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Evolution of the Rayleigh line wing and structural correlations for liquid-glass transition
Volume 123, number I
PHYSICS LETTERS A
13 July 1987
EVOLUTION OF THE RAYLEIGH LINE WING AND STRUCTURAL CORRELATIONS FOR LIQUID-GLASS TRANSITION V.K. MALINOVSKY, V.N. NOVIKOV and A.P. SOKOLOV Institute ofAutomation and Elecrrometry, Siberian Branch ofthe USSR Academy ofSciences, 630090 Novosibirsk, USSR Received 13 April 1987; accepted for publication 8 May 1987 Communicated by J.I. Budnick
The connection between the Rayleigh line wing in inelastic light scattering spectra in liquids and the boson peak observed at light scattering in glasses in the frequency range of 20—100 cm - has been found for the first time. The Rayleigh line wing is represented as a sum of boson and central peaks. The obtained results are evidence of the existence of structural correlations in high-viscosity liquid which decrease exponentially with the distance on the scale of 10 A.
A wide wing of the Rayleigh line [1] is characteristic of spectra of light scattered in liquids. Its spectral form depends on the chemical composition and the temperature of the liquid. It is well approximated by the sum of two (or more) Lorentz curves: a relatively narrow curve (a, < 10 cm—1) and a wide one (w ~ 100 cm-’) [1]. In spite of numerous investigations of the Rayleigh wing, a complete microscopic description of its nature has not been given so far. On the other hand, in all amorphous materials, particularly in glasses, a low-frequency peak, the so-called boson peak, is discovered in the same spectral region [2]. It is absent in crystals of the same composition, and in a number of papers it is associated with space correlations of elasto-optical and elastic constants fluctuations on the scale of R~~ 10 A [3,4]. A boson peak carries information on the radius ofthe structure correlations R~and the character of decreasing of these correlations with distance [3,4]. In this paper, using glycerine as an example, the connection between the Rayleigh line wing in liquid and a boson peak has been found for the first time. A boson peak defines a high-frequency part of the Rayleigh line wing. The results obtained allow to conclude about the existence of structural space correlations on the scale of 10—20 A in liquid. It is shown that structural correlations on this scale are the same for liquid and vitreous states.
Right-angle Raman spectra were measured with the use of a DFS-24 spectrometer. The spectral slit width was 2 cm-’ and the excitation wavelength was 676 nm. Two different polarizations were investigated: one with the incident beam polarized and scattered light analyzed perpendicular to the scattering plane (I J~), and one with the incident beam polarized parallel to and the scattered light analyzed perpendicular to the scattering plane (II .L). Normalization of all spectra has been carried out with regard to the temperature, the frequency factor of scattering and the spectral function of the instrument. Temperature has been measured according to the ratio of Stokes and anti-Stokes scattering. Test control, recording and subsequent processing of spectra as well as calculation oftheoretic curves have been carried out using the automated system “MicroCAMAC”. Glycerine has been chosen as a sample. Glycerine in a quartz ampule was placed in the cryostat. The sample temperature was changed in the range of T= 300—175 K. The obtained results (fig. 1) show that over the whole temperature range the Raman spectrum of glycerine does not undergo significant changes in the high-frequency region (w> 100 cm ~1)• At the same time variations of the amplitude and the shape ofthe Rayleigh line wing (the spectrum range a, < 100 cm—’) are observed. With the decrease of temperature in the Rayleigh line wing of liquid glycerine 19
Volume 123, number I
PHYSICS LETTERS A
U
________
‘~-
_
+ ~I1/
4
—4
1
there appears a shoulder which turns into a sharp peak at T~260 K. This peak remains at the transition of glycerine to a vitreous state (fig. 2) and corresponds to a boson peak characteristic for glasses. According to the model ofref. [4] the spectral form of the latter is defined by the structure correlation function F(R) for disordered materials, and in particular for F(R) =exp( —R/R~) and polarization (II I) it takes the form
~
/ I /
I—;
0 lOt) 200 300 400 CM~ Fig. 1. Raman spectra of glycerine at temperatures (1) 300 K, (2) 260 K, (3) 220 K, (4) 175 K.
