High-throughput thermodynamic computation and

High-throughput thermodynamic computation and experimental study of solid-state phase transitions in organic multicomponent orientationally disordered phase change materials for thermal energy storage

Renhai Shi*a, Dhanesh Chandra*b, Wen-Ming Chienb, and Jingjing Wangc a.

Department of Materials Science and Engineering, The Ohio State University, 384 Watts Hall, 2041 College Rd N., Columbus, OH 43210 USA. Email: [email protected]

b.

Department of Chemical and Materials Engineering, University of Nevada Reno, 1664 N. Virginia Street, Reno, NV, 89557, USA. Email: [email protected] c.

School of Materials Science and Engineering, Shanghai University, Shanghai, 200072, China.

Graphical abstract Prediction of optimal composition that has maximum energy storage in multi-component system via CALPHAD_based high-throughput calculation with key experimental validation.

High-Throughput Screening (HTS)

Output: type, composition and transitional enthalpy for interested Solid-solid phase transition

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Contents lists available at ScienceDirect

Calphad journal homepage: www.elsevier.com/locate/calphad

High-throughput thermodynamic computation and experimental study of solid-state phase transitions in organic multicomponent orientationally disordered phase change materials for thermal energy storage

T

Renhai Shia, , Dhanesh Chandrab, , Wen-Ming Chienb, Jingjing Wangc ⁎

⁎

a

Department of Materials Science and Engineering, The Ohio State University, 384 W Hall, 2041 College Rd N, Columbus, OH 43210 USA Department of Chemical and Materials Engineering, University of Nevada Reno, 1664 N. Virginia Street, Reno, NV 89557, USA c School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China b

A RT ICLE INFO

ABSTRACT

Keywords: High-throughput calculation CALPHAD Thermal energy storage Solid-state phase change materials

Understanding the behavior of solid-solid phase transformation in phase change materials is crucial to design advanced thermal energy storage materials. It is however challenging to study the complex solid-solid phase transition and predict the optimal composition with reliable performances (such as high energy storage at invariant phase transition temperature) in multi-component systems based on traditional empirical rules. Therefore, the high-throughput computational framework by coupling thermodynamic calculation via CALPHAD (CALculation of PHAse Diagrams) methodology with key experimental validation is firstly proposed for ternary Pentaglycerine-Tris-(hydroxymethyl)-aminomethane-2-amino-2-methyl-1,3-propanediol (PG-TRISAMPL) system. A self-consistent thermodynamic database of PG-TRIS-AMPL ternary system has been firstly assessed and validated by experimental measurements from in-situ X-Ray-Diffraction (XRD) and Differential Scanning Calorimetry (DSC). Using this thermodynamic database via CALPHAD method, the high-throughput calculation has been performed to seek the optimal composition in PG-TRIS-AMPL ternary system. It is found that two optimal ternary compositions in PG-TRIS-AMPL ternary system are designed as PG0.33TRIS0.07AMPL0.60 (ΔHmax = 137.5 kJ/kg) during the 1st invariant reaction αAMPL-rich+βPG-rich→δTRIS-rich+γAMPL-rich at 326.5 K (53.35 °C) and PG0.58TRIS0.069AMPL0.351 (ΔHmax = 52.44 kJ/kg) during the 2nd invariant reaction γAMPLrich+βPG-rich→δTRIS-rich+γ’PG-rich at 338.4 K (65.25 °C), respectively. This finding shows the good balance between high latent heat storage and low invariant phase transition temperature at mid-temperature (20–100 °C) application. Also, the present high-throughput computation approach can be extended into other multicomponent systems for various temperature range.

1. Introduction High consumption of energy derived from fossil fuels and natural gas is increasing the carbon footprint, and in addition depleting the available energy sources. This is a significant challenge to scientists and engineers to find new and alternative energy sources or conserve energy by using energy storing materials. In many areas of the world, clean solar energy is one of the most carbon free sources of energy. In order to efficiently conserve solar energy during the day heat, one may use thermal energy storage devices so that excess solar energy can be collected and stored during the day and may be utilized at the night. Phase change materials used as thermal energy storage devices can store heat from solar energy and other temporary sources, and release heat when needed. In general, conventional solid-liquid phase change materials

⁎

(SLPCMs) [1–6] as one of thermal energy storage materials suffer from severe supercooling, corrosion of containers, and chemical instability. The “solid-solid phase change materials” (SSPCMs) [7] are considered as potential candidates for thermal energy storage (TES). Organic (globular) molecular crystals that undergo orientationally disordered crystallographic phase changes, and reversibly absorb or release large amount of latent heat are the focus of this study. It should be noted that latent heat change and phase transition temperature in phase change materials are significant factors for selection of phase change materials in practical applications. Also, the thermal reproducibility is one of the major concerns in thermal energy storage application when phase change materials are cycled. The results of thermal recyclability of these materials used in present work are not a part of this study, although it is important for practical applications. In this work, we

Corresponding authors. E-mail addresses: [email protected] (R. Shi), [email protected] (D. Chandra).

https://doi.org/10.1016/j.calphad.2018.11.005 Received 5 September 2018; Received in revised form 28 October 2018; Accepted 14 November 2018 0364-5916/ © 2018 Elsevier Ltd. All rights reserved.

