Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

Water And Ice Nucleation Sites From Ion Implantation Of Silicon

Ion implantation has a substantial effect on the heterogeneous nucleation of water and ice. An enhancement of water nucleation and a suppression of ice nucleation occurred for samples of silicon implanted with ions of various species and dosage. These effects were noticeable only for samples implanted with ion doses approaching or exceeding the critical dose necessary to produce amorphous silicon. The behavior of the water droplet and ice crystal growth can be related to the amount of ion produced damage to the substrate surface. The nature of the damage can be controlled by variation of the incident ion species, dose, and energy and thus offers a means of quantifying the surface damage while studying its relationship to heterogeneous nucleation. © 1980 American Chemical Society

Influence of uniaxial stress on the lamellar spacing of eutectics

Directional solidification of lamellar eutectic structures submitted to uniaxial stress is investigated. In the spirit of an approximation first used by Jackson and Hunt, we calculate the stress tensor for a two-dimensional crystal with triangular surface, using a Fourier expansion of the Airy function. crystal with triangular surface in contact with its melt, given that a uniaxial external stress is applied. The effect of the resulting change in chemical potential is introduced into the standard model for directional solidification of a lamellar eutectic. This calculation is motivated by an observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H. M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces similar effects as a strong gravitational field in the case of dilute-alloy solidification. Therefore, the coupling between the Grinfeld and the Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the former instability gets reduced to a value close to that of the latter. Analogously, in the case of eutectics, the characteristic length scale of the Grinfeld instability should be reduced to a size not extremely far from typical lamellar spacings. In a Jackson-Hunt like approach we average the undercooling, including the stress term, over a pair of lamellae. Following Jackson and Hunt, we assume the selected wavelength to be determined by the minimum undercooling criterion and compute its shift due to the external stress. we realize the shifting of the wavelength by the application of external stress. In addition, we find that in general the volume fraction of the two solid phases is changed by uniaxial stress. Implications for experiments on eutectics are discussed.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.

Influence of external flows on crystal growth: numerical investigation

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Peclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Peclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some images had to be substantially reduced in comparison to original, resulting in low qualit

Spatial geometry of the rotating disk and its non-rotating counterpart

A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry of their proper space is hyperbolic. This has interesting consequences concerning their interpretation of the geometry of a non-rotating disk having the same radius. The influence of clock synchronization on spatial measurements is discussed.Comment: 10 pages, 3 figures, this is the version accepted by American Journal of Physics; I had to remove the special relativity part, which one of the referees did not like; it is still available in v

What are the interactions in quantum glasses?

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyse the case where the defects can be modelled either as simple 2-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to 2nd order in the displacement field. It is shown that the linear coupling generates not only the usual $1/r^3$ Ising-like interaction between the rotational tunneling defect modes, which cause them to freeze around a temperature $T_G$, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however the coupling of these to the frozen rotational modes, now via the 2nd-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range $1/r^5$ interactions between them). Detailed expressions for all these couplings are given.Comment: 12 pages, 2 figures. Minor modifications, published versio

Argonne National Laboratory Reports

The uniaxial stress-strain behavior of Zircaloy-2 and -4, Zircaloy-oxygen alloys with a uniform oxygen distribution, and composite specimens with a ZrO2/alpha/beta layer structure was investigated over the range of experimental conditions: temperature 25-1400 degrees C; strain rate ; oxygen content 0.11 - 4.4 wt %; grain size 5-50 micrometers; texture longitudinal, transverse, and diagonal orientations; and microstructural state, which consists of the equiaxed alpha phase and various transformed beta acicular structures. The work-hardening and strain-rate sensitivity parameters were determined from the experimental results, and the tensile properties were correlated with oxygen concentration, oxygen distribution in the material, and microstructure. Dynamic strain-aging phenomena were observed in Zircaloy at 200, 400, and 700 degrees C, and super-plastic deformation occurred at 850 and 1000 degrees C. An increase in the oxygen concentration in homogeneous Zircaloy-oxygen alloys increased the ultimate tensile strength and decreased the total strain, particularly below approximately 900/sup 0/C. In composite specimens with the ZrO2/alpha/beta structure, the total oxygen content had little effect on the ultimate tensile strength below approximately 1000 degrees C, but the strength increased with oxygen content at higher temperatures. Information on the effects of grain size, oxygen content, texture, and strain rate on the stress-strain behavior suggests that the dominant mechanism of super-plastic deformation in Zircaloy near approximately 850/sup 0/C is grain-boundary sliding at the alpha-beta interface with accommodation by diffusional creep, dislocation slip, and grain-boundary migration. Good correlation was obtained between ductility and values of the strain-rate sensitivity parameter

Test plan for high-burnup fuel cladding behavior under loss-of- coolant accident conditions

Excessive oxidation, hydriding, and extensive irradiation damage occur in high-burnup fuel cladding, and as result, mechanical properties of high-burnup fuels are degraded significantly. This may influence the current fuel cladding failure limits for loss-of- coolant-accident (LOCA) situations, which are based on fuel cladding behavior for zero burnup. To avoid cladding fragmentation and fuel dispersal during a LOCA, 10 CFR 50.46 requires that peak cladding temperature shall not exceed 1204 degrees C (2200 degrees F) and that total oxidation of the fuel cladding nowhere exceeds 0.17 times total cladding thickness before oxidation. Because of the concern, a new experimental program to investigate high-burnup fuel cladding behavior under LOCA situations has been initiated under the sponsorship of the U.S. Nuclear Regulatory Commission. A hot-cell test plan to investigate single-rod behavior under simulated LOCA conditions is described in this paper. In the meantime, industry fuel design and operating conditions are expected to undergo further changes as more advanced cladding materials are developed. Under these circumstances, mechanical properties of high-burnup fuel cladding require further investigation so that results from studies on LOCA, reactivity- initiated-accident (RIA), operational transient, and power-ramping situations, can be extrapolated to modified or advanced cladding materials and altered irradiation conditions without repeating major integral experiments in test reactors. To provide the applicable data base and mechanistic understanding, tests will be conducted to determine dynamic and static fracture toughness and tensile properties. Background and rationale for selecting the specific mechanical properties tests are also described

Evidence for a Second Order Phase Transition in Glasses at Very Low Temperatures -- A Macroscopic Quantum State of Tunneling Systems

Dielectric measurements at very low temperature indicate that in a glass with the eutectic composition BaO-Al$_2$O$_3$-SiO$_2$ a phase transition occurs at 5.84 mK. Below that temperature small magnetic fields of the order of 10 $\mu$T cause noticeable changes of the dielectric constant although the glass is insensitive to fields up to 20 T above 10 mK. The experimental findings may be interpreted as the signature of the formation of a new phase in which many tunneling systems perform a coherent motion resulting in a macroscopic wave function.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let