Cryogenic Optical Microscope

MIM U 701-702 Technical Design Report

Cryogenic Optical Microscope Project # 8

Final Report

Design Advisor: Prof. Gregory Kowalski

Design Team Mohammad Ali, John Delcore Sarah Kaufmann, David Rezac

April 17, 2007

Department of Mechanical, Industrial and Manufacturing Engineering College of Engineering, Northeastern University Boston, MA 02115

Cryogenic Optical Microscope

Design Team Mohammad Ali, John Delcore Sarah Kaufmann, David Rezac

Design Advisor Sponsor Prof. Gregory Kowalski Harvard Medical School

Abstract

The transmission electron microscope (TEM) is extensively used in medical research because of its high magnification and resolution capabilities. One drawback of the TEM is that as the magnification increases, its field of view decreases, and more time is required to identify points of interest on a biological sample. This longer exposure can degrade the sample integrity. A solution is to first map the sample with fluorescent nano- particles, flash freeze it in vitreous ice at cryogenic temperatures, then study the sample under the optical microscope (OM). The OM provides a much larger field of view, allowing the identification of the key points of interest, before transferring it to the TEM. The described solution is comprised of a custom optical microscope with a built-in cooling system that is compatible with current TEM equipment.

2 TABLE OF CONTENTS

Acknowledgements...... 7 Copyright ...... 7 1.0 PROBLEM STATEMENT...... 8 2.0 IMPACT STATEMENT...... 8 3.0 BACKGROUND ...... 8 3.1 Purpose...... 8 3.2 Patent Research...... 9 3.2.1 Cryogenic sample stage for an ion microscope ...... 10 3.2.2 High resolution electron microscope cold stage ...... 10 3.2.3 Freezing/perfusion microscope stage...... 11 3.3 Current Sample Preparation Method ...... 12 3.3.1 Vitrobot...... 13 3.3.2 Blotting of Specimen ...... 13 3.3.3 Vitreous Ice Formulation ...... 15 3.3.4 Properties of Liquid Nitrogen (LN2) and Liquid Ethane ...... 15 3.3.5 Intermediate Container...... 15 3.3.6 Transfer to Cold Finger...... 16 3.4 Transmission Electron Microscope (TEM) ...... 17 3.4.1 3-Dimensional Modeling in TEM...... 18 3.4.2 Electron versus Optical Microscopy...... 18 3.5 Optical Microscopy...... 19 3.5.1 Defining Optical Microscopes...... 19 3.5.2 Resolution...... 20 3.5.3 Objective Lens Properties...... 21 3.5.4 Use of Air Lenses...... 23 4.0 MAPPING...... 23 5.0 VITREOUS ICE ...... 24 6.0 INITIAL DESIGN CONCEPTS...... 25 6.1 Design Concept # 1...... 25 6.2 Design Concept # 2...... 26 6.3 Design Concept # 3...... 28 6.4 Design Concept # 4...... 29 7.0 PROGRESSION OF DESIGN ...... 29 7.1 Thermal Modeling ...... 30 7.2 Introduction of Cold Lens...... 33 7.3 Microscope Construction...... 34 7.4 Intermediate Design...... 35 8.0 CURRENT DESIGN ...... 37 8.1 Incorporating Microscopists’ Opinion...... 37 8.2 Translation of the Workstation Assembly ...... 41 8.3 Guide Rails/Vertical Motion of Objective Lens ...... 44 8.4 External Optical Microscope ...... 45 8.4.1 Light Source...... 46 8.4.2 Excitation Filter ...... 46

3 8.4.3 Emission Filter...... 47 8.4.4 Dichroic Beam Splitter...... 47 9.0 INTERMEDIATE MODIFICATIONS ...... 47 9.1 Attachment of X-Y Translator...... 47 9.2 Attachment of Upper Chamber and Collar ...... 48 9.3 Dry Zone Installment ...... 49 9.4 Opening Skirt Notch ...... 50 10.0 BOILING ...... 50 10.1 Boiling Curve...... 51 10.1.1 Free Convective Boiling...... 51 10.1.2 Nucleate Boiling ...... 51 10.1.3 Critical Heat Flux...... 52 10.1.4 Transition and Film Boiling...... 52 10.2 Cryo-Transfer Apparatus ...... 53 10.3 Thermal Modeling ...... 53 10.4 Initial Testing...... 57 10.5 Part Modifications and Further Modeling...... 58 10.5.1 Initial Modification Concept...... 58 10.5.2 Final Modification Concept...... 60 10.6 Further Testing...... 62 11.0 CONTINUED TESTING...... 63 11.1 Test #1…...... 63 11.2 Test #2…...... 67 11.3 Test #3…...... 68 11.4 Test #4…...... 70 11.5 Test #5…...... 71 12.0 IMAGING...... 72 12.1 Optical Mirror Images…...... 73 12.2 Resolution Target Images…...... 75 13.0 CONCLUSION...... 75 14.0 RECCOMENDATIONS...... 75 14.1 Thermal Mass Concept…...... 76 14.2 Automated Stage Scanning…...... 77 14.3 Z-Translator…...... 77 14.4 CCD Camera…...... 77 14.5 Encasing Optical Components…...... 78 15.0 REFERENCES ...... 79 16.0 APPENDIX A...... 81 16.1 Design Concept #1 Thermal Model A-1...... 82 16.2 Intermediate Design Thermal Model A-2...... 83 16.3 Deflection due to Vibration A-3 ...... 87 16.4 Drawing Package…...... 89

4 LIST OF FIGURES

Figure 1: Cryogenic sample stage for an ion microscope [1] ...... 10 Figure 2: High resolution electron microscope cold stage [2]...... 11 Figure 3: Freezing/perfusion microscope stage [3] ...... 12 Figure 4: The VitrobotTM [4]...... 13 Figure 5: Sample Grid (not to scale)...... 14 Figure 6: Tweezers used to grip the grid ...... 14 Figure 7: Specimen being applied using pipette...... 14 Figure 8: Liquid Ethane and Nitrogen ...... 15 Figure 9: Intermediate Container...... 16 Figure 10: Dual-Chamber Apparatus...... 16 Figure 11: LN2 Chamber...... 17 Figure 12: Transmission Electron Microscope...... 17 Figure 13: Transmission Electron Microscope Image of Polio Virus [7]...... 18 Figure 14: Optical Microscope Image of Onion Cells [8] ...... 18 Figure 15: Standard Optical Microscope ...... 19 Figure 16: Bench top optics with mirrors, filters, and light source ...... 19 Figure 17: Angular Aperture [11]...... 21 Figure 18: Snells Law [12] ...... 21 Figure 19: Numerical Aperture versus Objective Magnification [14]...... 22 Figure 20: Working Distance [13] ...... 23 Figure 21: Pressure-Volume-Temperature (PVT) diagram of water [14] ...... 25 Figure 22: Design Concept #1 ...... 26 Figure 23: Design Concept #2 ...... 27 Figure 24: Design Concept #3 ...... 28 Figure 25: Design Concept #4 ...... 29 Figure 26: Design 1 Thermal Model Diagram...... 31 Figure 27: Optical Components...... 35 Figure 28: Intermediate Design ...... 36 Figure 29: Intermediate Design Thermal Analysis Diagram...... 37 Figure 30: CAD model of current design ...... 39 Figure 31: ABS Prototype of Current Design...... 40 Figure 32: Cad of Workstation Assembly atop X-Y Translator...... 41 Figure 33: Workstation Assembly atop X-Y Translator...... 41 Figure 34: Axis of Stage ...... 42 Figure 35: Assumption of Cantilevered Beam...... 43 Figure 36: Plan and Section of Positioning Table ...... 44 Figure 37: Optical Microscope Schematic...... 45 Figure 38: Microscope Filters Schematic [17]...... 46 Figure 39: Holes in base station around center of mass...... 48 Figure 40: Tapped hole in collar for set screws...... 49 Figure 41: Brass valves attached to upper chamber...... 50 Figure 42: Notch in skirt...... 50 Figure 43: Water boiling curve [18] ...... 51 Figure 44: Nucleate boiling [20]...... 52

5 Figure 45: Film boiling [22] ...... 53 Figure 46: PTFE dewar...... 53 Figure 47: PTFE heat transfer model...... 54 Figure 48: PTFE dewar with aluminum base ...... 57 Figure 49: Cross-section of modified PTFE dewar ...... 58 Figure 50: Circuit Model of Modification Concept 1...... 59 Figure 51: Modified PTFE dewar...... 61 Figure 52: Temperature Positions of Pre-Cool ...... 64 Figure 53: Pre-Cool of Upper Assembly ...... 64 Figure 54: First Test Imaging Thermocouple Positions ...... 65 Figure 55: Test One Temperature Results ...... 66 Figure 56: Test Two Thermocouple Positions...... 67 Figure 57: Test Two Temperature Results...... 68 Figure 58: Test Three Thermocouple Positions...... 69 Figure 59: Test Three Temperature Results...... 70 Figure 60: Test Four Thermocouple Position ...... 70 Figure 61: Test Four Temperature Results ...... 71 Figure 62: Test Five Temperature Results...... 72 Figure 63: Unfocussed Image ...... 73 Figure 64: Partially Focussed Image...... 74 Figure 65: Fully Focussed Image...... 74 Figure 66: Image of Resolution Target...... 75 Figure 67: Image of Resolution Target...... 76

LIST OF TABLES

Table 1: Indices of Refraction……………………………………………………………18 Table 2: Common Objective Working Distance…………………………………………20

6 Acknowledgments

We would like to acknowledge the consistent and helpful advice provided by the following individuals from Harvard Medical School in the understanding of the project and the compilation of this report:

Dale Larson Jim Hogle Chen Xu Antoinne van Oijen Boerries Brandenburg

“We the team members,

Mohammad Ali John Delcore Sarah Kaufmann David Rezac

Faculty Advisor: Prof. Gregory Kowalski

Hereby assign our copyright of this report and of the corresponding Executive Summary to the Mechanical, and Industrial Engineering (MIE) Department of Northeastern University.” We also hereby agree that the video of our Oral Presentations is the full property of the MIE Department.

Publication of this report does not constitute approval by Northeastern University, the MIE Department or its faculty members of the findings or conclusions contained herein. It is published for the exchange and stimulation of ideas.

7 1.0 PROBLEM STATEMENT The study of biological samples requires the magnified views provided by optical and electron microscopes. The samples are viewed frozen to take a snapshot in time of what is happening within a cell’s components. A biological sample blotted on a grid can be imaged in a transmission electron microscope (TEM) for a minimal amount of time before it is rendered useless by the bombardment of electrons. A TEM is the optimal microscope because it offers the best image quality due to its high resolution capability. In order to locate small structures in the crowded environment of cells at that resolution and avoid the damage to the sample that accrues while finding these locations, it is necessary to first image the sample at cryogenic temperature in an optical microscope (OM) and identify those locations. Currently there is no method to achieve this. Additionally, the use of the OM provides the opportunity of having lower resolution images that are geometrically registered with the TEM images and can provide context to better understand the biological processes being studied. It is the goal of this Capstone project to develop a reliable method that can satisfy certain criteria, outlined below: • The process has to allow for imaging in the optical microscope while maintaining the specimen below -140oC for long enough to image. • It must enable the transfer from the optical microscope to the transmission electron microscope. • It must allow for mapping of the sample with florescent nano-particles and/or fluorophores that will provide reference points between the two microscopes. • There must be negligible vibrations within the system. • It cannot introduce any outside moisture or undue stresses on the grid that would result in deformation of the grid and/or the sample.

2.0 IMPACT STATEMENT The results of this project will aide research and development leading to better understanding of biological processes and to therapeutic advancements. It will lead to increased productivity by improving the quality and quantity of TEM images. The process enables a microscopist to specifically label molecular components with the large field of view of an OM, and then capture the images with the high resolution of the TEM. This will be accomplished without increasing the complexity of the current sample preparation, resulting in no additional user training or expertise.

3.0 BACKGROUND

3.1 Purpose

The application driving this invention is the ability to analyze polio virus cells by freezing them in vitreous ice at various increments of time in their development. By freezing and maintaining them at a temperature

8 below -140°C, the cells will preserve their original biological structure. The intent of the final design will impact all analysis done on any biological cell.

Another important factor that needs to be controlled is the prevention of any condensation on the sample. Any moisture will produce cubic ice which will result in a scattering of electrons when viewed in an electron microscope. This would generate useless images, so it is essential that moisture contamination is prevented. The maintenance of vitreous ice is also critical from the electron microscopist’s perspective because the vapor pressure of vitreous ice is low enough that there is no significant release of water vapor in the TEM’s vacuum system. Release of water vapor from cubic ice requires considerable time to recover the vacuum levels required to transmission electron microscopy and TEMs are routinely fully booked.

