Magnetic nanoparticles have proven to be valuable for biomedical applications. A prerequisite for the efficiency of these applications are precisely characterized particles. Thermal Noise Magnetrometry (TNM), unlike any other magnetic characterization method, allows to characterize the particles without the application of an external excitation. We present a theoretical framework to model the experiment in order to examine the magnetic noise power properties of particle ensembles in TNM and optimize the geometry of the nanoparticle sample. An optimized sample geometry is calculated to maximize the noise power measured by the detector. The theoretical framework and the newly designed sample holder are validated by measuring a sensitivity profile in the setup. The optimized sample holder increases the noise power with a factor of 3.5 compared to the regular sample holder, while its volume is decreased by more than half. Moreover, the experimental profiles are consistent with the simulated counterparts, confirming the relevance of the theoretical framework. These results contribute to the further establishment of TNM as magnetic nanoparticle characterization method.
The magnetic properties of Fe$_3$O$_4$ nanoparticle assemblies have been investigated in detail through a combination of vibrating sample magnetometry and muon spin relaxation ($μ$SR) techniques. Two samples with average particle sizes of 5 nm and 20 nm, respectively, were studied. For both samples, the magnetometry and $μ$SR results exhibit clear signatures of the superparmagnetic state at high temperature and the magnetically blocked state at low temperature. The $μ$SR data demonstrate that the transition from the superparamagnetic to the blocked state occurs gradually throughout the sample …
A tabletop Optically Pumped Magnetometer setup for the monitoring of magnetic nanoparticle clustering and immobilization using Thermal Noise Magnetometry
Magnetic nanoparticles offer a unique potential for various biomedical applications, but prior to commercial usage a standardized characterization of their structural and magnetic properties is required. For a thorough characterization, the combination of conventional magnetometry and advanced scattering techniques has shown great potential. In the present work, we characterize a powder sample of high-quality iron oxide nanoparticles that are surrounded with a homogeneous thick silica shell by DC magnetometry and magnetic small-angle neutron scattering (SANS). To retrieve the particle paramete…
The complex permittivity and permeability of superparamagnetic iron-oxide nanoparticles has been quantified using a circular waveguide assembly with a static magnetic field to align the nanoparticle's magnetization. The high sensitivity of the measurement provides the precise resonant feature of nanoparticles. The complex permeability in the vicinity of ferromagnetic resonance (FMR) is in agreement with the nanoparticle's measured magnetization via conventional magnetometry. A rigorous and self-consistent measure of complex permittivities and permeabilities of nanoparticles is crucial to ascer…
We show that by capping Co nanoparticles with small amounts of Pt strong changes of the magnetic properties can be induced. The Co nanoparticles have a mean diameter of 2.7 nm. From magnetometry measurements we find that for zero and for small amounts of Pt (nominal thickness t(Pt) < 0.7 nm) the nanoparticles behave superparamagnetic like. With increasing t(Pt) the blocking temperature is enhanced from 16 up to 108 K. Capping with Pd yields comparable results. However, for values t(Pt) > 1 nm a strongly coupled state is encountered resembling a ferromagnet with a T_c approx. 400 K
We report about the magnetic properties of antiferromagnetic (AF) MnO nanoparticles (NPs) with different sizes (6-19nm). Using a combination of polarized neutron scattering and magnetometry we were able to resolve previously observed peculiarities. Magnetometry, on the one hand, reveals a peak in the zero field cooled (ZFC) magnetization curves at low temperatures (~25K) but no feature around the Néel temperature at 118K. On the other hand, polarized neutron scattering shows the expected behavior of the AF order parameter vanishing around 118K. Moreover, hysteresis curves measured at various t…
We demonstrate the operation of low-noise nano superconducting quantum interference devices (SQUIDs) based on the high critical field and high critical temperature superconductor YBa$_2$Cu$_3$O$_7$ (YBCO) as ultra-sensitive magnetometers for single magnetic nanoparticles (MNPs). The nanoSQUIDs exploit the Josephson behavior of YBCO grain boundaries and have been patterned by focused ion beam milling. This allows to precisely define the lateral dimensions of the SQUIDs so as to achieve large magnetic coupling between the nanoloop and individual MNPs. By means of focused electron beam induced de…
We evaluate the impact of acoustic Mie resonance in nanoparticles on the thermal conductivity of semiconductor and polymer composites. By appropriately choosing the bulk modulus and density, and selecting the size of the nanoparticle to align the Mie resonances with the dominant portion of the thermal conductivity spectrum, we show that large reductions in thermal conductivity are achievable with dilute concentrations of nanoparticles. In semiconductor alloys, where the spectral thermal conductivity is known, our model can explain the steep reductions in thermal conductivity observed previousl…
: Understanding the correlations between magnetic nanoparticles is important for nanotechnologies, such as high-density magnetic recording and biomedical applications, where functionalized magnetic particles are used as contrast agents and for drug delivery. The ability to control the magnetic state of individual particles depends on the good knowledge of magnetic correlations between particles when assembled. Inaccessible via standard magnetometry techniques, nanoscale magnetic ordering in self-assemblies of Fe3O4 nanoparticles is here unveiled via x-ray resonant magnetic scattering (XRMS). M…
We develop a dipole model describing the thermal far-field radiation of a nanoparticle in close vicinity to a substrate. By including in our description the contribution of eddy currents and the possibility to choose different temperatures for the nanoparticle, the substrate, and the background, we generalize the existing models. We discuss the impact of the different temperatures, particle size, emission angle, and the distance dependence for all four combinations of gold and SiC nanoparticles or substrates.
