2C44/(C11-C12) which is > 1 for nickel and < 1 for YSZ. The aggregates exhibit generally transversal isotropic elastic symmetry but again with a different anisotropy in the metallic coating (C/C33< 1) and in the ceramic coating (C/C33> 1). This anisotropy causes a substantial difference between Ek normal and perpendicular to the coating surface.

While the data in Fig. 1 still depend on the crystallographic plane (hkl) they can also be used to estimate the overall elastic constants of the aggregates that, in turn, yield the directional dependence of the mechanical value of Young's modulus. This distribution forms a surface with rotational symmetry around the coating surface normal vector as illustrated by a central section shown in Fig. 2.

The elastic anisotropy of sprayed coatings has its roots in their microstructure. In the complete absence of preferred crystallite orientation, the responsible factor is the porosity and alignment of elongated voids and cracks resulting from the spray process. These voids can be treated as another phase with very low elastic moduli. This way it is possible estimate the overall elastic constants if the distribution of pore shapes and volume fractions are known.

In the case that the aggregate constants are already known, the reverse approach of estimating a pore distribution can offer some insight into the properties of different coatings. Figs. 3a and b show where the best agreement was found for plasma sprayed metallic and ceramic coatings. The main difference is that the pore structure of the ceramic coating is dominated by interlamellar (horizontal) voids, while the concentrations of horizontal voids and vertical cracks are more balanced in the metallic coating.

REFERENCES

[1]. T. Gnäupel-Herold, J. Matejicek, and H.J. Prask, "Mechanical Properties of Plasma Sprayed Coatings - Measured by Diffraction," to be published in Proc. of the 9th Int. Metallurgical Conf. Metal 2000, Ostrava, Czech Republic, May 16-18, 2000; T. Gnäupel-Herold, and H.J. Prask, “Diffraction Elastic Constants for Arbitrary Specimen and Crystal Symmetries: Theory and Practical Consequences,” in Proc. of the 6th Int. Conf. on Residual Stresses (ICRS-6), (IOM Communications Ltd., UK, 2000), pp. 243-250.

current question of fundamental interest concerns whether a vortex solid-liquid transition exists in type-II superconductors [1]. In addition to providing a possible model system for melting and freezing, vortex matter offers unprecedented opportunities to study the effects of quenched disorder on phase transitions. The peak effect, where the critical current exhibits a peak rather than decreasing monotonically with increasing temperature, has been found to occur at the same temperature as a magnetization jump, which suggests a melting of the vortex lattice. However, there has been no direct structural evidence indicating whether there is indeed an underlying phase transition, and if so, whether it is solid-to-solid, solid-to-liquid, or even liquid-to-liquid in origin. Moreover, since quenched disorder is known to have important consequences for phase transitions, whether a solid-liquid transition can occur when random pinning is effective has broad implications in condensed matter physics.

Here we report the first observation of a striking history dependence of the structure function of vortex matter in the peak effect regime in a Nb single crystal, using SANS combined with simultaneous magnetic susceptibility measurements [2]. Metastable supercooled vortex liquid and superheated vortex solid phases have been observed, providing direct structural evidence for a first-order vortex solid-liquid transition associated with the peak effect.

Measurements were performed on a Nb single crystal, with the incident neutron beam nominally along the cylindrical axis which coincides with the three-fold symmetric <111> crystallographic direction. A superconducting magnet applies a dc magnetic field along the same direction. The peak-effect regime is determined in situ by measuring the characteristic dip in the temperature dependence of the real-part of the ac magnetic susceptibility X', as shown in Fig. 1(a) for H = 3.75 kOe [2]. The pronounced diamagnetic dip in x'(T) of the ac susceptibility corresponds to a strong peak effect in the critical current. The onset, the peak, and the end of the peak effect are denoted by T(H), T,(H), and T(H), respectively. Figure 1(b) shows the window of the experiment.

For each (T,H), we measure the SANS patterns for different thermal paths. At sufficiently low temperatures the SANS images show sharp Bragg peaks with six-fold symmetry, independently of the thermal history. An example is shown in the inset of Fig. 1(b) for H = 3.75 kOe and T = 3.50 K. However, the vortex pattern starts to show striking history dependence as the peak-effect regime is approached. We define the field-cooled (FC) state as when the

X. S. Ling, S. R. Park, and

B. A. McClain
Department of Physics
Brown University
Providence, RI 02912

S.-M. Choi

D. C. Dender and J. W. Lynn

NIST Center for Neutron Research
National Institute of Standards and Technology
Gaithersburg, MD 20899-8562

the ZFC and FC images at (3.75 kOe, 4.40 K), which is just below T (3.75 kOe) = 4.50 K. The images in the mid panel are for (4.00 kOe, 4.40 K), which is 0.10 K above T,(4.0 kOe) = 4.30 K. The intensities at the radial maximum for the mid panel SANS data are plotted in the lower panel. The sharp Bragg spots for the ZFC state indicate a vortex lattice with long-range-order (LRO), while the very broad spots for the FC state signify a disordered phase with short-range-order.

The observed hysteresis suggests a first-order vortex solidliquid (or glass) transition. A controversial issue is the location.

FIGURE 2. History-dependent SANS patterns at 4.40 K. The SANS images of the ZFC and FC vortex states for H = 3.75 kOe (top panel: below the onset of the peak effect) and H = 4.00 kOe (mid panel: near the upper end of the peak-effect regime). The thick arrows indicate how the SANS images evolve after applying a small ac magnetic field. The lower panel shows the intensity data at the radial maximum as a function of the azimuthal angle for the ZFC and FC SANS data (H = 4 kOe).

