diff --git a/joss.06875/10.21105.joss.06875.crossref.xml b/joss.06875/10.21105.joss.06875.crossref.xml new file mode 100644 index 0000000000..d2b160e6b1 --- /dev/null +++ b/joss.06875/10.21105.joss.06875.crossref.xml @@ -0,0 +1,447 @@ + + + + 20240802081615-86fbeccb639492b8a884f9cecc25eca0e3c9b62c + 20240802081615 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 08 + 2024 + + + 9 + + 100 + + + + Equilipy: a python package for calculating phase +equilibria + + + + Sun Yong + Kwon + https://orcid.org/0000-0002-9212-8823 + + + Eric + Thibodeau + https://orcid.org/0000-0001-9853-2133 + + + Alex + Plotkowski + https://orcid.org/0000-0001-5471-8681 + + + Ying + Yang + https://orcid.org/0000-0001-6480-2254 + + + + 08 + 02 + 2024 + + + 6875 + + + 10.21105/joss.06875 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.13157238 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6875 + + + + 10.21105/joss.06875 + https://joss.theoj.org/papers/10.21105/joss.06875 + + + https://joss.theoj.org/papers/10.21105/joss.06875.pdf + + + + + + Material design and development: From +classical thermodynamics to CALPHAD and ICME approaches + Luo + CALPHAD + 50 + 10.1016/j.calphad.2015.04.002 + 2015 + Luo, A. A. (2015). Material design +and development: From classical thermodynamics to CALPHAD and ICME +approaches. CALPHAD, 50, 6–22. +https://doi.org/10.1016/j.calphad.2015.04.002 + + + Thermo-calc & DICTRA, computational tools +for materials science + Andersson + CALPHAD + 2 + 26 + 10.1016/S0364-5916(02)00037-8 + 2002 + Andersson, J.-O., Helander, T., +Höglund, L., Shi, P., & Sundman, B. (2002). Thermo-calc & +DICTRA, computational tools for materials science. CALPHAD, 26(2), +273–312. +https://doi.org/10.1016/S0364-5916(02)00037-8 + + + Reprint of: FactSage thermochemical software +and databases, 2010–2016 + Bale + CALPHAD + 55 + 10.1016/j.calphad.2016.07.004 + 2016 + Bale, C. W., Bélisle, E., Chartrand, +P., Decterov, S. A., Eriksson, G., Gheribi, A. E., Hack, K., Jung, +I.-H., Kang, Y.-B., Melançon, J., & others. (2016). Reprint of: +FactSage thermochemical software and databases, 2010–2016. CALPHAD, 55, +1–19. +https://doi.org/10.1016/j.calphad.2016.07.004 + + + PANDAT software with PanEngine, PanOptimizer +and PanPrecipitation for multi-component phase diagram calculation and +materials property simulation + Cao + CALPHAD + 2 + 33 + 10.1016/j.calphad.2008.08.004 + 2009 + Cao, W., Chen, S.-L., Zhang, F., Wu, +K., Yang, Y., Chang, Y., Schmid-Fetzer, R., & Oates, W. (2009). +PANDAT software with PanEngine, PanOptimizer and PanPrecipitation for +multi-component phase diagram calculation and materials property +simulation. CALPHAD, 33(2), 328–342. +https://doi.org/10.1016/j.calphad.2008.08.004 + + + The thermochemistry library +thermochimica + Piro + Computational Materials +Science + 67 + 10.1016/j.commatsci.2012.09.011 + 2013 + Piro, M., Simunovic, S., Besmann, T. +M., Lewis, B., & Thompson, W. (2013). The thermochemistry library +thermochimica. Computational Materials Science, 67, 266–272. +https://doi.org/10.1016/j.commatsci.2012.09.011 + + + The computation of chemical equilibrium in +complex systems containing non-ideal solutions + Capitani + Geochimica et Cosmochimica +Acta + 10 + 51 + 10.1016/0016-7037(87)90145-1 + 1987 + Capitani, C. de, & Brown, T. H. +(1987). The computation of chemical equilibrium in complex systems +containing non-ideal solutions. Geochimica Et Cosmochimica Acta, 51(10), +2639–2652. +https://doi.org/10.1016/0016-7037(87)90145-1 + + + Bemerkungen zur +Schichtkristallbildung + Scheil + International Journal of Materials +Research + 3 + 34 + 10.1515/ijmr-1942-340303 + 1942 + Scheil, E. (1942). Bemerkungen zur +Schichtkristallbildung. International Journal of Materials Research, +34(3), 70–72. +https://doi.org/10.1515/ijmr-1942-340303 + + + Using JMatPro to model materials properties +and behavior + Saunders + Jom + 12 + 55 + 10.1007/s11837-003-0013-2 + 2003 + Saunders, N., Guo, U., Li, X., +Miodownik, A., & Schillé, J.