We suggest to exploit the shape-dependence of the near-field heat transfer for nanoscale thermal imaging. By utilizing strongly prolate or oblate nanoparticles as sensors one can assess individual components of the correlation tensors characterizing the thermal near field close to a nanostructured surface, and thus obtain directional information beyond the local density of states. Our theoretical considerations are backed by idealized numerical model calculations.
We present a systematic numerical modeling investigation of magnetization dynamics and thermal magnetic moment fluctuations of single magnetic domain nanoparticles in a configuration applicable to enhancing inductive magnetic resonance detection signal to noise ratio (SNR). Previous proposals for oriented anisotropic single magnetic domain nanoparticle amplification of magnetic flux in MRI coil focused only on the coil pick-up voltage signal enhancement. Here we extend the analysis to the numerical evaluation of the SNR by modeling the inherent thermal magnetic noise introduced into the detect…
The spectral characteristics of near-field thermal emission from nanoparticle arrays are explained by comparison to the dispersions for propagating modes. Using the coupled dipole model, we analytically calculate the spectral emission from single particles, chains, planes, and 3D arrays of SiO2 and SiC. We show that the differences in their spectra are due to the existence or absence of propagating surface phonon polariton modes and that the emission is dominated by these modes when they are present. This work paves the way for understanding and control of near-field radiation in nanofluids, n…
We comment on some misleading and biased statements appearing in the manuscript arXiv:1209.0298 ("Thermal fluctuations of magnetic nanoparticles") about the use of the damped Landau-Lifshitz equation and the kinetic Langer theory for the calculation of the relaxation rate of magnetic nanoclusters. We reiterate simple scientific arguments, part of which is well known to the whole community, demonstrating that the authors' criticisms are unfounded and that they overstate the issue of damping in the Landau-Lifshitz equation with no unanimous experimental evidence.
The influence of a patterned substrate on obliquely deposited, exchange biased Co/CoO films was studied. It was found that substrates decorated with nanoparticle patterns provide the option to manipulate the orientation of the magnetic easy axis in obliquely deposited thin films. The complementary methods of SQUID magnetometry and polarized neutron reflectometry were used to disentangle the different contributions to the magnetic hysteresis of such complex magnetic systems.
