Temperature and pressure dependence of the Raman active modes of vibration of α-quartz

0584-8539/82/101 [email protected]/0 @ 1982 ~ergamon Press Ltd.

Spectrochimico Actn, Vol. 38A, No. IO, pp. 1105-1108. 1982 Printed in Great Britain.

Temperature and pressure dependence of the Raman active modes of vibration of a-quartz K. J. DEAN, W. F. SHERMANand G. R. WILKINSON Wheatstone Physics Laboratory, King’s College, Strand, London WCZR 2LS, U.K. (Received

14 June 1982)

Abstract-The

Raman spectra of a single crystal of natural quartz have been very carefully investigated as a function of temperature (range 77-300 K), and as a function of hydrostatic pressure (atmospheric up to 10 kbar). The temperature results shows that cooling the quartz increases the vibrational frequencies with corresponding reductions in linewidth, and that the 206 cm-‘, vibrational mode (the soft mode) is very strongly temperature dependent. The pressure dependent Raman data has been used to calculate the mode Gruneisen parameters yi, for the three strongest modes; these are 3.63,0.64 and 1.55 for the 206,464 and 128 cm-’ lines, respectively.

The room temperature Raman spectra of aquartz have previously been studied and the modes of vibration have been identified by SCOTT and PORTO [5]. The Raman spectrum of quartz has also been reported by several authors at various temperatures and at elevated pressures [6-91. The aim of this paper is to present the results of a very careful Raman investigation yielding the most precise results yet obtained [lo].

INTRODUCTION Quartz is a visibly transparent crystalline material that occurs abundantly in nature; well-developed crystals are hexagonal prisms terminated by hexagonal pyramids at each end. The quartz crystal structure consists of a screw axis of SiOZ molecular units parallel to the z-axis [l]. Crystalline quartz undergoes a reversible solid-state phase transition [2] at approximately 847 K, the low temperature phase being referred to as a-quartz, the high temperature phase as P-quartz. The application of group theory to the structure of quartz (having D3 symmetry with nine atoms per unit cell), predicts that there will be 27 normal modes, four of which are totally symmetric A1 modes and eight doubly degenerate E modes. The remainder are four A2 modes and three acoustic modes. The form of the Raman tensors and the activity of the various modes is shown below 4A1 modes 4A2 modes 8E modes (x 2)

vibrational

EXPERIMENTAL

Raman active Infrared active Raman and i.r. active

The i.r. absorption spectrum of crystalline quartz has been well studied by KLEIMAN and SPITZER [3,4], and by PRICE and WILKINSON [15] who analysed the region of strong lattice absorption (200-2200 cm-‘). The transmission and reflectivity at room temperature were measured using plane polarized radiation, for both the ordinary component (electric vector perpendicular to the optic axis) and extraordinary component (electric vector parallel to the optic axis), to determine the optical constants of quartz in the infrared.

The quartz crystal used for these experiments was optically polished, having completely parallel unscratched surfaces and was totally free from internal faults and imperfections. The Raman spectra were excited using incident radiation from the 488.0 nm line from a Spectra-Physics model 165 argon ion laser. Low temperature spectra were obtained using approximately 450mW of laser power, and the high pressure spectra were recorded using approximately 420 mW of laser power (measured at source). The spectra were recorded using a Spex Industries Ramalog 5M double grating monochromator with a cooled photodetector. The large sample size (0.5 x 0.5 x 0.5 cm) and large collection optics aperture enabled the low temperature Raman investigation to be carried out with an instrumental resolution of 0.75 cm-‘, whereas the high pressure spectra had to be obtained using 2.0 cm-’ resolution, due to the small f-number of the high pressure Raman cell windows. The temperature of the quartz crystal was controlled and measured very precisely (to an accuracy of + l.O”C) from liquid nitrogen temperature up to room temperature, using an Oxford Instruments CFlOO continuous flow cryostat. Good thermal contact was ensured by mounting the polished quartz crystal directly onto the cooling block of the cryostat. Every time the temperature of the quartz was changed the sample was allowed to establish thermal equilibrium for 20min before Raman spectra were recorded, and the relative intensity of the three strongest Stokes and anti-Stokes lines was measured as a means of checking the sample temperature using

1105

4 =m 5

exp - (hv,/kT).

The high pressure Raman experiments

were performed

1106

K. J. DEAN et al.

using a small sample of quartz (the dimensions after cutting and repolishing were 1.5 x 1.0 x 0.5 mm), using a 14 kbar two-stage hydrostatic high pressure Raman cell developed in this laboratory [ll]. The pressure was transmitted to the quartz sample hydrostatically through the medium of freshly distilled (to reduce the effects of background fluorescence) spectroscopic grade Octoil-S.

