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Single-crystal and synchrotron X-ray powder diffraction study of the one-dimensional orthorhombic polymer phase of C60
Chemical Physics Letters 460 (2008) 93–99
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Single-crystal and synchrotron X-ray powder diffraction study of the one-dimensional orthorhombic polymer phase of C60 R.J. Papoular a,*, B.H. Toby b, V.A. Davydov c, A.V. Rakhmanina c, A. Dzyabchenko d, H. Allouchi e, V. Agafonov f a
IRAMIS, Léon Brillouin Laboratory, CEA/CEN-Saclay, 91191 Gif-sur-Yvette, France Advanced Photon Source, Argonne National Laboratory, IL 60439-4856, USA c Vereshchagin Institute of High-Pressure Physics of the RAS, 142092 Troitsk, Russia d Karpov Institute of Physical Chemistry, Vorontsovo Pole 10, 103064 Moscow, Russia e Laboratoire de Synthèse Physico-Chimique et Thérapeutique, EA 3857, Université François Rabelais, 37200 Tours, France f Laboratoire d’Electrodynamique des Matériaux Avancés, UMR CNRS-CEA 6157, Université François Rabelais, 37200 Tours, France b
a r t i c l e
i n f o
Article history: Received 31 January 2008 In final form 15 May 2008 Available online 21 May 2008
a b s t r a c t The 1D-orthorhombic polymer phase of C60 was originally mentioned in 1995. The present work provides the first direct experimental quantitative evidences of the 1D-polymer chains, clearly seen by single-crystal diffraction. Geometrical details of the [2+2]-cycloaddition rings are compared with those of C60 dimers and 2D-polymers. Another key structural parameter is the angle of rotation W of the 1D chains about the polymerization axis. Single-crystal diffraction yields W 78°, whereas accurate synchrotron powder diffraction independently produces a similar W 73°. These values are in qualitative agreement with a former theoretical prediction (W 61°). Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Polymeric phases of C60 have been studied for the last 15 years and covered by books [1] and reviews [2]. If the key process to their elaboration remains the [2+2]- or [3+3]-cycloaddition between neighboring buckyballs, these polymerized crystalline materials can be obtained via many routes. The chemical way results in intercalated compounds, e.g. A1C60, where A is an alkali ion. Historically the first to be observed by X-ray [3] or neutron [4] powder diffraction, they are successfully understood using phenomenological models [5,6]. By contrast, pure C60 polymers are essentially elaborated through high-pressure high-temperature treatments (HPHTT) [7–9]. Only the following phases have been observed experimentally: 1D-orthorhombic (O), 2D-rhombohedral (R), 2Dtetragonal (T) and 3D-orthorhombic. The structures of all but the 1D-O phase have been characterized by single-crystal diffraction [10–13]. This Letter aims at filling this gap. It has recently been demonstrated [14–16] using either Raman or X-rays that this 1D-O phase can be further polymerized towards another new phase of lower symmetry under the in situ combined action of electromagnetic radiation and high-pressure, providing yet another incentive to understand its structure in more details. Most relevant published findings comprise: (i) the determination of the crystal spatial symmetry of the O phase using X-rays,
initially found to be Immm by powder diffraction [8] and later refined to be Pmnn by single-crystal diffraction [17], (ii) ab-initio modeling that involves molecular packing calculations based on an empirical atom–atom potential to account for both van der Waals and electrostatic interactions between buckyballs [18], and which predicts the results found in the present study semiquantitatively, and (iii) the description of the polymerized 1D chains as previously obtained with the A1C60 compounds by Xray [3] or neutron [4] powder diffraction. The O phase involves a periodic assembly of 1D-chain pairs, parallel to the polymerization shorter axis a of the orthorhombic unit cell and rotated by ±W about the latter axis. Within a given chain, neighboring buckyballs are arranged such that double bonds face each other prior to [2+2]-cycloaddition. Beside W, other salient features are the lengths d1 and d2 of the single intra- and inter-C–C bonds created during the cycloaddition process [3,4]. This work originates from the earlier observation made by Moret et al. [17], that the angle W cannot be derived reliably from their single-crystal study. It demonstrates that W can indeed be derived from single-crystal data, and also be estimated using powder diffraction.
2. Experimental 2.1. Preparation of the samples [HPHTT]
* Corresponding author. Fax: +33 (0)1 6908 8261. E-mail address: [email protected] (R.J. Papoular). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.05.046
The O phase was obtained from HPHT treatments of high-purity (99.98%) fullerite C60 in piston-cylinder-type high-pressure devices
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Table 1 Single-crystal experiment at T = 150 K: description and results Crystal data C60 Mr = 720.642 Orthorhombic, Pmnn [#58 ] a = 9.091(3) Å b = 9.780(3) Å c = 14.752(4) Å V = 1311.7(6) Å3 Z=2 Data collection Kappa CCD diffractometer (Nonius) Mo Ka [k = 0.71073 Å]
6131 measured reflections 1426 independent reflections 1240 reflections with I > 2 r (I)
Structure solution Structure refinement
SHELXS (tangent refinement) SHELXL
Model # 1: unrestrained (cf. Fig. 2) X C01 0.1400(15) C02 0.1565(11) C03 0.1498(14) C04 0.2798(12) C05 0.0800(12) C06 0.340(2) C07 0.0733(12) C08 0.2493(14) C09 0.1271(12) C10 0.066(2) C11 0.4065(18) C12 0.327(2) C13 0.0000 C14 0.2814(17) C15 0.257(2) C16 0.0000 Euler angle X = 80.2°