Another factor to consider is the duration of time that a biological sample can be imaged with a TEM. Electron microscopes operate by bombarding the sample with electrons, which damage the cell’s properties. Therefore, it is crucial that the areas of interest to be examined are first identified by the optical microscope, and then transferred to an electron microscope. Optical microscopes have a much larger field of view and do not compromise the integrity of the sample. For accurate relocation, a mapping system needs to be in place. Mapping is a method of translocation for points of interest on the sample from the optical microscope to the transmission electron microscope.

The cryogenic optical microscope will allow specimens of any living cells to be studied in this manner. This will enrich the quality of the data and accelerate the microscopy process. These two factors will advance medical developments.

The purpose of the background section is to provide information about the constraints and parameters that define the direction of this project. The previous applicable patents are illustrated first. Next is the explanation of the current sample preparation for the TEM, followed by an overview of the TEM. Finally, the key elements of optical microscopy are defined.

3.2 PATENT RESEARCH

Research was conducted to find patents relating to cold stages and cryo-holders. Three of the most relevant patents located are discussed below:

9 3.2.1 U.S. Patent 4,663,944 Cryogenic sample stage for an ion microscope.

Figure 1 shows an existing patent of a cryogenic sample stage for an ion microscope [1]. The sample holder mount (38 from Figure 1) controls the movement of the cold stage (36). A continuous liquid nitrogen feed climbs the cold stem and impinges on the copper flange and then filters back down. The sample sits in the slot on the top of the cold stage and is maintained at -150°C. The heat is transferred by means of conduction.

The primary obstacle to applying this technology is that the sample’s top surface would be exposed to atmosphere which would result in condensation forming on the sample. However the use of liquid nitrogen for cooling is realized throughout the entire design evolution.

Figure 1: Cryogenic sample stage for an ion microscope [1]

3.2.2 U.S. Patent 4,262,194 High resolution electron microscope cold stage. Figure 2 is comprised of four sub-figures [2]. Sub-figure 1 shows the top view of a high resolution electron microscope cold stage comprised of annular stainless steel (12) with a plastic insulator ring (15). The

10 sample sits in the specimen holder (24), shown in sub-figure 3. The purpose of this device is to minimize vibrations and disturbances in order to reduce relative motion between the microscope and sample. The setup is maintained at -120°C via the liquid nitrogen fed cold finger (30) that attaches to 40-1mm copper leaves. Again the drawback is that this leaves the sample exposed to the atmosphere.

Figure 2: High resolution electron microscope cold stage [2]

3.2.3 U.S. Patent 5,257,128 Freezing/perfusion microscope stage.

This patent creates a temperature controlled environment that is precisely adjustable between -100°C and +100°C [3]. It also controls the fluid environment surrounding the sample. The temperature control is by forced convection for cooling, and by resistance heaters for heating. It surrounds the sample with an assembly of copper tubes through which fluids are forced at a controlled temperature to induce the desired environment. Alternatively, a direct forced convection situation can be employed in which a particular

11 fluid is blown directly over the sample. (See Figure 3) There are several concerns with this approach, namely that it does not achieve the required temperature and that it exposes the sample to the air which results in contamination.

Figure 3: Freezing/perfusion microscope stage [3]

3.3 Current Sample Preparation Method In order to study the sample under the optical and transmission electron microscope, it needs to be blotted onto a grid and then flash frozen. This is done by a device called the VitrobotTM. This flash freezing process takes place by first plunging the sample into liquid ethane, and then removing it from the ethane and

12 placing it into a bath of liquid nitrogen (LN2). The current sample preparation method is detailed in the following section.

3.3.1 VitrobotTM: The Vitrobot is a fully automated vitrification device manufactured and sold by the FEI company. Vitrification is defined as the rapid flash freezing (also known as plunge-freezing) of the sample in order to form vitreous ice. Vitreous ice, in contrast to cubic ice, has no lattice structure and therefore does not provide any type of interference with the electron beams in a transmission electron microscope. Please see Section 5.0 for a more in-depth explanation of vitreous ice. The Vitrobot, as publicized on the official website, is shown in Figure 4 [4]:

Figure 4: The VitrobotTM [4]

3.3.2 Blotting of Specimen: The specimen of the virus mixed with fluorescent nano-particles is to be applied onto a metallic grid. The grids currently being used are made from either copper or gold, and have a very fine structure that allows the electron beams of the TEM to pass through without any interference.

A critical concern with the grid is the extent to which the grid may warp and deform. Even though the grid may warp during the initial plunge into the LN2, this does not pose a significant problem. The source for concern is possible warping between microscopes. Any warping would affect the mapping system. If warping does occur between the microscopes, the coordinates of a location on the sample will change.

13 Warping is to be avoided at all costs. An example of the sample grid on which the specimen is blotted is shown in Figure 5. The grid’s diameter is 2mm.

Figure 5: Sample Grid (not to scale)

A pair of specially designed tweezers is used to hold the grid. These tweezers are shown in Figure 6.

Figure 6: Tweezers used to grip the grid

The tweezers and grid are then inserted into the Vitrobot. The virus specimen with the fluorescent nano- particles is applied onto the grid using a pipette, from which the Vitrobot blots the grid with the specimen, as shown in Figure 7.

Figure 7: Specimen being applied using pipette

14 3.3.3 Vitreous Ice Formation The specimen is then rapidly submerged into liquid ethane. The technician then detaches the tweezers from the Vitrobot, and transfers the sample from the ethane into Liquid Nitrogen (LN2) to instantaneously freeze it into vitreous ice. The ethane and LN2 reservoirs are shown in Figure 8:

Boiling LN2

Liquid Ethane

Sample Location

Figure 8: Liquid Ethane and Nitrogen

3.3.4 Properties of Liquid Nitrogen & Liquid Ethane As previously discussed, the sample to be viewed must be flash frozen in such a way as to create vitreous ice and prevent the formation of cubic ice. Ethane gas is pumped into a container surrounded by liquid nitrogen, which cools it to the point of condensation and then maintains it at a liquid state. Both liquid o o nitrogen and liquid ethane are cold enough (TBoil, LN2= -195.9 C, TMelt, Ethane= -183.3 C) to maintain vitreous ice on a sample, but liquid ethane is used for flash freezing because of its higher heat capacity. If the sample were plunged into liquid nitrogen, the rapid heat transfer would cause some of the LN2 to heat up past its boiling point, and therefore lower its ability to transfer heat. In boiling near the sample, it would also introduce an added disturbance to the sample on the grid. Liquid ethane, however, has a much higher o boiling point (TBoil, Ethane= -88.7 C). This means that when the sample comes in contact with liquid ethane, it stays in a liquid state through the whole freezing process, allowing for faster and more controlled heat transfer, which is required in the formation of vitreous ice [5]. 3.3.5 Intermediate Container:

The specimen is then taken from the LN2 and transferred into an “intermediate container” which is only used to transport the specimen from the original ethane and LN2 reservoir to the apparatus that will be inserted into the electron microscope (i.e. the “Cold Finger”). This intermediate container is shown in Figure 9:

Figure 9: Intermediate Container

3.3.6 Transfer to Cold Finger: The specimen is then brought to the “Cold Finger” using the intermediate container. The cold finger is the device that is inserted into the electron microscope. It is part of a larger apparatus that consists of two

chambers. Both of these chambers are initially filled with LN2. This apparatus is shown in Figure 10:

Cold Finger LN2 Chamber Chamber

Figure 10: Dual-Chamber Apparatus

The specimen is removed from the intermediate container and placed into its precise location in the cold

finger. This occurs in the cavity shown in Figure 11. The cold finger is then detached from the other LN2 chamber; its opening is sealed, and it is inserted into the electron microscope.

16 Cavity for Specimen

Figure 11: LN2 Chamber

3.4 Transmission Electron Microscope: The transmission electron microscope (TEM) uses an electron beam that is scanned over the sample rather than light to form an image. The TEM has a large depth of field, which results in a relatively smaller section of the sample to be in focus at one time. The advantage of this is that closely spaced features of a sample can be viewed with high magnification and a degree of resolution is obtained that far exceeds that of the optical microscope [6]. A typical TEM, along with the controlling computer hardware, is shown in Figure 12.

Figure 12: Transmission Electron Microscope

17 3.4.1: 3-Dimensional Modeling in TEM One of the main reasons for using the TEM in this case is to obtain a 3-D model of the sample. Once the sample is inserted into the TEM, it can be viewed from various angles, resulting in different images of the sample. These different images can then be transferred to computer software that links them together to form a model of the sample that is 3-dimensional in nature. Using this model, the characteristics and points of interest of the sample can be analyzed with extreme accuracy. 3.4.2: Electron Versus Optical Microscopy Electron microscopes have the power to magnify up to 500,000X, whereas standard compound optical microscopes with oil immersion lenses can magnify up to 400 times. Figure 13 shows an image of polio virus captured with a TEM at a magnification of 46,050X [7]. In contrast Figure 14 displays an onion cell observed with an optical microscope magnified at 100X [8]. To optimize the quality of a specific cell’s image, it is essential to use the large field of view that the OM provides and then, via mapping quickly re- identify that point with the TEM.

Figure 13: Transmission Electron Microscope Image of Polio Virus [7]

Figure 14: Optical Microscope Image of Onion Cells [8]

18 3.5 Optical Microscopy

The design of the cold stage must take into account various optical phenomena that will influence its functionality while viewed with the optical microscope. Some of the important properties are discussed below.

3.5.1 Defining Optical Microscopes

Most microscopes used in biological research are manufactured products that have all of the required optics integrated into a package that includes means for adding accessories (cameras, filters, etc.) Such a microscope is shown in Figure 15. However, it is not uncommon for a researcher to build a custom microscope on an optical bench (see Figure 16).

Figure 15: Standard Optical Microscope

Figure 16: Bench top optics with mirrors, filters, and light source

19 Standard microscopes are fully calibrated, and allow for mobility. Bench top microscopes have adjustable components but cannot be moved easily once set up. When first originating design concepts the group took the approach assuming the former microscope would be used. However, after delving into the specific constraints discussed in section 7.0, it was realized that a custom bench top would have to be constructed.

3.5.2 Resolution

The resolution (R) of an optical lens is the single most defining parameter of an objective lens. It is defined as the minimum spacing between two points on a specimen that can be separated. The lower the resolution, the better the resolving power of the lens. Resolution is based on three basic variables: wavelength of the light (λ), refractive index (n), and angular aperture (θ). [9]

R = λ /( 2 n sin θ ) (Equation 1)

The light wavelength is determined by the light source used to illuminate the sample. In the case where fluorescent nano-particles need to be visible, λ needs to be a maximum of 649nm. This light source is typically a laser.

The second consideration, the refractive index, is a way to quantify how much of the light from the sample reaches the optical lens. Each medium (regardless of phase) has its own index of refraction. It is defined below where c is the speed of light (3.0x108 m/s), and V is the velocity of light in the chosen material.

n = c / V (Equation 2)

The higher the refractive index, the more light rays the lens sees. Table 1 displays indices of refraction for various materials. To optimize the refractive index, different immersion fluids are used with optical lenses. These are called immersion lenses and the appropriate fluid is added between the bottom of the lens and the top of the sample, contacting both. The refractive index ranges from 1.01 to 1.51 for specialized oil immersion liquids [10].

Table 1: Indices of Refraction [10]

20 The last parameter is angular aperture (θ). The angular aperture is the angle that the light from the sample hits the objective lens. Figure 17 shows a θ of 15˚. It has an upper limit approximately equal to 72°.

Figure 17: Angular Aperture [11]

The refractive index and angular aperture are inversely related, demonstrated by Figure 18.

Figure 18: Snells Law [12]

Equation 3 is defined as Snells Law. It demonstrates that with two mediums, the refractive indices have an inverse sinusoidal relationship to their respective angular apertures. The term: n*sinθ is then referred to as one term, the numerical aperture (NA).

n1 sin θ 1 = n 2 sin θ 2 (Equation 3)

3.5.3 Objective Lens Properties

Table 2 displays the three main properties of an objective lens: magnification, numerical aperture, and working distance.

21 Table 2: Common Objective Working Distances [13]

Equation 4 is the denominator of equation 1, therefore resolution decreases as NA increases, resulting in an overall increase in resolving power of a lens with a higher NA.

NA = nsinθ (Equation 4)

Magnification (M) affects the resolution by becoming a multiplying factor, altering equation 1 to the following.

R = Mλ /(2NA) (Equation 5)

The purpose of M is to magnify the distance between specimen points to a visible level. Figure 19 demonstrates the corresponding increase in numerical aperture and magnification in both dry and oil objective lenses. This supports the objective lenses shown in Table 2.

Figure 19: Numerical Aperture versus Objective Magnification [14]

The last property is the working distance (WD) of a lens. WD is the perpendicular distance between the lens and the closest surface of the cover slip with the sample in focus (see Figure 20) [12]. Anything smaller than 10mm is considered normal working distance. For oil and water immersion lenses the working distance needs to be minimal to ensure that there is a constant liquid layer between lens and cover slip. This value is commonly less than 1mm.

