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\title{\vspace{-4.0cm} Low-Profile Self-Sealing Sample Transfer Flexure Box}
\date{\today}
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\author{Kevin Simon}%
%\email{kevinpsi@mit.edu}
\affiliation{Department of Mechanical Engineering\\Massachusetts Institute of Technology\\Cambridge, Massachusetts 02144, USA}\author{Lukas Porz}
\affiliation{Institute of Materials Science\\Technische Univeritat Darmstadt\\ Darmstadt 64287, Germany}
\author{Tushar Swamy}
\affiliation{Department of Mechanical Engineering\\Massachusetts Institute of Technology\\Cambridge, Massachusetts 02144, USA}
\author{Yet-Ming Chiang}
\affiliation{Department of Materials Science and Engineering\\Massachusetts Institute of Technology\\Cambridge, Massachusetts 02144, USA}
\author{Alexander Slocum}
\email{Slocum@mit.edu}
\affiliation{Department of Mechanical Engineering\\Massachusetts Institute of Technology\\Cambridge, Massachusetts 02144, USA}

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\section{Abstract}
A flexural bearing mechanism has enabled the development of a self-sealing box for protecting air sensitive samples during transfer between glove boxes, micro-machining equipment, and microscopy equipment. The simplicity and self-actuating feature of this design makes it applicable to many devices that operate under vacuum conditions. The models used to design the flexural mechanism are presented in detail. The device has been tested in a Zeiss Merlin GEMINI II scanning electron microscope with Li$_3$PS$_4$ particles, showing effective isolation from air and corrosion prevention.

\keywords{scanning electron microscope, air-sensitive, flexure}

\section{Introduction}
Transferring air sensitive samples between scientific imaging equipment is challenging because standard Scanning Electron Microscopes (SEM), and other processing equipment often lack airtight transfer systems. Improper handling of air-sensitive samples can allow extensive chemical reaction. Exposure to oxygen, water vapor, or other contaminants must thus be prevented for research and quality control analyses.

Although other solutions exist for transferring air-sensitive samples, prior to this project, no low profile, self-actuating system has been produced. Howe et al. has developed a sample transfer system with a swinging lid, but does not re-seal to preserve the samples after imaging \cite{howe2012}. Hall et al. developed a re-sealing system that couples with the rotation stage on a Philips 501 SEM, but is not standardized for use with other instruments \cite{hall1981}. These devices, among the other sample transfer systems \cite{solliard1978,gaume2011,hobbs1970,gamer2010,marek2013} are limited in their use by the range of motion of the lid, inter-microscope compatibility, re-sealability, availability, and price.

Figure~\ref{isoView} shows the Sample Transfer Flexure Box (STFB), designed and demonstrated in this work, which uses an arrangement of 4-bar linkage flexures and an opposing piston, operated by the change in pressure in the SEM, to passively open and reseal the sample chamber with minimal vertical motion. The resulting system is effective, low-cost, and compatible with many SEMs, plus other advanced microscopy and micro-machining equipment such as focused ion beams (FIB) instruments.

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/isoView-label.jpg}
\caption{The Sample Transfer Flexure Box (STFB) in an open state}
\label{isoView}
\end{figure}


\section{Functional Requirements and Design Parameters}
 The design process began with the definition of the critical functional requirements (FRs) that satisfy the needs of the end user. The FRs were determined through unstructured interviews and observation of different experimental procedures. Once the FRs were specified, they were translated into measurable design parameters (DPs), which drive the design and analysis of the STFB. Both the FRs and the DPs are presented in table \ref{FRs}.
 