Rint = 0.0529
Model # 2: fully restrained (cf. Fig. 3)
Model # 3: partially restrained (best chemical model)
Z
X
Y
0.3210(8) 0.4680(6) 0.6227(7) 0.4853(6) 0.3867(7) 0.4227(6) 0.5523(7) 0.6820(8) 0.7221(9) 0.6922(9) 0.45380(13) 0.6118(6) 0.7409(13) 0.5805(6) 0.3386(7) 0.7197(11)
0.1296(6) 0.1573(9) 0.1553(10) 0.2853(12) 0.07975(11) 0.3349(13) 0.07699(11) 0.2550(11) 0.1293(6) 0.07974(11) 0.412(2) 0.3342(14) 0.0000 0.2821(12) 0.2542(10) 0.0000
0.7884(10) 0.3206(8) 0.6734(13) 0.4683(6) 0.7289(12) 0.6235(7) 0.7578(12) 0.4859(5) 0.6894(12) 0.3870(7) 0.8525(13) 0.4216(7) 0.6567(12) 0.5525(6) 0.9872(8) 0.6850(8) 0.9299(9) 0.7245(9) 0.7974(11) 0.6926(8) 0.9846(10) 0.4520(13) 0.9186(11) 0.6128(8) 1.0122(10) 0.7427(12) 0.7926(11) 0.5814(6) 0.8685(9) 0.3375(7) 1.1515(11) 0.7206(11) Euler angle X = 78.0°
Y
Z
X
Y
0.7940(12) 0.6740(8) 0.7274(12) 0.7574(10) 0.6941(10) 0.850(3) 0.6570(10) 0.9672(16) 0.9499(15) 0.795(2) 1.0134(19) 0.903(4) 1.010(2) 0.7986(14) 0.866(2) 1.130(2)
0.3279(7) 0.4651(7) 0.6258(7) 0.4796(8) 0.3894(8) 0.419(2) 0.5530(7) 0.6804(10) 0.7247(8) 0.6902(11) 0.4486(9) 0.6158(10) 0.7389(15) 0.5818(15) 0.3484(13) 0.7204(10)
0.1297(7) 0.7894(10) 0.1569(10) 0.6709(13) 0.1555(10) 0.7277(12) 0.2852(13) 0.7549(11) 0.07975(11) 0.6894(13) 0.3357(13) 0.8516(8) 0.07699(11) 0.6543(13) 0.2542(12) 0.9866(8) 0.1295(7) 0.9285(9) 0.07974(11) 0.7951(11) 0.3881(15) 0.9836(7) 0.3367(13) 0.9168(8) 0.0000 1.0104(11) 0.2821(13) 0.7915(11) 0.2549(11) 0.8684(9) 0.0000 1.1499(12) Euler angle X = 76.7°
Z
Bond lengths involved in the [2+2]-cycloaddition ring (Å): D(C11–C11) inter = 1.70(3) D(C11–C11) intra = 1.54(3) D(C11–C06) = 1.76(3) D(C11–C12) = 1.45(4)
D(C11–C11) inter = 2.04(2) D(C11–C11) intra = 1.400(2) D(C11–C06) = 1.450(2) D(C11–C12) = 1.4502(14)
D(C11–C11) inter = 1.61(4) D(C11–C11) intra = 1.45(4) D(C11–C06) = 1.535(17) D(C11–C12) = 1.519(18)
Comparison with previously published experimental results: Tetragonal polymer [11]: ring 1 D(C7–C7*) inter = 1.605(8) D(C7–C7) intra = 1.585(8) D(C6–C7) = 1.515(4)
Tetragonal polymer [11]: ring 2 D(C9–C9*) inter = 1.575(8) D(C9–C9) intra = 1.562(9) D(C9–C2) = 1.529(4)
Dimer [25] D(C1–C1*) inter = 1.575(7) D(C1–C2) intra = 1.581(7) D(C1–C6) = 1.528(7) D(C2–C3) = 1.530(8)
Tetragonal polymer [12]: ring 1 D(C1–C0 1) inter = 1.60(1) D(C1–C10 ) intra = 1.62(1) D(C1–C6) = 1.521(5)
Tetragonal polymer [12]: ring 2 D(C3–C0 3) inter = 1.56(1) D(C3–C30 ) intra = 1.58(1) D(C3–C4) = 1.529(5)
Rhombohedral polymer [10] D(C1–C1*) inter = 1.587(6) D(C1–C1) intra = 1.606(6) D(C1–C2) = 1.514(4) D(C1–C3) = 1.509(4)
All the 16 unique C-atoms are found by direct methods. The rotation angle X of the 1D polymer chains is derived from only one of them, C11, though the formula: tan X = {c j0.5 z j}/{b j1.0 yj}.
Fig. 1. Chemical characterization of the samples using Raman Spectroscopy. The single-crystal sample (left) evidences traces of the Tetragonal phase of 2D polymerized C60. The two corresponding characteristic spectral lines, at 1449 cm1 and 1465 cm1 respectively, are marked by (T). By contrast, the powder samples (right) used in this study do not hint at the presence of any impurity phase. Only parts of the measured Raman spectra are displayed.
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R.J. Papoular et al. / Chemical Physics Letters 460 (2008) 93–99 Table 2 Two powder diffraction experiments: Synchrotron vs. Laboratory. They yield the same rotation angle of the 1D chains 73°.The Rietveld refinements are first carried out at fixed values of the Euler angle X to find the optimal one
Crystal data C60 Mr = 720.642 Orthorhombic Pmnn [# 58, Pnnm] a (Å) b (Å) c (Å) V (Å3) Z=2 Data collection Powder diffractometer Wavelength (Å) Transmission mode Capillary geometry Angular range (°) Temperature (K) Refinement GSAS profile function (i) Without preferred orientation Rp Rwp R(F2) Reduced v2
Synchrotron X-rays: 11BM
Laboratory X-rays: INEL
9.0979 (12) 9.8325 (17) 14.6587 (27) 1311.3 (0.5)
9.1284 (26) 9.8938 (44) 14.6503 (53) 1323.14 (103)
0.40230
1.54060 [Cu Ka1]
Kapton [29], U = 0.8 mm 2.2–6.5 Room temperature
Lindemann, U = 0.5 mm 8–32 Room temperature
Constant wavelength, type 3
Constant wavelength, type 4
0.1247 0.1682 0.0780 2.248
0.0780 0.1117 0.0784 104.6
(ii) With preferred orientation P.O. order Texture index (TI) Rp Rwp R(F2) Reduced v2
(cf. Fig. 4)
(cf. Fig. 5)
6 1.195 0.0985 0.1355 0.0785 1.470
8 1.261 0.0399 0.0552 0.0302 26.30
Euler angle X (°)
72.5
73
Only then is preferred orientation refined, for that optimal value Xopt, resulting in a very mild texture index but in a susbtantial improvement of the Rietveld fit.
[9,19]. The O phase crystals were produced at ambient conditions by quenching down to room temperature under pressure. 2.2. Chemical characterization of the samples [Raman] HPHT crystals were first characterized by Raman spectroscopy, using a Dilor XY spectrometer equipped with a Kr+ laser operating at a wavelength of 568.2 nm (yellow). All three O, T and R C60 polymer phases are endowed with specific Raman fingerprints (see Fig. 3 of Ref. [20]). The Raman screening resulted into two kinds of crystals: (i) a pure O phase (A) and (ii) a phase (B) containing additional bands probably related to the 2D-T phase. All crystals (A) were found to be twinned. One item suitable for single-crystal work was eventually selected from batch (B). Crystals from batch (A) were ground for powder diffraction experiments. Relevant Raman spectra are shown in Fig. 1.
