Domain Size Scaling Research Articles

Microstructure control and property switching in stress-free van der Waals epitaxial VO2 films on mica

Realizing stress-free inorganic epitaxial films on weakly bonding substrates is of importance for applications that require film transfer onto surfaces that do not seed epitaxy. Film-substrate bonding is usually weakened by harnessing natural van der Waals layers (e.g., graphene) on substrate surfaces, but this is difficult to achieve in non-layered materials. Here, we demonstrate van der Waals epitaxy of stress-free films of a non-layered material VO2 on mica. The films exhibit out-of-plane 010 texture with three in-plane orientations inherited from the crystallographic domains of the substrate. The lattice parameters are invariant with film thickness, indicating weak film-substrate bonding and complete interfacial stress relaxation. The out-of-plane domain size scales monotonically with film thickness, but the in-plane domain size exhibits a minimum, indicating that the nucleation of large in-plane domains supports subsequent island growth. Complementary ab initio investigations suggest that VO2 nucleation and van der Waals epitaxy involves subtle polarization effects around, and the active participation of, surface potassium atoms on the mica surface. The VO2 films show a narrow domain-size-sensitive electrical-conductivity-temperature hysteresis. These results offer promise for tuning the properties of stress-free van der Waals epitaxial films of non-layered materials such as VO2 through microstructure control.

Saturation of Turbulent Helical Dynamos.

The presence of large scale magnetic fields in nature is often attributed to the inverse cascade of magnetic helicity driven by turbulent helical dynamos. In this Letter, we show that in turbulent helical dynamos, the inverse flux of magnetic helicity toward the large scales Π_{H} is bounded by |Π_{H}|≤cεk_{η}^{-1}, where ε is the energy injection rate, k_{η} is the Kolmogorov magnetic dissipation wave number, and c an order one constant. Assuming the classical isotropic turbulence scaling, the inverse flux of magnetic helicity Π_{H} decreases at least as a -3/4 power law with the magnetic Reynolds number Rm: |Π_{H}|≤cεℓ_{f}Rm^{-3/4}max[Pm,1]^{1/4}, where Pm is the magnetic Prandtl number and ℓ_{f} the forcing length scale. We demonstrate this scaling with Rm using direct numerical simulations of turbulent dynamos forced at intermediate scales. The results further indicate that nonlinear saturation is achieved by a balance between the inverse cascade and dissipation at domain size scales L for which the saturation value of the magnetic energy is bounded by E_{m}≤cL(εℓ_{f})^{2/3}Rm^{1/4}max[1,Pm]^{1/4}. Numerical simulations also demonstrate this bound. These results are independent of the dynamo mechanism considered. In our setup, they imply that inviscid mechanisms cannot explain large scale magnetic fields and have critical implications for the modeling of astrophysical dynamos.

Structure factor of a phase separating binary mixture with natural and forceful interconversion of species

Using a modified Cahn-Hilliard-Cook theory for spinodal decomposition in a binary mixture that exhibits both diffusion and interconversion dynamics, we derive the time-dependent structure factor for concentration fluctuations. We compare the theory and obtain a qualitative agreement with simulations of the temporal evolution of the order parameter and structure factor in a nonequilibrium Ising/lattice-gas hybrid model in the presence of an external source of forceful interconversion. In particular, the characteristic size of the steady-state phase domain is predicted from the lower cut-off wavenumber of the amplification factor in the generalized spinodal-decomposition theory. • A source of forceful interconversion may produce microphase separation. • The time evolution of the phase formation is characterized through two wavenumbers. • Steady-state domain size scales with square root of forceful interconversion rate • Results match with Monte Carlo simulations of a nonequilibrium hybrid model. • Source of forceful interconversion may be connected to an external energy source.

