Metal alloys thermal conductivity

[erickalle]

The KE of the gas molecules affects the pressure, not the speed of sound.

A more accurate expression is
c = \sqrt {\kappa \cdot R\cdot T}
where
* R (287.05 J/(kg·K) for air) is the universal gas constant (In this case, the gas constant R, which normally has units of J/(mol·K), is divided by the molar mass of air, as is common practice in aerodynamics)
* κ (kappa) is the adiabatic index (1.402 for air), sometimes noted γ
* T is the absolute temperature in kelvins.
In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure. Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere - actual conditions may vary.

For an ideal gas: KE=1/2mv^2=3/2kT.
I am not going to change my view wrt gasses but I still have to have a long hard look at metals. In the mean time if anybody has some more info I'd be greatfull.
eric

 

[Gokul43201]

Gokul this answer could finally solve my headache. As I understand it, this is indeed the case for gasses. An increase in temperature will increase KE and therefore the speed of sound in a gas will go up. Please correct me if this is wrong.

This is not wrong.

Now are you saying that this not applies to metals?

That's right.

Are you saying that KE and the speed of sound and are not connected in metals?

Not exactly, but the relationship is not straightforward. Besides, you've assumed that increasing temperature proportionately increases the KE of the atoms. While this is not an entirely unreasonable line of thinking (it is flawed however, and I may get to that later), you've probably forgotten that a large chunk of the heat can go into the KE of the free electrons, which do nothing for the propagation of sound. Additionally you've applied the same theory to a metal, as you have to an ideal gas. Unfortunately that is not a valid extension. An ideal gas is a non-dispersive medium, while a metal is not.

An ideal gas behaves like a bunch of marbles on the floor (or billiard balls, if you like) - they transfer momentum to each other only by colliding against each other, so the faster they cover the distance between nearby molecules/balls, the faster a disturbance can travel through the medium.

A metal, however, can be thought of like a network of balls connected by springs. An atom does not (and can not) have to travel all the way to its neighbor to transfer momentum. The momentum is transferred through the springs connecting the atoms/balls. The stiffer the springs are, the faster the disturbance travels down the metal.

Can you show me some theory?

The theory (beyond the simplistic picture painted above) is hardly trivial. It often takes up a few weeks in an upper undergraduate/graduate level solid state physics course, and even there is hardly ever covered satisfactorily.

The effect of raising the temperature in a metal is to increases the phonon energy density (or the amplitude of vibrtions in the springs), without drastically changing the dispersion relation (the properties of the spring). It is the dispersion relation (the "frequency" to "wavelength" relation) that determines the speed of sound in a dispersive medium.

 

[erickalle]

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.
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.

a large chunk of the heat can go into the KE of the free electrons

Gokul as you can see from your own statement the heat capacity of electrons is only ~1% of the total.
However I do agree that a large part of theory on this subject is missing. It is either explained in a simple way as you do or there is a lot of specific theory on special applications.
Correction: in a previous reply I stated that phonons are involved in electron and proton scattering this should read electron and neutron scattering.
At this point in time I cannot see much point in further discussion of this topic and I have to help my headache with a good dose of beer instead. Although if anybody wants to continue feel free. One more thing: I do enjoy PF a lot.
eric

 

[Gokul43201]

Gokul as you can see from your own statement the heat capacity of electrons is only ~1% of the total.

In general this is true for most metal, but not necessarily for all of them. Nevertheless, notice that this was not what I suggested was the primary reason. I admit, you are justified in neglecting the electronic component of the heat capacity, but that still doesn't solve the problem.

However I do agree that a large part of theory on this subject is missing.

It isn't missing at all - just not easy to get at and digest over a single sitting.

It is either explained in a simple way as you do or there is a lot of specific theory on special applications.

There is also a very carefully laid out theory in general - not just for specific applications. I'd recommend you find Ashcroft & Mermin (or Marder) from a nearby library, if you really want to spend some time on this.

At this point in time I cannot see much point in further discussion of this topic and I have to help my headache with a good dose of beer instead. Although if anybody wants to continue feel free. One more thing: I do enjoy PF a lot.
eric

Sheersh (hic) !

 

[zirconia]

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

This is definitely not true..incorect! Unalloyed zirconium has a higher conductivity than Zircaloy-4, a Zr-base alloy containing Sn, Fe, Cr, O. The conductivities are just the reverse of what has been quoted!

In general, alloys with elements in solid solution have lower conductivity than the pure base metal.

 

[amitkkamble]

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

Astronuc: where did you get the details of thermal conductivity of alloys?? for product development I'll require the thermal conductivity data for Ferro Boron alloy with 15-18% Boron?
Anybody who can help me out with the data??

 

[alirafique]

I need following publication

R.D. Pehlke, A. Jeyarajan and H. Wada, "Summary of Thermal Properties for Casting Alloys and Mold Materials," Report No. NSF/MEA-82028, Department of Materials and Metallurgical Engineering, University of Michigan, 1982, PB83 211003

With regards,