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Stabilization of Nanoscale Quasi-Liquid Interfacial Films in Inorganic Materials: A Review and Critical Assessment

Stabilization of Nanoscale Quasi-Liquid Interfacial Films in Inorganic Materials: A Review and Critical Assessment by Jian LuoPresented by George Ferko1

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Background: WettingAssumptions: all GBs are 1) high-angle, 2) random, and 3) have the same gbExcess free energiesNote difference between terms with and without adsorptioncl and lv are defined for thick films (may not be for very thin films)

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Adsorption at the surface must decrease the surface or GB interfacial energy for an equilibrium Gibbs excess to existSurfaces in equil. with a secondary liquid phase always have some adsorbates due to entropic effects

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Prewetting/PremeltingPrewetting adsorption transition when the phase that does the wetting is not yet stableFirst order or continuous transitionThin adsorption film of wetting phase is formedIs relevant to changes in and TComplete (thickness increases until bulk wetting) or incomplete (analogous to frustrated complete wetting)

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Cahn used a diffuse-interface model to determine the composition that would minimize excess free energyCritical point is where the difference between thin and thick films vanishes3

Prewetting/PremeltingPremelting - stabilization of thin quasi-liquid layers below bulk solidus temp. for unary systems or compounds that melt congruentlyUbiquitous due to entropy at surfaces and GBsCan also be complete and incompleteOnly relevant to changes in T

4From Alsayed AM, Islam MF, Zhang J, Collings PJ, Yodh AG, Premelting defects within bulk colloidal crystals, Science, 309, (2005), pp 1207.

(disorder transition)4

Prewetting/PremeltingPrewetting is typically coupled with premeltingIn principle, prewetting transitions can also occur in binary crystalline systems without interfacial disordering (premelting).

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Perhaps Complexion I is an example of prewetting w/o premelting Be sure to describe the different lines:first-order transitionContinuous transitionPartial (frustrated-complete)Layering transition5

Prewetting/Premelting + AdsorptionStructure and composition of nano-films differs from the bulkAnalogous to BET modelMulti-layer characterChemisorption of first layer followed by physical adsorption of subsequent layersAdaptation of BET to metal GBs is described by Lejek, et al. (Truncated BET)Space charge effects must be considered for ionic materialsGibbs adsorption theory always holds true for prewetting and other multilayer adsorption

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BET is similar to Langmuir-Mclean segregation in that it treats each single layer as its own monolayer applying the Langmuir-Mclean concept to infinite thickness.Brunauer-Emmett-Teller (BET)

Seah and Hondros reported the truncated BET in 1977 describing multilayer adsorption6

Frustrated-Complete WettingAnalogous to the coexistence of the partial wetting phase and the nanometer filmAttractive forces cause a divergence of film thicknessEquilibrium microscopically thick films can form of these films would be somewhere between that of a sub-monolayer film and complete wetting phaseEven with a non-zero wetting angle a stable film has formed and reached a finite thickness due to attractive dispersion forces

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This is a precursor film and is part of the spreading processThe partially wetting phase is in equil. With the prewetting film7

What are London Dispersion Forces?Dipole moments are induced on interatomic bonds by other atomic bondsUniversal motion of electrons results in a propagating EM wave that cannot be dissipatedResulting field induces a dipole moment in nearby electron clouds

8From RH French, Origins and applications of London dispersion forces and Hamaker constants in ceramics, J. Am. Ceram. Soc., 83(9) 2117-46 (2000).

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Relation to DLVO TheoryFirst used to describe equilibrium separation between charged colloidal particleApplied by Clarke to Si3N4 IGFs to explain equilibrium film thicknessIGFs are explained from a balance among attractive and repulsive interfacial forces in force-balance models that are extended from the DLVO theory9

From Electrostatic Charge and Bacterial Adhesion, http://www.ncl.ac.uk/dental/oralbiol/oralenv/tutorials/electrostatic.htm

Derjaguin-Landau-Verwey-Overbeek (DLVO)Attractive dispersion force and repulsive steric or electrical double layer force

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Widespread ExistenceDiscoveries in a multitude of systems suggest the possibility of a unifying thermodynamic framework

