Question

The goal of this problem is to obtain some results regarding the phase diagram (H,T) of a type-I superconductor, in particular the separation line HT) between the normal and the superconducting phase. The starting point is the differential form of the free energy density, dF -sdT -MdH a) Using the fact that at the transition the free energy of the two phases is identical, show that ан Sn-Ss Ms-Mn dT b) Rewrite this expression using good approximations for the behavior of the magnetization in the two phases dHe0 at T 0. c) Show that = d) Make a sketch of the phase diagram. Discuss qualitatively what happens to the latent heat of the transition as you move along the phase separation line, and based on that indicate the order of the transition. e) Show that at the critical point H(T)- 0there is a discontinuity in the specific heat given by (ignore the volume change at the transition) Т. (ане CsCn= dT 4T f) Assume that the phase separation line is well-described by Н.СТ) — Н.о (1-("т)?). For which temperature range is the specific heat of the superconducting phase higher than that of the normal phase at the phase boundary?

Solid State Physics,
Superconductor

Answer 1

Given free energy(dF) is continuous at the transition temperature(Tc)

Solution a) Differentes form of free encegy deneity – dr = – EdT - MdH of type I Superconductor at tranection H H . at transition file enugy of both phases are identual . Badt a hat- &dt – end the reaueanging (M. Ma dite (B-S) di dhe & IT S.-S. My-Ma M = -H 44 B. H + 4 KM for a Super Conductor B-0 7 tt 4TM = 0 = for a nolmas metal mno. Substeluting in die Weds – 4K (9. 3.) – HC q c) At To SS=0 & dhe at T=o= 4Ã Xo = d 7 normal HOM state (metalle). Feom eqn . H dH(G) 45. dT But is = AQ, where 4Q ce the latent heat Supe during > AQ -1 AQ = -I He dH. 42 IT Has no deconnuity so second ordee phare teanstha