Hydrophobically modified polyacrylates (hmPAAs) with long alkyl chains – Self-assembly in aqueous solution

Hydrophobically modified polyacrylates (hmPAAs) obtained by Atomic Transfer Radical Copolymerisation (ATRP) of mixtures of different alkyl acrylates and t-butyl acrylate and subsequent hydrolysis of the t-butyl acrylate to polyacrylic acid (PAA), were studied with respect to their aggregation behaviour in aqueous solution. The hydrophobic modifications were long alkyl chains that were varied systematically from dodecyl to stearyl, thereby expecting a strong propensity for hydrophobic aggregation. Their structure in aqueous solution was investigated comprehensively by small-angle neutron scattering (SANS) and complemented by dynamic light scattering (DLS) experiments. In these random copolymers the degree of amphiphilicity and hydrophobicity was varied by the percentage of alkyl chains and pH. Due to the length of the alkyl chain all these copolymers have a tendency for microphase separation, but this tendency and the structure of the formed hydrophobic domains depend in a systematic fashion on the precise molecular composition. The domain size scales with the length of the hydrophobic alkyl modification and, for chains of C16 and longer, there is apparently a tendency for elongation. Another interesting observation is that for 20 mol% hydrophobic modification rather self-contained and isolated hydrophobic micellar domains are formed. In contrast, the copolymers with 10 mol% alkyl modification contain interconnected hydrophobic domains as evidenced from the low-q scattering seen in SANS and confirmed by DLS observations. This tendency is further enhanced when fully charging the copolymers. In summary, the molecular design of such random amphiphilic copolymers allows in a nice way to control the aggregation state in solution.

Assessing quantitative metrics of transfer film quality as indicators of polymer wear performance

Reduced wear rates of filled polymeric tribomaterials consistently accompany improvements in the appearance of the transfer film, a protective layer of debris that adheres to the counterface. As a result, wear reductions are often attributed to the favorable effects of the filler on transfer film quality. However, the cause-effect relationship between fillers, transfer film quality, and polymer wear performance remains uncertain due, in part, to a lack of standard metrics for assessing transfer film quality. Methods for quantifying transfer film thickness and area fraction have been proposed previously; although some studies show strong correlations between these parameters and wear rate, others have demonstrated a lack of general applicability. In a more recent study, it was proposed that the characteristic size of the gaps in the transfer film (free-space length) may better reflect visual differences in transfer film quality and more directly relate to debris size and wear rate. In this paper, a representative collection of common tribological polymers and composites were subjected to wear testing and transfer film topology characterization to better generalize the link between polymer wear performance and transfer film topology (thickness, coverage, and domain size-scales). The free-space length provided the best correlation with steady state wear rates of the tribopolymers in this study and prediction of wear rates from previous studies. The results suggest that, among the metrics considered, the free-space length provides the best independent measure of transfer film quality in the context of polymer wear.

Thickness-dependent evolutions of domain configuration and size in ferroelectric and ferroelectric-ferroelastic films

Non-monotonous thickness-dependent ferroelectric and ferroelectric-ferroelastic domain size scaling behaviors were revealed in ferroelectric films, including three distinct regions: (I) a classical ½ power law relationship for thick films, (II) a deviation from the ½ scaling relationship for an intermediate thickness range, and (III) an exponential increase in ultrathin films when decreasing the film thickness. The calculations indicate a much narrower region (II) in ferroelectric films with ferroelectric domains than that with ferroelectric-ferroelastic ones. As the film thickness decreases, the stable domain pattern also changes from a ferroelectric-ferroelastic domain to a ferroelectric one, which leads to the divergence of domain size scaling.

Evolution of magnetic bubble domains in manganite films

We report a thickness-dependent evolution of magnetic domains from long stripe-like to bubble-like entities in La1−xSrxMnO3 (x ∼ 0.3) (LSMO) films grown on LaAlO3 substrates. By using 2-D fast Fourier transformation of magnetic force microscopy images and power spectral density function, we accurately determine the domain width in LSMO films with a wide range of thickness (50–325 nm). We find that the domain size scales with the Kittel’s square root law [C. Kittel, Phys. Rev. 70, 965 (1946).] only when reduced film thicknesses are used, which suggests the critical role of substrate-film interaction in domain formation.