We report about a combined structural and magnetometric characterization of self-assembled magnetic nanoparticle arrays. Monodisperse iron oxide nanoparticles with a diameter of 20 nm were synthesized by thermal decomposition. The nanoparticle suspension was spin-coated on Si substrates to achieve self-organized arrays of particles and subsequently annealed at various conditions. The samples were characterized by x-ray diffraction, bright and dark field high resolution transmission electron microscopy (HRTEM). The structural analysis is compared to the magnetic behavior investigated by superco…
We demonstrated visualization of Au nanoparticles buried 300 nm into a polymer matrix by measurement of the thermal noise spectrum of a microcantilever with a tip in contact to the polymer surface. The subsurface Au nanoparticles were detected as the variation in the contact stiffness and damping reflecting the viscoelastic properties of the polymer surface. The variation in the contact stiffness well agreed with the effective stiffness of a simple one-dimensional model, which is consistent with the fact that the maximum depth range of the technique is far beyond the extent of the contact stre…
Interest in creating magnetic metamaterials has led to methods for growing superstructures of magnetic nanoparticles. Mesoscopic crystals of maghemite ($γ\text{-Fe}_2\text{O}_3$) nanoparticles can be arranged into highly ordered body-centered tetragonal lattices of up to a few micrometers. Although measurements on disordered ensembles have been carried out, determining the magnetic properties of individual mesoscopic crystals is challenging due to their small total magnetic moment. Here, we overcome these challenges by utilizing sensitive dynamic cantilever magnetometry to study individual mic…
We showed in past work that nanopatterned monolayer graphene (NPG) enables spectrally selective thermal emission in the mid-infrared (mid-IR) from 3 to 12 $μ$m. In that case the spectral selection is realized by means of the localized surface plasmon (LSP) resonances inside graphene. Here we show that graphene decorated with metallic nanoparticles, such as Ag nanocubes or nanospheres, also realize spectrally selective thermal emission, but in this case by means of acoustic graphene plasmons (AGPs) localized between graphene and the Ag nanoparticle inside a dielectric material. Our finite-diffe…
We report a numerical investigation on the heat transfer through one dimensional arrays of metallic nanoparticles closely spaced in a host material. Our simulations show that the multipolar interactions play a crucial role in the heat transport via collective plasmons. Calculations of the plasmonic thermal conductance and of the thermal conductivity in ballistic and diffusive regime, respectively have been carried out. (a) Using the Landauer-Buttiker formalism we have found that, when the host material dielectric constant takes positive values, the multipolar interactions drastically enhance b…
We have measured the relaxation time of a thermally unstable ferromagnetic nanoparticle incorporated into a magnetic tunnel junction (MTJ) as a function of applied magnetic field, voltage V (-0.38 V < V < +0.26 V), and temperatures (283 K< T< 363 K) . By analyzing the results within the framework of a modified Néel-Brown formalism we determine the effective attempt time of the nanoparticle and also the bias dependences of the in-plane and out-of-plane spin torques. There is a significant linear modification of the effective temperature with voltage due to the in-plane torque and a significant …
We investigate the spatial distribution of spin orientation in magnetic nanoparticles consisting of hard and soft magnetic layers. The nanoparticles are synthesized in a core / shell spherical morphology where the magnetically hard, high anisotropy layer is CoFe$_2$O$_4$ (CFO) while the lower anisotropy material is Fe$_3$O$_4$ (FO). The nanoparticles have a mean diameter of $\sim$9.2 - 9.6 nm and are synthesized as two variants: a conventional hard / soft core / shell structure with a CFO core / FO shell (CFO@FO) and the inverted structure FO core / CFO shell (FO@CFO). High resolution electron…
Thermal rectification due to phonon confinement in nanoparticles
DLR Institute of Space Research（德国航空航天中心空间研究所）；PTB Berlin（德国联邦物理技术研究院柏林分院）；Physics Department “Aldo Pontremoli”, Università degli Studi di Milano（米兰大学阿尔多·蓬特雷莫利物理系）；Interdisciplinary Centre for Nanostructured Materials and Interfaces (CIMaINa)（纳米结构与界面跨学科中心）
We study the radiative heat flux between two nanoparticles in close vicinity to the natural hyperbolic material hBN with its optical axis oriented parallel to the interface. We show that the heat flux between the nanoparticles can be efficiently modulated when rotating the nanoparticles due to the coupling to the highly directional hyperbolic surface modes in hBN. Finally, we discuss the thickness and distance dependence of this effect.
We study the radiative cooling of polar and metallic nanoparticles immersed in a thermal bath close to a partially reflecting surface. The dynamics of relaxation is investigated at different distances from the surface, i.e., in the near-field and far-field zones. We demonstrate the existence of an oscillating behavior for the thermal relaxation time with respect to the separation distance from the surface, an analog of Friedel oscillations in Fermi liquids.
