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Magnetic field effects on recombination radiation in tetracene crystal
Volume 36, number
3
15 November 197.5
CHEMICAL PHYSlCS LETTERS
MAGNETIC FIELD EFFECTS ON RECOMBINATION
RADIATION
IN TETRACENE CRYSTAL*
5. KALRIOWSKI and J. GODLEWSKI Institute of PIyxics. Tecimicai University. Gdarisk. Polarid Received 29 April 1975 Revised manuscript received
1 July 1975
Recombination radiation in tetrncene crystal is shown io be modified by the application of a magnetic field. Rclztive variations of radiation intensity with field and orientation nn be explained in terms of molecular sir&t fission and triplet esciton-charge carrier interaction.
triplet exciton-charge
1. Introduction The influence of a magnetic field on recombination electroluminescence is known in the case of anthracene [I ,2] : the increase of the prompt electroluminescence intensity in 3 magnetic field is related to the decrease
of the rate of the charge transfer exciton (CT) fission into a pair of molecular triplet excitons and the decrease of delayed electrotuminescence intensity in the high limit magnetic field to the decrease of the triplettriplet fusion rate. A comparison of the action spectrum of the relative increase of the prompt fluorescence and intrinsic charge carrier creation efficiency at 77 K suggested that the process of singlet exciton fission responsible for the magnetic field effect on prompt fluorescence in tetra-
cene crystals, does not appear to t&e place from the thermally relaxed lowest CT state [3] . CT states are efficiently produced by charge carrier recombination in the crystal and the study of the magnetic field effect on recombination radiation in te tracene can give further information on the nature of the fissionable states. We studied the magnetic field effect on the total recombination electroluminescence (EL) in tetracene crystals at room temperature.
carrier interaction.
3. Experimental Vapour-grown
single
crystals
of tetracene
were
used.
Sodium-potassium alloy was utilized as the cathode and a semitransparent evaporated gold layer as the anode. Effective contact areas were x0.04 cm’. It was established [4] that an Na/K alloy forms a (liquid) ohmic contact for electron injection into sublimationgrown tetracene crystals. The applied electric field was alway? perpendicular to the ab crystal plane and tke crystals were placed between the poles of an electromagnet in such 3 w3y that the magnetic field could change its orientation in the ab plane of the crystals. The recombination radiation emanated from the crystal through the partially transparent gold electrode was collected with a iens and imaged onto one end of a suprasil
light guide and finally
onto the photocathode
of an EMI model 6256 S photomultiplier
operated a:
a single photon-counting apparatus. The influence of 3 magnetic field on the prompt fluorescence emission was also studied, with the same crystals. The prompt fluorescence was filtered and conducted through a fiber optic making with the gold elec-1300
V within
The results presented in this report may be understood in terms of molecular singlet exciton fission and
trode side of the crystal an angle of M.5”. In this case the suprasil rod serving previously as 3 light guide for the electroluminescence was used 3s 3 guide for the ex-
* Thb work was partly supported
citation light. The magnetic effects on the apparatus itself were verified to be very small.
of the Polish Academy
by of Sciences.
the Institute of Physics
345
Voiume.36, number 3
CHEMICAL PliYSlCS
15 November
LETTERS
3. Results
Fig. 1 illustrates the,reIative (percentagej increase of electrolum~esce~ce and prompt fluorescence intensities upon application of a magnetic field of 6 kG, measured as a function of angle 0 between the field vector in the ab plane and the b axis of the crystal. The angular separation and orientation of the resonance peaks observed are reproducible for different crystals used in the experiments and.agree with those previously reported for photoluminescence [5-71. In contradiction, the total electroluminescence intensity change as a function of magnetic field strength differs from that for photoluminescence and varies from crystal to crystal (figs. 2 and 3). In both cases presented the caystal orientation was such that 3 = -32’ (high-field resonznce direction, cf. fig. 1). The experimental situation for the electroluminescence study is also shown in fig. 3. The observed nsgnetic field effect for the longwavelength region of the elecrroiuminescence is lower lhan that for the emission maximum (curves C and B ti figs. 2 and 3). This is in contrast to the effect of a magnetic field on prompt fluorescence showing the same behaviour for these two wavelength regions (curve A in fig. 2). Schott and Coming ftiter combinations were used to isolate portions of the long-wavelength and maximum emission regions.
