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Stabilization of Nanoscale Quasi-Liquid Interfacial Films in Inorganic Materials: A

Review and Critical Assessment by Jian Luo

Presented by George Ferko

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Background: Wetting• Assumptions: all GBs are 1) high-angle, 2) random, and 3) have the

same γgb

• Excess free energies– Note difference between terms with and without adsorption– γcl and γlv are defined for thick films (may not be for very thin films)

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Prewetting/Premelting• Prewetting – adsorption transition when the phase that does the

wetting is not yet stable– First order or continuous transition– Thin adsorption film of wetting phase is formed– Is relevant to changes in μ and T– Complete (thickness increases until bulk wetting) or incomplete (analogous to

frustrated complete wetting)

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Prewetting/Premelting• Premelting - stabilization of thin quasi-liquid layers below bulk

solidus temp. for unary systems or compounds that melt congruently– Ubiquitous due to ↑ entropy at surfaces and GBs– Can also be complete and incomplete– Only relevant to changes in T

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

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Prewetting/Premelting• Prewetting is typically coupled with premelting• “In principle, prewetting transitions can also occur in binary

crystalline systems without interfacial disordering (premelting).”

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Prewetting/Premelting + Adsorption• Structure and composition of nano-films differs from the bulk• Analogous to BET model

– Multi-layer character– Chemisorption of first layer followed by physical adsorption of subsequent

layers• Adaptation of BET to metal GBs is described by Lejček, et al.

(Truncated BET)• Space charge effects must be considered for ionic materials• Gibbs adsorption theory always holds true for prewetting and other

multilayer adsorption

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Frustrated-Complete Wetting• Analogous to the coexistence of the partial wetting phase and the

nanometer film• Attractive forces cause a divergence of film thickness• Equilibrium microscopically thick films can form• μ of these films would be somewhere between that of a sub-

monolayer film and complete wetting phase• Even 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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What are London Dispersion Forces?• Dipole moments are induced on interatomic bonds by other atomic

bonds• Universal motion of electrons results in a propagating EM wave that

cannot be dissipated• Resulting field induces a dipole moment in nearby electron clouds

From 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 Theory• First used to describe equilibrium separation between charged

colloidal particle• Applied by Clarke to Si3N4 IGFs to explain equilibrium film thickness• IGFs are explained from a balance among attractive and repulsive

interfacial forces in force-balance models that are extended from the DLVO theory

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

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Widespread Existence• Discoveries in a multitude of systems suggest the possibility of a

unifying thermodynamic framework

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Equilibrium Thickness• Constant thickness on the order of 1 nm• Thickness varies little between high-angle random GBs• Film thickness is independent of fraction excess secondary phase as

long as μ is kept the same• Observations between different authors are within each others

experimental error

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Film Energy and Stability• Films exist after long annealing times and extensive grain growth• Excess free energy of an IGF must be lower then the sum of the two

crystal liquid interfacial energies• IGFs 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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Distinct Composition and Structure• IGFs and SAFs can have compositions not possible in the associated

bulk phases, e.g. Bi2O3-ZnO system• Composition is such that excess free energy is minimized• Short-range order in films detected by processing HRTEM images• Gradients in composition and structure have been predicted by

molecular dynamics and diffuse interface models• Extent of boundary misorientation on GB-to-GB variation is an open

question

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Value of SAFs• Can prove the existence of attractive forces other then LD forces that

result in equilibrium thickness• Dispersion interaction can only be repulsive in SAFs• Repulsive forces make films thicker resulting in continuous

transitions to complete wetting if there are no other forces at work• Hamaker constants at hetero-interface IGFs are difficult to quantify

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Diffuse Interface Theories• Why does a diffuse interface form?

– Minimize volumetric free energy by approaching properties of bulk liquid– Minimize interface energy by approaching properties of bulk substrate– Minimize short-range excess energy of a terminating surface

• Through thickness gradients in composition ( c), crystallinity (∇ ∇η), and orientation (∇θ) must exist

• Gradients 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-SiO2

• Dispersion interactions need to be added separately to diffuse interface models

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Do atomically abrupt interfaces disprove diffuse interface theories?

