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Abdellah Kharicha - One of the best experts on this subject based on the ideXlab platform.
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modeling diffusion governed solidification of ternary alloys part 2 macroscopic transport phenomena and macrosegregation
Computational Materials Science, 2014Co-Authors: Andreas Ludwig, Abdellah KharichaAbstract:Abstract Part 1 of this two-part investigation presented a multiphase solidification model incorporating the finite diffusion kinetics and ternary phase diagram with the macroscopic transport phenomena (Wu et al., 2013). In Part 2, the importance of proper treatment of the finite diffusion kinetics in the calculation of macrosegregation is addressed. Calculations for a two-dimensional (2D) square casting (50 × 50 mm 2 ) of Fe–0.45 wt.%C–1.06 wt.%Mn considering thermo-solutal convection and crystal sedimentation are performed. The modeling result indicates that the infinite liquid mixing kinetics as assumed by classical models (e.g., the Gulliver–Scheil or Lever Rule), which cannot properly consider the solute enrichment of the interdendritic or inter-granular melt at the early stage of solidification, might lead to an erroneous estimation of the macrosegregation. To confirm this statement, further theoretical and experimental evaluations are desired. The pattern and intensity of the flow and crystal sedimentation are dependent on the crystal morphologies (columnar or equiaxed); hence, the potential error of the calculated macrosegregation caused by the assumed growth kinetics depends on the crystal morphology. Finally, an illustrative simulation of an engineering 2.45-ton steel ingot is performed, and the results are compared with experimental results. This example demonstrates the model applicability for engineering castings regarding both the calculation efficiency and functionality.
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modeling diffusion governed solidification of ternary alloys part 1 coupling solidification kinetics with thermodynamics
Computational Materials Science, 2013Co-Authors: Andreas Ludwig, Abdellah KharichaAbstract:A method incorporating the full diffusion-governed solidification kinetics and the ternary phase diagram into a multiphase volume average solidification model is presented. The motivation to develop such a model is to predict macrosegregation in castings. A key feature of this model, different from most previous ones which usually assume an infinite solute mixing in liquid (e.g. Lever Rule, Gulliver–Scheil), is that diffusions in both liquid and solid phases are considered. It is known that models with assumption of an infinite liquid mixing lead to erroneous estimation of the solidification path at the initial stage. Here solidification of a ternary alloy (Fe–0.45 wt.%C–1.06 wt.%Mn) is examined. As the two chosen alloy elements (C and Mn) have large differences in the solute partition coefficient, liquidus slope and liquid diffusion coefficient, the solidification path shows differently from those predicted by infinite liquid mixing models. The first part of this two-part investigation evaluates the full diffusion-governed kinetics and its influence on solidification path and microsegregation. Applications of the model for the calculation of solidification and macrosegregation are presented in the accompanying paper [Part 2].
Andreas Ludwig - One of the best experts on this subject based on the ideXlab platform.
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modeling diffusion governed solidification of ternary alloys part 2 macroscopic transport phenomena and macrosegregation
Computational Materials Science, 2014Co-Authors: Andreas Ludwig, Abdellah KharichaAbstract:Abstract Part 1 of this two-part investigation presented a multiphase solidification model incorporating the finite diffusion kinetics and ternary phase diagram with the macroscopic transport phenomena (Wu et al., 2013). In Part 2, the importance of proper treatment of the finite diffusion kinetics in the calculation of macrosegregation is addressed. Calculations for a two-dimensional (2D) square casting (50 × 50 mm 2 ) of Fe–0.45 wt.%C–1.06 wt.%Mn considering thermo-solutal convection and crystal sedimentation are performed. The modeling result indicates that the infinite liquid mixing kinetics as assumed by classical models (e.g., the Gulliver–Scheil or Lever Rule), which cannot properly consider the solute enrichment of the interdendritic or inter-granular melt at the early stage of solidification, might lead to an erroneous estimation of the macrosegregation. To confirm this statement, further theoretical and experimental evaluations are desired. The pattern and intensity of the flow and crystal sedimentation are dependent on the crystal morphologies (columnar or equiaxed); hence, the potential error of the calculated macrosegregation caused by the assumed growth kinetics depends on the crystal morphology. Finally, an illustrative simulation of an engineering 2.45-ton steel ingot is performed, and the results are compared with experimental results. This example demonstrates the model applicability for engineering castings regarding both the calculation efficiency and functionality.