-P. (2003). Using JMatPro to model +materials properties and behavior. Jom, 55(12), 60–65. +https://doi.org/10.1007/s11837-003-0013-2 + + + Thermosuite + Cheynet + CALPHAD + 2 + 26 + 10.1016/S0364-5916(02)00033-0 + 2002 + Cheynet, B., Chevalier, P.-Y., & +Fischer, E. (2002). Thermosuite. CALPHAD, 26(2), 167–174. +https://doi.org/10.1016/S0364-5916(02)00033-0 + + + MTDATA-thermodynamic and phase equilibrium +software from the national physical laboratory + Davies + CALPHAD + 2 + 26 + 10.1016/S0364-5916(02)00036-6 + 2002 + Davies, R., Dinsdale, A., Gisby, J., +Robinson, J., Martin, & SM. (2002). MTDATA-thermodynamic and phase +equilibrium software from the national physical laboratory. CALPHAD, +26(2), 229–271. +https://doi.org/10.1016/S0364-5916(02)00036-6 + + + OpenCalphad-a free thermodynamic +software + Sundman + Integrating Materials and Manufacturing +Innovation + 4 + 10.1186/s40192-014-0029-1 + 2015 + Sundman, B., Kattner, U. R., Palumbo, +M., & Fries, S. G. (2015). OpenCalphad-a free thermodynamic +software. Integrating Materials and Manufacturing Innovation, 4, 1–15. +https://doi.org/10.1186/s40192-014-0029-1 + + + Pycalphad: CALPHAD-based computational +thermodynamics in python + Otis + Journal of Open Research +Software + 1 + 5 + 10.5334/jors.140 + 2017 + Otis, R., & Liu, Z.-K. (2017). +Pycalphad: CALPHAD-based computational thermodynamics in python. Journal +of Open Research Software, 5(1), 1–1. +https://doi.org/10.5334/jors.140 + + + An internally consistent thermodynamic +dataset with uncertainties and correlations: 3. Application methods, +worked examples and a computer program + Powell + Journal of Metamorphic +Geology + 2 + 6 + 10.1111/j.1525-1314.1988.tb00415.x + 1988 + Powell, R., & Holland, T. (1988). +An internally consistent thermodynamic dataset with uncertainties and +correlations: 3. Application methods, worked examples and a computer +program. Journal of Metamorphic Geology, 6(2), 173–204. +https://doi.org/10.1111/j.1525-1314.1988.tb00415.x + + + The computation of equilibrium assemblage +diagrams with Theriak/Domino software + Capitani + American mineralogist + 7 + 95 + 10.2138/am.2010.3354 + 2010 + Capitani, C. de, & Petrakakis, K. +(2010). The computation of equilibrium assemblage diagrams with +Theriak/Domino software. American Mineralogist, 95(7), 1006–1016. +https://doi.org/10.2138/am.2010.3354 + + + Computation of phase equilibria by linear +programming: A tool for geodynamic modeling and its application to +subduction zone decarbonation + Connolly + Earth and Planetary Science +Letters + 1-2 + 236 + 10.1016/j.epsl.2005.04.033 + 2005 + Connolly, J. A. (2005). Computation +of phase equilibria by linear programming: A tool for geodynamic +modeling and its application to subduction zone decarbonation. Earth and +Planetary Science Letters, 236(1-2), 524–541. +https://doi.org/10.1016/j.epsl.2005.04.033 + + + GeoPS: An interactive visual computing tool +for thermodynamic modelling of phase equilibria + Xiang + Journal of Metamorphic +Geology + 2 + 40 + 10.1111/jmg.12626 + 2022 + Xiang, H., & Connolly, J. A. +(2022). GeoPS: An interactive visual computing tool for thermodynamic +modelling of phase equilibria. Journal of Metamorphic Geology, 40(2), +243–255. https://doi.org/10.1111/jmg.12626 + + + Thermodynamic database MALT for windows with +gem and CHD + Yokokawa + CALPHAD + 2 + 26 + 10.1016/S0364-5916(02)00032-9 + 2002 + Yokokawa, H., Yamauchi, S., & +Matsumoto, T. (2002). Thermodynamic