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Calculations on crystal defects in trans-polyacetylene
Synthetic Metals, 55-57 (1993) 4332-4337
4 332
CALCULATIONS ON CRYSTAL DEFECTS IN TRANS-POLYACETYLENE
K. PRESSL, K.D. AICHHOLZER, G. LEISING and H. KAHLERT Institut fiir Festk0rperphysik, Technische Universit~it Graz Petersgasse 16, A-8010 Graz, AUSTRIA
AB STRACT A number of studies were focused on the structure and morphology of polyacetylene. But there is still a lack of reliable structural data caused by the difficult morphology and disorder of this material. There are two possible space groups fitting the experimental data of polyacetylene, P 21/a and P 21/n. A controversy appears also about the understanding of the doping and dedoping of this system. For instance, different doping levels may result in structural changes and disorder. To study the influence of the morphology on X-ray measurements we did computer simulations of different crystal defects. Depending on whether the bond alternation is in phase or out of phase on neighbouring chains, the (001) reflection is strongly allowed or forbidden. Random orientation of the chains requires the orthorhombic space group P nam. Therefore, we concentrate on the change of the calculated intensity of the (001) reflection as a function of the artificially introduced disorder. We show calculations based on the three space groups P 21/a, P 21/n and P nam.
INTRODUCTION The geometrical structure of polyacetylene (PA) is strongly related with the electronic structure of this material and is still controversial. It is impossible to describe the real structure of polyacetylene without considering the different types of disorder possible in this material. With respect to the understanding of the electronic properties it is important to have knowledge, how the real structure differs from the perfect lattice. For the discussion of the intrinsic transport properties it would be of great interest to know if the structure is single phase P 21/a or P 21/n or if there exists a non equilibrium phase mixture in trans-polyacetylene. 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
4333
METHOD OF CALCULATION The programs used for the calculations of the X-ray diffraction patterns are Lazy Pulverix [1] and a program for Rietveld refinement in the pattern calculation mode [2]. In the second program the use of anisotropic temperature parameters (Debye-Waller factors) is possible. Included in the input data of the programs are the size of the unit cell, its space group symmetry and the atom type with its fractional coordinates (the coordinates in units of the unit cell parameters). Since the aim of this report is to simulate diffraction pattern of disordered unit cells, it is reasonable to use the space group with the lowest symmetry, that is P 1. This space group only contains the identity as a symmetry operation and thereby enables the construction of cells with well defined defects. The starting point for the calculations formed the in-phase structure of PA, which corresponds to the space group P 21/a (see Fig. 1). The numerical values of the interchain distances a and b, the length c of the repeat unit in the c-direction and the monoclinic angle 13 are taken from X-ray studies by Leitner [3] • a = 4.17 A, b = 7.39 A, c = 2.46/~. and 13= 90.6 o Also the setting angle dp= 57 ° is taken from [3]. We also included the scattering from the hydrogen atoms within the unit cell in our calculations, although their contributions to the scattering intensity is very modest, because of their small scattering factor compared to carbon atoms. In our calculations we used two different sizes of monoclinic cells, denoted A and B. Their dimensions are listed in Table 1.
TABLE 1 The two monoclinic cells, used in our calculations Name
Cell parameter
Cell parameter
Cell parameter
in a-direction
in b-direction
in c-direction
A
a
b
c
B
2a
2b
c
RESULTS Considering the single-double bond alternation in the chain the crucial point in the three dimensional structure is the relation of the single and double bond sequences on neighbouring chains. Three kinds of phase relations are imaginable in trans PA: The out-of-phase dimerization on neighbouring chains leads to the monoclinic space group P 21/n (see Fig. 1), the in-phase correlation of the dimerized backbone gives the monoclinic space group P 21/a (see Fig. 1) and the random packing of the chains creates the orthorhombic space group Pnam. For the monoclinic structure P 21/n the (001) reflection is strongly forbidden. The same holds for the orthorhombic structure, where the (001) reflection is also forbidden. For the monoclinic structure P 21/a the (001) reflection is allowed. In the case o f P 21/n an out-of-phase dimerization on adjacent chains exists. Herewith the
4334
nearest neighbours of each single bond in the a,b-plane are four double bonds and vice versa. In case of P 21/a the dimerization occurs in-phase. That means, each double bond in the a,b-plane is surrounded by double bonds, each single bond is surrounded by single bonds.