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modeling diffusion governed solidification of ternary alloys part 1 coupling solidification kinetics with thermodynamics
Computational Materials Science, 2013Co-Authors: Andreas Ludwig, Abdellah KharichaAbstract:A method incorporating the full diffusion-governed solidification kinetics and the ternary phase diagram into a multiphase volume average solidification model is presented. The motivation to develop such a model is to predict macrosegregation in castings. A key feature of this model, different from most previous ones which usually assume an infinite solute mixing in liquid (e.g. Lever Rule, Gulliver–Scheil), is that diffusions in both liquid and solid phases are considered. It is known that models with assumption of an infinite liquid mixing lead to erroneous estimation of the solidification path at the initial stage. Here solidification of a ternary alloy (Fe–0.45 wt.%C–1.06 wt.%Mn) is examined. As the two chosen alloy elements (C and Mn) have large differences in the solute partition coefficient, liquidus slope and liquid diffusion coefficient, the solidification path shows differently from those predicted by infinite liquid mixing models. The first part of this two-part investigation evaluates the full diffusion-governed kinetics and its influence on solidification path and microsegregation. Applications of the model for the calculation of solidification and macrosegregation are presented in the accompanying paper [Part 2].
L. Eric Cross - One of the best experts on this subject based on the ideXlab platform.
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theoretical model for the morphotropic phase boundary in lead zirconate lead titanate solid solution
Physical Review B, 1993Co-Authors: L. Eric CrossAbstract:A statistical model is proposed to address the problem of two-phase coexistence near the morphotropic phase boundary (MPB) in Pb(Zr 1-x Ti x )O 3 solid-solution series. Functional forms for the molar fractions of tetragonal and rhombohedral phases inside the coexistence region are obtained, which may be used to replace the Lever Rule to describe the phase mixing in a complete binary solid-solution series without solubility gap. The model predicts that the width of this coexistence region is inversely proportional to the volume of each element in the statistical ensemble
Eric L Cross - One of the best experts on this subject based on the ideXlab platform.
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theoretical model for the morphotropic phase boundary in lead zirconate lead titanate solid solution
Physical Review B, 1993Co-Authors: Wenwu Cao, Eric L CrossAbstract:A statistical model is proposed to address the problem of two-phase coexistence near the morphotropic phase boundary (MPB) in Pb(${\mathrm{Zr}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ti}}_{\mathit{x}}$)${\mathrm{O}}_{3}$ solid-solution series. Functional forms for the molar fractions of tetragonal and rhombohedral phases inside the coexistence region are obtained, which may be used to replace the Lever Rule to describe the phase mixing in a complete binary solid-solution series without solubility gap. The model predicts that the width of this coexistence region is inversely proportional to the volume of each element in the statistical ensemble. In addition, the shift of the MPB composition from the composition of equal molar fraction of the two coexisting phases is found to be proportional to the width of the coexistence region. Several existing controversial experimental observations can be reconciled by this model.
Zhonghong Jiang - One of the best experts on this subject based on the ideXlab platform.
