From fb43a72cde0c81116187ea25f0b2c0fc30e4fe3a Mon Sep 17 00:00:00 2001
From: Kees van Kempen <k.vankempen@student.science.ru.nl>
Date: Fri, 18 Feb 2022 08:18:03 +0100
Subject: [PATCH] ass1: Switch B -> H for external magnetic field

---
 ...ure-2-slides-for-printing-type-i-vs-ii.pdf | Bin 183891 -> 183982 bytes
 ...ure-2-slides-for-printing-type-i-vs-ii.svg | 164 ++++++++++++------
 superconductivity_assignment1_kvkempen.tex    |  14 +-
 3 files changed, 120 insertions(+), 58 deletions(-)

diff --git a/Lecture-2-slides-for-printing-type-i-vs-ii.pdf b/Lecture-2-slides-for-printing-type-i-vs-ii.pdf
index 3cf9132422cd820db0071dab5a272d2d95e80997..647625f98e5ada3e72cde69d085ce8068ea47581 100644
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diff --git a/superconductivity_assignment1_kvkempen.tex b/superconductivity_assignment1_kvkempen.tex
index 28de944..a2f0822 100755
--- a/superconductivity_assignment1_kvkempen.tex
+++ b/superconductivity_assignment1_kvkempen.tex
@@ -129,27 +129,27 @@ such that the net field is zero.
 This is called the Meissner effect.
 The perfect diamagnetism is quantized as having susceptibility $\chi = -1$.
 There is, however, a limit to how large a field can be completely expelled.
-This is called the critical field $B_c$.
-If $B_c$ is exceeded, the superconductivity breaks down, thus the material will cease to expell the field,
+This is called the critical field $H_c$.
+If $H_c$ is exceeded, the superconductivity breaks down, thus the material will cease to expell the field,
 the diagmagnetism drops to $\chi = 0$.
 This effect is seen in the bottom-left plot in figure \ref{fig:typevs}.
 The relation between these two critical values is given as
 \[
-	B_c(T) = B_c(0) \left[ 1 - \frac{T}{T_c}^2 \right].
+	H_c(T) = H_c(0) \left[ 1 - \frac{T}{T_c}^2 \right].
 \]
 An example of this curve is plotted in the top-left of figure \ref{fig:typevs}.
 Two phases can be distinguished:
 the Meissner (or superconducting) state under the graph,
 and the normal state outside it.
-The transition between these states is a first-order phase transition due to the discontinuity in the magnetization $M = \frac{dF}{dB}$, the first derivative of the free energy to the applied field.
+The transition between these states is a first-order phase transition due to the discontinuity in the magnetization $M = \frac{dF}{dH}$, the first derivative of the free energy to the applied field.
 
 Then there are type-II sc, for example, niobium (Nb).
 Instead of only having a Meissner or sc phase, they have another phase:
 the vortex state.
-Below $T_c$ and lower critical field $B_{c1}(T)$, the type-II sc is in the Meissner state,
+Below $T_c$ and lower critical field $H_{c1}(T)$, the type-II sc is in the Meissner state,
 and the material thus completely cancels the externally applied field.
-Above the upper critical field $B_{c2}(T)$, the material is in the normal state.
-When the field is between these two critical fields, $B_{c1}(T) < B < B_{c2}(T)$,
+Above the upper critical field $H_{c2}(T)$, the material is in the normal state.
+When the field is between these two critical fields, $H_{c1}(T) < H < H_{c2}(T)$,
 the material is in the vortex state.
 In the vortex state, the externally applied magnetic field is not completely expelled.
 Instead, the material consists of normal and sc regions, the former called vortices.