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Equilibrium ThicknessConstant thickness on the order of 1 nmThickness varies little between high-angle random GBsFilm thickness is independent of fraction excess secondary phase as long as is kept the sameObservations between different authors are within each others experimental error

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This may be the best data on the chemistry dependence of OGF thickness11

Film Energy and StabilityFilms exist after long annealing times and extensive grain growthExcess free energy of an IGF must be lower then the sum of the two crystal liquid interfacial energiesIGFs can be at true thermodynamic equilibrium, e.g. in the SiO2-TiO2 hetero-interface and in the Bi2O3-doped ZnO GB

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Thus they are likely in an equil. ConfiurationDihedral angles are non-zero at 3 and 4 GB junctions indicatingFilm is not a kinetically limited remnant12

Distinct Composition and StructureIGFs and SAFs can have compositions not possible in the associated bulk phases, e.g. Bi2O3-ZnO systemComposition is such that excess free energy is minimizedShort-range order in films detected by processing HRTEM imagesGradients in composition and structure have been predicted by molecular dynamics and diffuse interface modelsExtent of boundary misorientation on GB-to-GB variation is an open question

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Value of SAFsCan prove the existence of attractive forces other then LD forces that result in equilibrium thicknessDispersion interaction can only be repulsive in SAFsRepulsive forces make films thicker resulting in continuous transitions to complete wetting if there are no other forces at workHamaker constants at hetero-interface IGFs are difficult to quantify14

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Diffuse Interface TheoriesWhy does a diffuse interface form?Minimize volumetric free energy by approaching properties of bulk liquidMinimize interface energy by approaching properties of bulk substrateMinimize short-range excess energy of a terminating surfaceThrough thickness gradients in composition (c), crystallinity (), and orientation () must existGradients are found by minimizing the diffuse interface equation

The existence of first-order and continuous transitions has been verified.Bishop, et al., have recently included the effects of electrostatic interactions between defects in Si3N4-SiO2Dispersion interactions need to be added separately to diffuse interface models

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Diffuse-interface models may not be good for systems where long range forces dominate or are significantBut are important for understanding through thickness comp and structural gradient15

Do atomically abrupt interfaces disprove diffuse interface theories?Diffuse interface models can be used to predict abrupt interfacesThe free energy barrier of formation must be high for the structural transition consideredModel agrees with systems with deep eutectic reactions where prewetting occurs near the bulk eutectic temperature (e.g. W-Ni or ZnO-Bi2O3)

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Force Balance Models

Existence of abrupt interfaces supports use of the simplified free energy treatment used in the force balance modelEquilibrium thickness represented as balance between attractive and repulsive forcesIn the model all energy terms drop to zero as h Equilibrium thickness represented by

Limitations:Based the assumption of uniform film thicknessComputing forces requires data on the film structure and compositionInterfacial forces are not completely independent

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2. Not know a priori2. Researchers use bulk properties

Most recently atomistic simulations and first-principle simulations have become realistic which can help overcome the limitations of the BF and DI models

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Volumetric Free EnergyOften the dominant attractive force limiting film thickness in subeutectic and undersaturation regionsGvol is the volumetric Gibbs free energy of forming a uniform liquid film from a mixture of bulk phasesNegative for spontaneous amorphization occurring from mixing 2 crystalline phases below solidus T that are not in equilibriumPositive when the bulk phases are in equilibriumIn the diffuse interface model 18

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Volumetric Free EnergyThe contribution of the Gvol term to the equilibrium thickness of films is apparent in the Bi2O3-ZnO thin filmsAbove the Teu the thickness would correspond to a balance between LD forces and short-range repulsion19

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Determining the Volumetric Free EnergyCan be difficult due to through thickness gradientsThere are 2 choices of how to compute GvolSelect c0 to be the average composition, but this will be a function of film thickness thus it will also be hard to computeSelect c0 to be the composition the minimizes Gvol then it will be independent of film thicknessGvol now represents the min. free energy require to form a liquid film of any composition (always zero or positive)Any other excess volumetric free energy should be considered in the short-range interactions20

Zero corresponds to the solid-liquid coexistence region and positive corresponds to the subeutectic or undersaturated condition

20

Short-range ForcesRepulsive forces that stabilize IGFs against disappea