High-pressure polymerized phases of C60

Carbon Vol. 36, No. 4, pp. 319-343,1998

0 1998ElsevierScienceLtd Printed in Great Britain. All rights reserved 0008-6223/98$19.00+ 0.00

Pergamon PII: SOOO8-6223( 97)00234-O

HIGH-PRESSUR

I: POLYMERIZED

PHASES OF C,,

V. D. BLANK,~,~* S. G. BuGA,~.~, G. A. DUBITSKY,~ N. R. SEREBRYANAYA,~,~’ M. Yu. PoPov,~‘~* and B. SUNDQVIST~‘* “Research Center for Superhard Materials, Centralnaya 7a, Troitsk, Moscow Region 142092, Russian Federation %stitute of Spectroscopy of the Russian Academy of Sciences, Troitsk, Moscow Region 142092, “Department

of Experimental

Russian Federation Physics, Umea University,

(Received 10 June 1997; accepted in revisedform

S-90187 UmeB, Sweden 28 November 1997)

Abstract-Data from recent experimental studies of C6,, under high pressures are collected and analyzed, concentrating on the polymerized states where covalent intermolecular bonds have been formed through treatment of molecular C,, at high pressures and temperatures at or above room temperature. We give an overview of the observed phase transformations and the structures of metastable polymeric phases, both crystalline and disordered, as analyzed under ambient conditions, and we present and discuss a pressure-temperature diagram showing which synthesis conditions result in which final phases in the pressure range up to 20 GPa (200 kbar) and at temperatures up to 2300 K. The physical properties of the various phases are discussed whenever enough data are available. The pressure-temperature stability limits for C, and the conditions for the transformation of C,, into graphite, diamond and chaoite-type carbon are derived. 0 1998 Elsevier Science Ltd. All rights reserved.

Key Words-A. transitions.

Fullerene,

B. high pressure, D. crystal structure,

1. INTRODUCTION

D. elastic properties,

D. phase

whether intermolecular bonds would form between the molecular cages and, if so, whether these bonds would disrupt the molecular structure which might then collapse to a (softer!) diamond or diamond-like structure. It should be pointed out here that the sp’ bonds in graphite and C,, are, in principle, stronger than the sp3 bonds of diamond, which might be of very large interest when looking for materials with extreme hardness. It is well known [3] that the interatomic distances in graphite layers are shorter than in diamond, at 1.42 and 1.54 A, respectively, and the binding energy is 7.4 eV atom-’ in graphite and 7.2 eV atom- 1 in diamond. The effective Debye temperature On for in-plane phonons in graphite is about 2500 K, while the On for diamond is 1860 K. Finally, the sound velocity in graphite is 2.63 x lo4 m s-l along the layers while that of diamond is 1.96 x lo4 m s-l. While the graphite sheets are thus more rigid than diamond, bulk graphite is much softer than bulk diamond because the rigid graphite layers are only two-dimensional and are connected by weak c-axis bonds due to n-orbital overlap. A possible approach to creating an ideal extremely rigid carbon structure might thus be to try to cross-link fullerene cages, with their extreme graphite-type bond strength, using three-dimensional intermolecular diamond-type bonds, thus forming a three-dimensional fullerene polymer. This model assumes, of course, that the C,, molecules do not instead collapse into graphite or diamond when submitted to high pressures. For “atomic” carbon, i.e. graphite and diamond, the phase diagram is well

Carbon solids such as graphite and diamond are of large interest not only because carbon is one of the most widespread chemical elements in nature but also because of the extensive industrial applications of, and the dramatic difference in properties between, the many forms of this element. Recent advances in the synthesis of bulk artificial diamonds, carbon fibers, and diamond and diamond-like films have significantly extended the range of applications of carbon solids in modern industry and in everyday life. Very recently, a completely new area in the exploration of carbon structures started with the discovery by Kroto et al. of molecular carbon in the form of C,, [ 1] and other members of the fullerene family, and enormous research activity began after Krgtschmer et al. [2] found a simple method to manufacture bulk fullerenes in macroscopic quantities. Solid fullerenes exhibit a large number of interesting physical and chemical properties such as a number of subtly different orientational phases, superconductivity after doping, unusual magnetic properties, strong optical nonlinearity, etc. [3]. One of the earliest theoretical predictions was that the &, molecule itself would have a bulk modulus even larger than that of diamond and that the soft Cso solid therefore on compression would become harder than the hardest known solid in nature, i.e. diamond [4-61. However, one question was whether the C,, molecule would be stable under these conditions or *Corresponding author. 319

V. D. BLAM rf d

320

known [ 71. At room temperature the thermodynamic equilibrium pressure between sp’-bonded graphite and sp3-bonded diamond is only about 2.3 GPa and this equilibrium pressure depends only weakly on temperature (the graphite--diamond equilibrium phase line is indicated by the almost vertical bold line near 335 GPa in Fig. 1, to be discussed further below). Although the practical stability limits for graphite and diamond are much wider, allowing diamond to exist for indefinitely long times even at atmospheric pressure, the sp’-bonded C,, might thus in principle collapse into some other carbon phase already at low pressures. However, as it turns out, this does not happen, and C,, is surprisingly stable under pressure. Recent calculations show that the C,, molecule should be thermodynamically stable against transformation to graphite or diamond to pressures well above 20 GPa at room temperature [ 81and to quite high temperatures at lower pressures. and in the following sections we will show that this is also observed experimentally. Because of the theoretical predictions discussed above, a number of high-pressure experiments wcrc carried out on C,, within a couple of years of it becoming available for practical experiments. Already the first attempts to probe the stability limit

of the C,, molecule under high pressure in diamond anvil cells [9 151 showed that the soft pristine Ch,, powder transformed into hard carbon states different from other known forms, such as diamond and amorphous diamond-like carbon films (ta-C). The new C,, derivatives were described as “strongly interacting C,, agglomerates”, “collapsed fullerite” [ 13 151. etc. Further investigations using shock-wave compression or large shear deformations under static pressures revealed that under extreme conditions solid C,, loses its molecular structure and transforms either into crystalline diamond [ 161, amorphous diamond-like carbon [ 171, so-called “new amorphous diamond” [ 181 or hard disordered carbon states [ 191. Investigations by Blank et ul. [20-221 using a specially designed high-pressure diamond anvil cell for shear deformation confirmed for the first time the theoretical predictions that a solid derived from C,, might be stiffer than diamond, and Raman studies showed that the structure of this state was amorphous but different from that of ta-C. Intense low-frequency dilTuse bands were found with maxima at frequcncics characteristic for the ChO molecule. The strongest peak was observed at 1S60 cm ‘, which is lower than the characteristic value for u-C. Kao czt(11.[23] first rcportcd that individual C,,,

2300

1900

Disordered

1500 M E-r 1100

700 Orthorhombic

300 _~

c

I

_

_-!

I

Glassycrystal I

I

I 9

I 11

I

/

I

I

P, GPa Symbols Fig. I Map of the pressure tempcraturc plant showing the various phases of C,, crcatcd under dilTerent conditions. denotc some of the p T coordinates where experiments have been carried out and where samples have been treated during at least one minute. The bold solid line near 2 3 GPa denotes the diamond graphite equilibrium line while the bold dashed cur\c at 9 16GPa divides scmimetal and semiconductor states at 7’> I IO0 K and “soft” and “hard” statcs at Ti 1IO0 K. Further details are discussed in the tat.

High-pressure polymerized phases of C,, molecules (“monomers”) can indeed be covalently linked together to form polymeric structures. They submitted C,, to strong visible light and found that the material became insoluble in common solvents for C,, and showed a large number of new lines in its optical spectra, indicating that the molecular symmetry had been reduced. It was concluded that individual molecules had been linked together by covalent intermolecular bonds, and also suggested that the probable mechanism was a 2 + 2 cycloaddition. Similar spectral changes were noted also in spectroscopic high-pressure studies [24], but it is uncertain whether these arose from photopolymerization by the excitation laser or from the high-pressure treatment. These results led Iwasa et al. [2.5] to carry out high-pressureehigh-temperature studies on C,,, which showed that quenching from high temperature led to the formation of at least two different structural phases, both of them insoluble and showing the same types of spectral changes as the photopolymerized material. A very rapid development followed, in which several groups explored the high-pressure phase diagram of C,, discovering many well defined high-pressure structural phases. In the range up to 8 GPa, a number of one- and two-dimensional polymers were found to form [23328]. Because of the weak interchain or interlayer bonds the mechanical properties of these polymers were not significantly different from those of pristine C,,. However, submitting C,, to static pressures in the range 9.5-13 GPa combined with elevated temperatures was found to create three-dimensionally polymerized structures still containing basically intact molecules. The first bulk samples of such 3-D-polymerized CeO were produced by Blank et al. [29-381 and were found to have hardness values in the range from 70 GPa to more than 150 GPa and densities of 2.1-3.4 g crnm3 depending on structure. Compared to pristine C,,, the electric conductivity also increased by several orders of magnitude and the activation energy dropped to 0.330.02 eV. Again, these polymers are not soluble in organic or inorganic solvents, and in contrast to the one- and two-dimensional polymers which revert to “normal” C,, on heating [25,26], their structures are stable upon annealing at temperatures up to 1000 K. The details of this 3-D polymerization are still not completely clear. Most of the samples obtained are inhomogeneous and consist of two or more phases. Annealing at temperatures above 1000 K in the pressure range S-13 GPa produces disordered carbon states with a hardness of 40-200 GPa and electrical properties corresponding to semimetals or semiconductors. X-ray powder diffraction, TEM, HRTEM and Raman studies have revealed three basic types of disordered states, layered cross-linked structures with interlayer distances in the range 3.0-3.34 A, disordered 3-D polymers of CeO molecules and amorphous cage nanostructures with remaining fractions of deformed C,, molecules.

321

In this review we will try to present a general and coherent overview of the phase diagram of C,, under high pressures. Although pressure also has very interesting effects on the structural and orientational order [39,40] as well as on other physical properties [40] of monomeric C,, we will here deal exclusively with the polymeric phases formed without the help of radiation treatment at pressures above 0.5 GPa (5 kbar). In Section 2 below we give first a brief overview of the whole phase diagram as we understand it today, showing the general structural evolution of C,, on heating and pressurization. We then discuss in Section 3 the structures and phase boundaries of the various crystalline phases that have been observed at high pressures and in Section 4 in the same way the amorphous or disordered structural phases, including the highly disordered and very hard materials obtained when the C,, molecules themselves have started to collapse at very high pressures and/or temperatures. Where possible we shall also describe very briefly the information available on the physical properties of the polymeric phases. If the highpressure treatment is extended into the range of even higher temperatures the molecules break down completely and the atoms revert to the normal “atomic” carbon phases diamond or graphite, depending on the actual conditions used, and this is briefly discussed in Section 5. Because there is such a large interest in the extremely hard phases that can be produced from C, we have also included a short Appendix A at the end, dealing with ways of estimating and measuring the hardness of materials, in particular C&. Finally, we note that C6,, is not the only fullerene material that can be polymerized, since there are recent reports [41] that C,, can be polymerized under pressure using the same procedures as for C,,,. However, since very little information is available on high-pressure polymerized C,, we shall not discuss this further here.