I,, =I/w[n(w) + 1] 2 ~2 { (0)2 + w~) + ~ ( V~/VQ) [a,2 + (a,
13 July 1987
.1’’ 0
25
50
75
Fig. 3. Comparison of the spectral shape of the Rayleigh wing with calculated curves for the boson peak (eq. (1)) (— — -) and forthe sum of central and boson peaks (—) at temperatures (1) 300Kand(2) 175 K.
malized intensities of scattered light, respectively; a, is the oscillating excitation frequency; n(w) = [exp( hw/kT) — 1] 1 are phonon occupation numbers; vQ and v~are longitudinal and transverse sound velocities and a, 0 v~/R~. The shape of a low-frequency peak in glycerine atofT= 175 K is well account the expression contribution peakapproxtointo the imated by (1) the (fig.central 3). Taking
0 z~/ v1) 2] —2
},
(1)
where land I,, are experimentally observed and norARB.UN.
Rayleigh wing (it is approximated by the Lorentz curve with a half-width 1—3 cm-’) one can achieve a sufficiently good agreement of the calculated spectra with experimental results in the whole investigated temperature range (1 .7Tg~Tg)from the melt to the vitreous state (fig. 3).
~ -f20
-80
-40
0
40
260K 20K 4CM
Fig. 2. Spectral shape of the Rayleigh wing at different temperatures.
20
v/xR~. A direct proof ofspectrum. the size effect manifestation inthe low-frequency regions ofRaman spectra Raman rials. intensity however, Itbeen is~ Itcorrelation known spectra accounts of there that isof whole no all for aradius common boson amorphous Raman 30% peak to viewpoint 90% isand characteristic of vitreous on the Until the integral boson matenow, for peak is ture has associated nature obtained [2]. with In the in most ref. size [5] developed effect in in which defined disordered models nucleatedglass by the [3,4] solids: strucit 0)max
0)
has been studied. By using heat treatment for changing the radius of microcrystals R0, which is controlled by small-angle neutron scattering, Duval et
Volume 123, number 1
PHYSICS LETTERS A
al. [5] showed that the peak maximum position is displaced as 0)ma,, 0.35v5/R0. The spectra shown in figs. 2 and 3 allow us to make the conclusion that the boson peak contributes greatly to the Rayleigh line wing of liquid glycerine. The Rayleigh wing is usually approximated by the sum of several Lorentz curves. It is, however, obvious that at T< 260 K a low-frequency the low-frequency spectrum of glycerine is no longer described by so simple an approximation. At the same time for all temperatures the spectral shape of the Rayleigh wing is sufficiently well described by the sum of central and boson peaks for F(R) = exp( — RIR~) (fig. 3). Note that the frequency dependences of high-energy tails of a boson peak (1) and a Lorentz curve are the same. For low viscosities when the boson peak is greatly overlapped by a narrow central part ofthe Rayleigh wing, the difference between the Lorentz curve and spectrum (1) becomes insignificant. Apparently, this fact has previously prevented from distinguishing the contribution of the boson peak to the Rayleigh line wing of liquids. The result obtained points to the existence of ordered microregions of the size R~ ~ V/7ta,max ~ 10 A with exponentially decreasing correlations in atomic arrangements in liquid glycerine, By distinguishing the boson peak from the Rayleigh wing (see fig. 3), we observed the temperature dependence of its amplitude and the position of the maximum for the two investigated polarizations. The peak amplitude (table 1) proved to have an anomaloustemperature dependence (which does not obey the law n(co) + 1): I,, T. This result 2> , agrees where well op iswith the the model [3,4]: I~( W max) <6p amplitude of density fluctuations increasing in liquid according to the law <&p2> T.