1 I
1 0
MCGA’ETIC
FIELD
ORIENTATION
(6)
Fig. 1. Change of electro- and photoluminescence in a magnetic field of 6 kG rotattis in the oE plane of a tetracene crystal (thickness d = 15.5 pm).
,/=
-
_____A
ELECTIWLU~INESCENCE
- - PHOTOLUMINESCENCE
Fig. 2. Comparison of magnetic field effect on the electroluminescence oE a crystal with a low delayed component of EL (curves B, C) and photoluminescence at low escitation levels (%X = 366 run) (curve A); the results obtained are for a highfield resonance position with a crystal of thickness d = 118 pm. The dependence wits measured in two different wavelength regions of the crystal emission: A, B-red edge, A, C-short-
wvelength and maximum emission. Note: there is no difference in the case of photoluminescence (curve A).
One Schott RGI falter was used to view the red edge of both electro- and photoluminescence. Electroluminescence light between short wavelengths and the maximum of the emission was viewed through Schott VG 9 and Corning CS 496titers whereas the prompt fluorescence in this case was viewed through a combination of Coming falters (CS 4-96 + CS 4-77 f CS 3-68). The results can be summarized as follows. (i) In the high field limit (B = 6 kG), the magnetic field effect on recombination radiation is anisotropic exibiting the level crossing resonances at orientations which are identical to those for prompt fluorescence (fig. 1). (ii) The magnetic field dependence of e!ectroluminescence at the resonance position (0 = -32”) differs, in
Volume 36, number
3
15 November 1975
CHEMICAL PHYSICS LETTERS
caD+cxKxx) 4.0
‘, ; -4
,I
-
ELEC7ROiUMlNESCEh’CE
- - -
FHOTOLUMINES
B/kGauss]
CENCE
3.0
60
B ikGaus.i]--
-
Fig. 4. Dependence Fig. 3. Relative chnrqe of clectro- and photoluminescence 8s ;1 function of magnetic field in a high-field resonance direction for a crystal with a large delayed component of EL (curves B, C); cute B is obtained for the red edge and C for the total EL (crystai the same as in fi,y. 1).
general, from that in photoluminescence (figs. 2 and 3) and in some cases can be a continously increasing functicn with a tendency to saturation at fields above = 3 kG (fig. 3). (iii) The low-field dip in the magnetic field dependence observed (fig. 2) is less the greater is the delayed component* of the total crystal electroluminescence and disappears when the delayed component becomes the dominant mechanism of emission from the crystal (fl?g_3). (iv) There is a similarity between the magnetic field dependence for the red edge EL in pure tetracene caystals (fig. 2, curve B) and that for total EL in pentacenedoped tetracene crystals (fig. 4). In particular, the ratio of the maximal positive to negative effects are the same and is equal to =z 2.
4. Discussion Observation (i) suggests that the process of molecular singlet exciton fission into a triplet pair (TT) is operative in tetracene recombination radiation. In such a case, at room temperature, the decrease of electroluminescence intensity in the limit of low * The contribution of the delayed electroluminescence to the total EL c=ln be established from 2 campIes supcrlinezr dependence of the total EL verws current density for the crystals 141.
troluminescence
of the relative intensity variation of elecon magnetic field strength, with the pentacenz-
doped
crystal
tetrnuene
in one of the hi$
&Id
resonance
rcctions. Thickness of the cystzl d = 36 ,um, pentaccne centration:
=2
X 103
di-
con-
ppm.
magnetic fields (below 0.5 kG) should take place due to the increase of the rste of molecular singlet fission 16,71-
This is not the case fur the crystal in fig. 3. Also for other crystals (fig. 2) this decrease is lower than that expected from magnetic field effects on photoluminescence. In addition the inversion in the sign of the magnetic field effect takes place at a lower field strength than that for photoluminescence (fig. 2 - top). This behaviour can be explained assum@ a. part of the electroluminescence to have originated from tripIet-triplet fusions leading to the creation of fluorescing singlets. This is the delayed electroluminescence. In the presence of charge the triplets are partly quenched as a result of triplet exciton-charge carrier interaction [S] . The triplet exciton-charge carrier interaction Tate constant is, on the other hand, influenced by a magnetic field [9] causing it ta be smaller for high as well as for low magnetic fields oriented along the high-field resonance directions [lo]. The resonance directions corresponding to tripletdoublet pair degeneracies were shown to be identical with those for triplet-triplet annihilation [IO-121 and consequently for singlet fission (see rcfs. [6,7,9]). The magnetic field decrease in the triplet-charge carrier rate constant is demonstrated by the increase in the delayed component of electroluminescence. If the delayed component is prevalent in the crystal electroluminescence observed, this increase tends to mask the low-field decrease due to the increase of the rate of molecular singlet fission. This Is in agreement
347
:
Vo!uri% 36, number 3
‘with the
experimental
pccording
CHEMICAL PHYSICS LETTERS
observations
(ii) and (iii).