Figure 20: Working Distance [13]

Working distance decreases as numerical aperture increases, as depicted in Table 2. When choosing an objective lens it is always the goal to have a high NA which results in higher resolving power. The limiting factor is then the working distance.

3.5.4 Use of Air Lenses

Currently optical microscopes are used to examine living cells at room temperature. For optimal resolution optical lenses are kept at the same temperature as the sample. One way this is done is to insert the sample stage into a highly conductive metal disk while fluid (e.g. water, LN2, etc.) is circulated through the conductor at a known temperature. As mentioned previously oil and water immersion lenses are most commonly used. For the purpose of this project the sample temperature must stay at a fixed temperature below -140°C. For a working distance of less than 10mm the temperature gradient to maintain immersion fluid of either oil or water above freezing is impossible with current market lenses. Therefore an air lens is the best candidate. The heat transfer will then be due to natural convection and radiation rather than conduction.

By using an air lens the working distance problem is overcome, however it compromises the resolution available in the optical lens. Air has the smallest index of refraction, resulting in a reduced numerical aperture. The air objective lens that has been chosen is manufactured by Mikrothek in Hamburg, Germany. It has a working distance of 0.96mm and a NA=0.8. Section 7.2 further explains how the air lens will be incorporated into the cryogenic optical microscope.

4.0 MAPPING An important aspect of the design is that it must allow for mapping of the sample. Mapping is a method of translocation of points of interest on the sample from the optical microscope to the transmission electron microscope. This is done because it is difficult to locate the polio virus in the TEM due to the fact that it is

23 found in relatively low abundance compared to the crowded environment of the cell. Since many different objects in the cell scatter electrons, the image appears cluttered around the areas of infection. In order to make these areas easier to locate, the virus is covered in fluorophores prior to being blotted onto the grid by the Vitrobot. In addition, the grid is dusted with fine gold beads to aid in position referencing. This makes it possible to filter the light being reflected from the fluorophores on the virus through the optical microscope and map where the most interesting points are according to the grid orientation and gold bead location. The sample can then be transferred to the TEM, which can focus in on those mapped locations for further imaging and analysis.

An alternative approach to using the gold beads is to scatter the sample with fluorescent nano-particles with wavelengths ranging between 5-20 nm. The advantage of this is that when fluorescent light is shed on the sample, these nano-particles illuminate in different colors, which means that filters can be used to identify different wavelengths of beads and dyes and maintain separate reference coordinate systems. The nano- particles are also very electron-dense, and can therefore be easily seen in the TEM.

5.0 VITREOUS ICE As stated previously, the sample to be viewed is first frozen in vitreous ice. Vitreous ice is the “glassy” low density amorphous (LDA) solid form of water [15]. The defining characteristic of vitreous ice is that it has no crystal structure. The long-range order of water molecules in everyday ice (cubic ice) are lined up in a constant repeating pattern creating a crystal lattice, making ice somewhat opaque. In vitreous ice the water molecules are randomly oriented. This random orientation creates a transparent solid, similar to glass.

This particular phase change of water is accomplished by rapidly cooling below its glass transition temperature (Tg) in atmospheric pressure. The exact glass transition temperature of water is uncertain. When looking at water in standard atmospheric pressure, the range of its glass transition temperature can be found to be approximately 136°K to 165°K. This approximation is depicted in Figure 21, which is the general PVT diagram of water [16]. This temperature drop must be done in a matter of milliseconds to prevent the spontaneous formation of crystals (i.e. freezing in liquid ethane).

Figure 21: Pressure-Volume-Temperature (PVT) diagram of water [14]

6.0 INITIAL DESIGN CONCEPTS The following possible solutions were generated as based on the background research and were formulated within the scope of the design constraints.

6.1 Design Concept # 1 One of the initial design concepts can be seen in Figure 22. It involves an inner bath of liquid nitrogen that contains the sample to be viewed, which is attached to an external reservoir. Both the top and bottom surfaces of this inner bath are made of glass, or some other optically equivalent material. The bath is vented in such a way as to allow controlled boiling of the liquid nitrogen into an outer chamber of gaseous N2.

This outer chamber surrounds the bath and acts to increase the overall heat gradient in the structure. The N2 gas is then vented out of this chamber into the atmosphere away from the optical equipment. Again, the upper and lower surfaces are made of a transparent material that allows for complete viewing of the sample with the microscope.

Several design modifications have been considered from this base model. For instance, utilizing a lens that could maintain its optical integrity at -195oC would allow for fewer surface separations between sample and lens. This means that the lens could be placed in the N2 gas region, eliminating the uppermost separation element. Another iteration is to introduce a vacuum in the outer chamber and vent the N2 gas directly into the atmosphere, which would effectively eliminate convection in the outer chamber and limit

25 all heat transfer to that which occurs by radiation. An additional concept included a removable top that would allow for easy access to the sample and transportation thereof, as well as possible incorporation of current electron microscope staging elements to streamline the overall process.

Figure 22: Design Concept #1

6.2 Design Concept # 2 This design consists of a vacuum sealed transport capsule in which the sample is held and kept at a desired temperature. The noteworthy characteristics of this design are: a docking apparatus, a cold finger, a cryo-trap, and a vacuum sealed chamber.

Figure 23: Design Concept #2

As seen in Figure 23, the base of this design is a capsule which can fit on the staging of an optical microscope. A revolving door enables the sample to enter the vacuum sealed chamber. When in the chamber, a pair of tweezers will grab the sample and move it to the middle. To perform this task, the tweezers have to be capable of pivoting from one side of the chamber to the other. The tweezers also act as a cold finger on the sample. This allows the sample to be maintained at a desired temperature below -140oC. The vacuum and capsule material will be able to create enough of a gradient that the objective lens and the oil which the lens is immersed in will not be affected. The tweezers then have to be able to return the sample to the revolving door when it is desired to switch to the staging for the transmission electron microscope (TEM).

When the sample is brought into the chamber, an undesired amount of moisture will be let in. To balance the system after this is done, a cryo-trap (not shown) will be required in the chamber.

27 6.3 Design Concept # 3 This design consists of a double concentric stream of vapor cooling the sample and creating a thermal gradient. A sturdy holder is needed to keep the sample still within the vapor stream, which has a high velocity.

Figure 24: Design Concept #3

As seen in Figure 24, a double concentric stream of vapor must be created. The inside stream consists of nitrogen (N2) vapor. The outside stream of vapor acts as an insulator for the liquid nitrogen vapor and a gradient to protect the object lens of the microscope. However, this could only work within short distances where laminar flow can be considered. After the sample is viewed, it would be plunged into a liquid nitrogen bath to enable it to be transferred in the TEM staging.

The other key component is the sample holder. It would have to be able to hold the sample in the stream of nitrogen vapor steady enough that the analysis of the sample is not affected. The rigidity of the sample holder would be determined by the velocity needed to create an effective vapor stream.

28 6.4 Design Concept # 4 Another design that was briefly discussed can be seen in Figure 25.

Figure 25: Design Concept #4

This design consists of a protective shield that would be used around the microscope instead of the sample. This would enable nitrogen vapor to be directed on the sample constantly while protecting the microscope from condensation resulting from the vapors. This idea was dismissed after viewing the types of microscopes, and their working areas. It would have required different sized protective shields for different microscopes, and therefore would not be compatible with all current microscopes.

7.0 Progression of Design The initial four design ideas were based on the group’s understanding of the problem after initial introduction and have served as a good brainstorming base to discuss further design iterations. Naturally, more research and discussions with microscopists have led to a better understanding of the problem at

29 hand, and therefore more design concepts to take into consideration. Some misconceptions reflected in the initial designs are: 1) the idea that the sample cold stage needs to be built into a conventional microscope body, 2) the lens used to view the sample must be kept at room temperature—a consequence of the first misunderstanding, and 3) the thought that the new design should include a separate viewing chamber for the sample, which would require an additional transfer step. The current design being refined and prototyped is very dissimilar from the initial designs previously discussed, which is largely due to the development of the key concepts discussed in subsequent sections. The main improvements include the use of thermal modeling to determine that a cold lens is necessary, the concept that the microscope can be built in a modular manner to separate key components and reduce heat sinking complications, and finally the incorporation of the cold finger, which reduces sample handling and streamlines the overall viewing process.

7.1 Thermal Modeling

In order to better understand the thermal constraints of the group’s initial design concepts, thermal modeling was carried out on design concept #1 (Figure 22). As shown in Figure 26, the model uses circuit analogies to split the design into individual thermal components between the sample and the objective lens. Vertical symmetry for materials and thicknesses is assumed in order to simplify initial analysis. The basic thermal constraint of this situation is that the sample must be maintained at liquid nitrogen temperature, so as not to jeopardize its state of vitreous ice, while the upper glass surface and objective lens cannot fall below the dew point temperature, as condensation on either surface would block the viewing path and render the microscope useless for imaging. The other physical constraint in this situation is that the sample and objective lens must be in very close proximity for imaging. A maximum distance is imposed on the setup based on the working distance and geometry of the lens.

Figure 26: Design 1 Thermal Model Diagram

Considering the constraints mentioned above, the model is based on a total distance from sample to upper glass surface of 4mm (maximum found in Table 2), and the assumption is made that Tsample=TLN2. The material above and below the sample is optical glass, as it must be transparent for imaging. The values of thermal conductivity for the staging body were varied to see how constructing it from different materials would affect the temperature on critical surfaces. Appendix A-1 displays the values used. The calculations for this model, shown below, give the circuit analogy setup and solution for T5UR (T at level five upper right surface), TgU (T at upper glass surface), and T5UL (T at level five upper left surface). These temperatures show whether or not a sufficient gradient can be achieved to avoid condensation at the outer surfaces of the cold stage. The results in the corresponding excel spreadsheet show that, according to this analysis, maintaining a sample temperature of -200 oC will result in surface temperatures of around 16 oC. With a common dew point temperature around 15.5 oC, and the extra cost imposed by having an environmentally controlled room for imaging, this result is right on the cusp of feasibility. Considering that this model assumes a separation from sample to lens of 4mm, which would require a lens with very low magnification and poor numerical aperture. This shows that the initial design concept #1 would not yield the desired imaging performance.

32 π A = (0.005) 2 = 1.9635e − 5m 2 1 4 π A = (0.005) 2 = 1.9635e − 5m 2 2 4 π A = (0.04) 2 − A = 0.001237m 2 => A = A = 6.185e − 4m 2 outer 4 1 2R 2L

−1 −1 −1 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 1 1 L5 L4 1 L5 L4 1 L5 L4 = ⎜ + + ⎟ + ⎜ + + ⎟ + ⎜ + + ⎟ RT∞−T 3 ⎝ hair A2L K 4 A2L K N 2 A2L ⎠ ⎝ hair A2 K 3 A2 K N 2 A2 ⎠ ⎝ hair A2R K 4 A2R K N 2 A2R ⎠ −1 −1 −1 −1 ⎡⎛ 1 L L ⎞ ⎛ 1 L L ⎞ ⎛ 1 L L ⎞ ⎤ R = ⎢⎜ + 5 + 4 ⎟ + ⎜ + 5 + 4 ⎟ + ⎜ + 5 + 4 ⎟ ⎥ T∞−T 3 ⎜ h A K A K A ⎟ ⎜ h A K A K A ⎟ ⎜ h A K A K A ⎟ ⎣⎢⎝ air 2L 4 2L N 2 2L ⎠ ⎝ air 2 3 2 N 2 2 ⎠ ⎝ air 2R 4 2R N 2 2R ⎠ ⎦⎥

⎛ L L L ⎞ ⎜ 3 2 1 ⎟ Rtot = RT∞−T 3 + ⎜ + + ⎟ ⎝ K N 2 A1 K1 A1 K LN 2 A1 ⎠

1 1 T3 = (T∞ − TLN 2 ) = (T∞ − T3 ) Rtot RT∞−T 3

∴T3 = T∞ − qtot RT∞−T 3 => qtot = q A + qB + qC

−1 ⎛ 1 L L ⎞ ⎜ 5 4 ⎟ q A = ⎜ + + ⎟ (T∞ − T3 ) ⎝ hair A2R K 4 A2R K N 2 A2R ⎠

−1 ⎛ 1 L L ⎞ ⎜ 5 4 ⎟ qB = ⎜ + + ⎟ (T∞ − T3 ) ⎝ hair A2 K 3 A2 K N 2 A2 ⎠

−1 ⎛ 1 L L ⎞ ⎜ 5 4 ⎟ qC = ⎜ + + ⎟ (T∞ − T3 ) ⎝ hair A2L K 4 A2L K N 2 A2L ⎠

q A qB qC T5UR = T∞ − , TgU = T∞ − , T5UL = T∞ − hair A2R hair A2 hair A2L

7.2 Introduction of Cold Lens Although this analysis focused specifically on design concept #1, it was invaluable in that it forced the group to look in detail at the thermal design issues involved and fostered several discussions about design efficiency that eventually led to the current design, which is discussed in Section 8.0. After confirming the extreme temperature gradient required to go from liquid nitrogen temperature to above the dew point temperature in ~4 mm, it became clear to the group that keeping the lens at room temperature posed a serious design issue. The solution to this problem came in the form of a German-manufactured lens that

33 had been shown to withstand dozens of cycles down to liquid Helium temperature (~1K). The lens has a numerical aperture (NA) of 0.8, a working distance of 0.96mm, and a magnification of 80X. Because the NA is not as high as some of the immersion objective lenses’ it has less resolution capabilities. However, the resolution of the air lens is acceptable because it can detect centroids and clusters of the fluorescent nano-particles. This is sufficient in cross-referencing with images obtained from the TEM.

