Hydrogen Properties for Energy Research (HYPER) Lab Brandt Pedrow’s Posts

Discovery and Origins – J. Willard Gibbs

Josiah Willard Gibbs, born in 1839, was deemed by Einstein as “the greatest mind in American history.” Gibbs primarily focused on physical chemistry and its chemical reaction relationship with thermodynamics. During the years 1876-1878, he published the famous “On the Equilibrium of Heterogeneous Substances” in the Transactions of the Connecticut Academy of Arts and Sciences. He will later earn the most prestigious international science award in its time, the “Copley Medal of the British Royal Society” in 1901. Within the publication, the discovery of free energy emerged; now known as Gibbs free energy1. Gibbs described this energy as:

“The greatest amount mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition.”

This “mechanical work” or energy can be thought of as the maximum amount of non-expansion work extracted from a closed system. The work done is at the expense of the internal energy of the system and any portion of the work not extracted is lost to the environment in the form of heat.

His discovery led to the development of quantum mechanics, further discoveries in theoretical physics, and in statistical mechanics.

Gibbs Free Energy

Gibbs free energy is usually expressed as:

The fundamental property relation can then be expressed as:

Where h is the enthalpy, T is the temperature, and s is the entropy, P is the pressure, and v is the specific volume.

The Gibbs fundamental property relation equation (dg) shows the most commonly used form of the Gibbs Free Energy Equation. Gibbs is most useful being in terms of temperature and pressure. This is because the ability to quantify entropy and -enthalpy pose to be a much more complicated task.

Although the Helmholtz Free Energy Equation is the most used fundamental property relation, Gibbs’ equation is still used primarily by chemists and physicists. Its primarily uses are to determine:

1. The chemical potential
2. Electrochemical properties of fluids
3. Excess enthalpies of fluid mixtures
4. Equilibrium properties of fluids when the temperature and pressure of the system is known

The dg predicts the direction of the chemical reaction and tells whether the reaction is spontaneous or nonspontaneous; meaning, whether the reaction may occur with or without applied external energy to the system. Note that a negative dg between two phases does not guarantee that a phase change will happen quickly, or even at all! At atmospheric temperature and pressure a diamond is NOT the lowest Gibbs energy state, however metastability means that it will take a time that is comparable with the duration of the universe before it will turn back into its Carbon form. The same can be seen in supercooled liquids below the freezing point, where an impurity or energy inputs can cause it to rapidly freeze. The use of a catalyst, impurities, or seed crystals can significantly lower the dg necessary to instigate a phase change. This is an important concept in interfacial phenomena where one can decrease, or even increase the energy barrier necessary to casue a phase change.

Although Gibbs’ equation is classified as an Equation of State, Gibbs’ equation is not the ideal fundamental property relation to use in plotting specific states; such as, density, pressure, temperature, etc.; s discussed in Lesson 10. This is because the Gibbs equation cannot accurately determine specific states when the temperature and pressure are not independent quantities; predominately at phase changes. As Dr. Leachman stated, the “inability of the Gibbs Energy to differentiate phase in the most commonly used temperature and pressure coordinates is why modern EOS are explicit in Helmholtz Energy.2

Below is the correlation between the commonly used form of Gibbs Free Energy and the most used form of the Helmholtz Energy Equation:

The Helmholtz Equation can be represented by:

The most common form of the Helmholtz Equation is in its reduced non-dimensionalized form:

The relation of Gibbs to Helmholtz energy equation can then be represented as:

Where α is the reduced Helmholtz energy and:

where tao is the reduced inverse temperature and delta is the reduced density. Typically, the critical density and temperature are used in place of the the reduced density and temperature. This is done to reduce the density and the inverse temperature.

Cryo-cycling for better leak testing

One of the biggest issues that you will run into working with cryogenic fluid systems is finding and fixing leaks, especially those leaks that open up at low temperature. A helium leak detector and a bottle of soapy water does wonders for finding leaks at room temperature, but in order to get components down to working temperature in the cryostat you have to enclose the entire experiment in a vacuum chamber and cool everything down via cryocooler – not a very easy environment to isolate the location of a leak! An example of this is that in some cases (usually poor joints between multiple different materials), brazed joints will have no leakage at room temperature, but new leaks will open up after getting really cold. We have had this happen anywhere from 80 to 200 Kelvin, and as these temperatures are far below your typical room conditions, they’re very difficult to isolate. To try and speed up the process of checking if leaks would open, our recommended practice for all cold joints and fittings is therefore to test in liquid nitrogen (LN2) before installation on the system.

