Linear thermal expansion, theoretical instead of experimental

[fluidistic]

Is there a known formula or method to find the linear coefficient of thermal expansion for all materials?
I'm curious about what are the variables.

 

[issacnewton]

read the equation here

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c1

 

[fluidistic]

read the equation here

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c1

I appreciate your help but I already know these equations. What I'm looking for is a way to calculate the $$\alpha$$ coefficient rather than getting it experimentally.

 

[issacnewton]

I appreciate your help but I already know these equations. What I'm looking for is a way to calculate the $$\alpha$$ coefficient rather than getting it experimentally.

at the end of the day, you will need to measure some quantity in those equations experimentally

 

[fluidistic]

at the end of the day, you will need to measure some quantity in those equations experimentally

Of course, to check if the model I used to calculate $$\alpha$$ is in agreement with the "measured" $$\alpha$$ coefficient.
I still do believe it's possible to calculate the $$\alpha$$ coefficient but I do not know how. That's why I asked this question in the Solid state physics, to see if any physicist working in this area has an idea.
Say I'm given the name of a complex molecule and I want to "guess" via a complex calculation the coefficient of linear thermal expansion of a material composed by it and I do not have this material and for some reasons I do not find the corresponding $$\alpha$$ in any books. And I want to have a rough idea of $$\alpha$$, what formula/method could I use, only knowing the atoms composing the molecules. I could determinate the molecular arrangements I guess and then what other data is important? How do they fit in a formula to calculate $$\alpha$$?

P.S.: It's not homework at all, just a curiosity to see if there is a model on how to calculate $$\alpha$$ theoretically. I find it hard to believe there isn't.

 

[issacnewton]

oh, ok now i understood. so you want to derive $$\alpha$$ from fundamental
properties of the matter. i am not sure. ask some guy in statistical physics area

good luck

 

[fluidistic]

oh, ok now i understood. so you want to derive $$\alpha$$ from fundamental
properties of the matter. i am not sure. ask some guy in statistical physics area

good luck

Thank you, yes.
I think Classical mechanics is enough and certainly has to see with the average kinetic energy of molecules at a given temperature. So yeah, statistical mechanics might be very important to derive the formula.
Let's hope someone will enlighten me on this.

 

[Mapes]

Generally, thermal expansion of solids largely arises from the asymmetry of the energy well between bonded atoms; see http://books.google.com/books?id=rV...energy asymmetry "thermal expansion"&f=false", for example. If you know the shape of this energy well, you can estimate $\alpha$.

You'd probably find Ho and Taylor's Thermal expansion of solids interesting.

 

[fluidistic]

Thanks a lot Mapes.

 

[alxm]

The short answer to your initial question is that there's basically no general method, unless you count "Solve the Schrödinger equation", which is more the problem than a solution.

Now if you restricted yourself to a particular class of solids, e.g. metals, you could possibly come up with some way, since it's a completely homogeneous material consisting of identical bonds. (Not being a solid-state person I don't know offhand what's available, but I know enough to know it's surely possible) But in general there's isn't a practical way to calculate this or almost any bulk property ab initio. Either you just measure it at the macroscopic scale, or you theoretically predict it from some empirical/semi-empirical model of the microscopic scale, because working from pure theory means quantum mechanics, which effectively limits you to either a homogeneous material, or a scale of only a few hundred atoms at the most.

 

[DrDu]

I once calculated the thermal expansion of gold nanoparticles upon laser excitation. There the expansion is due to the increase of the electronic pressure. The change of volume can then be calculated from the module of compressibility which itself can be calculated once you calculated the force constants of the bonds in the solid ab initio.
As Mapes already said, in general you will also have to calculate the anharmonicities.