database MALT for windows with gem +and CHD. CALPHAD, 26(2), 155–166. +https://doi.org/10.1016/S0364-5916(02)00032-9 + + + MAGEMin, an efficient Gibbs energy minimizer: +application to igneous systems + Riel + Geochemistry, Geophysics, +Geosystems + 7 + 23 + 10.1029/2022GC010427 + 2022 + Riel, N., Kaus, B. J., Green, E., +& Berlie, N. (2022). MAGEMin, an efficient Gibbs energy minimizer: +application to igneous systems. Geochemistry, Geophysics, Geosystems, +23(7), e2022GC010427. +https://doi.org/10.1029/2022GC010427 + + + Thermodynamics of mantle minerals-II. Phase +equilibria + Stixrude + Geophysical Journal +International + 3 + 184 + 10.1111/j.1365-246X.2010.04890.x + 2011 + Stixrude, L., & +Lithgow-Bertelloni, C. (2011). Thermodynamics of mantle minerals-II. +Phase equilibria. Geophysical Journal International, 184(3), 1180–1213. +https://doi.org/10.1111/j.1365-246X.2010.04890.x + + + CALPHAD (calculation of phase diagrams): A +comprehensive guide + Saunders + 1998 + Saunders, N., & Miodownik, A. P. +(1998). CALPHAD (calculation of phase diagrams): A comprehensive guide. +Elsevier. + + + An improved and extended internally +consistent thermodynamic dataset for phases of petrological interest, +involving a new equation of state for solids + Holland + Journal of metamorphic +Geology + 3 + 29 + 10.1111/j.1525-1314.2010.00923.x + 2011 + Holland, T., & Powell, R. (2011). +An improved and extended internally consistent thermodynamic dataset for +phases of petrological interest, involving a new equation of state for +solids. Journal of Metamorphic Geology, 29(3), 333–383. +https://doi.org/10.1111/j.1525-1314.2010.00923.x + + + Scheil–Gulliver constituent +diagrams + Pelton + Metallurgical and Materials Transactions +A + 48 + 10.1007/s11661-017-4059-0 + 2017 + Pelton, A. D., Eriksson, G., & +Bale, C. W. (2017). Scheil–Gulliver constituent diagrams. Metallurgical +and Materials Transactions A, 48, 3113–3129. +https://doi.org/10.1007/s11661-017-4059-0 + + + Modeling metamorphic rocks using equilibrium +thermodynamics and internally consistent databases: Past achievements, +problems and perspectives + Lanari + Journal of Petrology + 1 + 60 + 10.1093/petrology/egy105 + 2019 + Lanari, P., & Duesterhoeft, E. +(2019). Modeling metamorphic rocks using equilibrium thermodynamics and +internally consistent databases: Past achievements, problems and +perspectives. Journal of Petrology, 60(1), 19–56. +https://doi.org/10.1093/petrology/egy105 + + + + + + diff --git a/joss.06875/10.21105.joss.06875.pdf b/joss.06875/10.21105.joss.06875.pdf new file mode 100644 index 0000000000..42861afca5 Binary files /dev/null and b/joss.06875/10.21105.joss.06875.pdf differ diff --git a/joss.06875/paper.jats/10.21105.joss.06875.jats b/joss.06875/paper.jats/10.21105.joss.06875.jats new file mode 100644 index 0000000000..c1b5411780 --- /dev/null +++ b/joss.06875/paper.jats/10.21105.joss.06875.jats @@ -0,0 +1,1001 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6875 +10.21105/joss.06875 + +Equilipy: a python package for calculating phase +equilibria + + + +https://orcid.org/0000-0002-9212-8823 + +Kwon +Sun Yong + + +* + + +https://orcid.org/0000-0001-9853-2133 + +Thibodeau +Eric + + + + +https://orcid.org/0000-0001-5471-8681 + +Plotkowski +Alex + + + + +https://orcid.org/0000-0001-6480-2254 + +Yang +Ying + + + + + +Materials Science and Technology Division, Oak Ridge +National Laboratory, Oak Ridge, TN 37831, United States of +America + + + + +Independent Researcher, Canada + + + + +* E-mail: + + +15 +3 +2024 + +9 +100 +6875 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +CALPHAD +Thermodynamics +Gibbs Energy Minimization +Alloy Design +Python + + + + + + Summary +

