Why is silver (or silver alloy, Cusil), the best thermal conductor?

[junkerman123]

From Wikipedia:

Thermal conductivity is not a simple property, and depends intimately on structure and temperature. For instance, pure, crystalline substances also exhibit highly variable thermal conductivities along different crystal axes, due to differences in phonon coupling along a given crystal dimension. Sapphire is a notable example of variable thermal conductivity based on orientation and temperature, for which the CRC Handbook reports a thermal conductivity perpendicular to the c-axis of 2.6 W·m-1·K-1 at 373 K, and 6000 W·m-1·K-1 at 35 K for an angle of 36 degrees to the c-axis.

I'm having difficulty understanding this terminology. What structural properties within how silver atoms stack up make silver the best thermal conductor? And if so, why does adding copper to silver make the resulting alloy, Cusil, an even better conductor?

Can somebody please shed some light on the subject?

 

[f95toli]

There is no simple explanation. This is extremely complicated although I would like to emphasise that we DO understand how it works. However, you need a supercomputer of two if you want to predict the thermal (or electrical) conductivity of a "real" material (with impurities and imperfections).

I should say it is quite easy to model thermal conductivity in simple metalls if you introduce phenomenological parameters (e.g. scattering parameters etc), but if you want to calculate it from first principles (i.e. from the structure) you first need the phonon spectrum, electron-phonon interaction etc which, again, are things that are VERY tricky to calculate.

Generally speaking, materials that have a high electrical conductivity also have a high thermal conductivity; silver is one example. However, as the example of sapphire demonstrates this is not neccesarily true (sapphire is a very good insulator).

 

[silverpig]

f95toli gave a good answer. It's very complicated and goes deeply into condensed matter physics, but a very simple explanation could be this:

Imagine a group of people are standing side by side in a row. They all are holding hands so they are joined together. Now imagine a number of these rows of people all lined up beside one another. Let's say you are one of the people in this lattice. You are holding hands with the person on your right and on your left, and you see a row of people in front of you and behind you.

Now imagine trying to send a signal down one of the rows. Someone on your far left squeezes the hand of the person beside them, and they repeat the process until your left hand gets squeezed. You squeeze your right hand and pass the signal along until it gets to the far right edge of the lattice. Fairly efficient.

However, imagine trying to send a signal across the rows. You would have to get a kick in the arse, and then try to move forward, pulling your neighbours with you, to try to kick the person in front of you. It won't be so easy to do.

How the atoms are arranged matters for conduction as a simple approximation. There are of course many other factors.

 

[MrDudeMan]

Originally posted by: silverpig
f95toli gave a good answer. It's very complicated and goes deeply into condensed matter physics, but a very simple explanation could be this:

Imagine a group of people are standing side by side in a row. They all are holding hands so they are joined together. Now imagine a number of these rows of people all lined up beside one another. Let's say you are one of the people in this lattice. You are holding hands with the person on your right and on your left, and you see a row of people in front of you and behind you.

Now imagine trying to send a signal down one of the rows. Someone on your far left squeezes the hand of the person beside them, and they repeat the process until your left hand gets squeezed. You squeeze your right hand and pass the signal along until it gets to the far right edge of the lattice. Fairly efficient.

However, imagine trying to send a signal across the rows. You would have to get a kick in the arse, and then try to move forward, pulling your neighbours with you, to try to kick the person in front of you. It won't be so easy to do.

How the atoms are arranged matters for conduction as a simple approximation. There are of course many other factors.

that was a very good analogy. brilliant even.

 

[imported_Tick]

Originally posted by: MrDudeMan

Originally posted by: silverpig
f95toli gave a good answer. It's very complicated and goes deeply into condensed matter physics, but a very simple explanation could be this:

Imagine a group of people are standing side by side in a row. They all are holding hands so they are joined together. Now imagine a number of these rows of people all lined up beside one another. Let's say you are one of the people in this lattice. You are holding hands with the person on your right and on your left, and you see a row of people in front of you and behind you.

