electricitysolid-state-physicsthermal conductivity
Mica is a good conductor of heat but an electrical insulator.
According to free electron theory (which applies only to metals) free electrons carry heat and electricity. Therefore, thermal conductivity is directly proportional electrical conductivity.
What about dielectric materials? In the case of mica, it conducts heat but not electricity, so what are the carriers responsible for this behavior. If the are electrons as they are in metals then why they don't carry electricity too?
These are all good questions! Based on your description I assume you haven't had an introduction to solid state physics yet? Let's take your image of an electron that "jumps"
from atom to atom. In my understanding I wouln't describe it that way, to me it's a wavefunction of the electron that is almost independent from the valence electrons and you
can use the free electron gas approximation. Why is this band independent? See the following picture for an intuitive understanding how the atomic potentials define the possible energy levels within a periodic arrangement of atoms:
I think most of your questions will be easier to answer if you make yourself familiar with basic concepts and approximations people use to describe electrons in a solid first. Sure, a lot of things can be understood if we consider electrons to be little spheres that scatter from bigger spheres (ions), but you said you want to understand on the atomic level -> it's good to see the electron as a wave and see how this wave behaves in a lattice with certain boundary conditions.
First, I would read about a crystal. Atoms are arranged in a periodic lattice (assume a nice crystal for a first simple picture) and you can make assumptions based on this periodicity. You can define a unit cell and the Brillouin zone. You will see that the energy levels will sometimes split up in different bands and based on the filling of these bands you end up wih a metal, insulator etc. Electrons are fermions, can two electrons be in the same state? This defines the Fermi velocity.
This filling of the available energy levels describes the Fermi surface, a very useful tool to describe other more advanced concepts. Then you will see what happens if you change the arrangements of the atoms or why in different spatial directions electrons can move due to the bonding of different atomic orbitals.
This could be a good start ; ) -> http://britneyspears.ac/lasers.htm
There are other introductions out there, most of them describe the basics really well.
In metals, there is the Wiedemann-Franz law because in metals heat is carried mostly by electrons.
Alloying reduces the electron mean free path, but it does not affect the speed of sound that much. For example compare copper and brass (a Cu-Zn alloy) or iron and different steel alloys.
In insulators, thermal conductivity is mediated by phonons. Both speed of sound and mean free path are important there. But that was not what the question was about.
Best Answer
Electricity needs charged particles (or quasi-particles) to conduct it. Heat can be conducted with almost any quasi-particle. Diamond is one of the best conductors of heat in existence, and it's because of phonons, ie quasi-particles of lattice vibrations, which are strong because the diamond lattice is strong.