2.

THE PRESSURE-TEMPERATURE DIAGRAM

OF C,:

PHASE

AN OVERVIEW

To put all the information on the various highpressure phases of C& into perspective initially we show in Fig. 1 the pressureetemperature (p-T) phase diagram of this material as we understand it today. Before discussing the diagram in detail, it must be pointed out that most high-temperature studies have been carried out by rapidly heating a small sample to the conditions indicated, keeping it under these conditions for a relatively short time (minutes) and then rapidly quenching it back to room temperature before the pressure has been decreased to zero. The structural studies have thus been carried out on metastable phases and it is often not known whether the phases studied are true equilibrium phases or not. For this reason, Fig. 1 should not be considered a true “phase diagram”, but rather a “reaction diagram”, or a map showing the conditions under

322

V.D.

which a certain phase (metastable under normal atmospheric conditions) can be produced under high pressure. The diagram in Fig. 1 has been constructed by weighting together all information available to us in the summer of 1997. Already a quick glance shows that a large number of structural phases may form in C,, at high pressures. In order to give an idea about which conditions have actually been explored the symbols show a selection of (p-T) coordinates where structural studies have been carried out, and it is obvious that a very large area in the p-T plane has already been well investigated. In the following sections we shall discuss the various structural phases, their phase boundaries (lines and curves in Fig. 1) and their physical properties in more detail, but to put things in perspective as noted above we begin by a brief guided tour of the diagram. At elevated temperatures, pressureinduced polymerization of C,, has been observed already at pressures well below 1 GPa [26]. Because the formation of intermolecular bonds is a thermally activated process the polymerization reaction proceeds very slowly at room temperature, and molecular C,, is therefore stable to quite high pressures at temperatures below 350-400 K. However, both spectroscopic [24] and structural [9] studies show that a slow partial polymerization occurs above 4 GPa. Heating increases the polymerization rate at all pressures. At the lowest pressures the molecules are believed to form linear (one-dimensional) clusters or chains which should lead to an orthorhombic distortion of the original structure. However, structural studies often show [25,26,42] that the lattice can be indexed as a face-centered cubic (fee) lattice because of a random orientation of the chains and random cross-linking of the chains. At higher temperatures the number of intermolecular bonds increases, and above 700 K a complete two-dimensional polymerization in the (111) plane has been reported giving a rhombohedral structure [27] with some admixture of a tetragonal phase at low pressures. These structures are stable in the range up to 668 GPa, above which pressure further structural phases appear and the phase diagram becomes more complicated. In this range the intermolecular distance has been reduced to the point where three-dimensional polymerization becomes highly probable on heating. As will be shown below, submitting the material to high temperatures in this pressure range leads to a rapid decrease in volume because of the formation of a threedimensional network of intermolecular bonds [30,31,36]. Since these are basically random, structural studies indicate that the molecules still form an fee structure up to temperatures near 900 K, but above this the structure becomes random or amorphous although the molecules are still intact and form the basic building blocks of the structure. Increasing the pressure even further the molecules themselves start to disintegrate, partially or completely, and a second amorphous phase containing

BLANKH

al

molecular fragments is formed at pressures above 12 GPa. However, under hydrostatic conditions at room temperature the molecules are stable to significantly higher pressures in the range 18-25 GPa. When under extreme conditions the C,, molecules finally break down completely the resulting structure depends on the position in the phase diagram of atomic carbon. At temperatures near 2000 K diamond is formed at pressures above 10 GPa, while below 3 GPa graphitic materials are formed at sufficiently high temperatures. In the following sections we discuss this structural evolution in more detail, starting with the crystalline phases. In order to have a logical structure we shall start at the lowest pressures with the orthorhombic structure indicated in Fig. 1 and proceed towards increasing pressure and temperature.

3.

3.1 Nominally

CRYSTALLINE

orthorhombic

PHASES

structures

During a study of the pressure dependence of the rotational transition temperature in C,, by thermal analysis, Samara et al. [43] noted a very large change in the slope of the phase line, as indicated by the thermal anomalies observed, at pressures above 1.4 GPa. They assigned this change in slope to the formation of a C,,-pentane clathrate-type compound but were unable to deduce the resulting structure. Later studies [25,26,42] have shown that this anomaly is instead connected with the formation of covalent sp3 (diamond) type bonds between the C,, molecules themselves. The possibility of such polymerization at pressures near and above 5 GPa had already been indicated by the large changes in slope for volume V versus p observed by Duclos et ~1. [9], the appearance of new spectral lines in the IR study of Yamawaki et al. [24], and the high-temperature studies by lwasa et al. [25], but it was not until Bashkin ez al. [26,44] observed large volume changes in a compression experiment on C,, that it was realized that pressure-induced polymerization could occur at pressures as low as 1 GPa. The intermolecular bonds are formed by a (2 + 2) cycloaddition reaction occurring when double C-C bonds on two molecules come into close contact. The two bonds then break up and reform as two single covalent intermolecular CC bonds, giving rise to a fourmembered carbon ring with strongly strained bond angles and with three-dimensional (sp3-type) orbital hybridization in contrast to the normal sp’ character of the intramolecular bonds. Such a mechanism was suggested by Rao et ul. [23] based on spectroscopic data and later proved by the NMR studies of Persson et al. [42] and others [45,46]. At low pressures and/or temperatures few intermolecular bonds form and the resulting polymer is one-dimensional, nominally consisting of linear chains of molecules giving rise to an orthorhombic distortion of the originally cubic crystal structures.

High-pressure polymerized phases of C,, 3.1.1 Structures andphase boundaries. Fig. 1 indicates that an orthorhombic polymer is obtained whenever C,, is treated at low temperatures (320-600 K) under pressures up to several GPa. However, the structure obtained is not very well defined and very often disordered structures are observed instead. At atmospheric pressure, photopolymerization is observed to occur only in the fee phase where the molecular rotation is quasi-free, while the orientational order in the low-temperature simple cubic phase (“pentagon” orientation [3,47]) prevents neighboring double bonds from coming into contact and thus suppresses polymerization. Although pressure decreases the intermolecular distance, and the molecular reorientation under pressure in the simple cubic phase tends to line up double bonds on one molecule with hexagons on the neighbor [39,40,48,49], experiments show that the probability for polymerization is still very low at room temperature. Under hydrostatic conditions only a small fraction of the molecules are found to polymerize below 320 K and the structures of most samples are still indexable as simple cubic or fee. As discussed by Marques et al. [50] the pressure-induced “hexaorder of the pristine material gon” orientational above 2 GPa [39,40,48,49] leads to the formation of a well-ordered orthorhombic polymer at temperatures above 320 K [27,50], while polymerization from initially fee C,, at lower pressures should lead to a much more disordered material because the molecular rotation enables bonds to form in random directions. Such a disordered low-pressure phase is also observed in experiments. X-ray studies by Iwasa et al. [25], Bashkin et al. [26] and Persson et al. [42] on material polymerized from fee CGOhave all shown very disordered structures which could be indexed as either fee, orthorhombic or monoclinic structures, and recent results have also been interpreted as mixtures of orthorhombic, tetragonal and rhombohedral [ 51] structures. On the other hand it was recently found that large single crystals of C,, could be polymerized under carefully controlled conditions near 1.2 GPa [ 521. Structural studies on these crystals [ 53,541 have verified that a very well ordered orthorhombic structure can be obtained even at low pressures, but also that the detailed structure is different from that observed at higher pressures. The existence of such a different structure had already been suggested by Agafonov et al. [ 551 on the basis of powder diffraction studies, but the single crystal studies showed very clearly that the polymeric chains were rotated in a way different from that suggested for the high-pressure phase. The chains run along the original cubic (110) direction and the lattice parameters a, b and c are 9.14, 9.9 and 14.66 A, respectively, under ambient conditions [53,54]_, in contrast to the parameters 9.26, 9.88 and 14.22 A found by NitfiezRegueiro et al. under identical conditions for a sample synthesized at 8 GPa [27]. Although at least two different orthorhombic struc-

323

tures thus seem to exist, very little information is yet available on the details of the formation process or the conditions required. We have therefore not explicitly subdivided the very large pressure-temperature area indicating orthorhombic structures in Fig. 1, but it seems clear that the polymeric materials obtained at temperatures above the extrapolated phase boundary between the fee and SC orientational structures of monomeric C,, are very disordered. Bashkin et al. used their compression data to construct a phase map [26] showing both the pressure-temperature conditions under which polymerization occurs and the upper stability limit for the polymerized phase. However, since both polymerization and depolymerization are thermally activated processes the limits given are valid only over the time scales of their original experiments, i.e. several minutes to several hours, and later studies have shown that slow polymerization can also occur at lower pressures and/or temperatures [42,56]. Above 450 K reaction rates are sufficiently high that the boundaries given can be considered approximate equilibrium phase boundaries. At temperatures close to and below the fee-sc phase boundary well-ordered orthorhombic phases can form, and as discussed above it seems that at least two different phases can form in this range, one at pressures higher than 2-3 GPa [27,50] and a different one below [53-551. This difference in structure may, in principle, be connected with the pressure dependence of the orientational state [39,48,49] of SC c,,. A very interesting question is whether any of these orthorhombic phases is identical to the photopolymerized state obtained at zero pressure. This has recently been investigated by Wagberg et al. [57], who polymerized nominally identical C,, films by radiation and by submission to high pressure. Raman studies showed that the spectra of films with similar fractions of polymeric materials showed lines at the same frequencies and with the same relative intensities at all frequencies from 200 to 1600 cm-‘. Only in the very-low-frequency regime below 200 cm ’ did the spectra differ and then only in the observed intensities, and it was concluded that the two states are indeed equivalent except for a difference in cluster size and/or geometry. A very good agreement between the Raman spectra of these two materials was also noted by Rao et al. (Fig. 2) [51,58,59], but surprisingly they found the IR spectra (Fig. 3) to be very different, possibly because of oxygen contamination [58]. However, significant differences are also observed between films photopolymerized at different temperatures. Both Raman [60] and AFM [61] studies show that at temperatures above 350 K mainly dimers are formed, while films polymerized below 320 K mainly contain larger clusters. Although mass spectroscopy also shows practically identical results for photopolymerized and pressure polymerized materials [51] the final answer to this question has not yet been found.

V.D.