In this work, the near-field radiative heat transfer (NFRHT) between two Weyl semimetal (WSM) nanoparticles (NPs) is investigated. The numerical results show that negative differential thermal conductance (NDTC) effect can be obtained in this system, i.e., when the temperature of the emitter is fixed, the heat flux does not decrease monotonically with the increase of the temperature of the receiver. Specifically, when the temperature of the emitter is 300 K, the heat flux is identical when the temperature of the receiver is 50 K or 280 K. The NDTC effect is attributed to the fact that the perm…
In this letter, we address the thermal processes occurring in plasmonic nanoparticles. We determine constrains imposed upon the plasmonic excitation in such nanoparticle by the resulting heat generation. Taking into account temperature dependence of the metal losses, we predict the existence of the critical number of plasmons in the nanoparticle. We also allow for the temperature dependencies of the thermal-conductivity coefficient of the environment and the Kapitza heat boundary resistance. We show that the latter can dominate the overall heat resistance in the system. Strength limitations ca…
We derive a general expression for electric and magnetic part of the near-field energy density of $N$ dipoles of temperatures $T_1, \ldots, T_N$ immersed in a background field having a different temperature $T_b$. In contrast to former expressions this inclusion of the background field allows for determining the energy density of heated or cooled isotropic dipolar objects within an arbitrary environment which is thermalized at a different temperature. Furthermore, we show how the energy density is related to the local density of states. We use this general expression to study the near-field en…
In chains of closely-spaced nanoparticles supporting surface polaritons, near-field electromagnetic coupling leads to collective effects and super-Planckian thermal radiation exchange. Researchers have primarily used two analytical approaches to calculate radiative heat transfer in these systems: fluctuational electrodynamics, which directly incorporates fluctuating thermal currents into Maxwell's equations, and a kinetic approach where the dispersion relation provides modes and propagation lengths for the Boltzmann transport equation. Here, we compare results from the two approaches in order …
Light-assisted micro-nanoscale temperature control in complex nanoparticle network attracts lots of research interests. Many efforts have been put on the optical properties of the nanoparticle networks and only a few investigations on its light-induced thermal behavior was reported. We consider two-dimensional (2D) square-lattice nanoparticle ensemble made of typical metal Ag with a radius of 5 nm. The effect of complex optical coupling and thermal accumulation on the light-induced thermal behavior in plasmonic resonance frequency (around 383 nm) is analyzed by means of the Green\textquotesing…
The natural world is replete with examples of multistable systems, known to respond to periodic modulations and produce a signal, which exhibits resonance with noise amplitude. This is a concept not demonstrated in pure materials, which involve a measured physical property. In a thermoremanent magnetization experiment with a common magnetic material, Fe, in the nanoparticulate form, we establish how magnetization in a system of dilute spins during dissipation of stored magnetic energy, breaks up into spontaneous oscillatory behavior. Starting at 175 K and aided by temperature (stochastic noise…
It has been shown that a single-domain magnetic nanoparticle can be effectively switched by a linear down-chirp microwave field pulse (DCMWP) in zero temperature limit. However, finite temperature is ubiquitous in practice. Here, we study the effect of finite temperature on the DCMWP-induced magnetization reversal based on the stochastic Landau-Lifshitz-Gilbert equation. It is found that any one of the three controlling parameters of a DCMWP, i.e. the amplitude, chirp rate, or initial frequency, decreases with increasing temperature while the other two are fixed. The maximal temperature at whi…
The temperature dependence of the thermal boundary resistivity is investigated in glass-embedded Ag particles of radius 4.5 nm, in the temperature range from 300 to 70 K, using all-optical time-resolved nanocalorimetry. The present results provide a benchmark for theories aiming at explaining the thermal boundary resistivity at the interface between metal nanoparticles and their environment, a topic of great relevance when tailoring thermal energy delivery from nanoparticles as for applications in nanomedicine and thermal management at the nanoscale
Magnetic and structural properties of magnetite nanoparticles stabilized in polyvinyl-alcohol thin films are investigated by using X-ray diffraction (XRD), transmission electron microscopy (TEM), electron paramagnetic resonance (EPR) and static magnetometry techniques. The nanoparticles have well-defined crystallinity, and are superparamagnetic at room temperature. Their size distribution is characterized by the distinct log-normal law (with average diameters near 5-7 nm) and slight maximum near 70-80 nm. The EPR spectra and static magnetization data demonstrated pronounced anomalies in the in…