The lens costs about $290 U.S. dollars. This is low in comparison to most optical lenses according to referenced microscopists. Therefore the life cycle of the lens is reasonable and acceptable. By utilizing this lens, the design could be greatly simplified by bringing the lens and sample into the same thermally controlled chamber, eliminating the need to separate the sample and objective lens by any minimum distance. This means that the distance to the sample can be set to optimize imaging performance without external constraints.

7.3 Microscope Construction Once it was agreed that the design would incorporate this German “cold lens,” the group turned to the fact that working within the body of a conventional optical microscope presents a huge potential for heat- sinking. In other words, the relatively large mass of the microscope frame would work to heat up the liquid nitrogen dewar and any points in contact with it (i.e. the objective lens). This led to concerns that the lens would act as a thermal fin and deliver heat directly to the sample from the microscope body, destroying the vitreous ice structure as it moved in for imaging. Also, cooling such a large mass would take a great deal of liquid nitrogen and time. The concept of having such a warm body surrounding the dewar could lead to excessive boil off of liquid nitrogen, which would cause vibrations inside the controlled imaging chamber and likely compromise image quality.

In light of these concerns, the group conducted further research into the construction of microscopes and found that most advanced imaging systems of this caliber are not off-the-shelf products. In most cases, this type of microscope would be built in a “bread-board” manner, using a vibration isolated optical table to lay out the components and direct the image as necessary. This means that the camera, light source, processing equipment, and most importantly the sample chamber, can be separate parts of the microscope and spread out over the optical table as shown in Figure 27. Since the objective lens being used is not infinity corrected, a collimating lens is employed to make the image beams parallel and allow mirrors to transmit it to the camera at any distance. The sample and liquid nitrogen dewar can then be isolated from the most massive parts of the microscope setup. By separating these elements, the amount of liquid nitrogen and time to reach equilibrium within the imaging chamber can be minimized. In addition, moving the cold stage out from the body of a conventional microscope provides more space to insulate the sample, and to maneuver the setup in and out of place for imaging.

Figure 27: Optical Components

7.4 Intermediate Design After brainstorming on these key issues and coming to an agreement on their incorporation into the design, a fully defined solid model (shown in Figure 28) was generated. Representing everything that had been discussed, this design is intended to be separate from the microscope body. It places the objective lens in the same chamber as the sample at cryo-temperatures, and uses an outer vacuum chamber for insulation while holding the sample on a central post that is surrounded by a stainless steel skirt for temperature protection during sample transfer.

35 Vacuum chamber

Cold Lens Position

Inner Skirt to Hold N2 Gas

Outer Housing Post to Hold Sample for Imaging

Figure 28: Intermediate Design

Operation of this design involves filling the bottom dewar with liquid nitrogen and allowing the system to equilibrate, then transferring the sample onto the post from the liquid nitrogen bath. After slowly lowering the top half into position and allowing it to come to thermal equilibrium, the optics could be positioned and imaging carried out via an X-Y positioning system mounted to the bottom half. The main drawback still evident in this design is that it involves an additional handling step for the sample grid, and in doing so increases time required for imaging as well as the risk of damaging the sample. Thermal circuit analysis was conducted on this design as well, with full calculations found in Appendix A-2. Figure 29 shows the setup for this analysis, which concludes that the upper glass and housing surfaces would be 16.7 oC and 16.1 oC, respectively. This again leads to the potential problem of condensation that would jeopardize the whole imaging process.

Figure 29: Intermediate Design Thermal Analysis Diagram

8.0 Current Design: During the design evolution process the team continuously consulted with Dr. Antoinne Van Oijen and Dr. Chen Xu. The former is an optical microscopist and a professor at Harvard Medical School, whereas the latter is an electron microscopist at Brandeis University. The idea was to determine what opinions they had of the design, and to incorporate their suggestions to make the design as user friendly and efficient as possible. Because microscopists like these will be the eventual users of the cold stage, the team believed that incorporating their opinions into the various stages of the design would be beneficial in predicting and solving potential problems.

The concepts of bringing the objective lens very close to the sample by using the special cold lens manufactured in Germany, eliminating one step in the sample transfer process by using the electron microscope cold finger, and substituting the lower chamber of the intermediate design with the workstation assembly, are all ideas that were generated in brainstorming sessions with the above mentioned microscopists. Some details of this collaboration between the team and the microscopists are given below.

8.1 Incorporating Microscopists’ Opinion After “printing” a 3-D model of the intermediate design from ABS plastic in Northeastern University’s machine shop, it was taken to Brandeis University where it was presented to Dr. Chen Xu. This plastic model was of the design shown in Figure 29.

37 Upon studying the model and understanding how it would work, he stated that in his opinion the design was very promising. He believed that having a skirt around the sample holder would significantly isolate it from the temperature and humidity of the surrounding environment. He also stated that pre-cooling the objective lens before bringing it close to the sample would prove beneficial as it would reduce the temperature gradient between the sample and the objective lens, thus resulting in less turbulence in the liquid nitrogen.

The major concern that the Dr. Xu had was related to the deformation of the sample grid. In the original method that the group had outlined, after the sample was flash frozen onto the metallic grid using the Vitrobot, it would be transferred to the copper sample holder post in the lower chamber of the design. Then after the imaging process was completed, the sample would have to be taken off the holder post and inserted into the cold finger, which would ultimately be inserted into the TEM. The concern was that there was a good chance the grid could deform during one of these two transfer processes. Therefore he suggested that the design be somehow altered, so as to reduce the number of times the grid was transferred from one location to another.

With this in mind, the group determined that incorporating the cold finger (used currently to load into the TEM) into the design would be the best way to minimize further sample handling and keep the process familiar to operators. By making the optical microscope able to image the sample while it is in place on the cold finger, the operator can transfer the sample from the Vitrobot to the cold finger in a similar dewar as that currently used, image the sample, and then continue to the TEM without significant interruption or added complexity.

38 This current CAD design consisting of the TEM apparatus and a modified version of the upper chamber is shown in Figure 30, and the prototype made from ABS plastic is shown in Figure 31.

Optics Holder for the collimating lens

Cold Stage Upper Chamber Guide Rails

TEM apparatus inserts here

Metallic Skirt to Hold N2 Gas

Workstation Assembly

Styrofoam Insulation

X-Y Translator

Figure 30: CAD model of current design

39 Mirrors Guide Rails

Cold Stage Upper Chamber Optics Holder

Optical Components TEM Apparatus inserts here

Skirt to hold N2 gas

Workstation Assembly X-Y Translator

Figure 31: ABS Prototype of Current Design

The current design has some similarities with the intermediate design, shown in Figure 28, in that it still uses the concept of the objective lens being brought into the chamber of gaseous nitrogen, and the optical microscope being made by positioning components on an optical table. There are, however, certain differences between this design and the intermediate one. For example, it replaces the complete lower chamber of the intermediate design with the workstation assembly used for transfer to the electron microscope. As mentioned earlier, after the sample is flash frozen using the Vitrobot, it is transferred into the cold finger of the TEM. This transfer already takes place inside the workstation assembly. Therefore there will be no additional transfer stages other than those currently being performed. This will greatly reduce the probability of the grid being deformed in the process.

40 8.2 X-Y Translation of the Workstation Assembly: The workstation assembly is attached atop an x-y translator. This translator, along with the workstation assembly resting on it, is shown in Figures 32 and 33:

Workstation Assembly

X-Y Translator

Figure 32: Cad of Workstation Assembly atop X-Y Translator

Figure 33: Workstation Assembly atop X-Y Translator

41 The first phase of designs and theories were all based on the idea of having a stage, independent of the microscopes. For all of these designs and theories, current optical microscope staging and methods of translation would be used. As the design evolved, a new method of translation needed to be addressed. The exact method of translation had to be designed after the stage design and microscope layout were chosen. The size, shape, and weight of the stage, as well as the position of the optics, all play a major role in determining what type of method will work.

The first step of designing the method of translation was qualifying what was needed from the translator, and quantifying the distance of travel required. First and foremost, the cold stage had to be able to travel in the x and y-axis. The z-axis was deemed a separate entity that could be handled with the optics and the optics brackets that were positioned over the stage. Figure 34 displays the axis of the stage.

Figure 34: Axis of Stage

Another major design goal was to be able to record the viewing position on the cell relative to a zero-point. The method of translation had to have a repeatable zero-point and a system for regulating its movements. Finally, the system had to be stable and withstand any deflection caused from vibrations of the cold stage or any other outside influences.

There were two apparent ways to solve this problem. The method of translation could be specifically designed for the cold stage, or it could be a purchased item adapted for the cold stage. Each were reviewed.

The advantage of designing a method specifically for the cold stage was that all of the major design goals of the system could be taken into consideration with no adaptation. One idea was to use the stage itself, with Teflon tape on the bottom, and slide it across the optics table with motion controlled by micrometers.

42 This method would require the use of a set block, with an opposing force placed opposite the micrometers. This design optimized controlling vibration and stabilization of the cold stage. It also would be less expensive then purchasing a translation stage. However, the zero-point of this system would be very inconsistent and translation would not be smooth with direct movement across side forces and friction points.

In the end, it was decided that a purchased stage could easily be adapted to fit the cold stage at a minimal cost increase. The double axis positioning table will provide a precise and repeatable movement on the x and y-axis. The stage will use digital micrometers for movement, and will be accurate to 0.0005 inches when traveling. The cold stage extends over the edge of the positioning table; therefore the table will be located at the cold stage’s center of mass. Because of the unsupported overhang, the cold stage becomes susceptible deflection due to vibrations. Assuming the cold stage will act like a cantilevered beam, see Figure 35, the equation below was used to find the expected deflection (x) with the dependents of equivalent stiffness (k), mass (m), and acceleration due to gravity (g).

kx = mg (Equation 6)

It was determined that the deflection could reach up to 0.01 inches. Refer to Appendix A-3 for detailed calculations.

Figure 35: Assumption of Cantilevered Beam

To help correct this, the cold stage is clamped to the positioning table. An added corrective measure could also be to place Teflon coated spacers between the optics table and the exposed cold stage. This provides the needed support and stabilization to areas not directly connected to the positioning table.

Figure 36: Plan and Section of Positioning Table

As seen in Figure 36 the positioning table has the micrometers off to the sides and in an open flat stage area. The stage area also has a hole pattern that will be used for positioning pegs. By placing pegs in the given hole pattern and peg holes on the underside of the cold stage, an easy and repeatable zero-point will be created. All of the design goals for the stage have been accounted for.

8.3 Guide Rails / Vertical Motion of Objective Lens Figures 30 and 31 show the upper chamber of the cold stage connected to three guide rails. The tripod formed from these three guide rails provides the necessary vertical motion of the objective lens. The guide rail directly behind the workstation assembly contains a linear bearing that slides along the rail. Attached to this linear bearing is a dovetail translator that has the ability to provide both coarse and fine movement in the z-direction to position the lens with respect to the sample and provide for fine focus control. The other two guide rails provide support to the structure. Without the presence of these two rails, the structure would bend and oscillate similar to a cantilever.

After freezing the sample onto the metallic grid, the grid is placed into the workstation assembly and the cold finger is inserted from the side. The sample is then picked up and transferred onto the cold finger. During this entire process the objective lens has to be moved away from the cold finger to provide the necessary space needed to complete the transfer. To accomplish this, the upper chamber (along with the objective lens attached to it) is lifted up using the dovetail translator and linear bearing on the guide rail. After the transfer of the sample is complete, the chamber is lowered with the linear bearing. This provides

44 coarse positioning of the objective lens over the sample. The dovetail translator is then used for fine adjustment of the objective lens, until the image of the grid is in full focus.

8.4 External Optical Microscope As mentioned earlier, the optical microscope used in this design is custom made. That implies that it does not look like a traditional optical microscope, in which a metal assembly holds all the components together. Rather it is comprised of specifically selected filters, mirrors, lenses, a camera and a light source (shown in Figure 31) that are all be placed on a breadboard, in such a manner that transmits images from the sample to a CCD camera. A schematic of the external optical microscope is shown in Figure 37.