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Fig. 1. The molecular structures of PG, TRIS, and AMPL studied in present work. Table 1 List of symbols that denote phases in ternary system. Symbol

Phase

Liquid or L α β δ γ γ' γ_II

Liquid Low temperature phase of AMPL-Monoclinic Low temperature phase of PG-Tetragonal Low temperature phase of TRIS-Orthorhombic High temperature phase of AMPL-BCC_A2 High temperature phase of PG-FCC_A1 High Temperature phase of TRIS-BCC_A2

materials, the low temperature phase is either van der Wall bonded layers or chains with intermolecular O–H…O or O–H…N bonds within the layers or chains. When heated to certain temperature these bonds break during a first ordered solid-solid phase transition [11–13] and transform to an orientationally disordered cubic phase. There are only a few pure organic compounds of this type that are commercially available with invariant phase transition temperature, so there is need for binary or ternary systems of these compounds to achieve flexible phase transition temperatures at which the optimal heat is stored. Recently, organic SSPCMs binary systems [14–36] have been explored via CALPHAD phase diagram calculations and experimental methodologies. However, the mechanism of solid-state phase transition with the optimal latent heat storage at invariant phase transition temperature is not yet understood in multi-component systems. Compared with traditional “trial and error” method to design the thermal energy storage materials, there is also urging need to propose the novel methodology with time- and cost-saving to discover the promising materials with optimal thermal energy storage at interested phase transition temperature in multi-component systems. In this work, we firstly proposed a high-throughput computational approach (HTC) via coupling CALPHAD thermodynamic calculation method with key experimental validation. The HTC method enables us to study the mechanism of solid-solid phase transition and predict critical composition with optimal latent heat storage at invariant phase transition temperature in SSPCMs. Via this HTC approach, we also firstly studied ternary system Pentaglycerine [37,38] [PG: (CH3)C(CH2OH)3], Tris(hydroxymethyl) amino-methane [39,40] [TRIS: (NH2)C(CH2OH)3], and 2-amino-2-methyl-1,3-propanediol [41–43] [AMPL:(NH2)(CH3)C(CH2OH)2] with single molecular structures shown in Fig. 1. Finally, there are two types of solid-solid phase transitions (α+β→δ+γ and γ+β→δ+γ’) with invariant phase transition temperatures at 326.5 K (53.35 °C) and 338.4 K (65.25 °C), respectively, in PG-TRIS-AMPL ternary system. There are also two optimal ternary compositions, which are PG0.33TRIS0.07AMPL0.60 (ΔHmax = 137.5 kJ/kg) during α +β→δ+γ solid-solid phase transition at 326.5 K and PG0.58TRIS0.069AMPL0.351 (ΔHmax = 52.44 kJ/kg) during γ+β→δ+γ’ solid-solid phase transition at 338.4 K, respectively. It shows a good balance between high latent heat change and low phase transition temperature compared with most existing solid-solid phase change materials [32,44–66] in Fig. 2. The proposed computational

Fig. 2. Latent heat and invariant phase transition temperature for solid-solid phase change materials; the detail for each compound could be referred to the references [32,44–66] superimposed with each symbol.

Fig. 3. The Gibbs triangle showing PG-line (U-V), TRIS-line (W-X), AMPL-line (Y-Z), Line (M-N), Line (O-P), number of samples (S1-S12) made for XRD and DSC experiments.

present a special class of energetic organic SSPCMs with high entropy of solid-solid, and low entropy of solid-liquid phase changes. These are referred to as “Plastic Crystals” in which a group of bonds within molecules rotate around on or several axes [8]. In general, many of the thermal energy materials store latent heat of fusion [9,10], but Timmermans [11] showed that these “Plastic Crystals” have very small enthalpy of fusion and high enthalpy of solid-solid latent heat. In these 67

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Table 2 Crystal structure and thermal properties of PG, TRIS, and AMPL (values in bold used for calculations). Compound

Low Temp. phases

TTR (K)

∆HTR (kJ/mol)

∆STR (J/mol*K)

High Temp. phases

TF (K)

∆HF (kJ/mol)

∆SF (J/mol*K)

Refer.

PG

Tetragonal

Orthorhombic

AMPL

Monoclinic

19.06–22.7 21.5 20.94 19.94 32.7 32.9 34.0 ± 1.7 34.5 23.3 23.6 23.8 24.9

60 ± 5 60 60 60 80 80 80 80 70 70 70 70

FCC

TRIS

356.6 ± 1.0 351.3 356.7 357.5 408 407.3 406.8 ± 1.0 407.2 353 353 352.9 353.4

473.7 ± 1.0 497 474.4 474.1 445 446 442.7 ± 1.0 445.4 385 389 383.5 384.7

4.63–4.84 5.1 4.7 4.7 3.3 3.0 3.7 ± 0.2 3.4 3.0 3.3 2.7 3.0

10 ± 0.2 10 10 10 8 7 8 8 8 8 7 8

[69] [13] [67] [42] [68] [13] [25] [42] [68] [19] [73] [42]

BCC

BCC

framework as time- and cost-saving approach can be extended for other multi-component systems and significantly accelerate the discovery and design of SSPCMs in thermal energy storage application.

capillary. Temperature was maintained by using a Watlow temperature controller with a feedback to the hot air blower. A position sensitive detector, which is part of the PANalytical diffractometer, was used to capture the diffraction angles and intensities of the Bragg peaks. The diffraction scans were made using CuKα radiation, and the analyses were performed using MDI Jade computer programs to determine phase transformations and crystal structures.

2. Materials and methods 2.1. Solid-solid phase change materials (SSPCMs) Polyalcohol PG (0.99), amine TRIS (0.999) and AMPL (0.999) are obtained from the Aldrich Corporation. All compositions are reported in mole fraction in this paper, otherwise it will be stated. The powders of pure components are mixed and grounded to obtain ternary mixture samples at room temperature for different compositions. These mixtures are melted in loosely capped Pyrex test tubes and then a strain induced transformation method after solidification of mixtures is used to ascertain presence of equilibrium phases. This method involves placing the melted and then solidified ternary mixtures in a freezer (~253 K) for approximately 12 h, after which the solidified masses are subjected to high strain by pressing the powders in a small press with a piston to obtain equilibrium phases. We prepared several different samples strategically along the PG-line, TRIS-line, and AMPL-line shown in Fig. 3.