FR1 and FR6 arise because sensors, ion guns, or other sensitive equipment are often within 10mm of the focal plane. In a FIB, the sample stage is rotated about 2 orthogonal axes, meaning that a loose lid can crash into the instruments. Protecting the instrument in which the STFB is used is essential to the utility of this device. 

\begin{table*}
\centering
\begin{tabular}{| l | l | p{8cm} |}
\hline
FR\# & Functional Requirement & Design Parameter\\ \hline
1 & Open in small headspace & Lid vertical travel $<$5mm\\ \hline
2 & Expose a SEM pin and TEM grid & Lid horizontal travel $>$15mm\\ \hline
3 & Maintain air-tight seal & Evenly compress seal by $ >$5\% of the seal height\\ \hline
4 & Open for imaging & Open in response to a medium ambient vacuum, and close at 1atm ambient pressure\\ \hline
5 & Close after work & Trigger at 1atm ambient\\ \hline
6 & Fit in SEM + FIB & Modular bottom; max height $<$50mm; max length $<$150mm; max width $<$75mm\\ \hline
7 & Not damage equipment & Predictable, fail safe, no sliding, no ferromagnetic materials\\ \hline
8 & Work repeatably & Low off-axis loading \\
\hline
\end{tabular}
\caption{The functional requirements (FRs) and design parameters (DPs) necessary to achieve the desired performance}
\label{FRs}
\end{table*}

FR3 also motivates the use of linear flexural elements. Rotating lids apply uneven forces on the seal because different parts of the seal are at different lever-arm lengths. Linear flexures are natural countermeasures to this risk. A linear motion device can more evenly apply force to the seal. FR2, 4, and 5 are all necessary for the device to be of use for imaging air-sensitive samples.

FR7 requires that the lid, flexures, and piston have no ferromagnetic elements because some instruments induce a large magnetic field. Sliding elements must also be avoided if the STFB is to be used frequently. Sliding elements wear after regular use, particularly in a vacuum environment where lubrication is limited.  Wear can leave fine particles inside in the machine or on the sample. In discussions with users, some FIB operators have said that any risk of producing wear particles is unacceptable. 

Repeatability is necessary to ensure consistent sealing. Because load-induced geometric errors are small, friction is the biggest challenge to repeatability. FR8 requires the minimization of off-axis loading on the piston to minimize the risk of the piston sticking. Assuming that the coefficient of friction in a vacuum environment is approximately 1, the off-axis force must be less than 1/20$^{\text{th}}$ the piston force to make friction forces negligible compared to the piston force. Assuming that the leverage on the piston is approximately 10, the acceptable parasitic moment must be less than 1/200$^{\text{th}}$ the piston force to keep moment-induced friction similarly negligible.

\section{Design and Construction}
The selected design, which meets all of the FRs and DPs, is a double-acting piston opposed by an array of 4 parallel 3-stage blade flexures. The double acting piston has one port exposed to ambient pressure. The other port is sealed and held below -84kPa gauge pressure. In this configuration the lid is held closed by the piston under atmospheric ambient pressure, and is opened by the flexures in an ambient vacuum. When work with the STFB in an open, vacuum, state is finished, the work chamber is filled with an inert gas. The ambient pressure then closes the STFB, protecting the sample with inert gas. Because the flexures are in a relaxed state when the STFB is open in an ambient vacuum, this design ensures that structural failures on the box will not damage the instrument.

%This design prevents catastrophic failure because the flexures are in a relaxed state when the STFB is open in an ambient vacuum.

To combine the horizontal and vertical motion, the piston and flexure stages are rotated 10$^\circ$ from the rest of the STFB. This angle of motion, shown in Fig. 5, provides 3.6mm of vertical and 20.4mm of horizontal travel. When open, the lid is below the instrumentation and gives a wide work area.

The embodiment of the design principles presented is composed of an aluminum body with titanium flexures. The body of the STFB is CNC milled out of aluminum for stability in a vacuum environment and because it is easily machined for prototyping. The flexures are made of titanium strips, cut on a waterjet. Titanium was selected for it's ratio of stiffness to yield stress, which minimizes the flexure length required to achieve the target lid deflection. The flexures are connected by aluminum mounting blocks with 2 press-fit 1mm stainless steel spring-pins at each attachment point to constrain the blades. Each flexure stage mates with the body in machined slots and is clamped in place by setscrews. Torrseal$^{\text{TM}}$, a vacuum-grade epoxy, attaches the flexures to the lid at a mounting block with a mating feature. 