to this interpretation
the low-field decrease seen in the total electroluCinescence in fig. 2 should prackally disappear for the delayed component. The experimental result in fig. 3 is indeed that which is expected, indicating that triplet exciton-charge carrier interaction plays a significant role in magnetic field liehaviour of the recombination radiation of tetracene crystal. An examination of the results in the Iight of observations (iii) and (iv) leads to the conclusion that at the red edge the electroluminescence, at least partly, originates from trapped states (S,) which can fission into two inequivalent triplet exciLons (T, T,) (this is the socalled heterofission; see ref. [13]). It is seen that, over the whole field range which was explored, the relative change is smaller than the frectional intensity variations observed for EL within the emission maximum (figs. 2 and 3). This would indicate that the factor describing the specific field effect on the couplir_g between the St and the (T, Tt) states is here less sensitive to the magnetic !CieId than in the case of free excitons. Since
the trapped singlet states can be produced by an annihilation process of inequivalent lriplet excitons [ 141 a large delayed component at the red edge of EL can be expected in the case of the crystal in fig. 3. Consequently, tie low field dip in -Sle magnetic field dependence should disappear. This is indeed the experimental case. Finally, the relative magnetic field change of total electroluminescence contains three terms corresponding to three different components: prompt, delayed and trapped states emission. ‘Thus the variation of the total electrolilminescence with rnage tic field at room temperature is determined bq- thrj interplay of three effects: (1) magnetic field change of the effective rate constant for free singlet exciton fission; (2) magnetic field decrease of the rate of kiplet-charge carrier interaction and (3) magnetic field change in the rate of hetcrofission. Magnetic field effect on the emission originated from the triplet-triplet annihilation at room temperature is known to be r_egligible [6,7] _ At low excitation levels, the prompt fluorescence
34.8
1.5 November
i97.5
is the dominating mechanism of the crystal fluorescence and its chenge in a magnetic field must be attributed to the first of the above-mentioned effects. This is the reason for the observed difference in magnetic field behaviour of electro- and photoluminescence. Since the delayed component of EL is determined to a large extent by concentration and trap characteristics of the crystal [4], it is not surprising that the total electroluminescence shows 2 different magnetic field behaviour for various tetracene crystals.
Acknowledgement We are grateful to Professor crystals available to us.
M. Pope for making
the
References [l]
H.P.
Schwab
and D.F.
Willixns,
Chem. Phys. Letturs 13
(1972) 581. {Z] H.P. Schwab and D.F. Williams, I. Shem. Phys. 58 (1973) 1542. 131 G. Klein, R. VoItz and M. Schott, Chem. Phys. Letters 19 (1973) 391. [4] J. Kalinowski, J. God!ewski and R. Signerski, to be published. [51 N.E. Geacintov, hf. Pope and F. Vogel, Phys. Rev. Letters 22 (1969) 593. (61 R.P. Groff, P. Avnkiqn and R.E. Merrifield, J. Luminescence I,2 (1970) 218. 171R.P. Groff, P. Avakian and R.E. Merrifield, Phys. Rev. B l(1970) 815. 181I. Kalinowski and J. Godlewski, P!lys. Stat. Sol. 20a (1973) 403. PI N.E. Geacintov, hf. Pope and S. Fox, J. Phys. Chem. Solids 31 (1970) 1375. P. Delannoy and M. Schott, 1101H. Bouchriha, G. Delxote, J. Phys. (Paris) 35 (1974) 577. [Ill V. Em and R.E. hferrifield, Phys. Rev. Letters 21 (1968) 609. [I21 V. Em and A.R. XlcGhie, hIdI. Cryst. 1.5 (1971) 277. [I31 N.E. Ceacintov, J. Burgos, hf. Pope and C. Strom, Chem. Phys, Letters 11 (1971) 504, 1141 J. Kalinowski and J. Godlewski, Chem. Phys. Letters 2.5
(1974) 499.
