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FIGURE 2. Planer lattice constant variation of the total energy of (7,0) nanotube ropes in three different phases. Inset shows the view of the structures along c-axis. The zero of energy was taken to be the energy of vdW packing of the nanotubes.
ropes could occur at modest pressures and temperatures. Once the interlinked phase is reached, the energy barrier required to break the bonds and obtain free nanotubes is about 0.7 eV (25 meV/atom), which is comparable to that of 1D polymerized C, molecules (20 meV/atom).
Figure 2 also shows that another interlinked phase of (7,0) nanotubes becomes the ground state for lattice parameter smaller than 8.0 Å. In this new phase the nanotubes are interlinked along both a- and b-axes (see Fig. 3a). This 2-D interlinked structure is about four times stiffer than the 1-D interlinked phase and sixteen times stiffer than the vdW nanoropes.
We observe that applying even higher pressures yields more complicated and denser phases for many of the nanoropes studied here (see Fig. 3). For (9,0) nanoropes, we find that the nanotubes are interlinked along three directions forming a hexagonal network.
The length of the intertube bond, dec 1.644 Å, is significantly elongated for a sp3 C-C bond. The two dimensional interlinked phase of (7,0) nanotubes is further transformed to a denser structure at 30 Gpa with a band gap of 2 eV (Fig. 3c). By comparison, (6,6) nanotubes do not form an interlinked structure up to a pressure of 60 GPa. Rather the nanotubes are hexagonally distorted such that the local structure of the nanotube faces is similar to that in
FIGURE 3. Various high density phases of carbon nanotubes. (a) Twodimensional interlinked structure of (5,0) nanotubes, consisting of rectangularly distorted nanotubes interlinked on a 2-D network. (b) A hexagonal network of (9,0) nanotubes, (c) A very dense structure of (7,0) nanotubes obtained under 30 GPa pressure. (d) The optimized structure of (6,6) nanotubes under P = 53 GPa.
graphite sheets (Fig. 3d). Furthermore, releasing the pressure yields the original structure, indicating that the distortion is purely elastic. The structural changes clearly have strong effects on the electronic properties  and therefore should be detected in the pressure dependence of various transport properties of nanoropes.
The new pressure-induced, high density phases  reported here may provide a way of synthesizing novel carbon base materials. with interesting physical properties. For example interlinking of the nanotubes may improve the mechanical performance of composites based on these materials. The change in the band gap of a SWNT with applied pressure can be exploited to realize various quantum devices on a single nanotube with variable and reversible electronic properties . It will be an experimental challenge to confirm the structures predicted here. A difference-INS spectrum of two identical samples, one treated with pressure and the other not, may give some evidence for the new phases.
 T. Yildirim, O. Gulseren, C. Kilic, and S. Ciraci, Phys. Rev. B 62, 12648 (2000).  C. Kilic, S. Ciraci, O. Gulseren, and T. Yildirim, Phys. Rev. B 62, R16345 (2000).
DYNAMICS CHANGES IN THE
The function of a protein depends critically on its ability to adopt a specific structure. Remarkably, a protein can fold efficiently to this native state from the many unfolded states on physiological time scales. Understanding how this process occurs is one of the great challenges in biology. Proteins can also form partially folded, collapsed states under both equilibrium and non-equilibrium conditions [1,2]. Such partially folded proteins resemble the intermediate states along the protein folding pathway, and thus play an important role in understanding the mechanisms of protein folding. Moreover these partially folded proteins have also been shown to participate in important cell functions.
A molten globule is a compact, partially folded protein that has native-like secondary structure and backbone folding topology, but lacks the extensive, specific side-chain packing interactions of the native structure . Structural studies have shown that the sidechains in a molten globule can adopt a greater variety of conformations than in a native protein. The ability of the side chains to form the tight and specific interactions typical of a native protein, is the essential final step in the protein folding pathway. This packing process is considered to be energetically more difficult than forming the collapsed, disordered folding intermediates. However, little is known about the dynamics of this mostly folded state.
In order to understand the changes in protein dynamics that occur in the final stages of folding, we have used incoherent quasielastic neutron scattering (IQNS) to probe the differences in the dynamics between the native state and the almost completely folded, molten globule state of the protein, bovine a-lactalbumin in solution . Because hydrogen scatters neutrons much more strongly than deuterium, the exchangeable protons were deuterated and DO was used as the solvent. The scattering from the protein is then dominated by the non-exchangeable protons in the side-chains. Figure 1 shows the measured scattering function, S(Q, w), of bovine a-lactalbumin (BLA) and its molten globules (MBLA), as a function of the energy transfer hw at a momentum transfer Q = 1.08 Å1. The broader quasielastic peak of MBLA indicates that the side-chain protons within the molten globules move significantly faster than those in the native protein, which reflects the lack of the specific side chain interactions in MBLA compared to BLA.