Figure 37: Optical Microscope Schematic

In the above schematic, the black lines indicate the illumination path which originates from the light source and heads towards the sample. Conversely, the red line indicates the imaging path which originates from the sample and ends at the CCD camera. The light in the illumination path, after passing through the excitation filter and being reflected by the dichroic beam splitter, enters the sample and excites the fluorescent particles. After these particles are excited, the light they emit passes through the objective lens and onto a set of three mirrors. The sole purpose of these mirrors is to keep reflecting the rays of light at angles of 90o until they become parallel to the optical table and at a height which will allow them to pass through the other optical components. After becoming horizontal by being reflected from the third mirror, the light in the imaging path passes through the dichroic beam splitter. From there it strikes and passes through the emission filter and finally onto the CCD camera where the image is captured.

45 8.4.1 Light Source When the fluorescent particles embedded in the sample are excited with light of a certain wavelength, they emit light of a different wavelength. This light is always of a longer wavelength than the excitation light, i.e., it is more towards the red end of the light spectrum. It is this emitted light that is used for imaging purposes.

The fluorophore dye that is be used to label the virus specimen is known as the Cy5 dye. It has an excitation wavelength of 649nm, and an emission wavelength of 670nm. Keeping this in mind, there is a need for a light source which transmits light at or near the excitation wavelength of the Cy5 dye. For this purpose a red He-Ne (Helium Neon) laser is used that emits illumination light at 633 nm, with a power output of 35 mW. Because the components are sitting on the bench top, the laser is exposed, and appropriate safety goggles need to be worn when operating the optical microscope. Future plans include enclosing all of the optic components, so safety will no longer be a factor. 8.4.2 Excitation Filter The excitation filter is placed in front of the light source. Its purpose is to filter out all of the unnecessary wavelengths from the laser illumination light, and transmit only that specific wavelength that will excite the fluorophore dye.

A schematic of the excitation filter, along with the other two important filters (Emission Filter, and Dichroic Beam splitter), is shown in Figure 38 [17]. It is worth noting that although these three filters generally come pre-assembled in a fluorescent filter cube that is not how they are used in the scope of this project. Instead, the three filters are placed separately on the optical table so as to provide the same result.

Figure 38: Microscope Filters Schematic [17]

46 8.4.3 Emission Filter The emission filter is placed on the optical table in front of the CCD camera. It attenuates all of the light transmitted by the excitation filter, and transmits any fluorescence emitted by the specimen. 8.4.4 Dichroic Beam Splitter The dichroic beam splitter is placed at a 45o angle in the optical path of the microscope. It is a thin piece of coated glass with the ability to reflect light of one color (the excitation wavelength) and transmit another color (the emitted fluorescence).

9.0 Intermediate Modifications

The parts were received from the machinist and the first assembly stage began. Two things that were not finalized were the welding of the skirt to the upper chamber and the welding of the collar to the upper chamber. These two things were purposely left to the end to account for any tolerances not met in the fabrication process. This gave the design freedom to adapt and allowed for slight modifications deemed necessary in the first assembly stage. After piecing the fabricated parts together, four initial modifications needed to be done:

9.1 Attachment of X-Y Translator The cold-finger base station needed to be attached to the X-Y translating stage. The center of mass had already been calculated for the base station, the problem was not were to place it on the translation stage but how to attach it. Three methods were looked at:

A. The first method was to use placement pins. There would be two pins attached to the translation stage and two pin holes drilled into the base station. The user could then simply place the station onto the pins and it would be in the desired location. For this method to be effective, the pin holes in the base station would have to taper from larger to smaller the deeper in the base. This conical shape would be so that the user could easily put the base station on the pins but as the pins entered the station the taper would tighten around them and secure the base station in place. This method was not the easiest to machine, nor did it seem to be the best way to secure the base station tightly to the translation stage.

B. The next method was to use non-tapered placement pins and use a separate clamp to secure the base station to the translation stage. The pins would not have to be tapered, therefore easier to machine and the clamp would hold the base station in place better then the previously discussed method. However, all of the clamps looked at were not easily adaptable to the translation staged. This posed a problem that could be fixed with machining but was not logical due to time constraints.

47 C. The final method was to simply drill for holes placed equal distance around the base station’s center of mass, seen in the figure below, and use threaded rod and wing nuts to attach to the translation stage. This seemed the most logical and easiest method to fabricate. There is already a pre designed hole pattern in the translation stage and it four holes much easier to machine then tapered holes. This would save time and provide an effective clamping method.

Method C was chosen and has proven itself to be very effective and very easy to use. The wing nuts hold the stage in place at the holes shown in Figure 39 and attachment can be achieved in a minimal amount of time. As with all of the methods, this is simply a pre-positioning phase and the sample still needs to be adjusted when the lens is in place.

Holes

Figure 39: Holes in base station around center of mass

9.2 Attachment of Upper Chamber and Collar The upper chamber needed to be attached to the collar so that the assembly could move in the Z-direction. This was not initially welded in place, because positioning of this was critical and needed to be assessed when all of the parts were completed. When finally looking at the set up, it was determined that welding this piece together would not be the best method. Welding allowed for little error and no adjustment in a system that needed to constantly be fine tuned. It was decided that the best method would be to use set screws to hold the upper chamber in place. Because of the upper chamber’s weight, and the need to have a fairly repeatable position, a groove for the set screws was placed in the outer surface of the upper chamber. The screws would now be using not only friction to hold the upper chamber in place but the shear value of the screws. This modification also meant that the collar itself had to be modified. Three tapped holes (an example shown in Figure 40) were spaced evenly at 120° on center each way in the collar to mount the set

48 screws as seen in the figure below. The screws purchased are recessed into the collar so that the outside face is still flat and does not interfere with the Z-translation device.

Tapped Hole

Figure 40: Tapped hole in collar for set screws

9.3 Dry Zone Installment A gradient and/or dry zone needed to be created in the upper chamber between the objective lens and the outer face of the chamber. The first solution to this problem consisted of a slight vacuum seal in the inner portion of the upper chamber. This appeared to be more complicated then first thought and would be very time consuming. Also, a glass cover-slip is used on the outer face of the upper chamber so that the optics can have a clear viewing path. This glass cover-slip needed to be removable, so that if the viewing area became scratched or compromised it could be replaced. A vacuum seal would need to be done every time this cover slip was taken off. This method would be time consuming and difficult, so alternative methods were looked at. It was decided that a gradient and dry zone could be obtained by simply purging the inner portion of the upper chamber with nitrogen gas. For this to be accomplished, the upper chamber needs to have two ports, an inlet and outlet for the gas. Simple threaded brass valves were obtained and attached to the upper chamber, as seen in the figure below. Two holes were drilled and tapped in the upper chamber for the valves shown in Figure 41. Placement of these fittings was not critical, so the position of these holes were determined by the size and fit of the valves themselves.

49 Valves

Figure 41: Brass valves attached to upper chamber 9.4 Opening Skirt Notch The notch in the skirt, to be attached to the upper chamber, needed to be opened. Over sizing this notch would allow for more movement of the base station and compensate for any error in the skirt’s alignment on the upper chamber. If this notch was too small, or not properly aligned, the base station would not be able to align itself properly with the microscope objective lens and the whole sample would not be able to be imaged. The notch was simply opened up to 1.5 times the diameter of the tube passing through it and extended the whole length of the skirt (shown in Figure 42).

Notch

Figure 42: Notch in skirt

10.0 Boiling One of the main concerns with the current design is how the liquid nitrogen will behave in the dewar during imaging. Considering the cantilevered effect (see Figure 35) of this design and the extremely high magnifications used for imaging, any significant vibrations inside the dewar would seriously affect image quality and therefore the ability to accurately label points of interest on the sample. Because of this concern, the heat transfer characteristics of the dewar must be such that it prevents any kind of boiling that would adversely affect image quality.

50 10.1 Boiling Curve There are several different regimes of boiling that a given fluid can undergo, depending on the surface characteristics and temperature differential that the fluid is being subjected to. One of the most well understood fluids in relation to its boiling characteristics is water. The behavior of LN2 is less documented, and therefore its application in optical microscopy can only be related theoretically to the behavior of other fluids. Water is used here to illustrate the different types of boiling that can occur and shows the general interaction between a fluid and a surface causing it to boil. Shown in Figure 43 is the boiling curve for water.

CHF

Figure 43: Water boiling curve [18]

This curve shows four distinct heat transfer regions in which the water undergoes free convective boiling (black region below 1W/cm2), nucleate boiling, transition boiling, and film boiling. 10.1.1 Free Convective Boiling The first region shown is the calmest form of boiling. In free convective boiling, there is no active bubble formation. Instead, there is such a low heat flux that transfer can occur through the liquid until a vapor transition at the upper surface allows the heat to escape. The temperature differential at the contact surface is so small that bubble formation is not necessary. This form of boiling is most desired in applications of cryogenic microscopy because it does not introduce the vibrations caused by bubble formation, seen in other forms of boiling [19]. 10.1.2 Nucleate Boiling The nucleate region exhibits the most common characteristics of boiling. Shown below in Figure 44, nucleate boiling involves active bubble formation at the interface between liquid and a heated surface. The

51 vapor pockets produced then travel up through the fluid and escape to the surrounding atmosphere, generating a large disturbance in the process [19]. This type of boiling should be avoided wherever possible, as it is likely to introduce significant vibrations to a system, and distort any high magnification images being taken.

Figure 44: Nucleate boiling [20]

10.1.3 Critical Heat Flux Noted in Figure 43, the Critical Heat Flux (CHF) of a fluid is the point at which the maximum possible heat transfer is taking place. It is also the transition point between nucleate and transition boiling. The free convective boiling region and the CHF are offset by approximately a factor of 100 in the case of water. Considering this factor as a guidepost for liquid nitrogen behavior, the maximum allowable heat flux for free convective boiling can be related to the CHF for LN2, which is found to be in the range of 10-26 W/cm2 [21]. 10.1.4 Transition and Film Boiling The transition and film boiling regions noted on the graph are less commonly seen due to the very high temperature differential necessary to induce such rapid liquid to vapor conversion. Shown below in Figure 45, film boiling occurs when the contact surface is so hot that no liquid can be in direct contact with it without turning instantly to vapor. This creates a steady pocket or “film” of vapor between the heated surface and liquid. Transition boiling is simply a mix of nucleate and film boiling that occurs between the two regions [19].

Figure 45: Film boiling [22] 10.2 Cryo-Transfer Apparatus Early on in the project, the group was shown the current process for transferring the sample to be imaged into the TEM (see section 3.3.6). This involves a cryo-transfer apparatus (see Figure 10) that has been mimicked in the current design. In observing this transfer procedure, it appeared to the group that the boiling occurring in the liquid nitrogen dewar had calmed down enough that it was in the free convective boiling region. Under this assumption, the group proceeded to generate a similar dewar that would work in the current design and not introduce boiling disturbance to the system during imaging.

10.3 Thermal Modeling

After having the LN2 dewar (shown in Figure 46) machined out of PTFE, the group conducted thermal modeling to gain an understanding of what boiling behavior can be expected from this part.

Figure 46: PTFE dewar

From Figure 47 this initial heat transfer model simplifies the analysis by assuming that all internal wall temperatures are at liquid nitrogen temperature, and only considers heat transfer through the walls directly in contact with the liquid nitrogen. In addition, it does not consider the fin effect of the aluminum base.

53 This model results in a total heat flow of 9.47W and a maximum heat flux through the cylindrical wall of 2 q”max=0.081 W/cm . Though simplified, this model suggests that the system may calm to a steady state free convective condition because the maximum flux is less than the CHF by more than 2 orders of magnitude

(relating to the H2O relationship of 2 orders of magnitude).

Figure 47: PTFE heat transfer model

Values used in Calculations:

K p = K PTFE = 0.25W / mK

2 hair = 7W / m K

2 2 2 2 A1 = πR1 = π (1.25") = 4.9in = 3.16e − 3m

2 2 2 A2 = 2πR L = 2π (2.25")(1") = 14.1in = 9.13e − 3m

Steady State Heat Flux Analysis:

−1 −1 −1 ⎡⎛ ln(R / R ) 1 ⎞ ⎛ 2" 0.75" 1 ⎞ ⎤ R = ⎢⎜ 2 1 + ⎟ + ⎜ + + ⎟ ⎥ tot ⎢⎜ 2πK (1") h A ⎟ ⎜ K A K A h A ⎟ ⎥ ⎣⎝ p air 1 ⎠ ⎝ p 1 A 1 air 1 ⎠ ⎦

1 qtot = ()T∞ − TLN 2 Rtot

−1 ⎛ 0.0508m 0.01905m 1 ⎞ q = ⎜ + + ⎟ T − T = 2.05W 1 ⎜ ⎟ ()∞ LN 2 ⎝ K p A1 K A A1 hair A1 ⎠

−1 ⎛ ln(R / R ) 1 ⎞ q = ⎜ 2 1 + ⎟ T − T = 7.41W 2 ⎜ ⎟ ()∞ LN 2 ⎝ 2πK p (1") hair A1 ⎠

2 2 q1"= q1 / A1 = 648.7W / m = 0.065W / cm

55 2 2 q2 "= q2 / A2 = 811.6W / m = 0.081W / cm

2 ∴q"max = q2 "= 0.81W / cm

In addition to this analysis, the group looked at the transient effects of the system to find out how long it would take to reach steady state. Assuming a point mass (calculations shown below) for the PTFE dewar, the system would take 116 minutes to equilibrate and would require 1.98kg of LN2. The group turned to lab testing that would confirm or deny these assumptions and results.