General Instructions for LN2 Leak Checking, based off ASTM E499/E499M – 11 Test Method A:

• Cap the test specimen and connect to a helium bottle. Pressurize the test specimen with helium to the working pressure of the specimen.
• Dip the test specimen into LN2 to cool it down to the LN2 temperature of approximately 77 K.
• Sniff all fittings, welds, and solder joints with the mass spectrometer by passing the sniffer probe over likely leak points. Start at the bottom of the specimen and work your way up, holding the probe on or not more than 1mm from the surface. Do not move the probe faster than 20mm/s.
• Continue sniffing in an orderly procedure from bottom to top. Identify any leaks so they can be remedied. Be aware that helium will rise, so a leak above a previously found leak may not actually exist. It is also important to be aware of the airflow in the room, as helium can be blown around the experiment and produce small “leaks” that don’t actually exist. When testing with a short line from the helium bottle, be aware that the regulator connection into the bottle often leaks at a higher rate than is acceptable for our cryo experiments, and can cause false alarms (This can usually be remedied with longer lines to move the specimen farther from the bottle and by keeping the specimen low, well below the bottle).
• If any leaks are identified, take corrective action and perform this procedure again until leaks are no longer detected.

This is recommended for cryo-rated valves, small pressurized vessels, or any other cold equipment that you don’t mind completely submerging in LN2. It will definitely save yourself a lot of time by doing this every time!

Making a Cryogenic-compatible O-ring seal

One issue that I ran up against while re-designing CHEF for my thesis research was the connection point on the hydrogen liquefaction tanks. I decided to use VCR connectors because of their reliability at vacuum and low temperatures, this meant that a VCR connection directly to the tank would be easiest for design and build. As all VCR connections, off the shelf, are made of stainless steel, and the liquefier tanks were made from Aluminum (because of thermal concerns), welding a connector directly on was not an option. NPT connections were another possibility, but ultimately not chosen for fear of leakage at low temperatures. Luckily, Swagelok sells pass-through connectors, specifically a ‘Straight Thread O-ring Seal Male Connector’. Normally this would work well as the O-ring is what seals the connection, instead of the threads in a traditional NPT connection, however O-rings are usually made of synthetic rubber materials and do not work at temperatures much below room temperature (~298K). Because this needs to seal against liquid hydrogen (~20K), a rubber O-ring is not an option. We decided to try using indium as a stand-in O-ring. Indium is used in many cryogenic applications as a seal because of how well it conforms to whatever shape it is in, filling in tiny crevices and actually bonding to the metals, however it is usually used as a crush seal, meaning that there is no twisting involved in the sealing process.

After searching around I was unable to find much information on-line about an application of indium like this, only a comment made by Jake Leachman that he had seen a presentation on something similar to this at a cryogenics conference in the last year or two. So I decided to do what any engineer that’s faced with a new and untested idea does…just go for it!

For the seal I used:

1/16” Indium wire

SS-4-VCR-1-00032 ¼” Straight thread O-ring pass-through

Apiezon-N cryogenic high-vacuum grease

The top flange of the liquefier tanks had the correct size tapped hole machined into it. On each hole we had a 45 degree chamfer, 1/32” deep; we did this because we wanted somewhere for the indium to seal against instead of a sharp corner that might cut the indium instead of smear it.

To actually make the seal I had Casey Evans, our wonderful undergrad volunteer help me. Using gloves, we first cleaned all surfaces and indium with methanol and then acetone to first get rid of any oils on the surface and then any traces of the methanol left behind. The indium was cut to length by trial and error around the O-ring groove. We cut the end of the wire at about a 60 degree angle as shown below in the diagram. This is to ensure that as the pass-through is put in that it smashes and smears the indium seal together even more

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After the indium wire has been cut, we coat the wire in a thin layer of Apiezon-N high vacuum grease in order to help cut down on the friction seen by the indium. We want the indium to seal, but at the same time we don’t want it to be smearing the entire time it is being crushed, just at the end to get the final seal. We now used a small flat object to help press the indium edges together to help them fuse together. At this point the indium should look like that shown in the two picture below. Notice on the second one where the edges have been pressed together.