3
15 November 197.5
CHEMICAL PHYSlCS LETTERS
MAGNETIC FIELD EFFECTS ON RECOMBINATION
RADIATION
IN TETRACENE CRYSTAL*
5. KALRIOWSKI and J. GODLEWSKI Institute of PIyxics. Tecimicai University. Gdarisk. Polarid Received 29 April 1975 Revised manuscript received
1 July 1975
Recombination radiation in tetrncene crystal is shown io be modified by the application of a magnetic field. Rclztive variations of radiation intensity with field and orientation nn be explained in terms of molecular sir&t fission and triplet esciton-charge carrier interaction.
triplet exciton-charge
1. Introduction The influence of a magnetic field on recombination electroluminescence is known in the case of anthracene [I ,2] : the increase of the prompt electroluminescence intensity in 3 magnetic field is related to the decrease
of the rate of the charge transfer exciton (CT) fission into a pair of molecular triplet excitons and the decrease of delayed electrotuminescence intensity in the high limit magnetic field to the decrease of the triplettriplet fusion rate. A comparison of the action spectrum of the relative increase of the prompt fluorescence and intrinsic charge carrier creation efficiency at 77 K suggested that the process of singlet exciton fission responsible for the magnetic field effect on prompt fluorescence in tetra-
cene crystals, does not appear to t&e place from the thermally relaxed lowest CT state [3] . CT states are efficiently produced by charge carrier recombination in the crystal and the study of the magnetic field effect on recombination radiation in te tracene can give further information on the nature of the fissionable states. We studied the magnetic field effect on the total recombination electroluminescence (EL) in tetracene crystals at room temperature.
carrier interaction.
3. Experimental Vapour-grown
single
crystals
of tetracene
were
used.
Sodium-potassium alloy was utilized as the cathode and a semitransparent evaporated gold layer as the anode. Effective contact areas were x0.04 cm’. It was established [4] that an Na/K alloy forms a (liquid) ohmic contact for electron injection into sublimationgrown tetracene crystals. The applied electric field was alway? perpendicular to the ab crystal plane and tke crystals were placed between the poles of an electromagnet in such 3 w3y that the magnetic field could change its orientation in the ab plane of the crystals. The recombination radiation emanated from the crystal through the partially transparent gold electrode was collected with a iens and imaged onto one end of a suprasil
light guide and finally
onto the photocathode
of an EMI model 6256 S photomultiplier
operated a:
a single photon-counting apparatus. The influence of 3 magnetic field on the prompt fluorescence emission was also studied, with the same crystals. The prompt fluorescence was filtered and conducted through a fiber optic making with the gold elec-1300
V within
The results presented in this report may be understood in terms of molecular singlet exciton fission and
trode side of the crystal an angle of M.5”. In this case the suprasil rod serving previously as 3 light guide for the electroluminescence was used 3s 3 guide for the ex-
* Thb work was partly supported
citation light. The magnetic effects on the apparatus itself were verified to be very small.
of the Polish Academy
by of Sciences.
the Institute of Physics
345
Voiume.36, number 3
CHEMICAL PliYSlCS
15 November
LETTERS
3. Results
Fig. 1 illustrates the,reIative (percentagej increase of electrolum~esce~ce and prompt fluorescence intensities upon application of a magnetic field of 6 kG, measured as a function of angle 0 between the field vector in the ab plane and the b axis of the crystal. The angular separation and orientation of the resonance peaks observed are reproducible for different crystals used in the experiments and.agree with those previously reported for photoluminescence [5-71. In contradiction, the total electroluminescence intensity change as a function of magnetic field strength differs from that for photoluminescence and varies from crystal to crystal (figs. 2 and 3). In both cases presented the caystal orientation was such that 3 = -32’ (high-field resonznce direction, cf. fig. 1). The experimental situation for the electroluminescence study is also shown in fig. 3. The observed nsgnetic field effect for the longwavelength region of the elecrroiuminescence is lower lhan that for the emission maximum (curves C and B ti figs. 2 and 3). This is in contrast to the effect of a magnetic field on prompt fluorescence showing the same behaviour for these two wavelength regions (curve A in fig. 2). Schott and Coming ftiter combinations were used to isolate portions of the long-wavelength and maximum emission regions.