Values Used in Analysis:

3 ρ LN 2 = 0.807g / cc = 807kg / m

CLN 2 = 2.042kJ / kgC

2 hair = 7W / m K

3 ρ PTFE = 2.16g / cc = 2160kg / m

CPTFE = 0.30kJ / kgC

V = π (2.25") 2 (4") − π (1.25") 2 (2") = 53.8in3 = 8.82e − 4m3

2 2 2 Aouter = π (2.25")(4") + π (2.25") = 72.5in = 0.0468m

Transient Analysis: ρCV (2160kg / m3 )(0.30kJ / kgC)(8.82e − 4m3 ) τ = = = 1740s c hA (7W / m 2 K)(0.0468m 2 )

4τ c = tss = 6960s = 116min

Δu = mCΔT = ρVC(225o C) = 128.6kJ

Considering LN2 latent heat of vaporization=198.38 kJ/kg

128.6kJ = 0.648kg 198.38kJ / kg

56 Considering heat flow in:

2 2 q"max = 0.081W / cm = 810W / m

2 2 qmax = q"max A = (810W / m )(0.0468m ) = 37.9W

uss = (37.9W )(6960s) = 263.8kJ

263.8kJ m = 0.648kg + = 1.98kg LN 2 198.38kJ / kg

10.4 Initial Testing Having boiling in the system as a key lingering question, the group conducted testing to understand if free convective boiling could be maintained, and if so how long it would take to achieve it. By placing the PTFE dewar as it would be in the current design (shown in Figure 48) onto the aluminum base, and filling it with liquid nitrogen, the group observed that aggressive nucleate boiling occurred with continued LN2 refills for over half an hour. These test results, coupled with the calculations showing extremely long settling times for a model that did not consider all heat transfer paths led the group to consider part modifications that would insulate the system.

Figure 48: PTFE dewar with aluminum base

57 10.5 Part Modifications and Further Modeling It was clear that any mass of PTFE that could be removed and replaced by a more insulating material would be beneficial in reducing conduction paths and overall heat transfer, as well as the amount of time required to reach steady state. Coupled with new concept development, the group looked to more rigorous heat transfer modeling, considering worst case fin effects of the aluminum base and the fin behavior of the lower portion of the PTFE dewar. 10.5.1 Initial Modification Concept Figure 49 shows a section view of one change considered and modeled to determine its feasibility. This modification involves coring out the area directly below the LN2 reservoir and replacing it with Styrofoam, as well as reducing the wall thickness directly surrounding the LN2 reservoir and again replacing the removed material with Styrofoam insulation. The heat transfer model (shown in Figure 50) considers conduction through the side walls, conduction directly down through the lower Styrofoam piece, and the fin behavior of the PTFE material left on the lower portion of the dewar. Instead of modeling the attached aluminum base as a fin, this model considers the worst case that the temperature at the base of the part is T∞ (i.e. the aluminum base is infinitely effective in transferring surrounding heat to the part). The resulting overall heat flow into the part is 8.3W. This is a slight improvement over the previously modeled 9.47W, but carries more weight as it represents a more accurate heat transfer model.

Figure 49: Cross-section of modified PTFE dewar

Figure 50: Circuit Model of Modification Concept 1

Calculations:

2 2 2 2 A1 = πR1 = π (1.25") = 4.9in = 3.16e − 3m

2 2 A2 = 2π (2.25")(1") = 14.1in = 9.13e − 3m

2 2 2 A3 = π (1.5") = 7.1in = 4.6e − 3m

−1 ⎛ 0.00635m ⎞ q = ⎜ ⎟ T − T 1 ⎜ ⎟ ()1 LN 2 ⎝ K p A1 ⎠

−1 ⎛ ln(R / R ) ln(R / R ) 1 ⎞ q = ⎜ 2 1 + 3 2 + ⎟ T − T 2 ⎜ ⎟ ()∞ LN 2 ⎝ 2πK p (0.0254m) 2πK s (0.0254m) hair A2 ⎠

⎛ 0.00635m 0.0381m ⎞ R = ⎜ + ⎟ = 314.8K /W Li ⎜ ⎟ ⎝ K p A1 K s A3 ⎠

59 ⎛ ⎡ R + R ⎤ ⎞ ⎜ ⎛ 3 2 ⎞ ⎟ ln⎢⎜ ⎟ / R1 ⎥ ⎜ ⎣⎝ 2 ⎠ ⎦ 1 ⎟ R = + = 30.03K /W Lo ⎜ 2πK (0.0127m) mK A tanh(mL) ⎟ ⎜ p p c ⎟ ⎜ ⎟ ⎝ ⎠

hp (11W / m 2 K)2π (0.0572m) Where −1 m = = 2 2 = 52.6m K p Ac (0.25W / mK)π[(0.057m) − (0.0381m) ]

2 2 Ac = π (R3 −1.5 ) , h = hair , p = 2πR3

−1 ⎛ 1 1 ⎞ ⎜ ⎟ Req = ⎜ + ⎟ = 33.2K /W ⎝ RLi RLo ⎠

−1 ⎛ 1 ⎞ ⎛ 0.00635m ⎞ q = q + q + T − T = q + ⎜ + 33.2K /W ⎟ T − T = 8.3W tot 1 2 ⎜ ⎟()∞ 1 2 ⎜ ⎟ ()∞ LN 2 ⎝ 33.2K /W ⎠ ⎝ K p A1 ⎠

10.5.2 Final Modification Concept Looking to further improve the overall insulation of the part and move forward with testing, the group developed the final concept shown in Figure 51. This design is similar to modification concept 1 except that it reduces PTFE wall thickness, adds a deeper bore to the LN2 reservoir for greater capacity and reduces the lower portion to four legs instead of a full cylinder. This serves to give the part better overall heat sinking with the larger reservoir, greater thickness of insulation around the LN2 region, and minimizes the fin effects of the lower PTFE section by reducing its cross-sectional area and perimeter. Modifying the previous calculations for these changes demonstrates that the overall heat flow into the part is 3.08W, which is a great improvement over the previous designs.

Figure 51: Modified PTFE dewar

Calculations:

2 2 2 2 A1 = πR1 = π (1.25") = 4.9in = 3.16e − 3m

2 2 A2 = 2π (2.25")(1") = 14.1in = 9.13e − 3m

2 2 2 A3 = π (1.5") = 7.1in = 4.6e − 3m

hp (11W / m 2 K)(2 / 3)π (0.0572m) Where −1 m = = 2 2 = 52.6m K p Ac (0.25W / mK)(1/ 3)π[(0.057m) − (0.0381m) ]

1 2 A = π (R 2 −1.52 ) = 0.0019m 2 , h = h , p = πR = 0.1197m c 3 3 air 3 3

⎛ 0.00238m 0.0191m ⎞ R = ⎜ + ⎟ = 309.8K /W Li ⎜ ⎟ ⎝ K p A1 K s A3 ⎠

⎛ ⎡ R + R ⎤ ⎞ ⎜ ⎛ 3 2 ⎞ ⎟ ln⎢⎜ ⎟ /(0.1R1 )⎥ ⎜ ⎣⎝ 2 ⎠ ⎦ 1 ⎟ R = + = 176.1K /W Lo ⎜ (2 / 3)πK (0.0381m) mK A tanh(mL) ⎟ ⎜ p p c ⎟ ⎜ ⎟ ⎝ ⎠

61 −1 ⎛ 1 1 ⎞ ⎜ ⎟ Req = ⎜ + ⎟ = 112.3K /W ⎝ RLi RLo ⎠

−1 ⎛ 0.00238m ⎞ q = ⎜ ⎟ T − T 1 ⎜ ⎟ ()1 LN 2 ⎝ K p A1 ⎠

−1 ⎛ ln(R / R ) ln(R / R ) 1 ⎞ q = ⎜ 2 1 + 3 2 + ⎟ T − T = 1.13W 2 ⎜ ⎟ ()∞ LN 2 ⎝ 2πK p (0.0254m) 2πK s (0.0201m) hair A2 ⎠

−1 ⎛ 0.00238m ⎞ ∴q = q + ⎜ +112.3K /W ⎟ T − T = 3.08W tot 2 ⎜ ⎟ ()∞ LN 2 ⎝ K p A1 ⎠

10.6 Further Testing Having settled on the final modification concept, the group had the part machined and again conducted testing to compare improvement in boiling behavior. After cutting form fitting pieces of insulation to replace the cored out material, the group again poured liquid nitrogen into the PTFE dewar and tested boiling behavior and temperature at critical locations. Several key observations came out of this testing, including the following:

1) The reservoir of liquid nitrogen does not reach a steady state of convective film boiling. After the level of liquid nitrogen evaporates below the aluminum insert, the system is almost entirely quiescent except for the inner wall of the aluminum insert in the lower chamber, where there is relatively calm nucleate boiling. One potential ramification of this is that the group may have been mistaken in assuming that the current cryo-transfer apparatus totally eliminates nucleate boiling. It

is only necessary in the transfer step for the LN2 to be calm enough for transfer, which could easily have been carried out in the environment shown in this testing. Without close inspection, the group could not tell whether or not nucleate boiling was going on underneath the aluminum insert during the sample transfer.

2) The time constant of the system is greatly reduced (steady state reached in 10-15 minutes).

3) Placing a thermocouple at the sample location shows good temperature control while the LN2 is

boiling below the aluminum insert, maintaining the environment around -175°C. After the LN2 boils off, the temperature is controlled below -140°C for approximately 5 minutes.

62 4) The fact that the sample area is maintained below the critical temperature for vitreous ice some

time after the boil off of LN2 means that the sample may be kept cold without the presence of liquid nitrogen, conceivably for the amount of time required to image a sample. This means that, assuming the boiling seen below the aluminum insert introduces enough disturbance that the sample cannot be imaged during that cooling period, a thermal mass could be put in place to heat

sink from the sample region after the LN2 boils away. This heat sink could act to increase the 5 minute window of imaging opportunity to give the microscopist maximum time to view the sample without vibrations.

5) It should be noted that this testing was carried out with the PTFE dewar exposed to free air, whereas the actual application has the part shrouded with the pre-cooled upper assembly and skirt.

With these observations in mind, the group turned to more quantitative testing methods and setting up the optical equipment and camera so that it can be determined whether or not the boiling in the current PTFE dewar will significantly distort the image, and if so whether or not the addition of a thermal mass will address the issue by removing boiling liquid nitrogen from the situation altogether.

11.0 Continued Testing In order to better understand the exact behavior of the current setup in imaging situations, the group conducted further testing to determine the time dependence of temperature at key locations in the structure. By simulating an imaging situation, temperature data can be obtained that accurately represents the thermal performance of the group’s final design. The key variables introduced in this testing are: 1) the shrouding effect of the upper assembly and skirt, 2) pre-cooling of the upper assembly, 3) the effect of the cold lens and its fin behavior, potentially carrying heat to the sample, 4) the use of a secondary LN2 reservoir that is ported into the skirt and acts to purge the area with gaseous nitrogen, 5) variation in the amount of thermal mass within the LN2 reservoir, 6) the presence of the cold finger.

11.1 Test #1 In the first test used to obtain temperature data for the system, the upper assembly was monitored during pre-cooling, and the sample location, as well as between the dewar and skirt were monitored during the imaging simulation. The lens was not in place during this testing, but a thermocouple was held in the space it would occupy in the assembly (Figure 52). At 33 minutes into the pre-cooling test, a nitrogen flush was added to the system. In the pre-cool results shown below (Figure 53), the blue line gives the temperature at the objective lens position, and the pink line shows the temperature in the upper chamber (above objective lens in upper assembly).

63 T2: Upper Chamber (pink line)

T1: Lens Postion (blue line)

Skirt Dipped Into LN2 Dewar

Figure 52: Temperature Positions of Pre-Cool

Temperature (C) 10

0 0 5 10 15 20 25 30 35 40 45 Time (min ) Figure 53: Pre-Cool of Upper Assembly

64 This pre-cool test shows that both the upper chamber and lens position stay well above LN2 temperature after 40+ minutes of having the skirt dipped into liquid nitrogen. The main concern that this introduces is the effects of the lens as a thermal fin, delivering heat to the sample. It should also be noted that the relatively large drop in temperature at ~30 minutes corresponds to the introduction of a nitrogen flush.

