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Pressure dependence of the lattice frequencies of anthracene and naphthalene
Volume
22. number 3
CHEMICAL PHYSICS LETTERS
IS October
1973
PRESSURE DEPENDENCE OF THE LATTICE FREQUENCIES OF ANTHRACENE AND NAPHTHALENE”
S.S.MITR4 ‘Department
of Electrical
Engineering,
Kirrgston, Rhode
Univcrrity
Island 02881,
of Rhode
Island,
USA
0. BRAFMAN, M. HAYEK Physics Department,
Technion,
Haifa, Israel
and W.B. DANIELS+
and R.K. CRAWFORD*
Solid Spate and hlateriak Laboratory, Princeton Princeton, New Jersey 08.540, USA
University.
Received 25 June 1973
The pressure dependence of the Raman lattice modes of anthracenc and naphthalene molecular crystals has been studied in the range O-10 kbar, using hydrostatic pressure and laser excitation. Criineisen parameters in the range 3-6 have been observed. Calculations SC the elastic wnstants and the prcssurc dependence of the lattice frqucncizs have been carried out using an intermolecular potential of the atom-atom type, with parameters derived from other crystalline properties. Agrecmcnt with experimental data is good.
The temperature variation of the vibrational frequencies of crystal lattices involves a mixed dependence on both temperature and volume, whereas the effects of pressure involve the volume dependence only (to a good fast approximation), and allow a useful separation of the two dependences [l]. We report here a study of the pressure dependence of the Raman-active lattice vibrations of the molecular crystals anthracene and naphthalene, and the results of a
* Work supported by grants from the Army Research Office (Durham). + Present address: Physics Department, University of Delaware. Newark, Delaware 19711, USA. + Present address: Physics Department, University of Illinois, Urbana, Itlinois 61803, USA.
calculation of these frequencies and of the eIastic constants. We used a form of the intermolecular porenziat which has proved useful elsewhere for molecular crystals. Studies such as this are 2 new direction for molecular crystals, though some results on intramolecular frequencies at high pressure have appeared. We expect that pressure-dependence studies will play a valuable role in the molecular crystal field in the future. The experimental methods have been&described elsewhere [2]. Crystals cf anthracene and naphthalene were subjected to hydrostatic pressure up ta 10 kbar, and the Raman spectra were excited by a KeNe laser (50 .rnW at 6328 A). The crystals \vere oriented, and the spectra partially polarized, but the experimental conditions made polarization data unreliable. Polarized spectra are also taken at one atmosphere
Vollrmo 22, num!Ta- 3
CHPhfICAL
PHYSICS
LETiERS
1.5
Clcrobcr 1973
The elastic constants of anchracene [lo] and nnphthalene
[ 1 I] have been
measured
by acomtic
methods.
We have calculated the dispersion curves using the methods of Bouadeo and Taddei [12] znd from the limiting slopes of the acoustic frequency versus !vave vector have obtained the sound velocities. ‘HE sound velocities and dispersion curves obtained here are in reasonable agreement with those obtained by PawIey [8], allowing for the differences in potentiai ener_q parameters used. The elastic constants, derived directly from the velocities, will not be compared with errperiment since a certain amount of arbitrariness is involved in deriving the non-major constants from the velocities. Sufficient indication of the agreement with the direct experimental sound velocities is shown in table 2. Instead of maintaining a purely theoretical approach and using cur derived elastic constants to compute the effect of pressure on structure, we have chosen to use the constants taken from experiment [IO, 1 I]. A pressure is assumed (1000-2000 atmospheres) and the strains calculated. The compressions did not agee very closely with the pressure-voIume data [4], but any attempts to scale the calculations I 6.400
L
1
6375
63M
6335
6400
6375
6350
6335
xi
hi
Fig. 3. Pressure dependence of anthracene lattice Raman spectra. (a) c(bc)b polarization, (b) c(ac)b polarization. Due to scattering in the sample polarizatjon data ax not quantitative.
would
not
eters
derived.
I
1
53
loo
‘A’AVENUMEER
of the naphthalene
of the Griineisen
With the compressed
u4t
pnrzrn-
cell param-
were again calculzted~
and values of ^li obtained. The values of ri, calculated and observed, are given in table 3 for anthracene: and the agreement shown there is reasonable cause to accept the model potential as representing the intermo-
I
Fig. 4. Temperature dependence
the values
eters, the lattice frequencies
0
STOKES
affect
SHIFT
I
1.50 FROM
X5145
lattice Raman spectrum.
-
77”K, ---29°F:.
