544
J. Phys. Chem. 1083, 87, 544-551
ART'I CLES Structural Investigations of Amorphous Tetracene and Pentacene by Low-Temperature Electron Diffraction R. Elermann,+ 0. M. Parklnson,' H. Bassler," and J. M. Thomas' Fachbereich Physikaiische Chemie der Philipps-Universitdt, D-3550 Marburg, West Germany, and DepaHment of Physical Chemistry, University of CambrMge, CambrMge CB2 lEP, U.K. (Received: Juiy 22, 1982; In Final Form: September 14, 1982)
Electron diffraction studies on in situ grown films of tetracene (TC) and pentacene (PC) are reported. Sample formation temperatures ranged from 300 to 20 K. The diffractograms demonstrate the loss of long-rangeorder upon lowering the formation temperature Tf,yet persistence of short-rangeorder derived from the crystal structure down to the lowest Tf values attained. There is evidence for slight deviations of the average structural parameters of the films from single-crystal values and for a discontinuous change to occur near the phase-transition temperature of the single crystal. The characteristic feature of the amorphous phase turns out to be a random fluctuation of the intermolecular coordinates. Analysis of the width of various reflections yields a maximum variation in the intermolecular distances of about 20%. The effects of sample annealing and variation of the depoqition rate are briefly discussed.
Introduction Organic molecular species displaying a rich diversity of photophysical, photochemical, and electronic properties can be laid down on appropriate substrates as thin amorphous films.'-' A particularly convenient method is to evaporate the parent crystals and to let the films build up (to thickness of approximately 0.1-0.3 pm) at very low temperatures (from ca. 20 K upward) but at rapid rates of deposition (typically 0.5-50 A s-l) in vacuo. Another, more restricted, method is to irradiate monomeric crystals which, upon photoinduced dimerization or oligomerization, are then converted into amorphous films. This serves as a convenient, if specialized, method of generating amorphous films of dimeric substituted coumarins and dimeric cyclopentanone derivative^.^ Previously it has been shown that linear acenes, like anthracene and tetracene, are likely to form "structureleas" films when deposited rapidly at low temperatures. For tetracene, in particular, we established that, when the films were formed under conditions far removed from thermodynamic equilibrium, the frozen-in assemblage of individual molecules lacked long-range order, as revealed by electron diffraction? Our previous preliminary publication showed how the diffuse electron diffraction rings, characteristic of the amorphous films, were progressively converted to sharper ones as temperature was increased. Upon annealing at 295 K for several hours recrystallization is more or less complete. In our preliminary communication we interpreted our results on the assumption that the intermolecular coordinates were subject to statistical fluctuation around average values which were closely similar to, if not identical with, those of the parent crystal values. In this paper we present a detailed analysis of the structure of the amorphous tetracene and pentacene laid down at the lowest temperatures and endeavor to identify Fachbereich Physikalische Chemie der Philipps-Universitat. *University of Cambridge. 0022-3654I83l2087-0544$0 1.5010
the changes that take place in the films with increasing temperature. In so doing, we focus upon the degree of fluctuation that we may expect in properties such as the polarization energy of an exciton or a charge carrier. Such parameters hold the key to the deeper understanding of the electronic, transport, and optical properties of films which have been reviewed el~ewhere.~ One of the main conclusions that emerges from this study is that films of tetracene and pentacene deposited at low temperatures represent prototypes of amorphous organic solids in which so-called diagonal disorder by far outweighs off-diagonal disorder. This justifies neglect of fluctuations in the matrix elements for exchange of elementary excitation among neighboring molecules in theoretical treatments that set out to describe electronic transport. The proposal put forward in earlier that the transport properties of amorphous single-component organic solids can be explained in a satisfactory manner by considering only the dispersion of the site energies is thus placed on firmer physical grounds.
