Metal alloys thermal conductivity

[Pengwuino]

Someone once told me that almost all alloys have poorer thermal properties then their component metals. Is this true? I want to have a little experiment but I don't want to do it if I know all the results will be crap.

 

[Integral]

Poorer is not exactly are well defined term. Do alloys have DIFFERENT thermal properties...Yes.

 

[Astronuc]

Yes, in general it is true that alloys have differences in thermal properties, e.g. lower thermal conductivity, than pure elements. Some examples - thermal conductivities of Fe vs stainless steels, and Ti vs Ti-6V-4Al

Fe (pure) - Thermal Conductivity 76.2 W/m-K (529 BTU-in/hr-ft²-°F)

400 series stainless steel
24.9 W/m-K 173 (BTU-in/hr-ft²-°F) 100°C
28.6 W/m-K 198 (BTU-in/hr-ft²-°F) 500°C

300 series stainless steel
16.2 W/m-K 112 (BTU-in/hr-ft²-°F) 100°C
21.4 W/m-K 149 (BTU-in/hr-ft²-°F) 500°C

Thermal Conductivity
Ti (pure) - 17 W/m-K (118 BTU-in/hr-ft²-°F)

Ti6Al4V (grade 5) - 6.7 W/m-K (46.5 BTU-in/hr-ft²-°F)


If the alloying is very slight - e.g. 1-2%, then the differences may not be significant. For some Zr-alloys, alloying actually increases thermal conductivity.

Thermal Conductivity
Zr (pure) - 16.7 W/m-K (116 BTU-in/hr-ft²-°F)

Zircaloy-2 - 21.5 W/m-K (149 BTU-in/hr-ft²-°F), Zr-2 is about Zr-1.5Sn-0.2Fe-0.1Cr-0.05 Ni-0.12O

Grade 702 - 22 W/m-K (153 BTU-in/hr-ft²-°F). Zr-4.5Max Hf - 0.2(Fe+Cr)-0.16O

One could try comparisons of elements and alloys on Matweb, which is from where the thermal conductivity data were taken

 

[Pengwuino]

oops, bad wording.

I heard they have poorer thermal conductivity... that's what I'm focusing on here.

Guess that saves me a big waste of time and money. I was going go try to mix metals to determine if i can get some good thermal conductivity.

 

[Integral]

One frequent interesting property change is that many alloys have LOWER melting points then the constituent metals.

 

[Pieter Kuiper]

Someone once told me that almost all alloys have poorer thermal properties then their component metals. Is this true?

Yes, this is true, because (explanation that is probably over your head) the mean free path of phonons is shorter in alloys, in which there is more disorder. Roughly, the mean free path of electrons is about the same as that of phonons, so the electrical conductivity is also lower. This is the explanation for the http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thercond.html" .

I want to have a little experiment but I don't want to do it if I know all the results will be crap.

A qualitative experiment is easy. You can compare thermal conductivities of different rods with the same diameter by holding them in a candle flame. See for how long you can hold copper, aluminium, iron, brass, and steel.

 

[erickalle]

This is the explanation for the http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thercond.html" .
I just had a look at this site. According to this site clasical and qm theory suggest that KE of (roughly) 3kT is absorbed by each conduction electron. Since the total absorption per atom is also about 3kT, can I then draw the conclusion that no energy is transferred to the +ve ion?
What happens when we have more than one free electron per atom?
eric

 

[Danger]

One frequent interesting property change is that many alloys have LOWER melting points then the constituent metals.

Quite handy for those of us who like to solder.

 

[Gokul43201]

Pengwuino : An alloy of A,B,C,... will have a thermal conductivity, K(A,B,C,..) < K(A), where K(A) > K(B) > K(C) > ...