The hydrostatic pressure was generated with the low pressure intensifier stage of the Raman cell, using a single stage low pressure hydraulic hand pump. To ensure that the experiments were performed under isothermal conditions, the pressure changes were carried out very slowly (approximately 1.Okbar in 6 min), thus

avoiding any heating of the crystal as a result of its compression. RESULTS AND DISCUSSION

Table 1 shows the position and linewidth of all the Raman active lines of a-quartz at both room temperature (300 K) and at liquid nitrogen temperature (77 K). The room temperature data were the results of a very precise polarization study, using the following geometries: X(ZZ) Y, X(ZX) Y, X( YZ) Y and X( YX) Y. These spectra were obtained with an instrumental slit width corresponding to a frequency resolution of 0.75 cm-’ (slits = 73 pm for first-order dispersion of the 488.0nm exciting line using the 1800 lines mm-’

gratings). The 77 K Raman data were obtained using 2.0 cm-’ slits. The Raman spectrum of quartz contains a low intensity band centre at approximately 148 cm-’ at room temperature [12]. This controversial feature has been found to exhibit Al-symmetry type behaviour in polarization studies, but non-Al-type behaviour in low temperature studies. When the quartz was cooled to liquid nitrogen temperature, this line was observed to be of a double component nature, being composed of two separate low intensity bands (that were difficult to distinguish but with care this was possible) centred at approximately 149 and 155 cm-‘, respectively. The band intensity was observed to decrease as the sample temperature was lowered, in contradiction to the behaviour of the four AI-symmetry modes. This band was also found to be present in the Raman spectrum of synthetic quartz, but of a much lower intensity. The true nature of this controversial feature still remains unclear. Other A,symmetry type features of uncertain origin have been observed in the Raman spectra of both natural and synthetic quartz and are shown below in Table 2. Due to the fact that these bands display

Table 1. Raman active lines of quartz Frequency 300K Symmetry E(L0 + TO)

cg;) 20519 264.6 355.1 394.1 401.0 450.2 464.1 494.0 510.6 696.0 795.7 807.8 1069.4 1084.5 1161.5 1230.0 1235.0

:;TO) A, E(TO) E(L0) @TO) A, $(TO) E(L0 + TO) E(TO) E(L0) E(TO) Al E(L0 + TO) E(LO) E(L0)

(cm-‘) 77 K

300K

( 2 0.2 and 2 0.5)* 132.0 213.4 266.2 355.6 396.0 403.0 466.0 699.0 799.0 810.0 1072.0 1085.0 1162.5 1230.0

Linewidth (cm-‘) 77 K ( f 0.2 and * 0.5)*

( + 0.2) 3.7 23.1

1.9 6.9 2.1

:.: 3:6 4.2 3.2 7.4 6.0 4.5 8.4 8.1 7.9 6.5 7.1 9.5 14.0

::: 4.2 2.0 4.1 4.6 4.3 :? 412 9.5

* f 0.5 cm-’ refers to the error of weak bands.

Table 2. Combination bands in the Raman spectrum of a-quartz at room temperature

. v(cm-‘) observed 392 531 841 851 895

v(cm-‘) combination 128 + 265 = 1235 - 6% = 1235 - 394 = 450+401= 494 + 401=

393 539 841 851 895

difference (cm-‘) +1 +2 0 0 0

Temperature and pressure dependence of the Raman active modes Al-type behaviour it is believed that they are E-type combination bands. Figure 1 shows the temperature dependence of the Raman frequency of the three most intense lines in the Roman spectrum of quartz. The sample temperature was varied in approximately 25 K steps from liquid nitrogen temperature up to room temperature. From this figure it can be seen that the lowest lying A~-symmetry mode with a room temperature frequency of 206cm -~ (the soft mode), is the most strongly temperature dependent, increasing in frequency to approximately 213 cm t at liquid nitrogen temperature. It is believed that this is due to the fact that the vibrational eigenvectors for this mode have been found to be very similar to the atomic displacements that are known to occur during the phase transition, from the low temperature phase (a-quartz) to the high temperature phase (/3-quartz) [13, 14]. Figure 2 shows that the linewidth of the 206 cm -I mode is the most strongly temperature dependent. The linewidth varies from approximately 23 cm t at room temperature down to approximately 7 c m -~ at liquid nitrogen temperature. The narrow, room temperature linewidth of the 128cm -~ band is reasonable, considering that it is the lowest lying optical vibration and can therefore only decay into a relatively low density of acoustic states. The observed linewidth change (Fig. 2) was limited by the spectrometer slit width that was used. PINE and TANNENWALD [6] showed that the true bandwidth of the 128cm -~ band reduced to about 0.2 cm -I by a temperature of 77 K. Figures 3-5 show the Roman line frequency as a function of applied pressure, over the pressure range 0-10 kbar, for the three most intense lines having atmospheric pressure frequencies of 128, 206 and 464cm -~. The small single crystal sample was oriented such that the laser entered

I

I

1107 I

I

I

2/+-A 20 'e

16

cu

~ 8

,

i 100

150 200 250 Temperafure ['K]

300

Fig. 2. The temperature dependence of the Raman linewidths of the 206 (data A), 464 (data B) and 128 (data C) cm -I lines, respectively. Note that C is limited by the spectrometer slit width for temperatures below about 200 K, see PINE and TANNENWALD[6].

