Appl. Phys. A 62, 295—301 (1996)
High-temperature structure of C60 An in situ X-ray diffraction study W. Vogel Department of Surface Physics, Fritz-Haber-Institut der MPG, Faradayweg 4-6, D-14195 Berlin, Germany (Fax: #49-30/8413-5603, E-mail:
[email protected]) Received: 26 July 1995/Accepted: 8 November 1995
Abstract. High-purity C has been studied by in situ 60 X-Ray Diffraction (XRD). Between 300 and 900 K, the volume thermal expansion coefficient is a "4.57(4)] 7 10~5 K~1 with no observable deviations from linearity. Recrystallization is activated at ¹5600 K, as observed by the fast ((5 s) and slow ('10 min) variations in low-index Bragg intensities. At lower temperatures, thermal desorption of molecular oxygen at +420 K is accompanied with a step-wise increase of the 111-Bragg reflection intensity, but with no measurable change of the lattice parameter. The twin fault density has first been determined using high-resolution XRD. The twinning probability is 0.8%. Crystallites show a $0.3° intrinsic mosaic spread. Mechanical milling in acetone and in air increases the twinning probability to 1.8 and 3.1%, respectively. PACS: 61.16; 61.70; 65.00
Elastic and inelastic neutron scattering as well as X-ray diffraction has led to a high degree of knowledge concerning the structural and vibrational properties of crystalline C and the related rotational ordering transitions [1—4]. 60 The current knowledge of the properties of C has been 60 reviewed in a recent article [5]. In the majority of experiments, studies are carried out at sub-ambient temperatures in order to see the rotational ordering transitions. The aim of this work is to study the lattice dynamics and defects in polycrystalline C under vacuum at high tem60 peratures. Molecular dynamic calculations predict that even at 1800 K the cage structure of C should be preser60 ved [6]. However, experiments show that thermal decomposition to amorphous carbon occurs above 973 K, and irreversible defects at 773 K for vacuum heat-treated C [7]. 60 Chow et al. suggest a second-order transition to occur from a hindered rotation at Room Temperature (RT) to free rotation of the C molecule at elevated temperatures 60 [4]. The thermal expansivity should give indications of
such a transition at high temperatures. However, precise lattice parameter measurements in the high-temperature regime have, to our knowledge, not been published. Literature data are reported at sub-ambient temperatures (260—320 K), ranging from a "4.2—6.2]10~5 K~1 [8—11]. 7 Similarly a rather wide spread value of the C room 60 temperature lattice parameter is found in the literature. The highest accuracy is quoted by David et al. [8] using powder neutron diffraction: a"14.1543(2) As (¹"270 K) and Chow et al. [4]: a"14.1589(8) As by single-crystal XRD at RT. At plus-ambient temperatures Scanlon and Ebert [12] reported a "9]10~5 K~1 in the range 323—773 K for 7 C powder, measured both under vacuum and under 60 nitrogen. This number is seemingly too high and may be affected by impurities. A more realistic value of 4.7]10~5 K~1 at 295—1180 K was observed by Fischer and Heiney [13] for powder C , sealed in a quartz tube. 60 Sundar et al. [7] studied the thermal decomposition of vacuum-sealed C after high-temperature heat treatment 60 for 24 h. Due to the degradation at 973 K, the diffraction pattern became diffuse with a residual 111-peak being shifted towards smaller angles. The large irreversible expansion of a"14.72 As is probably induced by the intercalation of molecular C fragments. 60 Lattice defects in polycrystalline C will be studied in 60 this work by high-resolution X-ray line profile analysis. A recent study of the correlation between the thermal behaviour of C and stacking fault densities obtained by 60 X-ray diffraction has been performed by Vaughan et al. [14]. 1 Experimental Commercially available ‘‘gold grade’’ C (Hoechst), 60 purity 99.4% was used in this study. Samples were stored in air at RT before use (from several days to weeks) without any measurable ageing effects [15]. After storage in air at RT for 10 months, the sample showed a comparatively ‘‘clean’’ DSC signature at ¹ "250 K, enthalpy" # 11.3 J/g. The low-temperature precursor in the DSC scan
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Fig. 1. Open Slit (OS) measurement of as received, airexposed C : Temperature, 60 oxygen partial pressure, and 111-intensity during vacuum heat treatment are plotted as a function of time
