The vibrational and configurational entropy of α-brass

Complexity Parameters for Molecular Solids

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.

Structural complexity and configurational entropy of crystals

Using a statistical approach, it is demonstrated that the complexity of a crystal structure measured as the Shannon information per atom [Krivovichev (2012). Acta Cryst. A68, 393-398] represents a negative contribution to the configurational entropy of a crystalline solid. This conclusion is in full accordance with the general agreement that information and entropy are reciprocal variables. It also agrees well with the understanding that complex structures possess lower entropies relative to their simpler counterparts. The obtained equation is consistent with the Landauer principle and points out that the information encoded in a crystal structure has a physical nature.

The vibrational and configurational entropy of disordering in Cu3Au

The thermodynamics of disordering in Cu₃Au have been investigated by measuring the heat capacity of samples with different degrees of long- and short-range order between T = 5 and 720 K using relaxation and differential scanning calorimetry. The heat capacities of L1₂-ordered and fcc-disordered samples show similar behaviour at low temperatures (<300 K). They deviate positively from the linear combination of the end-member heat capacities between ∼30 and 160 K. However, small differences between the two samples exist, as the disordered sample has a larger heat capacity producing a vibrational entropy of disordering of ∼0.05 R. At temperatures higher than 300 K, the heat capacity of the ordered sample shows a prominent lambda-type anomaly at 675 K due to the diffusive L1₂-fcc phase transition. When starting these measurements with disordered samples, ordering effects are observed between 400 and 620 K, and the disordering reaction is observed at 660 K. Evaluation of the data gives an enthalpy and entropy of disordering at 683 K of 2.0 kJ mol^-1 and 0.39 R, respectively. However, these values increase with increasing temperature, thereby reducing the short-range order. Because the vibrational and configurational disordering effects become active at different temperature regimes, i.e., the vibrational effects at low temperatures (T ≪ 300 K) and the sum of both effects at higher temperatures (T > 300 K), they have been successfully separated.

First-principles investigation of the lattice vibrations in the alkali feldspar solid solution

The heat capacities of Al, Si ordered alkali feldspars of different Na, K compositions were calculated using the density functional theory. The effect of the Na, K distribution, if random, ordered or clustered, on the resulting heat capacity was investigated on different cells with Ab₅₀Or₅₀ composition. For all compositions and distributions studied, the excess heat capacity of mixing is positive at low temperatures with a maximum at ~60 K. This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K. The amount of the excess heat capacity of Ab₅₀Or₅₀, however, depends on the Na, K distribution. Best agreement with measured excess heat capacities is achieved, if the distribution of Na and K is either ordered or clustered. The positive excess heat capacities can be attributed to a strong softening of the acoustic and the lowest optical modes related to a strong increase of Na-O bond lengths in samples with intermediate compositions. The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data. Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.