Now that all the other steps have been completed all that is left is putting it on the tanks! Originally we thought that tightening the seal down all the way would not be necessary, and actually possibly be detrimental to the capacity of the indium to seal if it were cut during the crushing. In reality we found that the seal did not seal easily, and was extremely finicky, opening up leaks when I was trying to put VCR connections on because of the twisting motions. Rubber O-rings are resilient   to small shifts in how tight the pass-through is because it is able to expand to the shape, however because indium is so malleable, it also will not expand and therefor will open up leaks if the pass-through is loosened at all. The first picture blow shows how the seal looked when not completely crushed, while the second shows when it is fully crushed in place. I found that tightening the pass-through till it wouldn’t turn easily worked well for sealing. The indium was literally squeezed out around the edges, and if one were to take the pass-through out, would see that this is true down into the threads as well! All in all, I found that these connections are actually quite reliable when tightened enough, I have four of them on my experiment and have had no leaks after tightening them enough; however I would warn against using this on connections that will be not be at least semi-permanent as there is risk each time to open up leaks when loosening and tightening the VCR pass-through.

Musings of a Cryogenicist: Day 5 – Vacuum Gauges (everything you wanted to know and more!)

In my last post I talked about the 3 main types of Vacuum gauges available for use. They were:

1. Force measuring (105 – 10-2 Pa)
2. Heat transfer (10 – 10-2 Pa)
3. Electrical charge transfer (ionization) (100 – 10-9 Pa)

I also talked about how I have a FRG-700 Inverted Magnetron Pirani Gauge currently connected to my Cryostat chamber. Well now I want to look at each of these types of vacuum gauges in a little more depth giving the general method of vacuum measurement for each. Understanding how each of these work at a basic level and their limitations can be very helpful when designing your own experiment. All of the information that I present below can be found either from a quick Google search/Wikipedia, or from the High-Vacuum Technology book, by Marsbed Hablanian, that I noted in my last post.

First, let’s look at the force measuring vacuum gauges. As noted above, these are generally useful in the 105 – 10-1 Pa region of pressures, or more specifically from atmospheric pressure ranges down to medium vacuum ranges that a single roughing pump can reach. The main two types I’ll cover in here are Bourdon gauges (105-103 Pa) and Diaphragm gauges (105-10-2 Pa). A Bourdon gauge works by using the elastic deformation of a curved, twisted, or helical shaped tube when a pressure difference is present between the gas inside and outside of the tube. This is a simple method that works very well at pressure above atmospheric quite well, and to a degree within a vacuum as well. The drawback is that as the vacuum is reduced more and more, the pressure differences change less and less as the jump between 104 -> 103 Pa is 1000 times higher than the jump between 100 -> 10-1 so the force changes are smaller and smaller till eventually the tube does not move anymore as the pressure is still being decreased.

The next type of force measuring device is a diaphragm gauge; this system extrapolates the pressure from measurements of the deflection of a small membrane because it deflects in approximate proportion to the applied pressure difference across the membrane. The exact pressure ranges that these are useful for are dependent on the size and thickness of the membrane; smaller and thinner membranes can measure smaller pressure differences, but fail at larger pressure differences. For this reason, often a separate vacuum chamber is necessary to keep the pressure difference low enough for these to be used. Larger and thicker membranes are not as accurate because of their size, but they are able to resist the forces from much larger pressure differentials.

I’ll be moving on to heat transfer vacuum gauges now. The two types that I will be covering are the thermocouple gauge and Pirani gauge. I believe one of the best ways of describing these types of vacuum gauges can be read directly from ‘High-Vacuum Technology’: These gauges measure pressure in the range for which the mean free path is comparable to or greater than the dimensions across the flow of heat occurs – in other words, in the free molecular regime. This means that the pressure needs to be low enough for these types of gauges to work properly, namely in the 102-10-1 Pa range. The basis for their measurement comes from the fact that gas loses its ability to conduct heat as pressure is lowered because there are significantly less particles to transfer the heat through convection. From what I understand about these gauges a constant source of heat is produced by voltage run through a resistor. As the pressure of the gas is reduced, its ability to conduct away the heat is lessened, so the resistor will start to heat up. By using the temperature reading of the thermocouple, the pressure of the surrounding air is able to be extrapolated.