Experimental Section The electron diffraction experiments were carried out in the University of Cambridge in a specially adapted9 (1) Y. Maruyama and N. Iwasaki, Chem. Phys. Lett., 24, 26 (1974). (2) Y. Kamura, K. Seki, and H. Inokuchi, Chem. Phys. Lett., 30,35
11975). (3) J. Hofmann, K. P. Seefeld, W. Hofberger, and H. Biissler, Mol. Phys., 37, 973 (1979). (4) R. Hesse, W. Hofberger, and H. Biissler, Chem. Phys., 49, 201 '
11980). >-- -,-
(5) N. W. Thomas, G. M. Parkinson, and J. M. Thomas, unpublished results. (6) R. Eiermann, G. M. Parkinson, H. Biissler, and J. M. Thomas, J. Phys. Chem., 86, 9 (1981). (7) H. Biissler, Phys. S t a t u Solidi B , 107,9 (1981). (8)G.SchBnherr, H. Biissler, and M. Silver, Philos. Mag., [Part] B , 44, 47, 369 (1981). (9) G.M. Parkinson and J. M. Thomas, in preparation; see also G. M. Parkinson, M.-J. Goringe, W. Jones, W. Rees, J. M. Thomas, and J. U. Williams, 'Proc. EMAS 75: Developments in Electron Microscopy", J. A. Venables, Ed., Academic Press, New York, 1976, p 315.
0 1983 American Chemical Society
Structures of Amorphous Tetracene and Pentacene
HELIUM D E W A R
MIRROR
F IBRE-OPTIC
Figure 1. Liquldheiium-cooled specimen stage of the transmission electron microscope prepared for the in situ growth of amorphous solMs.
Siemens Elmiskop 1A transmission electron microscope operated a t 100 kV. The vacuum system has been modified to ensure a column pressure of lO”-lO* torr and also the specimen chamber is differentially pumped, giving pressure around the sample (especially with the cryopumping effect of the liquid-helium-cooledspecimen stage) of better than lo* torr. The modifications made to the specimen chamber area include the following: (i) A specimen stage is constructed so as to allow controlled cooling of samples in the range 300-10 K by the continuous flow of liquid nitrogen or liquid helium. The stage design permits double-tilting of the specimen by f45O at low temperatures and is arranged so that the contamination rate from gases in the microscope column is negligible. The stage incorporated movable apertures above and below the sample which keep the contamination rate low and which also are interchangeable so as to allow in situ deposition of samples by evaporation as well as irradiation with and collection of W and visible light (Figure 1). (ii) Above the specimen cartridge is positioned a movable Knudsen cell and an arrangement of movable, liquid-nitrogen-cooledapertures which reduce contamination of the specimen chamber by the organic sample under investigation and also provide a collimated beam of molecules for direction onto the cooled substrate. A temperature controller driving the Knudsen cell permits the variation of the evaporation rate between 1 and 60 A s-l a t the corresponding evaporator temperatures of 430 and 470 K, respectively. For the investigation of films prepared at the lowest temperatures, a nontilting holder was constructed, designed to ensure optimum specimen cooling. The samples were evaporated onto a very thin (estimated 50-100 A) film of evaporated carbon in intimate contact with a 400-mesh copper TEM grid. The grid was clamped tightly to the specimen holder which was itself given a thin coating of silicone grease in order to maximize thermal conduction to the liquid-helium Dewar of the specimen stage. The carbon support film itself gave very weak diffuse diffraction rings which, for the electron dose used to obtain the electron diffraction patterns of the organic films, introduce a negligible contribution. Owing to the very thin nature of the samples studied, and the problems of conduction through thermocouple wires, it was not feasible to measure the temperature of the substrate directly, but a reasonable estimate could be made by measuring the temperature at points as close to the film as possible. As shown in Figure
The Journal of Physical Chemistry, Vol. 87,No. 4, 1983 545
1,thermocouples were imbedded in narrow holes drilled into the wall of the liquid-helium Dewar and in the specimen holder, reaching close to the edge of the grid, the holes being packed with silicone grease to ensure good thermal contact. To estimate the order of magnitude of the temperature gradient between the specimen stage and the sample, we carried out a test run in which the stage was cooled at the maximum rate and the temperature monitored by both thermocouples. A reasonably constant temperature lag of 10-15 K between the two was observed, this dropping to less than 5 K upon reaching equilibrium. For normal observations, cooling was carried out more slowly and the stage was held at a constant temperature for ca. 15 min before evaporation was commenced. It is thus reasonable to ascribe a temperature difference of less than 10 K between the thermocouple temperature and the actual film temperature. The input of energy from the evaporated molecules under typical conditions (of evaporation temperature and rate) employed here may therefore