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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Residual stress within nanoscale metallic multilayer systems during thermal cycling

Projected applications for nanoscale metallic multilayers will include wide temperature ranges. Since film residual stress has been known to alter system reliability, stress development within new film structures with high interfacial densities should be characterized to identify potential long-term performance barriers. To understand factors contributing to thermal stress evolution within nanoscale metallic multilayers, stress in Cu/Nb systems adhered to Si substrates was calculated from curvature measurements collected during cycling between 25 °C and 400 °C. Additionally, stress within each type of component layers was calculated from shifts in the primary peak position from in-situ heated X-ray diffraction. The effects of both film architecture (layer thickness) and layer order in metallic multilayers were tracked and compared with monolithic Cu and Nb films. Analysis indicated that the thermoelastic slope of nanoscale metallic multilayer films depends on thermal expansion mismatch, elastic modulus of the components, and also interfacial density. The layer thickness (i.e. interfacial density) affected thermoelastic slope magnitude while layer order had minimal impact on stress responses after the initial thermal cycle. When comparing stress responses of monolithic Cu and Nb films to those of the Cu/Nb systems, the nanoscale metallic multilayers show a similar increase in stress above 200 °C to the Nb monolithic films, indicating that Nb components play a larger role in stress development than Cu. Local stress calculations from X-ray diffraction peak shifts collected during heating reveal that the component layers within a multilayer film respond similarly to their monolithic counterparts.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Novel Sustainable Process for Multilayer Graphene Synthesis Using CO 2 from Ambient Air

Graphene produced by different methods can present varying physicochemical properties and quality, resulting in a wide range of applications. The implementation of a novel method to synthesize graphene requires characterizations to determine the relevant physicochemical and functional properties for its tailored application. We present a novel method for multilayer graphene synthesis using atmospheric carbon dioxide with characterization. Synthesis begins with carbon dioxide sequestered from air by monoethanolamine dissolution and released into an enclosed vessel. Magnesium is ignited in the presence of the concentrated carbon dioxide, resulting in the formation of graphene flakes. These flakes are separated and enhanced by washing with hydrochloric acid and exfoliation by ammonium sulfate, which is then cycled through a tumble blender and filtrated. Raman spectroscopic characterization, FTIR spectroscopic characterization, XPS spectroscopic characterization, SEM imaging, and TEM imaging indicated that the graphene has fifteen layers with some remnant oxygen-possessing and nitrogen-possessing functional groups. The multilayer graphene flake possessed particle sizes ranging from 2 µm to 80 µm in diameter. BET analysis measured the surface area of the multilayer graphene particles as 330 m 2 /g, and the pore size distribution indicated about 51% of the pores as having diameters from 0.8 nm to 5 nm. This study demonstrates a novel and scalable method to synthesize multilayer graphene using CO 2 from ambient air at 1 g/kWh electricity, potentially allowing for multilayer graphene production by the ton. The approach creates opportunities to synthesize multilayer graphene particles with defined properties through a careful control of the synthesis parameters for tailored applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

3D simulations of spinlike flames in Co/Al multilayers with enhanced conduction losses

Reactive Co/Al multilayers are uniformly structured materials that may be ignited to produce rapid and localized heating. Prior studies varying the bilayer thickness (i.e., sum of two individual layers of Co and Al) have revealed different types of flame morphologies, including: (a) steady/planar, (b) wavy/periodic, and (c) transverse bands, originating in the flame front. These instabilities resemble the “spin waves” first observed in the early studies of solid combustion (i.e., Ti cylinder in a N 2 atmosphere), and are likewise thought to be due to the balance of heat released by reaction and heat conduction forward into the unreacted multilayer. However, the multilayer geometry and three-dimensional (3D) edge effects are relatively unexplored. In this work, a new diffusion-limited reaction model for Co/Al multilayers was implemented in large, novel 3D finite element analysis (FEA) simulations, in order to study the origins of these spinlike flames. This reaction model builds upon previous work by introducing three new phase-dependent property models for: (1) the diffusion coefficient, (2) anisotropic thermal conductivity tensor, and (3) bulk heat capacity, as well as one additional model for the bilayer-dependent heat of reaction. These novel 3D simulations are the first to predict both steady and unsteady flames in Co/Al multilayers. Moreover, two unsteady modes of flame propagation are identified, which depend on the enhanced conduction losses with slower flames, as well as flame propagation around notched edges. Finally, future work will consider the generality of the current modeling approach and also seek to define a more generalized set of stability criteria for additional multilayer systems.

