scholarly journals Imaging how thermal capillary waves and anisotropic interfacial stiffness shape nanoparticle supracrystals

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Zihao Ou ◽  
Lehan Yao ◽  
Hyosung An ◽  
Bonan Shen ◽  
Qian Chen
Keyword(s):  
Wave Theory ◽  
Lower Surface ◽  
Real Space ◽  
Construction Rule ◽  
Phonon Transport ◽  
Capillary Waves ◽  
Wulff Construction ◽  
Interfacial Stiffness ◽  
Exposed Facet ◽  
Phase Transmission

Abstract Development of the surface morphology and shape of crystalline nanostructures governs the functionality of various materials, ranging from phonon transport to biocompatibility. However, the kinetic pathways, following which such development occurs, have been largely unexplored due to the lack of real-space imaging at single particle resolution. Here, we use colloidal nanoparticles assembling into supracrystals as a model system, and pinpoint the key role of surface fluctuation in shaping supracrystals. Utilizing liquid-phase transmission electron microscopy, we map the spatiotemporal surface profiles of supracrystals, which follow a capillary wave theory. Based on this theory, we measure otherwise elusive interfacial properties such as interfacial stiffness and mobility, the former of which demonstrates a remarkable dependence on the exposed facet of the supracrystal. The facet of lower surface energy is favored, consistent with the Wulff construction rule. Our imaging–analysis framework can be applicable to other phenomena, such as electrodeposition, nucleation, and membrane deformation.

scholarly journals Determining the range of magnetic interactions from the relations between magnon eigenvalues at high-symmetry k points

2021 ◽  
Author(s):  
Di Wang ◽  
Jihai Yu ◽  
Feng Tang ◽  
Yuan Li ◽  
Xiangang Wan
Keyword(s):  
Magnetic Moments ◽  
A Priori ◽  
Exchange Interactions ◽  
Wave Theory ◽  
Real Space ◽  
Simple Relation ◽  
Magnetic Interactions ◽  
High Symmetry ◽  
Magnetic Exchange ◽  
The Fourier Transform

Abstract Magnetic exchange interactions (MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results. But how many MEIs need to be included in the fitting process for a material is not clear a priori, which limits the quality of results obtained by these conventional methods. In this paper, based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies (SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. We also develop a theoretical tool for tabulating the rule about SSME. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry k points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also general applicable for other Hamiltonian with quadratic Fermi or Boson operators.

scholarly journals The stability of capillary waves on fluid sheets

2016 ◽  
Vol 806 ◽  
pp. 5-34 ◽  
Author(s):  
M. G. Blyth ◽  
E. I. Părău
Keyword(s):  
Nonlinear Waves ◽  
Time Integration ◽  
Lower Surface ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Mapping Technique ◽  
Surprising Result ◽  
Periodic Waves ◽  
The Stability ◽  
The Waves

The linear stability of finite-amplitude capillary waves on inviscid sheets of fluid is investigated. A method similar to that recently used by Tiron & Choi (J. Fluid Mech., vol. 696, 2012, pp. 402–422) to determine the stability of Crapper waves on fluid of infinite depth is developed by extending the conformal mapping technique of Dyachenko et al. (Phys. Lett. A, vol. 221 (1), 1996a, pp. 73–79) to a form capable of capturing general periodic waves on both the upper and the lower surface of the sheet, including the symmetric and antisymmetric waves studied by Kinnersley (J. Fluid Mech., vol. 77 (02), 1976, pp. 229–241). The primary, surprising result is that both symmetric and antisymmetric Kinnersley waves are unstable to small superharmonic disturbances. The waves are also unstable to subharmonic perturbations. Growth rates are computed for a range of steady waves in the Kinnersley family, and also waves found along the bifurcation branches identified by Blyth & Vanden-Broeck (J. Fluid Mech., vol. 507, 2004, pp. 255–264). The instability results are corroborated by time integration of the fully nonlinear unsteady equations. Evidence is presented for superharmonic instability of nonlinear waves via a collision of eigenvalues on the imaginary axis which appear to have the same Krein signature.

scholarly journals Determination of the Range of Magnetic Interactions from the Relations between Magnon Eigenvalues at High-Symmetry κ Points

