Why are crystals more conductive then amorphous structures?

[Somali_Physicist]

TL;DR Summary

Hey guys basically why are copper crystals more conductive then the corresponding amorphous structure?

Hey guys basically why are copper crystals more conductive then the corresponding amorphous structure?
I know generally that electrical conductivity is reliant on:

σ = (e² * (v_f)² n τ)/3

My attempt of understanding is that the crystal structures are made up of unit cells which implies every section has a constant electric valence cloud surrounding it. Thus when applying an electric field there are already 'x' amount of electrons are constantly at fermi energy and also reducing the number of atomic collisions.

Amorphous solids are less rigid and hence there is no clear path for electrons to travel and randomly collide along the way hence decreasing the mean free time and the randomness of cloud implies less electrons are at fermi energy.

Any sources please??

https://www.physicsforums.com/file:///C:/Users/22273364/AppData/Local/Packages/oice_16_974fa576_32c1d314_275d/AC/Temp/msohtmlclip1/01/clip_image002.png

 

[Vanadium 50]

So you want us to find sources for your theory?

I would imagine that a) you don't want to be thinking about individual electrons, you want to be thinking about conduction bands, and b) amorphous metals likely have resistivities near what they are at the melting point.

 

[hagopbul]

Summary:: Hey guys basically why are copper crystals more conductive then the corresponding amorphous structure?

there are already 'x' amount of electrons are constantly at fermi energy

what you mean by that ?

Summary:: Hey guys basically why are copper crystals more conductive then the corresponding amorphous structure?

Amorphous solids are less rigid and hence there is no clear path

why rigid is related to "clear path"

 

[hutchphd]

Pssst. Bloch's Theorem

 

[Dr_Nate]

Pssst. Bloch's Theorem

He's pointing you in the right direction. In theory, in a perfectly transitionally periodic lattice (no thermal vibrations) the electron wave function will extend throughout the crystal and the atoms won't act like scattering centres. In an amorphous solid there are now a tremendous number of scattering centres because of the lack of periodicity.

 

[Somali_Physicist]

So you want us to find sources for your theory?

I would imagine that a) you don't want to be thinking about individual electrons, you want to be thinking about conduction bands, and b) amorphous metals likely have resistivities near what they are at the melting point.

It is a simple guess, after reading Electronic Properties of Materials, 4th Edition i have found it is due to crystals having electron scattering being more coherent compared to their amorphous counterparts.

However i am still abit confused , since polycrystalline is not a lot more conductive then amorphous systems.

 

[Somali_Physicist]

He's pointing you in the right direction. In theory, in a perfectly transitionally periodic lattice (no thermal vibrations) the electron wave function will extend throughout the crystal and the atoms won't act like scattering centres. In an amorphous solid there are now a tremendous number of scattering centres because of the lack of periodicity.

How exactly does that help conduction ?

If the electron wave extends throughout the crystal i don't see how that would help with the transport of electrons.

 

[Dr_Nate]

It is a simple guess, after reading Electronic Properties of Materials, 4th Edition i have found it is due to crystals having electron scattering being more coherent compared to their amorphous counterparts.

However i am still abit confused , since polycrystalline is not a lot more conductive then amorphous systems.

Can you provide the data you are using to conclude that?

 

[Somali_Physicist]

Can you provide the data you are using to conclude that?

Copper Bromide is around 3*10^3 S/m while copper ziroconium is around 500 S/m. Other data shows they are not extremely off.

 

[Dr_Nate]

How exactly does that help conduction ?

If the electron wave extends throughout the crystal i don't see how that would help with the transport of electrons.

You need to understand electronic band structures and the shift of the Fermi surface due to an electric field (plus the relaxation from scattering that keeps it in a steady state). The shift is in Fig. 3 here: https://unlcms.unl.edu/cas/physics/tsymbal/teaching/SSP-927/Section 08_Electron_Transport.pdf

 

[Dr_Nate]

Copper Bromide is around 3*10^3 S/m while copper ziroconium is around 500 S/m. Other data shows they are not extremely off.

That's comparing apples and oranges. You need to compare materials of the same composition, like say copper bromide, as a crystalline, polycrystalline, and amorphous solid. Then you can make comparisons.

 

[Somali_Physicist]

That's comparing apples and oranges. You need to compare materials of the same composition, like say copper bromide, as a crystalline, polycrystalline, and amorphous solid. Then you can make comparisons.

True, i was just assuming wrt to factors.

so I'm assuming that polycrystalline would be more conductive as its more ordered.

 

[Dr_Nate]

True, i was just assuming wrt to factors.

so I'm assuming that polycrystalline would be more conductive as its more ordered.

I agree that polycrystalline materials should be more conductive than amorphous materials other things being equal. Which leads me to wonder what data has led you to think otherwise. Can you show me what I mentioned above so that I can check it out?

 

[Somali_Physicist]

I agree that polycrystalline materials should be more conductive than amorphous materials other things being equal. Which leads me to wonder what data has led you to think otherwise. Can you show me what I mentioned above so that I can check it out?

embarrassingly it was due to a picture from a random person. Looking at it now it doesn't make sense and i had no data to back it up.

However from sources i think it should be :

single crystalline > polycrystalline > amorphous
(generally)

To be honest i just needed a few sources to understand why crystals are a lot more conductive then amorphous materials generally. Looking at the answers it seems to be just due to coherency of electron scattering , i will read that pdf and see if i can understand it.