The effect of probe tilt angle on the quality of scanning tunneling microscope measurements

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 39 ).The effect of probe tilt angle on the quality of Scanning Tunneling Microscopy (STM) measurements was explored. A small but consistent improvement in slope accuracy was documented lending some support to the effort to develop a new, five-axis STM capable of tilting in a controlled manner while scanning. The objective of such a machine would be to allow its probe to trace the sample's contour with greater accuracy than the currently available three-axis STM can. It is postulated that an STM with a probe that can change its roll and pitch in addition to its position along the traditional x, y, and z axes would be capable of reducing imaging errors produced as a result of geometric constraints, lateral electron discharge effects, and the tendency for the tip to bend during scanning due to electrostatic surface forces. In order to quantify the effects of incorporating probe tilt into the scanning process, a traditional, three-axis STM was manipulated in a way that allowed a standard sample grid to be imaged using a probe that was placed at seven different angles of tilt ranging from -13 to +13 degrees. Twenty-five different cavities in a standard STM scanning sample were scanned at these seven angles to determine notable trends and effects in the images produced.(cont.) It was determined that for each degree of angle change in the tilt of the probe, the slopes of the cavity walls imaged improved by an amount of slope equal to approximately 0.001 nm/nm, which corresponds to 0.0093% less imaging error. This seemingly trivial improvement in wall slope is significant in light of the fact that the change in slope per degree of probe tilt is on the same order of magnitude as the slopes of the cavity walls measured by the STM.by Jonathan B. Hopkins.S.B

Compliant rolling-contact architected materials for shape reconfigurability.

Architected materials can achieve impressive shape-changing capabilities according to how their microarchitecture is engineered. Here we introduce an approach for dramatically advancing such capabilities by utilizing wrapped flexure straps to guide the rolling motions of tightly packed micro-cams that constitute the material's microarchitecture. This approach enables high shape-morphing versatility and extreme ranges of deformation without accruing appreciable increases in strain energy or internal stress. Two-dimensional and three-dimensional macroscale prototypes are demonstrated, and the analytical theory necessary to design the proposed materials is provided and packaged as a software tool. An approach that combines two-photon stereolithography and scanning holographic optical tweezers is demonstrated to enable the fabrication of the proposed materials at their intended microscale

A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem

We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of at least $n^{1/2-c(d/\log n)^{1/2}}$ for some constant $c>0$. This yields a nearly tight $n^{1/2 - o(1)}$ bound on the value of this program for any degree $d = o(\log n)$. Moreover we introduce a new framework that we call \emph{pseudo-calibration} to construct Sum of Squares lower bounds. This framework is inspired by taking a computational analog of Bayesian probability theory. It yields a general recipe for constructing good pseudo-distributions (i.e., dual certificates for the Sum-of-Squares semidefinite program), and sheds further light on the ways in which this hierarchy differs from others.Comment: 55 page

Synthesizing Parallel Flexures That Mimic the Kinematics of Serial Flexures Using Freedom and Constraint Topologies

The principles of the freedom and constraint topologies (FACT) synthesis approach are adapted and applied to the design of parallel flexure systems that mimic degrees of freedom (DOFs) primarily achievable by serial flexure systems. FACT provides designers with a comprehensive library of geometric shapes. These shapes enable designers to visualize the regions wherein compliant flexure elements may be placed for achieving desired DOFs. By displacing these shapes far from the point of interest of the stage of a flexure system, designers can compare a multiplicity of concepts that utilizes the advantages of both parallel and serial systems. A complete list of which FACT shapes mimic which DOFs when displaced far from the point of interest of the flexure system's stage is provided as well as an intuitive approach for verifying the completeness of this list. The proposed work intends to cater to the design of precision motion stages, optical mounts, microscopy stages, and general purpose flexure bearings. Two case studies are provided to demonstrate the application of the developed procedure

