Coherent Interphase Research Articles

Electron microscope studies of minerals: phase boundaries in an extremely slowly cooled clinopyroxene (augite)

High resolution electron microscopy has been used to study the nature of exsolution lamellae that developed during extremely slow and prolonged cooling and depressurization of an aluminium rich augite (high Ca clinopyroxene) taken from a layer of garnet-augite rich gneiss that outcrops on the north side of Scourie Bay, Sutherland, northwest Scotland. The parent clinopyroxene structure evolved with an average cooling rate of ca . 6 x 10 -6 K per year and an average depressurization rate of ca . 0.75 Pa per year over a span of ca . 2 x 10 9 years between 3.0 x 10 9 and 1.0 x 10 9 years ago, and was subsequently stored at close to ambient surface conditions. Three sets of lamellae, which probably formed mainly during the middle of this evolution, were identified as amphibole, pigeonite and hypersthene. Coherent amphibole lamellae, ca . 10 nm thick, exsolved parallel to (010) of the host augite whereas hypersthene formed thicker lamellae 150-250 nm wide, parallel to (100) augite. Again the phase interface is coherent but contains ledges, a few lattice spacings wide, of a pigeonite structure suggesting that the growth of the hypersthene lamellae proceeded via the intermediate formation of pigeonite. Pigeonite forms ca . 90 nm thick lamellae, which extend parallel to an irrational plane (7.96, 0, 1) of host augite at 12° to (100) augite, yet at the same time maintains a coherent interphase boundary. The angle between lamellae of this type and (100) of the host augite is known to be dependent upon composition of the host augite. The quoted value indicates a (Fe+Mn)/(Fe+Mn+Mg) ratio of 0.30 ± 0.05, in good agreement with microprobe data for the host augite, which fall in the range 0.372–0.382. The micrographs also indicate that hypersthene lamellae precede amphibole. The above observations have enabled the relation between the phases and the cooling history of the rock to be established.

Part II crystallography and morphology of the β → ζ massive transformation in Ag-26 a/ o Al

Orientation relationships between parent β grains and grain face- or edge-nucleated ζ m crystals have been determined for the β → ζ m massive transformation in Ag-26 a/o Al, principally by means of selected area electron channelling, but supported by selected area electron diffraction. For 46 of 47 ζ m crystals analyzed a Burgers orientation relationship obtains exactly or nearly so with at least one of the parent grains forming the grain boundary at which nucleation occurred. Approximately half of the orientation relationships between ζ m and the non-Burgers related β grains can be expressed in terms of parallel planes and directions with relatively low indices. An O-lattice-based analysis of these nonBurgers orientation relationships indicates that somewhat more than half of them correspond to partially coherent interphase boundaries. However, the observation that β: ζ m interfaces between non-Burgers-as well as between Burgers-related ζ m and β grains are heavily faceted suggests that a much larger proportion of these boundaries has a partially coherent interfacial structure than either the orientation relationship data or the analyses of this data indicate. The observations that ζ m crystals with similar shape formed along a β grain face of approximately constant orientation have the same spatial orientation to within ±1° and that primary ζ m sideplates developed at a small-angle β grain boundary provide further support for the ubiquity of low energy orientation relationships between ζ m and β and for the similarity between the massive and precipitation reactions in all aspects other than that of a composition difference between product and matrix phases.

Anisotropy of coherent interphase boundary energy

A nearest neighbor, broken bond model is employed to develop general relationships for the concentration profile associated with a coherent interphase boundary and for the interfacial energy of such a boundary, σ c . This development incorporates a simple crystallographic method for describing the distribution of nearest neighboring atoms about a given atom in an interface of arbitrary orientation between two cubic-type crystals. Contours of constant σ c are constructed on the unit steriographic triangle at several temperatures and illustrate the manner in which the anisotropy of σ c evolves with decreasing temperature. Mathematical equivalency of the discrete lattice model and the continuum method of Cahn and Hilliard is demonstrated at high temperatures when the regular solution model is applicable. A comparison between the two approaches is used to demonstrate that σ c is relatively insensitive to the concentration profile.