The top of the STFB has a pocket with features that can hold a SEM sample-holding pin and a transmission electron microscope (TEM) grid. This allows for transfer of the sample directly to an SEM or to a sealed TEM sample holder, via a glovebox, after work in a FIB. Around this pocket is a square O-ring. Square O-rings resist twisting forces induced by the lid as it makes contact with a tangential motion component, and provide a longer leak-path at low compression. The bottom of the lid is lapped to a mirror finish to ensure a good seal.

\begin{figure*}
\centering
\includegraphics[width=17cm]{./images/sideView.jpg}
\caption{The STFB in closed (a) and open (b) with a vacuum applied to the cylinder to simulate operation in a vacuum environment.}
\label{openClose}
\end{figure*}

\section{Detailed Design}
The design of the STFB is driven by the force associated with vacuum pressure. The commercially available piston selected has a 12.4mm diameter bore. Neglecting friction, this piston nominally provides 12.5N of force with 1atm pressure across the piston. Providing a margin for manufacturing errors, friction on the piston seal, and additional force for the seal, the return flexures are sized to provide approximately 8N of reaction force when fully extended at 20.2mm. 

Preliminary flexure design uses a linear bending beam model and is refined with a large-deflection finite differences model. The simplest topology for a 1 degree of freedom (DOF) flexure is 2 or more parallel blade flexures \cite{hopkins2007}. Flexure geometry and the number of stages determine the lid's stiffness and range of motion through Eqs.~(\ref{beginBeam})-(\ref{endBeam}).

\begin{align}
F &= k_f x \label{beginBeam}\\
k_f &= \frac{12EI}{pl^3} \\
\sigma_b &= \frac{6Ext}{pl^2}\label{endBeam}
\end{align}

$F$ is the force at the tip of the flexure; $k_f$ is the stiffness of a blade flexure with parallel motion; $E$ is Young's modulus; $I$ is the second moment of inertia; $x$ is the tangential displacement of the tip; $L$ is the length of the flexure; $p$ is the number of parallel flexure stages; $\sigma_b$ is the maximum flexural bending stress, and $t$ is the thickness of the flexure blade. Equation 3 indicates that 0.406mm thick, 2mm wide grade 5 titanium ($E$=114GPa, $\sigma_{\text{yield}}$=830MPa) flexure blades keep the flexures from exceeding their yield stress over a range of motion of 20.2mm. Given the 50mm limit on height, flexure blocks, 10$^\circ$ angled flexure motion, and the lid height, 3 stages of 37mm long flexures are used in the preliminary design, shown in Fig.~\ref{topology}. Two flexures are unable to provide the range of motion in the space without yielding. Four flexures would also accomplish the same goal, but do not provide increased functionality. With a basic flexure topology selected, a non-linear finite differences model is used to refine the flexure model and minimize parasitic forces.

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/flexureSketchShort.png}
\caption{The topology of one of the parallel flexure stages }
\label{topology}
\end{figure}

The finite differences model assumes that tip forces translate and rotate with the tip of the flexure. Beginning with an applied moment and force at the tip, the finite differences model steps backwards along the length of the flexure with Eq. (\ref{normRot}), computing new moments via Eq. (\ref{newMom}) and incrementally rotating the trailing edge of the beam by Eqs.~(\ref{dths}) and (\ref{mat}) until the length of the beam has been traversed. This scheme is depicted in Fig.~\ref{math}.

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/mathFigure.pdf}
\caption{A graphic representation of the finite difference scheme. The indices `m' and `n' represent two different elements. The different subscripts and depiction of two different locations were chosen for clarity.}
\label{math}
\end{figure}


\begin{align}
r_i &= r_{i-1}-N_i ds \label{normRot}\\
M_i &= M_{i-1} - r_i \times F \label{newMom}\\
d\theta_i &= \frac{-M_ids}{EI} \label{dths}\\
N_{i+1} &= \begin{bmatrix} 1 & -d\theta_i \\ d\theta_i & 1 \end{bmatrix} N_i \label{mat}
\end{align}