Phenomenological analysis of domain width in rhombohedralBiFeO3films

The experimental domain size scaling law in epitaxial ${\text{BiFeO}}_{3}$ films shows a different behavior from predictions of the conventional elastic domains: the (101)-type $71\ifmmode^\circ\else\textdegree\fi{}$ domains are much wider than that of (100)-type $109\ifmmode^\circ\else\textdegree\fi{}$ despite the larger domain-wall energy in (100) boundary. A phenomenological analysis for rhombohedral ${\text{BiFeO}}_{3}$ film is proposed, and it reveals that both the depolarizing energy and the elastic energy are indispensable for the equilibrium domain structures. With the increase in the asymmetrical electrostatic boundary on the film surfaces, the dominant domain scaling mechanism changes from electrostatic-dependent domain structure to elastic-dependent one, which is consistent with the experimental data. The present results highlight the general role of depolarizing field in rhombohedral domain structures.

Effect of wall thickness on the ferroelastic domain size of BaTiO3

Extremely regular self-organized patterns of 90° ferroelastic domains have been reported in free-standing single crystal thin films of ferroelectric BaTiO3. Lukyanchuk et al. [Phys Rev B 79, 144111 (2009)] have recently shown that the domain size as a function of thickness for such free standing films can be well described assuming that the domains are due to stress caused by a surface tension layer that does not undergo the paraelectric–ferroelectric transition. From the starting point of Lukyanchuk’s model, it is shown here that the “universal” relationship between domain size and domain wall thickness previously observed in ferroelectrics, ferromagnets and multiferroics is also valid for ferroelastic domains. Further analysis of experimental data also shows that the domain wall thickness can vary considerably (an order of magnitude) from sample to sample even for the same material (BaTiO3), in spite of which the domain size scaling model is still valid, provided that the correct, sample dependent, domain wall thickness is used.

Fractal Dimension and Size Scaling of Domains in Thin Films of MultiferroicBiFeO3

Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic BiFeO3 have irregular domain walls characterized by a roughness exponent 0.5-0.6 and in-plane fractal Hausdorff dimension H||=1.4+/-0.1, and the domain size scales with an exponent 0.59+/-0.08 rather than 1/2. The domains are significantly larger than those of other ferroelectrics of the same thickness, and closer in size to those of magnetic materials, which is consistent with a strong magnetoelectric coupling at the walls. A general model is proposed for ferroelectrics, ferroelastics or ferromagnetic domains which relates the fractal dimension of the walls to domain size scaling.

Domain motion in the voter model with noise

We study the voter model with noise on one-dimensional chains using Monte Carlo simulations and finite-size scaling techniques. We observe that the system evolution toward consensus is deeply affected by the addition of noise, and that the time to reach complete ordering increases with the noise parameter q. In particular, the simulations show that the average domain size scales as xi approximately q(-1/2) whereas the magnetization scales with the number of nodes as m approximately N(-1/2).

Coarsening Rates of Bicontinuous Structures in Polymer Mixtures

We discuss the coarsening of domains in bicontinuous structure of aqueous polymer mixtures, driven by hydrodynamic flow. Taking into account the bending energy as a contribution to the interfacial energy, we derive a general expression for the coarsening rate in these mixtures. Examining the limiting behavior of small and large length scales, we find two regimes. For small length scales, the size of the domains (Λ) scales with time (t) as Λ ∼ τ1/3, while at large length scales, the domain size scales with time as Λ ∼ τ. The crossover between the two regimes occurs at a particular length scale, the critical radius Rc, which is dependent on the bending rigidity k, and the interfacial tension of a flat interface γ0 (Rc = ). In the case of aqueous biopolymer mixtures, we predict this particular length scale to be in the micron range. This new general expression for the coarsening of domains in aqueous polymer mixtures can explain experimental results [Lorén et al. Macromolecules 2001, 34, 8117], which show the two regimes of coarsening with a crossover at 4 μm.

Scaling theory for two-dimensional systems with competing interactions.

