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This research introduces dynamic modeling and real-time control of fractal structure in particulate materials fabricated by the ball milling process, specifically addressing challenges of unavailable real-time non-destructive and non-invasive imaging measurements in the enclosed rotating vials. A description of the internal temperature dynamics in the container is established along with a thermal regulator based on external temperature feedback. The fractal dimension is introduced as a structural measure, and its dynamics is established via an analytical formulation through a lumped model, along with a full thermostructural computational model of the ball milling particulate microstructure. These models are used as real-time observers of inaccessible internal states during the process. In addition, they are used as model references in an adaptive control system, regulating the fractal structure with adaptation via external temperature measurements, available experimentally via an infrared thermocouple. The controller is designed on the basis of the dynamic models and is tested experimentally. The controller is demonstrated to command the duration of the process at steady conditions to obtain the necessary thermal exposure yielding the desired microstructure for the ball-milled particulates. Keywords: Ball milling, Adaptive control, Aluminum alloys, Fractal dimension

This work establishes a computationally efficient model of temperature and diffusion dynamics in ball milled bimetallic Ni-Al particulates. Mechanical contact conditions between adjacent bimetallic domains and temperature fields generated upon impact define the diffusive fluxes through the domains' interfaces. The concentration distributions are studied via Green's function methods, by defining mirror images which reflect the boundary diffusive resistance conditions. Predictions of the model are validated against experimental open-loop scanning electron micrographs and X-ray diffraction spectra at steady-state. Dynamic models of diffusion saturation and internal temperature are developed for the design of closed-loop controller via simulation. This feedback controller is implemented on a laboratory device, equipped with infrared thermometry for external vial temperature measurement, as a self-tuning regulator. The controller adapts an efficiency parameter of the model that thus serves as a real-time observer for internal temperature and diffusion saturation, which are physically inaccessible during processing. Experimental open-loop results are employed to set thresholds of diffusion penetration to avoid early exothermic reaction during fabrication. By controlling the process duration, the regulation system successfully reproduces the material composition of the open-loop reference tests, to ensure desired thermodynamic properties of the ball milled products and safety of the operation. Keywords: Ball milling, Diffusion control, Thermal dynamics, Green's function, Self-tuning regulation

The reported research establishes a semi-analytical computational predictive model of fractal microstructure in ball-milled metal foils and powder particulates, with emphasis on its transformation mechanics via an energy-based approach. The evolving structure is composed of reconfigurable warped ellipsoid material domains, subjected to collisions with the ball milling impactors following Brownian motion energetics. In the first step of the model, impacts are assumed to generate ideal Hertzian elastic stress fields, with associated bulk deformations quantified as per Castigliano's strain energy methods. In the second stage of the model, elastic energies are recast to produce frictional slip and plastic yield, thus resulting in surface micro-joints. Only two parameters of the model necessitate experimental calibration, performed by comparison of joint energy with laboratory tensile measurements on ball-milled multilayer Al-Ni foils. Model predictions of evolving internal microstructure are validated against SEM micrographs of Al-Ni powder particulate samples for different ball milling durations. Results demonstrate the capability of the model to accurately capture relevant fractal measures of the microstructure of ball-milled powders. © 2016 Acta Materialia Inc. 123 305 316 305-316

Low-energy ball milling of aluminum and nickel particles with an overall composition corresponding to the NiAl intermetallic phase was performed up to milling durations of 13 h. The milled powders and cold-compacted pellets were ignited using a low-energy spark. Interrupted thermal analysis and X-ray diffraction was performed to investigate the effect of milling time on intermetallic phase formation. The results show that microstructural refinement with increasing milling times increases reactivity, where the intermetallic formation temperatures reduce to those of sputtered multilayer foils with a similar phase formation sequence. NiAl intermetallic phase starts forming at 12 h of milling. Loose powders milled for 11 and 12 h and the corresponding pellets ignite locally with uniform thermal wave fronts self-propagating at velocities up to 0.24 m/s. © © 2013 Elsevier B.V. All rights reserved. 101 275 278 275-278