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of the underlying equilibrium phase transition to the position of the peak effect. One interpretation places the conjectured vortex solid-liquid transition T at T, consistent with the recent experiments in YBCO. Another widely held view is based on the classical Lindemann criterion which would place T at T (H) for Nb, provided the vortex-lattice elastic moduli remain well-behaved. In this scenario, the FC disordered phase seen here (as well as in [3,4]) is a supercooled liquid and the thermodynamic ground state is an ordered solid across the entire peak-effect regime. The third scenario places T at or below the onset of the peak effect.

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To experimentally determine the ground state and approximate value of T, the susceptibility coil was used to shake the vortex assembly, using SANS to observe how the vortex structure evolves. The data show that above T, the Bragg peaks start to disappear within the first 102 sec of the shaking experiment, demonstrating that the equilibrium state is disordered. Similiarly, the FC disordered states for T<T, are metastable and the ordered ZFC state is the ground state, opposite to that for T> T. In the T<T, regime, though, the metastability is obviously stronger since a much larger ac field is needed to change the metastable state.

We conclude that for T> T, the ordered ZFC vortex lattice is a superheated state and the ground state of the vortex system is a disordered vortex liquid, while for T<T, the ground state is a vortex Bragg solid and the disordered FC state is a supercooled vortex liquid. A thermodynamic phase transition must therefore have taken place, with TT. These results also imply the absence of superheating in conventional transport experiments with a large drive current, which solves a longstanding puzzle in which the history dependence of the nonlinear resistance always vanishes at T(H); only with extremely low drive currents may one then observe the subtle effects of superheating in transport.

REFERENCES

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[1] For a review, see G. Blatter, Rev. Mod. Phys. 66, 1125 (1994).

[2] X.S. Ling and J.I. Budnick, in Magnetic Susceptibility of Superconductors and Other Spin Systems, R.A. Hein, et al., eds. (Plenum Press, 1991), p.377.

[3] J.W. Lynn, et al., Phys. Rev. Lett. 72, 3413 (1994).

[4] P.L. Gammel, et al. Phys. Rev. Lett. 80, 833 (1998).

The continued growth of the semiconductor industry depends

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on advances in lithographic processes and materials to enable the economical production of smaller device features. Precise measurement of the size and quality of lithographically prepared features is critical as their sizes continue to decrease, with dimensions approaching 100 nm. Current microscopy-based techniques such as scanning electron microscopy (SEM) and atomic force microscopy (AFM) often require special modifications to enable the measurement of either the critical dimensions or feature resolution parameters. More importantly, these techniques become extremely challenging as feature sizes continue to decrease.

In this highlight, we demonstrate the powerful use of smallangle neutron scattering (SANS) to quickly, non-destructively, and quantitatively characterize both the size and profile of lithographically prepared structures as prepared on a silicon wafer substrate [1]. Until recently, SANS instruments were unable to measure lithographic feature sizes (sizes greater than 300 nm) and neutron beam fluxes were insufficient to measure scattering from thin film structures. Today, with new focusing optics, the high intensity NCNR instruments allow routine SANS measurements of smaller lithographic features [2]. Other important advantages for the use of SANS to measure lithographic structures include a) the measurement of structures on silicon, because single crystal silicon wafers are generally transparent to neutrons, b) a measurement metric statistically averaged over an area of several square centimeters, and c) less stringent SANS instrument requirements as lithographic structures decrease in size.

As an example, periodic, equally spaced, parallel line patterns with a nominal size of 150 nm were prepared on a silicon single crystal wafer using standard 248 nm optical lithography, and placed directly in and normal to the neutron beam. Quantitative measurements of the size and average profile of these lines are extracted from the scattering data. SEM micrographs of these structures are shown in Fig. 1.

The SANS measurements were performed on the NG-7 30 m SANS line under ambient atmospheric conditions at the NCNR.

axis of the detector. Six orders of diffraction peaks are immediately observed in the horizontal axis of the detector because of the highly periodic pattern of the fabricated lines. By linearly fitting the peak position plotted as a function of the diffraction order index, the feature repeat distance for the structure in Fig. 1 is determined to be (3031 ±9) Å.

A more detailed analysis provides a quantitative determination of the average profile of the line structures, including a measure of the line-edge roughness (LER). We model the periodic line pattern as a convolution of a periodic delta function with the average cross-section of a line. In Fig. 3, the scattering intensity of a given diffraction peak is plotted as a function of the position of the peak. The solid line is the best theoretical fit to the experimental data and corresponds to a measure of the LER of (213 ± 13) Å. Also in Fig. 3, the second and fourth order diffraction peaks are visible and less intense than the first and third diffraction peaks. The measurable intensity of the even order diffraction peaks indicates that the line feature size is slightly less than one half the overall repeat distance. The model fit results in a line feature size of (1350 ± 60) Å.

The average line structural size and cross-section were determined in a configuration where the sample was placed perpendicular to the incident neutron beam. More three-dimensional information about the average line structure can be obtained by tilting the line pattern with respect to the incident beam. Varying projections of the line profile onto the detector plane provide an elegant method to deduce more specific structural information. In additional, the formalism to extend the SANS theoretical framework to arbitrary shapes is well established and will be applied in the future. With these advances, SANS may be used to identify resolution limits in new nanofabrication processes and materials and to serve as an important metrology tool in understanding the physical processes that control the resolution of these methods.

REFERENCES

[1] W. L Wu, E. K. Lin, Q. Lin, and M. Angelopolous, J. Appl. Phys., 88, (2000) (in press).

[2] S.-M. Choi, J. G. Barker, C. J. Glinka, Y. T. Cheng, and P. L. Gammel, J. Appl. Cryst. 33, 793 (2000). For a brief description of the lens system, see the highlight in NCNR 1999 Accomplishments and Opportunities, NIST SP 944, p. 14.