13 July 1987
Decrease of the glycerine temperature leads also to the displacement of the boson peak maximum to the high-frequency region (fig. 3, table 1). Variation of the sound velocity occurs, however, in this temperature range. Comparison of the temperature variations of a,max and v showed (table 1) that 0)max( T)/v( T) = const. Thus, structural correlations existing in a liquid state are preserved at the “liquid—glass” transition, while the structure correlation radius R~ 10 A remains unchanged during the process of vitrification. This corresponds completely to what is known about the glass structure as the structure of melt freezing at T5. It has previously been discovered [4] that the spectral shape ofthe boson peak is the same in different inorganic glasses and corresponds to the exponential function of structure correlations (unlike amorphous Si and Ge, where the correlation function is gaussian [4]). From this paper it follows that a low-molecular organic glass (glycerine) also possesses this property (see fig. 3, curve 2). Therefore, we can suppose that structural correlations appear to be the same in all glasses irrespective of their chemical composition and the crystalline prototype structure. This universality of a glassy material structure is explained by the identical method of their preparation quenching from the melt. In conclusion, decomposition of the Rayleigh line wing to the sum of central and boson peaks brings in the correspondence of the low-frequency spectra of light scattering in liquid and glass. Analysis of spectra shows thatthere in a high-viscosity such as aonmelt of glycerine, exist structuralliquid correlations the scale of some coordination spheres like those in glasses. —
Table 1 T (K)
300±5 260±5 220±5 210±5 190±5 175±5
I,, (arb. units)
~
±1
Ii.l~
2.52±0.2 2.43±0.14 2.17±0.11 1.94±0.1 1.66±0.1 1.69±0.1
1.70±0.1 1.70±0.1 1.25±0.07 1.11±0.07 1.14±0.07 1.0 ±0.06
(cm—’)
v [1] (kmls)
R=~r’vIa.’max(A)
11± 30 ±2 34 ±2 39 ±2 40.5±1 41 ±1 42 ±1
30±2 31±2 37±2 39±1 40±1 42±1
Iii2.85 3.19 3.56 3.65 3.82 3.90
10.0 9.9 9.6 9.5 9.8 9.8
10.0 10.8 10.1 9.9 10.0 9.8
21
Volume 123, number 1
PHYSICS LETTERS A
13 July 1987
[2] J. JackIe, in: Amorphous solids: low-temperature properties,
The authors are grateful to S.G. Rautian and the participants of his seminar for useful discussions.
ed. W.A. Phillips (Springer, Berlin, 1981). [3] A.J. 163. Martin and W. Brenig, Phys. Stat. Sol. (b) 64 (1974) [4] V.K. Malinovsky and A.P. Sokolov, Solid State Commun. 57
References
(1986) 757. [5] E. Duval, A. Boukenter and B. Champagnon, Phys. Rev. Lett.
[1] I.L. Fabelinsky, Molecular scattering of light (Nauka, Moscow, 1965) [in Russian].
22
56 (1986) 2052.
PHYSICS LETTERS A
13 July 1987
EVOLUTION OF THE RAYLEIGH LINE WING AND STRUCTURAL CORRELATIONS FOR LIQUID-GLASS TRANSITION V.K. MALINOVSKY, V.N. NOVIKOV and A.P. SOKOLOV Institute ofAutomation and Elecrrometry, Siberian Branch ofthe USSR Academy ofSciences, 630090 Novosibirsk, USSR Received 13 April 1987; accepted for publication 8 May 1987 Communicated by J.I. Budnick
The connection between the Rayleigh line wing in inelastic light scattering spectra in liquids and the boson peak observed at light scattering in glasses in the frequency range of 20—100 cm - has been found for the first time. The Rayleigh line wing is represented as a sum of boson and central peaks. The obtained results are evidence of the existence of structural correlations in high-viscosity liquid which decrease exponentially with the distance on the scale of 10 A.
A wide wing of the Rayleigh line [1] is characteristic of spectra of light scattered in liquids. Its spectral form depends on the chemical composition and the temperature of the liquid. It is well approximated by the sum of two (or more) Lorentz curves: a relatively narrow curve (a, < 10 cm—1) and a wide one (w ~ 100 cm-’) [1]. In spite of numerous investigations of the Rayleigh wing, a complete microscopic description of its nature has not been given so far. On the other hand, in all amorphous materials, particularly in glasses, a low-frequency peak, the so-called boson peak, is discovered in the same spectral region [2]. It is absent in crystals of the same composition, and in a number of papers it is associated with space correlations of elasto-optical and elastic constants fluctuations on the scale of R~~ 10 A [3,4]. A boson peak carries information on the radius ofthe structure correlations R~and the character of decreasing of these correlations with distance [3,4]. In this paper, using glycerine as an example, the connection between the Rayleigh line wing in liquid and a boson peak has been found for the first time. A boson peak defines a high-frequency part of the Rayleigh line wing. The results obtained allow to conclude about the existence of structural space correlations on the scale of 10—20 A in liquid. It is shown that structural correlations on this scale are the same for liquid and vitreous states.