The CALPHAD (CALculation of PHAse Diagram) approach + (Nigel + Saunders & Miodownik, 1998) provides predictions for + thermodynamically stable phases in multicomponent-multiphase materials + across a wide range of temperatures. Consequently, the CALPHAD + calculations became an essential tool in materials and process design + (Luo, + 2015). Such design tasks frequently require navigating a + high-dimensional space due to multiple components involved in the + system. This increasing complexity demands high-throughput CALPHAD + calculations, especially in the rapidly evolving field of alloy + design.

+

In response to the need, we developed Equilipy an open-source + Python package designed for calculating phase equilibria of + multicomponent-multiphase systems. Equilipy is specifically tailored + for high-throughput CALPHAD calculations, offering parallel + computations across multiple processors and nodes with the given + NPT input conditions namely elemental compositions + (N), pressure (P), and temperature + (T). Equilipy utilizes the program structure and + Gibbs energy functions from the Fortran-based program, Thermochimica + (Piro + et al., 2013), with incorporating a new Gibbs energy + minimization algorithm. This algorithm, originally developed by + Capitani and Brown in 1987 + (Capitani + & Brown, 1987), has been revised and implemented to enhance + the stability and performance of calculations. The Fortran codes are + precompiled and interfaced with Python via + F2PY, ensuring high computation speed. + Benchmark tests shown in [Fig1] + demonstrate that Equilipy’s computation speed is comparable to those + of established commercial software, TC-Python and PanPython. This + result highlights its efficiency and potential applications in various + scientific and industrial fields.

+ +

A parallel benchmark computation on (a) Windows (Intel + Core i7-12700, 2.1 GHz) and (b) Linux (Intel Xeon E5-2650, 2.0 GHz) + for multiple processors: The computation involves 8,096 equilibrium + calculations in a four-component system that has 63 different + phases.

+ + + + + Statement of need +

Commercial thermochemical software packages such as Thermo-Calc + (Andersson + et al., 2002), FactSage + (Bale + et al., 2016), and Pandat + (Cao + et al., 2009) are the standard for phase equilibrium + calculations. However, exploring a broad spectrum of alloy chemistries + is often hindered by the considerable computational time required. + Such computational demands create a bottleneck in effective alloy + design processes. While efforts to leverage high-performance computing + (HPC) have been initiated to expedite computational speed, these + attempts are often limited by licensing constraints such as the number + of processors available for use (e.g., TC-Python permits only up to 32 + logical processors per each license).

+

Given these limitations and the pressing need for more effective + alloy design processes, developing an open-source program tailored for + high-throughput CALPHAD calculations becomes imperative. The + envisioned program should not only eliminate the constraints on + processor usage, but also ensure high calculation stability. + Furthermore, the program should operate on Linux systems and support + parallel computing to be compatible with HPC environments. An + intuitive program architecture is preferred to enhance accessibility + for researchers and practitioners in the field.

+ + + Software overview +

Equilipy is designed to compute thermodynamically stable phases + from a specified NPT ensemble (i.e., + N: elemental composition, P: + pressure, T: temperature). The four-step process for + calculating phase equilibria is illustrated in + [Fig2]. This process closely + mirrors experimental procedures; thus, it is highly intuitive even for + the users primarily experienced in experimental work. Calculating + phase equilibria involves minimizing a set of Gibbs energy functions + for all relevant phases. Therefore, utilizing Equilipy necessitates a + Gibbs energy database developed through the CALPHAD approach.

+ +

The workflow of calculating phase equilibria with + Equilipy.

+ + + + + Features +

Equilipy (0.1.5) incorporates several key features:

+ + +

Phase equilibrium calculation for a single NPT + input condition,

+ + +

Parallel computations for multiple NPT input + conditions,

+ + +

Thermochemical property calculations,

+ + +

Scheil-Gulliver solidification,

+ + +

Metastable phase stability calculations.

+ + +

By default, phase equilibrium calculations consider all available + phases within the given thermochemical database, corresponding to the + input system elements. Consequently, we obtain thermodynamically + stable phases, their respective quantities through equilibrium + calculations, alongside pertinent thermochemical properties such as + Gibbs energy (G), enthalpy (H), + entropy (S), and heat capacity (Cp). + The demonstration of such calculations is given in Phase + equilibria section for multiphase equilibria. Moreover, we + introduce the application of thermodynamic calculations for + solidifications + (Scheil, + 1942) in Scheil-Gulliver solidification. + Metastable phase stability calculations are possible with the phase + selection option, as detailed in the step 2 of + [Fig2]. This option enables the + parsing of custom-selected phases within the relevant phase set for + metastable calculations. Examples showcasing the phase selection + feature in action, both for phase equilibrium calculation and + Scheil-Gulliver solidification, are presented in Metastable + phase equilibria.

+ + Phase equilibria +

[Fig3] presents the phase + equilibrium calculations of the Al-Cu-Mg-Si system. We conducted + Gibbs energy minimization of 63 distinct phases to derive the stable + phase assemblages and their respective quantities at each + calculation point. These calculations were performed using + equilib_batch() feature. The outcomes were + then compared with results from a commercial thermochemical + software, FactSage + (Bale + et al., 2016), employing an identical thermodynamic database + for both tools. [Fig3](a) + illustrates the stable phase quantities in a pseudo-binary section + (isopleth) between Cu99Mg and + Al89MgSi10 alloys at 600 K. Meanwhile, + [Fig3](b) shows the equilibrium + calculations across various temperatures for the A380 alloy, with + 89.260, 1.745, 0.114, and 8.881 mol%, for Al, Cu, Mg, Si, + respectively. The comparative analyses reveal that both programs + consistently predicted the same stable phases and their quantities. + It is worth noting that the equilib_batch() + feature processes each NPT condition independently, + ensuring consistent computation speed and accuracy irrespective of + the sequence or arrangement of the input conditions.

