A phase field study of morphological instabilities in multilayer thin films

We studied the microstructural evolution of multiple layers of elastically stiff films embedded in an elastically soft matrix using a phase field model. The coherent and planar film/matrix interfaces are rendered unstable by the elastic stresses due to a lattice parameter mismatch between the film and matrix phases, resulting in the break-up of the films into particles. With an increasing volume fraction of the stiff phase, the elastic interactions between neighbouring layers lead to: (i) interlayer correlations from an early stage; (ii) a longer wavelength for the maximally growing wave; and therefore (iii) a delayed break-LIP. Further, they promote a crossover in the mode of instability from a predominantly anti-symmetric (in phase) one to a symmetric (out of phase) one. We have computed a stability diagram for the most probable mode of break-up in terms of elastic modulus Mismatch and Volume fraction. We rationalize our results in terms of the initial driving force for destabilization, and corroborate our conclusions using simulations in elastically anisotropic systems.

Mesoscale description of an asymmetric lamellar phase

The relationship between the parameters in a description based on a mesoscale free energy functional for the concentration field and the macroscopic properties, such as the bending and compression moduli and the permeation constant, are examined for an asymmetric lamellar phase where the mass fractions of the hydrophobic and hydrophilic parts are not equal. The difference in the mass fractions is incorporated using a cubic term in the free energy functional, in addition to the usual quadratic and quartic terms in the Landau–Ginsburg formulation. The relationship between the coefficient of the cubic term and the difference in the mass fractions of the hydrophilic and hydrophobic parts is obtained. For a lamellar phase, it is important to ensure that the surface tension is zero due to symmetry considerations. The relationship between the parameters in the free energy functional for zero surface tension is derived. When the interface between the hydrophilic and hydrophobic parts is diffuse, it is found that the bending and compression moduli, scaled by the parameters in the free energy functional, do increase as the asymmetry in the bilayer increases. When the interface between the hydrophilic and hydrophobic parts is sharp, the scaled bending and compression moduli show no dependence on the asymmetry in the bilayer. The ratio of the permeation constant in between the water and bilayer in a molecular description and the Onsager coefficient in the mesoscale description is O(1) for both sharp and diffuse interfaces and it increases as the difference in the mass fractions is increased.

Phase-Field Simulation of Fusion Interface Events during Solidification of Dissimilar Welds: Effect of Composition Inhomogeneity

We investigate the events near the fusion interfaces of dissimilar welds using a phase-field model developed for single-phase solidification of binary alloys. The parameters used here correspond to the dissimilar welding of a Ni/Cu couple. The events at the Ni and the Cu interface are very different, which illustrate the importance of the phase diagram through the slope of the liquidus curves. In the Ni side, where the liquidus temperature decreases with increasing alloying, solutal melting of the base metal takes place; the resolidification, with continuously increasing solid composition, is very sluggish until the interface encounters a homogeneous melt composition. The growth difficulty of the base metal increases with increasing initial melt composition, which is equivalent to a steeper slope of the liquidus curve. In the Cu side, the initial conditions result in a deeply undercooled melt and contributions from both constrained and unconstrained modes of growth are observed. The simulations bring out the possibility of nucleation of a concentrated solid phase from the melt, and a secondary melting of the substrate due to the associated recalescence event. The results for the Ni and Cu interfaces can be used to understand more complex dissimilar weld interfaces involving multiphase solidification.

Unconventional mechanism of stabilization of a tetragonal phase in the perovskite ferroelectric (PbTiO3)(1-x)(BiFeO3)(x)

Temperature-dependent x-ray powder-diffraction study of the tetragonal compositions of PbTiO3-BiFeO3 series has revealed that, unlike for all the known ferroelectric perovskites, the compositions exhibiting giant tetragonality is stabilized from the cubic phase via a complex transition pathway which involve (i) formation of minor monoclinic phase with a large pseudotetragonality along with an intermediate tetragonal phase (major) with a small tetragonality, (ii) gradual vanishing of the intermediate tetragonal phase and concomitant increase in the monoclinic regions, and finally (iii) gradual transformation of the monoclinic phase to the tetragonal phase with giant tetragonality.The system seems to adopt such a complex transition pathway to create amicrostructure with very large number of domains and interfaces for stress relief, which would not have been possible in case of a direct cubic-tetragonal transition.