• Diffuse interface models can be used to predict abrupt interfaces• The free energy barrier of formation must be high for the structural

transition considered• Model 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 model

• Equilibrium thickness represented as balance between attractive and repulsive forces

• In the model all energy terms drop to zero as h →∞• Equilibrium thickness represented by …

• Limitations:1. Based the assumption of uniform film thickness2. Computing forces requires data on the film structure and composition3. Interfacial forces are not completely independent

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Volumetric Free Energy• Often the dominant attractive force limiting film thickness in

subeutectic and undersaturation regions• ΔGvol is the volumetric Gibbs free energy of forming a uniform liquid

film from a mixture of bulk phases• Negative for spontaneous amorphization occurring from mixing 2

crystalline phases below solidus T that are not in equilibrium• Positive when the bulk phases are in equilibrium• In the diffuse interface model …

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Volumetric Free Energy• The contribution of the ΔGvol term to the equilibrium thickness of

films is apparent in the Bi2O3-ZnO thin films• Above the Teu the thickness would correspond to a balance between

LD forces and short-range repulsion

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Determining the Volumetric Free Energy

• Can be difficult due to through thickness gradients• There are 2 choices of how to compute ΔGvol

1. Select c0 to be the average composition, but this will be a function of film thickness thus it will also be hard to compute

2. Select c0 to be the composition the minimizes ΔGvol then it will be independent of film thickness• ΔGvol 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 interactions

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Short-range Forces• Repulsive forces that stabilize IGFs against disappearing• Vanishes as h approaches zero• Clarke originally derived the force as a steric force that is an

interference of the partial orders induced by the abutting crystals• Least understood term• Complex dependence on film thickness and very complicated in

ceramics• Approximated as…

where ξ is a correlation length that scales with molecular bond or chain length and …

where Δγshort-range is the contribution of the short-range interaction to Δγ

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Long-range Dispersion Forces• Arise from electromagnetic interaction of fluctuating dipoles• Assumed to be the major attractive interaction limiting film thickness

in ceramics• The dispersion interaction for an IGF is calculated as follows…

where A121 is the Hamaker constant for a grain boundary• The constant only applies when the particle/crystal spacing is very

small, i.e. the GB is very thin• Dispersion energy diverges at h=0 in this equation, but this is not true

because the finite atomic sepparation must be considered• Film compositions and associated optical properties must be know the

calculate the Hamaker coeff.

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Electrostatic Interactions• Occur when ionic species are involved• Some ions will be preferentially adsorbed onto the crystal face and a

counter ion cloud will form in the film• In IGFs a screened Coulombic interaction results• Electrical interaction is given by…

where κ-1 is the Debye length, and Ke is a function of surface potential or surface charge density

• Can be more complex if the IGF is thinner then the Debye length or if there is more then one ionic species

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Metastable Equilibration• Is more likely in IGFs then in SAFs• Is more likely in ceramics then in metals• Primary min. only exists is the attractive forces are significant

compared to repulsive forces (c)• (b) corresponds to a shallow metastable equilibrium and (a) is the

same shallow metasable equilibrium but with the singularity artifact removed

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Example of Importance of IGFs and SAFs

• Enhanced diffusion in activated sintering has been found to occur in prewetting films, not in wetting films, in the W-Ni system– Activated sintering starts ~400oC below the bulk eutectic temperature– 2nd phase never actually wets the GBs– 2nd phase never even wet the GB triple point until ~50oC below the eutectic temperature

• Phase diagrams must be extended to include IGFs so that they may be more useful in determining final microstructure

From J Luo and J Shi, Young Investigator Program: Nanoscale quasi-liquid grain boundary films in refractory metals, Grant: FA9550-07-1-01525, AFOSR, (2010).

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Occurrence of complexions (layered transitions)

• As T ↓ or dopant activity ↓ IGFs should become thinner as the grain experience attractive forces due to ↑ΔGamorph

• When film thickness is close to the interatomic bond length an oscillatory force occurs due to atom size / steric effects

• Free energy minima will occur when the thickness is an integer number multiple of the bond length

• Complexion V has no discrete size because the thickness has grown to a point where other forces will play a role

From J Luo, Liquid like interface complexion: From activated sintering to grain boundary diagrams, Current Opinion in Solid State and Materials Science 12 (2008) 81–88.