+ +

Multiphase equilibrium calculations in comparison with + a commercial software, FactSage for the Al-Cu-Mg-Si system: (a) + isopleth at 600 K (b) A380 alloy in temperature range from 700 to + 900 K.

+ + +

[Fig4] showcases the + thermochemical properties of the A380 alloy where the temperature + range corresponds to the calculation depicted in + [Fig3](b). These properties + represent the total properties of the system which is composed of + four phases i.e., Liquid, FCC_A1, DIAMOND_A4, and ALCU_THETA. All + three major properties, Gibbs energy, enthalpy, and entropy of the + system calculated by FactSage + (Bale + et al., 2016) are reproduced by Equilipy. This congruent + result highlights Equilipy’s ability to match the calculation + precision of the established commercial software.

+ +

Thermochemical properties of the A380 alloy (one mole) + in the temperature range of 700 and 900 K: (a) Gibbs energy, (b) + Enthalpy, (c) Entropy, and (d) Heat capacity +

+ + + + + Scheil-Gulliver solidification +

Exploring Scheil-Gulliver solidification offers a robust + framework for assessing the performance of phase equilibria + calculations. In Scheil-Gulliver solidification, the liquid phase is + assumed to remain completely mixed, while no diffusion or reaction + is considered between solid phases once they precipitate from the + liquid. This approach effectively represents the characteristics of + rapid and slow diffusion in the liquid and solid phases during + solidification, respectively. A single Scheil-Gulliver cooling + computation necessitates multiple equilibrium calculation + iterations, i.e., one for each temperature step. This approach + serves as a rigorous benchmark to assess the accuracy and stability + of Equilipy in comparison with the well-established commercial + software, FactSage + (Bale + et al., 2016).

+

[Fig5] demonstrates the + progression of microstructural information and phase quantities + during Scheil-Gulliver solidification. The microstructural + information is presented in + [Fig5](a), where each color + represents a unique set of solidifying phases, termed a Scheil + constituent + (Pelton + et al., 2017). Initially, the FCC_A1 solid phase forms at 861 + K and continues to solidify as a primary phase until it reaches a + fraction of 20 mol%. Following this, the next Scheil constituent is + a two-phase eutectic structure comprised of FCC_A1 and DIAMOND_A4 + phases. This eutectic structure persists in solidifying until the + temperature reduces to 793 K. At this juncture of solidification, + over 90 mol% of the liquid has been consumed, followed by the + formation of less than 10 mol% of complex three- and four-phase + eutectic structures. [Fig5](b) + shows the respective quantity of each phase during Scheil-Gulliver + solidification. Various rates of solidifying amount for a phase + (e.g., FCC_A1) highlights that a phase can be involved in multiple + Scheil constituents. As depicted in the figure, the fractions of + Scheil constituents and respective phase quantities align closely + with those calculated by FactSage, demonstrating the reliability and + accuracy of the simulation results.

+ +

Phase stability diagram of the A380 alloy (one mole) + during Scheil-Gulliver solidification: the evolution of (a) Scheil + constituent quantities and (b) amount of each phase +

+ + + + + Metastable phase equilibria +

[Fig6] illustrates the + metastable phase equilibrium calculations for both (a) equilibrium + calculations and (b) Scheil-Gulliver solidification. For each case, + a set of custom-selected phases was applied as outlined in step 2 of + [Fig2]. The equilibrium + calculations shown in [Fig6](a) + use the same input conditions as those in + [Fig3](a), but with the + suppression of the GAMMA, ALCU_ETA, and ALCU_THETA phases. + Similarly, the conditions for Scheil-Gulliver solidification shown + in [Fig5](b) are replicated in + [Fig6](b) without taking into + account the FCC_A1 phase. This approach to calculate metastable + phase equilibria is also available in FactSage. As shown in + [Fig6], the results obtained + from both Equilipy and FactSage are remarkably consistent for the + calculations of metastable phase equilibria.

+ +

Metastable phase equilibria for (a) isopleth at 600 K + with suppressing GAMMA, ALCU_ETA, and ALCU_THETA phases, and (b) + Scheil-Gulliver solidification of the A380 alloy (one mole) with + suppressing FCC_A1 + phase.