324

BLANKET

al

wavenumbers Fig. 2. Raman spectra of C,,: (a) pristine, (b) photopolymerized, (c) orthorhombic phase produced at 4.8 GPa, (d) mixed orthorhombic-tetragonal phases, (e) rhombohedral phase and (f) mixed orthorhombic tetragonal rhombohedral phase. (Reprinted

with permission

3.1.2 Other physical properties. Because of the easily accessible polymerization conditions large bulk samples of the “disordered” (or “low-pressure polymerized”) orthorhombic C,, polymer can easily be produced, and as a consequence the physical properties of this material are known better than for any other polymeric phase of C,,, including the zeropressure photopolymerized state which can only be produced in the form of thin films, < 10 pm thick. A couple of brief general reviews of the properties of this phase have already appeared [ 52,621. As discussed above, the spectroscopic properties have been fairly well investigated. Polymerization leads to a distortion of the molecule and a large reduction in symmetry such that a very large number of previously forbidden lines appear in the IR and Raman spectra of the polymer (see Figs. 2 and 3). This was observed already in the first spectroscopic studies by Iwasa et ul. [25] and Kozlov and Yakushi [63], and the spectra have recently been analyzed in more detail by several groups [42,51,57--591. The most complete analysis has been presented by Rao et uf. [58], who discuss both the Raman and IR spectra above 200 cm-’ in detail for several highpressure phases (Fig. 3). The reduction in symmetry leads to a multiple splitting of the few allowed Raman and IR modes of C,, and a large number of new

from ref. [51].)

lines appear while the intensity of many original lines decreases. The redistribution of charge to form intermolecular bonds also decreases the strengths (“softening”) of the intramolecular bonds, leading to a decrease in the frequencies of most spectral lines. It should be noted that when pristine C,, is submitted to high pressure the Raman frequencies instead increuse with increasing pressure [ 11,12,40]. The high-frequency modes are mainly connected with tangential vibrations on the molecule and most studies have concentrated on the strong A,(2) “pentagonal pinch” Raman mode which in pristine C,, appears at 1469 cm-i (Fig. 2) and which shifts to lower frequencies on polymerization. Because of the high intensity of this line and the large shift the relative strengths of shifted and unshifted components are often used as indicators of the fraction of polymerized material. We note here that the two nominally orthorhombic structures observed may possibly also have different frequency shifts of this line. Studies by Persson and co-workers [42,52,57] on material polymerized near 1.2 GPa and 600 K have consistently shown a well-defined shift to material, and 1459 cm-‘, as for photopolymerized such a shift is also observed by Rao et ul. [51,58] on similar material. For material polymerized near 4.8 GPa and 525 K, however, Rao et al. instead lind

High-pressure polymerized phases of C,,

325

a) 576

526 1428

b)

400

600

800

1000

1200

1400

1600

1800

2000

wavenumbers Fig. 3. IR spectra

of C6,,. Letters

denote

the same materials

a sharp, well-defined peak with a much smaller shift ( 1464 cm-‘). Such a small shift was also observed at intermediate stages of the polymerization reaction by Persson et al. [42] and then tentatively correlated with the initial formation of dimers, as suggested by the calculations of Porezag et al. [64], since the peak observed shifted to 1459 cm-’ after longer reaction times. However, there is no reason to assume that the material studied by Rao et al. was not completely reacted. Spectral lines below about 800 cm-’ are mainly correlated with radial vibrations. It might be expected that the formation of intermolecular bonds would give larger effects on such modes than on the higher frequency modes, and this seems to be the case. For example, the relative intensity of the radial “breathing” A,( 1) mode at 496 cm - i decreases strongly and a large number of new modes appear in the range below 1000cm-l in both IR and Raman. At even lower frequencies, below 200 cm-i, the formation of chains should give rise to new modes not observed for molecular CeO, and such modes have indeed been observed near 120 cm-i for both photopolymerized [ 231 and pressure polymerized [42,57,65] materials. Photoluminescence studies [ 51,59,63] show that

as in Fig. 2. (Reprinted

the polymer

with permission

from ref. [51].)

is a semiconductor like the parent material but with a smaller band gap, and the presence of covalent intermolecular bonds has been verified by NMR, as already mentioned above [42,45,46]. A number of theoretical studies have been carried out on the electronic properties of linear polymers, but since we here concentrate on the present experimental situation we only give references to a small number of these [66-711, most of which agree that the band gap for the polymer should be smaller than that of the pristine material. It might be expected that the creation of strong covalent intermolecular bonds would also lead to significant changes in the bulk lattice properties, and this is also found in practice. The bulk modulus of the polymer increases by more than a factor of two [26] compared to the pristine material while the thermal expansion coefficient decreases by a similar factor (Fig. 4, taken from ref. [ 721). Neutron-scattering studies also show the appearance of new intermolecular modes [73-751 at low energies (~20 meV). Because of the increasing intermolecular interaction the acoustic lattice modes should also be expected to stiffen, leading to an increase in Debye temperature, and data for the specific heat cp show that the Debye

V. D.

326 II-

a)

thermal

expansion

6-

b) expansivity

”0

100

300

200

400

iO0

1‘ IKl

Fig. 4. Thermal expansion behaviors of pristine C,, and of disordered, nominally orthorhombic C,, polymerized at 1.2 GPa and 585 K, respectively. (Reprinted with permission from ref. [72].) temperature increases by almost 30% on polymerization [ 521. However, since the acoustic modes contribute significantly only at temperatures below 100 K, the magnitude of c, is practically unchanged by the formation of the orthorhombic polymer at room temperature and above where optical phonons dominate. The thermal conductivity has also been measured as a function of temperature and pressure [ 561. Surprisingly, the thermal conductivity does not increase significantly in magnitude as the intermolecular interaction increases, and even more surprisingly it becomes linear in temperature. This very unusual behavior is probabiy connected with the strong, almost glass-like structural disorder which more than offsets the increase in intermolecular interaction. Finally, the strength of the intermolecular bonds in the low-pressure polymerized orthorhombic phase has been investigated by two groups by heating the polymer at zero pressure while monitoring how the polymer breaks down with time. Persson et al. [ 57,651 have used the relative intensities of the shifted and unshifted components of the A,(2) Raman line to study the breakdown to find an activation energy near 0.75 eV, increasing to 0.9 eV at the highest temperatures studied. In another experiment, Nagel EC al. [72] measured the volume decrease during the transformation to normal C,, to find an activation energy of about 0.75 eV at the onset of the transition, increasing to 1.9 eV near 500 K. The results from both of these studies are in reasonable agreement with the value of 1.25 eV found by Wang et al. [76] for photopolymerized C,,. The formation of the polymer has also been investigated by thermal conductivity measurements in situ near 0.8 GPa [56], at which pressure Soldatov and Andersson deduce a significantly smaller activation energy of 0.4 eV.

BLANK

ef d

3.2 Rhombohedrul and tetragonal phases After heating C,, to temperatures up to 700 K at 5 GPa Iwasa et al. [25] found that their samples had transformed into a new phase which at the time was indexed as an fee phase with a reduced lattice parameter of 13.6 A (now known to be the disordered orthorhombic phase discussed above). A second, different phase which could be indexed as having a rhombohedral structure was found above 700 K. Later studies by Kozlov et al. [63], Nunez-Regueiro rt al. [27,50] and others [41,77] have verified that such a phase is formed at temperatures above 700 K over a very large range in pressure. The structure of this phase can be derived from the fee structure by assuming complete polymerization of the closepacked ( 111) planes in the crystal, and X-ray studies show that the molecules in this phase are slightly deformed (flattened) by the strain of the six covalent intermolecular bonds to each molecule [78]. This phase can therefore to some extent be considered as a two-dimensional (layered) fullerene analog to graphite. NMR studies also clearly show that the strain from the six bonds on each molecule distorts the molecular structure such that each carbon atom has one of several slightly different bonding states [46,79]. As a consequence, the normally very sharp NMR peak near 144 ppm for molecular C,, is split into five subpeaks corresponding to five different atomic environments for the atoms (Fig. 5). The increase in the average number of intermolecular bonds on each molecule also results in a strong increase in intensity for the sp3 peak near 77 ppm relative to that observed for the orthorhombic phase [42,46]. The rhombohedral phase appears on heating to above 700 K at pressures from about 2 to 9 GPa. As an example we show in Fig. 6 a set of diffraction diagrams [50] taken under ambient conditions on samples heat treated at 4.8 GPa at temperatures from 300 to 1500 K. The structural evolution with temperature is indicated in the figure, and goes from fee over orthorhombic to rhombohedral and finally to a disordered phase as will be discussed below. Marques ei a/. [SO] find that the transition from the orthorhombit to the rhombohedral structure is a continuous process which they explain in terms of a longitudinal shift in the relative positions of neighboring linear molecular chains. However, such a process does not seem to be possible for a transition from the alternative orthorhombic structure recently found by Launois it nl. in single crystals polymerized at lower pressures [ 53,541. At pressures below 4 GPa no pure rhombohedral phase is observed. Instead, analysis of the X-ray diffraction diagrams obtained show that the best fit is obtained if it is assumed that a significant fraction of the material has been transformed into a tetragonal structure [27.50]. This structure occurs only over a relatively limited part of the pressure-temperature phase diagram of C,,, as discussed by Marques et al. [50]. It is interesting to note that an extrapolation of

High-pressure polymerized phases of C,

I

I

160

170

327

I

I

I

I

150

140

130

120

wm

Fig. 5. NMR spectrum for rhombohedral components

10

15

C,,, showing the splitting of the original sharp peak for pristine due to molecular strain. (Reprinted with permission from ref. [79].)

20

28 (Zdseg.30

35

Fig. 6. X-ray patterns (and lattice structures) observed for C,, treated at 4.8 GPa and at the temperatures’indicated. (Reprinted with permission from ref. [50].) the phase boundary for the orientational transition near 260 K at zero pressure using the accepted slope 160 K GPa-’ intrinsic to pure C,, [40,43,80] delineates very precisely the low-pressure boundary of the area where Marques et al. observe the tetragonal phase [ 501. (The corresponding dashed line in Fig. 5

C,, into several

of Marques et al. was unfortunately calculated using the slope 109 K GPa-’ characteristic for He intercalated C6,, [40,43].) It is therefore possible that the formation of a “pure” layered rhombohedral phase can only occur in the (“hexagon”) orientationallyordered simple cubic phase of C,, [39,40] while the “tetragonal phase” is produced in the fee phase (with free molecular rotation) because of the formation of random or pseudo-random “interplanar” bonds during the transition. Another possible explanation preferred by Marques et al. is that the tetragonal phase is the stable high-temperature phase at low pressures because of its larger molecular volume (lower density). Both the orthorhombic, tetragonal and rhombohedral phases are insoluble in common solvents and revert to normal molecular C,, on heating. The rhombohedral phase has been reported [81] to be stable to a slightly higher temperature than the orthorhombic phase, as might be expected from the larger number of intermolecular bonds. Although the rhombohedral and tetragonal phases have been studied significantly less than the orthorhombic phase(s), at least the spectroscopic properties are reasonably well known. As can be seen in Figs. 2 and 3, the increase in molecular distortion compared to that in the orthorhombic structure leads to a further increase in the number of lines observed. Especially noticeable is the broadening of the high frequency tangential Raman lines near the A,(2) pentagonal pinch mode because of the large number of intermolecular bonds per molecule, and the proliferation of IR lines both at high frequencies, just below 800 cm-‘, and near 500 cm-’ [41,51,58,59,82]. The photoluminescence spectrum has also been studied [59,82], and even its pressure dependence up to 1.1 GPa which is found to be very

V.