be neglected. The design of the specimen stage (Figure 1)ensures that the film is surrounded almost completely by material at very low temperature so that thermal input by radiation is very small. Electron diffraction patterns were recorded with exposures of 1-10 s, with a typical electron dose rate of 5 X A. The critical dose for radiation damage of tetracene is ca.0.16 C cm-2 (100 electrons A-2). The diffraction patterns showed some change after 7-10 min under these conditions of exposure, and thus the amount of damage introduced by recording the data is insignificant. Furthermore, there was no indication that any photodimerization occurred at 20 K during electron irradiation, either directly as a result of energy input to the molecules by inelastic scattering of the electrons or indirectly as a result of absorption of photons from associated cathodoluminescence phenomena. Diffraction patterns were recorded on Kodak Kodirex X-ray film and Agfa “SCIENTIA” EM film, the latter giving better microdensitometer traces (the emulsion being less grainy), but requiring longer exposure times. Analysis of the electron diffraction pattern was carried out by recording microdensitometer traces of the films. To eliminate the noise produced by the graininess of the photographic material, we mounted the film on a rotating stage operated at 10 cycles s-l. Calibration of the diffraction patterns was carried out by previously evaporating a thin layer of aluminum onto some sample substrates.
Results Electron diffractograms of in situ grown films of tetracene (TC) and pentacene (PC) were taken (i) immediately after deposition as a function of the film-formation temperature (Tf),(ii) at distinct recording temperatures (T,) attained in the course of a variable heating program applied to a f i i deposited at a given Tf, (iii) as a function of deposition rate at given Tf, and (iv) upon varying the film thickness between 400 and 3000 A. The latter series of measurements indicated that the electron diffractograms are independent of film thickness. Since the effect of multiple electron scattering should increase in proportion to the sample thickness, its contribution to the width of the diffraction rings described below can safely be ignored. Figure 2 shows a series of diffractograms for PC as a function of T p For TC similar sets of diffractograms composed of concentric rings have been published earlier6 and shall only be elaborated further here. Evaluation of the diffractograms is illustrated in Figure 3a. The curve with poor signal-to-noise ratio represents the densitometer reading upon scanning along an arbitrary radius vector of the photographic diffraction ring system.
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Vol. 87, No. 4, 1083
O
.5
1
2
1.5
s [#'I
Flgure 4. Calculated contribution of molecular scattering to the total scattering intensity of tetracene.
Figure 2. Electron diffractograms of asgrown pentacene layers, typically 2000 A thick, deposited at substrate temperatures of 300 (a), 250 (b), 200 (c) 150 (d), 80 (e), and 28 (f) K. Each diffractogram is s u b d i i into four segments reproduced under various exposure times (in the course of the photographic copying procedure). The shortest exposure time (left upper segments) ensures reproduction of ring structure near the central spot whereas the longest exposure time (left lower segments) allows the reproduction of weak outer diffraction rings. a
the true elastic diffraction pattern of the sample, one has to subtract the structureless background arising from the scattering of the undeflected primary beam in the photographic film. In default of an appropriate analytical expression, this had been done by trial and error. It is obvious that both position and width of the diffraction maxima are rather insensitive to slight variations in the background. Inappropriate fitting of the background can, however, mask the presence of weaker signals, especially, if they are buried underneath broad, stronger features. This important point is relevant in subsequent discussions. Utilizing instrumental calibration factors diffraction vs. ring diameter diagrams are subsequently transformed into I(s) diagrams where s = 4 r / X sin (8/2) (see Figure 3b). To check whether the diffractograms for s values of interest (0.2 5 s 5 0.4) are obscured by molecular rather than structural diffraction peaks, we calculated the diffraction spectrum of randomly distributed TC molecules on the basis of the Wierl equation
Flgure 3. Illustration of the analysis of diffractograms. The noisy m e in part a is the densitometer reading upon linear scanning of the analyzing ray along a radius vector of the diffraction ring system: the full curve is the densitometer reading employing the rotating-stage technique; the dashed curve represents estimated background scattering. Part b shows the difference between signal and background taken from part a plotted vs. structure factor s.