being indicative for solvent impurities is small. HPLC measurements indicated a 0.37% fraction of C but 70 a relatively high amount of 1.5% C O. 60 A high-resolution Guinier counter diffractometer (Huber) was used for diffraction work, combined with an in situ reaction cell described elsewhere [16]. The C powders (&50 mg) were enclosed tightly (but not 60 vacuum tight) between two 0.1 mm Be platelets, separated by a 0.25 mm frame. For the lattice parameter measurements, the C powder was mixed intimately with 60 &15 wt % silicon (Alfa, lot D30D09, 99.9%, (325 mesh). Before use, the silicon powder was annealed in a flow of 5% H /Ar at 940 K. High-temperature measure2 ments were performed under dynamic vacuum (10~6 mbar. The specimen temperature was controlled by K-type thermocouple, inserted into the sample volume. For kinetic studies, the counter was set stationary to a certain Bragg angle with an open receiving slit (OSmode). A quadrupole mass spectrometer was connected to the reaction cell via a differentially pumped transfer system. For the high-resolution RT line profile measurements this films of C were sieved onto a 3-lm polyethylene foil 60 and fixed by UHU-acetone adhesive. To study cold work effects, a batch of C was milled in a motar at RT under 60 acetone and in air, respectively. Grain coarseness was tested by X-ray flat film transmission photographs. 2 Results and discussion 2.1 O desorption of air-exposed C 2 60 Side maxima of the 111-peak which are typical for domains with hexagonal stacking, also remained after vacuum treatment at 470 K but were only spuriously visible even in the as received state.
Figure 1 shows an ‘‘Open Slit’’ (OS) measurement of the 111-peak of air-exposed C during primary heat treat60 ment to 580 K. As a general rule an irreversible increase of the 111 integral intensity in the order of 15% was observed. At about 420 K there occurs a step-like change in intensity. At the same time, the mass spectrum shows a broad band for m/e"32. The desorption of molecular oxygen appears to be burst-like and is complete at &540 K. In a second heating cycle the m/e"32 peak disappeared. This agrees qualitatively with TPD-results of Werner et al. [17]. The anomalous behaviour of the 111C intensity therefore supports the lattice dynamics60 related desorption of gaseous species as suggested by these authors. However, we could not observe any measurable change in the unit cell dimension for the intercalated phase, i.e. before or after desorption (accuracy$0.002 As ). For simple steric reasons it has to be questioned whether or not molecules such as O or N can be accommodated 2 2 into the octahedral holes (R"2.06 As ) without affecting the unit cell volume, as has been suggested from single crystal work [17]. Most alkali—C compounds [18] and 60 the epoxide C O [19] are expanded in relation to pure 60 C . For alkali—C , however, the lattice expansion is 60 60 affected by the filling of the much smaller tetrahedral sites of the host lattice. Ismail and Rodgers [20] have measured the internal surface area and average micropore width of polycrystalline C by gas adsorption. For CO2 adsorption at RT, 60 these values are 132 m2/g and 12.2 As , respectively. The surface area, determined with Kr, N , O at liquid nitro2 2 gen temperature was low (4—7 m2/g). On repeated adsorption/desorption/evacuation-cycles the micropores became more constricted and less accessible to the adsorbates. These results are indicative of (i) a molecular sieving effect and (ii) a reduction of internal surface area by thermally activated recovery and grain growth.
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Fig. 4. 422-integral intensity of C vs temperature in high vacuum 60 after prolonged heating. Solid line: Fit by the Debye model Fig. 2. Integral intensities of C as function of temperature 60
2.2 Bragg intensities of vacuum-annealed C
60
Figure 2 shows the observed integral intensities vs temperature of 6 Bragg peaks. Deviations from linearity are far beyond experimental error. This unexpected behaviour was observed on heating as well as on cooling. It is thought that recrystalization processes at elevated temperatures affect the measured Bragg intensities. This is supported by isothermal OS-type measurements shown in Fig. 3. Beginning at &600 K the 111-intensity begins to strongly fluctuate. In terms of the time resolution given by the experiment, fast ((5s) and slow ('10 min) processes can be distinguished. These fluctuations are not restricted to the 111-peak, but are also observed at the 311-peak.