Here, $r_i$ is the vector from the tip of the beam to the $i^{th}$ segment; $N_i$ is the normal vector of the $i^{th}$ section; $M_i$ is the internal moment generated at the $i^{th}$ section; $ds$ is the segment length; and $d\theta_i$ is the rotation angle of the normal vector over the length of the $i^{th}$ segment. Once the rotation of each beam element is computed, Eq.~(\ref{rot}) describes the rotation of each beam segment relative to the base rotation, producing a new set of normals, $G_i$, in the ground reference frame. $R_n$ is the rotation matrix of the nth segment, the ground, in the tip's reference frame. Equation~(\ref{rotSum}) integrates the segment normals to calculate $D$, the displacement of the tip in the ground reference frame.

\begin{align}
G_i &= R_nN_i\label{rot} \\
D &= \sum G_i ds \label{rotSum}
\end{align}

This method ensures that the base of the beam has the correct orientation. The final tip position and rotation are turned into a homogeneous transformation matrix. That homogeneous transformation matrix can be used to predict the primary motion and also predict parasitic deflections from manufacturing tolerances that may prevent the lid from properly sealing \cite{slocum1992}. The tip deflection homogeneous transformation matrices and the rigid body homogeneous transformation matrices between the flexure stages can be used to propagate forces and moments through the system. Figure~\ref{htm} shows how homogenous transformations, $H$, can translate the moments and forces between the different reference frames shown in Fig.~\ref{topology}. The finite differences flexure model shows that a three-stage flexure with a 38mm ground stage, 38mm mid stage, and 35mm end stage, as shown in Fig.~\ref{lid}, enables a compact design with sufficiently small parasitic loading.

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/HTMflow.png}
\caption{Diagram of the propagation of moments, forces, and displacements through the flexure system}
\label{htm}
\end{figure}

\begin{align}
M_k &= M_{k+1}-\left(\prod_{j=3}^{k+1}H_j\right) F_0 \times D_{k+1} \\
F_k &= \left(\prod_{j=3}^{k-(k+1)}H_j\right) F_0\\
H_k &= f\left( F_k,M_k \right) \\
R &= \left( \prod^1_{j=2-3} H_j\right)D_3
\end{align}

Where $R$ is the displacement of the flexure end in the ground reference frame; $D_k$ is the tip displacement of the $k^{th}$ flexure; and $f(F_k,M_k)$ is the function which computes displacement and rotation of the $k^{th}$ flexure stage as described above. This framework is a common method for describing the error and motion of precision machines. It can be extended to different flexure topologies. Since flexure tip rotation and displacement can be efficiently computed from moments and forces, the inverse problem is solved with a nonlinear root-finder. The solution to this inverse problem yields the parasitic forces and moments that the linear translation of the piston induces.

\begin{align}
P_x &= -4F_x \label{beginLoad}\\
P_y &= -4F_y \\
M_p &= 2F_x(y_1+2y_2)-2F_y(x_1+2x_2)-M_f\label{endLoad}
\end{align}

Equations~(\ref{beginLoad})-(\ref{endLoad}) are based on the free-body diagram in Fig.~\ref{lid}. These equations provide the expected loading of the piston as it travels through the lid's range of motion. $F_x$ and $F_y$ are the x and y components of the flexure force vector. $M_f$ is the moment about the Z axis applied by the flexure. The factor of 4 in the equations emerges because there are four flexure stages, each one applying $F_x$ and $F_y$ to the lid. A design where x$_1$ = 30mm, x$_2$ = 17.1mm, y$_1$ = 5.3mm, and y$_2$ = 14.7mm fits the range of motion, compactness, and parasitic loading functional requirements.

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/lidSketch.png}
\caption{The layout and loading of the STFB lid}
\label{lid}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/loading.pdf}
\caption{The loading of the piston across the optimal lid's range of motion}
\label{loading}
\end{figure}

Figure~\ref{loading} shows that the off-axis loading and parasitic moment induced by a linear translation of 20.2mm are within the specifications of FR8. There are other topologies that can further reduce the parasitic loading. For example, a serial 4-stage blade flexure will nearly eliminate the off-axis parasitic force, but increase complexity and reduce off-axis stiffness.

