Response to “Comment on ‘Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems’” [J. Chem. Phys. 134, 147101 (2011)]

2011 ◽  
Vol 134 (14) ◽  
pp. 147102 ◽  
Author(s):  
John C. Mauro ◽  
Roger J. Loucks ◽  
Sabyasachi Sen
Keyword(s):  
Heat Capacity ◽  
Configurational Entropy ◽  
Chem Phys

Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems

2010 ◽  
Vol 133 (16) ◽  
pp. 164503 ◽  
Author(s):  
John C. Mauro ◽  
Roger J. Loucks ◽  
Sabyasachi Sen
Keyword(s):  
Heat Capacity ◽  
Configurational Entropy

Quantitative Predictions from Solid-State Physics - What do Phase Diagram Calculators Want?

1982 ◽  
Vol 19 ◽  
Author(s):  
Malcolm Rand
Keyword(s):  
Phase Diagram ◽  
Heat Capacity ◽  
Solid State ◽  
Binary Systems ◽  
High Pressures ◽  
Magnetic Moments ◽  
Configurational Entropy ◽  
Metastable Phases ◽  
Solid State Physics ◽  
Metastable Compounds

ABSTRACTThe types of information required for the calculation of phase diagrams are discussed by considering the computation of typical ternary sections from the constituent binary systems. Such calculations require a knowledge of the Gibbs energy of transformation (lattice stabilities) and Gibbs energies of mixing of wholly metastable, as well as the stable phases in binary systems. Similarly, the stabilities of metastable compounds such as Fe7C3 would be required for computations in the C-Cr-Fe system.These requirements are compared to the information provided by solid-state theoreticians. Essentially such calculations provide enthalpy values at 0 K (or some unspecified temperature for semi-empirical models); however the lattice dynamics and configurational entropy of simple phases have been included in some recent computations. The importance of predicting the entropy and thus heat capacity of metallic phases - particularly metastable phases - is therefore emphasized. Identification of those contributions to the heat capacity which are responsible for the differences between metal polymorphs is discussed, particularly the formalism for magnetic and atomic ordering phenomena. Predictions of ordering temperatures and magnetic moments as a function of composition would be of considerable help for phase diagram calculations.Ab-initio calculations already have considerable success in predicting molar volumes of both stable and metastable phases, so that such information will undoubtedly be of considerable value in studying alloy behaviour at high pressures.

Incommensurately modulated structure of morpholinium tetrafluoroborate and configurationalversuschemical entropies at the incommensurate and lock-in phase transitions

2017 ◽  
Vol 73 (5) ◽  
pp. 836-843
Author(s):  
Leila Noohinejad ◽  
Sander van Smaalen ◽  
Václav Petříček ◽  
Andreas Schönleber
Keyword(s):  
Phase Transitions ◽  
Conformational Changes ◽  
Ferroelectric Properties ◽  
Configurational Entropy ◽  
Chem Phys ◽  
Ambient Conditions ◽  
Disorder Phase Transition ◽  
The Difference ◽  
A Minor ◽  
Transition Entropy

Morpholinium tetrafluoroborate, [C4H10NO]+[BF4]−, belongs to a class of ferroelectric compoundsABX4. However, [C4H10NO]+[BF4]−does not develop ferroelectric properties because the incommensurate phase belowTc,I= 153 K is centrosymmetric with superspace groupPnam(σ100)00sand σ1= 0.42193 (12) atT= 130 K; the threefold superstructure belowTc,II= 117–118 K possesses the acentric but non-ferroelectric space groupP212121. At ambient conditions, [C4H10NO]+[BF4]−comprises orientationally disordered [BF4]−anions accommodated in cavities between four morpholinium cations. A structure model for the incommensurately modulated phase, which involves modulated orientational ordering of [BF4]−together with modulated distortions and displacements of the morpholinium ions is reported. A mechanism is proposed for the phase transitions, whereby at low temperatures morpholinium cations are shaped around the tetrafluoroborate anion in order to optimize the interactions with one orientation of this anion and, thus, forcing [BF4]−into this orientation. This mechanism is essentially different from a pure order–disorder phase transition. It is supported by consideration of the transition entropy. The difference in configurational entropy between the disordered and incommensurate phases has been computed from the structure models. It is shown to be much smaller than the experimental transition entropy reported by Owczareket al.[Chem. Phys.(2011),381, 11–20]. These features show that the order–disorder contribution is only a minor contribution to the transition entropy and that other factors, such as conformational changes, play a larger role in the phase transitions.

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