Fitting forms for isothermal data

Isothermal data in the (V, P)-plane are generally not sufficiently precise to determine the bulk modulus and its pressure derivative using finite differences. Instead the data are fit to an analytic expression and the derivatives of the analytic expression are used. The derivatives obtained in this fashion may be sensitive to the fitting form and the domain of data used for the fit. This point is illustrated by re-analyzing two data sets for beta-HMX. With the third order Birch-Murnaghan equation and a Hugoniot based fitting form we show that the uncertainty in the modulus due to the fitting forms is greater than the statistical uncertainty of the fits associated with the experimental error bars. Moreover, there is a systematic difference between the two data sets. Both fitting forms give statistically good fits for both experiments, although the modulus at ambient pressure ranges from 10.6 to 17.5 GPa. The large variation in the initial value of the modulus is due in part to the lack of data in the low pressure regime (below 1 GPa) and to the property of a molecular crystal, in contrast to a metal or atomic crystals, to stiffen substantially under a small amount of compression, The values of the modulus and its derivative are an important issue for an explosive like HMX because they affect predictions of the Hugoniot locus in the regime of the Chapman-Jouget detonation pressure.