1 I
1 0
MCGA’ETIC
FIELD
ORIENTATION
(6)
Fig. 1. Change of electro- and photoluminescence in a magnetic field of 6 kG rotattis in the oE plane of a tetracene crystal (thickness d = 15.5 pm).
,/=
-
_____A
ELECTIWLU~INESCENCE
- - PHOTOLUMINESCENCE
Fig. 2. Comparison of magnetic field effect on the electroluminescence oE a crystal with a low delayed component of EL (curves B, C) and photoluminescence at low escitation levels (%X = 366 run) (curve A); the results obtained are for a highfield resonance position with a crystal of thickness d = 118 pm. The dependence wits measured in two different wavelength regions of the crystal emission: A, B-red edge, A, C-short-
wvelength and maximum emission. Note: there is no difference in the case of photoluminescence (curve A).
One Schott RGI falter was used to view the red edge of both electro- and photoluminescence. Electroluminescence light between short wavelengths and the maximum of the emission was viewed through Schott VG 9 and Corning CS 496titers whereas the prompt fluorescence in this case was viewed through a combination of Coming falters (CS 4-96 + CS 4-77 f CS 3-68). The results can be summarized as follows. (i) In the high field limit (B = 6 kG), the magnetic field effect on recombination radiation is anisotropic exibiting the level crossing resonances at orientations which are identical to those for prompt fluorescence (fig. 1). (ii) The magnetic field dependence of e!ectroluminescence at the resonance position (0 = -32”) differs, in
Volume 36, number
3
15 November 1975
CHEMICAL PHYSICS LETTERS
caD+cxKxx) 4.0
‘, ; -4
,I
-
ELEC7ROiUMlNESCEh’CE
- - -
FHOTOLUMINES
B/kGauss]
CENCE
3.0
60
B ikGaus.i]--
-
Fig. 4. Dependence Fig. 3. Relative chnrqe of clectro- and photoluminescence 8s ;1 function of magnetic field in a high-field resonance direction for a crystal with a large delayed component of EL (curves B, C); cute B is obtained for the red edge and C for the total EL (crystai the same as in fi,y. 1).
general, from that in photoluminescence (figs. 2 and 3) and in some cases can be a continously increasing functicn with a tendency to saturation at fields above = 3 kG (fig. 3). (iii) The low-field dip in the magnetic field dependence observed (fig. 2) is less the greater is the delayed component* of the total crystal electroluminescence and disappears when the delayed component becomes the dominant mechanism of emission from the crystal (fl?g_3). (iv) There is a similarity between the magnetic field dependence for the red edge EL in pure tetracene caystals (fig. 2, curve B) and that for total EL in pentacenedoped tetracene crystals (fig. 4). In particular, the ratio of the maximal positive to negative effects are the same and is equal to =z 2.
4. Discussion Observation (i) suggests that the process of molecular singlet exciton fission into a triplet pair (TT) is operative in tetracene recombination radiation. In such a case, at room temperature, the decrease of electroluminescence intensity in the limit of low * The contribution of the delayed electroluminescence to the total EL c=ln be established from 2 campIes supcrlinezr dependence of the total EL verws current density for the crystals 141.
troluminescence
of the relative intensity variation of elecon magnetic field strength, with the pentacenz-
doped
crystal
tetrnuene
in one of the hi$
&Id
resonance
rcctions. Thickness of the cystzl d = 36 ,um, pentaccne centration:
=2
X 103
di-
con-
ppm.
magnetic fields (below 0.5 kG) should take place due to the increase of the rste of molecular singlet fission 16,71-
This is not the case fur the crystal in fig. 3. Also for other crystals (fig. 2) this decrease is lower than that expected from magnetic field effects on photoluminescence. In addition the inversion in the sign of the magnetic field effect takes place at a lower field strength than that for photoluminescence (fig. 2 - top). This behaviour can be explained assum@ a. part of the electroluminescence to have originated from tripIet-triplet fusions leading to the creation of fluorescing singlets. This is the delayed electroluminescence. In the presence of charge the triplets are partly quenched as a result of triplet exciton-charge carrier interaction [S] . The triplet exciton-charge carrier interaction Tate constant is, on the other hand, influenced by a magnetic field [9] causing it ta be smaller for high as well as for low magnetic fields oriented along the high-field resonance directions [lo]. The resonance directions corresponding to tripletdoublet pair degeneracies were shown to be identical with those for triplet-triplet annihilation [IO-121 and consequently for singlet fission (see rcfs. [6,7,9]). The magnetic field decrease in the triplet-charge carrier rate constant is demonstrated by the increase in the delayed component of electroluminescence. If the delayed component is prevalent in the crystal electroluminescence observed, this increase tends to mask the low-field decrease due to the increase of the rate of molecular singlet fission. This Is in agreement
347
:
Vo!uri% 36, number 3
‘with the
experimental
pccording
CHEMICAL PHYSICS LETTERS
observations
(ii) and (iii).