The rij's are the mutual distances between the atoms of the molecule and Zj and Z k are atomic numbers. Upon considering only the carbon skeleton of a TC molecule, one obtains a featureless intensity distribution for s < 0.4 A-1 (Figure 4). All observed diffraction features must therefore be characteristic for the intermolecular packing within TC or, similarly, PC films. The essential experimental information derived from the diffractograms is contained in Figures 5 and 6, which show the diffraction intensity I(s) of TC and PC as a function of the temperature of film formation. The diffraction patterns consist of a series of features which are subject to broadening as Tf is lowered. It is important to note that at least two strong features persist down to Tf 20 K and that the position of the maxima remains, to a first approximation, unchanged. To deduce details of the film structure requires assignment of the diffraction peaks. To this end the distances between equivalent lattice planes in the reciprocal lattice ("d spacings") were calculated for the triclinic TC and PC lattices by adopting the literature values for the lattice parameters (a = 7.90 A,b = 6.03 A,c = 13.53 A,a = 100.3', p = 113.2', y = 86.3' for TClO and a = 7.90 A, b = 6.06 A,c = 16.01 A,a = 101.9', p = 112.6', y = 85.8' for PCl'). Owing to the low lattice symmetry this procedure predicts
The ordinate scale is exponential, ensuring that the amplitude is proportional to the density of the diffracted electron beam. The smoothed curve is the densitometer reading employing the rotating-stage technique. To obtain
(10) R. B. Campbell, J. M. Robertson, and J. Trotter, Acta Crystallogr., 15, 289 (1962). (11) R. B. Campbell, J. M. Robertson, and J. Trotter, Acta Crystallogr., 14, 705 (1961).
I
1
I
20
30
40
1
50
1
60
radius [mml
-
.1
.2
.3
.4
s IR'3
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983 547
Structures of Amorphous Tetracene and Pentacene I
1
1
30
20
50
40
60
radius lmml
Figure 7. Band profile analysis of an electron diffractogram taken with a tetracene film (T, = 250 K). Dotted curves are Lorentzians. Peak assignment has been accomplished on the basis of calculated diffraction spectra.
I
I
Figwe 5. Diffraction intensity for asgrown tetracene films. Parameter 1s the film-formation temperature.
... .
.
'
x
2ii
0
020
A
25'TA
i
100
200
Tf
,I
.2
/A-'r
.3
.4
.20i
d
021
I
300 HA EK
IKI
Figure 8. d spacing vs. formation temperature of asgrown TC films. Data points at abscissa positions EK, HA, and TA, respectively, are d spacings calculated on the basis of the room-temperature singiecrystal data set (EK), the refined data set of Table I for a high-temperature phase (HA), and the refined data set of Table I for a iowtemperature phase (TA), respectively.
Figure 8. Diffraction intensity for asgrown pentacene films. Parameter is the film-formation temperature.
50hkl
a much larger number of reflections than are actually observed. Unambiguous assignment of observed to calculated reflections requires the additional knowledge of the intensity distribution within the theoretical diffraction spectrum. Therefore, the intensities of the individual reflections were calculated on the basis of the form factors determined by X-ray analysis.12 This procedure is not strictly correct but it is felt to be a reasonable approximation for finding out the dominant reflections. Finally, the diffraction spectra were subjected to a curve-analyzing procedure. The individual bands were assumed to be Lorentzians. The result is exemplified in Figure 7 for a highly structured TC spectrum. The deconvolution allows the extraction of the width of an individual diffraction peak as a function of temperature. Figures 8 and 9 compare the assigned experimental d spacings obtained for variable Tfwith the values calculated from the crystal structure at room temperature. The overall agreement is satisfactory, yet for some of the re(12) A. Guinier, 'X-ray Diffraction",W. H. Freeman, San Francisco, CA, 1963.