Table 3 Modeled C60 buckyball assuming d(C–C) = 1.45 Å and d(C@C) = 1.40 Å C#
X (Å)
Y (Å)
Z (Å)
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
0.014430 0.014430 1.226870 1.241300 1.226870 1.241300 2.322720 2.177270 2.322720 0.145450 2.177270 0.145450 3.000000 1.500000 1.500000 0.912620 2.168350 3.080970 3.080970 0.912620 2.168350 1.749770 1.749770 3.499550 2.685750 3.339670 0.653920 0.653920 3.339670 2.685750 3.339670 0.653920 2.685750 0.653920 2.685750 3.339670 1.749770 3.499550 1.749770 0.912620 3.080970 2.168350 2.168350 0.912620 3.080970 1.500000 1.500000 3.000000 0.145450 2.177270 0.145450 2.177270 2.322720 2.322720 1.226870 1.241300 0.014430 0.014430 1.241300 1.226870
1.425000 1.425000 0.725000 0.700000 0.725000 0.700000 1.173070 1.425000 1.173070 2.598070 1.425000 2.598070 0.000000 2.598070 2.598070 3.030700 2.305700 0.725000 0.725000 3.030700 2.305700 3.030700 3.030700 0.000000 2.305700 1.173070 3.478770 3.478770 1.173070 2.305700 1.173070 3.478770 2.305700 3.478770 2.305700 1.173070 3.030700 0.000000 3.030700 3.030700 0.725000 2.305700 2.305700 3.030700 0.725000 2.598070 2.598070 0.000000 2.598070 1.425000 2.598070 1.425000 1.173070 1.173070 0.725000 0.700000 1.425000 1.425000 0.700000 0.725000
3.249770 3.249770 3.249770 3.249770 3.249770 3.249770 2.412620 2.412620 2.412620 2.412620 2.412620 2.412620 1.895220 1.895220 1.895220 1.604330 1.604330 1.604330 1.604430 1.604330 1.604330 0.587380 0.587380 0.587380 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.587380 0.587380 0.587380 1.604330 1.604330 1.604330 1.604330 1.604330 1.604330 1.895220 1.895220 1.895220 2.412620 2.412620 2.412620 2.412620 2.412620 2.412620 3.249770 3.249770 3.249770 3.249770 3.249770 3.249770
The orthonormal coordinates of the 60 atoms define the rigid body used in the XRPD/GSAS refinements aiming at finding the optimal Euler angle X, which characterizes the rotation of the 1D C60 polymer chains. Neither do they depend on the crystal symmetry nor on the unit cell.
2.3. Single-crystal X-ray diffraction [SXD] 2.4. Synchrotron vs. laboratory X-ray powder diffraction [XRPD] A Nonius Kappa CCD diffractomer equipped with a graphite monochromator and Mo Ka radiation was used to collect a nearly complete dataset up to 2h = 57.2° (0.8 Å) at low temperature (T = 150 K) (Table 1). The limited quality of the crystal used prompted us to carry out the additional measurements described hereafter.
A first XRPD experiment was carried out on our in-house INEL CPS 120 diffractometer using Cu Ka monochromatic radiation at room temperature. The resulting value of the angle W of rotation of the 1D chains was checked via another experiment, carried out at the 11-BM synchrotron beamline of the APS/ANL using a
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Fig. 2. Unrestrained structure solution obtained by means of single-crystal diffraction at T = 150 K. The first view (top) down the short-axis a exhibits appreciably distorted buckyballs, whereas the second (bottom), perpendicular to this axis a, directly evidences the 1D-polymeric nature of the sample.
Fig. 3. Fully restrained structure solution obtained using single-crystal diffraction. A single independent C atom (boldened) is enough to derive: (i) the rotation angle X of 1D-polymer chains (top) and (ii) the inter- and intra- d(C–C) bond lengths resulting from the [2+2] cycloaddition between neighboring buckyballs (Bottom). X 78° turns out to be largely independent of the applied restraints.
much shorter wavelength (0.40230 Å) as well as a detector bank equipped with analyzers and featuring a perfect 2h-linearity. The latter is not warranted by the INEL CPS detector. Experimental details are listed and compared in Table 2. The same W value (73°) is found in both cases.
angle W is changed incrementally and then kept fixed in subsequent energy minimization runs. The absolute minimum yields the optimal W. In all configurations, the 1D chains rotate synchronously so that Pmnn symmetry is maintained.
3. Results
3.2. Analysis of the SXD data using ShelX [23]
3.1. Modeling
Direct methods are first applied to solve the crystal structure and retrieve the first 14 independent C-atoms, corresponding to C60 units located at (2-b) positions in the unitcell. The remaining 2 unique C-atoms are found by difference Fourier. The structure is then refined [model #1], yielding recognizable 1D chains of somewhat deformed buckyballs 1.7 Å apart, as visualized in Fig. 2 using Mercury [24]. A single unique atom, labeled C11 in Table 1 and emphasized in Fig. 3, contains all the wanted structural information: W, dintra and dinter. Most noticeably, W 80° and dinter 1.699 Å. Due to the real material used, with its 2D-T phase contamination mentioned above and possible disorder and defects, the final R1-factor remains large (0.28). Restraining the buckyballs to Ih symmetry worsens R1 to 0.43, but W 78° is hardly affected [model #2]. The optimal estimations of dintra 1.45 Å and dinter 1.61 Å are obtained by (i) relaxing the restraints involving the strategic C11 atom whilst maintaining the mirror plane throughout each 1D-chain and (ii) assuming an overall temperature factor (Uiso 0.035 Å2) [model #3]. W remains unchanged and the R1-factor settles at the intermediate value 0.418. In an attempt to get rid of extraneous contributions from the T phase
3.1.1. A single C60 unit Modeling an idealized buckyball assuming Ih symmetry, d(C–C) = 1.45 Å and d(C@C) = 1.40 Å, serves two purposes: (i) create appropriate restraints for single-crystal refinements, and (ii) build constraints for powder refinements via the use of a rigid body [Table 3]. It is the keystone of the XRPD data analysis discussed below. 3.1.2. The 1D-orthorhombic crystal The modeling procedure is partially described in [18]. Only additional details are given here. The van der Waals energy is calculated as a sum of atom–atom pairwise interactions involving a Lennard-Jones (6–12) potential, which is minimum (Vmin = 0.0722 kcal/mol) for rmin = 3.7 Å. The electrostatic energy is calculated assuming point charges of 0.5e and +0.25e placed at the middle of double and single bonds respectively, following a model proposed by Lu et al. [21]. Lattice sums are computed using an Ewald-like procedure introduced by Williams [22] and characterized by two parameters (Rcut = 9 Å; Kconv = 0.175). The rotation
