The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science

Kaptay, George

doi:10.1016/j.cis.2018.04.007

Cited by 53 publications

(54 citation statements)

References 237 publications

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“…[113] This question was reviewed recently. [95] In this section, the GB energy will be modeled without size restrictions, i.e., the bulk and average mole fractions will be taken as identical (denoted as x for the average mole fraction of component B). It will be supposed, however, that the mole fraction of component B in the GB will have a different value, denoted as x gb .…”

Section: A Model For the Concentration Dependence Of The Gb Energymentioning

confidence: 99%

“…[20][21][22][23][24][25][26][27][28] That is why the purpose of this paper is to develop a model for thermodynamic stability of such NG alloys. Although there is plenty of previous literature on both the synthesis [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] and on modeling the stabilization of NG alloys ) (see also reviews [89][90][91][92][93] ), the present paper is novel as it puts this question into a wider framework of the nano-Calphad method, [94,95] i.e., into the thermodynamic framework originally developed by Gibbs. [96] All previous models on GB stability apply the simplest Langmuir-McLean model [97,98] (see also Reference 99) for modeling grain boundary (GB) energy.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic Stability of Nano-grained Alloys Against Grain Coarsening and Precipitation of Macroscopic Phases

Kaptay

2019

Metall Mater Trans A

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Thermodynamic conditions are derived here for binary alloys to have their grain boundary (GB) energies negative, ensuring the stability of some nano-grained (NG) alloys. All binary alloys are found to belong to one of the following three types. Type 1 is the unstable NG alloy both against grain coarsening and precipitation of a macro-phase. Type 2 is the partly stable NG alloy, stable against coarsening but not against precipitation. Type 3 is the fully stable NG alloy, both against coarsening and precipitation. Alloys type 1 have negative, or low-positive interaction energies between the components. Alloys type 2 have medium-positive interaction energies, while alloys type 3 have high-positive interaction energies. Equations are derived for critical interaction energies separating alloys type 1 from type 2 and those from type 3, being functions of the molar excess GB energy of the solute, temperature (T) and composition of the alloy. The criterion to form a stable NG alloy is formulated through a new dimensionless number (Ng), defined as the ratio of the interaction energy to the excess molar GB energy of the solute, both taken at zero Kelvin. Systems with Ng number below 0.6 belong to alloy type 1, systems with Ng number between 0.6 and 1 belong to alloy type 2, while systems with Ng number above 1 belong to alloy type 3, at least at T = 0 K. The larger is the Ng number, the higher is the maximum T of stability of the NG alloy. By gradually increasing temperature alloys type 3 convert first into type 2 and further into type 1. The Ng number is used here to evaluate 16 binary tungsten-based (W-B) alloys. At T = 0 K type 3 NG alloys are formed with B = Cu, Ag, Mn, Ce, Y, Sc, Cr; type 2 is formed in the W-Ti system, while type 1 alloys are formed with B = Al, Ni, Co, Fe, Zr, Nb, Mo and Ta. For the WAg system the region of stability of the NG alloys is shown on a calculated phase diagram, indicating also the stable grain size.

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Section: A Model For the Concentration Dependence Of The Gb Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamic Stability of Nano-grained Alloys Against Grain Coarsening and Precipitation of Macroscopic Phases

Kaptay

2019

Metall Mater Trans A

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“…Our method is also extended to multicomponent solid solutions. Our method is equivalent to the Butler equations, without a need to introduce partial interfacial energies.Interfaces and particularly grain boundaries (GB) play an important role in materials science [1][2][3][4]. Therefore modelling equilibrium interface composition (segregation) and equilibrium interfacial energy in binary and multi-component solutions is one of the important tasks of materials science [5-10].An elegant method was introduced by Hillert [11], demonstrated in Fig.1 for a binary A-B solid solution α at a fixed temperature and at a fixed pressure.…”

mentioning

confidence: 99%

“…Interfaces and particularly grain boundaries (GB) play an important role in materials science [1][2][3][4]. Therefore modelling equilibrium interface composition (segregation) and equilibrium interfacial energy in binary and multi-component solutions is one of the important tasks of materials science [5-10].…”

mentioning

confidence: 99%

“…However, despite the same name of the two methods, the two problems are different and should not be confused or treated together. The first problem relates to adsorption / segregation of components from bulk phases to interfaces, while the second problem relates to nano-thermodynamics, extensively discussed by the author recently [3,[29][30][31]. In this paper only the problem of GB segregation, or more generally, the problem of interfacial segregation will be discussed.…”

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A correction to “parallel tangent” method for modelling segregation to grain boundaries and other interfaces for components of different atomic sizes

Kaptay

2019

Scripta Materialia

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Hillert showed an elegant way to obtain the equilibrium composition of interfaces (including grain boundaries) and the equilibrium interfacial energy for binary solutions using his "parallel tangent construction". However, this method is correct only for equal sizes of atoms of the components. A corrected equation is derived here from the two fundamental equations of Gibbs. Our resulting non-parallel tangent construction is less elegant, but more correct compared to the parallel tangent construction of Hillert. Our method is also extended to multicomponent solid solutions. Our method is equivalent to the Butler equations, without a need to introduce partial interfacial energies.Interfaces and particularly grain boundaries (GB) play an important role in materials science [1][2][3][4]. Therefore modelling equilibrium interface composition (segregation) and equilibrium interfacial energy in binary and multi-component solutions is one of the important tasks of materials science [5-10].An elegant method was introduced by Hillert [11], demonstrated in Fig.1 for a binary A-B solid solution α at a fixed temperature and at a fixed pressure. Suppose its integral molar Gibbs energy (denoted as G m,α , J/mol) is known as function of bulk mole fraction of component B (denoted as x B,α , dimensionless) at given temperature and pressure for a macroscopic solution. The chemical potentials of its components can be found by drawing a tangent line to the curve of the integral molar Gibbs energy at the selected composition, as shown in Fig.1. Suppose the integral molar Gibbs energy of the grain boundary (denoted as G m,gb , J/mole) is also known as function of the composition of the interfacial region (denoted as x B,gb , dimensionless) at the same temperature and pressure. Hillert suggests drawing a

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Acoustic‐Pressure‐Assisted Engineering of Aluminum Foams

et al. 2021

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Shaping metals as a foam modulates their physical properties, enabling attractive applications where lightweight, low thermal conductivity, or acoustic isolation are desirable. Adjusting the size of the bubbles in the foams is particularly relevant for targeted applications. Herein, a method with a detailed theoretical understanding of how to tune the size of the bubbles in aluminum melts in situ via acoustic pressure is provided. The description is in full agreement with the high‐rate 3D X‐ray radioscopy of the bubble formation. The study with the intriguing results on the effect of foaming on electrical resistivity, Seebeck coefficient, and thermal conductivity from cryogenic to room temperature is complemented. Compared with bulk materials, the investigated foam shows an enhancement in the thermoelectric figure of merit. These results herald promising application of foaming in thermoelectric materials and devices for conversion of thermal energy.

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The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science

Cited by 53 publications

References 237 publications

Thermodynamic Stability of Nano-grained Alloys Against Grain Coarsening and Precipitation of Macroscopic Phases

Thermodynamic Stability of Nano-grained Alloys Against Grain Coarsening and Precipitation of Macroscopic Phases

A correction to “parallel tangent” method for modelling segregation to grain boundaries and other interfaces for components of different atomic sizes

Acoustic‐Pressure‐Assisted Engineering of Aluminum Foams

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