328

D. BLANK et cci.

much smaller than for pristine C,, [59], as might be expected for a very much less compressible material. Above 2 GPa, Venkateswaran et al. [ 591 find that the spectral intensity decreases strongly and suggest the reversible formation of inter-layer bonds. Recent calculations [83,84] show that the electron band structure of this phase should be more threedimensional than for the orthorhombic phase and that the band gap is even smaller, about 0.7 eV smaller than for pristine ChO. The electrical resistance R of Ch,, has been measured in situ as a function of temperature from 300 to 950 K at 5 GPa by Ma and Zou [85], nominally in the fee, orthorhombic and rhombohedral structural phases and in the hightemperature disordered phase discussed below. However, it is difficult to correlate their results with the structural phases observed. 3.3 “H~vu”‘J~~e-centered cubic phases At pressures above 9 GPa the C,” molecules approach each other sufficiently that random intermolecular bonds form even on relatively mild heating. As a consequence, no well-ordered rhombohedral phase has been observed to form on heating [3037,77,86]. Instead, as shown in Figs. 7 and 8, heating to above 550 K in the range 9.5513 GPa only results in a rapid increase in the density p of the samples and a decrease in the unit-cell volume V with increasing temperature, indicating a continuous formation of intermolecular bonds. Within the uncertainty in treatment temperature (50 K) for the samples, the dependence of V on T is the same at 9.5 and 13 GPa. As shown by the diffraction results in Figs. 9 and 10, obtained after heating samples to different temper-

C 60

2001 500

I

1000 Temperature, K

IO

Fig. 8. Unit-ccl1 volume at atmospheric pressure as a function of the synthesis temperature for crystalline CbO phases qucnchcd from high temperature at I3 GPa: fee slructurc (’ 1); distorted bee structures (m); monoclinic phases (m). ( Adapted from ref. [ 361.)

13 GPa 0

10

20

30

40

50

2 theta, degrees 0

E

280

-

Sequence

12 GPa

0,

and different

240 320

-21

200

-

160

9.5 GPa

;

a GPa

I 500

I

I

1000

I

i

I

I

1500

Temperature,

of X-ray

diffraction

patterns

at atmoat 9.5 ClPa from ref. [86].)

spheric pressure for fullerite samples synthesized

2

I

2000

K

Fig. 7. Specific gravity (density) at atmospheric pressure for quenched samples as a function of treatment temperature and for four different treatment pressures. (Reprinted from ref. [%I.)

temperatures.

(Reprinted

atures at constant pressures of 9.5 and 13 GPa [30 36,861, respectively, and as also observed in a TEM study [29,87], the structure observed is still indexable as a slightly distorted fee structure over a large range in treatment temperature, probably because bonds form in random directions. Simultaneously with this decrease in lattice constant the previously forbidden (200) reflection appears and gradually grows stronger as the interference of the molecular form factor with this reflection decreases. Although no change in the lattice structure is observed by X-ray diffraction, large changes have been found in the macroscopic properties of the material in this range. In particular, measurements on samples heat treated between 550

High-pressure polymerized phases of C,,

1600

329

I 13 GPa.

01 0

’ 10

h

’

’

20

30

2 theta,

’

820

’ 40

K

1 50

degrees

Fig. 10. X-ray diffraction pattern of the polymerized facecentered cubic structure of C,, with lattice parameter a= 12.2 A, obtained by polymerization at 13 GPa and 820 K. (Adapted from ref. [36].)

and 800 K indicate a very large increase in hardness, such that these “hard fee” crystals can easily cut cubic BN, the hardness of which (9.5 on the Mohs’ scale, i.e. 50-60 GPa) is only exceeded by that of diamond. The onset of the rapid increase in hardness can be correlated with the sharp change in slope near 500@570 K of the lattice constant versus increasing treatment temperature (i.e. increasing degree of polymerization) in Fig. 8, near a lattice constant of 13.6 A. With increasing reaction temperature the diffraction peaks gradually broaden and lose intensity, but fee peaks corresponding to lattice constants down to 12.2-12.3 A can still be detected up to near 820 K (Fig. 10). A TEM study of samples obtained at 13 GPa and 900 K gave the smallest observed value of the lattice parameter, about 11.7 A [87]. At such a low lattice parameter new features begin to appear in the X-ray diffraction diagrams and the Raman spectra because the C,, molecules begin to be very strongly strained under these extreme conditions. This is evidenced by the appearance of very strong (111) reflections from the fee phase. (If the hightemperature structure with a= 12.3 A would differ from the fee structure with a= 13.6 A by only a scaling factor the (111) reflection should be absent because of the form factor of the spherical molecule.) Also, the relative intensities of the diffraction lines are different for pristine fee C,,, polymerized fee C,, with a = 13.6 A and the highly dense high-temperature phase. This may be due to the atomic scattering factor instead of the molecular form factor. At very high degrees of polymerization it is also possible that small new local clusters of carbon atoms may form between the sites of the distorted remains of the original molecules. This high-pressure, high-temperature fee phase is thus of great interest for further investigations. Again, samples have been studied by Raman spectroscopy [ 30-361 at zero pressure (Fig. 11). The spectrum develops with treatment temperature in much the same way as for material treated at lower

I

0

500

,

1

IWO

,

I

1500

,

,

2000

,

2500

Raman Shift, cm-’

Fig. 11. Raman spectra of fullerite quenched at 13 GPa from the different temperatures indicated. (Reprinted from ref. [361.)

pressures (Fig. 3) with a steady increase in the number of lines, a decrease in intensity and a broadening of the lines observed. A new band at 950-960 cm-’ appeared in the spectrum of the fee structure with a lattice constant of 13.6 A. Such a band was assigned by Martin et al. [88] to an intermolecular four-membered ring mode. During the increase in treatment temperature to 820 K the evolution of the three-dimensional polymerization process leads to dramatic changes in the Raman spectra (Fig. 11). Blank et al. [30,31] have also carried out a study of the activation energy of the bonds in this phase using the same Raman method as used by Wang et al. [76] for photopolymerized C,, and Persson et a/. [65] for orthorhombic C,,, and found a value of 0.24 eV. Although the basic lattice structures of pristine C,, and of the phase indexed as fee with a lattice parameter of 12.3 A are the same, the very different types of intermolecular interactions thus give rise to many differences in the X-ray diffraction patterns, the Raman spectra and other physical properties of the two phases. Early investigations in diamond anvil cells [9] showed that the limits of stability of the fee phase (or actually the orientationally-ordered simple cubic phase [39,40,43]) at room temperature was about 16 GPa under non-hydrostatic and 20 GPa under hydrostatic conditions, corresponding to a minimum lattice parameter of 12.45 A. Above these pressures

330

V. D.

BLANK

et al.

a transformation into a phase with an unidentified lattice structure was found. A recent X-ray study [89] using a shear diamond anvil cell with pattern registration on film confirmed the existence of a phase transformation at about 18 GPa under combined quasi-hydrostatic pressure and rotational shear deformation conditions. The high-pressure phase obtained under these conditions in believed to have a type of body-centered cubic (bee) structure. Highquality X-ray diffractograms of distorted body-centered structures were obtained on bulk samples synthesized at 13 GPa and moderate temperatures, as discussed below. 3.4 Body-centered cubic phase(s) As already discussed above, a complicated structural evolution with temperature is observed above 9.5 GPa. The initial structural evolution at 13 GPa is identical to that at lower pressures in that the fee structure remains stable, but the increase in density is again connected with a very large increase in hardness. Already after pressure treatment at room temperature, however, new diffraction lines appear. These lines become dominant at about 600 K where at least small parts of the samples have transformed completely into a new structure (Figs. 12 and 13) which can be indexed as a distorted body-centered cubic (bee) structure with a significantly smaller unitcell volume than the fee phase (see Fig. 8). A careful analysis of the data has shown that the diffraction diagram obtained on samples treated near 720 K at 13 GPa is in very good agreement with an orthorhombit pseudo-tetragonal body-centered lattice structure with an X-ray density of 3.39 g cm-j and lattice parameters a=9.53& b-8.87,& and c=8.34A. It is possible to represent these parameters on the basis of the fee lattice parameter afcc as a=(a,,/~+d), b=a,,/fi and c=(a,,/fi-A), where A=O.6 A, indicating that the polymerization probably takes place along the face diagonals [110] of the fee structure. Most samples remain two- (or multi-) phase on heating to higher temperatures. No true bee structure

K 13 GPa. 820 K

B

:: O0

10

20

30

40

50

2 theta, degrees

Fig. 13. X-ray diffraction pattern for an orthorhombic bodys$tcture with _the parameters a= 10.93 A, b = 8.98 A and c=7.62 A. (Adapted from ref. [36].)

centered

is observed in any experiment, but instead the orthorhombic distortion is observed to increase with increasing treatment temperature and a simultaneous broadening of the diffraction lines indicates an increasing degree of structural disorder. X-ray diffraction shows that, because of large pressure gradients and temperature variations in the chambers used, parts of the samples synthesized at 820 K still preserve an fee structure with a very small lattice constant of 12.3 A and a high degree of threedimensional polymerization (Fig. 10) while the rest of the sample has a completely different X-ray pattern (Fig. 13) assigned to an orthorhombic structure with the lattice parameters a= 10.93 A, b= 8.98 A and c=7.62 A. Above 850 K at the same pressure yet another new set of diffraction lines appear (Fig. 14). These lines can be indexed in terms of a monoclinic structure with the parameters a= 10.27 A, b=7.80 A and c= 9.49 A, with ,0 = 92.4”. Finally, above 900 K the intensity of the remaining diffraction lines decreases rapidly with increasing temperature and diffuse halos appear reflecting the disorder in the structure. Diffraction lines from the monoclinic phase in some samples remain up to almost 1300 K, but large 1000

% 400

f

13 GPa, 720 K

I

13 GPa. 870 K

I ; z

” 5 s .c f

200

S

0 0

10

20

30

40

50

2 theta, degrees

_J

0

10

20

30

40

50

2 theta, degrees

Fig. 12. X-ray diffraction pattern for an orthorhombic pseudo-tetragonal body-centered structufe with the parameters a=9.53 A, b=8.87 A and c=8.34 A. (Reprinted from ref. [36].)

Fig. 14. X-ray diffraction pattern of the monoclinic structure of C,, with the parameters o= 10.27 A, b=7.80 A and E= 9.49 A, and 0=92.4”. (Adapted from ref. [36].)

