Originally Posted by **FrankD** Hi all,
I'm not a physicist, but I need to calculate the lattice parameter of a cubic crystal in dependence of the temperature.
The linear expansion coefficient in dependence of Temperature is given by the general formula: $\displaystyle \alpha(T) = A+B*T+C*T^{2}+C*T^{3}+D*T^{4}$ where A,B, C, D are constants.
I have to calculate the lattice constant for various Temperatures between 300 and 1000K. I tried with a big spreadsheet through calculating the values for very small Temperature steps but I know there must be a more elegant way (maybe integrating?) but I'm not good at that so i would be glad if somebody can help me out here. |

The method you want to investigate is called "Least Squares Regression". This is the technique usually employed for curve fitting. Depending on the software you are using, you should have available to you some kind of curve fitting tool.

For Excel, perhaps this page will help:

https://www.jkp-ads.com/articles/leastsquares.asp
It requires a plug-in, but it should be able to help achieve what you're looking for.

I usually use python and numpy for tasks like that, so give me a shout if you want to try that instead.