In other words, you can only say for certain that the alloy will have a thermal conductivity that it poorer than the thermal conductivity of the best conducting component. But in most cases, the thermal conductivity is lower than that of all components. The exceptions usually happen at very small alloying levels where the mean separation between impurity particles is greater than the electron/phonon mean free path. Eg : 0.1% Cd in Cu has K = 377 W/Km which is greater than that of cadmium)

Astronuc : Where did you get that data for Zircaloy ? Page 12 from the link below gives different numbers.
http://www.insc.anl.gov/matprop/zircaloy/zirck.pdf

erickalle : I don't see how your question is related to Wiedemann-Franz. It is talking about heat capacity rather than thermal conductivity.

As for what you are saying, there are a few errors in your understanding. A free electron has only 3 (translational) degrees of freedom (rotation of a point particle takes no energy), and so can gain about (3/2)kT of thermal energy (not 3kT). To say that each of the free electrons can have this energy is wrong though - and that is a failing of the classical picture. The quantum statistics of the free electrons dictates that only a small fraction (~ 1% at room temperature) of them can actually gain this kind of energy. This follows from the Fermi distribution for particles that obey Pauli's Exclusion Principle.

Additionally, what you talk about is called the electronic heat capacity, and is only a part of the total heat capacity. The rest of it comes from the lattice of positive ions. The electronic heat capacity does scale with the number of electrons per atom.

 

[Pieter Kuiper]

... the mean free path of phonons is shorter in alloys, in which there is more disorder.

Sorry,while this is true, it is not the explanation for thermal conductivity, which in metals is by electrons.

I do not know what I was thinking

 

[erickalle]

Gogul, the next paragraph is from the above mentioned site:
For metals, the thermal conductivity is quite high, and those metals which are the best electrical conductors are also the best thermal conductors. At a given temperature, the thermal and electrical conductivities of metals are proportional, but raising the temperature increases the thermal conductivity while decreasing the electrical conductivity. This behavior is quantified in the Wiedemann-Franz Law:
As you can see it is talking about thermal coductivity. Thanks for pointing out the energy is 3/2kT.
If only ~1% of conduction electrons can reach this energy, it would be fair to say that the explanation of this site is ~99% wrong, and therefore gives a very distorted picture. Also, what do you make of the statement: "raising the temperature increases the thermal conductivity" ?
Sorry for the spelling mistakes but I can't find the spell check button anymore!
eric

 

[Gokul43201]

Gogul, the next paragraph is from the above mentioned site:
For metals, the thermal conductivity is quite high, and those metals which are the best electrical conductors are also the best thermal conductors. At a given temperature, the thermal and electrical conductivities of metals are proportional, but raising the temperature increases the thermal conductivity while decreasing the electrical conductivity. This behavior is quantified in the Wiedemann-Franz Law:
As you can see it is talking about thermal coductivity.

Yes that Hyperphysics article does talk about Wiedeman-Franz and thermal conductivity. That is not what I had a problem with. However, you said that :

I just had a look at this site. According to this site clasical and qm theory suggest that KE of (roughly) 3kT is absorbed by each conduction electron.

I don't see where that article says anything like this. In fact, I'm pretty sure this isn't stated anywhere on the site. If you got it from a particular page, show a link to that page. I'm pretty sure you just misunderstood something it said in one of its articles on heat capacity or some such.

Thanks for pointing out the energy is 3/2kT.
If only ~1% of conduction electrons can reach this energy, it would be fair to say that the explanation of this site is ~99% wrong, and therefore gives a very distorted picture.

It would be fair to say that, ONLY if you can actually quote a page on that site that says exactly what you said. In my opinion, the Hyperphysics site is a very high quality physics resource, and I would not expect it to have any gross errors. If it says something that I disagree with, I'd go back and recheck my understanding. While the Drude (classical) result is conceptually flawed, it ends up being very close to the correct result because of two offsetting errors : the heat capacity should be reduced by about 3 orders of magnitude (because of the effect described above), but the mean square thermal velocity (or mean KE) sould be raised by the same order.

Also, what do you make of the statement: "raising the temperature increases the thermal conductivity" ?

Can't disagree with that. Clearly, at a simplistic level, raising the temperature raises the mean velocity of the conduction electrons, and hence will raise the rate of electronic heat transfer.