42 ENGINEERING↗
DOE OSTI2018

The fabrication of nanoscale Bi 2 Te 3 /Sb 2 Te 3 multilayer thin film-based thermoelectric power chips

In this work, we report our method of fabricating nanoscale multilayered Bi 2 Te 3 /Sb 2 Te 3 thin film-based integrated thermoelectric devices, and detail the voltage and power produced by the device. The multilayered Bi 2 Te 3 /Sb 2 Te 3 thin film was grown via e-beam evaporation; it had 20 alternating Bi 2 Te 3 - and Sb 2 Te 3 -layers, each layer being 1.5 nm thick. We characterized the film using high-resolution transmission electron microscopy (HRTEM), revealing its excellent cross-sectional structure without any obvious interface defects. The Bi 2 Te 3 /Sb 2 Te 3 multilayer films were investigated by synchrotron x-ray scattering. An integrated device including 128×256 thermoelectric elements was fabricated from the multilayered film. An open-circuit voltage of 51 mV and a maximum power of 21 nW were produced from this 30 nm-thick Bi 2 Te 3 /Sb 2 Te 3 multilayer TE device. We found that the nanoscale multilayer structure significantly affects the voltage and power produced. Lastly, the fabrication of the integrated thermoelectric devices is compatible to that of generating standard integrated circuits (ICs), and is scalable for producing higher voltage and power, or achieving solid-state cooling for on-chip applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microstructure and mechanical properties of nanoscale Cu/(Ta50Nb25Mo25) multilayers

Nanoscale Cu/(Ta50Nb25Mo25) multilayers comprised of medium entropy alloy Ta50Nb25Mo25 and pure Cu are found to exhibit similar length-scale-dependent deformation mechanisms as metallic multilayers with elemental individual layers, i.e., confined layer slip at layer thickness of tens of nanometers and shear localization at several nanometers. The hardness of the nanoscale Cu/(Ta50Nb25Mo25) multilayers is higher as compared to the pure element FCC/BCC multilayers due to the extra solid solution strengthening contribution in the BCC layer. The synergy between the size effect and solid solution strengthening mechanism is discussed. In conclusion, this is an early report of the multi-component multilayers, which serves to provide directions for developing novel multilayer materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Strain-rate dependent deformation mechanisms in single-layered Cu, Mo, and multilayer Cu/Mo thin films

Here, strain-rate sensitivity and rate-dependent hardness, over a range of 10 -2 to 10 2 s -1 , of sputter-deposited single-layered Cu, Mo, and 5 nm Cu/ 5 nm Mo, and 100 nm Cu/ 100 nm Mo multilayer films with a total film thickness of 5 μm were measured using nanoindentation. The plastic zone underneath the nanoindents was characterized via cross-sectional transmission electron microscopy (XTEM). The multilayer films exhibited enhanced hardness but slightly reduced strain-rate sensitivity with decreasing layer thickness from 100 nm to 5 nm. Only the 5 nm Cu/ 5 nm Mo multilayer film exhibited shear bands underneath the nanoindents, and the size of the shear bands increased with increasing strain rate. In contrast, the 100 nm Cu/ 100 nm Mo multilayer film exhibited material pile-up around the indents and significant nanotwinning within Cu grains. The effect of strain rate and layer thickness on the hardness and strain rate sensitivity of the multilayer thin films is interpreted using a modified confined layer slip (CLS) model. The reduced rate sensitivity at 5 nm as compared to 100 nm correlates with abundant growth nanotwins in the Cu grains in 100 nm and formation of shear bands in 5 nm multilayers. In single layer films, a substructure with a high density of dislocations was observed consistent with the plastic strain gradient in the indent plastic zone. No evidence of deformation twins was noted in any of the samples.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Deposition of very thick Mo/Al multilayer films using magnetron sputtering

To understand materials at extreme conditions dynamic ramp compression techniques/experiments are critical, and gradient density impactors (GDIs) have the potential to enable high quality experiments. Very thick (i.e., hundreds of μm thick) multilayer films consisting of high z/low z layers with a gradient in z through the stack can serve as a GDI. Surprisingly while there is a large amount of literature on the topic of multilayer films, there is an absence of literature on very thick multilayer films. A number of multilayer film systems deposited by dc magnetron sputtering were evaluated as potential candidates, including Cu/Al, Ta/Al, and Mo/Al. The Mo/Al multilayer system was observed to be the most promising candidate and is the primary focus of this paper. Mo/Al multilayer films up to ∼400 μm thick with reasonable thickness uniformity were deposited.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Characterization of multilayer nitride coatings by electron microscopy and modulus mapping