In addition to the time scale, IQNS yields information on the geometry of the observed motion through the Q-dependence of S(Q, @). We have analyzed the Q-dependence for BLA and MBLA
Zimei Bu and Charles C. Han
NIST Polymers Division
National Institute of Standards and Technology Gaithersburg, MD 20899-8542
Dan A. Neumann, Seung-Hun Lee,
and Craig M. Brown
NIST Center for Neutron Research
Donald M. Engelman
Department of Molecular Biophysics and Biochemistry Yale University
New Haven, CT 06520-8114
using a model where some of the protons diffuse within a spherical cavity, while others are fixed on the≈ 70 ps time scale of these measurements. This is intended to capture the physical picture of side chain motion within a constrained volume imposed by the backbone topology of the protein. Within this model, the scattering consists of two components, a 8-function and a Lorenztian, each broadened with the experimental resolution≈ 60 μeV. Typical fits for individual spectra are shown in Fig. 1.
Figure 2 shows the half-width at half-maximum П of the Lorenztian component of the scattering as a function of Q2. The initial linear region indicates that on longer length scales (small Q), the protons undergo spatially-restricted diffusive motions, while the crossover to a consant width at higher Q reflects the granularity of the motion at these shorter, atomic length scales. The elastic incoherent structure factor, which gives the time-averaged spatial distribution of the protons, is formed by dividing the intenstity of the elastic (8-function) component by the total integrated intensity measured at each Q. The EISF is shown as a function of Q in Fig. 3. The solid lines show fits to the EISF expected for diffusion within a sphere, showing that the length scale of the motion increases by about 25% as the side chains become disordered. This is in contrast with the usual situation where slower motions tend to cover larger
length scales. The fact that the EISF plateaus at a higher value for BLA than MBLA indicates that more of the side chain protons are immobilized in the protein's native state.
The mean square amplitude <u2> of the high-frequency vibrational modes can be obtainted from the Q-dependence of the total scattering intensity through the Debye-Waller factor. The values of <u> extracted in this way are indistinguishable for BLA and MBLA, which suggests that chemical bond vibrational motions do not change significantly in the final stage of protein folding.
Overall, these results demonstrate that the side chains in molten globules are significantly more mobile than those in the native protein, and explore a larger length scale in a shorter time. This indicates that the specific side chain interactions responsible for the final step in protein folding both localize and slow the motions of the side chains.
1.0 1.5 2.0 2.5
2.5 3.0 3.5
Q2 (Å ̈2)
Q (Å ̈1)
FIGURE 2. The half-width at half-maximum I of the quasielastic Lorentzian peak as a function of the momentum transfer Q2; () is for BLA and (O) is for MBLA. The I vs. Q plot reflects the length dependence of the decay rate of the self-correlation function and is a measure of the mobility of the protons within the protein.
FIGURE 3. The elastic incoherent structure factor (EISF) of (m) BLA and (0) MBLA. The lines are fits to the EISF expected for diffusion within a sphere. The fits show that the length scale of the motion in MBLA is about 25% larger than in BLA.
SOFT PHONON ANOMALIES IN RELAXOR
ur current phonon studies of ferroelectrics at the NCNR are part of a systematic investigation of ABO, perovskite oxides that exhibit exceptionally high piezoelectric responses. Two solid solutions, (Pb[Zn,,Nb23]O3),.,(PbTiO3), (PZN-xPT) and (PbZrO3)1-x (PbTiO,), (PZT) have been extensively investigated in recent years. A common feature of these two systems is the morphotropic phase boundary (MPB), which separates the tetragonal and rhombohedral regions of the T-x phase diagram. The maximum piezoelectric activity is located on the rhombohedral side of the MPB for both systems. PZN-xPT, however, can sustain ultrahigh strain levels, with <1% hysteretic loss, fully one order of magnitude larger than those attainable with conventional PZT-based piezoelectric ceramics. These two remarkable properties suggest that PZN-xPT holds great promise for the next generation of solid-state transducers.