Conjectures about phase turbulence in the complex Ginzburg-Landau equation

In the complex Ginzburg-Landau equation, we consider possible ''phase turbulent'' regimes, where asymptotic correlations are controlled by phase fluctuations rather than by topological defects. Conjecturing that the decay of such correlations is governed by the Kardar-Parisi-Zhang (KPZ) model of growing interfaces, we derive the following results: (1) A scaling ansatz implies that equal-time spatial correlations in 1d, 2d, and 3d decay like e(-Ax2 zeta), where A is a nonuniversal constant, and zeta=1/2 in 1d. (2) Temporal correlations decay as exp(-t(2 beta)h(t/L(z))), with the scaling law <(beta)over bar> = <(zeta)over bar>/z, where z = 3/2, 1.58..., and 1.66..., for d = 1,2, and 3 respectively. The scaling function h(y) approaches a constant as y --> 0, and behaves like y(2(beta-<(beta)over bar>)), for large y. If in 3d the associated KPZ model turns out to be in its weak-coupling (''smooth'') phase, then, instead of the above behavior, the CGLE exhibits rotating long-range order whose connected correlations decay like 1/x in space or 1/t(1/2) in time. (3) For system sizes, L, and times t respectively less than a crossover length, L(c), and time, t(c), correlations are governed by the free-field or Edwards-Wilkinson (EW) equation, rather than the KPZ model. In 1d, we find that L(c) is large: L(c) similar to 35,000; for L < L(c) we show numerical evidence for stretched exponential decay of temporal correlations with an exponent consistent with the EW value beta(EW)= 1/4.

On the decomposition of ? phase in some rapidly quenched titanium-eutectoid alloys

The decomposition of the beta phase in rapidly quenched Ti-2.8 at. pet Co, Ti-5.4 at. pet Ni, Ti-4.5 at. pet, and 5.5 at. pet Cu alloys has been investigated by electron microscopy. During rapid quenching, two competitive phase transformations, namely martensitic and eutectoid transformation, have occurred, and the region of eutectoid transformation is extended due to the high cooling rates involved. The beta phase decomposed into nonlamellar eutectoid product (bainite) having a globular morphology in Ti-2.8 pet Co and Ti-4.5 pet Cu (hypoeutectoid) alloys. In the near-eutectoid Ti-5.5 pet Cu alloy, the decomposition occurred by a lamellar (pearlite) type, whereas in Ti-5.4 pct Ni (hypereutectoid), both morphologies were observed. The interfaces between the proeutectoid alpha and the intermetallic compound in the nonlamellar type as well as between the proeutectoid alpha and the pearlite were often found to be partially coherent. These findings are in agreement with the Lee and Aaronson model proposed recently for the evolution of bainite and pearlite structures during the solid-state transformations of some titanium-eutectoid alloys. The evolution of the Ti2Cu phase during rapid quenching involved the formation of a metastable phase closely related to an ''omega-type'' phase before the equilibrium phase formed. Further, the lamellar intermetallic compound Ti2Cu was found to evolve by a sympathetic nucleation process. Evidence is established for the sympathetic nucleation of the proeutectoid alpha crystals formed during rapid quenching.

Studies of interfaces in Al-65 Cu20Fe15

The study of interfaces in quasicrystalline alloys is relatively new. Apart From the change in orientation, symmetry and chemistry which can occur across homophase and heterophase boundaries in crystalline materials, we have the additional, exciting possibility of an interface between quasicrystalline and its rational approximant. High resolution electron microscopy is a powerful technique to study the structural details of such interfaces. We report the results of a HREM study of the interface between the icosahedral phase and the related Al13Fe4 type monoclinic phase in melt spun and annealed Al65Cu20Fe15 alloy.