This article reports investigation of the effects of high-rate stochastic micro-mechanics on the produced particulate size distribution during ball milling of reactive bimetallic foils (nanoheaters), by experimental and computational modeling. In particular, Ni-Al foils are ball-milled at various load charges, revolution rates and process durations, and the resulting particulate geometries are characterized by micrograph statistical analysis. Numerical simulation of the evolving particulate structure is based on coalescence and fragmentation of flexible monometallic ellipsoidal primitives, impacted by milling balls and vial walls with kinetic theory-based kinematics. Particulates are constrained by discrete compliant and continuum media and undergo conceptual ideal elastic transformations modeled by strain energy methods, and recast into inelastic frictional and plasticity-driven welding and fracture events. Finally the theoretical model predictions of particulate size distribution are validated against laboratory microscopy observations. © 2017 Materials Research Society. 2 897 904 897-904

The reported research establishes a semi-analytical computational predictive model of fractal microstructure in ball-milled metal foils and powder particulates, with emphasis on its transformation mechanics via an energy-based approach. The evolving structure is composed of reconfigurable warped ellipsoid material domains, subjected to collisions with the ball milling impactors following Brownian motion energetics. In the first step of the model, impacts are assumed to generate ideal Hertzian elastic stress fields, with associated bulk deformations quantified as per Castigliano's strain energy methods. In the second stage of the model, elastic energies are recast to produce frictional slip and plastic yield, thus resulting in surface micro-joints. Only two parameters of the model necessitate experimental calibration, performed by comparison of joint energy with laboratory tensile measurements on ball-milled multilayer Al-Ni foils. Model predictions of evolving internal microstructure are validated against SEM micrographs of Al-Ni powder particulate samples for different ball milling durations. Results demonstrate the capability of the model to accurately capture relevant fractal measures of the microstructure of ball-milled powders. 123 305 316 305-316

Nanoheaters are reactive nanostructures that can generate localized heat through controlled ignition. Besides the widely used nanofoil structure with multiple alternative Al-Ni layers, various new nanostructures have been fabricated in the last several years, including consolidated films, bimetallic nanoparticles and nanowires, and ball milled micro/nano powders. In this paper, we demonstrate the (1) Synthesis of Al-Ni bimetallic nanoparticles by a galvanic replacement reaction method using Al nanoparticle templates (2) Fabrication of Al-Ni nanowire structures by a two-step process involving electrodeposition and thermal evaporation (3) Fabrication of Al-Ni composites by a novel ultrasonic powder consolidation method, using Al and Ni nanoparticles as source materials and (4) Synthesis of nanostructured Al-Ni powders by low energy ball milling with microscale Al and Ni powders. The structure and compositions of the nanoheater structures have been characterized by scanning electron microscopy and transmission electron microscopy, energy dispersive X-ray spectroscopy, and X-ray diffraction. The thermal characteristics of the samples were studied using differential scanning calorimetry. These novel nanoheater structures have great potential to be used in micro-joining, microelectronics assembly, and flexible electronics bonding. © 2012 Elsevier B.V. 215 493 502 493-502

Ball milling motion has been previously studied through computationally expensive, off-line experimental video processing and numerical simulations by the discrete element method. This research establishes a more efficient formulation of the ball energetics and kinetics similar to the Brownian kinetic theory of statistical mechanics. Based on assumptions of thermomechanical equilibrium, negligible gravitational, aerodynamic and surface condition effects, and decoupled impact interaction among balls and with milled particulates, this model proposes mono-parametric spectral energy and velocity probability density functions akin to Maxwell-Boltzmann statistics, along with uniformly distributed impact directionality. The model predictions are calibrated and validated by comparison with published experimental measurements and computationally derived spectra. This descriptive Brownian-like motion model enables effective simulation of contact and impact, material deformation and micro-joining of ball milled bimetallic powders. A comprehensive simulation of the evolving internal fractal microstructure of the processed particulates is implemented at real-time computation speed, and its predictions are compared with experimental micrographs of ball milled [Formula presented] particulates. © 2016 301 1077 1084 1077-1084

The ability to detect explosive materials may be significantly enhanced with local increases in vapor pressure caused by an elevation of the materials'temperature. Recently, ultrasonic excitation has been shown to generate heat within plastic-bonded energetic materials. To investigate the impact of crystal morphology on this heating, samples of elastic binder are implanted with single ammonium perchlorate crystals of two distinct shape groups. Contact piezoelectric transducers are then used to excite the samples at ultrasonicfrequencies. The thermal responses of the crystals are recorded using infrared thermography, and the rate of heating is estimated. Surface temperature increases up to 15 °C are found to arise after 2 s of excitation, with much higher heating levels expected near the inclusions themselves as demonstrated by the chemical decomposition of some crystals under favorable excitation conditions. The rates of heat generation are compared to various crystal morphology features through 2D estimates of length scale, perimeter and irregularity. It is observed that crystals grown in the lab, featuring sharp geometric facets, exhibit a higher probability of significant heat generation than inclusions with more spherical shapes. However, no statistical link is found between the rates of heat generation and the crystal morphology in those samples that do generate significant heating, likely because variations in surface roughness cannot be entirely eliminated during experimentation. It is hoped that this study will lead to a better understanding of the nature of heat generation in energetic materialsfrom ultrasonic sources.