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[11,12], all 3067 hkl reflections with h + k + l = 2n were removed from the dataset, resulting in a mild improvement only and thus hinting at the presence of residual structural defects. Geometrical details of the [2+2]-cycloaddition rings for all three models are reported in Table 1, where they are compared with those obtained from previous studies of C60 2D-polymers [10–12] and dimers [25]. Model #3 is the most chemically sound, in spite of the too small value of dintra (1.45 Å) which is likely to result from the remaining applied restraints, borne from a single C60 unit for which dintra = d(C@C) = 1.40 Å [model #2]. 3.3. Analysis of the XRPD data using GSAS [26] The great number of independent atomic coordinates involved, the Bragg peak overlap and too few sizable intensities forbid the ab-initio solving of the O phase. A simple model with few structural parameters must be refined instead. Using the idealized Ih buckyballs defined in (3.1.1) as rigid bodies restricts the number of structural parameters to one: the angle W, which can be identified with the Euler angle X within GSAS. Centering the buckyballs
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at positions (2-a) within the unit cell turns out to be equivalent to using the positions (2-b) found by SXD. Hereafter, we stick to the former to comply with the Literature. We use a three-step Rietveld refinement strategy: (i) refine the lattice and instrument parameters. Then (ii) keep them fixed and refine only the scale factor at a given X-value, which results in a v2[X] dependence very similar to the V[W] dependence obtained above by modeling: the absolute minimum of v2[X] yields the optimal Xopt. Finally, (iii) optimize the Rietveld fit at constant Xopt, which does not affect the latter. The reliability of Xopt is first checked by comparing results obtained from two distinct experiments, whose results are reported in Table 2, Fig. 4 [Synchrotron] and Fig. 5 [Laboratory]. For either experiment, the instrument parameters are derived in different ways, which results in distinct v2[X] dependences. We use two different linewidth profiles with the synchrotron data, whereas we LeBail-fit and independently Rietveld refine an isotropic spherical shell mimicking the buckyball with the laboratory data. In all cases: (i) Xopt = Wopt 73°, a value close to WSXD 78° found by different means and in qualitative agreement with Wmodeling 61 ° [18] as
Fig. 4. Synchrotron powder diffraction is used to determine the rotation angle X (=?) of the 1D chains by making use of a single independent rigid body (ubiquitous C60 buckyball) and one appropriate Euler angle [X, within GSAS]. v2 exhibits a marked dependence with X and an absolute minimum for X 72.5°. Both of these results survive even if an inadequate linewidth profile is used (top). Rietveld refinements (bottom) are carried out at frozen sampled X values. Measurements carried out at room temperature.
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Fig. 5. Laboratory X-ray powder diffraction using an INEL CPS 120 detector was also used for comparison, yielding essentially the same results, i.e., X 73° and a similar trend for the v2-dependence on X (top, right), in agreement with the molecular modeling prediction (top, left) by [18]. Here, the robustness of the v2-dependence on X is demonstrated by optimizing the intrument parameters in two different ways: (i) via a model-free Le Bail analysis and (ii) via a Rietveld fit of a uniform spherical shell for C60, which is noncommittal about the X angle. The latter yields the best optimal Rietveld fit (bottom) since the fitted background parameters are closer to their end values. Measurements carried out at room temperature.
well as far distinct from WAC60 45° [3–5]. Not only (ii) is the v2[X] trend always the same but (iii) it remains in semi-quantitative agreement with the V[W] dependence predicted by modeling ([18], Fig. 5). 4. Concluding remarks Firstly, when analyzing powder data, going beyond an isotropic spherical model to describe buckyballs is only justified if the more elaborate model involving discrete C-atoms produces a better fit to the data. In the case of the powder laboratory data, v2 drops from 106.5 to 104.6 when preferred orientation (using spherical harmonics) is not refined, and from 27.93 to 26.30 when it is. Secondly, two phenomenological theoretical models are currently competing to account for orthorhombic (C60)n and related compounds. Dzyabchenko’s et al. [18] is the most successful in
connection with the present work but it introduces ad hoc electrical charges [21] the use of which remains to be justified from fundamental quantum mechanical considerations. Michel’s [5,6,27] involves a more elaborate forcefield that avoids these charges and the parameters of which are trained on other well-documented C60 compounds. Further developed by Verberck [28], it still fails to account for 1D-O C60. In conclusion, new experimental results have been presented, which provide one more step towards the understanding of the C60 polymerization process. Acknowledgements The authors gratefully acknowledge useful discussions with Prof. K.H. Michel and Dr. B. Verberck (University of Antwerp), help with the single-crystal measurements from Dr. L. Ricard (Ecole
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Polytechnique, Palaiseau) and assistance with the use of GSAS from Dr. R.B. Von Dreele (Argonne National Laboratory). This work is supported by the Russian Foundation for Basic Research [Grants No. 06-03-32050 and 05-03-32808 ]. Use of the APS is supported by the US Department of Energy under contract DE-AC0206CH11357. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2008.05.046. References [1] P.C. Eklund, A.M. Rao (Eds.), Fullerene Polymers and Fullerene Polymer Composites, Springer, Berlin, Heidelberg, 2000. [2] R. Moret, Acta Crystallogr. A61 (2004) 62. [3] P.W. Stephens, G. Bortel, G. Faigel, M. Tegze, A. Jánossy, S. Pekker, G. Oszlanyi, L. Forró, Nature 370 (1994) 636. [4] H.M. Guerrero, R.L. Cappelletti, D.A. Neumann, T. Yildirim, Chem. Phys. Lett. 297 (1998) 265. [5] K.H. Michel, A.V. Nikolaev, Phys. Rev. Lett. 85 (2000) 3197. [6] B. Verberck, K.H. Michel, A.V. Nikolaev, J. Chem. Phys. 116 (2002) 10462. [7] Y. Iwasa, et al., Science 264 (1994) 1570.