Design of flexure-based motion stages for mechatronic systems via FACT

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 191-195).The aim of this thesis is to generate the knowledge required to (i) synthesize serial flexure systems and (ii) optimally place actuators using a comprehensive library of geometric shapes called freedom, actuation, and constraint spaces. These geometric shapes guide designers through the creative process of concept generation without compromising engineering rigor. Each shape rapidly conveys the mathematics of screw theory, projective geometry, and constraint-based design by visually depicting regions where constraints and actuators may be placed for synthesizing optimal flexure concepts. In this way, designers may consider every flexure concept that satisfies the desired functional requirements before selecting the final design. FACT was created to improve the design processes for small-scale flexure systems and precision machines. For instance, there is a need to create multi-axis nanopositioners for emerging three-dimensional nano-scale research/manufacturing. Through this work the following contributions were made: (1) the fifty freedom and constraint space types were found that may be used to synthesize both parallel and serial flexure concepts, (2) intermediate freedom spaces were created that help designers stack conjugated flexure elements to avoid or utilize underconstraint, (3) a twist-wrench stiffness matrix was created to model the elastomechanic behavior of flexure systems, (4) the twenty-six actuation spaces were found that help guide designers in placing actuators that minimize motion errors, and (5) a theory was created that determines the force and displacement actuator outputs for accessing a desired DOF once actuators have been placed. A serially conjugated lead screw flexure was designed using the FACT design process and a parallel flexure system was built to validate the theory of actuation described in this thesis.by Jonathan Brigham Hopkins.Ph.D

Design of parallel flexure systems via Freedom and Constraint Topologies (FACT)

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 391-393).The aim of this thesis was to generate the knowledge required to represent the possible freedom topologies (motions of a mechanism) and the possible constraint topologies (flexural elements that guide the mechanism) in a form that designers can use to design parallel flexure systems. The framework that links these topologies enables designers to create three-dimensional, multi-axis flexure systems by using "Freedom and Constraint Topologies" (FACT). FACT embodies every possible design solution for parallel flexure systems. This information enables designers to consider every possible design and then select the design that is best suited for a specific application. FACT was created to improve the design processes for small-scale flexure systems and precision machines. For instance, there is a need to create multi-axis nanopositioners for emerging three-dimensional nano-scale research/manufacturing.(cont.) Through this work the following contributions were made: (1) twenty six unique matching pairs of freedom and constraint spaces were identified; (2) it was proven that these spaces embody all possible solutions; (3) a design process was created to guide a designer from design requirements, to freedom spaces, to constraint spaces, to mechanism designs; (4) a sub-process was created to guide designers in the selection of redundant constraints that help satisfy stiffness and symmetry requirements without altering the mechanism's kinematics; (5) mathematical expressions were created to represent the freedom and constraint spaces in a form that enables computers to identify and manipulate them. In this thesis, three case studies are provided to demonstrate the FACT design process for mechanisms of varying complexity: (1) a compliant spherical ball joint, (2) a compliant probe for a five axis STM, and (3) a compliant rotary flexure are designed. The second case study demonstrates the sub-process for selecting redundant constraints.by Jonathan Brigham Hopkins.S.M

Additively manufacturable micro-mechanical logic gates.

Early examples of computers were almost exclusively based on mechanical devices. Although electronic computers became dominant in the past 60 years, recent advancements in three-dimensional micro-additive manufacturing technology provide new fabrication techniques for complex microstructures which have rekindled research interest in mechanical computations. Here we propose a new digital mechanical computation approach based on additively-manufacturable micro-mechanical logic gates. The proposed mechanical logic gates (i.e., NOT, AND, OR, NAND, and NOR gates) utilize multi-stable micro-flexures that buckle to perform Boolean computations based purely on mechanical forces and displacements with no electronic components. A key benefit of the proposed approach is that such systems can be additively fabricated as embedded parts of microarchitected metamaterials that are capable of interacting mechanically with their surrounding environment while processing and storing digital data internally without requiring electric power

Polytope Sector-Based Synthesis and Analysis of Microstructural Architectures With Tunable Thermal Conductivity and Expansion

The aim of this paper is to (1) introduce an approach, called polytope sector-based synthesis (PSS), for synthesizing 2D or 3D microstructural architectures that exhibit a desired bulk-property directionality (e.g., isotropic, cubic, orthotropic, etc.), and (2) provide general analytical methods that can be used to rapidly optimize the geometric parameters of these architectures such that they achieve a desired combination of bulk thermal conductivity and thermal expansion properties. Although the methods introduced can be applied to general beam-based microstructural architectures, we demonstrate their utility in the context of an architecture that can be tuned to achieve a large range of extreme thermal expansion coefficients—positive, zero, and negative. The material-property-combination region that can be achieved by this architecture is determined within an Ashby-material-property plot of thermal expansion versus thermal conductivity using the analytical methods introduced. These methods are verified using finite-element analysis (FEA) and both 2D and 3D versions of the design have been fabricated using projection microstereolithography.United States. Defense Advanced Research Projects Agency. Materials with Controlled Microstructural Architectures Progra