Spatially resolved transient dynamics of charge density waves in NbSe(3).

We have developed methods for acquiring temporally and spatially resolved spectrograms of the velocity of sliding charge-density waves (CDWs), allowing unprecedented access to CDW dynamics. Complex transients arising from the interplay between elastic and plastic processes occur when the driving field direction is reversed. A transient spectral component due to shear elasticity can be unambiguously identified, and allows the most direct determination to date of the CDW's shear elastic modulus. Near current contacts, initially elastic displacements are followed by an elastic-to-plastic transition. A simple model provides a semiquantitative account of many aspects of these transients.

Correcting for surface topography in X-ray fluorescence imaging.

Samples with non-planar surfaces present challenges for X-ray fluorescence imaging analysis. Here, approximations are derived to describe the modulation of fluorescence signals by surface angles and topography, and suggestions are made for reducing this effect. A correction procedure is developed that is effective for trace element analysis of samples having a uniform matrix, and requires only a fluorescence map from a single detector. This procedure is applied to fluorescence maps from an incised gypsum tablet.

93Nb NMR spin echo spectroscopy in single crystal NbSe3.

We report electric field induced phase displacements of the charge density wave (CDW) in a single crystal of NbSe3 using 93Nb NMR spin-echo spectroscopy. CDW polarizations in the pinned state induced by unipolar and bipolar pulses are linear and reversible up to at least E = (0.96)ET. The polarizations have a broad distribution extending up to phase angles of order 60 degrees for electric fields close to threshold. No evidence for polarizations in excess of a CDW wavelength or for a divergence in polarization near ET are observed. The results are consistent with elastic depinning models, provided that the critical regime expected in large systems is not observable.

In-chain tunneling through charge-density-wave nanoconstrictions and break junctions.

We have fabricated longitudinal nanoconstrictions in the charge-density wave conductor (CDW) NbSe3 using a focused ion beam and using a mechanically controlled break-junction technique. Conductance peaks are observed below the TP1=145 K and TP2=59 K CDW transitions, which correspond closely with previous values of the full CDW gaps 2Delta1 and 2Delta2 obtained from photoemission. These results can be explained by assuming CDW-CDW tunneling in the presence of an energy gap corrugation epsilon2 comparable to Delta2, which eliminates expected peaks at +/-|Delta1+Delta2|. The nanometer length scales our experiments imply indicate that an alternative explanation based on tunneling through back-to-back CDW-normal-conductor junctions is unlikely.

Shear modulus and plasticity of a driven charge density wave.

We have probed the effects of transverse variations in pinning strength on charge-density-wave (CDW) structure in NbSe3 by x-ray micro-beam diffraction. In ribbonlike crystals having a large longitudinal step in thickness, the CDW first depins on the thick side of the step, causing rotations of the CDW wave vector. By measuring these rotations as a function of position and electric field, the corresponding shear strains are determined, allowing the CDW's shear modulus to be estimated. These results demonstrate the usefulness of x-ray microdiffraction as a tool in studying collective dynamics in electronic crystals.

Measurement of the shear strength of a charge density wave.

We have explored the shear plasticity of charge density waves (CDWs) in NbSe3 samples with cross sections having a single microfabricated thickness step. Shear stresses along the step result from thickness-dependent CDW pinning. For small thickness differences the CDW depins elastically at the volume average depinning field. For large thickness differences the thicker, more weakly pinned side depins first via plastic shear, and shear plasticity contributes substantial dissipation well above the depinning field. A simple model describes the qualitative features of our data and yields a value for the CDW's shear strength of approximately 9.5 x 10(3) Nm(-2). This value is orders of magnitude smaller than the CDW's longitudinal modulus but much larger than corresponding values for flux line lattices, and in part explains the relative coherence of the CDW response.

Sound velocity and elasticity of tetragonal lysozyme crystals by Brillouin spectroscopy.

