R. V. N. Melnik

Finite Element Analysis of Phase Transformation Dynamics in Shape Memory Alloys with a Consistent Landau-Ginzburg Free Energy Model

The Landau theory of phase transition has been successfully applied to solve a number of important problems in the dynamics of martensitic phase transformations in alloys. On the other hand, although a precise mathematical description of the microstructures is known within the framework of Cauchy-Born hypothesis, its discrete version is not well elucidated in the literature, especially for multivariant transformations in three-dimensional samples. A major reason for such a situation lies with computational difficulties connected with quasi-convexity of the associated minimization problem. In this paper we develop a Landau-Ginzburg free energy model for dynamic problems of phase transformations and show a possible link of the developed framework with the continuum description of phase transformations. We demonstrate how the precise description of compatible microstructures in the phase-field model can be used in computational finite element models. The developed framework is sufficiently general to be applied to different types of phase transforming alloys and under general thermo-mechanical loadings. We exemplify the developed technique and its finite element implementation on cubic to tetragonal transformations.

Electromechanical interactions in a carbon nanotube based thin film field emitting diode

Carbon nanotubes (CNTs) have emerged as promising candidates for biomedical x-ray devices and other applications of field emission. CNTs grown/deposited in a thin film are used as cathodes for field emission. In spite of the good performance of such cathodes, the procedure to estimate the device current is not straightforward and the required insight towards design optimization is not well developed. In this paper, we report an analysis aided by a computational model and experiments by which the process of evolution and self-assembly (reorientation) of CNTs is characterized and the device current is estimated. The modeling approach involves two steps: (i) a phenomenological description of the degradation and fragmentation of CNTs and (ii) a mechanics based modeling of electromechanical interaction among CNTs during field emission. A computational scheme is developed by which the states of CNTs are updated in a time incremental manner. Finally, the device current is obtained by using the Fowler-Nordheim equation for field emission and by integrating the current density over computational cells. A detailed analysis of the results reveals the deflected shapes of the CNTs in an ensemble and the extent to which the initial state of geometry and orientation angles affect the device current. Experimental results confirm these effects.

Characterization of Self-Assembly and Evolution in Carbon Nanotube Thin Film Field Emitter

Carbon nanotubes (CNTs) are found to be good sources of cold cathode electron for a variety of technological applications. In this paper, we analyze the evolution and self-assembly of randomly oriented CNTs in a thin film during field emission under diode configuration. A model of the evolution of CNT thin film is proposed, where the CNTs are assumed to decay by fragmentation and formation of plasma consisting of carbon atoms and impurities. The random orientation of the CNTs and the electrodynamic interaction among themselves are modeled to explain the self-assembly caused by dynamic reorientation of the CNTs. Finally, the nucleation coupled degradation model and the electrodynamic forcing model are employed to estimate the current-voltage characteristics based on the modified Fowler-Nordheim equation for field emission. The simulated results are in close agreement with the experimental results.

Multi-mode phonon controlled field emission from carbon nanotubes: Modeling and experiments

The main idea proposed in this paper is that in a vertically aligned array of short carbon nanotubes (CNTs) grown on a metal substrate, we consider a frequency dependent electric field, so that the mode-specific propagation of phonons, in correspondence with the strained band structure and the dispersion curves, take place. We perform theoretical calculations to validate this idea with a view of optimizing the field emission behavior of the CNT array. This is the first approach of its kind, and is in contrast to the the conventional approach where a DC bias voltage is applied in order to observe field emission. A first set of experimental results presented in this paper gives a clear indication that phonon-assisted control of field emission current in CNT based thin film diode is possible.

MODELING HETEROSTRUCTURES WITH SCHRODINGER-POISSON-NAVIER ITERATIVE SCHEMES, EFFECT OF CARRIER CHARGE, AND INFLUENCE OF ELECTROMECHANICAL COUPLING

This paper presents a detailed investigation of the erects of piezoelectricity, spontaneous polarization and charge density on the electronic states and the quasi-Fermi level energy in wurtzite-type semiconductor heterojunctions. This has required a full solution to the coupled Schrodinger-Poisson-Navier model, as a generalization of earlier work on the Schrodinger-Poisson problem. Finite-element-based simulations have been performed on a A1N/GaN quantum well by using both one-step calculation as well as the self-consistent iterative scheme. Results have been provided for field distributions corresponding to cases with zero-displacement boundary conditions and also stress-free boundary conditions. It has been further demonstrated by using four case study examples that a complete self-consistent coupling of electromechanical fields is essential to accurately capture the electromechanical fields and electronic wavefunctions. We have demonstrated that electronic energies can change up to approximately 0.5 eV when comparing partial and complete coupling of electromechanical fields. Similarly, wavefunctions are significantly altered when following a self-consistent procedure as opposed to the partial-coupling case usually considered in literature. Hence, a complete self-consistent procedure is necessary when addressing problems requiring more accurate results on optoelectronic properties of low-dimensional nanostructures compared to those obtainable with conventional methodologies.