.................-... 0
0
0 li3 _. .e
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03 40-
.23i
cn
.-c
0
0
200
* .
R35I
2ii x2ii
100 Ti
200
300
020
0
0
A
A021
HA EK
IKI
Figure 9. Equivalent to Figure 8 for pentacene films
flections the deviation is beyond the experimental uncertainty. We therefore aimed at improving agreement between theory and experiment by slightly modifying the
548
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
Eiermann et al.
7
TABLE I: Refined Lattice Parameters for 300 and 20 K Films of Tetracene and Pentacene, Respectivelya 7,
a, A
b, A
c, A
01,
p , deg
deg
deg
300 K 20 K singlecrystal
7.90 7.62 7.90
Tetracene 6.25 13.53 6.15 13.30 6.03 13.53
104.5 104.5 100.3
101.0 90.3 101.0 90.3 113.2 86.3
300 K 20 K single crystal
7.90 7.65 7.90
Pentacene 6.06 16.01 103.5 6.01 15.91 103.5 6.06 16.01 101.9
105.0 88.0 105.0 88.0 112.6 85.8
02? I
1
1
0201
20
2\
iio
\
- 0
aJ V c
r
-10
OlOC
E:
IE
005 - 0
200
100 TI
0151
20
100 Tf
200
g
g
300
[KI
Figure 11. Relative width of the 277 and 170 relfections of tetracene films as a function of film-formation temperature. The dashed line has been inferred from the width of optical absorption employing a computer method for correlating positional fluctuations of a molecule and concomitant change of the polarization energy of a singlet exciton. Full circles are analogous data derived from the wk3h of the distribution of valence-band states probed by means of the thermally stimulated current technique.** On the right scale the apparent coherence length is plotted, derived from the width of the diffraction rings under the assumption that scattering occurs by perfect crystallites of dimensions given by the coherence length.
300
IKI
Figure I O . Relative width of the 021, 020, 277, 170, and 200 reflections for asgrown pentacene films as a function of film-formation temperature. For definition of the apparent coherence length see Figure 11.
input lattice parameters. This was done separately for the 300 and 20 K data sets. The lattice parameters which provide an optimum fit are listed in Table I together with the single-crystal data. They are also included in Figures 8 and 9. It should, however, be stressed that the refined sets of lattice parameters may depend on the optimization procedure employed and therefore need not be unique. Figure 10 reveals the essence of the analysis of the PC diffractograms. Starting at high Tf,the relative breadths As/s of the individual reflections increase in qualitatively the same but quantitatively different manners. Thereby the weaker reflections (020) and (021) are amalgamated into the dominating (211) and (110) reflections. The analysis indicates that also the (200) reflection persists down to 28 K. Figure 11 presents the analogous data for the (211) and (1x0) diffraction peaks of TC. I t appears that the (201) reflection at d 4 A which is clearly discernible in Figure 6 at Tf > 120 K vanishes at lower Tp This is most likely an artifact caused by an overestimate of the base line for background scattering. It seems noteworthy to focus attention to some discontinuity in the d spacings occurring at Tfvalues between 175 and 200 K in the case of TC and 150 and 200 K in the case of PC, respectively. Admittedly, the changes are barely outside fluctuations of the experimental data below and above those temperature intervals. However, the dramatic change of the diffraction intensities in the same
-
J
Ig
a Single-crystal data are from ref 9 and 10, respectively, for TC and PC.
