233 research outputs found
Thermodynamics and its CALPHAD Modeling: Review, State of the Art, and Perspectives
Thermodynamics is a science concerning the state of a system, whether it is
stable, metastable, or unstable. The combined law of thermodynamics derived by
Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs
combined law, the entropy production due to internal processes was not
included, and the 2nd law was thus practically removed from the Gibbs combined
law, so it is only applicable to systems under equilibrium. Gibbs further
derived the classical statistical thermodynamics in terms of the probability of
configurations in a system. With the quantum mechanics (QM) developed, the
QM-based statistical thermodynamics was established and connected to classical
statistical thermodynamics at the classical limit as shown by Landau. The
development of density function theory (DFT) by Kohn and co-workers enabled the
QM prediction of properties of the ground state of a system. On the other hand,
the entropy production due to internal processes in non-equilibrium systems was
studied separately by Onsager and Prigogine and co-workers. The digitization of
thermodynamics was developed by Kaufman in the framework of the CALPHAD
modeling of individual phases. Our recently termed zentropy theory integrates
DFT and statistical mechanics through the replacement of the internal energy of
each individual configuration by its DFT-predicted free energy. Furthermore,
through the combined law of thermodynamics with the entropy production as a
function of internal degrees of freedom, it is shown that the kinetic
coefficient matrix of independent internal processes is diagonal with respect
to the conjugate potentials in the combined law, and the cross phenomena
represented by the phenomenological Onsager reciprocal relationships are due to
the dependence of the conjugate potential of the molar quantity in a flux on
nonconjugate potentials
Thermodynamics of the Mg-B system: Implications for the deposition of MgB2 thin films
We have studied thermodynamics of the Mg-B system with the modeling technique
CALPHAD using a computerized optimization procedure. Temperature-composition,
pressure-composition, and pressure-temperature phase diagrams under different
conditions are obtained. The results provide helpful insights into appropriate
processing conditions for thin films of the superconducting phase, MgB2,
including the identification of the pressure/temperature region for
adsorption-controlled growth. Due to the high volatility of Mg, MgB2 is
thermodynamically stable only under fairly high Mg overpressures for likely
growth temperatures. This constraint places severe temperature constraints on
deposition techniques employing high vacuum conditions
Zentropy Theory for Positive and Negative Thermal Expansions
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 major nonground-state configurations 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 expansion. 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
Quantified Uncertainty in Thermodynamic Modeling for Materials Design
Phase fractions, compositions and energies of the stable phases as a function
of macroscopic composition, temperature, and pressure (X-T-P) are the principle
correlations needed for the design of new materials and improvement of existing
materials. They are the outcomes of thermodynamic modeling based on the
CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD
predictions vary widely in X-T-P space due to experimental error, model
inadequacy and unequal data coverage. In response, researchers have developed
frameworks to quantify the uncertainty of thermodynamic property model
parameters and propagate it to phase diagram predictions. In previous studies,
uncertainty was represented as intervals on phase boundaries (with respect to
composition) or invariant reactions (with respect to temperature) and was
unable to represent the uncertainty in eutectoid reactions or in the stability
of phase regions. In this work, we propose a suite of tools that leverages
samples from the multivariate model parameter distribution to represent
uncertainty in forms that surpass previous limitations and are well suited to
materials design. These representations include the distribution of phase
diagrams and their features, as well as the dependence of phase stability and
the distributions of phase fraction, composition activity and Gibbs energy on
X-T-P location - irrespective of the total number of components. Most
critically, the new methodology allows the material designer to interrogate a
certain composition and temperature domain and get in return the probability of
different phases to be stable, which can positively impact materials design
Parameter-free prediction of phase transition in PbTiO3 through combination of quantum mechanics and statistical mechanics
Thermodynamics of ferroelectric materials and their ferroelectric to
paraelectric (FE-PE) transitions including those in PbTiO3 is commonly
described by the phenomenological Landau theory and more recently by effective
Hamiltonian and various potentials, all with model parameters fitted to
experimental or theoretical data. Here we show that the zentropy theory, which
considers the total entropy of a system as a weighted sum of entropies of
configurations that the system may experience and the statistical entropy among
the configurations, can predict the FE-PE transition without fitting
parameters. For PbTiO3, the configurations are identified as the FE
configurations with 90- or 180-degree domain walls in addition to the ground
state of the FE configuration without domain wall. With the domain wall
energies predicted from first-principles calculations based on the density
functional theory in the literature as the only inputs, the FE-PE transition
for PbTiO3 is predicted showing remarkable agreement with experiments,
unveiling the microscopic fundamentals of the transition
Experimental study and thermodynamic modeling of the Al–Co–Cr–Ni system
A thermodynamic database for the Al–Co–Cr–Ni system is built via the Calphad method by extrapolating re-assessed ternary subsystems. A minimum number of quaternary parameters are included, which are optimized using experimental phase equilibrium data obtained by electron probe micro-analysis and x-ray diffraction analysis of NiCoCrAlY alloys spanning a wide compositional range, after annealing at 900 °C, 1100 °C and 1200 °C, and water quenching. These temperatures are relevant to oxidation and corrosion resistant MCrAlY coatings, where M corresponds to some combination of nickel and cobalt. Comparisons of calculated and measured phase compositions show excellent agreement for the β–γ equilibrium, and good agreement for three-phase β–γ–σ and β–γ–α equilibria. An extensive comparison with existing Ni-base databases (TCNI6, TTNI8, NIST) is presented in terms of phase compositions
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