to this interpretation
the low-field decrease seen in the total electroluCinescence in fig. 2 should prackally disappear for the delayed component. The experimental result in fig. 3 is indeed that which is expected, indicating that triplet exciton-charge carrier interaction plays a significant role in magnetic field liehaviour of the recombination radiation of tetracene crystal. An examination of the results in the Iight of observations (iii) and (iv) leads to the conclusion that at the red edge the electroluminescence, at least partly, originates from trapped states (S,) which can fission into two inequivalent triplet exciLons (T, T,) (this is the socalled heterofission; see ref. [13]). It is seen that, over the whole field range which was explored, the relative change is smaller than the frectional intensity variations observed for EL within the emission maximum (figs. 2 and 3). This would indicate that the factor describing the specific field effect on the couplir_g between the St and the (T, Tt) states is here less sensitive to the magnetic !CieId than in the case of free excitons. Since
the trapped singlet states can be produced by an annihilation process of inequivalent lriplet excitons [ 141 a large delayed component at the red edge of EL can be expected in the case of the crystal in fig. 3. Consequently, tie low field dip in -Sle magnetic field dependence should disappear. This is indeed the experimental case. Finally, the relative magnetic field change of total electroluminescence contains three terms corresponding to three different components: prompt, delayed and trapped states emission. ‘Thus the variation of the total electrolilminescence with rnage tic field at room temperature is determined bq- thrj interplay of three effects: (1) magnetic field change of the effective rate constant for free singlet exciton fission; (2) magnetic field decrease of the rate of kiplet-charge carrier interaction and (3) magnetic field change in the rate of hetcrofission. Magnetic field effect on the emission originated from the triplet-triplet annihilation at room temperature is known to be r_egligible [6,7] _ At low excitation levels, the prompt fluorescence
34.8
1.5 November
i97.5
is the dominating mechanism of the crystal fluorescence and its chenge in a magnetic field must be attributed to the first of the above-mentioned effects. This is the reason for the observed difference in magnetic field behaviour of electro- and photoluminescence. Since the delayed component of EL is determined to a large extent by concentration and trap characteristics of the crystal [4], it is not surprising that the total electroluminescence shows 2 different magnetic field behaviour for various tetracene crystals.
Acknowledgement We are grateful to Professor crystals available to us.
M. Pope for making
the
References [l]
H.P.
Schwab
and D.F.
Willixns,
Chem. Phys. Letturs 13
(1972) 581. {Z] H.P. Schwab and D.F. Williams, I. Shem. Phys. 58 (1973) 1542. 131 G. Klein, R. VoItz and M. Schott, Chem. Phys. Letters 19 (1973) 391. [4] J. Kalinowski, J. God!ewski and R. Signerski, to be published. [51 N.E. Geacintov, hf. Pope and F. Vogel, Phys. Rev. Letters 22 (1969) 593. (61 R.P. Groff, P. Avnkiqn and R.E. Merrifield, J. Luminescence I,2 (1970) 218. 171R.P. Groff, P. Avakian and R.E. Merrifield, Phys. Rev. B l(1970) 815. 181I. Kalinowski and J. Godlewski, P!lys. Stat. Sol. 20a (1973) 403. PI N.E. Geacintov, hf. Pope and S. Fox, J. Phys. Chem. Solids 31 (1970) 1375. P. Delannoy and M. Schott, 1101H. Bouchriha, G. Delxote, J. Phys. (Paris) 35 (1974) 577. [Ill V. Em and R.E. hferrifield, Phys. Rev. Letters 21 (1968) 609. [I21 V. Em and A.R. XlcGhie, hIdI. Cryst. 1.5 (1971) 277. [I31 N.E. Ceacintov, J. Burgos, hf. Pope and C. Strom, Chem. Phys, Letters 11 (1971) 504, 1141 J. Kalinowski and J. Godlewski, Chem. Phys. Letters 2.5
(1974) 499.