Is the conduction band of metals empty at absolute zero?

[worwhite]

Hi,

I understand for metals the conduction band is usually partially filled.

However, at absolute zero, is the conduction band empty (for metals)?

I'm asking this because as far as I know, the definition of valence band is "the highest occupied band at absolute zero"

However, I have encountered a question that basically states that the conduction band of a metal is partially filled at absolute zero. This contradicts with the definition because that band would be the valence band, not the conduction band, according to the definition (and no, there is no overlapping of the valence and conduction bands of the metal in the question).

Could someone also please confirm the definition of a valence band and conduction band?

Thanks in advance.

 

[nasu]

For a typical metal the last energy band is partially filled with electrons. The electrons does no have to be promoted in the next, empty, band in order to contribute to conduction.
You can call it valence or conduction band or both. According to your definition, is a valence band. Due to the fact that (at least some of) the conduction electrons are in this band, it may be called conduction band, too.

 

[chrisbaird]

In a metal, there is no gap between the valence band and the conduction band, so they can be considered different regions of the same band. A better definition is that the valence band is the highest band in which the electrons are still locally bound to individual atoms. The conduction band is the one containing states that are delocalized, i.e. they are bound to the entire solid, and are therefore free to move around and conduct a current as they do. There is a reason it is called the "conduction band" and not the "high-temperature" band.

 

[ZapperZ]

Hi,

I understand for metals the conduction band is usually partially filled.

However, at absolute zero, is the conduction band empty (for metals)?

I'm asking this because as far as I know, the definition of valence band is "the highest occupied band at absolute zero"

However, I have encountered a question that basically states that the conduction band of a metal is partially filled at absolute zero. This contradicts with the definition because that band would be the valence band, not the conduction band, according to the definition (and no, there is no overlapping of the valence and conduction bands of the metal in the question).

Could someone also please confirm the definition of a valence band and conduction band?

Thanks in advance.

The definition of a standard, band metal is that at 0K, the band is partially filled. In fact, many of the standard band structure for metals are all calculated at T=0K.

Zz.

 

[worwhite]

Thanks for your replies. I think I get the fact that metal does have its conduction band partially filled at 0 K.

In a metal, there is no gap between the valence band and the conduction band, so they can be considered different regions of the same band.

Yes in my search almost everyone (Wiki, hyperphysics etc...) says this. However, in some sources (and in the question I was doing), it is said that metal can have separate valence and conduction bands, just that one of the bands is partially filled. Here's an image to illustrate and the accompanying website:

http://www.chemistryexplained.com/images/chfa_04_img0834.jpg
http://www.chemistryexplained.com/Ru-Sp/Semiconductors.html

Oh and note that it says in metals the valence band is partially filled, instead of the conduction band.

Are they incorrect to say that (1. there is a gap between the bands 2. it is the valence band that is partially filled in a metal, instead of the conduction band)?

(Oh and thanks for that definition of valence band. I was thinking of that, but so few sources use that definition even though it should be the obvious one - they just say it's the highest occupied band at 0K, and I can't help wondering why)

You can call it valence or conduction band or both.

I'm a little confused as to why. Are you referring to the overlapping of the valence and conduction band, such that it could be both?

 

[nasu]

You can call it valence or conduction band or both.

I'm a little confused as to why. Are you referring to the overlapping of the valence and conductionband, such that it could be both?

No, I was not referring to overlapping of the bands. The overlapping may occur but these cases are (or may) be called semi-metals (see Kittel for example). Also it may be possible to have a "semiconductor" with a zero band gap (between the valence and conduction bands) which will behave like a metal.
But I was not referring to any of these.

The typical metallic system I was referring to is one where the last (highest energy) populated band is not completely full. There are empty levels in the band. The electrons can easily move on these empty levels with no need to jump to a higher band.
You may call it a conduction band as it contains the electrons participating in the conduction. It is also the highest band with electrons in it so according to the definition in the OP, it will be a valence band.
It is not that the valence and conduction bands are overlapping but rather that the same band has features of both (depending on definition), if you wish.
Again, for metals is not a very useful distinction.

At zero K the electrons will occupy the lowest levels in this band. For simple metals it may be that lowest half of the band is occupied at zero K. The other half is empty. The last occupied level at zero K is called Fermi level.
As you increase temperature some of the electrons near the Fermi level will be "promoted" to some of the empty, higher levels, but still in the same band. The electric conduction is due to all the electrons in this band.

 

[worwhite]

Ah so what you mean is that the band is partially filled, and you can call that either a valence or conduction band depending on the definition.

"the definition" is exactly the problem I'm facing. I'm not sure what's the correct definition is for a valence band, and I'm seeking confirmation on it. I am reluctant to accept that a band can both be called a conduction and valence band, because the definition of the conduction band is (from the same source that gave the definition of the valence band):

the conduction band is the range of electron energies, higher than that of the valence band, sufficient to free an electron from binding with its individual atom and allow it to move freely within the atomic lattice

I'm interpreting that to mean they can't be the same, since the conduction band must be higher than the valence band.

I feel inclined to go with chrisbaird's definition:

A better definition is that the valence band is the highest band in which the electrons are still locally bound to individual atoms. The conduction band is the one containing states that are delocalized, i.e. they are bound to the entire solid, and are therefore free to move around and conduct a current as they do.

In other words: valence band is the band of energy associated with valence electrons in the solid

Would this be more correct?

 

[nasu]

I am not sure you meaningfully can say that a definition is more "correct" than another.
A definition is useful if it is generally accepted and contributes to easy communication but is arbitrary in the end. If you are trying to find which one is the most widely accepted, it may depend on the field or discipline (chemistry, solid state physics, electrical engineering, etc).

You don't learn much about how nature is nature is by focusing endlessly on definitions.
If you understand the structure of the band structure of the metals and how does it affects the properties of the metals, it's really irrelevant what you call the last populated band.

 

[worwhite]

I must say I half-expected that response. Yes I agree that it's all too common in physics to have muddled definitions, and as you pointed out, especially so between fields. I was hoping that this wasn't one of those cases (and I'm still not convinced that it is).

In any case, I certainly agree that merely memorizing definitions by itself is a poor way to do things. But I'd like to seek your understanding for my trying to grasp how the definitions fit the concepts, because for someone who doesn't already know these things, it is difficult to predict whether the definitions are arbitrary or have an important meaning, and I'd rather err on the side of caution. In my mind, physics is not a subject that gives a lot of leeway for ambiguity.

 

[nasu]

OK, when I said "arbitrary" I did not mean that the definitions are given without any reason or regard to some physical reality. I won't call them muddled either. It's just that each field may look at something from different points of view and define concepts accordingly.
The main point I tried to make is that for a definition there is no point to ask if it's right or true. It is not a statement about facts, which can be tested against reality. It's more like giving names to concepts.

You can definitely learn something even by comparing definitions and looking for cases when they may not apply very well.
For example, here you gave two definitions of the valence band:
1. "the highest occupied band at absolute zero"
2. "valence band is the band of energy associated with valence electrons in the solid"
You can ask all kind of questions.
Are these equivalent? Are the valence electrons always in the highest band?
If this were the case, the two definitions would be equivalent but "looking" at different aspects (energy level vs binding properties).
What if electrons in two different bands participate in the binding?
Looking for the answers you may learn a lot.

 

[worwhite]

I see, thanks.