X-ray reflectivity study of semiconductor interfaces

The results of an X-ray reflectivity study of thick AlAs-AlGaAs and thin GeSi-Ge multilayers grown using metal-organic vapour-phase epitaxy and ion-beam sputtering deposition techniques, respectively, are presented. Asymmetry in interfaces is observed in both of these semiconductor multilayers. It is also observed that although the Si-on-Ge interface is sharp, an Si0.4Ge0.6 alloy is formed at the Ge-on-Si interface. In the case of the III-V semiconductor, the AlAs-on-AlGaAs interface shows much greater roughness than that observed in the AlGaAs-on-AlAs interface. For thin multilayers it is demonstrated that the compositional profile as a function of depth can be obtained directly from the X-ray reflectivity data.

Phase separation in a simple model with dynamical asymmetry

We perform computer simulations of a Cahn-Hilliard model of phase separation that has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function that is order parameter dependent. Simulations of this model reveal morphological features similar to those observed in viscoelastic phase separation. In the early stages, the minority phase domains form a percolating structure that shrinks with time, eventually leading to the formation of disconnected regions that are characterized by the presence of random interfaces as well as isolated droplets. The domains grow as L(t)similar to t(1/3) in the very late stages. Although dynamical scaling is violated in the area shrinking regime, it is restored at late times. However, the form of the scaling function is found to depend on the extent of dynamical asymmetry. [S1063-651X(99)12101-9].

Interfaces In Quasicrystalline Systems

Structural relations between quasicrystalline and related crystalline rational approximant phases have been of interest for some time now. Such relations are now being used to understand interface structures. Interfaces between structural motif - wise related, but dissimilarly periodic phases are expected to show a degree of lattice match in certain directions. Our earlier studies in the Al-Cu-Fe system using the HREM technique has shown this to be true. The structural difference leads to well defined structural ledges in the interface between the icosahedral Al-Cu-Fe phase and the monoclinic Al13Fe4 type phase. In the present paper we report our results on the HREM study of interfaces in Al-Cu-Fe and Al-Pd-Mn systems. The emphasis will be on heterophase interfaces between quasiperiodic and periodic phases, where the two are structurally related. An attempt will be made to correlate the results with calculated lattice projections of the two structures on the grain boundary plane.

Interfaces In Quasicrystalline Systems

Structural relations between quasicrystalline and related crystalline rational approximant phases have been of interest for some time now. Such relations are now being used to understand interface structures. Interfaces between structural motif - wise related, but dissimilarly periodic phases are expected to show a degree of lattice match in certain directions. Our earlier studies in the Al-Cu-Fe system using the HREM technique has shown this to be true. The structural difference leads to well defined structural ledges in the interface between the icosahedral Al-Cu-Fe phase and the monoclinic Al13Fe4 type phase. In the present paper we report our results on the HREM study of interfaces in Al-Cu-Fe and Al-Pd-Mn systems. The emphasis will be on heterophase interfaces between quasiperiodic and periodic phases, where the two are structurally related. An attempt will be made to correlate the results with calculated lattice projections of the two structures on the grain boundary plane.

Functionalized and Postfunctionalizable Porous Polymeric Films through Evaporation-Induced Phase Separation Using Mixed Solvents

Condensation of water droplets during rapid evaporation of a polymer solution, under humid conditions, has been known to generate uniformly porous polymer films. Similar porous films are also formed when a solution of the polymer in THF containing small amounts of water, is allowed to evaporate rapidly under air flow; this suggests that water droplets may be formed during the final stages of film formation. In the presence of added surfactants, the interface of water droplets could become lined with the surfactants and consequently the internal walls of the pores generated, upon removal of the water, could become decorated with the hydrophilic head groups of the surfactant molecules. In a series of carefully designed experiments, we have examined the effect of added surfactants, both anionic and cationic, on the formation of porous PMMA films; the films were prepared by evaporating a solution of the polymer in THF containing controlled amounts of aqueous surfactant solutions. We observed that the average size of the pores decreases with increasing surfactant concentration, while it increases with increasing amounts of added water. The size of the pores and their distribution were examined using AFM and IR imaging methods. Although IR imaging possessed inadequate resolution to confirm the presence of surfactants at the pore surface, exchange of the inorganic counterion, such as the sodium-ion of SDS, with suitable ionic organic dyes permitted the unequivocal demonstration of the presence of the surfactants at the interface by the use of confocal fluorescence microscopy.