This paper discusses multi-scale characterization of physical vapour deposited multilayer nitride coatings using a combination of electron microscopy and modulus mapping. Multilayer coatings with a triple layer structure based on TiAlN and nanocomposite nitrides with a nano-multilayered architecture were deposited by Cathodic arc deposition and detailed microstructural studies were carried out employing Energy Dispersive Spectroscopy, Electron Backscattered Diffraction, Focused Ion Beam and Cross sectional Transmission Electron Microscopy in order to identify the different phases and to study microstructural features of the various layers formed as a result of the deposition process. Modulus mapping was also performed to study the effect of varying composition on the moduli of the nano-multilayers within the triple layer coating by using a Scanning Probe Microscopy based technique. To the best of our knowledge, this is the first attempt on modulus mapping of cathodic arc deposited nitride multilayer coatings. This work demonstrates the application of Scanning Probe Microscopy based modulus mapping and electron microscopy for the study of coating properties and their relation to composition and microstructure. - Highlights: • Microstructure of a triple layer nitride coating studied at multiple length scales. • Phases identified by EDS, EBSD and SAED (TEM). • Nanolayered, nanocomposite structure of the coating studied using FIB and TEM. • Modulus mapping identified moduli variation even in a nani-multilayer architecture.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Multilayered vacuum-arc nanocomposite TiN/ZrN coatings before and after annealing: Structure, properties, first-principles calculations

Highlights: • Multilayer TiN/ZrN films were deposited using sequential vacuum-arc deposition of Ti and Zr targets in nitrogen atmosphere; • Several samples were annealed in air at the temperature 700 °C; • First-principles calculations of TiN(111), ZrN(111) structures and TiN(111)/ZrN(111) multilayer were carried out; • All deposited samples were highly polycrystalline with quite large 20–25 nm crystals; • The nanohardness and elastic modulus of non-annealed coatings reached 42 GPa and 348 GPa, respectively; • Deposited coatings demonstrate good wear and oxidation resistance; - Abstract: Nanoscale multilayered TiN/ZrN films were deposited using sequential vacuum-arc deposition of Ti and Zr targets in a nitrogen atmosphere. Studies of film's properties were carried out using various modern methods of analysis, such as XRD, STEM, HRTEM, SIMS combined with results of nanoindentation and tribological tests. To interpret the mechanical properties of the deposited multilayer films first-principles calculations of TiN(111), ZrN(111) structures and TiN(111)/ZrN(111) multilayer were carried out. To study the influence of thermal annealing, several samples were annealed in air at the temperature 700 °C. All deposited samples were highly polycrystalline with quite large 20–25 nm crystals. The crystalline planes were very ordinated and demonstrated an excellent coordinated growth. The nanohardness and elastic modulus of non-annealed coatings reached 42 GPa and 348 GPa, respectively. Annealing in air at the temperature 700 °C led to partial oxidation of the multilayered coatings, however hardness of the non-oxidized part of the coatings remained as high, as for initial coatings. All deposited coatings demonstrate good wear resistance.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Nacre-like MXene/Polyacrylic Acid Layer-by-Layer Multilayers as Hydrogen Gas Barriers

MXenes are a promising class of 2D nanomaterials and are of particular interest for gas barrier applications due to their high aspect ratio. However, MXene nanosheets naturally bear a negative charge, which prevents assembly with negatively charged polymers, such as polyacrylic acid (PAA), into gas barrier coatings. Here, we present MXene- and PAA-based layer-by-layer (MXene/ PAA LbL) multilayers formed by leveraging hydrogen bonding interactions. When assembled in acidic conditions, MXene/PAA LbL multilayers exhibit conformal, pinhole-free, nacre-like structures. The MXene/PAA LbL multilayers yield high blocking capability and low permeability (0.14 ± 0.01 cc·mm·m −2 ·day −1 · MPa −1 ) for hydrogen gas which is over 9000 times lower than uncoated niobium (Nb) substrate. These nacre-like structures are also electronically conductive (σ DC , up to 370 ± 30 S cm −1 ). Because these multilayers utilize hydrogen bonding, their properties are highly sensitive to the pH of the assembly and its external environment. Specifically, the reversible deconstruction of these multilayers under basic conditions is experimentally verified. This study shows that hydrogen bonding interactions can be leveraged to form MXene LbL multilayers as gas barriers, electronically conductive coatings, and deconstructable thin films via pH control.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Microstructure evolution and magnetic properties of FeB/Pt multilayers and FeBPt composite films

