Free Energy of a Nonuniform System. I. Interfacial Free Energy
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Abstract: It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.
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3,822 citations
TL;DR: In this article, the stability of a solid solution to all infinitesimal composition fluctuations is considered, taking surface tension and elastic energy into account, and it is found that for infinite isotropic solids, free from imperfections, the spinodal marks the limit of metastability to such fluctuations only if there is no change in molar volume with composition.
2,762 citations
01 Jan 1979
TL;DR: In this paper, a microscopic diffusional theory for the motion of a curved antiphase boundary is presented, where the interfacial velocity is linearly proportional to the mean curvature of the boundary, but unlike earlier theories the constant of proportionality does not include the specific surface free energy.
Abstract: Abstract A microscopic diffusional theory for the motion of a curved antiphase boundary is presented. The interfacial velocity is found to be linearly proportional to the mean curvature of the boundary, but unlike earlier theories the constant of proportionality does not include the specific surface free energy, yet the diffusional dissipation of free energy is shown to be equal to the reduction in total boundary free energy. The theory is incorporated into a model for antiphase domain coarsening. Experimental measurements of domain coarsening kinetics in Fe-Al alloys were made over a temperature range where the specific surface free energy was varied by more than two orders of magnitude. The results are consistent with the theory; in particular, the domain coarsening kinetics do not have the temperature dependence of the specific surface free energy.
2,414 citations
TL;DR: It is demonstrated that nanoporosity in metals is due to an intrinsic dynamical pattern formation process, and that chemically tailored nanoporous gold made by dealloying Ag-Au should be suitable for sensor applications, particularly in a biomaterials context.
Abstract: Dealloying is a common corrosion process during which an alloy is 'parted' by the selective dissolution of the most electrochemically active of its elements. This process results in the formation of a nanoporous sponge composed almost entirely of the more noble alloy constituents. Although considerable attention has been devoted to the morphological aspects of the dealloying process, its underlying physical mechanism has remained unclear. Here we propose a continuum model that is fully consistent with experiments and theoretical simulations of alloy dissolution, and demonstrate that nanoporosity in metals is due to an intrinsic dynamical pattern formation process. That is, pores form because the more noble atoms are chemically driven to aggregate into two-dimensional clusters by a phase separation process (spinodal decomposition) at the solid-electrolyte interface, and the surface area continuously increases owing to etching. Together, these processes evolve porosity with a characteristic length scale predicted by our continuum model. We expect that chemically tailored nanoporous gold made by dealloying Ag-Au should be suitable for sensor applications, particularly in a biomaterials context.
2,348 citations
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TL;DR: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of liquid and the triple point temperature and pressure, the heat capacity of liquid, and the surface tension of liquid as mentioned in this paper.
Abstract: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of the liquid, the triple‐point temperature and pressure, the heat capacity of the liquid, and the surface tension of the liquid It has been shown that argon, krypton, xenon, and with less accuracy neon, follow the principle with respect to all these properties It has further been shown that nitrogen, oxygen, carbon monoxide, and methane follow the principle with fair accuracy as vapors and as liquids, but not as solids The relations between surface tension, temperature, and densities have been analyzed empirically For the ``ideal'' substances under consideration Katayama's modification of Eotvos' relation holds good, but McLeod's relation does not; in the relation γ∝ (ρl—ρc)s, the exponent s is
1,056 citations
TL;DR: The Slatersche Methode as mentioned in this paper is an analog zur Jordan-Kleinschen Theorie in eine nichtlineare Wellengleichung im dreidimensionalen Raum, wobei das Absolutquadrat der Wellenfunktion anschaulich als Spindichte gedeutet werden kann.
Abstract: Die Slatersche Methode zur Behandlung der Austauschaufspaltung und Termsystemeinteilung beim Mehrkorperproblem wird analog zur Jordan-Kleinschen Theorie umgeformt in eine nichtlineare Wellengleichung im dreidimensionalen Raum, wobei das Absolutquadrat der Wellenfunktion anschaulich als „Spindichte“ gedeutet werden kann (§ 1 und 2). Vernachlassigt man den q-Zahlcharakter der Wellenfunktion, so stellt die Wellengleichung analog zur Hartreeschen Methode eine klassisch-anschauliche Annaherungsgleichung fur das Verhalten der Spindichte dar, die zur Diskussion der Remanenz- und Hysteresiserscheinungen verwendet wird (§ 4 und 5). Ferner wird im Anschlus an das statistische Problem ein Zusammenhang zwischen den Wahrscheinlichkeiten der verschiedenen Konfigurationen eines Systems bei einer bestimmten Temperatur und den Kennardschen Transformationsfunktionen aufgestellt (§ 3).
419 citations
TL;DR: In this article, ausscheidung in einem ubersattigten binaren Mischkristall is considered, das die Energie eines Misch-kristalls durch einfache Addition of Nachbarbindungen berechnet werden darf.
Abstract: Unter der Annahme, das die Energie eines Mischkristalls durch einfache Addition von Nachbarbindungen berechnet werden darf, wird die Keimbildungsarbeit fur die Ausscheidung in einem ubersattigten binaren Mischkristall berechnet. Daraus last sich die Haufigkeit der Keimbildung bestimmen. Aus der Durchrechnung eines Zahlenbeispiels ergibt sich fur diejenige Unterkuhlung, bei welcher die Keimbildungshaufigkeit ihr Maximum erreicht, eine befriedigende Ubereinstimmung mit vorliegenden Messungen uber die Geschwindigkeit der Ausscheidung.
329 citations
TL;DR: In this paper, it has been shown that rochelle salt in the ferroelectric state consists of many domains and that the domain structure in an annealed crystal is caused by the electrostatic self energy.
Abstract: It has been verified by means of the polarization microscope that rochelle salt in the ferroelectric state consists of many domains. The domain structure in an annealed crystal is caused by the electrostatic self energy. When the electric field along the $X$ direction is increased and then decreased gradually, successive positions of the domain wall produce a hysteresis loop, which proves the existence of a restoring force on the wall. This restoring force causes lag of charging, and its variation with time produces a fatigue effect. The propagation velocity of a domain wall is about 0.2 cm/sec for 100 v/cm. A group of domains parallel to the $b$ axis has been created artificially. When a stress ${Y}_{z}$ is applied, a set of domains inverts its polarization direction. $Z$-cut specimens of K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ cooled below the Curie temperature divide into many regions which appear to be domains. The phase transition in K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ propagates from only one nucleus.Theoretically it has been concluded that the domain wall energy of rochelle salt is $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{{P}_{0}}^{3}$ erg/${\mathrm{cm}}^{2}$ and the wall width $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}/{P}_{0}$ cm, where ${P}_{0}$ is the saturation polarization.
309 citations