that the diphosphate ion had D,, symmetry, and an approximate description of the vibrational modes was assigned to the observed frequencies. The agreement between the observed and calculated frequencies is satisfactory; this indicated that the diphosphate ion in zmconium &phosphate had D,, symmetry to good approxima-

tion EXPERIMENTAL

INTRODUaION

The i.r. spectrum was recorded from 1300 to 200 cm-’ on Hitachi EPI-G2 and EPI-L spectrophotometers with samples prepared as nujol mulls. The Raman was measured from 1300 to 200cm-’ on a JRS-Sl laser Raman spectrophotometer of Japan Electron Optics Lab. using pressed pellet.

Diphosphates have been studied in some detail, particular interest being centered in the bond angle at the bridging 0 atom [l]. The configuration of the diphosphate ion varies somewhat with the size of M*’ for M,P,O, [2]. There are different values in the P-O-P angle; 134” in Na,P,O, . lOH,O [3], 139” and 148” in a-Zn,P,O, [2], 139” in one form [4] and 180” in the cubic form 151 of SiP,O, and 180” in ZrP,O, [6]. Therefore the diphosphate ion has different symmetry groups in diphosphates. Studies of the i.r. spectra of some diphosphate ion, such as Na4P207, Ba,P,O, [7,8] and MPzO, (M= Si(IV), Ti(IV), Sn(IV) and Zr(IV))[9] have been carried out and empirical band assignments have been made. However, it is difficult to assign the absorption bands of such molecules as P,0,4m on the basis of empirical data alone. Some investigators have made a normal coordinate analysis on the assumption that the diphosphate ion has a D,, [lo, 111, or a D,, [12, 131 symmetry. HEZEL and Ross [lo] treated it as having D3,, symmetry and compared the calculated values with observed frequencies in some bivalent metal diphosphates such as M2PZ07 (M= Pb(II), Ba(II), Sr(I1) and Ca(I1) etc.). They indicated that the point group of the diphosphate ion was either C,,, C,, or C,. But the i.r. spectra of these bivalent metal diphosphates are very complex and it is rather difficult to match the observed frequencies and the calculated values; MOONEY el al. [12, 131 calculated normal vibration using a Dxd model and compared their calculated values with the i.r. spectra of ZrP207 and /3but not with Raman data. In the F MgrP,O,, matrix, HEZEL neglected the off-diagonal elements and MOONEY used the valence force field in their calculation. In this investigation, the i.r. and Raman spectra of zirconium diphosphate, which seems to have a higher symmetry than the bivalent metal diphosphates, have been measured and a normal coordinate analysis has been made, using the modified Uray-Bradley force field.

NORMAL

COORDINATE

ANALYSIS

LEVI and PEYRONEL [6] carried out a crystallographic investigation of zirconium diphosphate and reported that the diphosphate ion does not have a true D,, symmetry, though the POP bridge is straight and there is a center of symmetry. However, in this investigation, the normal coordinate analysis has been made assuming that the diphosphate ion has a D3d symmetry and tetrahedral angles, because of the following reasons: first, the mutual exclusion rule can apply in practice, as shown in Table 2, and one would expect to obtain essentially the same results for a P,0,4ion with C,, symmetry and for one with D3d symmetry; moreover, redundancy has to be made equal to zero. An X,Y, molecule or ion with D,, symmetry [13] has 21 modes of normal vibration having the representation

The bond lengths used for the terminal and bridge PO bonds are 1.517 and 1.56 A [6], respectively. The frequencies were calculated using the internal and symmetry coordinates shown in Fig. 1 and Table 1. WILSON’S GF matrix method [14] was used, and all results were obtained using a FORTRAN program designed by SHIMANOUCHI [15]. The calculations were carried out on HITAC 5020E [16] and I.B.M. 1130 computers. The force field employed was of the modified Uray-Bradley type and the force constants reported by VENKATESWARLU [ 171 for a P03- ion were used as the initial values. They were refined so as to obtain the best fit between the calculated and the observed frequencies by a trial and error method, guided by 839

O

z

EU

E,

A 2u

AI,

Species

Ss SC S, S, S, S 1” S 11 S 12 S 13 S 14 S 15 S 16 S 17 S 18 S 19 S 2” S 21 S 22

S,

S,

S, S*

POP sym. str. PO, sym. str. PO, sym. def. Red. POP asym. str. PO, asym. str. PO, asym. def. Red. PO, deg. str. PO, deg. def. PO, rock. PO, deg. str. PO, deg. def. PO, rock. PO, deg. str. PO, deg. def. PO, rock. POP bending PO, deg. str. PO, deg. def. PO, rock. POP bending