CHEMICAL PHYSICS LE’MERS
Volume 22, number 3
Lattice frequencies and calculated
Table 1 of naphthalene and anthraccne,
Anthracene
Naphthalene “talc
“OIJS=)
%x.lc
106 19 52
121 70 39
120 76 40
125 71
101 73
125 65
109 67
46
47
45
49
102 49
97 50
101 44
101
55
65
60
62
YObS
a)
‘%
-%I
hl
observed
39
Yobs
Tabs
*rcalc
A8
109 74 51
3.1 4.9 6.2
3.2 4.1 5.1
%
125 71 46
3.6 5.0 6.3
3.1 4.7 5.4
frequencies.
Also, the elastic con-
vobsa)
“talc
“obs b,
“talc
only arise from
the close-range
,100
2.81
2.54
2.64
2.47
sions,
are an important
010
1.59
1.77
1.79
atom potential at distances lar contacts in crystals.
004
l.32
1.58
1.91 (1.94) 1.34
010
3.32
2.72
2.79
001 100
1.15 1.75
1.09 1.96
2.95 (2.93) 1.65 1.96
001
7.75
3.80
3.82
100
1.35
1.4:
010
1.39
1.53
3.35 (3.36) 1.07 (1.16) 1.71 (1.71)
Table 2 (in IO5 cm/set)
and naphthdene
Propagation
Displacemenr
100
at
observed
and calculated
for
298°K
Anthracenc
Naphthalene
(2.62)
a) Ref. [9]. b) Ref. [ 141; in parenthcscs
allowing
the orientations
end these
intermolecular feature
corresponding
repul-
of the atomto molecu-
1.45
References 1.51 2.23
1.25 2.10
ref. [IO].
lecular situation adequately. We must note that the calculation whose results are presented here did not include.all possible refmements. For example, the moleci&r orientations may change on compression; we have tried
Table 3 ri= -d log vi/d log V, for anthracene
sound velocities as a function of pressure (density) and have found these changes to be predicted. The results quoted above in table 3 are thus not to be taken as the best that theory can do; they are, however, representative of the results obtained with various reasonable variations on the calculations. The values of the Griineisen parameters, averaging about 5, are higher than those typically obtained for ionic crystals, and the implication is that a very distance-xnsitive potential is associated with the frequencies being observed. Such a steep potential can
Sound velocities
001
1973
stants may depend on pressure; we have calculated
data (Ag, Bg) from this work and ref. (2). Infrared (A,, 6,) from ref. [ 13).
010
Griineisen parameters,
in the calculated
a) Raman
anthracene
15 October
to relax to equi-
librium.* at the new density and’have found changes
[ 1) S.S. hfitra,
C. Potius
and J.R.
Ferraro,
Phys
Rev.
Letters 18 (1967) 455. [2] 0. Rrafman, S.S. Mitra, R.K. Crawford, W.B. Daniels, C. Postmus and R.J. Ferraro, Solid State Commun. 7 (1969) 449. [3] M. Suzuki, T. Yokoyama and M. Ito, Spectrochirn. Acta 24A (1968) 1091. [4] S.N. Vaidya and G.C. Kennedy, J. Chem. Phys. 55 (1971) 987. [S] G. Taddei, H. Bonndeo, M.P. Marzocchi and S. Califqo, J. Chem. Phys. 58 (1973) 966. 161 D.E. Williams, J. Chem. Phys. 47 (1967) 4680.
* Using the computer program PACK3, kin’dly provided by D.E. YQlliams, wiih the same intermolecular potential used in the lattice frequency calculatinnr
:
Volume 22, number 3 [7] D.W.J. Cruickshank,
CHEMICAL
Acta Cryst. 10 (1957) 504; 9
(1956) 915. [8) G.S. Pawlcy, Phys. Stat. Sol 20 (1967) 347. [9] P. Weulsrsse. Compt. Rend. Acad. Sci. (Paris) B264 (1967) 327. [lo] T. Danno and H. !nokucbi, Bull. Chem. Sot. Japan 41 (1968) 1783.
PHYSICS LE-RS
1s October 1973
[ 111 G.K. Afanas’eva, KristaUoyafiya
12 (1968: IO24 [English transl. Soviet Phys. Cryst. 13 (1969) 5921.
[ 121 H. Bonadeo and G. Taddei, J. Chem. Phys. 58 (1973) 979. [ 13) S.S. Micra, Bull. Am. Phys. Sot. 12 (1967) 79. [ 141 V.F. Tcslenko, Soviet Phys. Cryst. 12 (1960) 946.