Synthesis and phase evolution in Nb/Si multilayers obtained by sequential laser ablation

The paper reports the synthesis of Nb/Si multilayers (48/27 nm) deposited on Si single crystal substrate by sequential laser ablation of elemental Nb and Si. Significant amount of Nb is found in the amorphous Si layer (similar to 25-35 at.% Nb). The Nb layer is found to be polycrystalline. The phase evolution of the multilayer has been studied by annealing at 600 degrees C for various times and carrying out cross sectional electron microscopic studies. We report the formation of amorphous silicide layer at the Nb/Si interface followed by the formation of the NbSi2 phase in the Si layer. Further annealing leads to the nucleation of hexagonal Nb5Si3 grains in amorphous silicide layers at Nb/NbSi2 interfaces. These results are different from those reported for sputter deposited multilayer. (C) 2013 Elsevier B. V. All rights reserved.

Thermoelectric properties of PbTe with encapsulated bismuth secondary phase

Lead Telluride (PbTe) with bismuth secondary phase embedded in the bulk has been prepared by matrix encapsulation technique. X-Ray Diffraction results indicated crystalline PbTe, while Rietveld analysis showed that Bi did not substitute at either Pb or Te site, which was further confirmed by Raman and X-Ray Photoelectron Spectroscopy. Scanning Electron Microscopy showed the expected presence of a secondary phase, while Energy Dispersive Spectroscopy results showed a slight deficiency of tellurium in the PbTe matrix, which might have occurred during synthesis due to higher vapor pressure of Te. Transmission Electron Microscopy results did not show any nanometer sized Bi phase. Seebeck coefficient (S) and electrical conductivity (sigma) were measured from room temperature to 725 K. A decrease in S and sigma with increasing Bi content showed an increased scattering of electrons from PbTe-Bi interfaces, along with a possible electron acceptor role of Bi secondary phase. An overall decrease in the power factor was thus observed. Thermal conductivity, measured from 400K to 725K, was smaller at starting temperature with increasing Bi concentration, and almost comparable to that of PbTe at higher temperatures, indicating a more important role of electrons as compared to phonons at PbTe-Bi interfaces. Still, a reasonable zT of 0.8 at 725K was achieved for undoped PbTe, but no improvement was found for bismuth added samples with micrometer inclusions. (C) 2013 American Institute of Physics. http://dx.doi.org/10.1063/1.4796148]

Microstructure and texture evolution during sub-transus thermomechanical processing of Ti-6Al-4V-0.1B alloy: part I. hot rolling in (alpha plus beta) phase field

In the current study, the evolution of microstructure and texture has been studied for Ti-6Al-4V-0.1B alloy during sub-transus thermomechanical processing. This part of the work deals with the deformation response of the alloy by rolling in the (alpha + beta) phase field. The (alpha + beta) annealing behavior of the rolled specimen is communicated in part II. Rolled microstructures of the alloys exhibit either kinked or straight alpha colonies depending on their orientations with respect to the principal rolling directions. The Ti-6Al-4V-0.1B alloy shows an improved rolling response compared with the alloy Ti-6Al-4V because of smaller alpha lamellae size, coherency of alpha/beta interfaces, and multiple slip due to orientation factors. Accelerated dynamic globularization for this alloy is similarly caused by the intralamellar transverse boundary formation via multiple slip and strain accumulation at TiB particles. The (0002)(alpha) pole figures of rolled Ti-6Al-4V alloy shows ``TD splitting'' at lower rolling temperatures because of strong initial texture. Substantial beta phase mitigates the effect of starting texture at higher temperature so that ``RD splitting'' characterizes the basal pole figure. Weak starting texture and easy slip transfer for Ti-6Al-4V-0.1B alloy produce simultaneous TD and RD splittings in basal pole figures at all rolling temperatures.