+ + + + + + Parallel computing +

Equilipy leverages parallel computing to calculate multiple input + conditions simultaneously through its + equilib_batch() function. Since computations + between input conditions are fully independent, they are executed + through embarrassingly parallel runs. Note that parallel computing is + not applied to compute a single input condition. By default, Equilipy + uses all available processors on a single computing node, though users + have the option to specify a different number of processors. In + multi-node environments, users are required to configure the number of + nodes and processors using a Message Passing Interface (MPI) such as + OpenMPI or MPICH. + Equilipy employs mpi4py for interfacing with + MPI programs.

+ + + Related programs +

Table 1 presents a compilation of both commercial and + non-commercial programs similar to Equilipy, designed for computing + multicomponent-multiphase equilibria. Broadly, these programs split + into two categories: those employing the CALPHAD approach, and those + designed for geological applications. While both approaches share the + same fundamental principle of using Gibbs energies as the building + blocks of thermochemical properties, assessed from experimental data, + their primary distinction lies in their free energy model + descriptions.

+

Table 1 List of commercial and non-commercial programs + for multicomponent-multiphase equilibrium + calculations.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NameTypeReference
‡Software that use the CALPHAD + approach for free energy descriptions . *THERMOCALC calculates + the composition of a given phase assemblage ; however, it does + not ensure if the given assemblage is thermodynamically stable + (Lanari + & Duesterhoeft, 2019).
‡FactSage/ChemAppCommercial(Bale + et al., 2016)
‡Thermo-Calc/TC-PythonCommercial(Andersson + et al., 2002)
‡Pandat/PanPythonCommercial(Cao + et al., 2009)
‡JMatProCommercial(N. + Saunders et al., 2003)
‡ThermoSuiteCommercial(Cheynet + et al., 2002)
‡MALTCommercial(Yokokawa + et al., 2002)
‡MTDataNon-commercial(Davies + et al., 2002)
‡OpenCalphadNon-commercial(Sundman + et al., 2015)
‡PyCalphadNon-commercial(Otis + & Liu, 2017)
‡ThermochimicaNon-commercial(Piro + et al., 2013)
*THERMOCALCNon-commercial(Powell + & Holland, 1988)
Theriak-DominoNon-commercial(Capitani + & Petrakakis, 2010)
Perple_XNon-commercial(Connolly, + 2005)
GeoPSNon-commercial(Xiang + & Connolly, 2022)
MAGEMinNon-commercial(Riel + et al., 2022)
HeFESToNon-commercial(Stixrude + & Lithgow-Bertelloni, 2011)
+ +

For geological applications, the Gibbs energies of non-ideal + solution phases are described by Margules parameters as a function of + composition, pressure, and temperature. In contrast, the CALPHAD + approach focuses on structure-based Gibbs energy descriptions at 1 atm + pressure using solution models such as the compound energy formalism + (CEF) for long-range ordering and the modified quasichemical models + for short-range ordering. These variations in free energy descriptions + are well-documented in the literature for the CALPHAD approach + (Nigel + Saunders & Miodownik, 1998) and for geological applications + (Holland + & Powell, 2011).

+

Note that there is no general consensus on a thermochemical + database format. Each software often has its own format. The database + format used in Equilipy (.dat) is compatible in + FactSage + (Bale + et al., 2016), PyCalphad + (Otis + & Liu, 2017), and Thermochimica + (Piro + et al., 2013).

+ + + Limitation and future plan +

The current version of Equilipy (0.1.5) is specifically designed + for metallic systems and currently lacks the capability to handle + calculations for systems composed of non-elemental species, such as + oxides, sulfides, carbides, nitrides, etc. Integration of these + calculations with non-elemental species is planned for the upcoming + version. Additionally, the existing thermochemical database parser in + Equilipy is compatible only with the older ChemSage data format + .dat, available from FactSage 7.3. It’s + important to note that Equilipy does not support the newer ChemSage + .dat data format introduced in FactSage 8.0 or + later, nor the .tdb data format used by + Thermo-Calc and Pandat. Enhancements to incorporate parsers for these + newer database structures are also planned for the next release of + Equilipy.

+ + + Acknowledgements +

The development of Equilipy was sponsored by the U.S. Department of + Energy (DOE), Office of Energy Efficiency and Renewable Energy (EERE), + Office of Sustainable Transportation, Vehicle Technologies Office + (VTO). This manuscript has been authored by UT-Battelle, LLC under + Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The + publisher, by accepting the article for publication, acknowledges that + the United States Government retains a non-exclusive, paid-up, + irrevocable, world-wide license to publish or reproduce the published + form of this manuscript, or allow others to do so, for United States + Government purposes. The Department of Energy will provide public + access to these results of federally sponsored research in accordance + with the DOE Public Access Plan + (http://energy.gov/downloads/doe-public-access-plan). The authors + extend their gratitude to In-Ho Jung and Jaesung Lee from the + Department of Materials Science and Engineering at Seoul National + University for their valuable discussions on algorithms. Special + thanks are also due to Samuel T. Reeve and Gerald L. Knapp for their + technical support and insightful discussion concerning + programming.