Right-angle Raman spectra were measured with the use of a DFS-24 spectrometer. The spectral slit width was 2 cm-’ and the excitation wavelength was 676 nm. Two different polarizations were investigated: one with the incident beam polarized and scattered light analyzed perpendicular to the scattering plane (I J~), and one with the incident beam polarized parallel to and the scattered light analyzed perpendicular to the scattering plane (II .L). Normalization of all spectra has been carried out with regard to the temperature, the frequency factor of scattering and the spectral function of the instrument. Temperature has been measured according to the ratio of Stokes and anti-Stokes scattering. Test control, recording and subsequent processing of spectra as well as calculation oftheoretic curves have been carried out using the automated system “MicroCAMAC”. Glycerine has been chosen as a sample. Glycerine in a quartz ampule was placed in the cryostat. The sample temperature was changed in the range of T= 300—175 K. The obtained results (fig. 1) show that over the whole temperature range the Raman spectrum of glycerine does not undergo significant changes in the high-frequency region (w> 100 cm ~1)• At the same time variations of the amplitude and the shape ofthe Rayleigh line wing (the spectrum range a, < 100 cm—’) are observed. With the decrease of temperature in the Rayleigh line wing of liquid glycerine 19
Volume 123, number I
PHYSICS LETTERS A
U
________
‘~-
_
+ ~I1/
4
—4
1
there appears a shoulder which turns into a sharp peak at T~260 K. This peak remains at the transition of glycerine to a vitreous state (fig. 2) and corresponds to a boson peak characteristic for glasses. According to the model ofref. [4] the spectral form of the latter is defined by the structure correlation function F(R) for disordered materials, and in particular for F(R) =exp( —R/R~) and polarization (II I) it takes the form
~
/ I /
I—;
0 lOt) 200 300 400 CM~ Fig. 1. Raman spectra of glycerine at temperatures (1) 300 K, (2) 260 K, (3) 220 K, (4) 175 K.
I,, =I/w[n(w) + 1] 2 ~2 { (0)2 + w~) + ~ ( V~/VQ) [a,2 + (a,
13 July 1987
.1’’ 0
25
50
75
Fig. 3. Comparison of the spectral shape of the Rayleigh wing with calculated curves for the boson peak (eq. (1)) (— — -) and forthe sum of central and boson peaks (—) at temperatures (1) 300Kand(2) 175 K.
malized intensities of scattered light, respectively; a, is the oscillating excitation frequency; n(w) = [exp( hw/kT) — 1] 1 are phonon occupation numbers; vQ and v~are longitudinal and transverse sound velocities and a, 0 v~/R~. The shape of a low-frequency peak in glycerine atofT= 175 K is well account the expression contribution peakapproxtointo the imated by (1) the (fig.central 3). Taking
0 z~/ v1) 2] —2
},
(1)
where land I,, are experimentally observed and norARB.UN.
Rayleigh wing (it is approximated by the Lorentz curve with a half-width 1—3 cm-’) one can achieve a sufficiently good agreement of the calculated spectra with experimental results in the whole investigated temperature range (1 .7Tg~Tg)from the melt to the vitreous state (fig. 3).
~ -f20
-80
-40
0
40
260K 20K 4CM
Fig. 2. Spectral shape of the Rayleigh wing at different temperatures.
