scholarly journals The thermodynamics of the surfaces of solutions

1932 ◽  
Vol 135 (827) ◽  
pp. 348-375 ◽  
Keyword(s):  
Closed Surface ◽  
Total Entropy ◽  
Internal Equilibrium ◽  
Two Phases ◽  
Dividing Surface

In his classical treatment of the thermodynamics of capillarity* Gibbs considered the equilibrium of the matter contained within a closed surface (A, fig. 1), drawn so as to cut the dividing surface (S) between the two phases normally everywhere and to include part of the homogeneous mass on each side. The matter contained within this surface is divided into three parts by two surfaces (B, B), one on each side of S and very near to that surface, although at such a distance as to lie entirely beyond the influence of the discontinuity in its vicinity. If ε, ε', ε'' and η , η' , η" are the value of the energy and entropy of the part between the surfaces BB, and of the homogeneous parts outside these surfaces respectively, the condition of internal equilibrium of the whole mass is dε + dε' + dε" ≧ 0, (1) for all possible variations for which the total entropy remains constant, i. e ., for which dη + dη' + dη'' = 0. (2)

scholarly journals The equilibrium of heterogeneous systems including electrolytes. Part II.— equilibrium at interfaces and the theory of electro-capillarity

1927 ◽  
Vol 113 (765) ◽  
pp. 594-605 ◽  
Keyword(s):  
Heterogeneous Systems ◽  
Closed Surface ◽  
Unit Mass ◽  
Two Phases ◽  
Dividing Surface ◽  
General Method

It has been shown that, in a state of equilibrium, for every portion of the matter composing a system, whether contained in the homogeneous parts or in the non-homogeneous parts about the interfaces, the following equations hold :— t=T; μ 1 ≧ M 1 ⋅⋅⋅ μ≧M g ; for components,(μ h +a h V) ≧ M h ;⋅⋅⋅( μ h +a h V) ≧ M h ⋅⋅⋅(μ n a n V) ≧ M n ; for ions, where a h ⋅⋅⋅a n are the quantities of electricity associated with unit mass of ions, h⋅⋅⋅n, and where the equality refers to actual components of the matter in question, the inequality to possible components. The conditions at the interface between two phases may be obtained by the general method of Gibbs (1). A closed surface is drawn about the portion of the interface at which the conditions are to be investigated, containing parts of the two homogeneous phases and cutting the non-homogeneous parts normally to the interface. The volume V within this surface is divided into two parts I and II by a dividing surface s, which is drawn parallel to and sensibly coincident with the actual interface.

scholarly journals On the behaviour of certain substances at their critical temperatures

1906 ◽  
Vol 78 (524) ◽  
pp. 247-261 ◽  
Keyword(s):  
Critical Point ◽  
Critical State ◽  
Van Der Waals ◽  
Critical Temperatures ◽  
Liquid Phases ◽  
Coexisting Phases ◽  
Two Phases ◽  
Dividing Surface ◽  
Critical Constants

A work entitled “Le Point Critique des Corps Purs” has recently been published by E. Mathias, whose opinion on matters relating to the critical state must always carry weight. In this he discusses at length the various theories which have been put forward to explain certain irregularities observed in the behaviour of substances, which were supposed to be pure, at their critical temperatures. These irregularities are not accounted for by the simpler theories of Andrews and Van der Waals. He calls attention to the experiments of certain investigators, which appear to suggest that the currently-accepted values of the critical constants of many common substances may be vitiated, either owing to the time allowed for the establishment of equilibrium between the coexisting phases near the critical point being insufficient, or the temperature at which the dividing surface vanishes not being independent of the relative masses of the two phases at the temperature at which this takes place. According to I. Traube, substances contain different kinds of aggregates, which he calls “gasogenic” and “liquidogenic” molecules. It follows that if equilibrium demands that there shall be a certain concentration of these molecules in the vapour and liquid phases respectively, then unless dissociation and association take place instantaneously, there must elapse a time, following any change of condition, before equilibrium can be established between the two phases.