A Pirani gauge (the type in our Varian vacuum gauge as noted previously) is the other type of heat transfer vacuum gauge type I will cover. These gauges are accurate in pressure ranges from 102-10-3 or 10-4 Pa depending on the type of equipment used. This type of gauge used a Wheatstone bridge with a thermistor exposed both to the vacuum chamber and a compensating element that is sealed off in a glass enclosure at a pressure below 10-1 Pa. If the voltage is kept constant across the circuit then as the pressure changes in the test chamber, the resistance across the bridge is unbalanced, and depending on the magnitude of unbalance, the pressure is able to be extrapolated from this.

The last type of vacuum gauges that I will cover is ionization gauges. These are for high and ultrahigh vacuum range (10-1-10-8 Pa), which require a second vacuum pump, a turbomolecular pump, for a test chamber to reach. These types of gauges are split into cold and hot cathode versions. The cold cathode variant is useful for the 100-10-7 Pa range, well within the lower range of what I expect to get my test chamber down to (~10-5 Pa). While there are other types of cold cathode vacuum gauges, ours is of the Inverted magnetron variant, also called a Redhead gauge. The basis of operation is that electrons are produced by a high voltage electrical discharge through the surrounding gas molecules creating ion-electron pairs that start to fly around. The number of these pairs is proportional to the gaseous molecular density times the voltage that produces the electrons. It’s all a very complicated process that I’m happy is something I can just plug into my computer and have it give me what the vacuum pressure is! A hot cathode is very similar to the cold cathode mode of operation; however it uses a hot filament to introduce the electrons into the system instead of a straight electrical discharge.

Well that about wraps up everything I have to say about vacuum gauges. Its most likely way more information than anyone cares about, but I’ve found that getting the information into my mind, and then onto paper really helps me get it compartmentalized in there and I actually understand better how everything fits together better. If you want more information on pressure measurement in general, I would suggest looking at the Pressure Measurement page on Wikipedia. It gives a quick run through all the types I mentioned above plus many more! Also if you want more information on High-Vacuum technology then take a look at the “High-Vacuum Technology” book that I keep referencing in these posts.

Musings of a Cryogenicist: Day 4 – What’s in a Vacuum?

So what IS in a vacuum? Nothing? Something? Everything?! Well first we need to define what a vacuum is. In day to day life we consider any gas that has less pressure than its surroundings to be in a state of ‘vacuum.’ That doesn’t mean that it has NOTHING in it, it just really means it has less in it. So what’s a good practical example of this? A vacuum cleaner: it produces an area of lower pressure than the surrounding atmosphere giving it the ‘sucking’ capabilities that we use to clear an area of dirt or dust. Now I assume that most people know what a vacuum is already from the broader sense of things. But when we really get down to it, we can’t actually make a perfect vacuum; we can only get to a higher and higher quality of a partial vacuum.

Measurement of a vacuum is important because we can use it to quantify exactly what the quality of a vacuum is. A true vacuum is one that is absolutely devoid of any particles of any kind, it really is just a void. Even when there is a perfect vacuum it is not truly empty because of various energy waves that are able to transmit through with no medium such as many that are found in outer space. Note that even Space isn’t a true vacuum! If we quantify this perfect vacuum as having a pressure of 0, then we can start to build from here. In our day to day life generally we see pressure in two different formats, pounds per square inch (PSI – Imperial Unit), and kilopascals (kPa – SI), and this is very helpful in pressures ranges we generally deal with for day to day life. But when we measure vacuum generally it is measured in either Torr (1 Torr = 1/760 atmosphere) or Pascals (Pa). I won’t get into exactly what the units of all of these are, or how they are found as most people who are reading this should already be familiar. If you aren’t familiar however I highly suggest sliding on over to Wikipedia and brushing up on pressure and what exactly it is.