P21/n
P21/a
)-e
c
~
e--(
--e )-e
o-(
e-(
e-( C
)-e
)-'0
e-(
o-C
)-o b
b
%
Fig. 1. The two possible monoclinic structures for trans-polyacetylene P 21/a and P 21/n.
Early studies ofFincher et al. [4] on oriented Shirakawa samples of the trans-isomer did not show any measurable intensity of the (001) reflection. They assumed that if all neighbouring chains are in-phase, the intensity has to be sufficiently high to recognize the (001) reflection. Notwithstanding that the count rates were extremely low the authors concluded that the two chains within the PA unit cell are out-of-phase. This conclusion was open to question when Chien et al. [5] measured a weak (001) reflection intensity by electron diffraction studies on Shirakawa PA. This is indicating the space group P 21/a. Therefore they conclude that all chains in trans PA are in-phase. One should also think about the possibility that trans PA could be composed of regions with different types of packing with adjacent chains in-phase or out-of-phase or randomly phased. The first who referred to this possibility were Perego and his group [6], who assumed that in trans PA regions with neighbouring chains in-phase and out-of-phase coexist. Their conclusions that this would result in an overall space group P ham requires chains to shift one against the other. Samples of high crystallinity and good orientation are obtained, if they are prepared by stretchconverting the Durham precursor polymer to PA [7]. With this Durham-Graz PA we [8] were able to detect a strong (001) reflection and so we decided for P 21/a and the out-of-phase modulation of chains. We would like to note that a comparison of the (002) intensity observed by Fincher et al. [4] with the corresponding intensity observed in our measurements [9] indicated, that the number of counts collected for that reflection was about a factor of 104 larger in our case. Moon et.al. [10] also
4335
reported weak X-ray scattering intensity at the (001) peak position in stretch-oriented Durham PA. After n-type doping and subsequent undoping they observed a decrease in the (001) intensity. Therefore they considered the appearance of the (001) peak only as a result of residual disorder and defects in the pristine Durham PA. Moon and coworkers ruled out the in-phase configuration of the two chains in the unit cell and considered the anti-phase arrangement as preferred. The intensity ratio of the (002) peak relative to the (001) peak, I(0o2)/1(ool), measured by Chien and his group [5] was found to be -59 which is significantly larger than the value o f - 9 reported by us [8]. For the perfect P21/a structure 1(002)/1(001) is -26 without a correction for the temperature factors and -17 for using Bp= 1 A2 [8]. This value is estimated by the observation of the (001) peak, the (002) peak and the (003) peak. For the perfect out-of-phase arrangement of the chains the (001) intensity is zero and therefor the intensity ratio 1(002)/1(001)is climbing ad infinitum. It is important to answer the question, in what way the intensity ratio 1(002)/1(001) changes if the single-double bond sequences are disordered on neighbouring chains, so that they neither belong definitely to the inphase nor to the out-of-phase configuration of the chains. We calculated the intensity of the (001) peak when the structure shifts continuously from the in-phase to the out-of-phase arrangement of the bond alternation on the two PA chains within the unit cell. Therefore we shifted the center chain (see Fig. 1) from zero to one half of the c-dimension of the unit cell. The resulting intensity ratio, 1(o02)/1(001), is plotted in Fig. 2.