\section{System Performance}

The scientific instruments to which the STFB can be applied depends primarily on the quality of the seal. Better sealing enables applications with more air sensitive materials. To test the effectiveness of the STFB, we performed SEM examinations with and without the STFB of Li3PS4, a highly air-sensitive material that is the basis for solid electrolyte membranes proposed for use in all-solid-state batteries \cite{liu2013}. Upon exposure to air, the material develops a pattern of surface cracks within seconds. These cracks are a visible indicator of degradation from atmospheric exposure, as shown in Fig.~\ref{performance}(a). It is imperative for battery development or production quality control that samples of such atmospheric sensitivity can be transferred from a protected environment, such as a glovebox, to an SEM for examination.  Whether the surface cracks shown in Fig.~\ref{performance}(a) are able to form is a useful metric for the level of protection.

In a scanning electron microscope, in this case the Zeiss Merlin GEMINI II, it takes 20 seconds to transfer a sample from a sealed carrier into the microscope via the airlock. Unprotected, this exposure results in intense mud-crack patterns in the sample, making analysis impractical. Using the STFB to transfer a Li$_3$PS$_4$ sample from the glovebox to the SEM in a comfortable time span of 10 minutes (including the pumping time of the main chamber), surface cracks were absent, as shown in Fig.~\ref{performance}(b). Since aluminum absorbs some moisture and oxygen, the inside of the STFB was degassed in a vacuum chamber for 10 hours before testing.

To fully characterize the prototype, the leakage rate has to be tested over a longer period of time. Letting the closed STFB sit in air for 10 hours before inserting it into the SEM results in few individual cracks in the sample, as shown in Fig.~\ref{performance}(c). However, there is no practical reason why a sample cannot be transferred in a less than an hour. Hence, these tests demonstrate sufficient functionality of the STFB for use with air sensitive samples. 

\begin{figure}
\centering
\includegraphics[width=8.5cm]{./images/system_performance.jpg}
\caption{An electron micrograph of Li$_3$PS$_4$ sample after direct exposure to air (a), after 10 minutes transport with the STFFB (b), and after 10 hours in the STFB (c).}
\label{performance}
\end{figure}

\section{Conclusion and Future Work}
The design and performance of a device for preserving air sensitive materials during transfer between a glovebox and  instrumentation has been presented. The functional requirements, design principles, and analytical equations have been presented in detail. The functionality of the STFB has been demonstrated with Li$_3$PS$_4$ samples in a Zeiss Merlin Gemini II SEM.

The design analysis and testing show that repeatable motion with minimal parasitic loading is possible with 3 serial flexures. Further reductions in parasitic loading and device size can be achieved with 4 serial flexures, but increase complexity. Friction in the piston is still a possible source of non-repeatability. Replacing the piston with a welded metal bellows could eliminate friction in the mechanism. 

The STFB for air sensitive samples is valuable to research that use SEMs, FIB instruments, or other vacuum based instruments for studying battery materials, semiconductor processing, nano-materials, or similar research topics. Although several designs have been produced before, none of them combine all of the features necessary for low-profile safe, frequent, and reliable use presented here. 

This article is a pre-preprint of an article submitted to the Review of Scientific Instruments with the permission of AIP Publishing. This will be updated with the full citation and accepted manuscript immediately after acceptable by AIP Publishing.

\section{Acknowledgements}
This work made use of the MRSEC Shared Experimental Facilities at MIT supported by the National Science Foundation under award number DMR-1419807. We thank Patrick Boisvert for assistance and training in SEM operation. The authors gratefully acknowledge support from the US Department of Energy's Office of Basic Energy Science for the Chemomechanics of Far-From-Equilibrium Interfaces (COFFEI) small group, through award number DE-SC0002633 (J. Vetrano, Program Manager).

\bibstyle{plain}
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%\center
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%\includegraphics[width=\textwidth]{./figs/Progressive_cavity_pump_rotor.png}
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%\caption{The geometry of a PCP rotor, stator, and cavities.}
%\label{PCPgeom}
%\end{figure}



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