How electricity, and generating electricity works on the atomic level?

Different materials are made from molecules, those molecules are made from different atom types. Those atoms arrange themselves in in different configurations: ordered(called crystalline), random(amorphous), and a combination of both (Poly-crystalline).
The crystal is defined by a lattice and a basis. The lattice is a mathematical representation of points in space, and the basis is a "pattern" that gets pasted on each lattice point. The "pattern" is 1 or more atoms. The crystals are bound together by different types of bonds (ionic, covalent).
Since the lattice is just a representation, there is no meaning to start / end point, making the lattice havetranslational symmetry.Auguste Bravaisdiscovered there are only 14 ways you can rearrange the lattice and keep translational symmetry.
Naturally crystals are formed when liquid cools down, since it happens in many locations and at different orientations, mostly poly-crystalline are formed. There are severalcrystal growthmethods to create own more perfect crystals.
Each atom has anelectron configuration, and has several different shells / levels of energy. There can be 2n^2 electrons per level. The lower the level the higher energy needed to bump the electron to the next level (because is closer to nucleus - where the protons are).
When arranging several atoms together, due topauli exclusion principle(convoluted quantum mechanical principle that states two fermions(electrons) can not have the same quantum state) the atoms can not have the electrons at exactly the same energy level, forcing them to change slightly, split and spread intoenergy bands.
Conductivity determined by number offree electronsin the conductor that are free to move around. (more later)
The highest energy band available for material is calledvalence band. The next band is calledconduction band. The conductivity is affected by the number occupied of electrons in valence band and theband gapbetween the valence to the conduction band. (more now)
If the valance band is half filled, there is room for the electrons to move resulting in high conductivity (metals). If the band is full, but the band gap to the conduction band is small enough so electrons can be excited to the next band where they can move and there is conductivity(semi conductors).
In insulators the valance band is full and the gap is too big, and an electron cant carry enoughthermal energyto bump other electron through this gap.
Thus, the lattice, crystal structure and atom properties affect the band distribution which affect the number of free electrons.
When applying electric field on a wire, a force is applied to all the electrons, making them accelerate.Mean free pathandmean free timerepresent the length & time on average before a collision happens with other atom / electron / material impurities etc. All of those collision, stopping and pushing, contribute to the net directionaldrift velocityof the electron as it moves in the conductor.
drift velocity = current.
voltage drop = energy used for exciting electrons over the gap.

Thanks and Regards

Apoorva Arora

IIT Roorkee

askIITians Faculty