High-pressure polymerized phases of C,, fractions of the samples are probably more or less disordered or even amorphous well below this. Above 1300 K almost featureless diffraction diagrams are obtained and measurements of the physical properties of samples quenched from this temperature range have shown that the material has been transformed into an amorphous phase which easily scratches even the hardest ( 111) surface of crystalline diamond. It is important to note that Raman spectra taken on samples containing predominantly body-centered phases are different from spectra for the face-centered phases (Fig. 11). Although the bands in the lowfrequency range are typical for CGOdramatic changes occur in the main bands between 1300 and 1700 cm-i. Instead of the double peak observed after treatment at 580 K a single band was observed in the spectra of samples treated at 670 to 1070 K. Similar spectra were obtained for samples treated at 9.5 GPa in the range 670-770 K, but the shape of the main band is different for samples treated at different pressures. The Raman spectra of the orthorhombic and monoclinic phases synthesized at 13 GPa are very similar to those observed for samples treated at very high temperatures, 1270 and 1470 K, at the same pressure, samples for which X-ray diffraction shows an amorphous structure. The shape and position of the main Raman band may thus reflect a high degree of sp3 hybridization in both the body-centered structures and in the disordered states obtained at higher pressures and/or temperatures, which will be discussed further below. On the other hand, distinct lines are still observed at about 500, 710 and 770 cm-‘. These lines can be correlated with the A& 1 ), Hg( 3) and H,(4) modes of the starting material and thus show that at least some parts of the molecules preserve their original structure in these crystal lattices. A bee structure was predicted for C,,, in 1991 by O’Keeffe [90] who calculated a lattice parameter of 9.54 A, a value equal to the parameter a for the orthorhombic pseudo-tetragonal body-centered structure described here. His model assumes a polymerization by the formation of sp3-type intermolecular bonds through a hexagon-hexagon, i.e. 6 + 6 atom interaction instead of the 2 + 2 cycloaddition reaction known to occur for the linear and two-dimensional polymers discussed in Sections 3.1 and 3.2. Figure 15(a) shows a model for a part of the bee structure, a tetrahedron created from four C,, molecules. It is interesting to note that in this structure a new fullerene-like cage is formed inside the tetrahedron (Fig. 15(b)) by six hexagons, two pentagons and five squares (2 +2 intermolecular rings). Such polyhedra may be a carbon analogy of the Si,, clusters recently reported [91]. Finally, turning back to the description of the crystal structure of the samples synthesized at 9.5 GPa and 770 K (Fig. 16) we note that although the X-ray diffractogram can be indexed as a distorted fee structure, the Raman spectrum of this structure

W Fig. 15. Models of the body-centered cubic structure of 3-Dpolymerized C,,. (a) A tetrahedron formed by four C, molecules, and (b) the fullerene-like cluster of 22 carbon atoms created between the Cc,, molecules in the structure shown in (a). has a strong resemblance to the spectra of the bodycentered structures obtained at 13 GPa. We may thus assume that at 9.5 GPa the starting point for the transformation from face-centered to body-centered structures is near 800 K.

4. AMORPHOUS

AND DISORDERED

PHASES

Disordered cross-linked layered (“graphitized”) structures Kozlov et al. [19] reported that heating C,, to temperatures near 1000 K at 2.5 to 3 GPa resulted in the formation of a very disordered, hard phase. Later experiments by Blank et al. and Marques and co-workers [50] have shown that such a very disordered, partially graphite-like phase is always obtained at high temperatures over large ranges in pressure. Kozlov et al. also state that heating to 1200 K at 2.5 to 3 GPa results in the formation of a much softer graphitic structure, but at higher pressures such a structure has not been observed for pure C,,. We note that a change in transformation behavior in this 4.1

332

V. D.B~~x~etal.

Fig. 16. TEM diffraction pattern of a C,, sample quenched from 770 K at a pressure of 9.5 GPa. (Reprinted from ref. [37].)

pressure range correlates well with the graphiteediamond coexistence line [7] (shown as a bold line near 335 GPa in Fig. 1) and we speculate that prolonged heating to very high temperatures at pressures below (i.e. to the left of) this line results in graphitization of C,, towards turbostratic or even well-crystallized graphite. To the right of this line a much harder, disordered material is observed. However, the detailed structure is different for different specimens and probably depends on the detailed reaction conditions. Hodeau et al. [28] report that samples treated near 1300 K at 667 GPa were graphite-like with turbostratic disorder and a density 93% of that of graphite. We have also observed that samples treated in the range 6-8 GPa and T> 1100 K are not always stable with time, and that samples that are initially very hard and disordered develop with time into what seem to be composites, containing microscopic very hard particles in a softer, possibly graphite-like, matrix [92]. Usually, X-ray and Raman studies [ 19,86,92] indicate an overall similarity with turbostratic graphite or glassy carbon but the material is very much harder than expected for such carbon forms, with a measured hardness of up to about 50 GPa, probably because of a large number of threedimensional interplanar bonds formed due to the strong intermolecular interaction and possibly the deformation of the C,, cages under the reaction conditions. The densities of the samples are measured to be in the range 2.1-2.25 g cmm3, while values estimated from the X-ray results assuming a graphitelike structure fall in the range 2.15-2.4 g cmm3. We believe that these differences arise because of the existence of cages and cage remnants in the structure of these three-dimensional carbon networks. The densities are close to those measured by Li and

Lannin [93] on amorphous carbon (a-C) films in which ordered six-fold ring structures were found to be absent and the most intense peak in the structure factor function was found at approximately d= 1.16 A. As was shown earlier by Gao et al. [ 941 low density a-C films contain predominantly sp’ bonds and their conductivity and hardness may depend strongly on the structure of “medium-range” order. A low concentration of randomly distributed sp3 bonds appear as inclusions and do not significantly affect the properties of the material. Our diffraction patterns show some degree of order in the 002 planes, and thus the medium-range order is very different from the sp2-rich a-C films. We therefore conclude that the structures of the samples synthesized under the conditions indicated by the slanted lines in Fig. 1 correspond to a new form of amorphous carbon with medium-range order based on cross-linked and partially destroyed C,, molecules. The dashed curve divides this region of the p-T diagram into two parts. In the area below this line a random three-dimensional polymer of C,, molecules, cross-linked along either the two-fold, the three-fold or the five-fold axis and probably containing partially destroyed C,, molecules, is observed. The area between the bold solid and dashed lines may be considered as the region where a transition occurs from fullerite nanostructures to graphite and is labeled here as “partially graphitized fullerite”. Keita et ul. [77,95] have suggested the formation of a “polycondensated” structure in which the individual molecules coalesce to form large pseudo-linear clusters. Atomic force microscopy (AFM) studies of their samples show such quasi-linear clusters with apparent intermolecular distances of 6.557.7 A, practically identical for the typical diameter of a C,, molecule even at extreme pressures. In order to explain the very small intermolecular distances Keita et al. suggested that the molecules coalesce directly, each losing 445 carbon atoms from the wall near the point of contact. However, it is not always clear how such AFM pictures should be interpreted. As an example, Surjan et al. [96] recently obtained STM pictures of photopolymerized C,, showing a periodic intensity modulation along polymerized C,, chains with a modulation period of 4.5 A. In this case it is well known from X-ray diffraction studies that the distance between the centers of mass of the molecules is just above 9 A, and the 4.5 A modulation can be explained by assuming that the electron density on the molecule has two (apparently very similar) maxima, one near the “belly” of the molecule due to the electrons on the intramolecular sp2 bonds and one near the intermolecular sp3 bonds. Studies of samples treated at 8 GPa and temperatures higher than 1150 K [92] revealed a correlation between an increase in the hardness of the material and a decrease in the interplanar distances. The hardest samples, with a hardness of 38 GPa, showed a broad X-ray band with a maximum corresponding

High-pressure polymerized phases of C,,

333

based on intact Cso molecules, covalently linked into a disordered structure, and some indications of remaining crystallinity are still present. The main difference between the structures obtained in the regions 8-9 GPa and 9912 GPa probably arises from the fact that the materials should have different initial states, being polymerized in a two-dimensional structure in the lower-pressure range and in three dimensions at higher pressures. According to X-ray and TEM studies [29-31,371, the three-dimensionally polymerized disordered crystal state is characterised by a diffuse (002) ring corresponding to a lattice spacing of 3.14-3.3 A with four intense arcs (Fig. 16). A careful study of the TEM patterns [37] led to the conclusion that these diffraction patterns originate from tetrahedrons formed by { 111) planes of a cubic lattice. Tilting the sample by k60” from the original position led to a reappearance of the same diffraction pattern. The basic elements of this structure thus seem to be tetrahedrons consisting of four sp3-linked molecules. These tetrahedrons are probably ordered within small domains (clusters) but the domains have small misorientations at larger distances which destroys longrange order. As suggested by Blank et al. [86] and discussed above for the bee-type crystal structure, when molecules link together to form a tetrahedron, a 22-atom polyhedron is created between them (Fig. 15), and such tetrahedra thus probably form the basic building blocks of the disordered bee-type C,, structure. The other possibility is the formation of 24-atom polyhedra created by four hexagons. This type of polyhedron is formed by four CeO molecules

to an interplanar spacing of 3.32 A, which is even 3.36 A. smaller than the doo2 value for graphite, Samples treated under a pressure of 9.5 GPa and at temperatures of 11 OO- 1700 K [ 30,3 1] have hardness values in the range 50-80 GPa [97,98]. With an increase in T the interplanar spacings shift from the value 3.23 A to 3.34 A and the hardness decreases. Increasing T to above the thin dashed line in Fig. 1 causes an increase in d to 3.4 A and a decrease in the hardness, as was also observed at 8 GPa at similar temperatures [92]. Samples synthesized at 9.5 GPa and T= 1500 K have a measured Vickers hardness of H, =25 GPa [97,98]. It is important to note that all samples synthesized in the p-T region indicated by slanted lines in Fig. 1 are semimetals like graphite but have a conductivity which is lower by 2-3 orders of magnitude [92].