2.4. Computational method In this study, the fundamental understanding of complex solid-state phase transformation can be obtained via phase diagram methodology in multi-component systems, in which thermodynamic database of multi-component systems is needed to construct and provide the accurate description of phase equilibria as well as the corresponding transitional enthalpy on this purpose. Thus, based on the accurate thermodynamic database, it is capable of carrying out the highthroughput calculation via phase diagram methodology for the study of solid-state phase transition and prediction of corresponding transitional enthalpy in PG-TRIS-AMPL ternary system. 2.4.1. Modelling of thermodynamic database The thermodynamic database of PG-TRIS-AMPL ternary system is consisted of Gibbs energy function (shown in Eq. (1)) of each phase (ϕ). In PG-TRIS-AMPL ternary system, there are liquid, three low temperature solid solution phases, and three high temperature solid solution phases. No ternary compound or intermetallic is observed from available experimental investigation. Table 1 lists symbols for various solution phases used in this paper. The Gibbs energies of liquid and solid solution phases have been described by using regular and sub-regular solution models (More detail could be referred to our previous work [32–34,65]). A general expression for the solution phase ϕ (ϕ = α, β, δ, γ, γ’, γ_II, and L) is represented as follows (units of Gibbs energy in J/ mol is used throughout this work, where a “mol” is a mole of formula unit):

2.2. Differential scanning calorimetry (DSC) analysis A TA DSC Q100 Differential Scanning Calorimeter system is used for thermal analyses. Small amounts (~3 mg) of these powders of PG-TRISAMPL ternary samples are used for the DSC experiments; samples are weighed and sealed in aluminium hermetically in the sample pans with inverted lids to provide good thermal conductivity between the sample and the pan. The samples are heated and cooled at 5 °C/min scan rate. The instrument records the DSC signal and the data is analysed using TA's Universal Analysis 2000 program to obtain the onset temperatures and the enthalpies (ΔH) of the transitions. The calorimeter is calibrated in three steps: (1) balance calibration, (2) T-zero calibration with sapphire crystal, and (3) cell constant and temperature calibration. In Tzero calibration with sapphire crystal, two reference samples are used; a red sapphire was set on the reference holder, and a clear sapphire was set on the sample holder. For temperature calibration, Indium is used as a standard.

G = xPG °GPG + xTRIS °GTRIS + xAMPL °GAMPL + RT [xPG ln(xPG ) + xTRIS ln(xTRIS ) + xAMPLln(xAMPL)] + G EX,

(1)

where XPG, XTRIS, and XAMPL is the mole fraction of PG, TRIS, and AMPL, respectively, and R is equal to 8.314 J/(mol*K). °GPG , °GTRIS , and °GAMPL are the Gibbs energies of pure components PG, TRIS, and AMPL in phase ϕ. These pure organic materials (PG, TRIS, and AMPL) undergo the solid-solid phase transformation from the ordered low temperature layered or chained structures (tetragonal, orthorhombic, and monoclinic) to the high temperature orientationally disordered crystal structures (FCC: Face-Centered Cubic and BCC: Body-Centered Cubic). The details [65–68] about thermodynamic properties and crystallographic structures for these three pure compounds are summarized in Table 2; the contribution of heat capacity on Gibbs energy of pure PG,

2.3. X-ray diffraction (XRD) analyses The structural changes upon heating of the equilibrium phases are reported using in-situ x-ray diffraction studies on the PG-TRIS-AMPL samples by using PANalytical X′Pert PRO diffractometer. Powder samples of ternary mixtures were prepared by adding an internal standard silicon powder. X-ray diffractometer heating system was modified to accept sapphire capillaries as sample holders. This homemade device uses a hot air blowing system to heat the samples in the 68

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Table 3 Summary of thermodynamic parameters of solution phases in the PG-TIRS-AMPL ternary system. Phase

Parameters

Body Centered Tetragonal (BCT)

Tetragonal °LTRIS , PG = +2370.25

Orthorhombic

Temperature range (K) 0–800 K

24.04T

Tetragonal SER °GTRIS = GHTRIS +10, 608.94 (metastable) Tetragonal °LAMPL, PG = +7043.611 1.173T 1 Tetragonal LAMPL,PG = +2062.326 Tetragonal SER °GAMPL = GH AMPL + 497.06 (metastable) Orthorhombic °LTRIS , PG = + 489.63 + 16.776T Orthorhombic SER °GPG = GHPG + 4948.8 (metastable) Orthorhombic °LAMPL , TRIS = + 1552.99 + 17.28T 1 Orthorhombic

LAMPL,TRIS = + 1525.84

2

Monoclinic

Orthorhombic LAMPL , TRIS =

4510.85

Orthorhombic SER °GAMPL = GHAMPL + 460 (metastable) Monoclinic °LAMPL , PG = 1

1496.68 + 6.63T

Monoclinic LAMPL , PG = 2395.3

Monoclinic SER °GPG = GHPG + 4389.59 (metastable)

Monoclinic °LAMPL , TRIS = 636.78 + 22.05T 1

AMPD-II FCC_A1

Monoclinic LAMPL , TRIS = +115.61

Monoclinic SER °GTRIS = GHTRIS + 809 (metastable) AMPD °GPG

II

SER = GHPG +10, 788 (metastable)