Now imagine trying to send a signal down one of the rows. Someone on your far left squeezes the hand of the person beside them, and they repeat the process until your left hand gets squeezed. You squeeze your right hand and pass the signal along until it gets to the far right edge of the lattice. Fairly efficient.

However, imagine trying to send a signal across the rows. You would have to get a kick in the arse, and then try to move forward, pulling your neighbours with you, to try to kick the person in front of you. It won't be so easy to do.

How the atoms are arranged matters for conduction as a simple approximation. There are of course many other factors.

that was a very good analogy. brilliant even.

Very brilliant.

 

[Soccerman06]

My old chemistry teacher in HS taught us that the better the conductivity a material is, the more planar the bonds are in the material. Think of it like putting a piece of paper on top of another, that being very flat with a few ridges (bonds) that can impede electron flow/vibration/friction and being quite uniform in structure. I dont know if this is the same thing yall are talking about above me, so unless someone can confirm my analogy, dont really listen to it

 

[junkerman123]

Thanks for the answers guys, seems like it is not so simple to specifically relate structural features to thermal conductivity in precise terms. A follow-up question: we all know that electrons are arbitrarily flying around in every atom, and that heat is generated when these electrons collide with nearby atoms. Why would some elements be more likely to have these collisions than others? Are the nucleii closer together? Why wouldn't heavier elements with more electrons have a likelier probability of these collisions occuring? Is this difference dependant on the "unit cell" (the way several atoms are arranged to form a cell) or on the "crystal lattice" (the way these cells crystalize in 3 dimentions)? Hm....ok more than one follow-up question I guess.

Also, not to go off on a tangent, but what determines how HOT an element can get? Would some elements hypothetically reach the "plasma" stage (I believe this is what happens when "maximum temperature" is reached) more quickly than others? Does this also depend on the "crystal lattice"?

And tangent #2: do phonons carry heat in all solids to some degree? I read that metals have electrons as primary carriers of heat, and diamonds use phonons as primary carriers, which make the diamond the best thermal conductor. Do both phonons and electrons exist in all cases, but one just takes a backseat to another? This is the impression I got.

Sorry for all these questions, it's just really hard to understand anything written online, you guys do a better job of explaining.

 

[spikespiegal]

However, imagine trying to send a signal across the rows. You would have to get a kick in the arse, and then try to move forward, pulling your neighbours with you, to try to kick the person in front of you. It won't be so easy to do.

And when you apply liquid nitrogen to superconductors, all those hypothetical rows of people start to hug each other to stay warm, hence making the handshake process more efficient

Sorry, just trying to add to a brilliant analogy.

 

[f95toli]

Originally posted by: junkerman123
Thanks for the answers guys, seems like it is not so simple to specifically relate structural features to thermal conductivity in precise terms. A follow-up question: we all know that electrons are arbitrarily flying around in every atom, and that heat is generated when these electrons collide with nearby atoms. Why would some elements be more likely to have these collisions than others? Are the nucleii closer together? Why wouldn't heavier elements with more electrons have a likelier probability of these collisions occuring? Is this difference dependant on the "unit cell" (the way several atoms are arranged to form a cell) or on the "crystal lattice" (the way these cells crystalize in 3 dimentions)? Hm....ok more than one follow-up question I guess.

Also, not to go off on a tangent, but what determines how HOT an element can get? Would some elements hypothetically reach the "plasma" stage (I believe this is what happens when "maximum temperature" is reached) more quickly than others? Does this also depend on the "crystal lattice"?

And tangent #2: do phonons carry heat in all solids to some degree? I read that metals have electrons as primary carriers of heat, and diamonds use phonons as primary carriers, which make the diamond the best thermal conductor. Do both phonons and electrons exist in all cases, but one just takes a backseat to another? This is the impression I got.

Sorry for all these questions, it's just really hard to understand anything written online, you guys do a better job of explaining.