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[8] M. Nuñez-Regueiro, L. Marques, J.-L. Hodeau, O. Berthoux, M. Perroux, Phys. Rev. Lett. 74 (1995) 278. [9] V.A. Davydov et al., Phys. Rev. B61 (2000) 11936. [10] X. Chen, S. Yamanaka, K. Sako, Y. Inoue, M. Yasukawa, Chem. Phys. Lett. 356 (2002) 291. [11] X. Chen, S. Yamanaka, Chem. Phys. Lett. 360 (2002) 501. [12] B. Narymbetov, et al., Chem. Phys. Lett. 367 (2003) 157. [13] S. Yamanaka, A. Kubo, K. Inumaru, K. Komaguchi, N.S. Kini, T. Inoue, T. Irifune, Phys. Rev. Lett. 96 (2006) 076602. [14] K.P. Meletov, V.A. Davydov, A.V. Rakhmanina, V. Agafonov, G.A. Kourouklis, Chem. Phys. Lett. 416 (2005) 220. [15] R. Le Parc, et al., Chem. Phys. Lett. 438 (2007) 63. [16] K.P. Meletov, G.A. Kourouklis, Chem. Phys. Lett. 443 (2007) 127. [17] R. Moret, P. Launois, P.-A. Persson, B. Sundqvist, Europhys. Lett. 40 (1997) 55. [18] A.V. Dzyabchenko, V.N. Agafonov, V.A. Davydov, Crystallogr. Reports 44 (1999) 17. [19] V. Agafonov, et al., Chem. Phys. Lett. 267 (1997) 193. [20] V.M. Senyavin, et al., Chem. Phys. Lett. 313 (1999) 421. [21] J.P. Lu, X.-P. Li, R.M. Martin, Phys. Rev. Lett. 68 (1992) 1551. [22] D.E. Williams, Acta Crystallogr. A27 (1971) 452. [23] G.M. Sheldrick, SHELXL-97, Program for the Refinement of Crystal Structures, University of Göttingen, Germany, 1997. [24] Program MERCURY 1.4.2, Cambridge Crystallographic Data Center, UK. [25] G.-W. Wang, K. Komatsu, Y. Murata, M. Shiro, Nature 387 (1997) 583. [26] A.C. Larson, R.B. Von Dreele, Report No. LAUR 86-748, Program GSAS for Windows, Los Alamos National Laboratory, New Mexico, USA, 1987. [27] D. Lamoen, K.H. Michel, J. Chem. Phys. 101 (1994) 1435. [28] B. Verberck, PhD Thesis, Antwerpen, Belgium, 2005. [29] R.B. Von Dreele, J. Appl. Cryst. 39 (2006) 124.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Single-crystal and synchrotron X-ray powder diffraction study of the one-dimensional orthorhombic polymer phase of C60 R.J. Papoular a,*, B.H. Toby b, V.A. Davydov c, A.V. Rakhmanina c, A. Dzyabchenko d, H. Allouchi e, V. Agafonov f a
IRAMIS, Léon Brillouin Laboratory, CEA/CEN-Saclay, 91191 Gif-sur-Yvette, France Advanced Photon Source, Argonne National Laboratory, IL 60439-4856, USA c Vereshchagin Institute of High-Pressure Physics of the RAS, 142092 Troitsk, Russia d Karpov Institute of Physical Chemistry, Vorontsovo Pole 10, 103064 Moscow, Russia e Laboratoire de Synthèse Physico-Chimique et Thérapeutique, EA 3857, Université François Rabelais, 37200 Tours, France f Laboratoire d’Electrodynamique des Matériaux Avancés, UMR CNRS-CEA 6157, Université François Rabelais, 37200 Tours, France b
a r t i c l e
i n f o
Article history: Received 31 January 2008 In final form 15 May 2008 Available online 21 May 2008
a b s t r a c t The 1D-orthorhombic polymer phase of C60 was originally mentioned in 1995. The present work provides the first direct experimental quantitative evidences of the 1D-polymer chains, clearly seen by single-crystal diffraction. Geometrical details of the [2+2]-cycloaddition rings are compared with those of C60 dimers and 2D-polymers. Another key structural parameter is the angle of rotation W of the 1D chains about the polymerization axis. Single-crystal diffraction yields W 78°, whereas accurate synchrotron powder diffraction independently produces a similar W 73°. These values are in qualitative agreement with a former theoretical prediction (W 61°). Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Polymeric phases of C60 have been studied for the last 15 years and covered by books [1] and reviews [2]. If the key process to their elaboration remains the [2+2]- or [3+3]-cycloaddition between neighboring buckyballs, these polymerized crystalline materials can be obtained via many routes. The chemical way results in intercalated compounds, e.g. A1C60, where A is an alkali ion. Historically the first to be observed by X-ray [3] or neutron [4] powder diffraction, they are successfully understood using phenomenological models [5,6]. By contrast, pure C60 polymers are essentially elaborated through high-pressure high-temperature treatments (HPHTT) [7–9]. Only the following phases have been observed experimentally: 1D-orthorhombic (O), 2D-rhombohedral (R), 2Dtetragonal (T) and 3D-orthorhombic. The structures of all but the 1D-O phase have been characterized by single-crystal diffraction [10–13]. This Letter aims at filling this gap. It has recently been demonstrated [14–16] using either Raman or X-rays that this 1D-O phase can be further polymerized towards another new phase of lower symmetry under the in situ combined action of electromagnetic radiation and high-pressure, providing yet another incentive to understand its structure in more details. Most relevant published findings comprise: (i) the determination of the crystal spatial symmetry of the O phase using X-rays,
initially found to be Immm by powder diffraction [8] and later refined to be Pmnn by single-crystal diffraction [17], (ii) ab-initio modeling that involves molecular packing calculations based on an empirical atom–atom potential to account for both van der Waals and electrostatic interactions between buckyballs [18], and which predicts the results found in the present study semiquantitatively, and (iii) the description of the polymerized 1D chains as previously obtained with the A1C60 compounds by Xray [3] or neutron [4] powder diffraction. The O phase involves a periodic assembly of 1D-chain pairs, parallel to the polymerization shorter axis a of the orthorhombic unit cell and rotated by ±W about the latter axis. Within a given chain, neighboring buckyballs are arranged such that double bonds face each other prior to [2+2]-cycloaddition. Beside W, other salient features are the lengths d1 and d2 of the single intra- and inter-C–C bonds created during the cycloaddition process [3,4]. This work originates from the earlier observation made by Moret et al. [17], that the angle W cannot be derived reliably from their single-crystal study. It demonstrates that W can indeed be derived from single-crystal data, and also be estimated using powder diffraction.