4.2 Disordered molecular crystal states As already discussed above, heating CGOrapidly at pressures between 9.5 and 12 GPa to temperatures between 900 K and 1400-2000 K (depending on pressure-see Fig. 1) results in the formation of a very hard, amorphous black phase [29938,77]. Hardness tests indicate that this material is comparable to crystalline diamond in hardness [30-351 (see Table 1) and the measured density of this material is in the range 2.4-2.8 g cmm3 (Fig. 7). Very similar X-ray patterns were obtained on samples treated at 8-9 GPa and 9OOS1300 K [ 861, but these have a lower density of about 2.2-2.25 g cmm3 and a correspondingly lower hardness of only about 10 GPa. The structures of these states are very likely still

Table 1. Collected data for the observed structure, density pcxp, hardness Hv (including error interval CJ),activation energy E, (for semiconductor-type materials) and resistivity r for a large number of samples as functions of the treatment pressure p and treatment No.

p (GPa)

temperature

T

Hv (GPa)

T(R)

Structure

pexr, (g cmm3)

Rhombohedral Disord. cross-link. layered struct. Disord. cross-link. layered struct. Disord. graphite + disord. cross-link. layered struct. Disord. graphite fee 12.9 A fee 12.7 A + bet Disordered crystal state Disord. cross-hnk. layered struct. Disord. cross-link. lavered struct. Disordered crystal state fee 12.6 A fee 12.4 A + distorted bee Monoclinic + ultrahard amorph. caee nanostruct. Ultrahard amorph. cage nanostruct. + monoclinic Ultrahard amorph. cage nanostruct. Ultrahard amorph. cage nanostruct. Ultrahard amorph. cage nanostruct. + diamond

1.97 2.20 2.22 2.21

2 30 38 25

2.23 2.03 2.3 2.56 2.25 2.27 2.7 2.2 2.8

1 70 80 90-125 50 25 100 80 90-130

1 2 3 4

8 8 8 8

900 1200 1800 1900

5 6 7 8 9 10 11 12 13

8 9.5 9.5 9.5 9.5 9.5 12 13 13

2300 670 770 970 1100 1800 1300 670 770

14

13

970

15 16 16

13 13 13

1250 1500 1750

17

13

2100

Where a range of values are shown this corresponds to data obtained sample. (Data compiled from a number of studies by the authors.)

D (GPa) IL1 +2 +3 IL3

I?, (eV)

I (Q cm)

sm. s.m. sm.

>108 10-r IO-* lo-3

s.m. *5 k7 *lo *5 +3 +10 *lo +10

0.02 0.3 s.m. s.m. 0.1

lo8 lo2 10 lo3 lo4 >10*

2.9

140&160

+10

0.1

10s

3.1 3.2 3.3

140&160 170 200

* 10 +10 *20

0.2

lo6 lo5

3.45 in different

IO4 regions

of one single, inhomogeneous

334

V. D.

linked along the two-fold axes and has four vacancies, and the molecules are arranged in hexagonal layers perpendicular to their three-fold axes. The layered structure of this material can be seen in the HRTEM image of a sample synthesized at 9.5 GPa and 770 K shown in Fig. 17. The temperature dependence of the resistivity of these samples shows a behavior typical for a semiconductor, as in the crystalline phases, but with a higher conductivity and lower activation energy (381. Raman data [30,31] confirm the existence of intact C,, molecules and the creation of intermolecular sp3 bonds in the structures. However, it should be pointed out here that the characteristical “pentagonal pinch” Raman mode disappears in this structure, probably because the very large number of intermolecular bonds no longer allows this mode of vibration. The molecules thus experience a dramatic transformation of the vibrational spectra under random three-dimensional polymerization. X-ray diffraction studies on samples treated at 9.5 GPa and temperatures of 870&1070 K show an intense (002) halo (Fig. 9) with a maximum corresponding to an interplanar distance of 3.14p3.30A, while the (100) and (101) reflections at 2.0-2.2 A are very weak and not easily distinguished. This indicates a low degree of order in the 002 planes. At pressures of 12 12.5 GPa and temperatures in the range 1200&1800 K the position of the (002) halo maximum in the X-ray patterns shifts to a position corresponding to 2.983.02 A and a second intense diffuse peak corresponding to d=2.2 A appears (Fig. 18). The shift of the (002) reflection may indicate deformation of the molecular cages and the increase in the second halo may be due to a transformation into another amorphous structure which will be discussed in the following section. It is interesting that, as for samples treated at 9.5 GPa, the

Fig. 17. HRTEM image of a disordered cross-linked layered fullerite structure. (HRTEM image obtained by E. V. Tatyanin and B. A. Kulnitskiy.)

BLANK

et

ai.

2 theta,

degrees

Fig. 18. Sequence of X-ray diffraction patterns for samples quenched from temperatures of 1770 to 2100 K at different pressures.

density of these materials is lower than that of the densest crystal modification obtained at the same pressure, and that the increase in temperature from 800 to 1700 K leads to a decrease in the measured density (Fig. 7). The hardness of these materials is also very high, about 100 GPa for a sample synthcsized at 12 GPa and 1300 K. The high hardness, the semiconductor-like conductivity and the fact that the density is intermediate between that of graphite and diamond may lead to the conclusion that the structure of this material is similar to the structure of i-C films. However, according to the experimental data of Gaskell et al. [99], other experimental studies and simulation studies, the diffraction patterns of i-C films have no distinct peak at 3.0-3.3 A, but contain a 2.2 A halo and a very strong halo corresponding to 1.2 A. No fullerene samples synthesized under these pressuretemperature conditions have given such a diffraction pattern and a more detailed analysis of the short- and medium-range order of the fullerite samples is required. Extensive studies of simulated models of amorphous diamond-like carbon (i-C) have been carried out by Beeman et ul. [ 1001, Kelires et al. [ lOlL103] and Frauenheim et ul. [ 104-1061, and the models used in these works have been compared by Gilkes et al. [ 1071. Models were proposed for the hardest diamond-like amorphous carbon, i.e. the i-C state “as quenched” from liquid carbon, for the annealed i-C* state and for tetrahedral amorphous carbon (ta-C). The first model contains about 87% of fourfold coordinated (sp3) atoms while after annealing only about 27% of them remain. However, the calculated densities of both modifications are rather high, about 3.3 and 2.9 g cmm3. The model of ta-C included about 85% sp3 sites and provides the best fit of the simulated radial distribution function to that calculated on the basis of neutron-scattering diffraction

High-pressure polymerized phases of C,, data. These models are in good agreement with experimental data for films, but very different from diffraction data for high pressureetemperature treated C6,,. Values for elastic constants calculated from these models were found to be approximately 50-80% of the corresponding values for diamond. The very large differences between the diffraction patterns of high-pressure treated C,, and data for both real diamond-like amorphous films and simulated models for these show that the structure of the superhard fullerite samples is very different from that of i-C* and even more different from that of sp3-rich i-C or ta-C, and we conclude that the amorphous superhard form of fullerite created at 12-12.5 GPa is truly a new, unique form of amorphous carbon. 4.3 Ultrahard amorphous nanostructure As shown in Table 1 and mentioned above, the hardness of the disordered, three-dimensionally polymerized states produced at 9.5 and 12 GPa is close to that of the (100) face of diamond. However, at still higher static pressures samples with an even higher hardness have been created from solid C,,, by either very-high-temperature treatment at a pressure of 13 GPa [30,31,38] or large shear deformation at pressures higher than 18 GPa at room temperature, or under quasi-hydrostatic conditions at approximately 25 GPa [20-221. In previous publications [ 3036,381 this state has been denoted the Amorphous 2 (Am. 2) phase and it resembles the so-called “state V” in the earliest publications by Blank et al. [2& 221. The very first investigations of the Raman spectra of solid Ceo in diamond anvil cells [9,1 l-151 revealed transformations to new forms of amorphous carbon identified as “strongly interacting agglomerates of C,, molecules” [ 131 or “collapsed fullerite” [ 14,151. Blank et al. [20-221 observed that a “state V” sample initially opaque in the visible region became transparent after large shear deformation, but no noticeable change was observed in the mechanical properties of the samples at this transformation which probably corresponds to a change of the ratio of sp’ to sp3 bond states. As proposed by Kelires [101,102] this transformation has no threshold, although changes in the electronic properties and transparency may be significant. A study of the shear deformation process in a specially designed shear deformation diamond anvil cell allowed Blank et al. [20-221 to conclude that the hardness of “state V” exceeded the hardness of the (100) face of diamond, and smaller values for the shifts of Raman bands under pressure for the fullerite than for the corresponding shifts in diamond gave evidence that the bulk modulus of “state V” may be higher than that of diamond. Investigations of the low-frequency Raman spectrum of “state V” showed that the distinct lines of pristine C,, transformed to a broad band in the range 250&800 cm-’ with an intensity about 30% of the intensity of the main band in the region 1350-1700 cm-‘. From this

335

it was concluded that the “state V” material obtained at room temperature at pressures higher than 18 GPa is based on strongly cross-linked and deformed CeO molecules. Bulk samples of the Am. 2 state with weights up to 80 mg were synthesized under a pressure of 13 GPa in the wide temperature range 1000-1900 K. Their hardness, as measured by the sclerometry method (see Appendix A), exceeds the hardness of the hardest ( 111) face of diamond and attains values in the range 170-300 GPa [86,97,98]. Because of this extremely high hardness the materials with the Am. 2 structure were called “ultrahard fullerites”. The elastic properties of 3-D-polymerized fullerites have been investigated using acoustic microscopy [38,98,108]. The velocities of sound waves were measured in samples synthesized under pressures of 12.5 and 13 GPa and at different temperatures (Table 2). The elastic constants were calculated from these data and the measured densities of the samples. Data for monocrystalline diamond are given for comparison. As seen in Table 2, the velocities of the compressional sound waves in the samples obtained at 13 GPa and 1770&1870 K are higher than the highest value for diamond and the bulk elastic modulus attains a value of about 1360 GPa, i.e. three times higher than that of diamond [98,108]. However, the velocity of the shear acoustic wave in fullerite is much smaller than in diamond and thus the shear modulus is only about 50% of that of diamond. The Young’s modulus of these fullerites is also smaller than in diamond and the Poisson’s ratio is in the range 0.3550.45, which is typical for polymers and much higher than the value for diamond, 0.08. The elastic properties of ultrahard fullerites are therefore very different from the properties of mono- and polycrystalline diamond which implies that the structure of ultrahard fullerites should also be very different from that of diamond. It is interesting to note that the measured bulk moduli B = 590-640 GPa for samples treated at somewhat lower temperatures, 1500 and 1670 K, match perfectly the estimate of 640 GPa given by Ruoff and Ruoff [4,5]. We therefore assume that under these synthesis conditions the C6,, cages still remain intact in the nanostructure. The sharp increase in B into the TPa range at higher treatment temperatures was not predicted and may be ascribed to the formation of a different type of nanostructure based on carbon clusters created by the fusion of walls of adjacent C,, molecules. This particular nanostructure, with mixed sp2 and sp3 sites, may be stiffer than the diamond structure because the sp’ bonds are stronger than the diamond-like sp3 bonds. An increase in the elastic modulus and hardness of a solid by a factor of 2-4 due to the formation of a particular nanostructure (superlattice) is not unusual and has been observed previously in CuNi and TiN/NbN foils [109,110]. Thin plates of ultrahard fullerites look transparent

V. D. BLANK cl ul.

336 Table 2. Density

p, longitudinal

C, and transverse

modulus E and Poisson’s ratio Y as a function

/I (gCW3)

p (GPa)

T(K)