There is some debate out there as to which of the two vacuum measurement units should be used, considering that SI units are already used in about 95 percent of the world, and using its units down to low pressures is just moving a decimal point like any other operations with it, I lean towards the side that is rooting for Pa and nPa! Check out this post by Jake Leachman for a bit more info about the SI system, especially as it pertains to Engineering Education.

Instruments to measure a vacuum come in many shapes and sizes. Not all of them work for all vacuum ranges however, the higher the vacuum you have (read: closer to 0 pressure), the harder it is to get a higher vacuum AND to measure it. From the “High-Vacuum” technology book (by Marsbed H. Hablanian) there are three mains types of vacuum gauges:

1. Force measuring (105 – 10-2 Pa)
2. Heat transfer (10 – 10-2 Pa)
3. Electrical charge transfer (ionization) (100 – 10-9 Pa)

Each of these have pros and cons to their usage. In my experimental work I will be aiming for a vacuum of approximately 10-5 Pa (10-7 torr) and we use a FRG-700 Inverted Magnetron Pirani Gauge manufactured by Varian. It is a combination of a Pirani Gauge (heat transfer method measurement) and a Cold Cathode Gauge (ionization), and changes between the operating modes depending on the vacuum range.

Musings of a Cryogenicist: Day 3 – Interior Components

Alright, so you have a test chamber, you have a vacuum pump (I’ll get more in depth into in a future post), and you have a cryocooler. Now what? Well now we get down to the nitty gritty, now it’s all about designing the experiment itself. First you need to figure out what kind of measurements you need, and what other peripherals are necessary. In my case, so far I have figured that I need thermocouples for temperature measurements and fiber optical cable rated at cryogenic temperatures for my Raman Spectroscopy measurements. I also need some wires to run to my heater so that I can adjust the temperature from the baseline that the cryocooler tries to go to when it is operating. All these wires need to get out of the test chamber as well, so some sort of connector through one of the walls is necessary. Fortunately for me, there is already a connector so I can adapt it to my uses; this also means that for now I won’t learn exactly what components are necessary to make a new one. Below are some pictures for the current setup, including the heater along with many cords, the connector on the inside, as well as the connector through the wall.

Now we come to the test item setup itself. In my case I will be running my experiment in a SAC (Sapphire Anvil Cell), this is Bridgman type anvil cell that uses Sapphires instead of the more traditional Diamonds in a DAC (Diamond Anvil Cell). I am still designing how best to hold it in place with the least mass. The only real requirements that I have right now are that I can hook a thermal strap to it, that I can easily install it into its holder, and that it be at a thermal ‘dead end’. The last of these three is important because we want to draw the energy away from SAC without any way for more energy to be replenished to the system. This means that our supports to the overall structure will be on the other side of where the thermal strap hooks on.

To keep as little new energy from entering the SAC and holder, and helping to make it a thermal ‘dead end’, we have to look at the 3 basic ways that energy moves from Heat Transfer: Conduction, Convection, and Radiation. Conduction, heat transfer from through a sold, is very important in our experiment as noted above because it is how we get the energy to the cold head. Because we want the heat transfer from the cold head to the outside structure to be minimized, the walls of it are often very thin, meaning that it can’t handle large bending or torsion loads. This means that the supporting structure for the SAC and holder must attach directly to the wall of the test chamber. Using a material such as a G-10 epoxy fiberglass is a very appealing option for this as it has a very low coefficient of thermal expansion so it won’t move the attached equipment very much as the temperature lowers while having an extremely low thermal conductivity so very little heat from the surrounding walls are able to conduct through. Graphs with information about G-10 are shown below and are from ‘Experimental Techniques in Low Temperature Measurements’ by Jack Ekin. All the figures from the book are available here to look at for everyone: http://www.researchmeasurements.com/.

Convection, heat transfer through a fluid or gas, is one of the easier heat transfer pathways that we can block. We get around this by using a vacuum pump to evacuate the chamber of as much gas as we can, essentially isolating the SAC from the surrounding walls. This is exactly how most thermos bottles work. And lastly is Radiation, this is an issue for two reasons. One is that it requires no medium to travel across, so even in a vacuum it is still able to work, and the other reason that it is an issue is that the heat transfer is proportional to the difference in surface temperatures to the fourth power! This means that when temperature difference are small it is not very noticeable, but when the walls of the cryostat are around 290 K and our test apparatus is at 20 K we have a difference of 270 K!!! Luckily we can get around this by using a radiation shield. This is a two-fold shield, using a copper metal exterior and an MLI (multi-layer insulation) shroud. MLI shrouds can often be seen on satellites as space craft, are highly reflective, and are often gold, copper, or silver colored depending the material used.

