Hello,
this is a simple definition of the Langevin function I use a lot:
y=A*(cosh(N*0.672*B/T)/sinh(N*0.672*B/T)-T/(N*0.672*B))
Herein, the ingredients are as follows:
A: (arbitrary) amplitude
N: Magnitude of the paramagnetic moment (number of Bohr magnetons)
0.672: Bohr magneton / Boltzmann constant
T: temperature in K
Press F8 key to call the fit function builder, get and follow the documentation/instructions on making fit functions. In this way you will not have to fiddle around with putting files in the right position... Origin does it for you.
Good luck. And do "use your brain" when making use of this function. Concerning the arbitrary amplitude, this is not the standard textbook definition (but very close). Using different parameters for argument and overall amplitude makes it easier to cross-check physical consistency (well, at least I believe so).
Edit: Let me add that only in few cases does fitting with a simple Langevin function yield results which can be interpreted on a physically sound basis. As soon as there are e.g. size distributions (resulting in distributions of magnetic moments) these have to be modeled. Parameters such as the magnitude of the moment N above do not represent a correct average moment or size. this is because assuming a single size the saturation moment is proportional to N while the susceptibility (slope of (M(H)) at small fields) is proportional to N^2. What you need then is a properly weighted convolution of a size/moment distribution with associated Langevin curves. This is entirely possible but requires a lot more coding.
Langevin Function
Posted - 02/20/2006 : 7:13:19 PM