50 40 I(002)/30 I(001) 20
•
lO 0 0,1 0,2 0,3 0,4 displacement in c-direction Fig. 2. Intensity ratio of the (002) peak relative to the (001) peak versus the shift between two adjacent chains in cell A. (x-axis in units of the cell dimension c)
As mentioned above, neglecting the Debye-Waller factor I(002)/1(001) is -26 for the perfect P21/a structure, decreasing to 0 for dc = 2.5 and becoming larger if the configuration of the chains approaches the out-of-phase type P2l/n. What happens, if the shift between the two PA chains does not take place in every unit cell but in one of four unit cells, is depicted in Fig. 3. It is clearly shown, that the decrease of the (001) intensity slows down. There is no fundamental change of 1(0o2)/1(OOl) for 0_
4336
50
4°I
I(002)/30 I(001) 20
10 0
0
I
I
I
I
I
0, l
0,2
0,3
0,4
0,5
displacement in c-direction Fig. 3. Intensity ratio of the (002) peak relative to the (001) peak versus the shitt between two adjacent chains in cell B. (x-axis in units of the cell dimension c)
the intensity ratio I(002)/1(0Ol) is ---48. The coexistence of two or more phases is a possible type of disorder in polymers. An example of the coexistence of two separate phases is polyethylene. Considering a shift between adjacent chains of the kind discussed above implies that each chain is shifted with respect to the other by a certain amount in c-direction (see Fig. 1). Looking at the intensity ratio I(002)/1(001), we notice that it is an oscillating function of the c-direction displacement dc of the adjacent chain, where at dc=0.25 the value of I(0o2)/1(001) is infinitely large because of the vanishing I(001). Another possibility to decide between P 21/a and P 21/n is the observation of off-axis reflections from an carefully aligned sample. So the (107) and the (101) reflections appear only in the case of P 2l/n symmetry because they are forbidden in the P 21/a space group. The determination of the 1(021)/1(011) intensity ratio would also give hints for the correct space group because both reflections are allowed in both space groups with widely differing intensities. For a meaningful calculation of the intensities of this reflections it is necessary to use anisotropic Debey-Waller factors. The reflections (10].), (101), (02]) and (021) would appear together with the reflections (117) and (111) between 28, = 42 ° and 45 °. A deconvolution of this peaks would only be possible for highly oriented samples with large crystalline grains to reach a FWHM of less then 1°. In this paper we showed that the consideration of structural defects is of vital importance for the understanding of the real crystal structure of trans-PA. We discuss the problem of P 21/a versus P 21/n based on the idea of non equilibrium phase-arrangements between neighbouring chains. We followed the change of the X-ray intensity if adjacent chains which slide at each other changing their correlation from the in-phase arrangement to the out-of-phase configuration and the influence on the intensity ratio I(002)/1(001) if a two phase structure (P 21/a in coexistence with P 21/n ) exists. The quality of the presently available experimental data does not yet allow to resolve the issue from a comparison of calculated and observed intensities.
4337
ACKNOWLEDGEMENTS We would like to acknowledge O.Leitner for his contributions in experiment and discussion. This work was supported by the Fond zur F6rderung der wissenschaffiichen Forschung project number P 7949-TEC, which is a part of the BRITE/EURAM HICOPOL project.