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the structure of glass a phase equilibrium diagram approach
Progress in Materials Science, 2014Co-Authors: Zhonghong Jiang, Qinyuan ZhangAbstract:Abstract Glass is considered a vitreous supercooled liquid that is in a thermodynamically metastable state between the molten liquid state and the crystalline state. Different glass structures are influenced by the thermal history of the cooling process. In 1932, Zachariasen established the continuous random network (CRN) paradigm for the structure of glass in which the random structure of glass is similar to that of liquid. Prior to Zachariasen, diffraction patterns observed by Lebedev indicated that glass structures are comprised of microcrystallites approximately 20 A in size. According to the microcrystalline hypothesis, these microcrystallite domins are linked by amorphous interlayers. This debate on the predominant feature of glass structure (i.e. whether it exists in an ordered state) has lasted for more than half a century. Great efforts have been invested to develop a universal model to represent all glass structures. However, the concept of a universal structure model is incompatible with the fact that the vitreous state is in a thermodynamically metastable state because a specific structure can only arise in a thermodynamically stable state. To date, theories proposed on glass structures are based on various models rather than on the variability and diversity of glass structures in thermodynamically metastable states. The American Society for Testing and Materials (ASTM) International defines glass as “an inorganic product of fusion which has cooled to a rigid condition without crystallizing.” Therefore, glass structures lie between a melt state and a glassy state which may have undetectable microcrystalline domains. The gradual transformation from glass to crystal is controlled by local fluctuations in the structural order, the formation of a nucleus, and crystal growth. A fuzzy mathematical method can distinguish between glass and crystal better than a logical criterion based on a quantitative volume limitation. Therefore, the controversy surrounding the aforementioned hypotheses by Zachariasen and Lebedev lies in the estimation of the degree of order or disorder, i.e., whether the structure of glass is more ordered (“microcrystallite” hypothesis) or more disordered (“random network” hypothesis). While whether or not glass is an ordered state has long been a topic of debate, the structure–properties relationships are not much addressed. In recent years, we propose a phase diagram model that effectively explains various glass structures. Based on infrared spectroscopy, Raman and nuclear magnetic resonance (NMR) measurements, as well as the physical properties of relevant compounds in phase diagrams (e.g. density and refractive index), we conclude that glasses and crystalline congruent compounds exhibit similar NMR data and spectral features in a phase diagram. Thus, it is reasonable to consider glass as a product of mixed melts of nearest-neighbor congruent compounds in a phase diagram. Most importantly, the properties of glass can be calculated via the Lever Rule by applying the additive properties that can predict the structural units of glass with mutually miscible or immiscible phases. Based on NMR data, we are capable of predicting glass properties by employing the phase diagram model using data on congruent compounds through the additive properties of several binary and ternary borate systems such as Li2O3–B2O3, Na2O–B2O3, K2O3–B2O3, BaO–B2O3, La2O3–B2O3, Na2O–B2O3–V2O5, Na2O–B2O3–GeO2, Na2O–B2O3–MgO and K2O–B2O3–Al2O3. The authors also calculated the [BO4]/[B2O3] ratios in binary and ternary borate systems. The calculated results confirm the experimental data. Moreover, estimates based on the refractive index and density using the same model, are also well consistent with the experimental data. For some other glass systems where NMR could not be used, e.g., the Na2O–CaO–SiO2 system, the refractive index and density calculated from the nearest congruent compounds match well with the experimental data. Further, this approach can be used to determine the relationship between glass compositions and properties in multi-component glass systems. This review summarizes the recent progress made in understanding glass structure and describes the technological developments driven by this new information. The review is organized as follows: Sections 1–4 introduce the classical approaches to understanding glass structure, outline the fundamental thermodynamic characteristics of glass, discuss the Krogh-Moe’s structural model approach, summarize measurements of glasses using IR, Raman and NMR spectral measurements, and introduce the basics of the phase diagram structural model of glass. Section 5 presents a detailed description of the phase diagram structural model of glass, a universal analytical model from the thermodynamic perspective, the phase diagram, and spectral measurements that elucidate the new structural model of glass and its relevant novel physical and chemical properties. Section 6 discusses the phase diagram structural model of silicate glass and other oxide glass systems, as well as their properties. Finally, Section 7 discusses the universal character of the phase diagram structural model for glass from both the thermodynamic and phase diagram kinetic perspectives. The conclusions of this review are then summarized in Section 8, which include: (1) the vitreous state is in a thermodynamic metastable state, and a fuzzy mathematical method is better to distinguish glass from crystal than a logical criterion of quantitative volume limitation. Neither the “crystalline” hypothesis nor the “random network” hypothesis is a universal structural model for glass. (2) Glasses and crystalline congruent compounds in a phase diagram exhibit similar NMR data and spectral structures. (3) In a phase diagram structural approach, binary glass is considered to be a mixture of the melts of the two nearest congruent compounds in a binary phase diagram. The structures and properties of glass can be predicted and calculated from the properties of the two congruent compounds by applying the Lever Rule. (4) Ternary glass is composed of a mixture of the three nearest congruent compounds in a ternary phase diagram. The structures and properties of the resulting glass can be predicted and calculated from the characteristics of the three congruent compounds. (5) In addition to borate and silicate glasses, the phase diagram structure approach could be applied to chalcogenide, halogenide, and metallic glasses.