AMPD °GTRIS

II

SER = GHTRIS + 8850 (metastable)

FCC_A1 °LTRIS , PG = +6113.87

22.27T

1

FCC_A1 LTRIS , PG = + 4898.21

20.59T

2

FCC_A1 LTRIS , PG =

2096.48

FCC_A1 BCC_A2 °GTRIS = GHTRIS + 1198.49 (metastable)

FCC_A1 °LAMPL , PG =

12, 639.514 + 30.876T

1 FCC_A1

2519.161 + 3.314T

LAMPL,PG =

FCC_A1 BCC_A2 °GAMPL = GHAMPL + 1151.94 (metastable)

BCC_A2

FCC_A1 °LPG , TRIS , AMPL = 6800 + 25.5T BCC_A2 °LPG , TRIS = + 4457.79

12.48T

1 BCC_A2

LPG, TRIS = + 12, 614.55

2 BCC_A2

LPG, TRIS =

32.66T

648.59

BCC_A2 FCC_A1 °GPG = GHPG + 90.505 (metastable) BCC_A2 °LPG , AMPL =

10, 312.341 + 30.157T

1 BCC_A2

11, 199.258 + 24.066T

LPG, AMPL =

BCC_A2 °LTRIS , AMPL = +5853.25

9.43T

1

BCC_A2 LTRIS , AMPL =

844.46 + 3.13T

2

BCC_A2 LTRIS , AMPL =

3180

4.31T

BCC_A2 °LPG , TRIS , AMPL = 6500 + 9.5T 2 BCC_A2

Liquid

LPG, TRIS , AMPL = 6500 + 23.3T

Liquid °LPG , TRIS = 39, 084.64 1 Liquid

LPG, TRIS =

2013.72

95.98T

3.6T

Liquid °LAMPL , PG = 1850.971 1 Liquid

1487.397

2 Liquid

2.5T

LAMPL,PG =

LAMPL,PG =

Liquid °LAMPL , TRIS = + 1841.32 1 Liquid

LAMPL,TRIS = +811.31

2 Liquid

LAMPL,TRIS =

3678.32

Liquid °LPG , TRIS , AMPL = 8300

1.87T 36.5T

2 Liquid

LPG, TRIS , AMPL = 15, 223

TRIS, and AMPL is also taken from our previous study [70–72]. G EX , represents the excess Gibbs energy of the phase ϕ, which can be described using the Redlich-Kister-Muggianu formalism:

G EX , = xPG xTRIS LPG, TRIS + xPG xAMPL LPG, AMPL + xAMPL xTRIS LAMPL, TRIS + xPG xTRIS xAMPL LPG, TRIS, AMPL

(2)

where the Li, j and Li, j, k are binary and ternary interaction parameters which show the difference between the idea mixture and non-idea 69

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Fig. 4. (a) Reassessed AMPL-TRIS binary phase diagram in this work from 280 K to 500 K, superimposed with experimental data [66,76] and (b) calculated AMPLTRIS binary system from 0 K to 800 K showing no metastable phases present.

Fig. 5. (a). Isothermal section of PG-TRIS-AMPL ternary at 298 K superimposed experimental data points from XRD in this study, (b) XRD pattern for S5 sample at 298 K, and (c) XRD pattern for S12 at 298 K (points are from Fig. 3).

mixture of solution phase. In this study, binary interaction parameters for sub-binary PG-TRIS and PG-AMPL systems have been assessed in our previous work [65,73] and adopted into PG-TRIS-AMPL ternary system. However, the binary interaction parameters for sub-binary AMPL-TRIS system from Mekala et al. [66] is not adopted and needs to be reassessed in this work by considering the reasonable Gibbs energy [65,74,75] of pure AMPL and TRIS. These binary and ternary interaction parameters are optimized by minimizing the sum of the square of the differences between calculated and measured values via PARROT module of Thermo-Calc software with the following form of a power series:

mn

Li, j =

Li, j (x i

x j )n

(3)

n= 0

Li, j, k = x i n

0

1

2

Li, j, k + x j Li, j, k + xk Li, j, k

Li, j,(k ) = a + b*T

(4) (5)

where a and b are excess Gibbs energy parameters used in this study, n is the continuous integer. 2.4.2. High-throughput computation concept In order to seek the solid-solid phase transition with invariant phase transition temperature in PG-TRIS-AMPL ternary system, the criteria 70

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Fig. 6. (a). Isothermal section of PG-TRIS-AMPL phase diagram at 373 K using ternary interaction parameters; (b) isothermal section at 373 K without ternary interaction parameters; (c)-(g) XRD patterns taken at compositions of S1, S5, S2, S12, and S9 at 373k. More XRD results for other samples are shown in Appendix (Table S-1).

need to be established for high-throughput screening. The solid-solid phase transition with invariant phase transition temperature can be considered as an invariant reaction in which the reaction temperature will not be changed. In this work, Gibbs phase rule is used as criteria to seek invariant reaction:

F=C

P+ 2;

3. Results and discussion 3.1. Assessment of three sub-binary systems (PG-TRIS, PG-AMPL, and TRIS-AMPL) with experimental validation The binary thermodynamic databases of PG-TRIS and PG-AMPL binary systems from our previous work [65] are adopted with minor adjustment to calculate and reproduce the experimental phase boundaries. The optimized consolidated interaction parameters are listed in Table 3. In this work, binary interaction parameters for various phases in AMPL-TRIS binary system are reassessed and the calculated phase diagram in the range 280–500 K shows good agreement with experimental XRD and DSC data as shown in Fig. 4(a). For this AMPL-TRIS binary system, the high temperature phases often have been calculated incorrectly by using thermodynamic database in which the improper heat capacity equations lead to metastable phases, for example liquid phases appearing near 0 K. The non-linear equations of heat capacity have been introduced by Witusiewicz et al. [75] to solve this metastable phase issue, more details are discussed in our previous work [65,74]. Thus, it is important to check phase stabilities in a wide range of temperature; a calculated phase diagram in the range of 0–800 K shown in Fig. 4(b) does not exhibit presence of any metastable phases. Similar, optimized TRIS-PG and AMPL-PG phase diagrams are shown in Appendix (Fig. S-1 & S-2).