I

i

i

i

l

]

i

i

i

_j

133 SLope = 0-S/* crn-I kbar'-I

132

I

•

131 13o

129 ] 1281 I

I

I

I

I

2

3

L, 5 6 Pressure [kbor]

I

I

I

I

I

I

7

8

9

10

Fig. 3. The pressure dependence of the 128 cm -I Raman line of E(LO +TO) symmetry.

1

I

I

I

I

= •

-

_

I

I

i

I

I

I

l

228 /*66 I - - - - ~ - ~ _ . ~

_

22/*

'~ 220 v~ 216 _ 212 ~-E 211 21/* 210

I

~212 20B

209

206

I

I

I

I

1

I

L

I

I

2

3

/* 5 6 7 Pressure Ikbar]

8

9

10

Fig. 4. The pressure dependence of the 206 cm -1 Raman line of A~ symmetry (note large size).

~0 t- "

-

~

1281._ [

- .,. 1

100

I

I

i

150 200 250 Temperafure ['K1

I

300

Fig. 1. The temperature dependence of the three strongest Raman active internal modes: the 464, 206 and 128 cm -~ lines, respectively.

the quartz along the y-axis and the Raman scattering was collected from the x-axis. It can be seen from these figures that the Raman frequencies of these three lines are linearly dependent on the applied pressure, increasing by 0.54, 2.04 and 0.81 cm -I k b a r - ' for the 128, 206 and 464cm - '

K. J. DEAN et al.

1108

Table 2 ~i (cm-')

(Svil,SP)r (cm-' kbar-')

~/i

3', [9]

0.54 2.04 0.81

1.55 3.63 0.64

1.7 3.2 0.7

128 206 464

I

I

I

I

I

I

I

I

I

I

/~7t~ -1.72

Slope = 0 8 1 tm -1 kbar -1

IE ~70

~t~68 c t,66 t,6ta I

I

I

I

I

I

I

t

I

I

1

2

3

/~

5

6

7

8

9

10

Pressure

[kbar]

Fig. 5. The pressure dependence of the 464 cm-~ Raman line of A~ symmetry.

lines, respectively. It should be pointed out that as in the case of the variable temperature studies, the vibrational frequency of the 206 cm -1 (sort-mode) is very much more strongly influenced by applied pressure than the other two vibrational frequencies that have been studied. From the data shown in Figures 3-5, the respective mode Gruneisen constants 3'i (the parameter which serves to quantify the degree of anharmonicity within vibrational modes) were calculated and are shown in Table 2. The calculated values of ~ for the three strongest Raman active modes were observed to be constant over the pressure range 0-10kbar, suggesting that the mode anharmonicities are independent of the mean atomic separations for this pressure range. For comparison the values of yl calculated from ref. [9] are also shown. The agreement is very good since ASELL and NICOL only quote single figure values for the frequency change as a function of applied pressure. To conclude, the effects of low temperature and

high pressure on the three most intense Raman active vibrations of a single crystal of quartz have been demonstrated, and it has been shown that the 206 cm -1 soft-mode vibrational frequency is particularly sensitive to both temperature and pressure Calculated mode Gruneisen parameters are also shown, which can be interpreted as being a useful parameter in quantifying vibrational mode anharmonicities. Acknowledgements--One of us (K. J. D.) would like to thank the Science and Engineering Research Council and King's College London for financial support. REFERENCES

[1] R. G. D. WYCKOFF, Crystal Structures, 2nd edn. Vol. 1, p. 312. Interscience, New York (1963). [2] C. N. RAO and K. J. RAO, Phase Transitions in Solids, p. 204. McGraw-Hill, New York (1978). [3] O. A. KLEINMANand W. G. SPITZERPhys. Rev. 125, 16 0%2). [4] W. G. SPITZERand D. A. KLEINMAN,Phys. Rev. 121, 1324 (1%1). [5] J. F. SCOTTand S. P. S. PORTO,Phys. Rev. 161,903 (1%7). [6] A. S. PINE and P. E. TANNENWALD,Phys. Rev. 178, 1424 (1969). [7] Y. D. HARKER,C. Y. SHE and D. F. EDWARDS,Appl. Phys. Lett. 15, 272 (1%9). [8] R. J. BRIGGSand A. K. RAMDAS,Phys. Rev. B. 16, 3815 (1977). [9] J. F. ASELL and M. NICOL, J. Chem. Phys. 49, 5395 (1%8). [10] K. J. DEAN Ph.D. thesis, University of London (1981). [11] A. A. STADTMULLER,Ph.D. thesis, University of London (1982). [12] J. F. SCOTT,Phys. Rev. Lett. 21,907 (1%8). [13] M. M. ELCOMBE,Proc. Phys. Soc. 91,947 (1967). [14] I. LAULICHT, I. BAGNO and Y. SCHLESINGER, J. Phys. Chem. Soc. 33, 319 (1972). [15] W. C. PRICE and G. R. WILKINSON, U.S. Army report DA92-591-EUC-212701-26489-B (1%2-1%3).