Sorry for the spelling mistakes but I can't find the spell check button anymore!
eric

I believe spell-check has not yet been restored since the upgrade.

 

[Astronuc]

Astronuc : Where did you get that data for Zircaloy ? Page 12 from the link below gives different numbers.
http://www.insc.anl.gov/matprop/zircaloy/zirck.pdf

The number I posted came from Matweb, and it did look a bit high.
http://www.matweb.com/search/SpecificMaterial.asp?bassnum=MZRN10

I checked our code and we use the MATPRO expression, which gives a value of about 12.7 W/m-K at 300K, so I think the MATWEB value is incorrect - possibly a typo. Perhaps is should have been 12.5 W/m-K rather than 21.5 W/m-K.

On the other hand, the value given for Grade 702 is correct according to a datasheet from Wah Chang. If this is the case, then perhaps the 21.5 W/m-K is correct, which I find hard to believe. So now I have to get to the bottom is this discrepancy. Nuts!

 

[erickalle]

Gokul, next formula is from HyperPhysics:
Using the expression for mean particle speed from kinetic theory v=(8kT/PI*m)^1/2.
This suggest to me that the KE is ~3/2kT. If the heat capacity of conduction electrons is in fact 3 orders of magnitude out it would have been nice if the site made a mention of that. Equivalent: length wise we are now compairing meters with millimeters!
Can you give me (us) a rough idea of what you mean by the mean KE should be raised by the same amount, don't we end up with the same value for the heat capacity?
As for the statement increased temperature results in increased thermal conductivity: I have in front of me a table of most of the metals mentioned in this article. From 1 to ~10 or 20 K this conductivity is indeed increasing. Higher than this all the way up to melting point, thermal conductivity is decreasing. On a scale of 1k up to melting point it means decreasing for ~95% of the way.
eric

 

[Pieter Kuiper]

Erickalle: For heat capacities we have the law of Dulong & Petit, that says that the heat capacity of solids is about 25 joule per mole per kelvin. This is about the same for metals and non-metals. From this you can see that the heat capacity of the electron gas is much smaller than what a classical theory would predict.

So instead, you have to look at it as degenerate gas of fermions, with electron energies that follow the Fermi-Dirac distribution. The heat capacity is then of order kT/Ef smaller than the classical prediction. The Fermi energy Ef of metals is of the order of 3 eV. At room temperature kT is about 25 meV. So that is a ratio of 10^2.

 

[erickalle]

Thanks Pieter Kuiper.
I have a couple more blind spots for certain aspects related to heat.
For instance: I can onderstand readily where the heat content of (ideal) gas atoms end up. Clearly the KE of 3/2kT is converted in the atomic speed and a PE of the same amount in elastic energy. For solids where the speed of sound ie the speed of the atoms doesn't change its a different case. I understand that increased temperature results in increased phonon density, but no atom no phonon. Where does the KE end up?
eric

 

[Gokul43201]

I understand that increased temperature results in increased phonon density, but no atom no phonon.

What does (the last part of) this sentence mean ?

 

[erickalle]

Yes, that last sentence was written in a bit of a haste. I’ll try to explain. As far as I am aware heat energy in metals (say mono-atomic & pure) is stored in the form of phonons. Phonons are built up by lattice vibrations of a metal, this lattice in turn is built up by atoms. Now here comes my head ache : how can phonons get more KE (in case we increase temperature) if the individual atoms are not moving any faster, because the speed of sound is constant ie the speed of atoms is independent of temperature?
eric

 

[Pieter Kuiper]

The number of phonons is increasing with temperature.

It is easier to do this in a simpler model, where atoms are tied by an imaginary spring (harmonic potential) to a lattice point. Assume the oscillations are independent. There are six degrees of freedom (3 momenta, 3 positions) giving Cv = 3k_B per atom, or 25 J/mol.