Well I feel that about wraps up everything I have to say about interior components for today! In my upcoming posts I hope to talk more about the materials selection, seals/sealing surfaces, and the concept of a vacuum.

Musings of a new Cryogenecists: Day 2 – The test chamber

The test chamber may not be the most technically challenging or complicated part of the cryo-design, but it is arguably the most important. Without it, you have no chamber to pull a vacuum on, no enclosed boundaries for your cryocooler to take energy from, and nothing to mount your experiment to. Luckily I am inheriting an already functioning test chamber from Jake Fisher. As I noted in the first post, you must balance time, cost, and ease of design. This means that while I could design a completely new test chamber that fit the specifications for my experiment exactly, it really isn’t worth my time or money when I can adapt it to my uses. I simply need to change out some parts to make it work for me. Pictures of the test chamber/other components can be seen below.

The chamber is a cube shape comprised of 6 26 inch steel walls with a hole in each to allow from any side as well as customization for future experiments. Circular steel coverings are made for each individual hole. We can design and machine these to serve our individual purposes, such as including viewing ports for optical information, or holes to serve as ports for our vacuum pump, cryocooler, and various other needed components. Currently 4 of the 6 plates are whole and only act as coverings. The plate on the side has one hole and is where the vacuum pump systems hook into the chamber. The plate on top has two holes currently, one for the cryocooler to attach in, and one for wiring and other components to pass through. You can see the cold head on the inside to the right, one half of the copper radiation shield in the background, and the current test set up in the chamber, a twin screw extruder. For the most part I will keep the same set-up in the test chamber, putting my experiment where Jake Fishers currently is. I will get more into the details of what exact changes I am looking at in a later post.

Musings of a new Cryogenecists: Day 1 – A new journey

This post is my thoughts as I’m designing my graduate experiment setup. If you’ve never done anything with cryogenics, but are planning on doing it in the future, hopefully it will dissuade you from some of the pit falls that I will invariably fall into; and for those that have done cryogenic work in the past, you can see me as I walk head-long into some of those pit falls. This is by no means supposed to be a comprehensive list to follow!

Designing any scientific experiment is an acquired skill, requiring some experience before it really becomes second nature. You have to figure out what specific data is most important to you, whether resistivity of a metal, thermal capacity some new insulating material, or a myriad of other things. Then you have to start thinking of how you can best measure that, balancing time, cost, and ease of design. And once you come up with a good idea, you have to iterate, iterate, and then once again iterate until you come up with the most robust design that you can manage and gets the job done. Sometimes it’s not the prettiest thing to look at, but when it works, and moreover works WELL, then you know you’ve really done what you wanted. You can feel accomplished. I still feel that I’m at the beginning of the journey to really feeling like I know exactly what I’m doing when it comes to experimental design from scratch.

Now, designing a scientific experiment that will go down to cryogenic temperatures (below 123K) is an even harder task. Not only do you have to worry about all the items I mentioned above, but now you have the added difficulties of low temperatures, vacuum pumps and all the fittings, and long set-up times just to get it down to temperatures that you are looking for. Whether you are cooling your experiment with a closed cycle cryocooler, or using liquid cryogenics (ex. Helium, Argon, Nitrogen), you can’t directly touch your experiment anymore; one, because getting it down to those low temperatures is difficult enough, and your body outputs more than enough heat energy to really warm things up (and give yourself some serious frostbite in the process), but also because these systems often need to be in a vacuum environment to reduce convective heat transfer, so are sealed from the surrounding environment.

As someone that has had little experience with cryo-designs, those examples given above and many others must be taken into account to get a design that not only works, but works well. It’s no wonder that my adviser, Jake Leachman, told me that “cryogenics work makes very good and very thorough engineers.”

Let’s look over some of the most important details that I need to take into consideration on the cryogenics side of things:

• Test Chamber
• Vacuum
• Components inside
• Connection to the cold head