2. Experimental 2.1. Preparation of the samples [HPHTT]
* Corresponding author. Fax: +33 (0)1 6908 8261. E-mail address: [email protected] (R.J. Papoular). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.05.046
The O phase was obtained from HPHT treatments of high-purity (99.98%) fullerite C60 in piston-cylinder-type high-pressure devices
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Table 1 Single-crystal experiment at T = 150 K: description and results Crystal data C60 Mr = 720.642 Orthorhombic, Pmnn [#58 ] a = 9.091(3) Å b = 9.780(3) Å c = 14.752(4) Å V = 1311.7(6) Å3 Z=2 Data collection Kappa CCD diffractometer (Nonius) Mo Ka [k = 0.71073 Å]
6131 measured reflections 1426 independent reflections 1240 reflections with I > 2 r (I)
Structure solution Structure refinement
SHELXS (tangent refinement) SHELXL
Model # 1: unrestrained (cf. Fig. 2) X C01 0.1400(15) C02 0.1565(11) C03 0.1498(14) C04 0.2798(12) C05 0.0800(12) C06 0.340(2) C07 0.0733(12) C08 0.2493(14) C09 0.1271(12) C10 0.066(2) C11 0.4065(18) C12 0.327(2) C13 0.0000 C14 0.2814(17) C15 0.257(2) C16 0.0000 Euler angle X = 80.2°
Rint = 0.0529
Model # 2: fully restrained (cf. Fig. 3)
Model # 3: partially restrained (best chemical model)
Z
X
Y
0.3210(8) 0.4680(6) 0.6227(7) 0.4853(6) 0.3867(7) 0.4227(6) 0.5523(7) 0.6820(8) 0.7221(9) 0.6922(9) 0.45380(13) 0.6118(6) 0.7409(13) 0.5805(6) 0.3386(7) 0.7197(11)
0.1296(6) 0.1573(9) 0.1553(10) 0.2853(12) 0.07975(11) 0.3349(13) 0.07699(11) 0.2550(11) 0.1293(6) 0.07974(11) 0.412(2) 0.3342(14) 0.0000 0.2821(12) 0.2542(10) 0.0000
0.7884(10) 0.3206(8) 0.6734(13) 0.4683(6) 0.7289(12) 0.6235(7) 0.7578(12) 0.4859(5) 0.6894(12) 0.3870(7) 0.8525(13) 0.4216(7) 0.6567(12) 0.5525(6) 0.9872(8) 0.6850(8) 0.9299(9) 0.7245(9) 0.7974(11) 0.6926(8) 0.9846(10) 0.4520(13) 0.9186(11) 0.6128(8) 1.0122(10) 0.7427(12) 0.7926(11) 0.5814(6) 0.8685(9) 0.3375(7) 1.1515(11) 0.7206(11) Euler angle X = 78.0°
Y
Z
X
Y
0.7940(12) 0.6740(8) 0.7274(12) 0.7574(10) 0.6941(10) 0.850(3) 0.6570(10) 0.9672(16) 0.9499(15) 0.795(2) 1.0134(19) 0.903(4) 1.010(2) 0.7986(14) 0.866(2) 1.130(2)
0.3279(7) 0.4651(7) 0.6258(7) 0.4796(8) 0.3894(8) 0.419(2) 0.5530(7) 0.6804(10) 0.7247(8) 0.6902(11) 0.4486(9) 0.6158(10) 0.7389(15) 0.5818(15) 0.3484(13) 0.7204(10)
0.1297(7) 0.7894(10) 0.1569(10) 0.6709(13) 0.1555(10) 0.7277(12) 0.2852(13) 0.7549(11) 0.07975(11) 0.6894(13) 0.3357(13) 0.8516(8) 0.07699(11) 0.6543(13) 0.2542(12) 0.9866(8) 0.1295(7) 0.9285(9) 0.07974(11) 0.7951(11) 0.3881(15) 0.9836(7) 0.3367(13) 0.9168(8) 0.0000 1.0104(11) 0.2821(13) 0.7915(11) 0.2549(11) 0.8684(9) 0.0000 1.1499(12) Euler angle X = 76.7°
Z
Bond lengths involved in the [2+2]-cycloaddition ring (Å): D(C11–C11) inter = 1.70(3) D(C11–C11) intra = 1.54(3) D(C11–C06) = 1.76(3) D(C11–C12) = 1.45(4)
D(C11–C11) inter = 2.04(2) D(C11–C11) intra = 1.400(2) D(C11–C06) = 1.450(2) D(C11–C12) = 1.4502(14)
D(C11–C11) inter = 1.61(4) D(C11–C11) intra = 1.45(4) D(C11–C06) = 1.535(17) D(C11–C12) = 1.519(18)
Comparison with previously published experimental results: Tetragonal polymer [11]: ring 1 D(C7–C7*) inter = 1.605(8) D(C7–C7) intra = 1.585(8) D(C6–C7) = 1.515(4)
Tetragonal polymer [11]: ring 2 D(C9–C9*) inter = 1.575(8) D(C9–C9) intra = 1.562(9) D(C9–C2) = 1.529(4)
Dimer [25] D(C1–C1*) inter = 1.575(7) D(C1–C2) intra = 1.581(7) D(C1–C6) = 1.528(7) D(C2–C3) = 1.530(8)
Tetragonal polymer [12]: ring 1 D(C1–C0 1) inter = 1.60(1) D(C1–C10 ) intra = 1.62(1) D(C1–C6) = 1.521(5)
Tetragonal polymer [12]: ring 2 D(C3–C0 3) inter = 1.56(1) D(C3–C30 ) intra = 1.58(1) D(C3–C4) = 1.529(5)
Rhombohedral polymer [10] D(C1–C1*) inter = 1.587(6) D(C1–C1) intra = 1.606(6) D(C1–C2) = 1.514(4) D(C1–C3) = 1.509(4)
All the 16 unique C-atoms are found by direct methods. The rotation angle X of the 1D polymer chains is derived from only one of them, C11, though the formula: tan X = {c j0.5 z j}/{b j1.0 yj}.
Fig. 1. Chemical characterization of the samples using Raman Spectroscopy. The single-crystal sample (left) evidences traces of the Tetragonal phase of 2D polymerized C60. The two corresponding characteristic spectral lines, at 1449 cm1 and 1465 cm1 respectively, are marked by (T). By contrast, the powder samples (right) used in this study do not hint at the presence of any impurity phase. Only parts of the measured Raman spectra are displayed.