0 25
-
c
5100
.-
Q)
c Y
0
:50 aJ
2
+ 0 A
aJ L
I
0
200
100
300
1
T f [KI Flgure 12. Relative peak height of the 170, 020, and 200 reflections for as-grown tetracene films as a function of film-formation temperature.
temperature interval signals some reorganization within the lattice (Figure 12). Interestingly enough, single crystals of tetracene are known to undergo a phase transition near 180 K, the exact value of the transition temperature being subject to modification by external effects, like crystal mounting.13-16 There could well be a correlation between these effects; unfortunately analogous information is not available for the structure of singlecrystalline PC. Remarkably, the width of the reflections, which later will be shown to be a measure for the degree of disorder, is (13)G.Vaubel and H. Biissler, Mol. Cryst. Liq. Cryst., 12,39(1970). (14)J. M.Turlet and M. R. Philpott, J. Chem. Phys., 62,4260(1975). (15)D.D.Kolendritski, M. V. Kurik, and Yu. P. Piryatinski, Phys. Status Solidi B , 91,741 (1979). (16)J. Kalinowski, R.Jankowiak, and H. Bassler, J . Lumin., 22,397 (1981).
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
Structures of Amorphous Tetracene and Pentacene
I
/\
549
a
L
v
I
>
b
0 .I
,2
s lA.7
,3
.4
Figure 13. Diffraction intensity for tetracene films deposited at various depositlon rates. Films in part a were deposited at T I = 80 K: films in part b were deposited at T , = 175 K.
fresh
25 min
35 min
TO
position r
Flgure 15. Schematic representatlon of the mutual potential between two molecules. The smooth curve is the interaction potential for isotropic molecules. Anisotropy of the Intermolecular interaction causes superposition of local fluctuations as a function of intermolecular coordinates. A molecule deposited from the vapor phase onto a condensed fllm will Inblly go Into one of the shallow potential mlnima. At low temperature this structure will be frozen in. At high temperature thermal activation is sufficient to allow attainment of equilibrlum (dashed lines). The dashdotted line represents nonactivated structural relaxation.
80 min 12 hours
24 hours
Flgurs 14. Effect of annealing on the diffraction spectra of a pentacene fllm originally depositedat 28 K. The annealing time is the time elapsed between film formation and recording of the diffractogram. Recording temperatures were 150 K (25 min), 250 K (35 min), and room temperature for the curves corresponding to longer annealing times.
essentially independent of deposition rate if Tf 5 80 K an increase in the deposition rate from 2.3 to 66 A s-l has no effect on the diffraction pattern of a sample deposited at Tf= 80 K (Figure 13a). However, some additional broadening is observed for Tf = 175 K. Further, the diffractograms indicate that films formed at Tf 2 175 K exhibit features of the low-temperature micromodification if the deposition rate was high, whereas at low deposition rate only the high-temperature structure is formed (Figure 13b). This observation lends support to the hypothesis that the ambiguities related with the phase transition in crystalline tetracene near 180 K are due to material inhomogeneities which derive from different crystal growth conditions or from strain developing in nonfreely mounted crystals in the course of a temperature cycling experiment.16 Upon warming TC and PC films originally formed at Tf < 150 K, one observes irreversible narrowing of the diffraction rings indicative of structure ordering (see Figure 14). When annealing occurs above 180 K for 1 day or longer, recrystallization sets in which causes the diffraction rings to decompose into a concentric array of diffraction spots. Evidence for formation of microcrystals can also be obtained by running the TEM experiments in the direct image rather than the diffraction mode. Ultimately, growth of crystallites is visible even under the polarizing
microscope. Further details will be communicated elsewhere.