20
v/xR~. A direct proof ofspectrum. the size effect manifestation inthe low-frequency regions ofRaman spectra Raman rials. intensity however, Itbeen is~ Itcorrelation known spectra accounts of there that isof whole no all for aradius common boson amorphous Raman 30% peak to viewpoint 90% isand characteristic of vitreous on the Until the integral boson matenow, for peak is ture has associated nature obtained [2]. with In the in most ref. size [5] developed effect in in which defined disordered models nucleatedglass by the [3,4] solids: strucit 0)max
0)
has been studied. By using heat treatment for changing the radius of microcrystals R0, which is controlled by small-angle neutron scattering, Duval et
Volume 123, number 1
PHYSICS LETTERS A
al. [5] showed that the peak maximum position is displaced as 0)ma,, 0.35v5/R0. The spectra shown in figs. 2 and 3 allow us to make the conclusion that the boson peak contributes greatly to the Rayleigh line wing of liquid glycerine. The Rayleigh wing is usually approximated by the sum of several Lorentz curves. It is, however, obvious that at T< 260 K a low-frequency the low-frequency spectrum of glycerine is no longer described by so simple an approximation. At the same time for all temperatures the spectral shape of the Rayleigh wing is sufficiently well described by the sum of central and boson peaks for F(R) = exp( — RIR~) (fig. 3). Note that the frequency dependences of high-energy tails of a boson peak (1) and a Lorentz curve are the same. For low viscosities when the boson peak is greatly overlapped by a narrow central part ofthe Rayleigh wing, the difference between the Lorentz curve and spectrum (1) becomes insignificant. Apparently, this fact has previously prevented from distinguishing the contribution of the boson peak to the Rayleigh line wing of liquids. The result obtained points to the existence of ordered microregions of the size R~ ~ V/7ta,max ~ 10 A with exponentially decreasing correlations in atomic arrangements in liquid glycerine, By distinguishing the boson peak from the Rayleigh wing (see fig. 3), we observed the temperature dependence of its amplitude and the position of the maximum for the two investigated polarizations. The peak amplitude (table 1) proved to have an anomaloustemperature dependence (which does not obey the law n(co) + 1): I,, T. This result 2> , agrees where well op iswith the the model [3,4]: I~( W max) <6p amplitude of density fluctuations increasing in liquid according to the law <&p2> T.
13 July 1987
Decrease of the glycerine temperature leads also to the displacement of the boson peak maximum to the high-frequency region (fig. 3, table 1). Variation of the sound velocity occurs, however, in this temperature range. Comparison of the temperature variations of a,max and v showed (table 1) that 0)max( T)/v( T) = const. Thus, structural correlations existing in a liquid state are preserved at the “liquid—glass” transition, while the structure correlation radius R~ 10 A remains unchanged during the process of vitrification. This corresponds completely to what is known about the glass structure as the structure of melt freezing at T5. It has previously been discovered [4] that the spectral shape ofthe boson peak is the same in different inorganic glasses and corresponds to the exponential function of structure correlations (unlike amorphous Si and Ge, where the correlation function is gaussian [4]). From this paper it follows that a low-molecular organic glass (glycerine) also possesses this property (see fig. 3, curve 2). Therefore, we can suppose that structural correlations appear to be the same in all glasses irrespective of their chemical composition and the crystalline prototype structure. This universality of a glassy material structure is explained by the identical method of their preparation quenching from the melt. In conclusion, decomposition of the Rayleigh line wing to the sum of central and boson peaks brings in the correspondence of the low-frequency spectra of light scattering in liquid and glass. Analysis of spectra shows thatthere in a high-viscosity such as aonmelt of glycerine, exist structuralliquid correlations the scale of some coordination spheres like those in glasses. —
Table 1 T (K)
300±5 260±5 220±5 210±5 190±5 175±5
I,, (arb. units)
~
±1
Ii.l~
2.52±0.2 2.43±0.14 2.17±0.11 1.94±0.1 1.66±0.1 1.69±0.1
1.70±0.1 1.70±0.1 1.25±0.07 1.11±0.07 1.14±0.07 1.0 ±0.06
(cm—’)
v [1] (kmls)
R=~r’vIa.’max(A)
11± 30 ±2 34 ±2 39 ±2 40.5±1 41 ±1 42 ±1
30±2 31±2 37±2 39±1 40±1 42±1
Iii2.85 3.19 3.56 3.65 3.82 3.90
10.0 9.9 9.6 9.5 9.8 9.8
10.0 10.8 10.1 9.9 10.0 9.8
21
Volume 123, number 1
PHYSICS LETTERS A
13 July 1987
[2] J. JackIe, in: Amorphous solids: low-temperature properties,
The authors are grateful to S.G. Rautian and the participants of his seminar for useful discussions.
ed. W.A. Phillips (Springer, Berlin, 1981). [3] A.J. 163. Martin and W. Brenig, Phys. Stat. Sol. (b) 64 (1974) [4] V.K. Malinovsky and A.P. Sokolov, Solid State Commun. 57
References
(1986) 757. [5] E. Duval, A. Boukenter and B. Champagnon, Phys. Rev. Lett.
[1] I.L. Fabelinsky, Molecular scattering of light (Nauka, Moscow, 1965) [in Russian].
22
56 (1986) 2052.