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Fine thermal actuation by miniature heat sources enables applications from electronics fabrication to tumor cauterization. This paper introduces the concept of nanoheaters, i.e., reactive bimetallic material dots (0D), ignited electrically to exothermically release precise heat amounts where and when needed. This concept is extended to nanoheater wires (1D) and foils (2D), as well as bulk nanoheaters (3D) manufactured via ball milling and ultrasonic consolidation of nickel and aluminum powders. The fractal structure of such powders and consolidates, with self-similar, multiscale Apollonian or lamellar packaging, is discovered to hold the key for their ignition sensitivity: nanoscale structures ignite first, to produce enough heat and raise the temperature of submicron formations, which then ignite microscale regions and so on while inert areas quench and arrest the self-propagating exothermic reaction. Therefore, such engineered fractal reactive heaters lend themselves to affordable, high-throughput manufacture and controllable, safe, efficient, supplyless in situ thermal release. This can be transformative for innovations from self-healing composites and self-heating packages to underwater construction and mining. © 2015 IOP Publishing Ltd. 2

The Ru/Al system integrates high energy density and high product ductility and serves as an alternative for utilization as nanoscale reactive multilayer. We present a modeling study that relates the Ru-Al phase transformations occurring during self-propagating reactions with macroscopic reaction parameters such as net front velocity and reaction temperature. We coupled equations for mass and thermal transport and used a numerical scheme to solve the differential equations. We calculated the temporal evolution of the temperature distribution in the reaction front as a function of the multilayer bilayer thickness. The calculated net velocities were between 4.2 m/s and 10.8 m/s, and maximal reaction temperatures were up to 2171 K, in good agreement with measured data. Interfacial premixing, estimated to be around 4 nm, had a large influence on reaction velocities and temperature at smaller bilayer thicknesses. Finally, the theoretical results of the present study help to explain the experimental findings and guide tailoring of reactive properties of Ru/Al multilayers for applications. ABSTRACT FROM AUTHOR] Copyright of Applied Physics Letters is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) 107 73103 073101; 073103-073101; 073103-5

High-frequency mechanical excitation can induce heating within energetic materials and may lead to advances in explosives detection and defeat. In order to examine the nature of this mechanically induced heating, samples of an elastic binder (Sylgard 184) were embedded with inert and energetic particles placed in a fixed spatial pattern and were subsequently excited with an ultrasonic transducer at discrete frequencies from 100 kHz to 20 MHz. The temperature and velocity responses of the sample surfaces suggest that heating due to frictional effects occurred near the particles at excitation frequencies near the transducer resonance of 215 kHz. An analytical solution involving a heat point source was used to estimate heating rates and temperatures at the particle locations in this frequency region. Heating located near the sample surface at frequencies near and above 1 MHz was attributed to viscoelastic effects related to the surface motion of the samples. At elevated excitation parameters near the transducer resonance frequency, embedded particles of ammonium perchlorate and cyclotetramethylene-tetranitramine were driven to chemical decomposition.

Ball milling of aluminum (Al) and nickel (Ni) particles at the NiAl composition can produce reactive powders with low spark ignition thresholds similar to magnetron sputtered multilayer foils (MFs). Such powders can replace MFs for bonding applications when fashioned into suitable geometries. For this purpose, Al and Ni particles were milled in a planetary ball mill for 9hours at 300rpm. Loose powder piles and 840μm thick cold-compacted pellets with 25.4μm Al overlayers were ignited using a low-energy spark. Additionally, the loose particles were used for bonding Al cylinders, whereas pellets with overlayers were used to bond silicon (Si) wafer pieces. Maximum temperature observed in loose powders was around 1770K, consistent with differential scanning calorimetry results. The maximum temperature of the freestanding pellet was 1610K, close to the calculated adiabatic temperature of 1575K. The thermal front velocities were 0.06 and 0.22m/s for loose powder piles and pellets, respectively. Bond interfaces of Al cylinders showed formation of NiAl3 within regions close to the interface, indicating large amounts of Ni diffusion. Likewise, bonded Si interfaces showed evidence of Si melt and dissolution into Al-rich liquid and Ni diffusion into the Al overlayers forming dendritic NiAl3. © 2014 Elsevier B.V. 260 396 400 396-400