2021 ◽  
Vol 38 (11) ◽  
pp. 117101
Author(s):  
Di Wang ◽  
Jihai Yu ◽  
Feng Tang ◽  
Yuan Li ◽  
Xiangang Wan
Keyword(s):  
Magnetic Moments ◽  
A Priori ◽  
Exchange Interactions ◽  
Wave Theory ◽  
Real Space ◽  
Simple Relation ◽  
Magnetic Interactions ◽  
High Symmetry ◽  
Magnetic Exchange ◽  
The Fourier Transform

Magnetic exchange interactions (MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results. Unfortunately, how many MEIs need to be included in the fitting process for a material is unclear a priori, which limits the results obtained by these conventional methods. Based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies (SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry k points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also generally applicable for other Hamiltonian with quadratic Fermi or Boson operators.

scholarly journals Ultrasonic Piezoelectric Atomizers: Electromechanical Modeling and Performance Testing

2018 ◽  
Author(s):  
Eric D. Dupuis ◽  
Ayyoub M. Momen ◽  
Viral K. Patel ◽  
Shima Shahab
Keyword(s):  
Numerical Model ◽  
Removal Rate ◽  
Performance Testing ◽  
Spray Coating ◽  
Wave Theory ◽  
Capillary Waves ◽  
Bulk Liquid ◽  
Moisture Removal ◽  
Ultrasonic Vibrations ◽  
Oak Ridge

Ultrasonic atomization of bulk liquids has received extensive attention in the past few decades due to the ability to produce controlled droplet sizes, a necessity for many industries such as spray coating and aerosol drug delivery. Despite the increase in attention, one novel application of this technology has been overlooked until recently, and that is the moisture removal capabilities of atomization. The first ever ultrasonic dryer, created by researchers at Oak Ridge National Lab in 2016, applies the mechanisms of atomization to mechanically remove moisture from clothing. The process utilizes the ultrasonic vibrations created by a piezoelectric transducer in direct contact with a wet fabric to rupture the liquid-vapor boundary of the retained water. Once ruptured, smaller droplets are ejected from the bulk liquid and are actively removed from the fabric pores. The mechanisms of droplet ejection from this event are related to both capillary waves forming on the liquid surface (Capillary Wave Theory), as well as the implosion of cavitation bubbles formed from the hydraulic shocks propagating from the transducer (Cavitation Theory). In this work, we present an analytical model for predicting the moisture removal rate of a wet fabric exposed to ultrasonic vibrations, and connect the atomization events to a global variable, acceleration, in order to decouple the relationship between the transducer and applied voltage. The acceleration governing atomization is predicted using a verified numerical model. The numerical model is shown to assist in developing ultrasonic drying by means of efficiently evaluating transducer design changes.

Real-Space Analysis of Grain Boundary Fluctuations in Two Dimensional Colloidal Crystals

2012 ◽  
Vol 715-716 ◽  
pp. 901-901
Author(s):  
Thomas O.E. Skinner ◽  
Dirk G.A.L. Aarts ◽  
Roel P.A. Dullens
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Colloidal Crystal ◽  
Colloidal Crystals ◽  
Wave Theory ◽  
Real Space ◽  
Model System ◽  
Phase Behaviour ◽  
Two Dimensional ◽  
Colloidal Systems

The characteristics of grain boundary motion and evolution are of fundamental importance in material science. Optical microscopy is used to analyse grain boundary fluctuations in two-dimensional colloidal crystals. Colloidal systems are particles (colloids) on the order of 1µm dispersed in a solvent where they display rich phase behaviour of colloidal 'crystal', liquid' and 'gas' phases. They are widely used as a model system to study many fundamental issues in condensed matter physics and statistical mechanics. The intrinsic slowness and increased length scales of colloidal systems make them an excellent model system to study grain boundaries as an analogy to atomic systems. Static and dynamic correlation functions are compared with capillary wave theory to calculate the grain boundary mobility and stiffness. These fundamental properties of grain boundaries determine the kinetics of curvature-driven grain growth.

scholarly journals The Electronic Transport Channel Protection and Tuning in Real Space to Boost the Thermoelectric Performance of Mg3+δSb2-yBiy near Room Temperature

Research ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zhijia Han ◽  
Zhigang Gui ◽  
Y. B. Zhu ◽  
Peng Qin ◽  
Bo-Ping Zhang ◽  
...  
Keyword(s):  
Power Factor ◽  
Thermoelectric Materials ◽  
Room Temperature ◽  
Average Power ◽  
Real Space ◽  
Phonon Transport ◽  
Transport Channel ◽  
Thermoelectric Power Factor ◽  
Network Protection ◽  
Strong Candidate