In this letter, we have demonstrated the possibility to efficiently relay the radiative heat flux between two nanoparticles by opening a smooth channel for heat transfer. By coating the nanoparticles with a silica shell and modifying the substrate with multilayered graphene sheets respectively, the localized phonon polaritons excited near the nanoparticles can couple with the multiple surface plasmon polaritons near the substrate to realize the heat relay in the long distance. The heat transfer can be enhanced by more than six orders of magnitude and the relay distance can be as high as 35 tim…
The thermal properties of an epoxy-based binary composites comprised of graphene and copper nanoparticles are reported. It is found that the "synergistic" filler effect, revealed as a strong enhancement of the thermal conductivity of composites with the size-dissimilar fillers, has a well-defined filler loading threshold. The thermal conductivity of composites with a moderate graphene concentration of ~15 wt% exhibits an abrupt increase as the loading of copper nanoparticles approaches ~40 wt%, followed by saturation. The effect is attributed to intercalation of spherical copper nanoparticles …
We have used an atomistic {\it ab initio} approach with no adjustable parameters to compute the lattice thermal conductivity of Si$_{0.5}$Ge$_{0.5}$ with a low concentration of embedded Si or Ge nanoparticles of diameters up to 4.4 nm. Through exact Green's function calculation of the nanoparticle scattering rates, we find that embedding Ge nanoparticles in $\text{Si}_{0.5}\text{Ge}_{0.5}$ provides 20% lower thermal conductivities than embedding Si nanoparticles. This contrasts with the Born approximation which predicts an equal amount of reduction for the two cases, irrespective of the sign o…
We discuss the design of the thermal analog of logic gates in systems made of a collection of nanoparticles. We demonstrate the possibility to perform NOT, OR, NOR, AND and NAND logical operations at submicrometric scale by controlling the near-field radiative heat exchanges between their components. We also address the important point of the role played by the inherent non-additivity of radiative heat transfer in the combination of logic gates. These results pave the way to the development of compact thermal circuits for information processing and thermal management, which might also be reali…
Thermal activation tends to destroy the magnetic stability of small magnetic nanoparticles, with crucial implications in ultra-high density recording among other applications. Here we demonstrate that low blocking temperature ferromagnetic (FM) Co nanoparticles (TB<70 K) become magnetically stable above 400 K when embedded in a high Néel temperature antiferromagnetic (AFM) NiO matrix. The origin of this remarkable TB enhancement is due to a magnetic proximity effect between a thin CoO shell (with low Néel temperature, TN; and high anisotropy, KAFM) surrounding the Co nanoparticles and the NiO …
Recent advances in our understanding of thermal transport in nanocrystalline systems are responsible for the integration of new technologies into advanced energy systems, including thermoelectric refrigeration systems and renewable energy platforms. However, there is little understanding of heat energy transport mechanisms that govern the thermal properties of disordered nanocomposites. In this work, we explore thermal transport mechanisms in disordered packings of amorphous nanoparticles with and without a polymer filling the interstices in order to quantify the impact of thermal boundary sca…
Systems of many nanoparticles or volume-discretized bodies exhibit collective radiative properties that could be used for enhanced, guided, or tunable thermal radiation. These are commonly treated as assemblies of point dipoles with interactions described by Maxwell's equations and thermal fluctuations correlated by the fluctuation-dissipation theorem. Here, we unify different theoretical descriptions of these systems and provide a complete derivation of many-dipole thermal radiation, showing that the correct use of the fluctuation-dissipation theorem depends on the definitions of fluctuating …
We present here an original process combining top-down and bottom-up approaches by annealing a thin gold film evaporated onto a hole template made by etching a PS-PMMA copolymer film. Such process allows a better control of the gold nanoparticle size distribution which provides a sharper localized surface plasmon resonance. This makes such route appealing for sensing applications since the figure of merit of the Au nanoparticles obtained after thermal evaporation is more than doubled. Such process could besides allow tuning the localized surface plasmon resonance by using copolymer with variou…
We analyze the heat transfer between two nanoparticles separated by a distance lying in the near-field domain in which energy interchange is due to Coulomb interactions. The thermal conductance is computed by assuming that the particles have charge distributions characterized by fluctuating multipole moments in equilibrium with heat baths at two different temperatures. This quantity follows from the fluctuation-dissipation theorem (FDT) for the fluctuations of the multipolar moments. We compare the behavior of the conductance as a function of the distance between the particles with the result …