Discussion One of the essential results of this work is the observation that the d spacings of TC and PC films are to a first approximation both independent of the temperature of film formation as well as identical with the d spacings expected for single-crystallinematerial. This demonstrates the presence of short-range order, which obviously derives from the molecular packing. According to Kitaigorodsky," the latter is mainly determined by the atom-atom interaction potentials of the molecules involved. Due to their short-range nature in a molecular solid the intermolecular packing should be rather insensitive to the conditions under which a solid structure is formed. Whereas growth of a single crystal will usually proceed under conditions close to thermodynamic equilibrium, vapor deposition onto a cold substrate occurs under constraints imposed by external means, like deposition rate and substrate temperature, and is as such a process far from thermodynamic equilibrium. A molecule impinging on the surface of the substrate will not, in general, be able to relax to the position of minimum potential energy but will be trapped in shallow local minima of the potential surface (see Figure 15). A8 a consequence, the spatial coordinates of an array of molecule will on average be close to those of the fully relaxed crystal structure, but the coordinates of individual molecules will be subject to statistical fluctuation. The result will be a structure which lacks long-rangeorder and which will be subject to disorder on the short-range-order level. There is no way to derive directly information on both degree and kind of disorder from the diffraction pattern. This would require the setting up of a model lattice in which both positions and orientations of the molecules are subject to some fluctuations. Even such a procedure ap(17)A. I. Kitaigorodski, Tetrahedron, 9, 183 (1960).
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The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
Flgure 18. View of the ab plane of the tetracene unit cell. The dashed area at (1/2,’/2,0) indicates the average posttional fluctuation of the center of mass of a tetracene molecule in an amorphous film deposlted at T , < 80 K. For comparison the projection of a molecule at (O,O,O,) onto the (0,O.l) plane is included.
pears unrealistic for a structure of low symmetry, if positional correlations are properly included. Alternatively two routes can be followed to derive information regarding disorder from the width of the diffraction rings. As one extreme case the structure can be considered as being a composite of perfect crystallites of limited size. Simple theory says that in this case the relative reciprocal width s/As of a certain reflection equals the number of lattice planes within the crystallite.12 Absolute numbers are included in Figures 10 and 11. For the (1iO) reflection the limiting value at T = 20 K is s/As 5. Since the d spacing is about 4.7 a “coherence length” of the structure of -24 A follows, equivalent to about 4 unit cells within the ab plane. In the other extreme the broadening of a particular reflection may arise as the result of uncorrelated linear fluctuations of the d spacing between a given set of lattice planes. According to the paracrystal concept for a onedimensional array of lattice points with average mutual distances a f Aa, the average positional fluctuation along a certain lattice direction is related to the relative width of a reflection feature by hala = (l/a)(A~/s)~/~.~~ Using the PC data from Figure 10 in the T 0 limit, one can estimate the positional fluctuations of a molecule located at (1/2,1/2,0) along the [IIO], [2,1,1], [2,0,0], and [0,2,0] directions. The result shown in Figure 16 indicates that on average the position of the molecule at (1/2,1/2,0) agrees with the position in the single-crystal structure but is subject to fluctuation on the order of 10%. It is noteworthy that the positional fluctuations are slightly anisotropic. They are highest in directions pointing to the openings of the unit cell. This appears to be a reasonable result and in turn raises confidence in this procedure of data evaluation. Clearly, absolute values for positional fluctuation should be considered with caution, since correlation in the fluctuation of neighboring molecules has been ignored. Since no (0,0,1) reflections are observed, no information concerning the positional fluctuation of the molecules along the [0,0,1] direction, which is close to the direction of long molecular axes, is available. One reason is that in a pseudo P2/a crystal structure the (0,0,1)reflection is very weak and, owing to the large value of c, would be buried underneath the central spot in the dif-
1,
-
-
81.
fraction pattern. The allowed (0,0,2) reflection would be difficult to distinguish from the strong (201) or (2,0,0) reflections. In addition, it seems likely that amorphous organic films of the thickness employed herein exhibit features of epitaxial growth. There is clear evidence that polycrystalline films deposited at Tf > 180 K grow with their (0,0,1) faces parallel to the substrate which is kept perpendicular to the electron beam. This is a consequence of the anisotropic intermolecular coupling among neighboring polyacene molecules. Since this anisotropy is strong enough to establish short-range order within the amorphous phase, it is likely to control also the surface orientation of a TC or PC layer even when deposited onto a substrate held at Tf