In metals you can forget about the properties of the ions. In a metal the conduction electrons are NOT bound to any particular ion (this is the definition of what consitutes a metal) . The free electrons basically form an "electron gas". The electrons "see" the electric potential created by the ions which is nominally perodic. Now, it can be shown using some basic quantum mechanics (electron transport in solids is ALWAYS "quantum mechanical) that if this periodic potential is "perfect" meaning the ions are not moving and there are no defects; the electrons would move without resistance (the wavefunctions are so-called Bloch waves). However, at non-zero temperature the ions ARE moving (by definition, temperature of a solid=kinetic energy of the particles) meaning electrons will be scattered from time to time,
Moreover, in real materials there are always impurties, interfaces (grain boundaries) and dislocations which also "distort" the potential causing resistance. If you cool down a metal you will find that the resistance drops until you reach about 20-30K or so where the resistivity stops decreasing, this "residual" resistance is because of these imperfections.


Depends on what you mean by "hot", metals melt if you heat them up. The melting temperature depends on the strength of the bonds.

And yes, phonons DO carry heat. In a good insulator there are no free electrons meaning all the heat is carried by phonons.

 

[junkerman123]

Thank you for the reply, you answered all of my questions but the first one. I am still trying to get at what exactly makes one metal a better conductor of heat than another (why is silver the best...why does adding a little copper make the allow even better). You said:

Originally posted by: f95toli
...if you want to calculate [thermal conductivity] from first principles (i.e. from the structure) you first need the phonon spectrum, electron-phonon interaction etc...

Can you perhaps go into a little more detail about these "structural" differences? What would these spectra(?) show as far as structure is concerned? How is the structure of silver different from the structure of Iron, which is an inferior thermal conductor. Is this "structure" the only contributing factor or does the makeup of the atoms have an effect?

I appreciate your patience in explaining this.

 

[silverpig]

Calculating quantities like that in condensed matter is quite difficult. Electronic structure is important as you're asking about conductors and when you start talking about hybridized orbitals that can get quite complicated.

There was a question about plasma which is fairly easy to answer, and that is that different metals, after of course melting, then boiling, will have different plasma temperatures. A plasma occurs when the nuclei are fully ionized (have all of their electrons ripped off), so the heavier elements will have a higher plasma temperature as that last electron is more tightly bound.

 

[sao123]

Originally posted by: junkerman123
Thank you for the reply, you answered all of my questions but the first one. I am still trying to get at what exactly makes one metal a better conductor of heat than another (why is silver the best...why does adding a little copper make the allow even better). You said:

Originally posted by: f95toli
...if you want to calculate [thermal conductivity] from first principles (i.e. from the structure) you first need the phonon spectrum, electron-phonon interaction etc...

Can you perhaps go into a little more detail about these "structural" differences? What would these spectra(?) show as far as structure is concerned? How is the structure of silver different from the structure of Iron, which is an inferior thermal conductor. Is this "structure" the only contributing factor or does the makeup of the atoms have an effect?

I appreciate your patience in explaining this.

Another simple anaolgy to help you.

Heat is essentially an energetic vibration. Heat is the measure of the kinetic energy of a particular atom, with no true net displacement.
Heat is transferred through 3 ways.
Radiation (infrared)
Convection (heat transfer through fluid like movement)
Conduction (through the touching & bumping of atoms)

for this I am only addressing conduction.
Now, the way that certain elements bond together, determins the shape of the inter- atomic bonds. Depending on this shape, a vibrating atom is more likely to *bump into* one or more other atoms. This is how heat transfer occurs, through conduction.
just like in billiards when one ball strikes another, energy is transferred- this same behavior explains how conduction transfers heat.

Now, why silver, more so that some other metal?
The alignment of atoms in a piece of pure silver, is such that the atoms will bump more often (size and space restrictions), and more efficiently (full contact vs clipping) than most if not all other metals. Impurities change the geometry, and can even increase the efficiency of the transfer. (Imagine, having a box of rubber balls which you shake, they all bounce around. Now add a tennis ball and shake...im sure that adds a lot more commotion inside the box.)

