Study of Zone Center Phonons in CdWO₄

Study of Zone Center Phonons in CdWO₄

Ruby Jindal1, M.M.Sinha2 and H.C.Gupta3

1Department of Applied Science and Humanities, ITM University Gurgaon (Haryana) -122017(Email: gr_rby@yahoo.com)

2Department of Physics, Sant Longowal Institute of Engineering and Technology Longowal, Sangrur-148106

3Physics Department, IIT Delhi, Hauz Khas, New Delhi, India 110016

Abstract

Raman and the infrared wave numbers in CdWO4 in monoclinic phase having space group P2/c, have been investigated by applying short-range force constant model. The calculation of zone center phonons has been made with eight stretching and five bending force constants. The calculated Raman and infrared wavenumbers are in good agreement with the observed ones. The potential energy distribution has also been investigated for determining the significance of contribution from each force constant toward the Raman and the infrared wave numbers.

1. Introduction

   Metal tungstates has been studied due to many applications [1-2]. Tungstates AWO4 crystallize in either the tetragonal scheelite structures or the monoclinic wolframite structures depending on the size of cation A i.e tungstates of relatively large bivalent cations crystallize in scheelite structure and of smaller bivalent cations exhibit the wolframite structure. CdWO4 has the wolframite crystal structure.

   Phonon properties of CdWO4 are very important and have not been studied widely. R.Lacomba et al. [3] had studied CdWO4 compound with the help of Raman spectroscopy and density functional theory. In infrared modes they have calculated two frequencies which are very near to each other i.e 252.9 cm-1 and 255.1 cm-1 by ab-initio method which is not generally possible in experiment. Also there is not a good agreement between their calculated values and experimentally observed higher infrared modes. Hence in this paper we have presented the calculated values of Raman and infrared modes using short range force constant model in P2/c structure with eight stretching and five bending force constants, which are in very good sync with the experimental results. Also all the infrared modes have

   been assigned properly. The PED (potential energy distribution) has also been investigated which determined the contribution of each force constant towards the Raman and infrared wavenumbers.

2. Structure

   CdWO4 crystallizes in a monoclinic structure. Lattice parameters are a = 5.028 Å, b = 5.862 Å, c = 5.067 Å, =91.50°, V=149.3 Å3 and Z=2 [1]. Atomic co-

   ordinates are taken from the work of J. Macavei et al. [4]. The total no. of zone center phonon modes present for each species of space group is total =8 Ag +10 Bg

   +8 Au+10 Bu. Out of these normal modes, 1Au+2Bu are acoustical and rest are optical modes.Out of thoes 8 Ag

   + 10Bg are Raman active and 7 Au + 8Bu are infrared active.

3. Theory

   The frequency of normal mode vibrations is determinate by solving the secular equation using Wilsons GF matrix method [5]. If F is the potential energy matrix and G is the inverse kinetic energy matrix, then the secular equation can be written as det | FG E | = 0, where = 42c22 and E is the unit matrix, c is velocity of light and is the wave number. The stretching forces between two atoms were assumed to be obeying the Hooks law. The input parameters used for the calculation are the lattice parameter, masses of the atoms, symmetry coordinates [2] and the available Raman and infrared wavenumbers [3,6].

4. Results and discussion

   In this work we have calculated the Raman and infrared wavenumbers given in Table 1 by using force constants (N/cm) given below

   K1(W-O2):3.681; K2(W-O1):1.775; K3(Cd-O1):

   0.669; K4(W-O1):1.102; K5(Cd-O2):0.400; K6(Cd-

   O2): 0.351; K7(O2-O2):0.117; K8(W-Cd):2.509;

   H1(O1-Cd-O2): 0.277; H2(O1-W-O2):0.089; H3(O1-

   W-Cd):0.452; H4(W-O1-W):1.609; H5(Cd-W- O1):0.593.

   The calculated Raman and infrared modes are compared with the experimently results of Lacomba et al.[3] and Daturi et al.[6]. Higher infrared modes calculated by Lacomba et al. [3] are not in good agreement with the experimental values [6] of the infrared modes. But it is clear from Table 1 that present calculations provide a very good agreement with the experimental results of the Raman and the infrared modes. It can be seen from Table 1 that our calculated results are better than the theoretically calculated results of Lacomba et al.[3]. The PED for each mode has also investigated in this work. The interpretations drawn from the PED are described below.

   For the high frequency mode i.e. 827 cm-1 of Ag mode,

   Table 1. Calculated and observed Raman and infrared active zone center modes (cm-1) for CdWO4

   830 cm-1

   of Bg mode, 834 cm-1

   of Au mode, 876 cm-1

   of Bu mode, the force constant W-O1-W contributes in a dominant way. For frequencies 700 cm-1 of Ag, 699 cm-1 of Bg , 699 cm-1 of Au and 698 cm-1 of Bu , W-O2 force constant was found as leading force constant.