12 5 13 13* 13 13% Diamond

1000

3.1

1500 1670 1770 1870

3.15 3.1 3.3 3.15 3.51

C, acoustic wave velocities, shear modulus G, bulk modulus B, Young’s of synthesis temperature T of fullerire samples treated under a pressure oi 13 GPa

c, (km SC’)

q (km s-‘)

C (GPa)

B (GPa)

17 0 17.0 16.2 20.2 22.3 17.5 19.6

9.36 8.0 7.4 8.5 7.0 II.6 12.8

280 200 170 240 155 354 535

540 640 590 1030 1360 445

*Denotes samples prepared for the synthesis in a dry argon diamond are given for comparison purposes only.

and have a yellow-brown colour. However, SEM and acoustic microscopy studies have shown that this state is not uniform, and grains (clusters) of different reflectivity were found in the SEM images as well as in the acoustic images. Clusters are randomly distributed and neither Raman spectra nor X-ray patterns could distinguish the true contribution of each type of cluster to the total pattern or spectrum. As mentioned above, the Raman spectra of the Am. 2 state [30-361 are similar to the spectra of the “state V” [20-221, but the relative intensities of the low-frequency and high-frequency bands are different and

the

position

of the

maximum

in the

high-fre-

quency band is about 1560-1570 cm-” in the Am. 2 state and 1550 cm -’ in “state V”. The Raman spectra of the Am. 2 state arc thus close lo the Raman spectra of ta-C films containing ZO-30% sp2 sites [Ill 1. However, this symmetric Raman band does not show the vibrational frequencies of amorphous sp3 sites or, in other words, “amorphous diamond”. Instead, according to Prawer rt ul. [ 1121 this band monitors the state of sp2-bonded material within an of sp2 sites sP3 matrix. At higher concentrations either the band has a skewed Lorentzlan shape with a peak at about 1500&1550 cm-‘, or the main maximum shifts to 1580cm I and another distincr peak with a maximum at about 1350 cm-’ appears. In the first case the spectrum is ascribed to the vibrational density of states of amorphous sp2-sp3 carbon [ 1131, but in the second case the peak at 1350 cm- ’ probably originates from the phonon spectrum of graphite with crystal sizes of 2.5 300 nm. Therefore, the Raman spectra of both ta-C and Am. 2 fullerite show only that the contents of sp* sites in their structure does not exceed 30% and that graphite clusters are absent. The spectra do not supply exact data about the structure of the sp3 matrix because Raman scattering from sp3 sites is much less intense than that fi-om sp2 ates. On the other hand, a very recent study of the Raman spectrum of amorphous sp3 carbon obtained in a diamond irradiated with MeV He ions [ 1141 has shown a set of sharp peaks at 1422. 1447, 1467, 1496, 1540, 1563, 1631, 1649, 1683 and 1726 cm ‘. Among them, the lines at 1496 and 1631 cm-’ arc 2--5 times more intense than the others. The normalised Raman

atmosphere.

The other samples

E

were prepared

(GPd)

710 550 460 660 450 1040

!’

I) 2s I).36 0.37 0.39 0.45 0 08

in air. Dala Lbr

spectrum agrees closely with the calculated density of states fol- diamond and the positions of the peaks do not depend on the frequency of the exciting laser beam. These facts prove that these sp3-bonded carbon samples consist of real “amorphous diamond”. However, the presence of such an “amorphous diamond” state m the structure of ta-C fiims and in the Am. 2 fullerite state cannot be identified from their Raman spectra because these particular lines arc swamped by a wide intense band arising from the scattering on sp2 sites. In contrast to “amorphous diamond”. the Raman spectra of both ta-C and the Am. 2 state have shown a shift of the main band when excited with lasers of different wavelength [36,115]. This dependence of the Raman spectra on excitation wavelength is interpreted in terms of resonant Raman scattering from aromatic rings with various sizes [ 1151 and compared with the effects observed on polymeric structures containing fragments of different sizes [36]. Such an effect is known for polymers [116] and should not take place m a completely Isotropic amorphous solid. These observations reveal that some kind of intermediate-range order exists in La-C and Am. 2 fullerite. We conclude that although the Raman spectra ot the Am. 2 state and of t&-C films are very similar and reveal some intermediate-range order in both structures, the data are not sufficient to deLerminc the degree of short- and medium-range order in the two states to compare them. It is clear that isotropic simulated models of the “collapsed fullerite” and ta-C [ 100~~106.117,118] do not indicate any intermediate-range order, and thus the calculated elastic moduli of ta-C [ 1031 did not exceed the values for diamond. The density of the ultrahard fullerite samples obtained was found to be in the range ol 3.1. 3.3 g cmm3. According to data for different simulated models [I 191 the sp” fraction in amorphous carbon structures with such a density may fall in a very wide range from about 30 to 80%. Thcrcfore these estimates support our conclusion based on the comparison of Raman spectra for ultrahard fullerites and ta-C that the sp’ fraction in ultrahard fullentes can be in the range of 20 to 30%. These values are consistent with the measured electric resistivity of

High-pressure polymerized phases of C,, ultrahard fullerites and ion-implanted ta-C [ 11 l] which is of the order of lo’-lo6 Q cm. More information about the short- and intermediate-range order in the Am. 2 state can be provided by X-ray data [36] (Fig. 18), but because of limited experimental facilities X-ray diffraction data have only been obtained in the wave vector range k=0.3-4.5 A-‘. In the range 4.5-20 A-’ data could only be obtained by means of registration of the diffraction patterns on film. Still, the data obtained were enough to reveal the main features of the whole diffraction pattern. An intense band with maxima corresponding to d=2.87-2.94 A-’ and low intensity bands corresponding to 1.771.9 A-’ and 5.2A-’ were found, and the diffraction patterns of the Am. 2 samples may be compared only with the ta-C films made by Gaskell et al. [99] and mentioned above. However, although the peaks at 2.9 and 5.2A’ coincide well with the data of Gaskell et al., the extreme hardness of the fullerite samples (170-300 GPa, compared to 100-l 10 GPa for ta-C [99,120]) and the Raman evidence for a peculiar intermediate-range order make us suspect essential differences between the structures of ultrahard amorphous fullerites and ta-C. Zhang et al. [ 1171 simulated a model of the high-pressure-high-temperature collapsed solid C,,. They calculate a density of 3.35 g crnm3 in the quenched state, a 21-71% ratio for the fractions of sp2 and sp3 bonds and a radial distribution function that agrees well with the radial distribution function of ta-C [99,107]. Also, the picture of the simulated structure presented in Fig. 2 of ref. [ 1171 looks very much like the model of i-C in ref. [ 101,102]. Therefore, different simulated models of the amorphous diamond-like carbon and collapsed C,, describe the short-range order of real ta-C films but do not describe intermediate-range order and cannot explain the high hardness of the Am. 2 state of fullerite. Investigations of rapidly quenched shock-compressed C,, by Hirai et al. [ 181 have shown that even at very high shock pressures, 50-55 GPa, and temperatures up to 2000 K samples transform to an amorphous diamond-like state with a structure very different from the structure of ta-C and the simulated models. From electron diffraction patterns they have calculated the radial distribution function of this so-called “new form of amorphous diamond” and found distances of 0.152, 0.253, 0.312, 0.378, 0.44 and 0.68 nm, values different from the experimental data for i-C and ta-C and from data calculated in a simulated model of collapsed C,, [ 1171. Of particular interest is the value 0.68 nm, which is actually the diameter of the C,, molecule. It is thus possible that fullerene-like cages exist in the structure of shocktreated fullerite. It should also be noted here that the position of the first peak in the electron diffraction patterns of ref. [18] is 3.0 A-’ and that of the following is at 4.9 A-‘. These values are different from those found in X-ray patterns for C,, treated

331

at static high pressure and high temperature, and the “new amorphous diamond” [ 181 is thus different from the Am. 2 state obtained under static pressure. Taking into account the structure and properties of i-C, ta-C films and amorphous diamond-like fullerite [ 181 we can conclude that none of these solids is identical to the Am. 2 state of fullerite [30-361. The extremely high hardness of this state, its unusual elastic constants and X-ray diffraction patterns allow us to deduce that the main difference is the existence of a fullerene-cage nanostructure, consisting of more or less broken-down fullerene molecule remnants, in a mixed sp2-sp3 amorphous carbon state. The observed inhomogenous microstructure of this state (partly opaque, partly transparent) may originate in a varying sp2-sp3 ratio in adjacent grains in the same sample. Further investigations are clearly required in order to find an adequate model for this structure. 5. CONVERSION DIAMOND

OF C,, INTO GRAPHITE,

AND CHAOITE-LIKE

CARBON

Under extreme conditions the C,, molecules themselves break down more or less completely and under these conditions the material tends to revert to the lowest energy states of carbon, i.e. graphite or diamond, depending on the ambient conditions. In Fig. 1 we have shown as a full line the graphite/diamond equilibrium line as given by Bundy et al. [7]. At pressures below 2 GPa at room temperature graphite is known to be the stable state of carbon and at higher pressures diamond is preferred. From the position of this line we would thus expect that if C,, were heated to very high temperatures at pressures below about 3 GPa the final state after a very long time would be graphite or a graphite-like material. Conversely, heating C& at pressures near 10 GPa or higher or submitting C,, to extreme pressures at “low” temperatures should result in the production of crystalline diamond. Experimentally, Kozlov et al. [ 191 report that heating C,, to very high temperatures at “low” pressures (1200 K at 3 GPa) results in the formation of relatively soft, graphite-like but disordered materials, and Blank et al. [36] report a direct transformation of C,, into diamond at 13 GPa and 2100 K. Nufiez-Regueiro et al. [ 16,281 have reported that C,, may transform into crystalline diamond even at room temperature at very high pressures (20 GPa) under extreme non-hydrostatic conditions. However, this report has not yet been independently verified. Diamond can also be produced from C,, at significantly lower pressures and temperature by the standard catalyst method. Addition of the usual iron group metal catalysts (Fe, Ni, Co, Mn) in different proportions has been shown to result in an almost complete conversion of C,, into diamond. This has been reported to occur over rather wide ranges in T and p, ranging from 8 GPa and 1800 K [36] to 5.5 GPa and 1400 K [85]. In this case the transforma-

338

V.D.