+ + + + + + + + + LuoAlan A + + Material design and development: From classical thermodynamics to CALPHAD and ICME approaches + CALPHAD + Elsevier + 2015 + 50 + 10.1016/j.calphad.2015.04.002 + 6 + 22 + + + + + + AnderssonJan-Olof + HelanderThomas + HöglundLars + ShiPingfang + SundmanBo + + Thermo-calc & DICTRA, computational tools for materials science + CALPHAD + Elsevier + 2002 + 26 + 2 + 10.1016/S0364-5916(02)00037-8 + 273 + 312 + + + + + + BaleChristopher W + BélisleE + ChartrandPatrice + DecterovSergui A + ErikssonG + GheribiAı̈men E + HackK + JungI-H + KangY-B + MelançonJ + others + + Reprint of: FactSage thermochemical software and databases, 2010–2016 + CALPHAD + Elsevier + 2016 + 55 + 10.1016/j.calphad.2016.07.004 + 1 + 19 + + + + + + CaoWeisheng + ChenS-L + ZhangFan + WuK + YangY + ChangYA + Schmid-FetzerR + OatesWA + + PANDAT software with PanEngine, PanOptimizer and PanPrecipitation for multi-component phase diagram calculation and materials property simulation + CALPHAD + Elsevier + 2009 + 33 + 2 + 10.1016/j.calphad.2008.08.004 + 328 + 342 + + + + + + PiroMHA + SimunovicSrdjan + BesmannTheodore M + LewisBJ + ThompsonWT + + The thermochemistry library thermochimica + Computational Materials Science + Elsevier + 2013 + 67 + 10.1016/j.commatsci.2012.09.011 + 266 + 272 + + + + + + CapitaniChristian de + BrownThomas H + + The computation of chemical equilibrium in complex systems containing non-ideal solutions + Geochimica et Cosmochimica Acta + Elsevier + 1987 + 51 + 10 + 10.1016/0016-7037(87)90145-1 + 2639 + 2652 + + + + + + ScheilErich + + Bemerkungen zur Schichtkristallbildung + International Journal of Materials Research + De Gruyter Berlin + 1942 + 34 + 3 + 10.1515/ijmr-1942-340303 + 70 + 72 + + + + + + SaundersN + GuoUKZ + LiX + MiodownikAP + SchilléJ-Ph + + Using JMatPro to model materials properties and behavior + Jom + Springer + 2003 + 55 + 12 + 10.1007/s11837-003-0013-2 + 60 + 65 + + + + + + CheynetBertrand + ChevalierPierre-Yves + FischerEvelyne + + Thermosuite + CALPHAD + Elsevier + 2002 + 26 + 2 + 10.1016/S0364-5916(02)00033-0 + 167 + 174 + + + + + + DaviesRH + DinsdaleAT + GisbyJA + RobinsonJAJ + Martin + SM + + MTDATA-thermodynamic and phase equilibrium software from the national physical laboratory + CALPHAD + Elsevier + 2002 + 26 + 2 + 10.1016/S0364-5916(02)00036-6 + 229 + 271 + + + + + + SundmanBo + KattnerUrsula R + PalumboMauro + FriesSuzana G + + OpenCalphad-a free thermodynamic software + Integrating Materials and Manufacturing Innovation + Springer + 2015 + 4 + 10.1186/s40192-014-0029-1 + 1 + 15 + + + + + + OtisRichard + LiuZi-Kui + + Pycalphad: CALPHAD-based computational thermodynamics in python + Journal of Open Research Software + 2017 + 5 + 1 + 10.5334/jors.140 + 1 + 1 + + + + + + PowellR + HollandTJB + + An internally consistent thermodynamic dataset with uncertainties and correlations: 3. Application methods, worked examples and a computer program + Journal of Metamorphic Geology + 1988 + 6 + 2 + 10.1111/j.1525-1314.1988.tb00415.x + 173 + 204 + + + + + + CapitaniChristian de + PetrakakisKonstantin + + The computation of equilibrium assemblage diagrams with Theriak/Domino software + American mineralogist + Mineralogical Society of America + 2010 + 95 + 7 + 10.2138/am.2010.3354 + 1006 + 1016 + + + + + + ConnollyJames AD + + Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation + Earth and Planetary Science Letters + Elsevier + 2005 + 236 + 1-2 + 10.1016/j.epsl.2005.04.033 + 524 + 541 + + + + + + XiangHua + ConnollyJames AD + + GeoPS: An interactive visual