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We analyze the stability of a planar solid-solid interface at which a chemical reaction occurs. Examples include oxidation, nitridation, or silicide formation. Using a continuum model, including a general formula for the stress-dependence of the reaction rate, we show that stress effects can render a planar interface dynamically unstable with respect to perturbations of intermediate wavelength.
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Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential convergence in weighted $L^p$ and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a point-wise Green function decomposition reconciling spectral decomposition and short-time Nash-Aronson estimates and an instantaneous tracking scheme similar to that used in the study of stability of viscous shock waves.
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion process in the reference frame moving with the average velocity of the front. Here we address pushed fronts, where the front velocity in the deterministic limit is affected by higher-order reactions and is therefore larger than the linear spread velocity. For a subclass of these fronts -- strongly pushed fronts -- the effective diffusion constant $D_fsim 1/N$ of the front can be calculated, in the leading order, via a perturbation theory in $1/N ll 1$, where $Ngg 1$ is the typical number of particles in the transition region. This perturbation theory, however, overestimates the contribution of a few fast particles in the leading edge of the front. We suggest a more consistent calculation by introducing a spatial integration cutoff at a distance beyond which the average number of particles is of order 1. This leads to a non-perturbative correction to $D_f$ which even becomes dominant close to the transition point between the strongly and weakly pushed fronts. At the transition point we obtain a logarithmic correction to the $1/N$ scaling of $D_f$. We also uncover another, and quite surprising, effect of the fast particles in the leading edge of the front. Because of these particles, the position fluctuations of the front can be described as a diffusion process only on very long time intervals with a duration $Delta t gg tau_N$, where $tau_N$ scales as $N$. At intermediate times the position fluctuations of the front are anomalously large and non-diffusive. Our extensive Monte-Carlo simulations of a particular reacting lattice gas model support these conclusions.
Poly(vinylidene fluoride) (PVDF) has long been regarded as an ideal piezoelectric plastic because it exhibits a large piezoelectric response and a high thermal stability. However, the realization of piezoelectric PVDF elements has proven to be problematic, amongst others, due to the lack of industrially-scalable methods to process PVDF into the appropriate polar crystalline forms. Here, we show that fully piezoelectric PVDF films can be produced via a single-step process that exploits the fact that PVDF can be molded at temperatures below its melting temperature, i.e. via solid-state-processing. We demonstrate that we thereby produce d_PVDF, the piezoelectric charge coefficient of which is comparable to that of biaxially stretched d_PVDF. We expect that the simplicity and scalability of solid-state processing combined with the excellent piezoelectric properties of our PVDF structures will provide new opportunities for this commodity polymer and will open a range of possibilities for future, large-scale, industrial production of plastic piezoelectric films
We describe the microstructure, shape and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of conventional affine, elastic deformations and {em non-affine} degrees of freedom. Non-affineness, $phi$, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. A description in terms of $phi$ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ({hv I}, {hv II} and {hv III}) for the structure of the product droplet depending on the scaled mobilities of $phi$ parallel and perpendicular to the parent-product interface and the stress threshold. In {hv I}, $phi$ is vanishingly small, {hv II} involves large $phi$ localized in regions of high stress within the parent-product interface and {hv III} where $phi$ completely wets the parent-product interface. While width $l$ and size $W$ of the twins follows $lproptosqrt{W}$ in solution {hv I}, this relation does not hold for {hv II} or {hv III}. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.
The negatively-charged nitrogen vacancy (NV$^-$) centre in diamond is a remarkable optical quantum sensor for a range of applications including, nanoscale thermometry, magnetometry, single photon generation, quantum computing, and communication. However, to date the performance of these techniques using NV$^-$ centres has been limited by the thermally-induced spectral wandering of NV$^-$ centre photoluminescence due to detrimental photothermal heating. Here we demonstrate that solid-state laser refrigeration can be used to enable rapid (ms) optical temperature control of nitrogen vacancy doped nanodiamond (NV$^-$:ND) quantum sensors in both atmospheric and textit{in vacuo} conditions. Nanodiamonds are attached to ceramic microcrystals including 10% ytterbium doped yttrium lithium fluoride (Yb:LiYF$_4$) and sodium yttrium fluoride (Yb:NaYF$_4$) by van der Waals bonding. The fluoride crystals were cooled through the efficient emission of upconverted infrared photons excited by a focused 1020 nm laser beam. Heat transfer to the ceramic microcrystals cooled the adjacent NV$^-$:NDs by 10 and 27 K at atmospheric pressure and $sim$10$^{-3}$ Torr, respectively. The temperature of the NV$^-$:NDs was measured using both Debye-Waller factor (DWF) thermometry and optically detected magnetic resonance (ODMR), which agree with the temperature of the laser cooled ceramic microcrystal. Stabilization of thermally-induced spectral wandering of the NV$^{-}$ zero-phonon-line (ZPL) is achieved by modulating the 1020 nm laser irradiance. The demonstrated cooling of NV$^-$:NDs using an optically cooled microcrystal opens up new possibilities for rapid feedback-controlled cooling of a wide range of nanoscale quantum materials.
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