(6)

where F is the number of independent intensive variable; C is the number of components; and P is the number of phases. In the closed PGTRIS-AMPL ternary system at constant pressure, the degree of freedom (F) is also expressed as:

F=C

P+ 1;

(7)

In closed PG-TRIS-AMPL ternary system at constant pressure, the invariant reaction (F=0) has P = 4. Thus, the solid-solid phase transition related to four phase equilibria must be considered as an invariant reaction in PG-TRIS-AMPL ternary system. Using POLY module in Thermo-Calc software with reliable thermodynamic database, the initial condition satisfying F= 0 will be firstly set up to seek four phase equilibria. Then, the high-throughput screening, based on the initial condition, can be performed in POLY module via stepping composition for PG-TRIS-AMPL ternary system. Finally, the type, compositional region, and phase transition temperature of solid-solid phase transition can been predicted, the corresponding enthalpy change will be calculated as difference of enthalpy at initial and end states of solid-solid phase transition; therefore, the optimal composition with maximum transitional enthalpy will be determined. For brevity, more detail could be referred in Appendix (High-throughput computation detail section).

3.2. Assessment of ternary system PG-TRIS-AMPL with experimental validation Ternary thermodynamic database has initially been constructed by 71

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Fig. 7. (a) Optimized isopleth across the PG-line (U-V line in ternary inset) in PG-TRIS-AMPL system; (b–h) XRD patterns for some of these samples taken at different temperatures (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.).

directly extrapolating thermodynamic database from three sub-binary systems without considering the influence of ternary interaction parameters. The first ternary isothermal section is calculated at 298 K shown in Fig. 5(a). Three single solid solution phases (αAMPL-rich, βPG-rich, and δTRISrich), three two-phase regions (αAMPL-rich+βPG-rich, αAMPL-rich+δTRIS-rich, and βPG-rich+δTRIS-rich), and one three-phase region (αAMPL-rich+βPGrich+δTRIS-rich) have been predicted and agree with the present XRD results in Fig. 5(b)-(c). Thus, the influence of ternary interaction parameters of low temperature solid solution phases (αAMPL-rich, βPG-rich, and δTRIS-rich) on the phase regions only including low temperature solid solution phases can be ignored in this case. In order to study the influence of ternary interaction parameters of high temperature solid solution phases on the phase regions including high temperature solid solution phases, the ternary isothermal section at 373 K has been calculated with considering ternary interaction parameters of high temperature solid solution phases shown in Fig. 6(a) and without considering ternary interaction parameters of high temperature solid solution phases in Fig. 6(b). The addition of ternary interaction parameters changes the phase boundary positions and the new phase boundaries with ternary interaction parameters can match very well with the present XRD patterns in Fig. 6(c–g). For example, the calculated isothermal phase diagram without considering ternary interaction parameters in Fig. 6(b) shows that the sample S12 has two equilibrium phases (δTRIS-rich+γ′PG-rich) at 373 K, but the XRD result for S12 in Fig. 6(f) shows that S12 should have three equilibrium phases (δTRISrich+γ′PG-rich+γAMPL-rich) at 373 K. By considering ternary interaction parameters, the optimized isothermal phase diagram in Fig. 6(a) shows that the calculation can match the XRD results. In this isothermal section at 373 K, there are three single phases (γAMPL-rich, γ′PG-rich, and δTRIS-rich), three two-phase regions (δTRIS-rich+γAMPL-rich, δTRIS-rich+γ′PG-rich, and γAMPL-rich+γ′PG-rich), and one three-phase region (γAMPL-rich+γ′PGrich+δTRIS-rich). In this work, we used the PARROT program to assess ternary interaction parameters in solid solution γ′PG-rich and γAMPL-rich phases based on our in-situ X-ray data between 298 K and 383 K and ternary interaction parameters in liquid phase based on DSC data summarized in Appendix (Table S-1). In order to further verify the availability and accuracy of this ternary thermodynamic database including ternary