Quasilongitudinal sound velocities and the second-order elastic moduli of tetragonal hen egg-white lysozyme crystals were determined as a function of relative humidity (RH) by Brillouin scattering. In hydrated crystals the measured sound velocities in the [110] plane vary between 2.12 +/- 0.03 km/s along the [001] direction and 2.31 +/- 0.08 km/s along the [110] direction. Dehydration from 98% to 67% RH increases the sound velocities and decreases the velocity anisotropy in (110) from 8.2% to 2.0%. A discontinuity in velocity and an inversion of the anisotropy is observed with increasing dehydration providing support for the existence of a structural transition below 88% RH. Brillouin linewidths can be described by a mechanical model in which the phonon is coupled to a relaxation mode of hydration water with a single relaxation time of 55 +/- 5 ps. At equilibrium hydration (98% RH) the longitudinal moduli C(11) + C(12) + 2C(66) = 12.81 +/- 0.08 GPa, C(11) = 5.49 +/- 0.03 GPa, and C(33) = 5.48 +/- 0.05 GPa were directly determined. Inversion of the measured sound velocities in the [110] plane constrains the combination C(44) + (1/2)C(13) to 2.99 +/- 0.05 GPa. Further constraints on the elastic tensor are obtained by combining the Brillouin quasilongitudinal results with axial compressibilities determined from high-pressure x-ray diffraction. We constrain the adiabatic bulk modulus to the range 2.7-5.3 GPa.

Unusual spectral behavior of charge-density waves with imperfect nesting in a quasi-one-dimensional metal.

Low-temperature electronic properties of the charge-density-wave system NbSe3 are reported from angle-resolved photoemission at 15 K. The effect of two instabilities q(1) and q(2) on the k-resolved spectral function is observed for the first time. With a pseudogap background, the gap spectra exhibit maxima at Delta*(1) approximately 110 meV and Delta*(2) approximately 45 meV. Imperfectly nested sections of the Fermi surface lack a Fermi-Dirac edge, and show the signature of a dispersion that is modified by self-energy effects. The energy scale is of the order of the effective gap 2 Delta*(2). The effect disappears above T2, suggesting a correlation with the charge-density-wave state.

Heat transfer from protein crystals: implications for flash-cooling and X-ray beam heating.

Three problems involving heat transfer from a protein crystal to a cooling agent are analyzed: flash-cooling in a cold nitrogen- or helium-gas stream, plunge-cooling into liquid nitrogen, propane or ethane and crystal heating in a cold gas stream owing to X-ray absorption. Heat transfer occurs by conduction inside the crystal and by convection from the crystal's outer surface to the cooling fluid. For flash-cooling in cold gas streams, heat transfer is limited by the rate of external convection; internal temperature gradients and crystal strains during cooling are very small. Helium gas provides only a threefold improvement in cooling rates relative to nitrogen because its much larger thermal conductivity is offset by its larger kinematic viscosity. Characteristic cooling times vary with crystal size L as L(3/2) and theoretical estimates of these times are consistent with experiments. Plunge-cooling into liquid cryogens, which can give much smaller convective thermal resistances provided that surface boiling is eliminated, can increase cooling rates by more than an order of magnitude. However, the internal conduction resistance is no longer negligible, producing much larger internal temperature gradients and strains that may damage larger crystals. Based on this analysis, factors affecting the success of flash-cooling experiments can be ordered from most to least important as follows: (1) crystal solvent content and solvent composition, (2) crystal size and shape, (3) amount of residual liquid around the crystal, (4) cooling method (liquid plunge versus gas stream), (5) choice of gas/liquid and (6) relative speed between cooling fluid and crystal. Crystal heating by X-ray absorption on present high-flux beamlines should be small. For a fixed flux and illuminated area, heating can be reduced by using crystals with areas normal to the beam that are much larger than the beam area.

Flash-cooling and annealing of protein crystals.

Flash-cooling and annealing of macromolecular crystals have been investigated using in situ X-ray imaging, diffraction-peak lineshape measurements and conventional crystallographic diffraction. The dominant mechanisms by which flash-cooling creates disorder are suggested and a fixed-temperature annealing protocol for reducing this disorder is demonstrated that should be more reliable and flexible than existing protocols. Flash-cooling tetragonal lysozyme crystals degrades diffraction resolution and broadens the distributions of lattice orientations (mosaicity) and lattice spacings. The diffraction resolution strongly correlates with the width of the lattice-spacing distribution. Annealing at fixed temperatures of 253 and 233 K consistently reduces the lattice-spacing spread and improves the resolution for annealing times up to approximately 30s. X-ray images show that this improvement arises from the formation of well ordered domains with characteristic sizes >10 microm and narrower mosaicities than the crystal as a whole. Flash-cooled triclinic crystals of lysozyme, which have a smaller water content than the tetragonal form, diffract to higher resolution with smaller mosaicities and exhibit pronounced ordered domain structure even before annealing. It is suggested that differential thermal expansion of the protein lattice and solvent may be the primary cause of flash-cooling-induced disorder. Mechanisms by which annealing at T << 273 K reduce this disorder are discussed.

