Modeling of Gibbs energies of pure elements down to 0 K using segmented regression

Roslyakova, Irina; Sundman, Bo; Dette, Holger; Zhang, Lijun; Steinbach, Ingo

doi:10.1016/j.calphad.2016.09.001

Cited by 40 publications

(16 citation statements)

References 22 publications

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“…Mg system that extends down to 0 K using segmented regression models for the Cu and Mg 13 unary descriptions [5]. The equilibrium Cu-Mg system has four stable solid phases: fcc and hcp solutions, an intermetallic compound, CuMg 2 , and a C15-type Cu 2 Mg Laves phase with considerable solubility.…”

Section: Cu-mg Systemmentioning

confidence: 99%

ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

et al. 2019

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The software package ESPEI has been developed for efficient evaluation of thermodynamic model parameters within the CALPHAD method. ESPEI uses a linear fitting strategy to parameterize Gibbs energy functions of single phases based on their thermochemical data and refine the model parameters using phase equilibrium data through Bayesian optimization within a Markov Chain Monte Carlo machine learning approach. In this paper, the methodologies employed in ESPEI are discussed in detail and demonstrated for the Cu-Mg system down to 0 K using unary descriptions based on segmented regression. The model parameter uncertainties are quantified and propagated to the Gibbs energy functions. a − J J J , where J is the chemical potential of the target hyperplane calculated in step 1.

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Section: Cu-mg Systemmentioning

confidence: 99%

ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

et al. 2019

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“…Polynomial expressions (not including the constant term) are added to the lowtemperature models to capture high-temperature properties [29]. Additionally, we employ a segmented regression model developed by Roslyakova et al [11]. In this four parameter model, two linear segments are smoothly connected by a quadratic bend.…”

Section: Model Selectionmentioning

confidence: 99%

“…Both frequentist [2,3] and Bayesian [4][5][6][7][8][9][10] approaches have been employed to construct models that best represent the data, ensure thermodynamic consistency and provide estimates of parameter and model uncertainties. Furthermore, authors have employed such approaches to build thermodynamic property models for single-component systems [5,11].…”

Section: Introductionmentioning

confidence: 99%

“…In the low temperature regime we utilize the Einstein and Debye models of specific heat to account for quantum effects. At higher temperatures, both polynomial models and the segmented regression model developed by Roslyakova et al [11] are investigated. The resulting property models are compared with assessments performed using the HSC Chemistry software package [18] and the recent assessment by Arblaster [17].…”

Section: Introductionmentioning

confidence: 99%

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Bayesian strategies for uncertainty quantification of the thermodynamic properties of materials

Paulson

Jennings

Stan

2019

International Journal of Engineering Science

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Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution. The goal of thermodynamic models is to capture data from both experimental and computational studies and then make reliable predictions when extrapolating to new regions of parameter space. These predictions will be impacted by artifacts present in real data sets such as outliers, systematics errors and unreliable or missing uncertainty bounds. Such issues increase the probability of the thermodynamic model producing erroneous predictions. We present a Bayesian framework for the selection, calibration and quantification of uncertainty of thermodynamic property models. The modular framework addresses numerous concerns regarding thermodynamic models including thermodynamic consistency, robustness to outliers and systematic errors by the use of hyperparameter weightings and robust Likelihood and Prior distribution choices. Furthermore, the framework's inherent transparency (e.g. our choice of probability functions and associated parameters) enables insights into the complex process of thermodynamic assessment. We introduce these concepts through examples where the true property model is known. In addition, we demonstrate the utility of the framework through the creation of a property model from a large set of experimental specific heat and enthalpy measurements of Hafnium metal from 0 to 4900K.

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“…The Gibbs energy G is the central quantity of such calculations, and an exact description of G in terms of the temperature T and Institute for Applied Thermo-and Fluiddynamics, Mannheim -University of Applied Sciences, Mannheim, Germany the systems composition is the key for a reliable description of material systems and their properties. G and other thermodynamic quantities are related to one another, and the different quantities of interest can be expressed as sets of partial derivatives of G. Expressions for G are usually derived by approximating the temperature-dependent isobaric heat capacity C p based on suitable models (Dinsdale 1991;Chase et al 1995;Chen and Sundman 2001;Roslyakova et al 2016), where the free model parameters are optimized to fit measurement data. G is then calculated by a subsequent integration of the optimized model for C p .…”

Section: Introductionmentioning

confidence: 99%

An artificial neural network model for the unary description of pure substances and its application on the thermodynamic modelling of pure iron

Länge

2020

Soft Comput

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The aim of this work is to introduce a novel approach for the universal description of the thermodynamic functions of pure substances on the basis of artificial neural networks. The proposed approximation method is able to describe the thermodynamic functions (C p (T), S(T), H (T) − H (T ref), G(T)) of the different phases of unary material systems in a wide temperature range (between 0 and 6000 K). Phase transition temperatures and the respective enthalpies of transformation, which are computationally determined by the minimization of the Gibbs free energy, are also approximated. This is achieved by using artificial neural networks as models for the thermodynamic functions of the individual phases and by expressing the thermodynamic quantities in terms of the free network parameters. The resulting expressions are then optimized with machine learning algorithms on the basis of measurement data. A physical basis for the resulting approximation is given by the use of, among others, Planck-Einstein functions as activation function of the neurons of the network. This article provides a description of the method and as an example of a specific application the approximation of the thermodynamic functions of the different phases of pure iron. The article focuses on the problem of the representation of thermodynamic data and their practical application.

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Modeling of Gibbs energies of pure elements down to 0 K using segmented regression

Cited by 40 publications

References 22 publications

ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

Bayesian strategies for uncertainty quantification of the thermodynamic properties of materials

An artificial neural network model for the unary description of pure substances and its application on the thermodynamic modelling of pure iron

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