i Electrostatic Pull-in Test Structure Design for in-situ Mechanical Property Measurements of Microelectromechanical Systems (MEMS) submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy

a b s t r a c t Elastic properties play a key role in materials science and technology. The elastic tensors at any order are defined by the Taylor expansion of the elastic energy or stress in terms of the applied strain. In this paper, we present ElaStic, a tool that is able to calculate the full second-order elastic stiffness tensor for any crystal structure from ab initio total-energy and/or stress calculations. This tool also provides the elastic compliances tensor and applies the Voigt and Reuss averaging procedure in order to obtain an evalua- tion of the bulk, shear, and Young moduli as well as the Poisson ratio of poly-crystalline samples. In a first step, the space-group is determined. Then, a set of deformation matrices is selected, and the corre- sponding structure files are produced. In a next step, total-energy or stress calculations for each deformed structure are performed by a chosen density-functional theory code. The computed energies/stresses are fitted as polynomial functions of the applied strain in order to get derivatives at zero strain. The knowl- edge of these derivatives allows for the determination of all independent components of the elastic tensor. In this context, the accuracy of the elastic constants critically depends on the polynomial fit. Therefore, we carefully study how the order of the polynomial fit and the deformation range influence the numer- ical derivatives, and we propose a new approach to obtain the most reliable results. We have applied ElaStic to representative materials for each crystal system, using total energies and stresses calculated with the full-potential all-electron codes exciting and WIEN2k as well as the pseudo-potential code

[Yu, R.; Zhu, J.] Tsinghua Univ, Beijing Natl Ctr Electron Microscopy, Dept Mat Sci & Engn, Beijing 100084, Peoples R China. [Yu, R.; Zhu, J.] Tsinghua Univ, Adv Mat Lab, Dept Mat Sci & Engn, Beijing 100084, Peoples R China. [Yu, R.; Zhu, J.] Tsinghua Univ, State Key Lab New Ceram & Fine Proc, Dept Mat Sci & Engn, Beijing 100084, Peoples R China. [Ye, H. Q.] Chinese Acad Sci, Shenyang Natl Lab Mat Sci, Inst Met Res, Shenyang 110016, Peoples R China.;Yu, R (reprint author), Tsinghua Univ, Beijing Natl Ctr Electron Microscopy, Dept Mat Sci & Engn, Beijing 100084, Peoples R China;ryu@tsinghua.edu.cn

[1] The Campi Flegrei (CF) Caldera experiences dramatic ground deformations unsurpassed anywhere in the world. The source responsible for this phenomenon is still debated. With the aim of exploring the structure of the caldera as well as the role of hydrothermal fluids on velocity changes, a multidisciplinary approach dealing with three-dimensional delay time tomography and rock physics characterization has been followed. Selected seismic data were modeled by using a tomographic method based on an accurate finite difference travel time computation which simultaneously inverts P wave and S wave first-arrival times for both velocity model parameters and hypocenter locations. The retrieved P wave and S wave velocity images as well as the deduced V p /V s images were interpreted by using experimental measurements of rock physical properties on CF samples to take into account steam/water phase transition mechanisms affecting P wave and S wave velocities. Also, modeling of petrophysical properties for site-relevant rocks constrains the role of overpressured fluids on velocity. A flat and low V p /V s anomaly lies at 4 km depth under the city of Pozzuoli. Earthquakes are located at the top of this anomaly. This anomaly implies the presence of fractured overpressured gas-bearing formations and excludes the presence of melted rocks. At shallow depth, a high V p /V s anomaly located at 1 km suggests the presence of rocks containing fluids in the liquid phase. Finally, maps of the V p *V s product show a high V p * V s horseshoe-shaped anomaly located at 2 km depth. It is consistent with gravity data and well data and might constitute the on-land remainder of the caldera rim, detected below sea level by tomography using active source seismic data.

Zero-gap half-metallic fully-compensated ferrimagnets (ZG-HM-FCFs) and fully-compensated ferrimagnetic spin-gapless semiconductors (FCF-SGSs) are promising candidates for spintronic applications due to the complete (100%) spin polarization of electrons around the Fermi level. Motivated by recent experimental and theoretical findings on binary Mn2-based C1b-type Heusler compounds, by means of first-principles calculations, we found that Mn2Sn exhibits metallic ferrimagnetism properties. Most interestingly, at a uniform strain, there is a novel transition in the physics from a metallic ferrimagnet (MFi) to true ZG-HM-FCF, HM-FCF, and FCF-SGS, and then to a fully-compensated ferrimagnetic semiconductor (FCF-S). The binary Mn2Sn compound remains as a MFi under tetragonal distortion, however. We also reveal that the structure of Mn2Sn is stable, according to its mechanical properties, calculated cohesion energy, and formation energy. Our work demonstrates that Mn2Sn is potentially an all-round candidate for spintronic applications because it shows a full spectrum of spintronic properties at a uniform strain.