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R.J. Papoular et al. / Chemical Physics Letters 460 (2008) 93–99 Table 2 Two powder diffraction experiments: Synchrotron vs. Laboratory. They yield the same rotation angle of the 1D chains 73°.The Rietveld refinements are first carried out at fixed values of the Euler angle X to find the optimal one
Crystal data C60 Mr = 720.642 Orthorhombic Pmnn [# 58, Pnnm] a (Å) b (Å) c (Å) V (Å3) Z=2 Data collection Powder diffractometer Wavelength (Å) Transmission mode Capillary geometry Angular range (°) Temperature (K) Refinement GSAS profile function (i) Without preferred orientation Rp Rwp R(F2) Reduced v2
Synchrotron X-rays: 11BM
Laboratory X-rays: INEL
9.0979 (12) 9.8325 (17) 14.6587 (27) 1311.3 (0.5)
9.1284 (26) 9.8938 (44) 14.6503 (53) 1323.14 (103)
0.40230
1.54060 [Cu Ka1]
Kapton [29], U = 0.8 mm 2.2–6.5 Room temperature
Lindemann, U = 0.5 mm 8–32 Room temperature
Constant wavelength, type 3
Constant wavelength, type 4
0.1247 0.1682 0.0780 2.248
0.0780 0.1117 0.0784 104.6
(ii) With preferred orientation P.O. order Texture index (TI) Rp Rwp R(F2) Reduced v2
(cf. Fig. 4)
(cf. Fig. 5)
6 1.195 0.0985 0.1355 0.0785 1.470
8 1.261 0.0399 0.0552 0.0302 26.30
Euler angle X (°)
72.5
73
Only then is preferred orientation refined, for that optimal value Xopt, resulting in a very mild texture index but in a susbtantial improvement of the Rietveld fit.
[9,19]. The O phase crystals were produced at ambient conditions by quenching down to room temperature under pressure. 2.2. Chemical characterization of the samples [Raman] HPHT crystals were first characterized by Raman spectroscopy, using a Dilor XY spectrometer equipped with a Kr+ laser operating at a wavelength of 568.2 nm (yellow). All three O, T and R C60 polymer phases are endowed with specific Raman fingerprints (see Fig. 3 of Ref. [20]). The Raman screening resulted into two kinds of crystals: (i) a pure O phase (A) and (ii) a phase (B) containing additional bands probably related to the 2D-T phase. All crystals (A) were found to be twinned. One item suitable for single-crystal work was eventually selected from batch (B). Crystals from batch (A) were ground for powder diffraction experiments. Relevant Raman spectra are shown in Fig. 1.
Table 3 Modeled C60 buckyball assuming d(C–C) = 1.45 Å and d(C@C) = 1.40 Å C#
X (Å)
Y (Å)
Z (Å)
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
0.014430 0.014430 1.226870 1.241300 1.226870 1.241300 2.322720 2.177270 2.322720 0.145450 2.177270 0.145450 3.000000 1.500000 1.500000 0.912620 2.168350 3.080970 3.080970 0.912620 2.168350 1.749770 1.749770 3.499550 2.685750 3.339670 0.653920 0.653920 3.339670 2.685750 3.339670 0.653920 2.685750 0.653920 2.685750 3.339670 1.749770 3.499550 1.749770 0.912620 3.080970 2.168350 2.168350 0.912620 3.080970 1.500000 1.500000 3.000000 0.145450 2.177270 0.145450 2.177270 2.322720 2.322720 1.226870 1.241300 0.014430 0.014430 1.241300 1.226870
1.425000 1.425000 0.725000 0.700000 0.725000 0.700000 1.173070 1.425000 1.173070 2.598070 1.425000 2.598070 0.000000 2.598070 2.598070 3.030700 2.305700 0.725000 0.725000 3.030700 2.305700 3.030700 3.030700 0.000000 2.305700 1.173070 3.478770 3.478770 1.173070 2.305700 1.173070 3.478770 2.305700 3.478770 2.305700 1.173070 3.030700 0.000000 3.030700 3.030700 0.725000 2.305700 2.305700 3.030700 0.725000 2.598070 2.598070 0.000000 2.598070 1.425000 2.598070 1.425000 1.173070 1.173070 0.725000 0.700000 1.425000 1.425000 0.700000 0.725000
3.249770 3.249770 3.249770 3.249770 3.249770 3.249770 2.412620 2.412620 2.412620 2.412620 2.412620 2.412620 1.895220 1.895220 1.895220 1.604330 1.604330 1.604330 1.604430 1.604330 1.604330 0.587380 0.587380 0.587380 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.249780 0.587380 0.587380 0.587380 1.604330 1.604330 1.604330 1.604330 1.604330 1.604330 1.895220 1.895220 1.895220 2.412620 2.412620 2.412620 2.412620 2.412620 2.412620 3.249770 3.249770 3.249770 3.249770 3.249770 3.249770
The orthonormal coordinates of the 60 atoms define the rigid body used in the XRPD/GSAS refinements aiming at finding the optimal Euler angle X, which characterizes the rotation of the 1D C60 polymer chains. Neither do they depend on the crystal symmetry nor on the unit cell.
2.3. Single-crystal X-ray diffraction [SXD] 2.4. Synchrotron vs. laboratory X-ray powder diffraction [XRPD] A Nonius Kappa CCD diffractomer equipped with a graphite monochromator and Mo Ka radiation was used to collect a nearly complete dataset up to 2h = 57.2° (0.8 Å) at low temperature (T = 150 K) (Table 1). The limited quality of the crystal used prompted us to carry out the additional measurements described hereafter.
A first XRPD experiment was carried out on our in-house INEL CPS 120 diffractometer using Cu Ka monochromatic radiation at room temperature. The resulting value of the angle W of rotation of the 1D chains was checked via another experiment, carried out at the 11-BM synchrotron beamline of the APS/ANL using a
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Fig. 2. Unrestrained structure solution obtained by means of single-crystal diffraction at T = 150 K. The first view (top) down the short-axis a exhibits appreciably distorted buckyballs, whereas the second (bottom), perpendicular to this axis a, directly evidences the 1D-polymeric nature of the sample.
Fig. 3. Fully restrained structure solution obtained using single-crystal diffraction. A single independent C atom (boldened) is enough to derive: (i) the rotation angle X of 1D-polymer chains (top) and (ii) the inter- and intra- d(C–C) bond lengths resulting from the [2+2] cycloaddition between neighboring buckyballs (Bottom). X 78° turns out to be largely independent of the applied restraints.
much shorter wavelength (0.40230 Å) as well as a detector bank equipped with analyzers and featuring a perfect 2h-linearity. The latter is not warranted by the INEL CPS detector. Experimental details are listed and compared in Table 2. The same W value (73°) is found in both cases.
angle W is changed incrementally and then kept fixed in subsequent energy minimization runs. The absolute minimum yields the optimal W. In all configurations, the 1D chains rotate synchronously so that Pmnn symmetry is maintained.