High-temperature symmetry breaking in the electronic band structure of the quasi-one-dimensional solid NbSe3.

The electronic band structure of the Peierls compound NbSe3 has been explored for its symmetries with microspot synchrotron photoemission. The Fermi level crossings and deviations from one-dimensional behavior are identified. Density-functional calculations of the Fermi surfaces confirm the nesting conditions relevant for the two phase transitions. The instability along the chains with superstructure periodicity q = 0.44 A(-1) induces a backfolding of the electronic bands, and the Fermi level crossings appear suppressed. This broken symmetry is observed in the fluctuation regime at more than twice the critical temperature, where the correlation length is strongly reduced.

Night-time predation by Steller sea lions.

New insight into the feeding habits of these mammals will help conservation attempts.

Dynamic response of tetragonal lysozyme crystals to changes in relative humidity: implications for post-growth crystal treatments.

The dynamic response of tetragonal lysozyme crystals to dehydration has been characterized in situ using a combination of X-ray topography, high-resolution diffraction line-shape measurements and conventional crystallographic diffraction. For dehydration from 98% relative humidity (r.h.) to above 89%, mosaicity and diffraction resolution show little change and X-ray topographs remain featureless. Lattice constants decrease rapidly but the lattice-constant distribution within the crystal remains very narrow, indicating that water concentration gradients remain very small. Near 88% r.h., the c-axis lattice parameter decreases abruptly, the steady-state mosaicity and diffraction resolution degrade sharply and topographs develop extensive contrast. This transformation exhibits metastability and hysteresis. At fixed r.h. < 88% it is irreversible, but the original order can be almost completely restored by rehydration. These results suggest that this transformation is a first-order structural transition involving an abrupt loss of crystal water. The front between transformed and untransformed regions may propagate inward from the crystal surface and the resulting stresses along the front may degrade mosaicity. Differences in crystal size, shape and initial perfection may produce the observed variations in degradation timescale. Consequently, the success of more general post-growth treatments may often involve identifying procedures that either avoid lattice transitions, minimize disorder created during such transitions or maintain the lattice in an ordered metastable state.

Macromolecular impurities and disorder in protein crystals.

The mechanisms by which macromolecular impurities degrade the diffraction properties of protein crystals have been investigated using X-ray topography, high-resolution diffraction line shape measurements, crystallographic data collection, chemical analysis, and two-photon excitation fluorescence microscopy. Hen egg-white lysozyme crystals grown from solutions containing a structurally unrelated protein (ovotransferrin) and a related protein (turkey egg-white lysozyme) can exhibit significantly broadened mosaicity due to formation of cracks and dislocations but have overall B factors and diffraction resolutions comparable to those of crystals grown from uncontaminated lysozyme. Direct fluorescence imaging of the three-dimensional impurity distribution shows that impurities incorporate with different densities in sectors formed by growth on different crystal faces, and that impurity densities in the crystal core and along boundaries between growth sectors can be much larger than in other parts of the crystal. These nonuniformities create stresses that drive formation of the defects responsible for the mosaic broadening. Our results provide a rationale for the use of seeding to obtain high-quality crystals from heavily contaminated solutions and have implications for the use of crystallization for protein purification. Proteins 1999;36:270-281.

X-ray topographic studies of protein crystal perfection and growth.

The effects of solution variations during growth on the perfection of tetragonal lysozyme crystals have been characterized using X-ray topography and high angular and wavevector resolution reciprocal-space scans. X-ray images of crystals grown under nearly uniform conditions show little contrast or evidence of defects, and mosaic widths of these crystals are comparable with those reported for microgravity-grown crystals. Images of crystals for which solution conditions (temperature, pH or salt concentration) are changed after an initial period of uniform growth can show extensive contrast, indicating the presence of disorder. The X-ray mosaic widths of these crystals can be significantly broadened, but their radial widths are at most very slightly broadened, indicating that image contrast is primarily due to mosaicity. Comparison of X-ray images with mosaic scans indicates that regions grown after the change in solution conditions have broader mosaicities and are more disordered; that regions grown immediately after the change tend to have broader mosaicities than subsequent growth regions; and that the pre-change growth region is largely unaffected by solution changes. The observed disorder may arise from solution change-related transient growth instabilities, from transient liquid-liquid phase separation that can occur during the change, and from post-change relaxation of the lattice constant of the pre-change growth regions. These results suggest that solution variations during growth, including those typical of macroseeding, vapor-diffusion growth and other widely used techniques, may be an important source of disorder in some protein crystals.