The effect of Ni on the decomposition of austenite in Fe-Cu alloys

This paper is concerned with the effect of ternary additions of Ni on the decomposition of austenite in Fe-Cu alloys. It is shown that the transformation kinetics, transformation structures and associated precipitate morphologies are sensitive functions of the Ni content. Specifically the results show that the addition of nickel increases the transformation times and also leads to a change in resultant ferrite morphology from equiaxed to Widmanstatten, with a concomitant increase in the partially coherent interphase boundary growth mode. The increase in transformation time allows precipitation of Cu to occur on the interphase boundary and in the matrix. It is also shown that the exact details of the ∈-Cu dispersion is controlled both by the nature of the austenite/ferrite interface and the kinetics of the transformation.

Perfection et stabilité thermique des structures lamellaires de l'eutectique Pb–Sn

In directionally solidified Pb–Sn eutectic, prepared by the Bridgman technique, it has been found that it is possible to obtain grains of nearly perfect lamellar structure and stable at elevated temperatures. The interlamellar spacing λ is 1 μm and the mean distance \bar D between fault lines 20 λ whereas they are respectively 1.5 μm and 7 λ in neighbouring grains. The orientation relation is: growth direction || [2\bar 11]Pb and ⊥ (12\bar 1)Sn, lamellar interfaces || (47\bar 1)Pb and (523)Sn. The spacing between planes perpendicular to the growth direction is the same in both phases. By studing the orientation relation with Bollmann's theory, zero planes and interfaces are found to be parallel. The coherent interphase boundary can explain the particularities of these grains. Their origin is discussed and related to the nucleation conditions.

Microemulsions versus micelles

To differentiate between microemulsions and micellar solutions, an examination was undertaken of the molecular interactions taking place in the interphase of very small droplets. When the interphase is 25 A thick, there is an abrupt change in the ratio of the volume of the interphase to the volume of the core in the neighborhood of a droplet diameter of 100 A. Below this diameter, the degree of aggregation, or curvature of the noncoherent interphase, is primarily determined by interactions between water and the heads of the surfactant species. Above this diameter, curvature is determined by specific interactions among oil molecules and surfactant tails as well as by the interactions among the surfactant heads and water in a well-defined coherent interphase. It is such a duplex film, capable of having different tensions at each of its sides, that distinguishes the microemulsion from the micellar solution. A tension or pressure gradient across a freshly formed interphase is able to control its curvature, and thus droplet size, over a much wider range than can the interaction among surfactant heads and water alone. The data of two of Schulman's alcohol and soap stabilized dispersions were used for this analysis. In one, the oil phase was benzene, in the other hexadecane. It was recalled that as the water content of these inverted micelles was increased, the increase in droplet size was accompanied by an increase in the ratio of alcohol to soap in the interphase. This is important because zero interfacial tension, considered necessary for microemulsions, only occurs at intermediate values of this ratio. In the benzene system this ratio was quickly exceeded, resulting in a macroemulsion at low water content. In the hexadecane system, because of better association between oil molecules and the tails of the surfactant species, the aggregates retained their equilibrium status, despite a high ratio, by changing into cylindrical or lamellar micelles. This behavior was ascribed to a limit in the system of the ratio of alcohol to soap and the amount of oil, suggesting how phospholipids might form liposomes or membrane layers. As more water was added to the lamellar micelles, o/w microemulsions formed providing certain new criteria were met. Emphasis was placed on the choice of components. Because of space limitations in the center of the droplet, long alcohol tails and more than stoichiometric amounts of, or large, cations increased the chances of forming these rare systems. A hypothetical phase equilibria diagram was presented in which the regions of microemulsions, micellar solutions, and liquid crystalline phases were defined qualitatively. In this diagram microemulsions and micellar solutions were distinguished on the basis of aggregate size.