3. Results
3.2. Analysis of the SXD data using ShelX [23]
3.1. Modeling
Direct methods are first applied to solve the crystal structure and retrieve the first 14 independent C-atoms, corresponding to C60 units located at (2-b) positions in the unitcell. The remaining 2 unique C-atoms are found by difference Fourier. The structure is then refined [model #1], yielding recognizable 1D chains of somewhat deformed buckyballs 1.7 Å apart, as visualized in Fig. 2 using Mercury [24]. A single unique atom, labeled C11 in Table 1 and emphasized in Fig. 3, contains all the wanted structural information: W, dintra and dinter. Most noticeably, W 80° and dinter 1.699 Å. Due to the real material used, with its 2D-T phase contamination mentioned above and possible disorder and defects, the final R1-factor remains large (0.28). Restraining the buckyballs to Ih symmetry worsens R1 to 0.43, but W 78° is hardly affected [model #2]. The optimal estimations of dintra 1.45 Å and dinter 1.61 Å are obtained by (i) relaxing the restraints involving the strategic C11 atom whilst maintaining the mirror plane throughout each 1D-chain and (ii) assuming an overall temperature factor (Uiso 0.035 Å2) [model #3]. W remains unchanged and the R1-factor settles at the intermediate value 0.418. In an attempt to get rid of extraneous contributions from the T phase
3.1.1. A single C60 unit Modeling an idealized buckyball assuming Ih symmetry, d(C–C) = 1.45 Å and d(C@C) = 1.40 Å, serves two purposes: (i) create appropriate restraints for single-crystal refinements, and (ii) build constraints for powder refinements via the use of a rigid body [Table 3]. It is the keystone of the XRPD data analysis discussed below. 3.1.2. The 1D-orthorhombic crystal The modeling procedure is partially described in [18]. Only additional details are given here. The van der Waals energy is calculated as a sum of atom–atom pairwise interactions involving a Lennard-Jones (6–12) potential, which is minimum (Vmin = 0.0722 kcal/mol) for rmin = 3.7 Å. The electrostatic energy is calculated assuming point charges of 0.5e and +0.25e placed at the middle of double and single bonds respectively, following a model proposed by Lu et al. [21]. Lattice sums are computed using an Ewald-like procedure introduced by Williams [22] and characterized by two parameters (Rcut = 9 Å; Kconv = 0.175). The rotation
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[11,12], all 3067 hkl reflections with h + k + l = 2n were removed from the dataset, resulting in a mild improvement only and thus hinting at the presence of residual structural defects. Geometrical details of the [2+2]-cycloaddition rings for all three models are reported in Table 1, where they are compared with those obtained from previous studies of C60 2D-polymers [10–12] and dimers [25]. Model #3 is the most chemically sound, in spite of the too small value of dintra (1.45 Å) which is likely to result from the remaining applied restraints, borne from a single C60 unit for which dintra = d(C@C) = 1.40 Å [model #2]. 3.3. Analysis of the XRPD data using GSAS [26] The great number of independent atomic coordinates involved, the Bragg peak overlap and too few sizable intensities forbid the ab-initio solving of the O phase. A simple model with few structural parameters must be refined instead. Using the idealized Ih buckyballs defined in (3.1.1) as rigid bodies restricts the number of structural parameters to one: the angle W, which can be identified with the Euler angle X within GSAS. Centering the buckyballs
97
at positions (2-a) within the unit cell turns out to be equivalent to using the positions (2-b) found by SXD. Hereafter, we stick to the former to comply with the Literature. We use a three-step Rietveld refinement strategy: (i) refine the lattice and instrument parameters. Then (ii) keep them fixed and refine only the scale factor at a given X-value, which results in a v2[X] dependence very similar to the V[W] dependence obtained above by modeling: the absolute minimum of v2[X] yields the optimal Xopt. Finally, (iii) optimize the Rietveld fit at constant Xopt, which does not affect the latter. The reliability of Xopt is first checked by comparing results obtained from two distinct experiments, whose results are reported in Table 2, Fig. 4 [Synchrotron] and Fig. 5 [Laboratory]. For either experiment, the instrument parameters are derived in different ways, which results in distinct v2[X] dependences. We use two different linewidth profiles with the synchrotron data, whereas we LeBail-fit and independently Rietveld refine an isotropic spherical shell mimicking the buckyball with the laboratory data. In all cases: (i) Xopt = Wopt 73°, a value close to WSXD 78° found by different means and in qualitative agreement with Wmodeling 61 ° [18] as
Fig. 4. Synchrotron powder diffraction is used to determine the rotation angle X (=?) of the 1D chains by making use of a single independent rigid body (ubiquitous C60 buckyball) and one appropriate Euler angle [X, within GSAS]. v2 exhibits a marked dependence with X and an absolute minimum for X 72.5°. Both of these results survive even if an inadequate linewidth profile is used (top). Rietveld refinements (bottom) are carried out at frozen sampled X values. Measurements carried out at room temperature.
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Fig. 5. Laboratory X-ray powder diffraction using an INEL CPS 120 detector was also used for comparison, yielding essentially the same results, i.e., X 73° and a similar trend for the v2-dependence on X (top, right), in agreement with the molecular modeling prediction (top, left) by [18]. Here, the robustness of the v2-dependence on X is demonstrated by optimizing the intrument parameters in two different ways: (i) via a model-free Le Bail analysis and (ii) via a Rietveld fit of a uniform spherical shell for C60, which is noncommittal about the X angle. The latter yields the best optimal Rietveld fit (bottom) since the fitted background parameters are closer to their end values. Measurements carried out at room temperature.
well as far distinct from WAC60 45° [3–5]. Not only (ii) is the v2[X] trend always the same but (iii) it remains in semi-quantitative agreement with the V[W] dependence predicted by modeling ([18], Fig. 5). 4. Concluding remarks Firstly, when analyzing powder data, going beyond an isotropic spherical model to describe buckyballs is only justified if the more elaborate model involving discrete C-atoms produces a better fit to the data. In the case of the powder laboratory data, v2 drops from 106.5 to 104.6 when preferred orientation (using spherical harmonics) is not refined, and from 27.93 to 26.30 when it is. Secondly, two phenomenological theoretical models are currently competing to account for orthorhombic (C60)n and related compounds. Dzyabchenko’s et al. [18] is the most successful in
connection with the present work but it introduces ad hoc electrical charges [21] the use of which remains to be justified from fundamental quantum mechanical considerations. Michel’s [5,6,27] involves a more elaborate forcefield that avoids these charges and the parameters of which are trained on other well-documented C60 compounds. Further developed by Verberck [28], it still fails to account for 1D-O C60. In conclusion, new experimental results have been presented, which provide one more step towards the understanding of the C60 polymerization process. Acknowledgements The authors gratefully acknowledge useful discussions with Prof. K.H. Michel and Dr. B. Verberck (University of Antwerp), help with the single-crystal measurements from Dr. L. Ricard (Ecole
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