Dataset Information

The vibrational and configurational entropy of disordering in Cu3Au.

ABSTRACT: 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.

SUBMITTER: Benisek A

PROVIDER: S-EPMC4394139 | biostudies-literature | 2015 May

REPOSITORIES: biostudies-literature

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The vibrational and configurational entropy of disordering in Cu3Au.

Benisek Artur A Dachs Edgar E

Journal of alloys and compounds 20150501

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. Howev ...[more]

PMID: 26019405

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Project description:Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1) the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2) the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3) given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4) for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5) demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6) I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7) I show that the configurational entropy of a landscape is highly related to the dimensionality of the landscape, the number of cover classes, the evenness of landscape composition across classes, and landscape heterogeneity. These advances provide a means for researchers to directly estimate the frequency distribution of all possible macrostates of any observed landscape, and then directly calculate the relative configurational entropy of the observed macrostate, and to understand the ecological meaning of different amounts of configurational entropy. These advances enable scientists to take configurational entropy from a concept to an applied tool to measure and compare the disorder of real landscapes with an objective and unbiased measure based on entropy and the second law.

Dataset Information

The vibrational and configurational entropy of disordering in Cu3Au.

Publications

The vibrational and configurational entropy of disordering in Cu<sub>3</sub>Au.

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