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Metal alloys thermal conductivity

  1. Oct 29, 2005 #1

    Pengwuino

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    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.
     
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  3. Oct 29, 2005 #2

    Integral

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    Poorer is not exactly are well defined term. Do alloys have DIFFERENT thermal properties...Yes.
     
  4. Oct 29, 2005 #3

    Astronuc

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    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
     
  5. Oct 29, 2005 #4

    Pengwuino

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    oops, bad wording.

    I heard they have poorer thermal conductivity... thats 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.
     
  6. Oct 29, 2005 #5

    Integral

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    One frequent interesting property change is that many alloys have LOWER melting points then the constituent metals.
     
  7. Oct 30, 2005 #6
    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 Wiedemann-Franz law.
    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.
     
  8. Nov 9, 2005 #7
    This is the explanation for the Wiedemann-Franz law.
    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 absorbtion 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
     
  9. Nov 9, 2005 #8

    Danger

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    Quite handy for those of us who like to solder.
     
  10. Nov 9, 2005 #9

    Gokul43201

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    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.
     
    Last edited: Nov 10, 2005
  11. Nov 10, 2005 #10
    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 :redface:
     
  12. Nov 10, 2005 #11
    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 cant find the spell check button anymore!
    eric
     
  13. Nov 10, 2005 #12

    Gokul43201

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    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 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.

    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.
    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.
    I believe spell-check has not yet been restored since the upgrade.
     
    Last edited: Nov 10, 2005
  14. Nov 10, 2005 #13

    Astronuc

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    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! :grumpy:
     
  15. Nov 10, 2005 #14
    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
     
  16. Nov 10, 2005 #15
    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.
     
  17. Nov 11, 2005 #16
    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
     
  18. Nov 11, 2005 #17

    Gokul43201

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    What does (the last part of) this sentence mean ?
     
  19. Nov 12, 2005 #18
    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
     
  20. Nov 12, 2005 #19
    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.
     
  21. Nov 13, 2005 #20
    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
     
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