The compositions of the perovskite B-sites of PZN-xPT and PZT differ in a key respect. Whereas an isovalent mixture of Zr++ and Ti++ ions occupies the PZT B-site, a more disparate group of heterovalent Zn2+, Ti4+, and Nb5+ ions shares the PZN-xPT B-site. This creates intense quenched random electric fields that are thought to produce the so-called relaxor phase, which is characterized by a diffuse phase transition and a broad and strongly dispersive peak in the dielectric susceptibility. Despite years of research, the physics of this diffuse phase transition is still not well understood. In prototypical ferroelectric systems such as PbTiO,, it is well known that the softening of a zone-center transverse optic (TO) phonon drives the transition from a cubic paraelectric phase to a tetragonal ferroelectric phase. In relaxor compounds such as pure PZN, however, the mixed-valence character of the B-site sharply breaks the translational symmetry, resulting in much more complex lattice dynamics. In fact, no definitive evidence for a soft mode has been found in these relaxor systems.
Motivated by these results, we have examined the lattice dynamics of the polar TO phonon mode in a high quality single crystal of PZN-8 %PT, for which the measured value of the piezoelectric coefficient d1, is a maximum. Figure 1 shows neutron scattering data taken on PZN-8 %PT in its cubic phase at 500 K (~50 K above T) . The maximum scattered neutron intensity has been plotted as a function of energy transfer ho and momentum
transfer q along the symmetry directions  and . The lowest-energy data points trace out a normal TA phonon branch along both  and . What is striking, however, is that Fig. 1 shows no evidence of a zone center TO mode at all. Instead, the data suggest a precipitous drop of the TO branch into the TA branch, somewhat resembling a waterfall. This anomalous feature is highlighted by the shaded regions in Fig. 1, and stands in marked contrast to the behavior of PbTiO, where the same TO phonon branch intercepts the ho-axis at a finite energy.
To clarify the nature of this unusual observation, we show a constant-E scan at ho= 6 meV in Fig. 2 along with a constant-Q scan in the insert . Both scans were taken at 500 K near the (220) Bragg peak, and along the  direction. The small horizontal
bar shown under the left peak of the constant-E scan represents the instrumental FWHM q-resolution. We see immediately that the constant-Q scan shows no evidence of any well-defined phonon peak, most likely because the phonons near the zone center are overdamped. However, the constant-E scan indicates the presence of a ridge of scattering intensity at = 0.13 r.l.u., or about 0.2 Å1. Thus, the sharp drop in TO branch that appears to take place in Fig. 1 does not correspond to a real dispersion. Rather, it simply indicates a region of (ho,q)-space in which the phonon scattering cross section is enhanced. The question remains why does this happen?
In 1983 Burns and Dacol proposed a seminal model for the disorder intrinsic to relaxor ferroelectrics . Using measurements
The presence of such randomly oriented PMR above T in PZN-8 %PT should effectively impede the propagation of polar phonon modes whose wavelength exceeds the size of the PMR. The observation that the phonon scattering cross section is dramatically affected ≈ 0.2 Å1 from the zone center gives a measure of the dynamic size of these polarized domains. If the length scale associated with the anomalous "waterfall" is of order 2π/q, this would correspond to 31 Å, or about 7 to 8 unit cells, a size that is consistent with Burns and Dacol's conjecture. We have recently been able to model this behavior quite well for PZN using a simple coupled-mode that assumes a highly q-dependent linewidth П(q) that increases sharply for q<0.2 Å1 . Hence we speculate that the striking anomalies in the TO phonon branch shown in Fig. 1 (the same branch that goes soft at the zone center at T in PbTiO,) for q< 0.2 Å1 are directly caused by these PMR which serve to dampen the zone center TO phonon modes. If true, then this unusual behavior should be observed in other related relaxor systems. Direct evidence for this has already been observed at room temperature in neutron scattering measurements on PMN (M = Mg) .
 P. M. Gehring, S.-E. Park, and G. Shirane, Phys. Rev. Lett. 84, 5216 (2000).
 P. M. Gehring, S.-E. Park, and G. Shirane, to be submitted to Phys. Rev. B.
 G. Burns and F. H. Dacol, Phys. Rev. B 28, 2527 (1983); ibid. Solid State Commun. 48,853, (1983).
 P. M. Gehring, S. B. Vakhrushev, and G. Shirane, in Proceedings of the Fundamental Physics of Ferroelectrics 2000 Winter Workshop, Aspen, 2000, edited by R. E. Cohen (American Institute of Physics, 2000), p. 314.
FIGURE 2. Constant-E scan measured along  at 6 meV at 500 K near the (220) Bragg peak. Solid line is a fit to a double Gaussian function of C. No peak is discernible in the constant-Q scan shown in the insert.