Xin-Ling He,1 Xiao Dong,1 QuanSheng Wu,2 Zhisheng Zhao,3 Qiang Zhu,4 Artem R. Oganov,5,6,7 Yongjun Tian,3 Dongli Yu,3 Xiang-Feng Zhou,1,* and Hui-Tian Wang1,8 1Key Laboratory of Weak-Light Nonlinear Photonics, School of Physics, Nankai University, Tianjin 300071, China 2Institute of Physics, National Centre for Computational Design and Discovery of Novel Materials MARVEL, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 3State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China 4Department of Physics and Astronomy, High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, USA 5Skolkovo Institute of Science and Technology, 3 Nobel Street, Moscow 143026, Russia 6Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia 7International Center for Materials Discovery, Northwestern Polytechnical University, Xi’an 710072, China 8National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Wyllie's time-average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)-wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)-wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S-wave information can be obtained from the sonic log, it may be used with P-waves to provide a better understanding of pore structure. A new acoustic velocities-to-porosity transform based on an elastic velocity model developed by Kuster and Toksoz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional-and shear-wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time-average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self-consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed.

Wie in allen kristallinen Festkorpern sind die zwischenatomaren Krafte in Metallen und Legierungen an die Kristallsymmetrie gebunden. Die elastischen Eigenschaften sind dementsprechend im allgemeinen anisotrop. Das elastische Verhalten — und damit die elastische Anisotropie — ist besonders unter drei Gesichtspunkten von Interesse: 1. als physikalische Eigenschaft eines Stoffes in Verbindung mit seinem Kristallgitter 2. als Grundlage des elastischen Verhaltens von Werkstoffen, deren elastische Eigenschaften als solche genutzt werden wie elastisch beanspruchte Konstruktionswerkstoffe, Federwerkstoffe und mechanische Verzogerungsleitungen und Frequenzfilter in elektronischen Schaltkreisen und 3. als Grundlage der plastischen Verformung von Werkstoffen, weil die Grose der plastischen Anisotropie u. a. von der elastischen Anisotropie des Kristallgitters abhangt.

When reasonably soluble substances (c*> 0.1mol l–1) are crystallized at a high specific power input and within their metastable zone, attrition is a primary source of nucleation. The study presented here is an attempt to quantify this attrition mechanism. Firstly, a physical model is introduced which relates the attrition resistance of a crystalline substance to its mechanical properties. In the second part, the emphasis is placed on the determination of the relevant mechanical properties, hardness, elastic constants, and fracture resistance. The physical model will finally be compared to experimental results. A good agreement is found between the experimentally determined and theoretically predicted attrition behaviour.

We study the elastic moduli and structure of boron carbide/aluminum (B4C/Al) multiphase composites using rigorous bounding and experimental characterization techniques. We demonstrate that rigorous bounds on the effective moduli are useful in that they can accurately predict (i) the effective elastic moduli, given the phase moduli and volume fractions, or (ii) the phase moduli (volume fractions), given the effective moduli and phase volume fractions (moduli). Using the best available rigorous bounds on the effective elastic moduli of multiphase composites involving volume-fraction information, we are able to predict the bulk and shear moduli of the Al4BC phase, a reaction product that forms during heat treatment. These theoretical predictions are in very good agreement with recent experimental measurements of the moduli of the Al4BC phase. Moreover, we evaluate more-refined bounds involving three-point structural correlation functions by extracting such information from an image of a sample of the B4C/Al composite. Although experimental data for the effective moduli are unavailable for this sample, our predictions of the effective moduli based on three-point bounds should be quite accurate.

We study the elastic constants and electronic properties of orthorhombic BiMnO3 under uniaxial strain along the c-axis using the first-principles method. It is found that, beyond the range −0.025 < < 0.055, the predicted stiffness constants cij cannot demand the Born stability criteria and the compliance constant s44 shows abrupt changes, which accompany phase transition. In addition, the results for magnetism moments and polycrystalline properties are also reported. Additionally, under compressive strain, a band gap transition from the indirect to the direct occurs within −0.019 < < −0.018. Furthermore, the response of the band gap of orthorhombic BiMnO3 to uniaxial strain is studied.

We study quasiconvex quadratic forms on n × m matrices which correspond to nonnegative biquadratic forms in ( n, m ) variables. We disprove a conjecture stated by Harutyunyan– Milton (Comm. Pure Appl. Math. 70(11), 2017) as well as Harutyunyan–Hovsepyan (Arch. Ration. Mech. Anal. 244, 2022) that extremality in the cone of quasiconvex quadratic forms on 3 × 3 matrices can follow only from the extremality of the determinant of its acoustic tensor, using previous work by Buckley–ˇSivic (Linear Algebra Appl. 598, 2020). Our main result is to establish a conjecture of Harutyunyan–Milton (Comm. Pure Appl. Math. 70(11), 2017) that weak extremal quasiconvex quadratics on 3 × 3 matrices are strong extremal. Our main technical ingredient is a generalization of the work of Kunert–Scheiderer on extreme nonnegative ternary sextics (Trans. Amer. Math. Soc. 370(6), 2018). Specifically, we show that a nonnegative ternary sextic, which is not a square, is extremal if and only if its variety (over the complex numbers) is a rational curve and all its singularities are real.