Precipitation of NiHfsi phase in NiAl single crystals containing Hf

1995 ◽  
Vol 53 ◽  
pp. 532-533
Author(s):  
A. Garg ◽  
R. D. Noebe ◽  
R. Darolia
Keyword(s):  
High Temperature ◽  
Single Crystals ◽  
High Temperature Strength ◽  
Bridgman Technique ◽  
Shell Mold ◽  
Third Phase ◽  
Unknown Phase ◽  
Transmission Electron ◽  
Two Phases ◽  
Nial Matrix

Small additions of Hf to NiAl produce a significant increase in the high-temperature strength of single crystals. Hf has a very limited solubility in NiAl and in the presence of Si, results in a high density of G-phase (Ni16Hf6Si7) cuboidal precipitates and some G-platelets in a NiAl matrix. These precipitates have a F.C.C structure and nucleate on {100}NiAl planes with almost perfect coherency and a cube-on-cube orientation-relationship (O.R.). However, G-phase is metastable and after prolonged aging at high temperature dissolves at the expense of a more stable Heusler (β'-Ni2AlHf) phase. In addition to these two phases, a third phase was shown to be present in a NiAl-0.3at. % Hf alloy, but was not previously identified (Fig. 4 of ref. 2 ). In this work, we report the morphology, crystal-structure, O.R., and stability of this unknown phase, which were determined using conventional and analytical transmission electron microscopy (TEM).Single crystals of NiAl containing 0.5at. % Hf were grown by a Bridgman technique. Chemical analysis indicated that these crystals also contained Si, which was not an intentional alloying addition but was picked up from the shell mold during directional solidification.

Imaging of Al-Li-Cu alloys with a Scanning Ion Microprobe

1990 ◽  
Vol 48 (2) ◽  
pp. 314-315
Author(s):  
K.K. Soni ◽  
D.B. Williams ◽  
J.M. Chabala ◽  
R. Levi-Setti ◽  
D.E. Newbury
Keyword(s):  
Mass Spectrometry ◽  
Secondary Ion Mass Spectrometry ◽  
Equilibrium Phase ◽  
Icosahedral Symmetry ◽  
Ion Microprobe ◽  
X Ray ◽  
Cu Alloys ◽  
Two Phases ◽  
The University ◽  
Secondary Ion

In contrast to the inability of x-ray microanalysis to detect Li, secondary ion mass spectrometry (SIMS) generates a very strong Li+ signal. The latter’s potential was recently exploited by Williams et al. in the study of binary Al-Li alloys. The present study of Al-Li-Cu was done using the high resolution scanning ion microprobe (SIM) at the University of Chicago (UC). The UC SIM employs a 40 keV, ∼70 nm diameter Ga+ probe extracted from a liquid Ga source, which is scanned over areas smaller than 160×160 μm2 using a 512×512 raster. During this experiment, the sample was held at 2 × 10-8 torr.In the Al-Li-Cu system, two phases of major importance are T1 and T2, with nominal compositions of Al2LiCu and Al6Li3Cu respectively. In commercial alloys, T1 develops a plate-like structure with a thickness <∼2 nm and is therefore inaccessible to conventional microanalytical techniques. T2 is the equilibrium phase with apparent icosahedral symmetry and its presence is undesirable in industrial alloys.

Defect structures of Nb1+αS2 sulfidation scales

1992 ◽  
Vol 50 (1) ◽  
pp. 38-39
Author(s):  
Chuxin Zhou ◽  
L. W. Hobbs
Keyword(s):  
Stacking Faults ◽  
Rhombohedral Structure ◽  
Stacking Sequence ◽  
Defect Structures ◽  
X Ray Diffraction ◽  
X Ray ◽  
Plane Normal ◽  
Lower Case ◽  
Sulfur Layer ◽  
Two Phases