Comparisons of microstructural evolution and magnetic properties were made of a FeB12/Pt10/[FeB1.2/Pt1]{sub 15}/Ta5 nm multilayered structure with a FeB12/Pt10/FeBPt33/Ta5 nm co-deposited structure. The Ta capping layer was used to protect the films from oxidation. Both these samples were sputtered in the same planetary deposition system onto thermally oxidized silicon substrates. They both represent layer-by-layer deposition, with the second type of deposition having atomically fine layers, more than an order of magnitude finer than the first type. The samples were annealed at a range of times, temperatures, and vacuum conditions. X-ray diffraction (XRD), transmission electron microscopy, and alternating gradient magnetometry were employed to characterize the structural and magnetic properties, respectively. Significant differences were observed between the two types of structures. A maximum coercivity of 8.9 kOe was seen for the atomically fine multilayer, about 10% more than that for the coarse multilayer. XRD analysis confirmed that both the coarse and fine multilayers were in the L1{sub 0} phase after annealing. Our results indicate that the co-deposited film, which is really composed of atomically fine multilayers, is superior to the coarse multilayered FeB/Pt for the formation of L1{sub 0}-phase FePt.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Shock compression response of highly reactive Ni + Al multilayered thin foils

The shock-compression response of Ni + Al multilayered thin foils is investigated using laser-accelerated thin-foil plate-impact experiments over the pressure range of 2 to 11 GPa. The foils contain alternating Ni and Al layers (parallel but not flat) of nominally 50 nm bilayer spacing. The goal is to determine the equation of state and shock-induced reactivity of these highly reactive fully dense thin-foil materials. The laser-accelerated thin-foil impact set-up involved combined use of photon-doppler-velocimetry to monitor the acceleration and impact velocity of an aluminum flyer, and VISAR interferometry was used to monitor the back free-surface velocity of the impacted Ni + Al multilayered target. The shock-compression response of the Ni + Al target foils was determined using experimentally measured parameters and impedance matching approach, with error bars identified considering systematic and experimental errors. Meso-scale CTH shock simulations were performed using real imported microstructures of the cross-sections of the multilayered Ni + Al foils to compute the Hugoniot response (assuming no reaction) for correlation with their experimentally determined equation of state. It was observed that at particle velocities below ∼150 m/s, the experimentally determined equation of state trend matches the CTH-predicted inert response and is consistent with the observed unreacted state of the recovered Ni + Al target foils from this velocity regime. At higher particle velocities, the experimentally determined equation of state deviates from the CTH-predicted inert response. A complete and self-sustained reaction is also seen in targets recovered from experiments performed at these higher particle velocities. The deviation in the measured equation of state, to higher shock speeds and expanded volumes, combined with the observation of complete reaction in the recovered multilayered foils, confirmed via microstructure characterization, is indicative of the occurrence of shock-induced chemical reaction occurring in the time-scale of the high-pressure state. TEM characterization of recovered shock-compressed (unreacted) Ni + Al multilayered foils exhibits distinct features of constituent mixing revealing jetted layers and inter-mixed regions. These features were primarily observed in the proximity of the undulations present in the alternating layers of the Ni + Al starting foils, suggesting the important role of such instabilities in promoting shock-induced intermetallic-forming reactions in the fully dense highly exothermic multilayered thin foils.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Development of a flat-field spectrometer with a wideband Ni/C multilayer grating in the 1–3.5 keV range

To develop a flat-field spectrometer with coverage of the 1–3.5 keV range, a wideband Ni/C multilayer grating was invented. The multilayer consists of two kinds of layer structures. One is a conventional periodic multilayer of thickness D{sub 1} = 5.6 nm, Ni thickness ratio to the multilayer period γ{sub 1} = 0.5 and the number of layers N{sub 1} = 79. Both the first and last layers are Ni. The other is a C/Ni bilayer of D{sub 2} = 8.4 nm, γ{sub 2} = 0.53 and N{sub 2} = 2. The first layer is C and then Ni. The aperiodic multilayer from the topmost C/Ni bilayer was coated on a laminar-type grating having an effective grating constant of 1/2400 mm, groove depth of 2.8 nm, and duty ratio (land width/groove period) of 0.5. In a preliminary experiment, the diffraction efficiency was in excess of 0.8% in the energy range of 2.1-3.3 keV and the maximum of 5.4% at 3.1 keV at a constant angle of incidence of 88.54°, which is considerably higher than that of an Au-coated grating before deposition of the multilayer.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Ignition and self-propagating reactions in Al/Pt multilayers of varied design