Modeling of GaN/AlN heterostructure-based nano pressure sensors

We quantify the influence of thermopiezoelectric effects in nano-sized AlxGa1-xN/GaN heterostructures for pressure sensor applications based on the barrier height modulation principle. We use a fully coupled thermoelectromechanical formulation, consisting of balance equations for heat transfer, electrostatics and mechanical field. To estimate the vertical transport current in the heterostructures, we have developed a multi-physics model incorporating thermionic emission, thermionic field emission, and tunneling as the current transport mechanisms. A wide range of thermal (0-300 K) and pressure (0-10 GPa) loadings has been considered. The results for the thermopiezoelectric modulation of the barrier height in these heterostructures have been obtained and optimized. The calculated current shows a linear decrease with increasing pressure. The linearity in pressure response suggests that AlxGa1-xN/GaN heterostructure-based devices are promising candidates for pressure sensor applications under severe environmental conditions.

Mesoscopic dynamics of piezoelectric copolymer thin films

A mesoscopic model to analyze various effects of electroactive and flow related properties in piezoelectric copolymer composite thin film has been developed in this paper. A three-phase composite with piezoelectric particulate phase, electroactive polymer phase and graft polymer-matrix phase is considered. The homogenized constitutive model takes into account the local transport of cations in polymer, electrostriction and anhysteretic polarization. A finite strain description is given which includes the mesoscopic dispersion of copolymer chains. Finite element simulation is carried out by considering a P(VDF-TrFE)-PZT-Araldite thin film. Analysis of the results indicate that an increasing copolymer content substantially changes the deformation pattern in the film.

Modeling the essential atomistic influence in the phase transformation dynamics of shape memory materials

A Ginzburg-Landau free energy model of multivariant phase transformation in shape memory alloy has been developed. This paper is focused on linking the developed microscopic model with the atomistic reordering process which finally give rise to self-accommodating microstructure. It is analyzed how the kinetics influences the computation of stress-temperature induced dynamics of phase transformation in microscopic and larger length-scales without attempting to solve a molecular dynamic problem in a coupled manner. A variational approach is adopted and phase transformation in Ni-Al thin film is simulated. The simulations capture a qualitative picture of the onset of microstructure formation.

FIELD EMISSION EFFICIENCY OF A CARBON NANOTUBE ARRAY UNDER PARASITIC NONLINEARITIES

Carbon Nanotubes (CNTs) grown on substrates are potential electron sources in field emission applications. Several studies have reported the use of CNTs in field emission devices, including field emission displays, X-ray tube, electron microscopes, cathode-ray lamps, etc. Also, in recent years, conventional cold field emission cathodes have been realized in micro-fabricated arrays for medical X-ray imaging. CNTbased field emission cathode devices have potential applications in a variety of industrial and medical applications, including cancer treatment. Field emission performance of a single isolated CNT is found to be remarkable, but the situation becomes complex when an array of CNTs is used. At the same time, use of arrays of CNTs is practical and economical. Indeed, such arrays on cathode substrates can be grown easily and their collective dynamics can be utilized in a statistical sense such that the average emission intensity is high enough and the collective dynamics lead to longer emission life. The authors in their previous publications had proposed a novel approach to obtain stabilized field emission current from a stacked CNT array of pointed height distribution. A mesoscopic modeling technique was employed, which took into account electro-mechanical forces in the CNTs, as well as transport of conduction electron coupled with electron phonon induced heat generation from the CNT tips. The reported analysis of pointed arrangements of the array showed that the current density distribution was greatly localized in the middle of the array, the scatter due to electrodynamic force field was minimized, and the temperature transients were much smaller compared to those in an array with random height distribution. In the present paper we develop a method to compute the emission efficiency of the CNT array in terms of the amount of electrons hitting the anode surface using trajectory calculations. Effects of secondary electron emission and parasitic capacitive nonlinearity on the current-voltage signals are accounted. Field emission efficiency of a stacked CNT array with various pointed height distributions are compared to that of arrays with random and uniform height distributions. Effect of this parasitic nonlinearity on the emission switch-on voltage is estimated by model based simulation and Monte Carlo method.

Stabilizing a pulsed field emission from an array of carbon nanotubes

In this paper, we propose a new design configuration for a carbon nanotube (CNT) array based pulsed field emission device to stabilize the field emission current. In the new design, we consider a pointed height distribution of the carbon nanotube array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The randomly oriented CNTs are assumed to be grown on a metallic substrate in the form of a thin film. A model of field emission from an array of CNTs under diode configuration was proposed and validated by experiments. Despite high output, the current in such a thin film device often decays drastically. The present paper is focused on understanding this problem. The random orientation of the CNTs and the electromechanical interaction are modeled to explain the self-assembly. The degraded state of the CNTs and the electromechanical force are employed to update the orientation of the CNTs. Pulsed field emission current at the device scale is finally obtained by using the Fowler-Nordheim equation by considering a dynamic electric field across the cathode and the anode and integration of current densities over the computational cell surfaces on the anode side. Furthermore we compare the subsequent performance of the pointed array with the conventionally used random and uniform arrays and show that the proposed design outperforms the conventional designs by several orders of magnitude. Based on the developed model, numerical simulations aimed at understanding the effects of various geometric parameters and their statistical features on the device current history are reported.