One of the major purposes in the present work is to study the high temperature sulfidation properties of Nb in severe sulfidizing environments. Kinetically, the sulfidation rate of Nb is satisfactorily slow, but the microstructures and non-stoichiometry of Nb1+αS2 challenge conventional oxidation/sulfidation theory and defect models of non-stoichiometric compounds. This challenge reflects our limited knowledge of the dependence of kinetics and atomic migration processes in solid state materials on their defect structures.Figure 1 shows a high resolution image of a platelet from the middle portion of the Nb1+αS2 scale. A thin lamellar heterogeneity (about 5nm) is observed. From X-ray diffraction results, we have shown that Nb1+αS2 scale is principally rhombohedral structure, but 2H-NbS2 can result locally due to stacking faults, because the only difference between these 2H and 3R phases is variation in the stacking sequence along the c axis. Following an ABC notation, we use capital letters A, B and C to represent the sulfur layer, and lower case letters a, b and c to refer to Nb layers. For example, the stacking sequence of 2H phase is AbACbCA, which is a ∼12Å period along the c axis; the stacking sequence of 3R phase is AbABcBCaCA to form an ∼18Å period along the c axis. Intergrowth of these two phases can take place at stacking faults or by a shear in the basal plane normal to the c axis.

Convergent-bceam diffraction studies on lead zirconate titanate Ceramics

1986 ◽  
Vol 44 ◽  
pp. 482-483
Author(s):  
M.L.A. Dass ◽  
T.A. Bielicki ◽  
G. Thomas ◽  
T. Yamamoto ◽  
K. Okazaki
Keyword(s):  
Lead Zirconate Titanate ◽  
Direct Proof ◽  
Lead Zirconate ◽  
Subsolidus Phase ◽  
Pzt Ceramics ◽  
Subsolidus Phase Diagram ◽  
Zirconate Titanate ◽  
Two Phases ◽  
Cbd Method ◽  
Titanate Ceramics

Lead zirconate titanate, Pb(Zr,Ti)O3 (PZT), ceramics are ferroelectrics formed as solid solutions between ferroelectric PbTiO3 and ant iferroelectric PbZrO3. The subsolidus phase diagram is shown in figure 1. PZT transforms between the Ti-rich tetragonal (T) and the Zr-rich rhombohedral (R) phases at a composition which is nearly independent of temperature. This phenomenon is called morphotropism, and the boundary between the two phases is known as the morphotropic phase boundary (MPB). The excellent piezoelectric and dielectric properties occurring at this composition are believed to.be due to the coexistence of T and R phases, which results in easy poling (i.e. orientation of individual grain polarizations in the direction of an applied electric field). However, there is little direct proof of the coexistence of the two phases at the MPB, possibly because of the difficulty of distinguishing between them. In this investigation a CBD method was found which would successfully differentiate between the phases, and this was applied to confirm the coexistence of the two phases.

The stabilization of B.C.C. Cu in Cu/Nb nanolayered composites

1996 ◽  
Vol 54 ◽  
pp. 228-229
Author(s):  
H. Kung ◽  
A.J. Griffin ◽  
Y.C. Lu ◽  
K.E. Sickafus ◽  
T.E. Mitchell ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Layer Thickness ◽  
Volume Fraction ◽  
Ion Beam ◽  
High Strength ◽  
Cross Sectional ◽  
Metastable Structure ◽  
High Resolution Tem ◽  
Potential Improvement ◽  
Two Phases

Materials with compositionally modulated structures have gained much attention recently due to potential improvement in electrical, magnetic and mechanical properties. Specifically, Cu-Nb laminate systems have been extensively studied mainly due to the combination of high strength, and superior thermal and electrical conductivity that can be obtained and optimized for the different applications. The effect of layer thickness on the hardness, residual stress and electrical resistivity has been investigated. In general, increases in hardness and electrical resistivity have been observed with decreasing layer thickness. In addition, reduction in structural scale has caused the formation of a metastable structure which exhibits uniquely different properties. In this study, we report the formation of b.c.c. Cu in highly textured Cu/Nb nanolayers. A series of Cu/Nb nanolayered films, with alternating Cu and Nb layers, were prepared by dc magnetron sputtering onto Si {100} wafers. The nominal total thickness of each layered film was 1 μm. The layer thickness was varied between 1 nm and 500 nm with the volume fraction of the two phases kept constant at 50%. The deposition rates and film densities were determined through a combination of profilometry and ion beam analysis techniques. Cross-sectional transmission electron microscopy (XTEM) was used to examine the structure, phase and grain size distribution of the as-sputtered films. A JEOL 3000F high resolution TEM was used to characterize the microstructure.