We propose and theoretically analyze an experiment where displacement sensing of an optically levitated nanoparticle in front of a surface can be used to measure the induced dipole-dipole interaction between the nanoparticle and its thermal image. This is achieved by using a surface that is transparent to the trapping light but reflective to infrared radiation, with a reflectivity that can be time modulated. This dipole-dipole interaction relies on the thermal radiation emitted by a silica nanoparticle having sufficient temporal coherence to correlate the reflected radiation with the thermal f…
Radiant emittance of dimers and ensembles of particles consisting of gold, graphite and silica glass nanoparticles in vacuum is studied numerically based on the fluctuation-electromagnetic theory. The presence of neighboring particles of the same temperature causes an oscillating character of radiant emittance (per one particle) depending on the particle size, interparticle distance and temperature. We conclude that an ensemble of particles could be a much more intense source of thermal radiation than an equivalent solid body with the same outer surface area. Alternatively, when the neighborin…
Thermal Rectification from Size-Dependent Phonon Confinement in Nanoparticle Assemblies
Università degli Studi di Milano（米兰大学）；Interdisciplinary Centre for Nanostructured Materials and Interfaces (CIMaINa)（纳米材料与界面跨学科中心）；German Aerospace Centre (DLR), Institute of Space Research（德国航空航天中心空间研究所）；Physikalisch-Technische Bundesanstalt (PTB) Berlin（德国联邦物理技术研究院）
An important question in the physics of superconducting nanostructures is the role of thermal fluctuations on superconductivity in the zero-dimensional limit. Here, we probe the evolution of superconductivity as a function of temperature and particle size in single, isolated Pb nanoparticles. Accurate determination of the size and shape of each nanoparticle makes our system a good model to quantitatively compare the experimental findings with theoretical predictions. In particular, we study the role of thermal fluctuations (TF) on the tunneling density of states (DOS) and the superconducting e…
We argue that macroscopic electrodynamics is unsuited to describe the process of radiative thermalization between a levitated nanoparticle in high vacuum and the thermal electromagnetic field. Based on physical arguments, we propose a model to describe such systems beyond the quasi-equilibrium approximation. We use path integral techniques to analytically solve the model and exactly calculate the time evolution of the quantum degrees of freedom of the system. Free parameters of the microscopic quantum model are determined by matching analytical results to well-known macroscopic response functi…
Controlling the temperature in architectures involving nanoparticles and substrates is a key issue for applications involving micro and nanoscale heat transfer. We study the thermal behavior of a single nanoparticle interacting with a flat substrate under external monochromatic illumination, and with thermal radiation as the unique heat loss channel. We develop a model to compute the temperature of the nanoparticle, based on an effective dipole-polarizability approach. Using numerical simulations, we thoroughly investigate the impacts of various parameters affecting the nanoparticle temperatur…
We evaluate the thermal conductivity of a model nanofluid at various volume fractions of nanoparticles with equilibrium (EMD) and non-equilibrium (NEMD) molecular dynamics simulations. The Green-Kubo formalism is used for the EMD simulations while a net heat flux is imposed on the system for the NEMD simulations. The nanoparticle-nanoparticle, fluid-fluid and fluid-nanoparticle interactions are all taken as Lennard-Jones potentials. An empirical parameter is added to the attractive part of the potential to control the hydrophilicity of the nanoparticles, hence controlling how well dispersed ar…
In this work we conduct a transient heat conduction experiment with an aqueous suspension of nanoparticle disks of Laponite JS, a sol forming grade, using laser light interferometry. The image sequence in time is used to measure thermal diffusivity and thermal conductivity of the suspension. Imaging of the temperature distribution is facilitated by the dependence of refractive index of the suspension on temperature itself. We observe that with the addition of 4 volume % of nano-disks in water, thermal conductivity of the suspension increases by around 30%. A theoretical model for thermal condu…
We introduce a many body theory for thermal far-field emission of dipolar dielectric and metallic nanoparticles in the vicinity of a substrate within the framework of fluctuational electrodynamics. Our theoretical model includes the possibility to define the temperatures of each nanoparticle, the substrate temperature, and the temperature of the background thermal radiation, separately. To demonstrate the versatility of our method, we apply it in an exemplary way by discussing the thermal radiation of four particle assemblies of SiC and Ag nanoparticles above a planar SiC and Ag substrate. Fur…
