skip to main content


Title: Zentropy Theory for Positive and Negative Thermal Expansion
It has been observed in both natural and man-made materials that volume sometimes decreases with increasing temperature. Though mechanistic understanding has been gained for some individual materials, a general answer to the question “Why does volume sometimes decrease with the increase of temperature?” remains lacking. Based on the thermodynamic relation that the derivative of volume with respect to temperature, i.e., thermal expansion, is equal to the negative derivative of entropy with respect to pressure, we developed a general theory in terms of multiscale entropy to understand and predict the change of volume as a function of temperature, which is termed as zentropy theory in the present work. It is shown that a phase at high temperatures is a statistical representation of the ground-state stable and multiple nonground-state metastable configurations. It is demonstrated that when the volumes of the nonground-state configurations with high probabilities are smaller than that of the ground-state configuration, the volume of the phase may decrease with the increase of temperature in certain ranges of temperature-pressure combinations, depicting the negative divergency of thermal expansion at the critical point. As examples, positive and negative divergencies of thermal expansion are predicted at the critical points of Ce and Fe3Pt, respectively, along with the temperature and pressure ranges for abnormally positive and negative thermal expansions. The authors believe that the zentropy theory is applicable to predict anomalies of other physical properties of phases because the change of entropy drives the responses of a system to external stimuli.  more » « less
Award ID(s):
2050069
NSF-PAR ID:
10318667
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Phase Equilibria and Diffusion
ISSN:
1547-7037
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The hydrostatic equilibrium addresses the approximate balance between the positive force of the vertical pressure gradient and the negative gravity force and has been widely assumed for atmospheric applications. The hydrostatic imbalance of the mean atmospheric state for the acceleration of vertical motions in the vertical momentum balance is investigated using tower, the global positioning system radiosonde, and Doppler lidar and radar observations throughout the diurnally varying atmospheric boundary layer (ABL) under clear-sky conditions. Because of the negligibly small mean vertical velocity, the acceleration of vertical motions is dominated by vertical variations of vertical turbulent velocity variances. The imbalance is found to be mainly due to the vertical turbulent transport of changing air density as a result of thermal expansion/contraction in response to air temperature changes following surface temperature changes. In contrast, any pressure change associated with air temperature changes is small, and the positive vertical pressure-gradient force is strongly influenced by its background value. The vertical variation of the turbulent velocity variance from its vertical increase in the lower convective boundary layer (CBL) to its vertical decrease in the upper CBL is observed to be associated with the sign change of the imbalance from positive to negative due to the vertical decrease of the positive vertical pressure-gradient force and the relative increase of the negative gravity force as a result of the decreasing upward transport of the low-density air. The imbalance is reduced significantly at night but does not steadily approach zero. Understanding the development of hydrostatic imbalance has important implications for understanding large-scale atmosphere, especially for cloud development.

    Significance Statement

    It is well known that the hydrostatic imbalance between the positive pressure-gradient force due to the vertical decrease of atmospheric pressure and the negative gravity forces in the vertical momentum balance equation has important impacts on the vertical acceleration of atmospheric vertical motions. Vertical motions for mass, momentum, and energy transfers contribute significantly to changing atmospheric dynamics and thermodynamics. This study investigates the often-assumed hydrostatic equilibrium and investigate how the hydrostatic imbalance is developed using field observations in the atmospheric boundary layer under clear-sky conditions. The results reveal that hydrostatic imbalance can develop from the large-eddy turbulent transfer of changing air density in response to the surface diabatic heating/cooling. The overwhelming turbulence in response to large-scale thermal forcing and mechanical work of the vast Earth surface contributes to the hydrostatic imbalance on large spatial and temporal scales in numerical weather forecast and climate models.