22. number 3
CHEMICAL PHYSICS LETTERS
IS October
1973
PRESSURE DEPENDENCE OF THE LATTICE FREQUENCIES OF ANTHRACENE AND NAPHTHALENE”
S.S.MITR4 ‘Department
of Electrical
Engineering,
Kirrgston, Rhode
Univcrrity
Island 02881,
of Rhode
Island,
USA
0. BRAFMAN, M. HAYEK Physics Department,
Technion,
Haifa, Israel
and W.B. DANIELS+
and R.K. CRAWFORD*
Solid Spate and hlateriak Laboratory, Princeton Princeton, New Jersey 08.540, USA
University.
Received 25 June 1973
The pressure dependence of the Raman lattice modes of anthracenc and naphthalene molecular crystals has been studied in the range O-10 kbar, using hydrostatic pressure and laser excitation. Criineisen parameters in the range 3-6 have been observed. Calculations SC the elastic wnstants and the prcssurc dependence of the lattice frqucncizs have been carried out using an intermolecular potential of the atom-atom type, with parameters derived from other crystalline properties. Agrecmcnt with experimental data is good.
The temperature variation of the vibrational frequencies of crystal lattices involves a mixed dependence on both temperature and volume, whereas the effects of pressure involve the volume dependence only (to a good fast approximation), and allow a useful separation of the two dependences [l]. We report here a study of the pressure dependence of the Raman-active lattice vibrations of the molecular crystals anthracene and naphthalene, and the results of a
* Work supported by grants from the Army Research Office (Durham). + Present address: Physics Department, University of Delaware. Newark, Delaware 19711, USA. + Present address: Physics Department, University of Illinois, Urbana, Itlinois 61803, USA.
calculation of these frequencies and of the eIastic constants. We used a form of the intermolecular porenziat which has proved useful elsewhere for molecular crystals. Studies such as this are 2 new direction for molecular crystals, though some results on intramolecular frequencies at high pressure have appeared. We expect that pressure-dependence studies will play a valuable role in the molecular crystal field in the future. The experimental methods have been&described elsewhere [2]. Crystals cf anthracene and naphthalene were subjected to hydrostatic pressure up ta 10 kbar, and the Raman spectra were excited by a KeNe laser (50 .rnW at 6328 A). The crystals \vere oriented, and the spectra partially polarized, but the experimental conditions made polarization data unreliable. Polarized spectra are also taken at one atmosphere
Vollrmo 22, num!Ta- 3
CHPhfICAL
PHYSICS
LETiERS
1.5
Clcrobcr 1973
The elastic constants of anchracene [lo] and nnphthalene
[ 1 I] have been
measured
by acomtic
methods.
We have calculated the dispersion curves using the methods of Bouadeo and Taddei [12] znd from the limiting slopes of the acoustic frequency versus !vave vector have obtained the sound velocities. ‘HE sound velocities and dispersion curves obtained here are in reasonable agreement with those obtained by PawIey [8], allowing for the differences in potentiai ener_q parameters used. The elastic constants, derived directly from the velocities, will not be compared with errperiment since a certain amount of arbitrariness is involved in deriving the non-major constants from the velocities. Sufficient indication of the agreement with the direct experimental sound velocities is shown in table 2. Instead of maintaining a purely theoretical approach and using cur derived elastic constants to compute the effect of pressure on structure, we have chosen to use the constants taken from experiment [IO, 1 I]. A pressure is assumed (1000-2000 atmospheres) and the strains calculated. The compressions did not agee very closely with the pressure-voIume data [4], but any attempts to scale the calculations I 6.400
L
1
6375
63M
6335
6400
6375
6350
6335
xi
hi
Fig. 3. Pressure dependence of anthracene lattice Raman spectra. (a) c(bc)b polarization, (b) c(ac)b polarization. Due to scattering in the sample polarizatjon data ax not quantitative.
would
not
eters
derived.
I
1
53
loo
‘A’AVENUMEER
of the naphthalene
of the Griineisen
With the compressed
u4t
pnrzrn-
cell param-
were again calculzted~
and values of ^li obtained. The values of ri, calculated and observed, are given in table 3 for anthracene: and the agreement shown there is reasonable cause to accept the model potential as representing the intermo-
I
Fig. 4. Temperature dependence
the values
eters, the lattice frequencies
0
STOKES
affect
SHIFT
I
1.50 FROM
X5145
lattice Raman spectrum.
-
77”K, ---29°F:.
