[nietzscheswoman]

What is essentially at hand when two atoms come into contact? I'm resigned to limiting the discussion to solid-state chemistry if speaking so generally is too general. I'm interested in the equilibrium (of forces?) that's maintained between atoms as they form and re-form solid material.

Band gaps, and electrical conductivity is one concept that I thought might encompass this equilibrium-- but as I read on I realize that conductors don't have band gaps. (or is it that they only have a negligible one?) - So what does that mean that atoms can combine with no space between them, as well?

Would anyone be able to touch on some general ideas, besides band gaps (but elaborate on band gaps as well, if you can) that I can learn about that is relevant to a discussion on what happens when two or more atoms combine? And what ideas are at hand that allow the materials they form to possess the properties that they do?

[Enthalpy]

Welcome, Nietzschewoman!

Solids are complicated and you deserve all our encouragements on your path. While questions like "what makes bonds" are more or less answerable, "what makes semiconductors" can't be told from simple reasons. I regret it, but blame for that whoever or whatever created our Universe, not me.

==========

Strictly speaking, and in solid state theory's wording, metals have no bandgap at all. In case you were influenced by models with atoms put on a line and a bandgap appearing necessarily then: remember that semiconductors use to be 3D objects, where the energy-versus-momentum relation depends on the direction, so the energy of the bands in varied directions can easily (and they do) overlap. And even in one direction, different bands can overlap their energies at different momenta.

You can admire true band diagrams (... though I'm not sure how much was measured in detail - more probably computed in detail and checked at a few strategic points) there
http://www.ioffe.ru/SVA/NSM/Semicond/
http://www.ioffe.ru/SVA/NSM/Semicond/Si/bandstr.html
http://www.ioffe.ru/SVA/NSM/Semicond/AlN/bandstr.html second diagram
https://www.researchgate.net/figure/269775630_fig1_Figure-2-Calculated-band-structure-of-aluminium-along-the-symmetry-axes-Reprinted-from
metals tend to be more complicated. And these are simplified diagrams along a few directions: only E versus simultaneous k_x, k_y and k_z would make sense, which is impossible to draw.

As a sidenote, components use presently "wide-gap semiconducting" materials that were defined as "insulators" three decades ago.

==========

A few solids have a bandgap small enough that even solid state scientists may call them "metal", in the sense that room temperature suffices to put many mobile carriers in the conduction and valence bands and achieve metal-like conductivity. Grey tin is one example
https://en.wikipedia.org/wiki/List_of_semiconductor_materials

For chemists, a metal has at least one basic oxide. The chemists' definition results from single atom properties, while for solid state, it's a collective property. Both definitions overlap almost. Grey tin is one exception.

==========

You wrote "two atoms". I misuse it as an excuse to put that two atoms don't make a solid nor a semiconductor. This needs millions of atoms.

Just to tell that solid properties don't result easily from atom properties:

• Solid hydrogen becomes a solid if putting enough pressure on it.
• Tin is a metal in one crystal form and a semi-metal in an other (grey).
• The band diagrams depend fundamentally on the crystal structure, SiC being one example
  http://www.ioffe.ru/SVA/NSM/Semicond/SiC/bandstr.html
• Si and Ge have different band structures, with conduction band minima in <100> and <111> directions, despite having both s²p² orbital filling and diamond crystal structure, so the lower (non-binding) atomic orbitals matter too.

There are few general trends, supposedly with exceptions: lighter atoms tend to make bigger bandgaps, and combining atoms of different electronegativity tends to increase the bandgap.