Neat problem of the week: researchers just announced roughly-room-temperature superconductivity at pressures around 270 GPa. That’s stupidly high pressure—a friend tells me “they’re probably breaking a diamond each time they do a measurement”. That said, pressures in single-digit GPa do show up in structural problems occasionally, so achieving hundreds of GPa scalably/cheaply isn’t that many orders of magnitude away from reasonable, it’s just not something that there’s historically been much demand for. This problem plays with one idea for generating such pressures in a mass-produceable way.
Suppose we have three materials in a coaxial wire:
innermost material has a low thermal expansion coefficient and high Young’s modulus (i.e. it’s stiff)
middle material is a thin cylinder of our high-temp superconducting concoction
outermost material has a high thermal expansion coefficient and high Young’s modulus.
We construct the wire at high temperature, then cool it. As the temperature drops, the innermost material stays roughly the same size (since it has low thermal expansion coefficient), while the outermost material shrinks, so the superconducting concoction is squeezed between them.
Exercises:
Find an expression for the resulting pressure in the superconducting concoction in terms of the Young’s moduli, expansion coefficients, temperature change, and dimensions of the inner and outer materials. (Assume the width of the superconducting layer is negligible, and the outer layer doesn’t break.)
Look up parameters for some common materials (e.g. steel, tungsten, copper, porcelain, aluminum, silicon carbide, etc), and compute the pressures they could produce with reasonable dimensions (assuming that their material properties don’t change too dramatically with such high pressures).
Find an expression for the internal tension as a function of radial distance in the outermost layer.
Pick one material, look up its tensile strength, and compute how thick it would have to be to serve as the outermost layer without breaking, assuming the superconducting layer is at 270 GPa.
Neat problem of the week: researchers just announced roughly-room-temperature superconductivity at pressures around 270 GPa. That’s stupidly high pressure—a friend tells me “they’re probably breaking a diamond each time they do a measurement”. That said, pressures in single-digit GPa do show up in structural problems occasionally, so achieving hundreds of GPa scalably/cheaply isn’t that many orders of magnitude away from reasonable, it’s just not something that there’s historically been much demand for. This problem plays with one idea for generating such pressures in a mass-produceable way.
Suppose we have three materials in a coaxial wire:
innermost material has a low thermal expansion coefficient and high Young’s modulus (i.e. it’s stiff)
middle material is a thin cylinder of our high-temp superconducting concoction
outermost material has a high thermal expansion coefficient and high Young’s modulus.
We construct the wire at high temperature, then cool it. As the temperature drops, the innermost material stays roughly the same size (since it has low thermal expansion coefficient), while the outermost material shrinks, so the superconducting concoction is squeezed between them.
Exercises:
Find an expression for the resulting pressure in the superconducting concoction in terms of the Young’s moduli, expansion coefficients, temperature change, and dimensions of the inner and outer materials. (Assume the width of the superconducting layer is negligible, and the outer layer doesn’t break.)
Look up parameters for some common materials (e.g. steel, tungsten, copper, porcelain, aluminum, silicon carbide, etc), and compute the pressures they could produce with reasonable dimensions (assuming that their material properties don’t change too dramatically with such high pressures).
Find an expression for the internal tension as a function of radial distance in the outermost layer.
Pick one material, look up its tensile strength, and compute how thick it would have to be to serve as the outermost layer without breaking, assuming the superconducting layer is at 270 GPa.