CHEMICAL PHYSICS LE’MERS
Volume 22, number 3
Lattice frequencies and calculated
Table 1 of naphthalene and anthraccne,
Anthracene
Naphthalene “talc
“OIJS=)
%x.lc
106 19 52
121 70 39
120 76 40
125 71
101 73
125 65
109 67
46
47
45
49
102 49
97 50
101 44
101
55
65
60
62
YObS
a)
‘%
-%I
hl
observed
39
Yobs
Tabs
*rcalc
A8
109 74 51
3.1 4.9 6.2
3.2 4.1 5.1
%
125 71 46
3.6 5.0 6.3
3.1 4.7 5.4
frequencies.
Also, the elastic con-
vobsa)
“talc
“obs b,
“talc
only arise from
the close-range
,100
2.81
2.54
2.64
2.47
sions,
are an important
010
1.59
1.77
1.79
atom potential at distances lar contacts in crystals.
004
l.32
1.58
1.91 (1.94) 1.34
010
3.32
2.72
2.79
001 100
1.15 1.75
1.09 1.96
2.95 (2.93) 1.65 1.96
001
7.75
3.80
3.82
100
1.35
1.4:
010
1.39
1.53
3.35 (3.36) 1.07 (1.16) 1.71 (1.71)
Table 2 (in IO5 cm/set)
and naphthdene
Propagation
Displacemenr
100
at
observed
and calculated
for
298°K
Anthracenc
Naphthalene
(2.62)
a) Ref. [9]. b) Ref. [ 141; in parenthcscs
allowing
the orientations
end these
intermolecular feature
corresponding
repul-
of the atomto molecu-
1.45
References 1.51 2.23
1.25 2.10
ref. [IO].
lecular situation adequately. We must note that the calculation whose results are presented here did not include.all possible refmements. For example, the moleci&r orientations may change on compression; we have tried
Table 3 ri= -d log vi/d log V, for anthracene
sound velocities as a function of pressure (density) and have found these changes to be predicted. The results quoted above in table 3 are thus not to be taken as the best that theory can do; they are, however, representative of the results obtained with various reasonable variations on the calculations. The values of the Griineisen parameters, averaging about 5, are higher than those typically obtained for ionic crystals, and the implication is that a very distance-xnsitive potential is associated with the frequencies being observed. Such a steep potential can
Sound velocities
001
1973
stants may depend on pressure; we have calculated
data (Ag, Bg) from this work and ref. (2). Infrared (A,, 6,) from ref. [ 13).
010
Griineisen parameters,
in the calculated
a) Raman
anthracene
15 October
to relax to equi-
librium.* at the new density and’have found changes
[ 1) S.S. hfitra,
C. Potius
and J.R.
Ferraro,
Phys
Rev.
Letters 18 (1967) 455. [2] 0. Rrafman, S.S. Mitra, R.K. Crawford, W.B. Daniels, C. Postmus and R.J. Ferraro, Solid State Commun. 7 (1969) 449. [3] M. Suzuki, T. Yokoyama and M. Ito, Spectrochirn. Acta 24A (1968) 1091. [4] S.N. Vaidya and G.C. Kennedy, J. Chem. Phys. 55 (1971) 987. [S] G. Taddei, H. Bonndeo, M.P. Marzocchi and S. Califqo, J. Chem. Phys. 58 (1973) 966. 161 D.E. Williams, J. Chem. Phys. 47 (1967) 4680.
* Using the computer program PACK3, kin’dly provided by D.E. YQlliams, wiih the same intermolecular potential used in the lattice frequency calculatinnr
:
Volume 22, number 3 [7] D.W.J. Cruickshank,
CHEMICAL
Acta Cryst. 10 (1957) 504; 9
(1956) 915. [8) G.S. Pawlcy, Phys. Stat. Sol 20 (1967) 347. [9] P. Weulsrsse. Compt. Rend. Acad. Sci. (Paris) B264 (1967) 327. [lo] T. Danno and H. !nokucbi, Bull. Chem. Sot. Japan 41 (1968) 1783.
PHYSICS LE-RS
1s October 1973
[ 111 G.K. Afanas’eva, KristaUoyafiya
12 (1968: IO24 [English transl. Soviet Phys. Cryst. 13 (1969) 5921.
[ 121 H. Bonadeo and G. Taddei, J. Chem. Phys. 58 (1973) 979. [ 13) S.S. Micra, Bull. Am. Phys. Sot. 12 (1967) 79. [ 141 V.F. Tcslenko, Soviet Phys. Cryst. 12 (1960) 946.