Description of coordinate

-1

-1

1

1

1

1

1

1

-1

-1

-1

1

-1

-1

-1

-1

1

1

-2

2

-1

1

-1

-1

-1

1

1

1

1

1

-1

I

-1

-1

1

1

1 1

1 1

2

2

1 1

1 1

-1

-1

-1

-1

1 1

-1

-1

-1 -1

1

1

1 1 1111111111

-2

2

-1 -1

1

-1

-1

-1 -1

1

1

1

Table 1. Symmetry coordinates of the i.r. and Raman active species for P20j4

1

2

2

-1

-1

_____

1

1

1

-1

-1

-1

-1

1

-1

-1

-1

-1

-1

-1

--

-1

-1

-1

-1

_.-

1

1

1

1

2

-2

-1

-1

1

1

1

-1

-1

-1

-1

1

1

Infrared and Raman spectra and normal coordinate analysis of zirconium diphosphate

841

Fig. 1. Internal coordinate of P,O;“. the values of a Jacobian matrix. In the F matrix, the force constant K refers to the PO stretching vibration, H to the OPO bending, and F to the repulsion. Subscripts r and R refer to the terminal and bridge stretching vibrations, and (Y and /3 to the OPO terminal-terminal and terminal-bridge bending vibrations, respectively. RESULTS AND DISCUSSION

Infrared and Raman spectra of zirconium diphosphate are shown in Fig. 2. These spectra indicate that mutual exclusion rule applies between the i.r. and the Raman spectra, except for a very weak band at 744 cm-’ in the i.r. spectrum and a medium band at 741 cm-r in the Raman spectrum. Therefore, it can be assumed that zirconium diphosphate has a center of symmetry. All vibrations above 900 cm ’ could be assigned to PO stretching vibrations, because the PO stretching vibrations in PO:- have been observed at 900800 cm-’ [7]. All vibrations below 600 cm -I could be assigned to the OPO deformation vibrations. The band at 741 cm-’ in the Raman was assigned to the PO bridge stretching vibration by MOONEY et al. [12, 131 and to the deformation vibration by HEZEL and Ross [lo]. In this study, three bands were observed above 900 cm-’ in the i.r. spectrum, but only two bands in the Raman spectrum, though three stretching vibrations of 2A1,, 2A,,, E, and E, should be theoretically observed in both the i.r. and the Raman spectra as shown in Table 1. In the study of the dichromate ion having the same structure as the diphosphate ion, CrOCr antisymmetric and symmetric bridge stretching vibrations were observed at 780 and 561 cm-‘, respectively [18]. Therefore, if the difference of the two bridge Table

2. Calculated

i.r. cm-’

1161 1110 1093 976 741 557 544 405 330 370 250

S..&(A) 36/9--o

Calcd. cm-’ 1163 1165 1111 1091 971 743 550 548 416 326 378 240

and Raman

spectra

of ZrP,O,.

stretching vibrations of the diphosphate ion is approximately of the same order as that for the dichromate ion, the observed band at 741 cm-’ in Raman spectrum of the diphosphate can be assigned to the POP symmetric bridge stretching vibration. As for the deformation vibrations, MOONEY [13] assigned the bands at 561 and 546 cm-’ in the i.r. spectrum to OPO bending deformations E, and AZ,,, respectively. However, in our study the absorption bands were observed at 544 and 405 cm -’ in the i.r. and 557 and 330 cm-’ in the Raman spectra. From the normal coordinate analysis and the assignments of MOONEY [13], it seems to be reasonable that the bands at 500 cm-’ region, at 405 and at 330 cm-’ may be assigned to the PO, degenerate (E), asymmetric (A,,), and symmetric deformation (A,,) vibrations, respectively. The remaining bands at 370 cm-’ in the i.r. and at 250 cm-’ in the Raman spectrum may be assigned to PO, rocking vibrations, which are lacking in the case of the orthophosphate ion. In Table 2, the observed and calculated frequencies are listed, in along with potential energy distributions to the symmetry coordinates and approximate descriptions of the vibrational modes for the diphosphate ion. The force constants used in this calculation are shown in Table 3. The agreement between observed and calculated values is satisfactory, but these calculated values differ from the values calculated by HEZEL [lo] and MOONEY [12]

and observed frequencies of ZrP,O, distribution among symmetry coordinates

Raman cm-’