interaction parameters, different pseudo binary isopleth along PG-line, TRIS-line, and AMPL-line (shown in Fig. 3) have been calculated and have a good agreement with in-situ XRD and DSC experimental results. Fig. 7(a) shows the isopleth along PG-line. Some representative in-situ XRD patterns are shown in Fig. 7(b–h); others are summarized in Appendix (Table S-1). In this isopleth along PG-line in Fig. 7(a), there are two invariant reactions (shown as two red tectic lines) at 326.5 K and 338.4 K. At 1st invariant reaction of 326.5 K, this invariant reaction behaves like “eutectoid” reaction. The “hypoeutectoid” reaction involves with four-phase equilibrium for solid-solid phase transition (αAMPL-rich+βPG-rich+δTRIS-rich→γAMPLrich+βPG-rich+δTRIS-rich) and the “hypereutectoid” reaction shows fourphase equilibrium (αAMPL-rich+βPG-rich+δTRIS-rich→γAMPL-rich+αAMPL-rich+ δTRIS-rich); the “eutectoid” point ( called as critical point thereafter) shows the invariant reaction with αAMPL-rich+βPG-rich+δTRIS-rich→γAMPLrich+δTRIS-rich. At this critical point, the low temperature ordered phases (αAMPL-rich and βPG-rich) completely transfer into high temperature disordered phase γAMPL-rich that may introduce the maximum energy absorption. At 2nd invariant reaction of 338.4 K, the “eutectoid” reaction is also observed. The “hypoeutectoid” reaction shows the solid-solid phase transition with γAMPL-rich+βPG-rich+δTRIS-rich→γ′PG-rich+βPG-rich+δTRIS-rich. The “hypereutectoid” reaction presents the four-phase equilibrium with γAMPL-rich+βPG-rich+δTRIS-rich→γ′PG-rich+γAMPL-rich+δTRIS-rich; At this critical point, low temperature ordered βPG-rich phase and high temperature disordered γAMPL-rich phase have been completely dissolved via phase transition γAMPL-rich+βPG-rich+δTRIS-rich→γ′PG-rich+δTRIS-rich which may contribute the formation of high temperature disordered γ′PG-rich phase with more energy storage. The similar two invariant reactions at 326.5 K and 338.4 K are also observed in isopleth along TRIS-line and AMPL-line shown in Appendix (Fig. S-3 and S-4) for brevity. 3.3. High-throughput screening of invariant reaction and the corresponding transitional enthalpy in ternary PG-TRIS-AMPL The interested solid-solid phase transition at invariant phase transition temperature can be considered as the invariant reaction with four-phase equilibrium, it has been found and shown as red tectic line 72

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Fig. 8. (a). Transitional enthalpy projection of 1st invariant reaction (αAMPL-rich+βPG-rich→δTRIS-rich+γAMPL-rich) at 326.5 K in PG-TRIS-AMPL ternary system superimposed with data points from DSC; (b) DSC pattern for sample S4 (hatched region 4–1 is the transitional enthalpy for first invariant reaction); (c)–(e) the corresponding change of phase fraction along compositional line A-B, C-Q1, and Q1-D from Fig. 8(a), respectively.

in pseudo-binary phase diagrams along PG-line in Fig. 7(a) and TRISline, AMPL-line in Appendix (Fig. S-3 and S-4). Based on Gibbs phase rule (Eq. (7)), the degree of freedom at invariant reaction in PG-TRISAMPL ternary system is zero (F = 0). This property (F = 0) will be used as a criterion in high-throughput screening approach to seek all invariant reactions and predict the corresponding transitional enthalpy in

PG-TRIS-AMPL ternary system by using POLY module of Thermo-Calc software with the reliable ternary thermodynamic database shown in Appendix (Ternary thermodynamic database section). The detail of programming high throughput computation will be discussed in Appendix Fig. S-6 for brevity. Via high throughput screening in PGTRIS-AMPL ternary system using ternary thermodynamic database, 73

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Table 4 The calculated phase transition in first invariant reaction and second invariant reaction. Invariant reaction

Temperature (K)

Region/line

Type in solid-solid phase transition

1st: αAMPL-rich+βPG-rich→ δTRIS-rich+γAMPL-rich

326.5

2nd: βPG-rich+γAMPL-rich→ δTRIS-rich+γ′PG-rich

338.4

Region: A-C-Q1 Region: Q1-C-B Region: Q1-B-D Region: D-Q1-A Line: A-Q1 Line: Q1-B Line: C-Q1 Line: Q1-D Region: A-C-Q1 Region: E-G-Q2 Region: Q2-G-F Region: Q2-F-H Region: H-Q2-E Line: E-Q2 Line: Q2-F Line: G-Q2 Line: Q2-H

αAMPL-rich+βPG-rich+δTRIS-rich → αAMPL-rich+δTRIS-rich+γAMPL-rich αAMPL-rich+βPG-rich+γAMPL-rich → αAMPL-rich+δTRIS-rich+γAMPL-rich αAMPL-rich+βPG-rich+γAMPL-rich → δTRIS-rich +βPG-rich +γAMPL-rich αAMPL-rich+βPG-rich+δTRIS-rich → βPG-rich +δTRIS-rich+γAMPL-rich αAMPL-rich+βPG-rich+δTRIS-rich → δTRIS-rich+γAMPL-rich αAMPL-rich+βPG-rich +γAMPL-rich → δTRIS-rich+γAMPL-rich αAMPL-rich+βPG-rich → αAMPL-rich +δTRIS-rich+γAMPL-rich αAMPL-rich+βPG-rich → βPG-rich +δTRIS-rich+γAMPL-rich δTRIS-rich+βPG-rich+γAMPL-rich → γ′PG-rich+δTRIS-rich+γAMPL-rich βPG-rich+γAMPL-rich+γ′PG-rich → δTRIS-rich+γAMPL-rich+γ′PG-rich βPG-rich+γAMPL-rich+γ′PG-rich → βPG-rich+δTRIS-rich+γ′PG-rich δTRIS-rich+βPG-rich+γAMPL-rich → δTRIS-rich+βPG-rich+γ′PG-rich δTRIS-rich+βPG-rich+γAMPL-rich → δTRIS-rich+γ′PG-rich βPG-rich+γAMPL-rich+γ′PG-rich → δTRIS-rich+γ′PG-rich βPG-rich+γAMPL-rich→ δTRIS-rich+γAMPL-rich+γ′PG-rich βPG-rich+γAMPL-rich → βPG-rich+δTRIS-rich+γ′PG-rich αAMPL-rich+βPG-rich+δTRIS-rich → αAMPL-rich+δTRIS-rich+γAMPL-rich