REFERENCES 1
K. Yvon, W. Jeitschko and E. Parthe, J.AppI.Cry_st., 10 (1977) 73
2
R.A. Young, School of Physics, Georgia Inst. of Technology, Atlanta
3
O. Leitner; Ph.D. Thesis, Graz University of Technologic, Austria 1990
4
CR. Fincher Jr., C.-E. Chert, A.J. Heeger, A.G. MacDiarmid, JB.Hastings; Phys.Rev.Lett., 48 (1982) 100
5
J.C.W. Chien, FE. Karasz; MacromoI.Chem., Rapid Commun, 3 (1982) 655
6
G. Perego, G. Lugli, U. Pedretti; Mol.Cryst.Liq.Cryst., 117 (1985) 67
7
G. Leising; Polymer Bulletin, 11 (1984) 401
8
H. Kahlert, O. Leitner, G. Leising; Synthetic Metals, 17 (1987) 467
9
G. Leising, H. Kahlert, O. Leitner; Electronic Properties of Polymers and Related Compounds, Springer Series in Solid-State Sciences, 63 (1985) 56
10
YB. Moon, M. Winokur, A.J. Heeger, J. Baker, D.C. Bott; Macromolecules, 20 (1987) 2457
4 332
CALCULATIONS ON CRYSTAL DEFECTS IN TRANS-POLYACETYLENE
K. PRESSL, K.D. AICHHOLZER, G. LEISING and H. KAHLERT Institut fiir Festk0rperphysik, Technische Universit~it Graz Petersgasse 16, A-8010 Graz, AUSTRIA
AB STRACT A number of studies were focused on the structure and morphology of polyacetylene. But there is still a lack of reliable structural data caused by the difficult morphology and disorder of this material. There are two possible space groups fitting the experimental data of polyacetylene, P 21/a and P 21/n. A controversy appears also about the understanding of the doping and dedoping of this system. For instance, different doping levels may result in structural changes and disorder. To study the influence of the morphology on X-ray measurements we did computer simulations of different crystal defects. Depending on whether the bond alternation is in phase or out of phase on neighbouring chains, the (001) reflection is strongly allowed or forbidden. Random orientation of the chains requires the orthorhombic space group P nam. Therefore, we concentrate on the change of the calculated intensity of the (001) reflection as a function of the artificially introduced disorder. We show calculations based on the three space groups P 21/a, P 21/n and P nam.
INTRODUCTION The geometrical structure of polyacetylene (PA) is strongly related with the electronic structure of this material and is still controversial. It is impossible to describe the real structure of polyacetylene without considering the different types of disorder possible in this material. With respect to the understanding of the electronic properties it is important to have knowledge, how the real structure differs from the perfect lattice. For the discussion of the intrinsic transport properties it would be of great interest to know if the structure is single phase P 21/a or P 21/n or if there exists a non equilibrium phase mixture in trans-polyacetylene. 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
4333
METHOD OF CALCULATION The programs used for the calculations of the X-ray diffraction patterns are Lazy Pulverix [1] and a program for Rietveld refinement in the pattern calculation mode [2]. In the second program the use of anisotropic temperature parameters (Debye-Waller factors) is possible. Included in the input data of the programs are the size of the unit cell, its space group symmetry and the atom type with its fractional coordinates (the coordinates in units of the unit cell parameters). Since the aim of this report is to simulate diffraction pattern of disordered unit cells, it is reasonable to use the space group with the lowest symmetry, that is P 1. This space group only contains the identity as a symmetry operation and thereby enables the construction of cells with well defined defects. The starting point for the calculations formed the in-phase structure of PA, which corresponds to the space group P 21/a (see Fig. 1). The numerical values of the interchain distances a and b, the length c of the repeat unit in the c-direction and the monoclinic angle 13 are taken from X-ray studies by Leitner [3] • a = 4.17 A, b = 7.39 A, c = 2.46/~. and 13= 90.6 o Also the setting angle dp= 57 ° is taken from [3]. We also included the scattering from the hydrogen atoms within the unit cell in our calculations, although their contributions to the scattering intensity is very modest, because of their small scattering factor compared to carbon atoms. In our calculations we used two different sizes of monoclinic cells, denoted A and B. Their dimensions are listed in Table 1.
TABLE 1 The two monoclinic cells, used in our calculations Name
Cell parameter
Cell parameter
Cell parameter
in a-direction
in b-direction
in c-direction
A
a
b
c
B
2a
2b
c
RESULTS Considering the single-double bond alternation in the chain the crucial point in the three dimensional structure is the relation of the single and double bond sequences on neighbouring chains. Three kinds of phase relations are imaginable in trans PA: The out-of-phase dimerization on neighbouring chains leads to the monoclinic space group P 21/n (see Fig. 1), the in-phase correlation of the dimerized backbone gives the monoclinic space group P 21/a (see Fig. 1) and the random packing of the chains creates the orthorhombic space group Pnam. For the monoclinic structure P 21/n the (001) reflection is strongly forbidden. The same holds for the orthorhombic structure, where the (001) reflection is also forbidden. For the monoclinic structure P 21/a the (001) reflection is allowed. In the case o f P 21/n an out-of-phase dimerization on adjacent chains exists. Herewith the
4334
nearest neighbours of each single bond in the a,b-plane are four double bonds and vice versa. In case of P 21/a the dimerization occurs in-phase. That means, each double bond in the a,b-plane is surrounded by double bonds, each single bond is surrounded by single bonds.