   From theoretical calculations, W-O1 force constant plays an important role for frequencies 493 cm-1 of Ag, 508 cm-1 of Bg, 500 cm-1 of Au and 508 cm-1 of Bu.

   Force constant Cd-W-O1 plays a very significant role in frequencies 388 cm-1 of Ag, 392 cm-1 of Bg, 383 cm- 1 of Au and 376 cm-1 of Bu. Force constant W-Cd is of utmost importance for frequencies 291 cm-1 of Ag, 278 cm-1 of Bg, 309 cm-1 of Au and 310 cm-1 of Bu.

   Frequencies 244cm-1 of Ag, 245 cm-1 of Bg, 232 cm-1 of Au and 244 cm-1 of Bu are mainly contributed by Cd-O2 force constant. For lower frequencies i.e 125 cm-1 of Ag, 74 cm-1 of Bg, 127 cm-1 of Au and 83 cm-1 of Bu force constant O1-W-O2 dominates.

   Daturi et al [6] had observed experimentally only seven frequencies of Bu mode. The present calculation has mentioned the remaining one frequency i.e. 310 cm-1 of Bu mode which is found to be in agreement with the experimental result of similar compounds [7] . Lacomba et al had not calculated frequency of this range in Bu mode.

   It is important to mention that the bond between W

   Cd is very important for explaining the lower set of frequencies. When this bond is not considered the lower frequencies of Bu mode become very small in comparison to the experimental value.

   249

   Species	Exp.[3]	Exp.[6]	Present cal.	Cal.[3]
   Ag	897	896	827	864
   	707	706	700	684
   	546	547	493	530
   	388	387	388	357
   	306	307	291	287
   	229	229	244	220
   	177	177	150	177
   	100	99	125	97
   Bg	771	771	830	742
   	688	687	699	655
   	514	514	508	490
   	352	351	392	338
   	269	269	278	252
   	248	245	238
   	148	148	191	142
   	134	133	153	126
   	118	117	119	111
   	78	77	74	67
   Au	–	835	834	839
   	–	693	699	627
   	–	455	500	471
   	–	354	383	379
   	–	310	309	322
   	–	230	232	270
   	–	131	127	121
   	–	0.0	0.0	0.0
   Bu	–	884	876	744
   	–	595	698	524
   	–	510	508	421
   	–	408	376	—-
   	–	—-	310	—-
   	–	260	244	253,255
   	–	161	165	145
   	–	107	83	105
   	–	0.0	0.0	0.0
   	–	0.0	0.0	0.0

5. References

1. T. T. Monajemi, D. Tu, B. G.Fallone and S. Rathee, A bench-top megavoltage fan-beam CT using CdWO4 – photodiode detectors: II. Image performance evaluation, Med. Phys. Vol. 33, Apr. 2006, pp. 1090-1100.

2. Ruby Jindal, M. M Sinha and H. C. Gupta, Study of zone

   center phonons in wolframite ZnWO4, Turkish Journal of Physics, vol. 37, 2013,pp. 107-112

3. R. Lacomba-Perales, D. Errandonea, D. Mart´nez- Grac´a, P. Rodr´guez-Hern´andez, S. Radescu, A. M´ujica, A Munoz, J. C.Chervin, and A. Polian, Phase transitions in wolframite-type CdWO4 at high pressure studied by Raman spectroscopy and density-functional theory, Phys. Rev. B, vol.79, March 2009,pp. 094105-10.

4. J.Macavei and H. Schulz, Z. Kristallogr, The crystal structure of wolframite type tungstates at high pressure, vol. 207,1993, pp. 193-208.

5. T. Shimanouchi, M. Tsuboi and T. Miyazawa, Optically Active Lattice Vibrations as Treated by the GF-Matrix Method, J. Chem. Phys., vol. 35, 1961, pp. 1597

6. M. Daturi, G. Busca, M. M. Borel, A. Leclaire, and P. Piaggio, Vibrational and XRD Study of the System CdWO4- CdMoO4, J. Phys. Chem. B, vol. 101, 1997, pp. 4358-4369.

7. M. Maczka, M. Ptak, K. Hermanowicz, A. Majchrowski,

A. Pikul, J. Hanuza , Lattice dynamics and temperature- dependent Raman and infrared studies of multiferroic Mn0.85Co0.15WO4 and Mn0.97Fe0.03WO4 crystals, Phys. Rev. B, vol. 83, May 2011, pp. 174439-14.