computing tool for thermodynamic modelling of phase equilibria + Journal of Metamorphic Geology + Wiley Online Library + 2022 + 40 + 2 + 10.1111/jmg.12626 + 243 + 255 + + + + + + YokokawaHarumi + YamauchiShigeru + MatsumotoTakafumi + + Thermodynamic database MALT for windows with gem and CHD + CALPHAD + Elsevier + 2002 + 26 + 2 + 10.1016/S0364-5916(02)00032-9 + 155 + 166 + + + + + + RielNicolas + KausBoris JP + GreenECR + BerlieNicolas + + MAGEMin, an efficient Gibbs energy minimizer: application to igneous systems + Geochemistry, Geophysics, Geosystems + Wiley Online Library + 2022 + 23 + 7 + 10.1029/2022GC010427 + e2022GC010427 + + + + + + + StixrudeLars + Lithgow-BertelloniCarolina + + Thermodynamics of mantle minerals-II. Phase equilibria + Geophysical Journal International + Blackwell Publishing Ltd Oxford, UK + 2011 + 184 + 3 + 10.1111/j.1365-246X.2010.04890.x + 1180 + 1213 + + + + + + SaundersNigel + MiodownikA Peter + + CALPHAD (calculation of phase diagrams): A comprehensive guide + Elsevier + 1998 + + + + + + HollandTJB + PowellR + + An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids + Journal of metamorphic Geology + Wiley Online Library + 2011 + 29 + 3 + 10.1111/j.1525-1314.2010.00923.x + 333 + 383 + + + + + + PeltonArthur D + ErikssonGunnar + BaleChristopher W + + Scheil–Gulliver constituent diagrams + Metallurgical and Materials Transactions A + Springer + 2017 + 48 + 10.1007/s11661-017-4059-0 + 3113 + 3129 + + + + + + LanariPierre + DuesterhoeftErik + + Modeling metamorphic rocks using equilibrium thermodynamics and internally consistent databases: Past achievements, problems and perspectives + Journal of Petrology + Oxford University Press + 2019 + 60 + 1 + 10.1093/petrology/egy105 + 19 + 56 + + + + +
diff --git a/joss.06875/paper.jats/Fig1.svg b/joss.06875/paper.jats/Fig1.svg new file mode 100644 index 0000000000..055c7313ac --- /dev/null +++ b/joss.06875/paper.jats/Fig1.svg @@ -0,0 +1,2250 @@ + + + + + + + + 2024-07-29T14:17:37.984006 + image/svg+xml + + + Matplotlib v3.8.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/joss.06875/paper.jats/Fig2.pdf b/joss.06875/paper.jats/Fig2.pdf new file mode 100644 index 0000000000..561e4bf2c5 Binary files /dev/null and b/joss.06875/paper.jats/Fig2.pdf differ diff --git a/joss.06875/paper.jats/Fig3.svg b/joss.06875/paper.jats/Fig3.svg new file mode 100644 index 0000000000..a5fb350dd7 --- /dev/null +++ b/joss.06875/paper.jats/Fig3.svg @@ -0,0 +1,5810 @@ + + + + + + + + 2024-05-03T11:57:03.987298 + image/svg+xml + + + Matplotlib v3.8.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/joss.06875/paper.jats/Fig4.svg b/joss.06875/paper.jats/Fig4.svg new file mode 100644 index 0000000000..9f881e9fbe --- /dev/null +++ b/joss.06875/paper.jats/Fig4.svg @@ -0,0 +1,3934 @@ + + + + + + + + 2024-05-03T13:27:06.307190 + image/svg+xml + + + Matplotlib v3.8.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/joss.06875/paper.jats/Fig5.svg b/joss.06875/paper.jats/Fig5.svg new file mode 100644 index 0000000000..d82bee190d --- /dev/null +++ b/joss.06875/paper.jats/Fig5.svg @@ -0,0 +1,3133 @@ + + + + + + + + 2024-05-03T13:36:37.464513 + image/svg+xml + + + Matplotlib v3.8.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/joss.06875/paper.jats/Fig6.svg b/joss.06875/paper.jats/Fig6.svg new file mode 100644 index 0000000000..ffac7efda8 --- /dev/null +++ b/joss.06875/paper.jats/Fig6.svg @@ -0,0 +1,4803 @@ + + + + + + + + 2024-05-03T12:09:27.623217 + image/svg+xml + + + Matplotlib v3.8.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +