Applied Thermodynamics: Grain Boundary Segregation

Lejček, Pavel; Liu, Zheng; Hofmann, S.; Sob, M

doi:10.3390/e16031462

Cited by 45 publications

(19 citation statements)

References 31 publications

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“…While this equation has been initially developed for binary metal systems based on Gibbs adsorption isotherm, similar equations have been derived for ternary alloys, with the interaction between elements playing a role in the respective enthalpy of segregations. 16,17 Achieving a zero energy GB state is however limited by the saturation of the GB. According to Eq.…”

Section: Introductionmentioning

confidence: 99%

Direct measurements ofquasi-zero grain boundary energies in ceramics

Nafsin

Castro

2016

J. Mater. Res.

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Nanocrystalline bulk materials (also called nanograined materials) are intrinsically unstable due to the excess grain boundary (GB) free energies. Dopants designed to segregate to boundaries have been proposed to lower excess GB energies, increasing stability against coarsening and enabling nanostructure features to survive high temperature processing and operational environments. It has been theoretically proposed that the GB energy of a material can eventually become zero as a function of dopant concentration, signifying negligible driving force for growth-an infinitely stable nanomaterial. In this work we use ultrasensitive microcalorimetry to experimentally measure the absolute GB energy of gadolinium-doped nanocrystalline zirconia as a function of grain size and show that the energy can indeed reach a quasi-zero energy state (;0.05 J/m 2 ) when a critical GB dopant enrichment is achieved. This thermodynamic condition leads to unprecedented coarsening resistance, but is a temperature dependent function; since increasing temperatures deplete the GB as the dopant dissolves back in the crystalline bulk.

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Section: Introductionmentioning

confidence: 99%

Direct measurements ofquasi-zero grain boundary energies in ceramics

Nafsin

Castro

2016

J. Mater. Res.

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“…The discrepancy may be due to the temperature dependence of the segregation energy (entropy contribution) and magnetism evolution as the Curie temperature is approached. More generally speaking about finite temperature effects, segregation entropy is important to consider for relevant modeling/experiment comparison [18,52]. In our LTE model, we can easily use a free energy for each configuration.…”

Section: Discussion About Current Model Limitationsmentioning

confidence: 99%

Ab initio investigation of phosphorus and hydrogen co-segregation and embrittlement in α-Fe twin boundaries

Schuler

Christien

Ganster

et al. 2019

Applied Surface Science

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We propose a new statistical physics model to study equilibrium solute segregation at grain boundaries and the resulting embrittlement effect. This low-temperature expansion model is general and efficient, and its parameters can be obtained from atomistic calculations. It is possible to take into account multiple species, multiple segregation sites with different segregation free energies, account for configurational entropy, grain radius and site competition between solutes. As an example, the model is then applied to the study of phosphorus and hydrogen co-segregation at Σ3 109.5° 011 {111} twin boundaries in α-Fe, using energetic parameters from density-functional theory calculations. We show that P-H interactions may lead to increased P segregation at grain boundaries and cause additional embrittlement compared to the case where P and H are considered separately. cient statistics over a large number of GBs. Consequently, the study of GB segregation usually resorts to a combination of experimental techniques [7, 8] and results depend on the annealing temperature, bulk chemical composition, chemical environment and GB structure. The task becomes even more complicated when studying cosegregation effects, i.e. the simultaneous segregation of at least two chemical species which occurs all the time in real-life materials. There are several mechanisms at work: solute-GB interaction, solute-solute interaction at the GB and in the bulk, site competition, concentration ratio between solutes and kinetic properties of each solute [9]. For instance in Fe-P-C alloys, it was noted that intergranular P segregation decreases with increasing C content but the reason why this happens is not clear [8,10]. If Cr is added to this alloy it seems that P segregation increases only when C concentration is above a certain level [10].The pioneering work of Wu et al.[6] on Σ3[110](111) GB in α-Fe showed that ab initio methods were able to provide some insight on solute properties at GBs, as the authors were able to explain the strengthening by B additions and the embrittlement by P additions in terms of electronic structure at the GB and at free surfaces. These methods are fast-growing, and computation capabilities have increased a lot such that ab initio studies on GBs

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“…(1)- (3) in [3] clearly gives DG seg 0 in equilibrium, principally at any temperature. It is clear since DG seg considered in [3] is not the characteristic segregation Gibbs energy as the authors claim but the balance of the ''reaction'' describing redistribution of solvent A and solute B, between the grain interior I and the grain boundary, [4][5][6] which can affect the rate of reaching equilibrium or -as the authors in [3] give correctly -the change of the grain boundary energy with changing grain boundary area. The characteristic quantity controlling the extent of the segregation in a particular system is DG ex seg .…”

Section: Introductionmentioning

confidence: 92%