Einstein quantized these oscillators, which gives a lower Cv when the temperature is low (when there is on average less then one quantum of vibration per oscillator). But at high temperatures, the oscillater is at n=2 or higher, and Cv is close to the classical value of 3R.

Now phonons arise by coupling the oscillators together. It gives the Debye T^3 theory of specific heats, which is a real improvement at very low temperatures.

 

[erickalle]

Pieter, for reasons of clarity I try to keep this discussion as simple as possible, eg pure, mono-atomic metals. I want to be able to walk before I run. I also should have mentioned to keep away from extreme temperatures. But I do like your idea of simplifying with the help of a spring. I am now going to hang a (slightly longer) spring horizontally between 2 walls. On the middle of this spring I attach a small mass and give it a push. This mass is now oscillating and I can work out KE and PE. If I want to increase KE the only option I have is to give the mass an extra push so that the speed of the mass increases. If I am not allowed to increase this speed (analogy: constant speed of sound in metals) there’s no way I can further increase KE.
eric

 

[erickalle]

I've done some research on the net and found the following:
1

MadSci Network: Physics
Re: Does sound travel in metals faster, farther than rocks? Why?
Area: Physics
Posted By: Steve Chu, Graduate Student,A secondary school in H.K.
Date: Fri Apr 25 09:27:44 1997
Area of science: Physics
ID: 857314635.Ph
Message:
Sound propagation requires a medium. In air, air molecules movement can
transmit sound. In water, water molecules are responsible. It is true that
sound travels faster in a denser medium and therefore sound travels faster
in water than in air. Of course much faster in metals.
However, if you compare sound traveling in metal and in rock, you have
to be aware that metals conduct electricity not by the movement of the
atoms or molecules but by the movement of mobile electrons. These electrons
may also carry sound wave. I would say sound travels faster in metals than
in rocks because rocks may be harder than metals but they don't have mobile
electrons to pass sound wave through.

2

The speed of sound in copper is about 3,353 meters per second or 12,070 KPH (7,497 MPH) at normal temperatures, but oddly decreases with temperature, because the metal's elasticity falls off.

Does anybody know anything about electrons propagating sound in metals?
Does the second statement mean that the speed of sound decreases as temperature increases? Both would indeed be odd!
eric

 

[Gokul43201]

The speed of sound goes like c = \sqrt{K/\rho}. It is inversely proportional to the density but increases with the elastic/bulk modulus of the material. Sound is not carried by electrons in metals...so that post you quoted is not correct.

 

[Astronuc]

I would say sound travels faster in metals than in rocks because rocks may be harder than metals but they don't have mobile electrons to pass sound wave through.

That is definitely wrong.

Adding to what Gokul mentioned, metals are usually denser that rock and ceramics. Compare with steel's specific gravity of ~ 7.5-8, depending on alloying elements and composition.

Density of common minerals - http://www.mininglife.com/Miner/general/Density.htm.

Specific Gravity Table For Ceramics, Metals & Minerals - http://www.reade.com/Particle_Briefings/spec_gra.html

Generally metals are two or three time denser than minerals/ceramics (i.e. metal oxides). Also, surface minerals are likely to have porosity of several %.

 

[erickalle]

This time I do agree with both replies. It would be interesting to have a look at both density and elastic/bulk modulus versus temperature of some metals.
eric

 

[erickalle]

Turned out to be extremely interesting. Young’s elastic modulus (Y) drops by increasing temperature not only for pure metals but just about any material.
Take copper. From T=0 to 800C , Y=130 to 75 GPa.
For expansion (a) I’ve only found the linear value at room temperature. a=1.65E-5 K^-1 Multiplying by 3 for bulk value and guessing that it’s value is not going to change too much, density is also not changing much. It is clear from Gokuls formula that upon heating we are now losing a lot velocity and a lot of energy.

Do we need to change the laws of physics as we know it? Astronuc help me out!
eric

 

[asterix]

why?

Eric, why do you think we need to change the laws of physics? Please explain more fully.