These are related to secondary recrystallization [21], with the driving force related to the release of the energy stored in grain boundaries. For metals secondary recrystallization is known to be accompanied with the formation of annealing twins of low specific interfacial energy. Some secondary grains are appreciably larger than the mean primary grain and grow suddenly and rapidly above a well-defined temperature. In Fig. 4 the 422 integral intensity vs temperature after prolonged vacuum high-temperature treatment is shown. The solid line represents a Debye approximation [8] with a Debye temperature of # "57(6) K. So far Debye- and D Einstein- temperatures have been measured only in the low-temperature regime. Most of the values found in the
Fig. 3. OS-measurement of the 111-intensity. Strong fluctuation indicate ‘‘slow’’ and ‘‘fast’’ recrystallization process (time scale of 5 s) beginning at &600 K
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Fig. 5. High-temperature lattice parameter of C (open symbols). Silicon was used as 60 reference sample. The solid line is a linear regression
literature are close to the number given in this report (compare, cf. [8]). From a single crystal at RT Chow et al. [4] found a harmonic Debye—Waller parameter º "Su2T" *40 0.0223(3) As 2, where u is the translational amplitude. The related Root Mean Square (RMS) displacement is u "0.149 As . From our measurements we got u "0.14 As x x at RT, and u "0.24 As at 910 K. The latter value is x &1.2% of the inter-molecular distance. According to the well-known Lindemann criterion, the RMS displacement at the melting temperature should be nearly 10% of the inter-atomic distance. More realistically, for C the inter60 molecular vibrational amplitude should be related to the 2.8 As free space between the rigid cage molecules. Close to sublimation temperature, this ratio is 8.5%, in accordance with the Lindemann criterion. 2.3 High-temperature lattice parameters Figure 5 shows the high-temperature lattice parameters up to 900 K, measured under high vacuum. The sample has been annealed previously in vacuum for 12 h at 627 K. We show in Fig. 6 the line profiles of the three peaks 331-C , 420-C , and 111-Si (dots) measured at 930 K 60 60 and a least-square fit (solid line). We applied Pearson VII functions and a nonlinear parameter fitting routine [22]. Accurate angular peak positions can then be determined from this fit in relation to the known Bragg angle of the 111-silicon peak. The temperature dependence of the silicon lattice parameters has been measured with high precision by Okada and Tokumaru [23]. The solid line in Fig. 5 is a linear regression (R"0.998), which suggests the expansion of the C lat60 tice to be linear at high temperatures. The related volume
Fig. 6. Line profiles of C , lines 331-C , 420-C and 111-Si, 60 60 60 measured at 908 K. The solid line is a fit with symmetrical PearsonVII functions
expansion coefficient is 4.57(4)]10~5 K~1, which agrees reasonably well with the less accurate value of Fischer and Heiney [13] mentioned in the Introduction. The observed value is close to the average low-temperature expansion coefficient of 4.64]10~5 K~1 observed by Prassides et al. [11]. Anomalies have been observed at 425 K for singlecrystalline C both in the electrical conductivity [24], 60 and in the specific heat [25]. If these anomalies are related
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to a transition from the hindered rotation found at RT [4] to a free rotation at higher temperatures as suggested by [24], this anomaly should also show up in the expansion coefficient. Within the accuracy of the data given in this study, this assumption cannot be confirmed. From our RT-measurements of the thin sieved samples, the lattice constant is a"14.155(2) As and a"14.168(2) As for C as received and milled in acetone, 60 respectively. The increase of lattice spacing after milling may either be affected by impurities (e.g. acetone molecules) that are occluded during milling, or by the mechanical impact itself. An anomalous high spacing of 14.192(4) As was, e.g. found for ‘‘smashed’’ C single crystals by 60 Haluska et al. [26]. The above value of a"14.155 As is in the range covered by the high-precision literature data mentioned in the introduction [4, 8]. The difference between the RT-value of a"14.162 As given in Fig. 5 is a result of a systematical offset due to the need to use thick samples (0.25 mm) for in situ XRD, but does not affect the expansion coefficient. 