P21/n
P21/a
)-e
c
~
e--(
--e )-e
o-(
e-(
e-( C
)-e
)-'0
e-(
o-C
)-o b
b
%
Fig. 1. The two possible monoclinic structures for trans-polyacetylene P 21/a and P 21/n.
Early studies ofFincher et al. [4] on oriented Shirakawa samples of the trans-isomer did not show any measurable intensity of the (001) reflection. They assumed that if all neighbouring chains are in-phase, the intensity has to be sufficiently high to recognize the (001) reflection. Notwithstanding that the count rates were extremely low the authors concluded that the two chains within the PA unit cell are out-of-phase. This conclusion was open to question when Chien et al. [5] measured a weak (001) reflection intensity by electron diffraction studies on Shirakawa PA. This is indicating the space group P 21/a. Therefore they conclude that all chains in trans PA are in-phase. One should also think about the possibility that trans PA could be composed of regions with different types of packing with adjacent chains in-phase or out-of-phase or randomly phased. The first who referred to this possibility were Perego and his group [6], who assumed that in trans PA regions with neighbouring chains in-phase and out-of-phase coexist. Their conclusions that this would result in an overall space group P ham requires chains to shift one against the other. Samples of high crystallinity and good orientation are obtained, if they are prepared by stretchconverting the Durham precursor polymer to PA [7]. With this Durham-Graz PA we [8] were able to detect a strong (001) reflection and so we decided for P 21/a and the out-of-phase modulation of chains. We would like to note that a comparison of the (002) intensity observed by Fincher et al. [4] with the corresponding intensity observed in our measurements [9] indicated, that the number of counts collected for that reflection was about a factor of 104 larger in our case. Moon et.al. [10] also
4335
reported weak X-ray scattering intensity at the (001) peak position in stretch-oriented Durham PA. After n-type doping and subsequent undoping they observed a decrease in the (001) intensity. Therefore they considered the appearance of the (001) peak only as a result of residual disorder and defects in the pristine Durham PA. Moon and coworkers ruled out the in-phase configuration of the two chains in the unit cell and considered the anti-phase arrangement as preferred. The intensity ratio of the (002) peak relative to the (001) peak, I(0o2)/1(ool), measured by Chien and his group [5] was found to be -59 which is significantly larger than the value o f - 9 reported by us [8]. For the perfect P21/a structure 1(002)/1(001) is -26 without a correction for the temperature factors and -17 for using Bp= 1 A2 [8]. This value is estimated by the observation of the (001) peak, the (002) peak and the (003) peak. For the perfect out-of-phase arrangement of the chains the (001) intensity is zero and therefor the intensity ratio 1(002)/1(001)is climbing ad infinitum. It is important to answer the question, in what way the intensity ratio 1(002)/1(001) changes if the single-double bond sequences are disordered on neighbouring chains, so that they neither belong definitely to the inphase nor to the out-of-phase configuration of the chains. We calculated the intensity of the (001) peak when the structure shifts continuously from the in-phase to the out-of-phase arrangement of the bond alternation on the two PA chains within the unit cell. Therefore we shifted the center chain (see Fig. 1) from zero to one half of the c-dimension of the unit cell. The resulting intensity ratio, 1(o02)/1(001), is plotted in Fig. 2.
