Stefano de Gironcoli wrote: > Stefano de Gironcoli wrote: >> ... Usually one takes a larger range (let's say 5-10 >> %) which reduces the signal/noise ratio. >> > actually it increases the ratio... which is what one wants.
On the other hand, I think that if one uses a range that is too large then the bulk modulus comes out worse from the fit because the fitting model is not as good as near the minimum (you need more fitting parameters to describe properly the curve on a larger range). Anyway, in my tests on a simple metal (bulk gold), the bulk modulus is not very sensitive to the fitting range. The "goodness" of the fit (chisq) seems to decrease with the range span (at fixed number of points), but the program does not give an estimate of the error on the fitting parameters. I think that a good estimate of the bulk modulus can be obtained also with a small range (if your data is not too noisy and well centered around the minimum), but other paraters need a larger range. From the data below you can see that k0 (the bulk modulus) is very stable from a range span of 1% up to 5%, but in order to estimate dk0 you need at least 2%. Maybe in other system this behaviour changes. HTH, Gabriele ==> Au.ev.1perc <== # equation of state: murnaghan. chisq = 0.7465D-12 # a0 = 7.67 a.u., k0 = 1923 kbar, dk0 = 1.76 d2k0 = 0.000 emin = -66.84630 # a0 = 4.058 A, V0 =112.706 (a.u.)^3, V0 = 16.701 A^3 ==> Au.ev.2perc <== # equation of state: murnaghan. chisq = 0.1161D-11 # a0 = 7.67 a.u., k0 = 1927 kbar, dk0 = 5.32 d2k0 = 0.000 emin = -66.84630 # a0 = 4.057 A, V0 =112.696 (a.u.)^3, V0 = 16.700 A^3 ==> Au.ev.3perc <== # equation of state: murnaghan. chisq = 0.1454D-11 # a0 = 7.67 a.u., k0 = 1925 kbar, dk0 = 5.51 d2k0 = 0.000 emin = -66.84630 # a0 = 4.057 A, V0 =112.693 (a.u.)^3, V0 = 16.699 A^3 ==> Au.ev.4perc <== # equation of state: murnaghan. chisq = 0.1438D-11 # a0 = 7.67 a.u., k0 = 1926 kbar, dk0 = 5.57 d2k0 = 0.000 emin = -66.84630 # a0 = 4.057 A, V0 =112.692 (a.u.)^3, V0 = 16.699 A^3 ==> Au.ev.5perc <== # equation of state: murnaghan. chisq = 0.1006D-10 # a0 = 7.67 a.u., k0 = 1922 kbar, dk0 = 5.61 d2k0 = 0.000 emin = -66.84630 # a0 = 4.057 A, V0 =112.692 (a.u.)^3, V0 = 16.699 A^3 ==> Au.ev.6perc <== # equation of state: murnaghan. chisq = 0.3205D-10 # a0 = 7.67 a.u., k0 = 1916 kbar, dk0 = 5.68 d2k0 = 0.000 emin = -66.84630 # a0 = 4.057 A, V0 =112.688 (a.u.)^3, V0 = 16.699 A^3 ==> Au.ev.7perc <== # equation of state: murnaghan. chisq = 0.1013D-09 # a0 = 7.67 a.u., k0 = 1909 kbar, dk0 = 5.70 d2k0 = 0.000 emin = -66.84629 # a0 = 4.057 A, V0 =112.689 (a.u.)^3, V0 = 16.699 A^3 ==> Au.ev.8perc <== # equation of state: murnaghan. chisq = 0.2887D-09 # a0 = 7.67 a.u., k0 = 1903 kbar, dk0 = 5.71 d2k0 = 0.000 emin = -66.84629 # a0 = 4.057 A, V0 =112.691 (a.u.)^3, V0 = 16.699 A^3 ==> Au.ev.9perc <== # equation of state: murnaghan. chisq = 0.7385D-09 # a0 = 7.67 a.u., k0 = 1894 kbar, dk0 = 5.70 d2k0 = 0.000 emin = -66.84627 # a0 = 4.058 A, V0 =112.697 (a.u.)^3, V0 = 16.700 A^3 -- o ------------------------------------------------ o | Gabriele Sclauzero, PhD Student | | c/o: SISSA & CNR-INFM Democritos, | | via Beirut 2-4, 34014 Trieste (Italy) | | email: sclauzer at sissa.it | | phone: +39 040 3787 511 | | skype: gurlonotturno | o ------------------------------------------------ o
