Thermodynamic characteristics up to the melting point and phonon density of states of Al(C11H19O2)3

Reliability of the Phonon Density of States Determined by Real-Coded Genetic Algorithm from Heat Capacities of Benzoic Acid Crystals

“…However, low-energy g (ω) has not been determined in most materials so far because such experiments encounter difficulties in determining the absolute value of g (ω) directly. Calorimetry is superior to the spectroscopic methods in that all the vibration modes contribute equally to C V according to their degrees of freedom, as given in eq , and the absolute value of g (ω) is determinable from a set of C V data by solving the inverse problem. − …”

Determination of Phonon Density of States from Constant-Pressure Heat Capacity Data of Soft Organic Materials in the Glassy and Crystalline States by Using the Real-Coded Genetic Algorithm

“…Phonon density of states [ g (ω), where ω is the frequency of lattice/molecular vibration and was taken in K unit in the present work] can be determined from a set of heat capacity versus temperature data by solving the inverse problem. Such a determination method was developed first by Debye (1912), and so far some g (ω)­s have been tried to be determined from sets of heat capacity data. − While an inelastic neutron scattering technique has also been experimentally applied to determine g (ω), − the absolute values of g (ω) could be determined only from heat capacity data. ,− Although the heat capacity data are obtained experimentally under constant pressure as C P , g (ω) has been determined analytically from a constant-volume heat capacity ( C V ) in most of the previous works; in other words, the difference between C P and C V has been ignored as an approximation. Recently, g (ω) was apparently successfully derived for the Al­(C 11 H 19 O 2 ) 3 crystal by using C P data in which the difference between C P and C V was regarded as smaller than the inaccuracy of heat capacity measurement; namely, the thermal volume-expansion coefficient was considered to be too small to make significant differences between the two.…”

“…3,5−7 Although the heat capacity data are obtained experimentally under constant pressure as C P , g(ω) has been determined analytically from a constant-volume heat capacity (C V ) in most of the previous works; in other words, the difference between C P and C V has been ignored as an approximation. Recently, g(ω) was apparently successfully derived for the Al(C 11 H 19 O 2 ) 3 crystal by using C P data in which the difference between C P and C V was regarded as smaller than the inaccuracy of heat capacity measurement; 7 namely, the thermal volume-expansion coefficient was considered to be too small to make significant differences between the two. However, the difference between C P and C V in such soft materials amounts often to 5% at room temperature; it is too large to be neglected.…”