The different rate-limiting processes underlying ignition and self-propagating reactions in Al/Pt multilayers are examined through experiments and analytical modeling. Freestanding, ~1.6 μm-thick Al/Pt multilayers of varied stoichiometries and nanometer-scale layer thicknesses ignite at temperatures below the melting point of both reactants (and eutectics) demonstrating that initiation occurs via solid-state mixing. Equimolar multilayers exhibit the lowest ignition temperatures when comparing structures having a specific bilayer thickness. An activation energy of 76.6 kJ/mol at. associated with solid state mass transport is determined from the model analysis of ignition. High speed videography shows that equimolar Al/Pt multilayers undergo the most rapid self-sustained reactions with wavefront speeds as large as 73 m/s. Al- and Pt-rich multilayers react at reduced rates (as low as 0.3 m/s), consistent with reduced heat of reaction and lower adiabatic temperatures. An analytical model that accounts for key thermodynamic properties, preliminary mixing along interfaces, thermal transport, and mass diffusion is used to predict the wavefront speed dependencies on bilayer thickness. Finally, good fits to experimental data provide estimates for activation energy (51 kJ/mol at.) associated with mass transport subject to high heating rates and thermal diffusion coefficient of premixed interfacial volumes (2.8 × 10 -6 m 2 /s). Pt dissolution into molten Al is identified as a rate-limiting step underlying high temperature propagating reactions in Al/Pt multilayers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Low-temperature formation of Ti2AlN during post-deposition annealing of reactive multilayer systems

M n+1 AXn-phase Ti 2 AlN thin-films were synthesized using reactive sputtering-based methods involving the deposition of single-layer TiAlN, and Ti/AlN and TiN/TiAl multilayers of various modulation periods at ambient temperature and subsequent annealing at elevated temperatures. Ex situ and in situ x-ray diffraction measurements were used to characterize the Ti 2 AlN formation temperature and phase fraction. During annealing, Ti/AlN multilayers yielded Ti 2 AlN at a significantly lower in situ temperature of 650 °C compared to TiN/TiAl multilayers or single-layer TiAlN (750 °C). The results suggest a reactive multilayer mechanism whereby distinct Ti and AlN layers react readily to release exothermic energy resulting in lower phase transition temperatures compared to TiN and TiAl layers or mixed TiAlN. With a modulation period of 5 nm, however, Ti/AlN multilayers yielded Ti 2 AlN at a higher temperature of 750 °C, indicating a disruption of the reactive multilayer mechanism due to a higher fraction of low-enthalpy interfacial TiAlN within the film.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Inert mesoscale simulations

Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm 2 ) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.

Kittell, David E. [Sandia National Laboratories (S↗
DOE OSTI2025

Collective Modes in Multilayer Graphene/𝛼−RuCl 3 Heterostructures

Collective modes in multilayer graphene, such as plasmons and phonons, exhibit sensitivity to displacement fields and interlayer coupling, distinguishing them from their counterparts in single-layer graphene. Here, we engineer collective modes in charge-transfer heterostructures composed of multilayer graphene and 𝛼−RuCl 3 . In heterostructures with a single 𝛼−RuCl 3 interface, the charge transfer generates displacement fields up to 7 V/nm at the interface between 𝛼−RuCl 3 and the adjacent graphene layer—the highest value achieved through charge-transfer methods. As a result of the broken inversion symmetry, we discover enhanced nonlinear optical response and modified phonon selection rules. Conversely, we find that multilayer graphene sandwiched between two 𝛼−RuCl 3 flakes causes displacement fields to cancel. There, we achieve carrier densities as high as 8 ×10 13 cm −2 in multilayer graphene and restore the phonon selection rules to their unperturbed state. Meanwhile, we demonstrate that plasmonic properties derive from the depletion of multiple valence bands. As a result of the quasilinear band dispersion, these “Dirac multiband plasmons” are relatively unaffected by displacement fields. On the other hand, the inverted heterostructure sequence—two multilayer graphene sheets encapsulating 𝛼−RuCl 3 —activates significant alteration of the plasmons via interlayer plasmon-plasmon coupling. Hence, multilayer graphene and 𝛼−RuCl 3 heterostructures offer a gate-free platform for engineering collective modes derived from inversion symmetry and interlayer coupling.

Moore, Samuel L. [Columbia University, New York, N↗
DOE OSTI2016

Multilayer spectral graph clustering via convex layer aggregation

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theoretical framework for multilayer spectral graph clustering of the nodes via convex layer aggregation. Under a novel multilayer signal plus noise model, we provide a phase transition analysis that establishes the existence of a critical value on the noise level that permits reliable cluster separation. The analysis also specifies analytical upper and lower bounds on the critical value, where the bounds become exact when the clusters have identical sizes. Numerical experiments on synthetic multilayer graphs are conducted to validate the phase transition analysis and study the effect of layer weights and noise levels on clustering reliability.

97 MATHEMATICS AND COMPUTING↗