     
    more » « less
  2. Deep-focus earthquakes that occur at 350–660 km, where pressures p =12-23 GPa and temperature T =1800-2000 K, are generally assumed to be caused by olivine→spinel phase transformation, see pioneering works [1–10]. However, there are many existing puzzles: (a) What are the mechanisms for jump from geological 10−17−10−15 s−1 to seismic 10−103s−1(see [3]) strain rates? Is it possible without phase transformation? (b) How does metastable olivine, which does not completely transform to spinel at high temperature and deeply in the region of stability of spinel for over the million years, suddenly transforms during seconds and generates seismic strain rates 10−103s−1 that produce strong seismic waves? (c) How to connect deviatorically dominated seismic signals with volume-change dominated transformation strain during phase transformations [9,11]? Here we introduce a combination of several novel concepts that allow us to resolve the above puzzles quantitatively. We treat the transformation in olivine like plastic strain-induced (instead of pressure/stress-induced) and find an analytical 3D solution for coupled deformation-transformation-heating processes in a shear band. This solution predicts conditions for severe (singular) transformation-induced plasticity (TRIP) and self-blown-up deformation-transformation-heating process due to positive thermomechanochemical feedback between TRIP and strain-induced transformation. In nature, this process leads to temperature in a band exceeding the unstable stationary temperature, above which the self-blown-up shear-heating process in the shear band occurs after finishing the phase transformation. Without phase transformation and TRIP, significant temperature and strain rate increase is impossible. Due to the much smaller band thickness in the laboratory, heating within the band does not occur, and plastic flow after the transformation is very limited. Our findings change the main concepts in studying the initiation of the deep-focus earthquakes and phase transformations during plastic flow in geophysics in general. The latter may change the interpretation of different geological phenomena, e.g., the possibility of the appearance of microdiamond directly in the cold Earth crust within shear-bands [12] during tectonic activities without subduction to the mantle and uplifting. Developed theory of the self-blown-up transformation-TRIP-heating process is applicable outside geophysics for various processes in materials under pressure and shear, e.g., for new routes of material synthesis [12,13], friction and wear, surface treatment, penetration of the projectiles and meteorites, and severe plastic deformation and mechanochemical technologies. 
    more » « less
  3. We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative. The ground state is a volume- and color-weighted superposition of classical bi-color vertex configurations with non-negative heights in the bulk and zero height on the boundary. The entanglement entropy between subsystems has a phase transition as the q q -deformation parameter is tuned, which is shown to be robust in the presence of an external field acting on the color degree of freedom. The ground state undergoes a quantum phase transition between area- and volume-law entanglement phases with a critical point where entanglement entropy scales as a function L\log L L log L of the linear system size L L . Intermediate power law scalings between L\log L L log L and L^2 L 2 can be achieved with an inhomogeneous deformation parameter that approaches 1 at different rates in the thermodynamic limit. For the q>1 q > 1 phase, we construct a variational wave function that establishes an upper bound on the spectral gap that scales as q^{-L^3/8} q − L 3 / 8 . 
    more » « less
  4. Density functional theory (DFT) prescribes the existence of a ground-state configuration at 0 K for a given system. However, the ground-state configuration alone is insufficient to describe a phase at finite temperatures as symmetry-breaking non-ground-state configurations are excited statistically at temperatures above 0 K. Our multiscale entropy approach, Zentropy, postulates that the entropy of a phase is composed of the sum of the entropy of each configuration weighted by its probability plus the configurational entropy among all configurations. Consequently, the partition function of each configuration in statistical mechanics needs to be evaluated by its free energy rather than total energy. The combination of the ground-state and symmetry-breaking non-ground-state configurations represents the building blocks of materials and can be used to quantitatively predict free energy of individual phases with the free energy of each configuration predicted from DFT as well as all properties derived from free energy of individual phases. 
    more » « less
  5. Metastable phases of the photoswitchable molecular magnet K0.3Co[Fe(CN)6]0.77 ⋅  nH2O in sub-micrometer particles have been structurally investigated by synchrotron powder x-ray diffraction (PXRD) measurements. The K0.3Co[Fe(CN)6]0.77 ⋅  nH2O bulk compound (studied here with a sample having average particle size of 500 nm) undergoes a charge transfer coupled spin transition (CTCST), where spin configurations change between a paramagnetic CoII( S = 3/2) –FeIII( S = 1/2) high-temperature (HT) state and a diamagnetic CoIII( S = 0) –FeII( S = 0) low-temperature (LT) state. The bulk compound exhibits a unique intermediate (IM) phase, which corresponds to a mixture of HT and LT spin states that depend on the cooling rate. Several hidden metastable HT states emerge as a function of thermal and photo stimuli, namely: (1) a quench (Q) state generated from the HT state by flash cooling, (2) a LTPX state obtained by photoexcitation from the LT state derived by thermal relaxation from the Q state, and (3) an IMPX state accessed by photo-irradiation from the IM state. A sample with a smaller particle size, 135 nm, is investigated for which the particles are on the scale of the coherent LT domains in the IM phase within the larger 500 nm sample. PXRD studies under controlled thermal and/or optical excitations have clarified that the reduction of the particle size profoundly affects the structural changes associated with the CTCST. The unusual IM state is also observed as segregated domains in the 135 nm particle, but the collective structural transformations are more hindered in small particles. The volume change decreases to 2%–3%, almost half the value found for 500 nm particles (5%–8%), even though the linear thermal expansion coefficients are larger for the smaller particles. Furthermore, photoexcitation from the IM and LT states does not turn into single phases in the smaller particles, presumably because of the multiple interfaces and/or internal stress generated by the coexistence of small CoII–FeIIIand CoIII–FeIIdomains in the lattice. Since the reduced particle size limits cooperativity and domain growth in the lattice, CTCST in the small particle sample becomes less sensitive to external stimuli.

     
    more » « less