We show here that machine learning is a powerful new tool for predicting the elastic response of zeolites. We built our machine learning approach relying on geometric features only, which are related to local geometry, structure, and porosity of a zeolite, to predict bulk and shear moduli of zeolites with an accuracy exceeding that of force field approaches. The development of this model has illustrated clear correlations between characteristic features of a zeolite and elastic moduli, providing exceptional insight into the mechanics of zeolitic frameworks. Finally, we employ this methodology to predict the elastic response of 590 448 hypothetical zeolites, and the results of this massive database provide clear evidence of stability trends in porous materials.

We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness phases). Using arguments of Hill and Koiter, we show that for statically stable bodies the classical displacement-based variational principles for Dirichlet and Neumann boundary problems hold but that the dual variational principle for traction boundary problems does not apply. We illustrate our findings by the example of a coated spherical inclusion whose stability conditions are obtained from the variational principles. We further show that the classical Voigt upper bound on the linear elastic moduli in multi-phase inhomogeneous bodies and composites applies and that it imposes a stability condition: overall stability requires that the effective moduli do not surpass the Voigt upper bound. This particularly implies that, while the geometric constraints among constituents in a composite can stabilize negative-stiffness phases, the stabilization is insufficient to allow for extreme overall static elastic moduli (exceeding those of the constituents). Stronger bounds on the effective elastic moduli of isotropic composites can be obtained from the Hashin–Shtrikman variational inequalities, which are also shown to hold in the presence of negative stiffness.

We report the elastic properties of Cu3Sn superstructure based on first-principles calculations. Polycrystalline Young’s modulus and Poisson’s ratio are deduced from the calculated elastic stiffness. The calculations of electronic structures with the principal strains along different directions unravel the electronic nature of anisotropic elasticity of Cu3Sn. Weak Sn–Cu bonding in Cu3Sn suggests that Sn atoms are the dominant diffusion species, revealing the mechanism of vacancy formation within the Cu3Sn superstructure.

We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application allowing the visualization of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots.

We report in tins paper Young's moduli and hardness of Cu₆Sn₅, Cu₃Sn, and Ni₃Sn₄ intermetallic compounds (IMCs) measured by nanoindentation. The samples were prepared by annealing Sn-Cu and Sn-Ni diffusion couples. Indentations performed along the directions lateral and perpendicular to the IMC layers show statistically indistinguishable Young's moduli and hardness for each of the three IMCs. implying that these polycrystalline IMC aggregates are rather isotropic. Nanomechanical responses of the IMCs were shown to depend greatly on the strain rate during loading while independent of the strain rate during unloading. Multiple pop-in events were observed for Cu₆Sn₅ during loading at a strain rate lower than about 0.1 s^-1 to 0.5 s^-1. Topographies of the residual impressions were quantitatively measured and the pile-up features were apparent for the three IMCs.

We report ab initio computer modeling of the high-pressure cubic forms of Zr 3 N 4 and Hf 3 N 4 . Equilibrium structural parameters were derived at 0 K and zero pressure for different exchange-correlation functionals. Singlecrystal elastic constants and bulk moduli were then computed at the athermal limit in order to quantify the stiffness of the investigated nitrides. We find that Hf 3 N 4 should have a Vickers hardness similar to that of Si 3 N 4 .

We propose herein four types of anisotropic pentamode metamaterials (PMs) created by shifting the thin-end contention points along the space-diagonal, x-axis, y-axis, and z-axis directions. The phononic band structure and figure of merit (FOM) of the four types of anisotropic PMs are systematically investigated by using the finite-element method. Compared with isotropic PMs, the first phononic bandgaps appear in low-frequency regions, and the FOM increases by a factor of 6.9 when the thin-end connection area shifts along the z-axis direction. This study investigates how anisotropy affects PM properties and provides a reference to design acoustic cloaks, acoustic waveguides, and acoustic barriers.

We propose a microstructural model for the uniaxial tensile constitutive and failure behavior of soft skeletal connective tissues. The model characterizes the tissues as two-phase composites consisting of collagen fibers embedded in ground substance. Nonlinear toe region behavior in the stress versus strain curve results from the straightening of crimped fibers and from fiber reorientation. Subsequent linear behavior results from fiber stretching affected by fiber volume fraction, collagen type, crosslink density, and fiber orientation. Finally, the tissue fails when fibers successively rupture at their ultimate tensile strain. We apply the model to tendon, meniscus, and articular cartilage. The model provides a consistent approach to modeling the tensile behavior of a wide range of soft skeletal connective tissues.