Linear thermal expansion, theoretical instead of experimental

• fluidistic
In summary: This is not easy and requires calculating the second or third order derivatives of the energy with respect to the atomic positions, which is quite demanding. Besides that, you also have to know the shape of the potential energy surface, which is very challenging and for most materials it is not known. So, in summary, it is possible to calculate the thermal expansion coefficient for a specific material, but it requires a lot of knowledge and computational resources. It is not possible to derive a general formula or method that would work for all materials.
fluidistic
Gold Member
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 said:
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.

fluidistic said:
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

IssacNewton said:
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.

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

IssacNewton said:
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.

Last edited by a moderator:
Thanks a lot Mapes.

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.

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.

What is linear thermal expansion?

Linear thermal expansion is the tendency of a material to increase its length when heated and decrease its length when cooled. This phenomenon occurs due to the increased kinetic energy of the molecules in the material, causing them to vibrate and take up more space.

Why is theoretical linear thermal expansion important?

Theoretical linear thermal expansion allows scientists to predict and understand the behavior of materials when exposed to temperature changes. This information is crucial for designing structures and materials that can withstand different temperature conditions without experiencing damage.

How is theoretical linear thermal expansion different from experimental?

Theoretical linear thermal expansion is calculated based on the physical properties of a material, such as its coefficient of thermal expansion and Young's modulus. Experimental results, on the other hand, are obtained by directly measuring the change in length of a material when subjected to temperature changes. Theoretical calculations provide a more precise and general understanding, while experimental results can vary depending on the specific conditions and techniques used.

What factors influence the linear thermal expansion of a material?

The linear thermal expansion of a material is influenced by its chemical composition, crystal structure, and temperature range. Materials with a higher coefficient of thermal expansion and weaker bonds between molecules will exhibit a larger change in length when heated or cooled. Additionally, the temperature range in which the material is exposed can also affect its linear thermal expansion.

How is linear thermal expansion used in practical applications?

Linear thermal expansion is used in various practical applications, such as in the construction of bridges, buildings, and pipelines. By understanding the thermal expansion behavior of materials, engineers and architects can design structures that can accommodate changes in temperature without causing damage or deformation. It is also utilized in the manufacturing of precision instruments and devices, where precise measurements are required even when exposed to temperature variations.

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