After the pre-cool was complete, the assembly was placed into imaging position and the thermocouples moved to measure the temperature at the sample location and in the space between the PTFE dewar and the

outer skirt (Figure 54). As shown, the only mass within the LN2 dewar was the aluminum insert, and the rest was filled with liquid nitrogen.

T1: Sample Postion T2: Inside Skirt (blue line) (pink line)

Figure 54: First Test Imaging Thermocouple Positions

The temperature results (shown below, Figure 55) indicate that the position between the skirt and PTFE dewar remains relatively constant around –10°C to –20°C. The sample position on the other hand has large, incremented changes with time. At around 6 minutes into the test, a large increase in temperature from – 180°C to –100°C occurs. It is hypothesize that this corresponds to the point at which the liquid nitrogen boils down so that it is no longer in contact with the aluminum insert, but only occupies the cored out space below in the PTFE dewar. By removing contact, the direct conduction path is lost and heat transfer must occur through the PTFE part (relatively insulating) and by convection through the nitrogen gas. In addition to this large jump in temperature, another one occurs at approximately 12 minutes into the test in which the

65 temperature goes from –100 to almost –20 degrees Celsius. This change is thought to correspond with the total evaporation of liquid nitrogen.

It should be noted that during this test, boiling was heard for the first 5.5 minutes of testing, and then not thereafter. This supports the hypothesis above when considering that the LN2 only tends to boil on the inner wall of the aluminum insert. When the nitrogen level lowers to the cored out section below the aluminum insert and is no longer in contact, the boiling regime changes to free convection.

0 02 46 810121416 -20

-40

-60

-80

-100

-120 Temperature (C) -140

-160

-180

-200 Time (min) Figure 55: Test One Temperature Results

66 11.2 Test #2 The second test carried out served to measure the effects of an added thermal mass below the aluminum insert. The upper assembly was pre-cooled for 15 minutes in this case, but the temperatures were not monitored. This test also includes a continuous nitrogen flush through a port in the skirt. Another difference in this test is that the objective lens was in position. Figure 56 shows the thermocouple locations for this test.

T1: Sample Position T2: Lens Position (blue line) (pink line)

0.75” Thick 1.5” Diameter Copper Slug

Figure 56: Test Two Thermocouple Positions

Shown below are the temperature results (Figure 57). This test indicates that the sample temperature is not greatly affected by the presence of the cold lens, as the plot shows the two to be offset be a large differential and relatively independent of one another. This configuration maintains a colder temperature at the sample position for a longer period of time than in the first test, not reaching –100 degrees Celsius until almost 15 minutes into the test. Another interesting observation here is that the temperature of the copper slug underneath the aluminum insert was measured at the end of the test and found to be much lower than the sample position. When the sample position was measuring around –60°C, the copper slug was at – 115.4°C. This temperature difference indicates that the heat sinking ability of the thermal mass was not used to its full extent, most likely due to the fact that there was a slight separation between the copper slug and the aluminum insert.

67 0 0 5 10 15 20 25 30 35

-50

-100 p() Temperature (C) -150

-200

-250 Time (min) Figure 57: Test Two Temperature Results

11.3 Test #3 Continuing on with the concept of using a thermal mass as a heat sink to the sample position, the group carried out the third temperature test. In this test there was a lens in position, constant nitrogen purge, and 10 minute pre-cool of the upper assembly. The main difference here is that an additional copper mass was put in place, and the three elements inside the PTFE dewar (aluminum insert and two copper masses) were

pre-cooled by being totally submerged in a dewar of LN2 for over 10 minutes prior to testing. Figure 58 shows the thermocouple positions for this test.

68 T1: Sample Position T2: Lens Position (blue line) (pink line)

Added Copper Mass Sitting in Aluminum Insert

Figure 58: Test Three Thermocouple Positions

The temperature results for this test show a much more drastic improvement, maintaining the sample below –140 degrees Celsius for over 11 minutes (shown in Figure 59). This is likely due to the fact that the additional thermal mass was placed in direct contact with the aluminum insert, and that all three inner

components were pre-cooled to ensure LN2 temperature throughout. The temperature is kept almost constant for the first three minutes of testing, but begins a gradual rise thereafter. This is likely the point at

which all LN2 in the system boils off. It also makes sense that this boil off would occur quicker than in the first test because there is a lesser volume of liquid nitrogen in the system with a good deal of the lower chamber being occupied by the copper slug.

69 0 0 5 10 15 20 25 30

-50

-100

Temperature (C) -150

-200

-250 Time (min) Figure 59: Test Three Temperature Results 11.4 Test #4 At this point in the testing, the group was able to obtain a cold finger assembly that had been out of use at Brandeis University. The test was run in the same manner as Test #3, but with the pre-cooled cold finger in place. The sample position was the only temperature measured in this case, and the thermocouple was placed in direct contact with the tip of the cold finger (shown in Figure 60).

T1: Sample Position (blue line)

Figure 60: Test Four Thermocouple Position

The temperature results for this test (shown below Figure 61), reveal that the cold finger actually has a negative effect on the sample temperature. In this case, the sample position temperature rose about –140°C in less than 5 minutes. However, the cold finger used had a problem with the vacuum sealed chamber, which is why it had not been used for years at Brandeis. Because of this defect, the cold finger reservoir became covered in frost and was likely not sinking heat from the tip as affectively as can be expected with a fully functional unit. Therefore, these results cannot be used as a direct comparison to behavior expected in actual use.

0 0 5 10 15 20 25 30

-50

-100

-150 Temperature (C)

-200

-250 Time (min) Figure 61: Test Four Temperature Results 11.5 Test #5 The final test conducted takes the concept of a thermal mass to heat sink the sample position to an extreme. In this case, the upper assembly was pre-cooled, the nitrogen flush was in place, but the PTFE dewar was filled entirely with the two copper masses previously used and copper-coated lead BBs. By filling the entire reservoir with porous thermal mass, it can be determined whether or not a design based solely on a massive

heat sink to the sample position is viable. Again, the copper pieces and BBs were pre-cooled in an LN2 dewar and then placed in the PTFE dewar with LN2 filling the gaps. The temperature results are shown below (Figure 62).

71 0 0 5 10 15 20 25 30

-50

-100 (C)

Temperature -150 Temperature (C)

-200

-250 Time (min) Figure 62: Test Five Temperature Results

As shown in this plot, the thermal characteristics of the system are greatly improved using a thermal mass in place of a full volume of LN2. The point at which the temperature begins to rise around 4 minutes into the test is when the nitrogen boil off is complete, and the sample temperature is maintained below –140 degrees Celsius for over 16 minutes. Maintaining this sample temperature is a great improvement over test #3, and is certainly far better than test #1. The main complication introduced by using a heat-sink rather than an LN2 reservoir is the loss of a continuous flush of gaseous nitrogen that keeps the sample in a dry region. However, this can be overcome by using an external reservoir for boil off that is then ported into the sample location, keeping the area dry.

12.0 Imaging After assembling the prototype and aligning the optical components, the group tested the external microscope to determine whether or not a satisfactory image could be obtained from it. Due to the lack of time and the unavailability of an electron microscopist, a fluorescently labeled virus specimen blotted on a grid could not be obtained. To compensate for this, an imaging target and an optical mirror were used for these tests and were placed on the aluminum insert at the sample position. During this imaging process, the group received valuable advice and guidance from Antoine van Oijen, an Assistant Professor at Harvard Medical School.

For initial image testing, the group decided to use a 40x magnification objective lens instead of the 80x lens that will be used for imaging the sample. Except for the magnification, this lens was almost identical to the 80x lens. Because of the fact that the objective lenses take a long time to arrive after the order has been

72 placed, the group did not want to risk damaging the 80x lens during the testing process. The group was assured that if images can be obtained from the 40x lens, they can definitely be obtained from the 80x lens as well.

The purpose of using the optical mirror was to determine the extent to which the laser light, which will be used to excite the fluorophores, is reflected back along the same optical path into the CCD camera. The imaging target was used to capture an actual image, and thus determine the resolution of the objective lens and the microscope The results from these initial imaging tests were very promising. The group was able to get several images from both the resolution target and the optical mirror, thus proving that a functional microscope prototype had been built. A few of these images are shown below.

12.1 Optical Mirror Images

φ=10.2 microns

Figure 63: Unfocussed Image

Figure 63 shows the first image that was captured by the CCD camera. It is an image of the laser light being reflected back from an optical mirror with a diameter of 12.7mm. This light originated from the laser, and after passing through the excitation filter, dichroic beamsplitter, a set of mirrors, and the objective lens, hit the optical mirror placed in the sample position. From there it was reflected back through the objective lens, mirrors, dicroic beamsplitter, collimating lens, emission filter, and finally into the CCD camera where the image was captured (See Figure 37).

As seen in this figure, the image appears to be blurry and indistinct. Looking closely, one can see various “rings” formed around the center of the image. This is due to the fact that when this image was taken, the microscope was not fully focused. The spherical aberrations that resulted in the objective lens caused this blurriness, and the formation of the “rings”. A spherical aberration is an image imperfection that results due to the increased refraction of light rays that hit the edge of the lens as compared to the rays that hit the

73 center of the lens [24]. In order to eliminate these spherical aberrations, the distance between the objective lens and the optical mirror was adjusted so that the mirror was within the working distance of the lens.

φ=7.4 microns

Figure 64: Partially Focussed Image

Figure 64 shows an image while this focusing is taking place. It clearly shows how the spherical aberration is decreasing, and the rings are “merging” together closer to the center of the image. Figure 65 shows the image when the optical mirror is in full focus. Here the spherical aberration is at a minimum, and no such rings can be seen.

φ=2.7 microns

Figure 65: Fully Focussed Image

74 12.2 Resolution Target Images Figure 66 shows an image of the resolution target obtained from the optical microscope.

10 micron spacing between lines

Figure 66: Image of Resolution Target

The resolution target used was a thin slide of glass etched with parallel lines. There were 100 lines per millimeter on the target, thus making the spacing between these lines 0.01x 10-3 mm, or 10 microns.

13.0 Conclusion This Capstone project resulted in the construction of an optical microscope and a cooler that maintains the sample under -140oC for approximately 10-15 minutes. The designed microscope consists of: manual x-y and z translators, a dewar with an outer insulating skirt, a system that continuously flushes gaseous nitrogen throughout the container, and custom optics coupled with a cryogenic air lens. This has been accomplished with specific feedback from end users (microscopists) and is compatible with the existing TEM cold finger. Testing of the microscope has generated many modification suggestions and the next steps to proceed with the goal of the project outlined in the following section.

14.0 Recommendations This Capstone project was established for the purpose of proof of concept. The sponsors required a prototype of the cryogenic optical microscope which could be used to obtain an image of the sample grid, while keeping the grid below -140oC. This image would then be used for comparison with the image from the TEM.

As the semester comes to a conclusion, the group believes that it has successfully built a prototype which is capable of capturing images of the sample grid. Some images obtained from the prototype have been shown

75 in Section 12.0. The prototype built allows for easy transfer of the sample from the Vitrobot to the optical microscope, and then from the optical microscope to the TEM. Thus two of the most important design requirements have been satisfied.

However, due to time constraints, the group was unable to fully satisfy some of the other design requirements of the project. For example as Test # 3 in Section 11.3 shows, the maximum time that the prototype was able to keep the temperature of the sample area below -140 oC was approximately 12 minutes. While this does provide a window of time for imaging, the more time available the more images produced, resulting in better quality data.

In order to achieve these requirements and to optimize the time-consumption and accuracy of the process, some improvements to the design have been suggested. These suggestions are explained below in detail.

14.1 Thermal Mass Concept Section 12.0 gives the results of the thermal testing of the prototype. Test 2 was conducted by placing a thermal mass of copper underneath the aluminum insert. This resulted in the sample area being under the desired temperature of -140oC for approximately 3.5 minutes. In order to increase this time period, another similar copper mass was incorporated in Test 3. Both these thermal masses were pre-cooled to liquid nitrogen temperature. This test resulted in the sample area being below the desired temperature for about 10 minutes. To further increase this time duration, in Test #5 the aluminum insert was removed and the entire chamber was filled with copper coated BBs. The result was an increase in the time duration from 10 to 16 minutes.

Using the results from these tests, the group has concluded that in order to maximize the time below the desired -140oC, the aluminum insert present in the current design should be eliminated and be replaced with a modified one made out of copper. CAD models of both the current aluminum and the modified copper inserts are shown in Figure 67.

Figure 67: Image of Resolution Target

76 Because copper has a higher heat capacity than aluminum, it can maintain its temperature longer. If both the aluminum and the copper inserts were pre-cooled to liquid nitrogen temperature, the aluminum insert would gain heat faster, and return to room temperature quicker, than the copper insert after both were removed from the liquid nitrogen. Therefore if the insert is made out of copper, it will keep the sample at the desired temperature for a longer period of time.