This is a way elementary explanation, but i hope it helps.

 

[junkerman123]

Thanks for the replies sao123 and silverpig, definitely cleared things up a lot.

I was getting at one more thing. You said:

Originally posted by: sao123
Now, why silver, more so that some other metal?
The alignment of atoms in a piece of pure silver, is such that the atoms will bump more often (size and space restrictions), and more efficiently (full contact vs clipping) than most if not all other metals. Impurities change the geometry, and can even increase the efficiency of the transfer. (Imagine, having a box of rubber balls which you shake, they all bounce around. Now add a tennis ball and shake...im sure that adds a lot more commotion inside the box.)

This is a way elementary explanation, but i hope it helps.

As an elementary explanation, that is great. But I was actually looking for a more in depth explanation, i.e. a comparison between the molecular structures of something like Silver vs Iron. What aspects of this alignment make silver a better thermal conductor than other metals. Are the atoms merely closer together? Is there some kind of structure that creates more collisions? I am basically looking for an answer from a molecular geometry perspective.

Please, do not hesitate to answer in more advanced terms. Although I probably won't know what you're talking about I am not afraid of doing research to make sense of your replies! It's just so freakin hard to find anything cohesive on Google about this, and I don't know what other sources to turn to for this kind of information, besides you geniuses!

Thanks for the help so far.

 

[sao123]

Originally posted by: junkerman123
Thanks for the replies sao123 and silverpig, definitely cleared things up a lot.

I was getting at one more thing. You said:

Originally posted by: sao123
Now, why silver, more so that some other metal?
The alignment of atoms in a piece of pure silver, is such that the atoms will bump more often (size and space restrictions), and more efficiently (full contact vs clipping) than most if not all other metals. Impurities change the geometry, and can even increase the efficiency of the transfer. (Imagine, having a box of rubber balls which you shake, they all bounce around. Now add a tennis ball and shake...im sure that adds a lot more commotion inside the box.)

This is a way elementary explanation, but i hope it helps.

As an elementary explanation, that is great. But I was actually looking for a more in depth explanation, i.e. a comparison between the molecular structures of something like Silver vs Iron. What aspects of this alignment make silver a better thermal conductor than other metals. Are the atoms merely closer together? Is there some kind of structure that creates more collisions? I am basically looking for an answer from a molecular geometry perspective.

Please, do not hesitate to answer in more advanced terms. Although I probably won't know what you're talking about I am not afraid of doing research to make sense of your replies! It's just so freakin hard to find anything cohesive on Google about this, and I don't know what other sources to turn to for this kind of information, besides you geniuses!

Thanks for the help so far.

The simple solution you search for does not exist, it is very complex mathematical equations (think PHD level question), and its been far too long since I studied Thermodynamics & Solid State Physics for me to give you an expert analysis of Silver vs Iron.
You might need to speak with a professional thermodynamics engineer to gain this insight. However Wiki has some decent articles which may guide you with knowledge and other terms of interest to further your study.


Metallic Bonding
Thermal Conductivity
Solid State Physics
Phonons
Crystal Structure

 

[junkerman123]

I was not looking for a simple solution! If I was, I would not have come here for it, that's for sure.

Thanks for the links. I have looked at most of them but I will read them more carefully again. I do have a much better understanding of the dynamics now thanks to you guys, and I appreciate your help! If I have more questions I won't hesitate to ask. :beer:

 

[sao123]

Originally posted by: junkerman123
I was not looking for a simple solution! If I was, I would not have come here for it, that's for sure.

Thanks for the links. I have looked at most of them but I will read them more carefully again. I do have a much better understanding of the dynamics now thanks to you guys, and I appreciate your help! If I have more questions I won't hesitate to ask. :beer:

I apologize... I see I gave you the article which you quoted in your OP...
but at least i gave you a few more.

EDIT: You might want to try buying a textbook on thermodynamics or solid state physics.