there are two invariant reactions at 326.5 K and 338.4 K, respectively. The compositional region of the first invariant reaction at 326.5 K (αAMPL-rich+βPG-rich→γAMPL-rich +δTRIS-rich) in PG-TRIS-AMPL ternary system is calculated and shown in A-C-B-D region in Fig. 8(a). The various solid-state phase transition types in A-C-B-D region is summarized in Table 4. The corresponding iso-transitional enthalpy is projected as dash-line into compositional region A-C-B-D in Fig. 8(a), the calculated transitional enthalpy has a good agreement with DSC measurement. One of DSC patterns is shown in Fig. 8(b); other samples are shown in Appendix Fig. S-5. In Fig. 8(a), there are four high energetic valleys shown as A-Q1 line, Q1-B line, C-Q1 line, and Q1-D line which are composed of critical points (like “eutectoid points” shown in isopleth in Fig. 7(a)). The highest transitional enthalpy for first invariant reaction at 326.5 K has been observed at point Q1 (PG0.33TRIS0.07AMPL0.60, ΔHmax = 137.5 kJ/kg) crossed by four high energetic valleys. The change of phase fraction along these four valleys is also calculated in Fig. 8(c)–(e) to understand the influence of solidsolid phase transformation on transitional enthalpy. With regard to the change of the calculated phase fraction, the negative change of phase fraction means consumption of phase at one composition undergoing the first invariant reaction and the positive change of phase fraction means formation of phase. Fig. 8(c) shows that the consumption of αAMPL-rich and βPG-rich (low temperature ordered phases) significantly increases from point A to Q1 and slightly decreases from point Q1 to B. At meantime, high temperature disordered phase (γAMPL-rich) is significantly formed with slight formation of low temperature ordered phase (δTRIS-rich). Therefore, the most energy should be stored at point Q1 due to the maximum consumption of low temperature ordered phases (αAMPL-rich and βPG-rich) and the maximum formation of high temperature disordered phase (γAMPL-rich). Similar phenomenon has also been observed at valley C-Q1 and Q1-D in Fig. 8(d)–(e). It has a good correspondence with present high-throughput screening in Fig. 8(a), thus, the point Q1 has the highest energy storage at first invariant reaction of 326.5 K. The second invariant reaction (βPG-rich+γAMPL-rich→δTRIS-rich+γ′PGrich) at 338.4 K is composed of compositional region E-G-F-H in PGTRIS-AMPL ternary system shown in Fig. 9(a). The solid-state phase transition in different E-G-F-H region is summarized in Table 4. The corresponding iso-transitional enthalpy of second invariant reaction is projected as dash line into region E-G-F-H and has a good agreement with DSC measurement in Fig. 9(a). One of DSC patterns is shown in Fig. 9(b); other samples are shown in Appendix Fig. S-5. There are also four high energetic valleys (E-Q2 line, Q2-F line, G-Q2 line, and Q2-H line) at second invariant reaction. The highest energy storage is shown at point Q2 (PG0.58TRIS0.069AMPL0.351, ΔHmax = 52.44 kJ/kg) which is crossed by these four valleys. The evolution of phase change on these

valleys has been calculated and shown in Fig. 9(c)–(e) to understand the influence of solid-state phase transformation on transitional energy. Fig. 9(c) shows that the consumption of low temperature ordered phase (βPG-rich) and high temperature disordered phase (γAMPL-rich) is significantly increasing from point E to Q2 and decreasing from point Q2 to F. At meantime, the formation of high temperature disordered phase (γ′PG-rich) is significantly increasing up to Q2 with slight formation of low temperature ordered phase (δTRIS-rich). Similar results have been observed in Fig. 9(d) and (e) for valley G-Q2 and Q2-H, respectively. The point Q2 should have the highest energy storage due to the maximum consumption of low temperature ordered phase (βPG-rich) and maximum formation of high temperature disordered phase (γ′PG-rich). It has a good correspondence with the high-throughput screening in Fig. 9(a). However, the energy storage at Q2 (second invariant reaction, 338.4 K) is about 52.44 (kJ/kg) which is much lower than 137.5 (kJ/kg) at Q1 (first invariant reaction, 326.5 K). The reason could be that the high temperature disordered phase (γAMPL-rich) is dissolved at second invariant reaction (338.4 K) and releases the storing energy of high temperature disordered phase in PG-TRIS-AMPL ternary system. 4. Conclusions In conclusion, we firstly and successfully propose a time- and costsaving high-throughput computation approach to discover the optimal capacity of energy storage in multi-component systems. In this work, binary AMPL-TRIS system has been reassessed and ternary PG-TRISAMPL system has firstly been assessed in PARROT module. The calculated stable phases shown in binary phase diagrams, ternary isothermal diagrams, and pseudo-binary phase diagrams have a good agreement with the present in-situ XRD and DSC results. Via the available thermodynamic database of PG-TRIS-AMPL ternary system, the solid-state phase transformation and the corresponding transitional enthalpy can be studied. Based on the Gibbs phase rule, the zero degree of freedom is designed as criteria for high throughput screening via CALPHAD methodology to seek the interested solid-solid phase transition with invariant phase transition temperature in Poly module of Thermo-Calc software. Calculations show that PG-TRIS-AMPL ternary system has two invariant reactions (αAMPL-rich+βPG-rich→γAMPL-rich+δTRIS-rich and βPGrich+γAMPL-rich→δTRIS-rich+γ′PG-rich) at 326.5 K and 338.4 K, respectively. At first invariant reaction of 326.5 K, four high energetic valleys (A-Q1, Q1-B, C-Q1, and Q1-D) are found in compositional region A-C-BD of first invariant reaction ((aAMPL-rich+bPG-rich®gAMPL-rich+dTRIS-rich) and the highest energy storage is about 137.5 kJ/kg at point Q1 (PG0.33TRIS0.07AMPL0.60) crossed by four valleys. At point Q1, it should be noted that the low temperature ordered phases (αAMPL-rich and βPGrich) have been consumed maximally and the high temperature 74