Triply-periodic nanostructures in surfactant, block copolymer, and biomembrane systems, and simulation of TEMs

1993 ◽  
Vol 51 ◽  
pp. 884-885
Author(s):  
David M. Anderson ◽  
Tomas Landh
Keyword(s):  
Liquid Crystalline ◽  
Diblock Copolymers ◽  
Cubic Phase ◽  
List Type ◽  
Interpenetrating Networks ◽  
Triply Periodic ◽  
Wide Range ◽  
Bicontinuous Cubic ◽  
Phase Liquid ◽  
Dividing Surface

First discovered in surfactant-water liquid crystalline systems, so-called ‘bicontinuous cubic phases’ have the property that hydropnilic and lipophilic microdomains form interpenetrating networks conforming to cubic lattices on the scale of nanometers. Later these same structures were found in star diblock copolymers, where the simultaneous continuity of elastomeric and glassy domains gives rise to unique physical properties. Today it is well-established that the symmetry and topology of such a morphology are accurately described by one of several triply-periodic minimal surfaces, and that the interface between hydrophilic and hydrophobic, or immiscible polymer, domains is described by a triply-periodic surface of constant, nonzero mean curvature. One example of such a dividing surface is shown in figure 5.The study of these structures has become of increasing importance in the past five years for two reasons:1)Bicontinuous cubic phase liquid crystals are now being polymerized to create microporous materials with monodispersed pores and readily functionalizable porewalls; figure 3 shows a TEM from a polymerized surfactant / methylmethacrylate / water cubic phase; and2)Compelling evidence has been found that these same morphologies describe biomembrane systems in a wide range of cells.

Direct imaging of order-disorder and antiphase domain structures in Ti3Al intermetallic compound

1990 ◽  
Vol 48 (4) ◽  
pp. 480-481
Author(s):  
H. Q. Ye ◽  
T.S. Xie ◽  
D. Li
Keyword(s):  
Intermetallic Compound ◽  
Volume Fraction ◽  
Fundamental Problem ◽  
Antiphase Domain ◽  
Atomic Scale ◽  
Orientation Relationships ◽  
Domain Structures ◽  
Α Phase ◽  
Diffraction Patterns ◽  
Two Phases

The Ti3Al intermetallic compound has long been recognized as potentially useful structural materials. It offers attractive strength to weight and elastic modulus to weight ratios. Recent work has established that the addition of Nb to Ti3Al ductilized this compound. In this work the fundamental problem of this alloy, i.e. order-disorder and antiphase domain structures was investigated at the atomic scale.The Ti3Al+10at%Nb alloys used in this study were treated at 1060°C and then aged at 700°C for 2 hours. The specimens suitable for TEM were prepared by standard jet electrolytic-polishing technique. A JEM-200CX electron microscope with an interpretable resolution of about 0.25 nm was used for HREM.The [100] and [001] projections of the α2 phase were shown in Fig.l.The alloy obtained consist of at least two phases-α2(Ti3Al) and β0 structures. Moreover, a disorder α phase with small volume fraction was also observed. Fig.2 gives [100] and [001] diffraction patterns of the α2 phase. Since lattice parameters of the ordered α2 (a=0.579, c=0.466 nm) and disorder α phase (a0=0.294≈a/2, c0=0.468 nm) are almost the same, their diffraction patterns are difficult to be distinguished when they are overlapped with epitaxial orientation relationships.

Misfit Dislocations in the Ilmenite (FeTiO3)-Hematite (Fe2O3) System

1980 ◽  
Vol 38 ◽  
pp. 212-213 ◽  
Author(s):  
K.P.D. Lagerlöf ◽  
A.H. Heuer ◽  
T.E. Mitchell
Keyword(s):  
Misfit Dislocation ◽  
Lattice Parameters ◽  
Dislocation Network ◽  
Misfit Dislocations ◽  
Space Group ◽  
Two Phases ◽  
Hematite Fe2o3

It has been reported by Lally et. al. [1] that precipitates of hematite (Fe2O3, space group R3c) in a matrix of ilmenite (FeTiO3, space group R3) are lens shaped and flattened along the [0001]-direction. The coherency across the interface is lost by the introduction of a misfit dislocation network, which minimizes the strain due to the deviation in lattice parameters between the two phases [2]. The purpose of this paper is to present a new analysis of this network.

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