We derive an analytic scaling theory for a two-dimensional system in which spontaneous patterns of stripes, bubbles, and intermediately shaped domains arise due to the competition of short-range attractions and long-range dipolar repulsions. The theory predicts temperature and domain-size scaling as a function of the relative repulsion strength eta, the ratio of the repulsive to the attractive coupling constant in the system's Hamiltonian. As eta decreases, the domain size explodes exponentially and the melting temperature for a system of ordered stripes increases. Our findings shed new light on the phase diagram and critical excitations for the dipolar Ising ferromagnet or lattice gas and their continuum analogs. We show that the features described by the scaling theory are insensitive to details like cutoffs for the dipolar interactions and, therefore, should be widely applicable. Our corresponding states analysis explains the experimentally observed stripe melting upon compression in a Langmuir monolayer. A phenomenological extension of the analytic scaling theory describes how the system's behavior is modified in the presence of magnetization or density fluctuations. Fluctuations are found to suppress domain size and the stripe melting temperature. In regimes where fluctuations are important, we predict that domain size will decrease with increasing temperature.

Arrested volume-phase transition of gel around a hole and crossover of domain size scaling

We theoretically study the phase coexistence in gel upon the volume phase transition. We focus on the geometry where the gel with a rod-like shape has a thin coaxial hole. We demonstrate how the concaved surface of gel affects the coexisting domains in equilibrium. The calculation is similar to the fixed-point analysis of renormalization group theories. We also predict the existence of a crossover temperature across which we have different scaling behaviors of the thickness of the deswollen domain around the free surface of the hole: At temperatures between the transition point and the crossover temperature, the thickness of the domain is roughly proportional to the thickness of the hole, while at the temperatures farther than the crossover temperature the thickness of the domain is rather scaled linearly with the radius of the outer fixed boundary of gel.

Monte Carlo simulations of phase separation in chemically reactive binary mixtures.

We present Monte Carlo simulations of a binary mixture simultaneously undergoing spinodal decomposition and the chemical reaction A\ensuremath{\rightleftarrows}B. The competing processes give rise to novel, steady-state pattern formation with domain size scaling with reaction rate to a power, s, which equals the domain growth exponent, \ensuremath{\alpha}, in the absence of chemical reactions. Our findings support recent numerical simulations of a Cahn-Hilliard-type model, suggesting that chemical reactions can be used to stabilize and tune patterns arising during phase separation.

Phase formation sequence and domain structure: A low-energy-electron-microscopy study of the Si(111)-( sqrt 3 x sqrt 3 )Ag surface.

Changes in nucleation and phase formation sequence with temperature may strongly affect the morphology of the final phase. The Si(111)-(\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )Ag structure develops directly from the clean (7\ifmmode\times\else\texttimes\fi{}7) structure at lower temperatures (500--700 K). Preferred nucleation at step edges and (7\ifmmode\times\else\texttimes\fi{}7) domain boundaries reduces the effective dimensionality of the substrate and explains anomalies in domain size scaling observed by Zuo and Wendelken. An intermediate three-domain (3\ifmmode\times\else\texttimes\fi{}1) structure precedes the \ensuremath{\surd}3 structure at higher temperatures, leading to a complete change in \ensuremath{\surd}3 nucleation and growth, as well as final domain size distribution and total Ag coverage.

Impurity effects on domain-growth kinetics. I. Ising model.

The development of order for the Ising model in the presence of static, random impurities is studied following a quench from high temperature (T\ensuremath{\gg}${T}_{c}$) to T${T}_{c}$. We find that for quenches to T=0, the system becomes pinned for long times for any value of c0 and never reaches its final equilibrium ferromagnetic ground state. The average linear pinned domain size scales as the inverse square root of the concentration c. For quenches to a final T0, the long-time behavior of the correlation length R and the energy E are slower than a power law, suggesting a logarithmic growth law for long times. The time that is required to reach this asymptotic logarithmic behavior increases as the impurity concentration decreases and/or the temperature increases.