Self-propagating reactions in compacted pellets of continuously low-energy ball-milled aluminium (Al) and nickel (Ni) powders at a composition corresponding to AlNi3 were investigated. The formation of a bi-modal structure with nanoscale lamellae of Al and Ni surrounding thicker Ni layers was observed. The milled powder sizes decreased for milling durations longer than 4 h, but the pellet green densities remained mostly constant for longer than 2 h of milling. The ignited pellets observed using high-speed optical and infrared imaging revealed that the thermal wave velocity, maximum reaction temperature, ignition initiation duration and ignition temperature decreased with increasing milling times due to solid-state diffusion. X-Ray Diffraction (XRD) analysis after ignition tests showed that the AlNi3 amount increased with milling time. Thermal analysis using interrupted Differential Scanning Calorimetry (DSC) in combination with XRD revealed that the ball-milled pellets have similarities to nanoscale magnetron sputtered multilayer foils in terms of phase formation sequence and exothermic peak shifts. © 2013 Elsevier Ltd. All rights reserved. 96 73 78 73-78

Ball milling (BM) was used to produce reactive Al–Ni powder mixtures that exhibit self-propagating exothermic reactions (SPER) for nano–micro heater applications. Powders with an Al–Ni molar ratio of 1:3 were milled, cold pressed into pellets and ignited using a heat source. The structural and thermal properties of the pellets were characterized before and after ignition using X-ray diffraction (XRD), scanning electron microscopy (SEM) and differential scanning calorimetry (DSC). The reaction characteristics of the pellets were evaluated using an infrared camera during ignition experiments. Pellet microstructures show that the BM technique created nanoscale lamellar structures, with dimensions diminishing with increasing milling time. Pellets milled longer than 16h exhibited SPER. Flame velocity increased with pellet density. 505 467 471 467-471

Porous alumina templates are attracting increasing attention for the growth of nanowires and nanodots. We demonstrate here the fabrication of reactive bimetallic nanoporous Al/Ni films and Al/Ni nanorods by electron gun evaporation on a very thin porous alumina template, with vertical cylindrical pores 160nm in height and 60nm in diameter. Al and Ni were deposited consecutively on the template and a bimetallic Al/Ni nanorod 60nm in height and in diameter was formed in each pore, while a porous bimetallic Al/Ni capping layer was produced on top of the porous alumina template. The porous reactive bimetallic capping layer was ignited using a spark and a crater was formed around each ignition point with microspheres of the nickel aluminides products. The obtained results offer a first insight into the development of reactive nanorods and porous thin films capable of providing a thermally actuated valving mechanism for flows into and/or out of anodized aluminium oxide membranes and nanotubes, e.g. for targeted drug delivery. 86 836 839 836-839

In this study, we performed simulations of self-propagating reactions of nanoscale nickel-aluminum multilayers using numerical methods. The model employs two-dimensional heat transfer equations coupled with heat generation terms from, (1) 1D parabolic growth of intermetallic phases Ni2 Al3 and NiAl in the thickness direction and (2) phase transformations such as melting and peritectic reactions. The model uses temperature dependent physical and chemical data, such as interdiffusion coefficients, specific heat capacities, and enthalpy of reactions obtained from previous independent work. The equations are discretized using a lagged Crank-Nicolson method. The results show that initially, the reaction front velocity is determined by the rapid growth of Ni2 Al3 and the front temperature is limited by the peritectic reaction at ∼1406 K. After the front completely traverses the foil and the temperature reaches the peritectic point, the reaction slows down and the temperature rises by the growth of NiAl which is the only stable phase at these temperatures. The reaction is completed when the initial constituents are consumed and the temperature reaches the melting point of NiAl. Subsequently, the foil cools and solidifies to the final phase dictated by the overall composition. The computational results show excellent fit to experimental velocity and temperature measurements. © 2009 American Institute of Physics. 105