In addition to being made out of copper rather than aluminum, the modified insert shown in Figure 67. will also be longer and more massive than the current one. Instead of being shelled out from the bottom, it will be a solid that occupies most of the space inside the chamber. This will result in an increase in the time that the sample will be at the desired temperature.

14.2 Automated Stage Scanning The microscope will use an x-y translator to image different locations of the sample grid (see section 8.2). Because of budget constraints, the group has used a manual translator for the prototype. The drawback is that after every image, it would require the technician to manually adjust the position of the sample relative to the objective lens. If the technician were to do this, it would take a long time for the entire grid to be imaged and consequently would make the sample unusable because of the melting of vitreous ice. For this reason, the x-y translator will need to be automated. Several such translators exist and are currently used in research labs for automated stage scanning.

14.3 Z-Translator In addition to the x-y translator used to move the sample around for imaging, the microscope prototype is also equipped with a z-translator for vertical motion of the chamber consisting of the objective lens. At present, a dovetail translator is being used, which has both coarse and fine movement capability. However this too is a manual translator. In order for the sample to be in full focus, the distance between the sample and the objective lens must be shorter than the working distance of the lens. Being a manual translator, it would be difficult to consistently place the objective at the exact height, each time a sample needs to be imaged. In order to provide this consistency and ensure the proper imaging distance, an electronic computerized translator will be required in the actual microscope.

14.4 CCD Camera The camera that has been used in the project until now is suitable for the prototype of the cryogenic optical microscope. However, because various laboratories could benefit from such a microscope, the sponsor intends to commercialize it in the future. In that case, a more powerful CCD camera is required.

One such model that has been taken into consideration is the Hamamastu electron-multiplying CCD. It has an adequate signal-to-noise ratio for single molecule fluorescence imaging. With an 80x magnification

77 objective lens, similar to the one the group is using, there would be 3 pixels per single-molecule spot. This would be perfect for centeroid determination of the fluorescently labeled virus particle. In addition the 100 x 100 micron2 field of view on the camera would allow the entire sample grid to be mapped using close to 400 images in approximately one minute (with automated stage scanning) [23].

14.5 Encasing Optical Components In the current prototype the optical components (including lenses, mirrors, and filters) have been mounted on a breadboard. The positioning of these components is crucial in obtaining a satisfactory image. (See Section 8.4, Figure 37). This is because each component has a certain purpose, and in order for it to serve that purpose correctly it has to be in a precise location. For example, the excitation filter has to be placed directly in front of the laser. Similarly the dichroic beam splitter has to be at an angle of exactly 45o for it to reflect the illumination light and transmit the emission light.

Although the positioning of these components is not difficult and is done on a regular basis in research labs, it is however time consuming. Each time the objective lens is raised and then lowered, it requires adjustment of the three sets of mirrors, and consequently adjustment of the remainder of the components. In order to eliminate this need for repeated adjustment, all of the optical components will be encased into a single chamber in such a way that their positions will not change relative to one another during subsequent imaging sessions.

As stated earlier, all these desired improvements will make the use of the microscope easier and faster. This will result in ease of use for the technician, and an increase in image quality. The sponsors at Harvard Medical School have decide to fund another Capstone group that will work on these and other aspects of the microscope, as phase II of the project.

78 15.0 REFERENCES [1] Bernius; Mark T. (Ithaca, NY); Morrison; George H. (Ithaca, NY), “Cryogenic sample stage for an ion microscope”, U.S. Patent 4,663,944, May 12, 1987. [2] Hayward; Steven B. (Berkeley, CA), “High Resolution Electron Microscope Cold Stage”, U.S. Patent 4,262,194, April 14, 1981.

[3] Diller; Kenneth R. (Austin, TX); Walcerz; Douglas B. (Medford, NY), “Freezing/Perfusion Microscope Stage”, U.S. Patent 5257128, August 4, 1989.

[4] FEI Company: Tools for Nano-Technology, http://www.feicompany.com/systems/product.aspx?id=217&m=2&reloaded=true, last accessed February 22, 2007. [5] “Curo-Freezing the Sample”, Electron Microscopy for Dummies, http://cryoem.berkeley.edu/~nieder/em_for_dummies/freeze.html, last accessed February 22, 2007. [6] “What is the S.E.M”, Department of Material Science, Iowa State University, http://mse.iastate.edu/microscopy/whatsem.html, last accessed February 22, 2007. [7] Dennis Kunkel Microscopy, Inc. Education Web Site, http://education.denniskunkel.com/catalog/product_info.php?products_id=75, last accessed February 22, 2007. [8] Morgue File, http://morguefile.com/archive/?display=96350&, last accessed February 22, 2007. [9] Nikon Microscopy U, “Basic Concepts and Formulas in Microscopy-Resolution”, http://www.microscopyu.com/articles/formulas/formulasresolution.html, last accessed April 10, 2007. [10] Olympus Microscopy Resource Center, “Refraction of Light”, http://www.olympusmicro.com/primer/lightandcolor/refraction.html, last accessed February 22, 2007. [11] Nikon Microscopy Interactive Java Tutorials ,“Numerical Aperture Light Cones”, http://www.microscopyu.com/tutorials/java/objectives/nuaperture/index.html, last accessed February 22, 2007.

[12] Nikon Microscopy U, “Basic Concepts and Formulas in Microscopy-Refractive Index”, http://www.microscopyu.com/articles/formulas/formulasri.html, last accessed February 22, 2007.

[13] Nikon Microscopy Interactive Java Tutorials, “Objective Working Distance”, http://www.microscopyu.com/tutorials/java/workingdistance/index.html, last accessed February 22, 2007. [14] Nikon Microscopy Interactive Java Tutorials ,“Numerical Aperture”, http://www.microscopyu.com/articles/formulas/formulasna.html, last accessed April 10, 2007. [15] Wikipedia, The Free Encyclopedia, “Amorphous Ice”, http://en.wikipedia.org/wiki/Very_high_density_amorphous_ice, last accessed February 22, 2007. [16] PVT Diagram of Water,

79 http://www.nims.go.jp/water/L_wtarepd.html, last accessed February 22, 2007. [17] Chroma Technology, http://www.chroma.com/resources/PDF_files/handbook4.pdf, last accessed February 22, 2007. [18] Alam Thermal Solutions, http://www.alamthermal.com/thermoloop.html, last accessed April 10, 2007. [19] Incropera, Frank P. et al. (2007). Introduction to Heat Transfer (5th ed.). Hoboken, NJ: Wiley & Sons, Inc. [20] ESA “What is fluid physics?”, http://www.spaceflight.esa.int/users/fluids/intro_physics.htm, last assessed April 10, 2007. [21] Ye, Hua et al. (2006). Numerical Thermal Simulation of Cryogenic Power Modules Under Liquid Nitrogen Cooling. Journal of Electronic Packaging, Vol. 128, 267. [22] Department of Nuclear Engineering, UC Berkeley, http://www.nuc.berkeley.edu/thyd/ne161/rahmed/fig3.gif, last assessed April 10, 2007. [23] van OIjen, Antoinne, Personal Interview, January 25, 2007. [24] Wikipedia, The Free Encyclopedia, “Spherical Aberration”, http://en.wikipedia.org/wiki/Spherical_aberration, last assessed April 15, 2007.

80 16.0 APPENDIX A

81 16.1 Design Concept #1 Thermal Model A-1

Rough Circuit Analogy-Initial Staging Idea Known: K, LN2 K, N2 h, air K, glass T, inf. T, LN2 D, inner D, outer 0.14 9.58E-03 7 1.4 22 -200 0.005 0.04

Level 0 to 1 1 to 2 2 to 3 3 to 4 4 to 5 5 to air

K, left *** *** *** 9.58E-03 1 *** L, left *** *** *** 0.00075 0.001 *** 6.19E- A, left *** *** *** 6.19E-04 6.19E-04 04

K 0.14 1.4 9.58E-03 9.58E-03 1.4 *** L 0.0005 0.001 0.00075 0.00075 0.001 *** 1.96E- A 1.96E-05 1.96E-05 1.96E-05 1.96E-05 1.96E-05 05

K, right *** *** *** 9.58E-03 1 *** L, right *** *** *** 0.00075 0.001 *** 6.19E- A, right *** *** *** 6.19E-04 6.19E-04 04

R, left *** *** *** 126.58 1.62 230.97 R 181.89 36.38 3987.18 3987.18 36.38 7275.65 R, right *** *** *** 126.58 1.62 230.97

R, tot q, tot R, inf-3 T3 q, C q, B q, A 4382.22 0.0507 176.774 13.0448 0.0249 0.000793 0.0249

T, 5UL 16.2411 T, GU 16.2337 T, 5UR 16.2411

82 16.2 Intermediate Design Thermal Model A-2

7 14 RA = ∑ Ri and RB = ∑ Rj i=1 j=8

1 1 L3 + L5 L2 L1 / 2 L1 / 2 RA = + + + + + hairA2 hrA2 KgA2 KoA2 KN 2 A2 KN 2 A1

1 1 L3 + L5 L2 + L1 RB = + + + hairA3 hrA3 KmA3 KN 2 A3

−1 −1 −1 RTOT = []RA + RB

[]T∞ − Tsample qTOT = = q A + qB RTOT

[]T∞ − Tsample [T∞ − Tsample] where, q A = and qB = RA RB

[]T∞ − Tg,1, u [T∞ − Tm,1, u] Next, q A = and qB = 1/ h∞A2 1/ h∞A3

Therefore,

q A T g ,1, u = T ∞ − h ∞ A 2

q B T m ,1, u = T ∞ − h∞ A 3

84 Numerical Values:

o T∞ = 22 C = 295K o Tsample = −196 C = 77K W Kg = 1.4 mK W KN 2 = (9.58e − 3) mK W Km =16.3 (Assuming Stainless Steel) mK W Ko =16.3 (Assuming Stainless Steel) mK W h = 7 ∞ m 2 K

2 2 2 2 W hr = εσ (Tm,1, L + Tm,2, u)(T m,1, L + T m,2, u) = (1)(5.67e − 8)(293 + 103)(293 + 103 ) = 2.17 m 2 K o o Assuming ε =1, Tm, i, L = 20 C = 293K,..and..Tm,2, u = −170 C =103K L1 =1mm L2 = 44mm L3 = 5mm L4 =10mm L5 = 5mm

Dsample ≅ 3mm

Dobjective ≅ 30mm

Dcoldstage ≅ 100mm

2 2 A1 = Asample = (π / 4) * D sample = (7.07e − 6)m 2 2 Therefore, A2 = Aobjective = (π / 4) * D objective = (7.07e − 4)m 2 2 A3 = Acoldstage = (π / 4) * D coldstage = (7.85e − 3)m

85 Results:

Known Thermal Conductivities K_glass k_N2 k_material k_objective 1.4 W/mK 0.00958 W/mK 16.3 W/mK 16.3 W/mK

Known Lengths L1 L2 L3 L4 L5 0.001 m 0.044 m 0.005 m 0.01 m 0.005 m

Known Temperatures and Conv. Coefficients T_inf T_sample h_inf 295 K 77 K 7 W/m2K

Known Areas A1 A2 A3 7.07e-6 m2 W/mK 7.07e-4 m2 7.85e-3 m2

Radiation Coefficients Emissivity S.B. Constant Tm,1,L Tm,2,u h_rad 1 5.67e-8 293 K 103 K 2.165791 W/m2K

Individual Resistances R1 R2 R3 R4 R5 R6 R7 202.10 K/W 5.05 K/W 653.21 K/W 5.05 K/W 3.82 K/W 73.84 K/W 7383.67 K/W R8 R9 R10 R11 R12 R13 R14 18.19 K/W 0.04 K/W 58.79 K/W 0.04 K/W 584.79 K/W 6.65 K/W 6.65 K/W

Addition of Resistances R_A R_B R_tot 8326.74 K/W 675.13 K/W 624.50 K/W

Rates of Heat Flow q_A q_B 0.026181 W 0.322900 W

Surface Temperatures Tg_1_u Tm_1_u 289.71 K 289.13 K 16.71 oC 16.13 oC

86 16.3 Deflection due to Vibration A-3

Unforced vibration of slab on top of xy translator without bearings:

Assume cantilevered beam with a cross-section of 5 x 1:

3EI k = eq L3

bh 3 5 I = = in 4 12 12

6 Ealu min um = 10.3*10 psi

L = 7.5"

5 3(10.3*106 )( ) lb k = 12 = 30520 eq 7.53 in

Total weight of system=20 lbs Only looking at half Æ m=10 lbs

k rad ω = = 55 n m s

π t = = 0.0571Hz ωn

.. . m x(t) + c x(t) + kx(t) = F(t) Æ kx = mg

87 lb in ft 30520 *12 x = 10lb *32.2 in ft sec2

x = 8.79*10−4 ft = 0.0106"deflection due to unforced vibration