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When we talk about electricity we say that flowing electrons experience resistance by the lattice atoms.
But how do lattice atoms provide resistance? They have their shell, their electrons, and their own nucleus.
So what thing provides the resistance? Does the electric field of electrons of lattice provide that resistance?

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  • $\begingroup$ It is unclear to me what you are asking. Most materials have enormous resistance, some materials are conductors. Are you wondering about the enormous resistances? Or do you ask why the relatively small resistances of metals are not zero? Or do you ask about the difference? There are answers on this site. $\endgroup$ – user137289 Jan 14 '20 at 15:10
  • $\begingroup$ So let get this straight.when we study bremsstrahlung radiations,we say that when electron passes near the field of nucleus it slow down.As a result radiating energy.Same case here.If collision of electron with lattice atoms means that they are slow down by electric field of electron so we can say that as a result energy would release.I just want to know weather my thinking about is right or not. $\endgroup$ – It doesn't matter Jan 14 '20 at 15:14
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Classically, we picture electrons being drawn towards the ions and, on impact, dispersing energy throughout the lattice. The higher the electromagnetic attraction of the individual ion the more likely that an electron is going to be drawn to and collide with it.

Quantum mechanically, we picture it as electron waves being dispersed due to defects in the crystal lattice, which is caused by the motion of ions.

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  • $\begingroup$ I cannot see that this explains anything. The higher the attraction the higher the resistance? Or the conductivity? The invocation of quantum mechanics explains what? $\endgroup$ – user137289 Jan 14 '20 at 16:55
  • $\begingroup$ The net conductivity/resistance is entirely dependent upon the structure you're working with. The invocation of quantum mechanics offers an alternative explanation of resistance by viewing electrons as waves rather than particles. $\endgroup$ – Dominic Reeves Jan 15 '20 at 9:02
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First of all, you indeed have the periodic potential of the lattice, formed by the positive ions. Remarkably enough, it is not this periodic structure that is the main origin of the resistance. Bloch's wave function given by $$\Psi (r) = u(r)e^{ikr}$$ takes into account this periodic structure of the material. As you can see, this is still a stationary states, that means that once it has a non-vanishing velocity, it will persist to have that velocity throughout the lattice. This seems quite disturbing? However, this can be understood if we appeal to the wave nature of the electron. So does this mean that the resistance will be zero? Unfortunately, this is only the case in the ideal case of a perfect periodic static lattice. In reality, temperature will cause the atoms to vibrate disturbing the perfect periodic potential and causing scattering of the electrons. Moreover, this scattering takes place at room temperature, down to $\pm 100$ K and causes a non-vanishing resistance. Does this mean that below this temperature the resistance will become zero? No unfortunately again.. a lattice wiil inevitable contain impurities to which the electrons will scatter, causing a non-vanishing resistance, even at $T=0$ (this is called the residual resistance).

Keep in mind, this is a really simple and intuitive picture I tried to give, but I just wanted to emphasize that it is not simply the lattice itself which causes the resistance!

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