 

[erickalle]

First a correction. In one of the previous repies I said that we also need to take account of PE, however for an ideal mono atomic gas we only have to take in account KE. So: 1/2mV^2=3/2kT per atom.
Now my main problem. How is it that upon heating copper from 0C to 800C each atom is losing KE?
Gokul used K (=bulk modulus) which is more accurate then my Young modulus. They are related via the Poissons ratio. K is in fact a bit higher then Y.
Searching through some pages on the net about phonons you can see that they are used to explain a lot of properties of solids such as electron and proton scattering.
But I come back to the idea that atoms form the base for phonons, just like water waves cannot exist without water molecules. Ultimately water wave KE can be traced to the water molecules.
Conclusion: Perhaps we need to change our ideas about the heat content in metals.
eric

 

[mezarashi]

Do we need to change the laws of physics as we know it? Astronuc help me out!

I think you are in some state of incredulity. Some of your quotes regarding material properties are relatively 'dangerous' in that you are going off in a very wrong approach. You let your immediate intuition set you in the wrong direction. These phenomena are true not because the laws of physics are violated, but because they hold!

We are not "losing energy" by having the material lowering its bulk modulus. Generally, denser materials will allow mechanical waves to propagate through them at a faster speed. This has nothing to do with internal energies. You are confusing wave propagation with temperature.

As far as I know, phonons are not used in this field. Phonons are 'bundles' of momentum used in proton, electron scattering phenomena. I'd like to re-emphasize what has been emphasized many times already. Protons and electrons (i.e. thermal or electrical conductivity) has about nothing to do with the speed of mechanical waves in materials. That only applies in the propagation of light in the material.

 

[armandowww]

make this traffic analogue!
you have a great deal of autovehicles at a crossroad with a traffic light at the end. When green light switches to red light the first car is going to stop. It was going ahead with some speed... we don't care on a fine level!
What we care above all is: when first car begin to stop the stop lights of that vehicle switch on and after a certain reaction so the second car ... the n-th.. etc!
The speed we are dealing with is related to the propagation of a signal!
No real particle is to be taken into account

 

[Astronuc]

Turned out to be extremely interesting. Young’s elastic modulus (Y) drops by increasing temperature not only for pure metals but just about any material.
Take copper. From T=0 to 800C , Y=130 to 75 GPa.
For expansion (a) I’ve only found the linear value at room temperature. a=1.65E-5 K^-1 Multiplying by 3 for bulk value and guessing that it’s value is not going to change too much, density is also not changing much. It is clear from Gokuls formula that upon heating we are now losing a lot velocity and a lot of energy.
Do we need to change the laws of physics as we know it?

I am not sure why one would think that the laws of physics must be changed. What contradiction does one perceive?

As Gokul and mezarashi mentioned, electrons are responsible for thermal conduction in metals.

Metals are much better thermal conductors than non-metals because the same mobile electrons which participate in electrical conduction also take part in the transfer of heat.

from http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thercond.html

Heating a metal obviously changes the 'elasticity' (changes in interatomic bond strength) and increases the interatomic spacing.

Here is a nice discussion of the speed of sound - http://en.wikipedia.org/wiki/Speed_of_sound

I diverge a little, but this article raises an important issue.

Elevated Temperature Modulus Measurements using the Impulse Excitation Technique (IET) - http://midas.npl.co.uk/midas/content/mn049.html-

There is not a wealth of information in the literature on the variation of elastic modulus with temperature. Data is available in a number of handbooks, but often only over a limited temperature range. Also, much of the fundamental work on the elastic properties has focused on pure metals and only a limited number of materials and there is relatively little information in the literature on modulus measurement methods at elevated temperatures for engineering alloys.

I can testify this these statements. I have been in situations where I have had to approximate (guesstimate!) thermophysical properties because they simply did not exist - no one had bothered to measure them, especially at high temperature because we simply have not used certain alloys under those conditions.

Here is another interesting article - http://www.stormingmedia.us/81/8120/A812004.html