#PhysicsFactlet: The "Ashcroft/Mermin Project"
I will try to (likely very slowly) go through the classic textbook "Solid State Physics" by Ashcroft and Mermin and make one or more animation/visualization per chapter.
This will (hopefully) help people digest the topic and/or be useful to lecturers who are teaching about it. As with all my animations, feel free to use them.
The idea is that the animations are a companion to the book, so I will give only very brief explanations here.
#PhysicsFactlet: The "Ashcroft/Mermin Project"
Chapter 1: The Drude Theory of metals
Electrons in a metal are accelerated by an electric field, but they keep bouncing on the metal defects/impurities. The resulting diffusion-like motion produces a roughly steady current.
@cortogantese You don't scatter on the crystal, you scatter on the defects.
As per why you don't scatter on the crystal, you need Bloch modes to explain that. In the Drude model it is just postulated.
Released into the #PublicDomain and uploaded to #WikimediaCommons together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Drude_Model.gif
#PhysicsFactlet: The "Ashcroft/Mermin Project"
Chapter 2: Sommerfeld model
Electrons in a metal can be approximated as a Fermi gas, where only one electron can occupy a given state. At low temperature most of them are difficult to excite, because there is no free state available.
Released into the #PublicDomain and uploaded to #WikimediaCommons together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Fermi_Gas.gif
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices
A Bravais lattice is an infinite array of points generated by discrete translations, so that every point can be written as a (integral) linear combination of the basis vectors.
(If you are wondering where Chapter 3 has gone: Chapter 3 is literally 5 pages long, and it just enumerates all the reasons why everything done in chapter 1 and 2 must be wrong.)
@johncarlosbaez To be fair, chapter 1 and 2 cover two very useful and powerful models. But being models based on some major simplifying assumptions, they are expected to fail somewhere. And chapter 3 explains clearly where they do fail. A large chunk of the rest of the book is devoted to developing a better (quantum mechanical) model 😉
@j_bertolotti@johncarlosbaez
1/2
"Solid State Physics"
by Neil W. Ashcroft, N. David Mermin; 1976
ISBN: 0030839939 , 9780030839931
Widely recommended regardless of its age.
Contents
Preface ... vii
Important Tables ... xiv
Suggestions for Using the Book ... xviii
The Drude Theory of Metals ... 1
The Sommerfeld Theory of Metals ... 29
Failures of the Free Electron Model ... 57
Crystal Lattices ... 63
The Reciprocal Lattice ... 85
Determination of Crystal Structures by X-Ray Diffraction ... 95
Classification of Bravais Lattices and Crystal Structures ... 111
Electron Levels in a Periodic Potential: General Properties ... 131
Electrons in a Weak Periodic Potential ... 151
The Tight-Binding Method ... 175
Other Methods ffor Calculating Band Structure ... 191
The Semiclassical Model of Electron Dynamics ... 213
The Semiclassical Theory of Conduction in Metals ... 243
Released into the #PublicDomain and uploaded to #WikimediaCommons, together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Bravais_Lattices.gif
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices
The "Wigner-Seitz" primitive cell is the region of space that is closer to a given point in the lattice. It has the advantage of being a primitive cell with the same symmetries as the Bravais lattice.
Released into the #PublicDomain and uploaded to #WikimediaCommons together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Wigner-Seitz_Cell.gif
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices
Once we have the Bravais lattice, we can fully describe a crystal structure by specifying how the atoms are arranged around the lattice points (i.e. the "basis").
Released into the #PublicDomain and uploaded to #WikimediaCommons together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Crystal_Structure_as_Lattice_and_Basis.gif
#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 5: The reciprocal lattice
The "reciprocal" of a Bravais lattice is the set of k-vectors that yield a plane wave with the same periodicity of the Bravais lattice (i.e. effectively the Fourier transform of the lattice).
Released into the #PublicDomain and uploaded to #WikimediaCommons together with the #Mathematica script used to generate it: https://commons.wikimedia.org/wiki/File:Ashcroft-Reciprocal_Lattice.gif
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