2.4 Lattice defects related to Bragg reflection line profiles On account of the high quality of the material, defectrelated effects on the diffraction line-profiles are small but yet detectable. We refer here to Warren’s treatment of diffraction effects by stacking defects in cubic closedpacked structures [27]. Depending on the respective Miller indices chosen, line broadening and asymmetries are to be expected. Twin faults (probability b) and deformation faults (probability a) both act on the line width, but only twin faults produce line asymmetries. The broadening is proportional to a#1 b. For example should the 420-line 2 be about 4 times less affected by stacking faults compared to the 331-line. The twin-related line asymmetry should act on the low-angle wing of the 420-line profile. This asymmetry is visible in Fig. 6 (not milled C ), as the fitted 60 Pearson-VII-function is symmetrical. The line width, measured at the Full Width at Half-Maximum (FWHM), is given in Table 1. In general the 420-line shows a narrower profile than seen in the 331-line. Both lines decrease in width with increasing annealing temperature and suggests the presence of stacking faults even at temperatures close to sublimation. 2.5 Quantitative determination of stacking faults In what follows quantitative ex situ RT studies of defects will be discussed. For the sake of high resolution, samples are prepared as thin films. With respect to instrumental broadening effects, only the high angle wings of 8 lines were fitted by Pearson-VII functions, plus a linear background. According to Warren, deformation faulting a should produce a fractional change in the interplanar spacing (*d/d) &a. Certain close-lying pairs of Bragg peaks are hkl oppositely shifted, most effectively the pair M111, 200N [27]. However, the 200-peak is known to be suppressed by
Table 1. FWHM line width of as received C . Line profiles 331 and 60 420 measured at different annealing temperatures, not corrected for instrumental broadening Temperature [K]
FWHM (331) [10~3 As ~1]
FWHM (420) [10~3 As ~1]
295 830 908
2.32 2.15 2.05
2.18 1.72 1.66
the structure factor of the C molecule. The next best 60 suited pair is M220, 311N. In general, for two lines represented by the indices 1, 2 we have a"[(b !b ) !(b !b ) ]/(G b !G b ), (1) 2 1 %91 2 1 *$. 2 2 1 2 where b"2sin(h)/j (2h"scattering angle, j"wavelength). G and G are constants related to the indices hlk, 1 2 e.g., G "!0.0345 and G "0.0125. 220 311 The observed RT-values for C as received and 60 milled in acetone are (b311!b220 ) "0.03450(2) As ~1 %91 (0.03449(2) As ~1), and 0.03442(2) As ~1 (0.03446(2) As ~1), respectively. The numbers in parentheses are the expected values of the unfaulted lattice and depend, of course, on the errors in the lattice parameters. In the presence of deformation faults, the measured difference should be lower than the expected value. Accordingly a very low deformation fault probability of a"0.04% may be present at least for cold worked C . However, in general, this 60 type of defect is negligible. The integral line width db vs b can be expressed by [28]: db"1/D#(1.5a#b) » /a#2 Se2T1@2b. (2) hkl The first term in (2) is a constant contribution due to the finite crystallite size D. Since 1/D is (10~4 As ~1 (see below) size broadening can be neglected. The second term is a contribution related to stacking faults, with » takhkl ing a value between 0 and 1. For an elastically isotropic material, the third term increases linearly with b. e describes the strain-induced fluctuations of the average net plane spacing. According to Hook’s law e"p/E , where hkl E is the Young’s modulus in the direction orthogonal to hkl the net plane (hkl). Generally speaking (2) holds if each term contributing to the line width is related to a Lorenzian type function, including the intrinsic instrumental line broadening [29]. Only then, the single contributions to the width can be added linearly. This approximation is justified since the observed line profiles are very close to a Lorenzian type. Figure 7 shows the measured integral line width in units of reciprocal space. The nearly angle-independent instrumental broadening of &0.9]10~3 As ~1 has not been subtracted. Equation (2) was used to fit the measured widths, as is indicated by the solid symbols in Fig. 7. A noticeable isotropic strain contribution to the line width of e"0.3% was found only for the sample milled in air. The dominant contribution to the width is due to stacking faults. The probabilities (1.5a#b) are 0.77 and 1.77% for the as received and the milled material, respectively. According
300