Observations on interphase boundary structure

SUMMARYA review is presented of experimental observations reported on the structure of interphase boundaries since 1968. Nearly all observed boundaries are of the partially or fully coherent type, and hence the principal structural features examined were misfit dislocations and ledges. Observations were drawn from studies of precipitation, spinodal decomposition, oriented overgrowths and eutectics. Interphase boundary structures were found to be little affected in the main by the type of reaction through which they were developed and were consistent with Van der Merwe theory and a theory of precipitate morphology. Observations of these structures have been considerably facilitated by the efforts of Weatherly and co‐workers to define the visibility and the optimum TEM viewing conditions of misfit dislocations and ledges. Important new observations on misfit dislocations made since 1968 include: misfit dislocation spacing in the Cr(Mo)/NiAl eutectic in good agreement with theoretical expectation because misfit dislocations are also glide dislocations and the interface plane is also the glide plane; misfit dislocations on θ′ Al‐Cu and η Al‐Au plates with a Burgers vector (a/2<100>) stable only at an interphase boundary; reduction of the interfacial energy of partially coherent boundaries on the same precipitates by dislocation interactions and rearrangements; reduction of interfacial energy of interfaces developed during spinodal decomposition through rotation of the interface itself from {100} to {110}; and misfit dislocation boundaries between f.c.c. (Cu‐rich) and b.c.c. (Cr) crystals made possible with the assistance of ‘structural ledges’. Growth ledges have now been observed in a number of alloy systems which have undergone precipitation from solid solution or eutectic solidification; they appear to be confirmed as a customary feature of migrating partially or fully coherent interphase boundaries. Much new experimental information has been obtained on the sources (exceedingly diverse), heights (usually appreciably higher than monatomic), spacings (irregular) and migration kinetics (diffusion‐controlled if their edges are disordered) of ledges. New observations continue to confirm the complexity of the processes through which misfit dislocations are acquired. The Ashby‐Johnson and the Brown‐Woolhouse theories of misfit dislocation nucleation or acquisition by spherical precipitates are in encouraging agreement with experiment.

Structure of crystalline interfaces

The structure of crystalline interfaces, as observed by transmission electron microscopy, is reviewed with emphasis on the similarity of grain and interphase boundaries of the dislocation type. Small-angle grain boundaries and low misfit interphase boundaries between similar crystal structures largely condense their mismatch into arrays of interfacial dislocations having Burgers vectors in common with dislocations located in the bulk crystals. Large-angle grain boundaries near certain misorientations corresponding to good fit between the abutting grains contain dislocations with Burgers vectors which are not found in the bulk crystal. Partially coherent interphase boundaries between quite dissimilar crystals, for example, f.c.c. and b.c.c., may also contain such dislocations. Principally, because of the difficulties involved in the acquistion of interfacial dislocations, dislocation interphase boundaries, in particular, usually do not have the minimum energy structure.

An assessment of the morphology of two-phase microstructures involving coherent superlattice phases—I. Interphase and antiphase boundaries

The energies of fully coherent interphase and antiphase boundaries have been calculated in the zeroth order pair approximation. The calculation represents a unified scheme for taking differences in composition, type and degree of order, and antiphase relations into account. Results for the L1 2, B2 and D0 3 type superlattices are given. The orientation dependence of antiphase boundary energies obtained here and reported previously are compared. The application of the present results to the interpretation of coherent two-phase microstructures is discussed.

Interfacial Energy of Dislocation and of Coherent Interphase Boundaries

Abstract A consolidated semi-empirical method is presented for calculating the interfacial free energy of dislocation and of coherent interphase boundaries. The broad faces of γ plates in α-Al-Ag and of θ′ plates in α-Al-eu are used as examples of the two types of boundary. New results are reported for the enthalpic and for the positional entropic components of the chemical part of the total interfacial free energy. A result due to Taylor (J. Inst. Metals, 1957–58, 86, 456) is used to show that the total energy, as calculated by present methods, is appreciably too high, and must be scaled down empirically.