The optimization of thermoelectric materials involves the decoupling of the transport of electrons and phonons. In this work, an increased Mg1-Mg2 distance, together with the carrier conduction network protection, has been shown as an effective strategy to increase the weighted mobility (U=μm∗3/2) and hence thermoelectric power factor of Mg3+δSb2-yBiy family near room temperature. Mg3+δSb0.5Bi1.5 has a high carrier mobility of 247 cm2 V-1 s-1 and a record power factor of 3470 μW m-1 K-2 at room temperature. Considering both efficiency and power density, Mg3+δSb1.0Bi1.0 with a high average ZT of 1.13 and an average power factor of 3184 μW m-1 K-2 in the temperature range of 50-250°C would be a strong candidate to replace the conventional n-type thermoelectric material Bi2Te2.7Se0.3. The protection of the transport channel through Mg sublattice means alloying on Sb sublattice has little effect on electron while it significantly reduces phonon thermal conductivity, providing us an approach to decouple electron and phonon transport for better thermoelectric materials.

scholarly journals Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 430
Author(s):  
Vicenta Sánchez ◽  
Chumin Wang
Keyword(s):  
Degrees Of Freedom ◽  
Reciprocal Lattice ◽  
Standard Technique ◽  
Structural Disorder ◽  
Real Space ◽  
Phonon Transport ◽  
Structural Defects ◽  
Space Theory ◽  
Solid State Physics ◽  
The Real

Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities.

Comment on “Delta Wings of Shapes Amenable to Exact Shock-Wave Theory“

1963 ◽  
Vol 67 (629) ◽  
pp. 301-301 ◽  
Author(s):  
A. C. Southgate ◽  
J. R. Pedersen
Keyword(s):  
Cross Sections ◽  
Convex Bodies ◽  
Wave Theory ◽  
Lower Surface ◽  
Plane Shock ◽  
Two Dimensional ◽  
Delta Wings ◽  
Isentropic Compression ◽  
Two Dimensional Flow ◽  
Shock Wave Theory

Finite bodies supporting two-dimensional under surface flows behind “contained” plane shock waves of the type discussed by Professor Nonweiler in a recent paper are currently receiving attention from both theoretical and experimental workers. The experimental work already undertaken by the RAE has given hopeful indications that such bodies, characterised by a re-entrant lower surface in cross section, compete closely with more familiar convex bodies in terms of lift/drag ratio, and furthermore preserve the two-dimensional character of the flow away from the design incidence.The purpose of this note is to point out that:(a) Delta wings with inverted V or W cross sections are geometrically simple examples of a more general family of possible shapes supporting two-dimensional flow behind a plane shock.(b) The concept may be extended to bodies supporting two-dimensional flows with multiple shocks (leading to isentropic compression in the limit) or shock-expansion systems.

Monte Carlo Simulation of Silicon Nanowire Thermal Conductivity

2005 ◽  
Vol 127 (10) ◽  
pp. 1129-1137 ◽  
Author(s):  
Yunfei Chen ◽  
Deyu Li ◽  
Jennifer R. Lukes ◽  
Arun Majumdar
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Silicon Nanowire ◽  
Wave Theory ◽  
Momentum Conservation ◽  
Phonon Transport ◽  
Recent Experimental Data ◽  
Si Nanowires ◽  
Nanowire Diameter

Monte Carlo simulation is applied to investigate phonon transport in single crystalline Si nanowires. Phonon-phonon normal (N) and Umklapp (U) scattering processes are modeled with a genetic algorithm to satisfy energy and momentum conservation. The scattering rates of N and U scattering processes are found from first-order perturbation theory. The thermal conductivity of Si nanowires is simulated and good agreement is achieved with recent experimental data. In order to study the confinement effects on phonon transport in nanowires, two different phonon dispersions, one from experimental measurements on bulk Si and the other solved from elastic wave theory, are adopted in the simulation. The discrepancy between simulations using different phonon dispersions increases as the nanowire diameter decreases, which suggests that the confinement effect is significant when the nanowire diameter approaches tens of nanometers. It is found that the U scattering probability in Si nanowires is higher than that in bulk Si due to the decrease of the frequency gap between different modes and the reduced phonon group velocity. Simulation results suggest that the dispersion relation for nanowires obtained from elasticity theory should be used to evaluate nanowire thermal conductivity as the nanowire diameter is reduced to the sub-100 nm scale.

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