Fig. 7. Integral line width vs reciprocal lattice spacing of C , as received (open circles), and after 60 milling in acetone (open triangles) and in air (open squares), respectively. The constant instrumental width (0.9]10~3 As ~1) is not subtracted. The filled symbols are calculated by use of (2) and twin densities of 0.8, 1.8 and 3.1%, respectively
Fig. 8. X-ray plane-camera photographs of C in transmission. Sample-film distance: 60 65 mm, pinhole diameter: 0.5 mm, 30 kV, Cu-K , Ni-filtered. (a) C as received, and a 60 (b) after milling in acetone. The radial streaks in (a) (asterism) are white radiation diffractions of mosaic blocks within large single-crystalline grains
to the statements discussed above, most likely a+0, and only twin faults produce measurable line broadening. The related twinning probability of the starting material is b"0.77% and b"1.77% for C milled in acetone. An 60 even higher twinning probability of b"3.1% is achieved after dry milling in air. 2.6 Grain coarseness and mosaic spread Figure 8 shows X-ray plane-camera photographs of the above samples, taken at 30 kV in transmission and Nifiltered Cu-K radiation. For as received C (Fig. 8a) the a 60 Debye-Scherrer rings are completely resolved into spots.Photographs like this allow, in principle, grain-size determination by counting the number of spots in a ring and comparing with standards of known crystallite size.
However, as a general rule, independent of the respective diffraction geometry, spotted rings will emerge if crystallite sizes exceed &1 lm [30]. Beside the rings, radial streaks are seen in Fig. 8a. These streaks are known as asterism and occur in deformed metals. They are related to white radiation diffraction effects on curved areas of the net planes. The angular spread 2q is related to the length d of the asterism, the sample-film distance D and also to the diffraction angle 2h by q"dcos2(2h)/4D [30]. For the coarse grain C under investigation, the angular spread is 60 most likely due to a mosaic spread of a single-crystalline grain in order of q"$0.3°. Chow et al. [4] observed a mosaic spread of 0.03° for a C single crystal of 60 0.14 mm average size. The number of spots is strongly reduced after milling the C sample (Fig. 8b). The spots are superimposed by 60 continuous rings due to the formation of much smaller
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crystallites. But the crystallites are still large enough (5103 As ) as to produce no size-related broadening effects. As a second consequence of milling, the asterisms of Fig. 8a vanish.
3 Conclusion In situ X-ray powder diffraction was applied to characterize Hoechst ‘‘gold grade’’ C . In conclusion, this material 60 was shown to be thermally stable under high vacuum conditions up to 910 K with respect to its X-ray structure. The linear behaviour of the C expansion coefficient 60 observed in this work gives no indication of a hightemperature transition to random rotational orientation as suggested by Peimo et al. [24] and Chow et al. [4]. The desorption of O from air-exposed samples was 2 shown to be related to a step-like increase of the 111Bragg reflection intensity at &420 K, with no measurable change in the lattice parameter. This suggests, that ambient gases desorb not only as intercalated species but partly from internal surfaces, the latter being rearranged during this process. Above &600 K recrystallization processes can be visualized as time-dependent 111-intensity fluctuations. The decrease of the 422-Bragg intensity between 300 and 930 K is related to the inter-molecular vibrations of the C . From this a Debye temperature of 57 K was 60 deduced, in good agreement with low-temperature neutron scattering results obtained by David et al. [8]. The influence of defects on the X-ray line profiles is well known for metals. Statistically representative data on the twin fault density in polycrystalline C were obtained 60 by this method. Unlike metals, minor deformation faults and micro-strains are reproduced by cold working at RT, but the density of twins is increased up to 4 times. For many aspects, the knowledge of crystalline perfection of fullerenes and the related derivatives is desirable. Special attention should be paid to alkali—C supercon60 ducting compounds, for which granularity and crystallite perfection are of supreme importance Acknowledgements. Helpful discussions with Prof. R. Schlo¨gl are greatly acknowledged. I thank D. Cunningham for the effort in the revision of the manuscript. The chemical analysis by DSC and HPLC was performed by M. Wohlers and A. Bauer. Fa. Hoechst AG kindly supplied the ‘‘gold grade’’ C . 60
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