Superconducting Materials Primer

To become more familiar, I am putting together a "crash course" from a materials science perspective on superconducting materials. It's a work in progress and far from complete. I am primarily jotting down notes from reading a few good books, such as the introductory book by Speller. It's a straightforward read and will get you started.

Warning

These are working notes, so there are bound to be errors and missing content.

Once I am done with my notes, I likely won't follow up on this subject unless there is compelling interest. One small reason for this is that, upon reading various sources, I became bothered by the "hand-wavy" approach to describing the physics of high-temperature¹ superconducting materials. BCS theory, which describes low-temperature (i.e., < 30 Kelvin) superconductors, is not well-suited for high-temperature materials due to factors such as strong electron-electron interactions and the presence of other exotic states of matter. To my knowledge, there is no all-encompassing HTSC theory.

References

[1] Speller, Susannah. A Materials Science Guide to Superconductors and How to Make Them Super. Oxford: Oxford University Press, 2022.

Footnotes

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1. High-temperature superconductors are meaningful only in the context of cryogenics, which involves the application of refrigeration to cool samples down; they operate at temperatures up to about -150 degrees Celsius. ↩

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XKCD Productivity

Having a difficult day so took my mind off things by creating a XKCD style plot on how my productivity feels at times. Let me know if this captures your day!

How at times I feel the productivity of my day goes!

If you want to modify to fit "your" function here is the Pluto.jl notebook.

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Sept: Reading & Thinking

I don't have too much to write about these days as I'm spending a lot of my free time reading various books. I've been doing some reading on superconducting materials given all the attention in July and August on LK-99. Most the texts I'm reading on this topic are introductory so they don't cover the theory that well, which I would eventually like to have a good understanding of.

I've also been focusing on some computational neuroscience via the online course. Its pretty interesting how underlying model for neurons is some variation of an RC circuit. This is captured with the nobel prize winning model proposed by the Hodgkin-Huxley model, which is a gated version of a RC circuit and described by a set of nonlinear ordinary differential equations¹. The cool thing is its very easily to play around with this type of model using the SciML Julia language framework, specifically the DifferentialEquation.jl package. I'm in the process of creating a computational blog entry on it.

Finally, I've been thinking about some self-driving lab activity using a 3D printer. I would love to use a metal/ceramic FDM²/FFF³ than a polymer-based printer. It looks like there are some good options by Markforged and Desktop Metal. I don't know much about the technology used by these manufactures or the feasibility of doing materials development. What my dream would be is to tie a 3D printer like those into some filament synthesis and printed part testing apparatus. Then using concepts of self-driving labs, we can define a goal/policy for the system to work towards. For example find the pareto front⁴ for optimal tensile strength and minimal density. I've contributed to a awesome-self-driving-labs github repo that has some good resource materials to learn about this field.

Footnotes

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1. A nonlinear ordinary differential equation (ODE) is an equation involving a function and its derivatives in which the relationship between the variables is not proportional. In mathematical terms, if $F(x, y, y')$ represents the ODE, it is nonlinear if it can't be written as a linear combination of $y$ and its derivatives. These equations frequently emerge in complex systems such as biological processes. For example, the equation $\frac{dy}{dx} = y^2$ is nonlinear because of the $y^2$ term. Unlike linear ODEs, a small change in initial conditions can lead to substantial differences in outcomes, making them inherently more complex to solve and analyze. ↩

2. Stands for fused deposition modeling. Its a poor name if you ask me but I believe the name comes from the fact that STL files are used to print single printed object. ↩

3. Stands for fused filament fabrication. Almost the same as FDM with some minor differences. ↩

4. The pareto front or frontier is the set of solutions that provide a the best options between a multi-objective function. It captures the trade-offs. ↩

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