| Author |
 Topic  |
|
|
wyxsdu
Japan
Posts |
 Posted - 05/18/2006 : 02:37:24 AM
|
Origin Version (Select Help-->About Origin): 7.5SR0
Operating System:WIN XP
I want to obtain the Bulk modulus by fitting energy (y) and volume (x) with the Birch-Murnaghna equations:
y=F0+(9/16)*B0*V0*((B1-4)*(V0/x)^(2/3)-B1+6)*(((V0/x)^(2/3)-1)^2);
But the obtained value of B0 is so far from the resonable results.
Below is the data:
53.53 -62.36712
51.53 -62.57045
49.53 -62.63955
47.53 -62.54852
45.53 -62.26342
43.53 -61.74277
41.53 -60.93502
39.53 -59.77616
37.53 -58.18574
35.53 -56.06269
33.53 -53.27732
31.53 -49.66295
The fitting value:
F0 -111.62691 0.00102
B0 2.40077 0.00446
B1 4.71658 0.09634
V0 107.48548 0.01122
B0 is so small. In fact it should be about 260 |
|
|
larry_lan
China
Posts |
Posted - 05/18/2006 : 04:11:30 AM
|
Hi
I think it is the best result yet if fit the data directly.
The Birch-Murnaghan equation you give is:
I am not familiar to this function, but you can see that the variable B0 and V0 is correlated, and from the fitting interface, there is an column named "Dependency", which shows the dependency of the parameter, a value very close to 1 indicates strong dependency, and therefore, over parameterization. So we can see that B0, B1 and V0 are over parameterization.
Of course, sometimes over parameterization can not be avoid, because there are some physicaly meanings. So I think If you can fixed V0, maybe it is the initial volume, you can rise the value of B0 a little. However, I have tried it and can't reach 260, maybe the equation should be modify a little. So what do you think?
Larry
OriginLab GZ Office |
 |
|
|
wyxsdu
Japan
Posts |
Posted - 05/18/2006 : 04:50:45 AM
|
I find the reason
Because the unit of energy and volume are not in same unit form.
energy eV
Pressur GPa
We must use the same unit system such as SI unit |
|
|
|
vagos21
Greece
Posts |
Posted - 08/18/2006 : 6:12:39 PM
|
Hello,
i'm doing molecular dynamics and following some info i found around the net, i got the energy vs volume curve like yours, and i'm trying to do the same fit to get the Bulk modulus for my samples.
But i haven't done any custom fitting before, so i'm doing this:
analysis->non-linear curve fit->advanced fitting tool
check user-defined parameters
Parameter names: F0,B0,B1,V0
Independent var: x
Dependent var: y
Formula: y=F0+(9.0/16.0)*B0*V0*((B1-4)*(V0/x)^(2.0/3.0)-B1+6)*(((V0/x)^(2.0/3.0)-1)^2)
save it
then enter the fitting session
for a test i used your points, and then i just don't know what to do?
i hit 1 Iter and i get this error message:
Parameters F0,B0,B1,V0 are not properly initialized. Check their values.
so what values do i have to give as initial and where do i put them?
sorry if it sounds too rookie for this forum :D
thanks for your time
(edit: origin version: 7.0SR0)
Edited by - vagos21 on 08/18/2006 6:19:45 PM |
|
|
|
minimax
348 Posts |
Posted - 08/18/2006 : 9:17:30 PM
|
Hi Vangelis Pantouvas,
Before hitting 1 Iter, I think you can see the following boxes in the upper position of the dialog.
You will need to put the initial values in it before Iter.
With regard to the question what is the initial values, it is a much more complicated issue.
For Origin built-in functions, we have provided initialization scripts to auto-calculate the initial values.
For user-defined functions, you will have to provide the initial values by yourself. You can select Scripts menu--Parameter initialization and then write you own scripts in it to calculate the values. Moreover, you can select the built-in functions to take a look of the built-in scripts and then imitate to write your owns.
A simpler way is to directly provide a "guess" value in the above boxes. And such "guess" values are based the function itself. Following I show a simple example on how to provide a reasonable guess value.
Suppose you are fitting a linear function y= a*x + b, what are the appropriate initial values for a and b? Since a and b stand for the slope and intercept of the line respectively, therefore, look at the original data and find out the approximate values of the slope and intercept: these will be the reasonable guess values.
Of course it will be more difficult to guess the appropriate values when the function is complicated. But I hope it will give you some helpful hints.
Max
OriginLab GZoffice |
|
|
|
vagos21
Greece
Posts |
Posted - 08/28/2006 : 5:58:21 PM
|
thanks for your answers, i found out on the way about initial values, and the results are great :)
also the tip about the same unit system by wyxsdu was very useful!!
thank you very much for your time problem solved :) |
|
|
| |
Topic |
|
|
|
fitting error