1200

Fig. 2. Infrared

and

P.E.D. %

s,,,s,,uw s,,S,,(lW S&4), S&7) S,(100) S,(95) S,(o5), S,(35) S,“, S,,(95) S,,, S&96) S,WO) S,(59), S,(30) S,,, S,,(90) s,,. S,,(lOO)

potential

energy

Description PO, PO, PO, PO,

deg. str. E, deg. str. E, asym. str. A,, sym. str. A,,

POP asym. str. A,, POP sym. str. Al, PO, deg. def. E, PO, deg. def. E,, PO, asym. def. A,, PO, sym. def. A,, PO, rock. E, PO, rock. E,

842

Y. INOMATA, T. INOMATAand T. MORIWAKI

Table 3. Force constants used in the calculation K, KP. H, H, K, K rR K RR H_ H u0 H F,BP F,

7.36 5.65 0.73 0.25 0.33 0.58 2.51 0.15 0.22 0.16 0.45 0.55

for ZrP,O, mdyn/A

mdyn.A

mdyn/A

The force constants with two subscripts refer to interactions. extent. The assignments also differ; HEZEL and Ross assigned the band at around 700 cm-’ to the PO, degenerate deformation vibration [lo], whereas it was assigned to the POP symmetry bridge stretching vibration (A,,) by MOONEY [13] and in this investigation. MOONEY and GOLDSMITH assigned the bands at -1180 and 1116 cm-’ to the PO, antisymmetric stretching vibration (AZ,,) and the PO, degenerate stretching vibration (E,), respectively [13], but their assignments are reversed in this study. There are also some differences in the assignments of the bands below 600 cm-‘. HEZEL and Ross [lo], however, observed more bands than symmetry; MOONEY and expected from D3,, GOLDSMITH did not make their own measurements. Neither had any Raman data. Therefore, their assignments could be incorrect. The results of the normal coordinate analysis in Table 2 show that the assignments in this study are reasonable, except for the POP bridge bending mode, which was not observed in this study, and the PO, torsional vibrations, which are inactive in both Lr. and Raman spectra. The force constants shown in Table 3 differ from those of HEZEL [lo] and MOONEY [13]. This may be due to the differences of assignments and of methods of calculation. The force constants obtained in this study also differ from those of orthophosphate. For example, the terminal PO to some

stretching force constants are 6.15 mdyn/A in orthophosphate [lo] and 7.36mdynlA in this diphosphate. However, there have been various values obtained by different investigators [lo, 12, 191 for the force constants of the orthophosphate ion and there seem to be no definite values for them. Therefore, it seems to be necessary to calculate the force constants of the PO bond for many different compounds which include the PO bond in order to obtain more general Uray-Bradley force constants, as was the case for the CH bond.

REFERENCES [l] A. F. WELLS, Structural Inor8amc Chemistry, 4th edition, p. 689. Clarendon Press, London (1975). [2] B. E. ROBERTSONand C. CALVO, J. Solid State Chem. 1, 120 (1970). [3] D. W. J. CRUICKSHANK, Acfa Cryst. 17, 672 (1964). [4] V. G. BISSERT and F. LIEBAU, Acta Cryst. 26B, 233

(1970). [5] E. TILLMANNS and W. GEBERT, J. 7, 69 (1973) [6] G. R. LEVI and

Solid State Chem.

G. PEYRONEL, Z. Kristallogr.

92,

190 (1935). [7] D E. C. CORBRIDGE and E. J. LOWE, J. Chem. Sot. 493 (1954). [8] W G. PALMER, I Chem. Sac. 1552 (1961). [9] E. STEGER and G. LEIJKROTH, Z. Anorg Allgem. Chem. 303, 169 (1960). [lo] A. HEZEL and S. D. Ross, Spectrochim. Acra 23A, 1583 (1967). [ll] A. HEZEL and S. D. Ross, Spectrochlm. Acta 24A, 131 (1968). R. W. MOONEY, S. Z. TOMA and J. BRUNVOLL, Spectrochlm. Acta 23A, 1541 (1967). R. W MOONEY and R. L. GOLDSMITH,J. Inorg. Nucf.Chem. 31, 933 (1969). E. B. WILSON,J. Chem. Phys. 7, 1047 (1939); 9, 76 (1941). T. SHIMANOUCHI,Computer Programs for Normal Coordmare Treatment of Pofyatomic Molecules, Tokyo University, Tokyo (1968). These calculations are performed at Computer Center, Tokyo University. K. VENKATESWARLU and S. SUNDARAM, J. Chem. Phys. 23, 2365 (1955). H. STAMMREICH,D. BASSI, 0. SALA and H. SIEBERT, Spectrochim. Acta 13, 1958 (1962). A. C. CHAPMAN, D. A. LONG and D. T. L. JONES, Spectrochlm. Acta 21, 633 (1965).