50 40 I(002)/30 I(001) 20
•
lO 0 0,1 0,2 0,3 0,4 displacement in c-direction Fig. 2. Intensity ratio of the (002) peak relative to the (001) peak versus the shift between two adjacent chains in cell A. (x-axis in units of the cell dimension c)
As mentioned above, neglecting the Debye-Waller factor I(002)/1(001) is -26 for the perfect P21/a structure, decreasing to 0 for dc = 2.5 and becoming larger if the configuration of the chains approaches the out-of-phase type P2l/n. What happens, if the shift between the two PA chains does not take place in every unit cell but in one of four unit cells, is depicted in Fig. 3. It is clearly shown, that the decrease of the (001) intensity slows down. There is no fundamental change of 1(0o2)/1(OOl) for 0_
4336
50
4°I
I(002)/30 I(001) 20
10 0
0
I
I
I
I
I
0, l
0,2
0,3
0,4
0,5
displacement in c-direction Fig. 3. Intensity ratio of the (002) peak relative to the (001) peak versus the shitt between two adjacent chains in cell B. (x-axis in units of the cell dimension c)
the intensity ratio I(002)/1(0Ol) is ---48. The coexistence of two or more phases is a possible type of disorder in polymers. An example of the coexistence of two separate phases is polyethylene. Considering a shift between adjacent chains of the kind discussed above implies that each chain is shifted with respect to the other by a certain amount in c-direction (see Fig. 1). Looking at the intensity ratio I(002)/1(001), we notice that it is an oscillating function of the c-direction displacement dc of the adjacent chain, where at dc=0.25 the value of I(0o2)/1(001) is infinitely large because of the vanishing I(001). Another possibility to decide between P 21/a and P 21/n is the observation of off-axis reflections from an carefully aligned sample. So the (107) and the (101) reflections appear only in the case of P 2l/n symmetry because they are forbidden in the P 21/a space group. The determination of the 1(021)/1(011) intensity ratio would also give hints for the correct space group because both reflections are allowed in both space groups with widely differing intensities. For a meaningful calculation of the intensities of this reflections it is necessary to use anisotropic Debey-Waller factors. The reflections (10].), (101), (02]) and (021) would appear together with the reflections (117) and (111) between 28, = 42 ° and 45 °. A deconvolution of this peaks would only be possible for highly oriented samples with large crystalline grains to reach a FWHM of less then 1°. In this paper we showed that the consideration of structural defects is of vital importance for the understanding of the real crystal structure of trans-PA. We discuss the problem of P 21/a versus P 21/n based on the idea of non equilibrium phase-arrangements between neighbouring chains. We followed the change of the X-ray intensity if adjacent chains which slide at each other changing their correlation from the in-phase arrangement to the out-of-phase configuration and the influence on the intensity ratio I(002)/1(001) if a two phase structure (P 21/a in coexistence with P 21/n ) exists. The quality of the presently available experimental data does not yet allow to resolve the issue from a comparison of calculated and observed intensities.
4337
ACKNOWLEDGEMENTS We would like to acknowledge O.Leitner for his contributions in experiment and discussion. This work was supported by the Fond zur F6rderung der wissenschaffiichen Forschung project number P 7949-TEC, which is a part of the BRITE/EURAM HICOPOL project.
REFERENCES 1
K. Yvon, W. Jeitschko and E. Parthe, J.AppI.Cry_st., 10 (1977) 73
2
R.A. Young, School of Physics, Georgia Inst. of Technology, Atlanta
3
O. Leitner; Ph.D. Thesis, Graz University of Technologic, Austria 1990
4
CR. Fincher Jr., C.-E. Chert, A.J. Heeger, A.G. MacDiarmid, JB.Hastings; Phys.Rev.Lett., 48 (1982) 100
5
J.C.W. Chien, FE. Karasz; MacromoI.Chem., Rapid Commun, 3 (1982) 655
6
G. Perego, G. Lugli, U. Pedretti; Mol.Cryst.Liq.Cryst., 117 (1985) 67
7
G. Leising; Polymer Bulletin, 11 (1984) 401
8
H. Kahlert, O. Leitner, G. Leising; Synthetic Metals, 17 (1987) 467
9
G. Leising, H. Kahlert, O. Leitner; Electronic Properties of Polymers and Related Compounds, Springer Series in Solid-State Sciences, 63 (1985) 56
10
YB. Moon, M. Winokur, A.J. Heeger, J. Baker, D.C. Bott; Macromolecules, 20 (1987) 2457