tion probably occurs indirectly by first breaking down the C,, into atomic carbon which then recrystallizes as diamond through the standard diamond production reaction [7]. It is quite probable that a similar mechanism acts in the case of shock pressure but we consider conversion of C,, into diamond, that such studies are far outside the subject of the present review and we shall not discuss these any further here. Yet another crystalline form of carbon was observed to form after large shear deformation under pressure and after treatment under strongly nonhydrostatic conditions in a wide range of pressures between 9.5 and 13 GPa at temperatures of 500 to 900 K [30-35,121]. The X-my patterns from these materials showed a number of interplanar distances; according to the latest analysis these are 7.07, 4.40, 4.17, 3.74, 3.58, 2.56, 2.49, 2.34, 2.29 and 2.23 A, numbers slightly different from those given in the original reference. The sharpness of the X-ray lines for this phase in comparison with the broad peaks from the molecular C,, crystals discussed above indicates scattering from an atomic lattice instead of a molecular one. Similar sets of interplanar distances are known for some natural carbon minerals such as chaoite [ 1221 and carbyne structures [ 1231. Blank [124] observed an analogous set of diffraction lines on single crystal graphite after combined high-pressure (12 GPa) and shear deformation treatment at room temperature (4.42, 4.11, 3.68, 3.22, 3.06, 2.53, 2.47 and 2.28 A). Recently Blank et al. [121] described this lattice as a new phase of carbon which differs from chaoite by having a triclinic distortion. The structure of this phase is intermediate between that of diamond and graphite, in that graphite sheets are connected by regularly spaced sp3 bonds and the ratio of sp3 to sp* sites is about 1:2. 6. SUMMARY AND CONCLUSIONS During the last five or six years a very large number of studies have been carried out regarding the effects of combined high pressure and high temperature on C&. These experiments, whether carried out in situ or on metastable materials quenched from high temperatures under pressure, have revealed a very large number of new structures and phases in the phase diagram of C&, as shown in Fig. 1. Although both low- and high-temperature treatment at atmospheric pressure, irradiation by laser or strong lamps and high-pressure shock treatment may provoke structural changes and widen our knowledge about C,,, its properties, stability and ability to polymerize, the most advanced and versatile procedure to create new materials on the basis of C,, is clearly static pressure-temperature treatment. In this review we have described the structures and main physical properties of a wide variety of highpressure polymerized modifications of C,, in the forms of both crystalline materials and disordered

BLANKCT&

derivatives. The existence of these phases confirms theoretical predictions that strong covalent intermolecular bonds may form between the individual molecules which in the pristine state have a very weak intermolecular interaction. The formation of strong intermolecular bonds may lead to a variety of crystal structures built from linear, planar or bulk polymer networks, depending on the relative orientations of the molecules and the fractions of sp*- and sp3-type bonds. These parameters, in turn, mainly depend on the actual pressure and temperature during the reaction. The variations in structure, lattice parameter and number of intermolecular bonds provide a wide variety of physical properties for the resulting materials. Some of these, the orthorhombic and rhombohedrdl materials, are rather soft like graphite, but semiconducting. Other structures with three-dimensional networks of intermolecular bonds, such as the 3-D-polymerized fee and the distorted bee structures, are very hard, and in fact the densest of these are equal in hardness to diamond. Unfortunately, so far detailed studies of their physical properties have been limited by inhomogeneities in the samples produced, and further developments in the synthesis conditions and equipment are required in order to obtain these materials in larger and more homogeneous quantities for future studies. The disordered derivatives obtained by high-pressure treatment either at or well above room temperature are perhaps of particular interest. Although the very first observations showed large similarities between these and different known types of amorphous carbon later studies have revealed important peculiarities in the detailed structure and the properties of these materials which sets them apart from other known types of carbon. The main differences probably arise because of the special fullerene-type short-range order in these structures which promotes a particular arrangement of sp* and sp3 bonds in their layered structures which look graphite-like but usually have a smaller interplanar distance. Above, we have called this type of disordered state a crosslinked layered carbon structure. Under pressures higher than 13 GPa a so-called nanostructure was ultrahard amorphous cage obtained with a very high hardness, exceeding that of diamond, and some peculiar polymeric properties. Yet another interesting type of disordered fullerite state was discovered with a medium-range order attributed to the formation of a network of crosslinked four-molecule tetrahedra with random relative orientations. This type of structure is most clearly observed in samples synthesized under pressures of 9.5 to 13 GPa. Finally, transformations of C,, into crystalline diamond, so-called “new amorphous diamond” and chaoite-type structures are also of great interest both from the point of view of basic science and as a new way to synthesize these materials for commercial applications.

High-pressure polymerized phases of C, High-pressure studies of C,, have thus resulted in the creation of a very large number of new materials. Although the low-pressure phases are rather well ordered such that their structures and properties can fairly easily be understood and even calculated theoretically, increasing pressure and temperature continuously increases the number of intermolecular bonds and the structural complexity of the materials produced. Although the low-pressure, low-temperature phases of C,, are thus already reasonably well investigated and understood, it is evident that large gaps still exist in our knowledge about the many forms of CeO that are formed under more extreme conditions. A better theoretical understanding of the properties of these materials is therefore needed both to and structures of new, predict the properties improved materials, to develop new or improved procedures to produce old and new materials, and to asses the possibilities of future practical and commercial applications of these materials, perhaps in particular the disordered high-pressure phases with their extreme mechanical properties. This area will therefore remain an interesting and rewarding field of investigation for several more years, both for experimentalists and for theorists. Acknowledgements-This work was financially supported by the Royal Swedish Academy of Sciences, by the Russian National Foundation for Intellectual Collaboration (Grant No. 95 076) and by the International Center for Diffraction Data (grant-in-aid No. 97-06). B. S. also acknowledges financial support from the Swedish Research Councils for Natural Sciences (NFR) and the Engineering Sciences (TFR).

APPENDIX

Measurements

339

does not imply a special standard for the shape of the indenter, and thus this method is preferable in the case of tests for extreme hardness. The simplest and oldest kind of sclerometric test is known as the Mohs’ hardness test. The Mohs’ scale is not linear with respect to Vickers hardness and it gives only qualitative information about whether one solid is harder or softer than another. On the Mohs’ scale the highest known value of hardness, i.e. that of diamond, was defined to be 10. The first evidence that the new states of carbon produced by high-pressure or simultaneous high-pressure and hightemperature treatment of CeO were harder than diamond was found by the Mohs’ method [2fL22,30,31]. Traces of plastic deformation were observed on the (100) face of a diamond anvil after shear deformation of C,, under pressure in the range 18-37 GPa [2&22] (Fig. 19). It is important to point out here that in this experiment the fullerite specimen slides on the surface of the diamond at about 20 GPa instead of moving through the material in the body of the sample when the anvil is rotated. This fact implies that the yield limit of the fullerite is greater than 20 GPa [ 1281, a value close to the yield limit of diamond. Traces of plastic deformation on the surface of the diamond anvils were obtained under lower pressures (2-3 GPa) while studying the metastable phases of C,, obtained after quenching samples from 670 K at 9.5 GPa [30,31]. In the same publication scratches were observed even on the (11 I) face of diamond, produced by samples obtained from C,, by treatment at 13 GPa in the temperature range 870-2100 K. The character of the deformation of the (111) face of diamond has recently been studied after scratching by both ultrahard fullerite samples and, for comparison, by carbonado-type diamond [86,97,98,129,130]. It is known that polycrystalline synthetic carbonado-type diamonds are harder than natural diamond, probably because of the small grain size and dislocation hardening, etc. The microrelief of the scratches (Fig. 20(a) and (b)) was studied with a Nanoscan measurement system, based upon the principles of the scanning force microscope (SFM) [ 1311. The scratches made by the carbonado tip were accompanied by numerous microcracks transverse to the scratch (Fig. 20(a)), as is typical for diamond at room temperature f 1251. The relief of the scratch produced by the fullerite sample synthe-

of hardness and elastic constants

As already mentioned above, the hardness of the C,, derivatives obtained over wide ranges in pressure and temperature is close to, and even exceeds, the hardness of diamond. However, measuring these extreme hardness values correctly has always been a problem. The most widespread procedure for testing the Vickers hardness assumes that the solid under test can be indented plastically by an absolutely rigid body. This condition is actually very well satisfied when a diamond indenter is applied to other solids. However, indenting diamond by diamond produces plastic indentation only in the special case when the diamond under test is heated to high temperature [ 1251. Only the hardness of the relatively “soft” (100) face of diamond could be measured in this way and this hardness was found to be about 130 GPa. Plastic deformation of the hardest face of diamond, the (111) face, has never been observed in this type of experiment, and thus the estimates 150-180 GPa for the hardness of this face have been obtained using different comparative models. However, plastic deformation of the (100) face of diamond at room temperature was indeed observed by Mao et al. [ 1261 after high-pressure experiments with diamond anvils at 170 GPa. An alternative method of testing hardness is the sclerometric method and it has been proved that in the case of plastic deformation of the solid under test the results of such tests provide the same Vickers hardness [ 1271. Unlike the Vickers method (or the Knoop method, which uses an indenter with a different shape) the sclerometric method

Fig. 19. The (100) surface of a diamond anvil deformed’by ultrahard fullerite under a pressure of 30 GPa by rotation of one anvil with respect to the other by 15” around the symmetry axis (the 100 direction in the anvil diamonds). The diameter of the working face on the anvil is 0.6 mm.

340

V. D. BLANK et (11.

400

800

1200

1600

2000

T W)

Fig. 21. Measured hardness as a function of treatment temperature for C,, samples treated at 9.5 and 13 GPa. (Reprinted from ref. 1971.)

(4

tips were used [ 129,130]. However, attempts to measure the hardness of ultrahard fullerites using diamond tips usually failed because diamond tips do not produce traces on the surface of the hardest fullerite samples. It was possible to scratch ultrahard fullerite samples only when using a fullerite tip, while the diamond surfaces could bc scratched by both diamond and fullerite tips. Using an ultrahard fullerite tip the hardness of both the (100) and the (I 11) faces of diamond could be measured, with the results 137*6 and 167_+5 GPa, respectively [38,129,130]. The ultrahard fullerite tips were 5 10 times more durable than the diamond tips. The hardness of different fullerite samples, cubic BN and diamond were measured after calibration of the device by hard solids with known hardnesses, such as sapphire, topaz, etc. More detailed descriptions of these measurements are presented in ref. [ 129,130]. The results obtained in the measurements of the hardness of fulleritcs polymerized at 9.5 and 13 GPa arc presented as functions of the treatment temperature in Fig. 21, reprinted from ref. [97].

REFERENCES

(b) Fig. 20. Nanoscan images of scratches on the ( 111) surface of a natural diamond crystal. The scratches were created at room temperature by (a) carbonado-type diamond and (b) ultrahard fullerite. Both plates show an area of 6 x 6 pm’. (Reprinted from ref. [86].)

sized at 13 GPa and 1770 K looks like a typical plastic indentation (Fig. 20(b)). This means that the fullerite sample is sufficiently hard to create a pressure at the contact point large enough for diamond to flow plastically at room temperature, and that the hardness of ultrahard fullerite exceeds the hardness of diamond. Quantitative measurements of the hardness of different forms of fullerites were made by the sclerometric method using the same Nunoscan microscope but in a specially designed regime for hardness tests by the sclerometric method [129-l 311. For comparison, both diamond and ultrahard fullerite indenting tips were used. It was found that the measured values for the hardness of different solids, including superhard fullerites and cubic boron nitride, using this method coincide well if diamond or ultrahard fullerite

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