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Fig. 9. (a). Transitional enthalpy projection of 2nd invariant reaction (βPG-rich+γAMPL-rich→δTRIS-rich+γ′PG-rich) at 338.4 K in PG-TRIS-AMPL ternary system superimposed with data points from DSC; (b) DSC pattern for sample S3 (hatched region 3–2 is the energy change for second invariant reaction); (c)–(e) the corresponding change of phase fraction along compositional line E-F, G-Q2, and Q2-H from Fig. 9(a), respectively.

disordered phase (γAMPL-rich) has been formed maximally. Thus, the phase transition at point Q1 can go through the maximum energy change. At second invariant reaction of 338.4 K in compositional region E-G-F-H, the highest energy storage is about 52.44 kJ/kg at point Q2 (PG0.58TRIS0.069AMPL0.351) crossed by four high energetic valleys (EQ2, Q2-F, G-Q2, and Q2-H). The highest energy storage at point Q2 can be contributed by the maximum consumption of βPG-rich (low temperature ordered phase) and maximum formation of γ′PG-rich (high

temperature disordered phase). As a result, the optimal capacity of energy storage can be observed at the crossed point of high energetic valleys in PG-TRIS-AMPL ternary system. The high-throughput screening approach via CALPHAD methodology can assist in fundamentally understanding the influence of various solid-state phase transformation on the capacity of energy storage and also accelerating the discovery and development of the novel multi-component phase change materials with optimal capacity of thermal energy storage. 75

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Acknowledgements

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SUPPORTING INFORMATION

High-throughput thermodynamic computation and experimental study of solid-state phase transitions in organic multicomponent orientationally disordered phase change materials for thermal energy storage Renhai Shi*a, Dhanesh Chandra*b, Wen-Ming Chienb, and Jingjing Wangc a.

Department of Materials Science and Engineering, The Ohio State University, 384 Watts Hall, 2041 College Rd N. Columbus, OH 43210 USA. Email: [email protected] b.

Department of Chemical and Materials Engineering, University of Nevada Reno, 1664 N. Virginia Street, Reno, NV, 89557, USA. Email: [email protected] c.

School of Materials Science and Engineering, Shanghai University, Shanghai, 200072, China.

Figure S-1 the calculated TRIS-PG binary phase diagram (a) from 280K to 500K and (b) from 10K to 800K.

Figure S-2 the calculated AMPL-PG binary phase diagram (a) from 280K to 500K and (b) from 10K to 800K.

Table S-1 Experimental results from XRD and DSC used for optimizing database of PG-TRIS-AMPL ternary system

Figure S-3. Optimized isopleth along with TRIS-line in PG-TRIS-AMPL ternary system superimposed with experimental data from XRD and DSC; (b) and (c) the XRD patterns for samples S5 and S7 at 313K; (d) and (e) the XRD patterns of samples S5 and S7 at 353K; (f) and (g) the XRD patterns for samples S5 and S7 at 383K.

Figure S-4. (a) Optimized isopleth along with AMPL-line in PG-TRIS-AMPL ternary system superimposed with experimental data from XRD and DSC; (b) the XRD pattern for sample S10 at 313K; (c) and (d) the XRD patterns for samples S11 and S12 at 353K; (e) the XRD pattern for S10 at 383K.

Figure S-5. (a)- (g) DSC patterns of samples S2, S6-S8, and S10-S12. In which the transitional enthalpy of first invariant reaction at 326.5K and/or second invariant reaction at 338.4K are measured and hatched; An integral enthalpy (H) calculation program from TA instrument Company are used to calculate H at each temperature and extrapolate the H that have a close correspondence with calculated H in Fig. 8(a) and Fig. 9(a).

High-throughput computation detail

Figure S-6. (a) 3D schematic diagram of projection of critical points at various invariant reactions into compositional Gibbs triangle in PG-TRIS-AMPL ternary system (not to scale); (b) compositional Gibbs triangle consisted of all critical points from Fig. S-6(a) in PG-TRIS-AMPL ternary system; (c) the calculated transitional enthalpy H (kJ/kg) of all critical points at invariant reaction from Figure S-6(b); (d) the enthalpy as function of temperature for composition of point X-3 at isopleth x(PG)=0.2 shown in Figure S-6(a). (For the interpretation of the references to color in this figure, readers are referred to the web version of this article.) Note: In order to clearly show the projection for reader’s view, we only present the projection of critical points and their transitional enthalpy, other compositional points at invariant reactions will use the similar manner.

In this section, a new manner is firstly proposed for the high-throughput calculation shown in Figure S6 to seek the optimal composition with maximum energy storage in PG-TRIS-AMPL ternary system; this approach can be extended to other ternary and high-order system. Several steps in this case are summarized as: 1) Numerous isopleth at constant concentration of PG are generated from mole fraction of PG as zero to PG as one (here as an example, two isopleth with constant x (PG) =0.2 and x (PG) =0.4 are shown in Figure S-6(a), respectively); 2) the invariant reactions (shown as red tectic lines) in each isopleth from step 1) are tracked; the compositions at each invariant reaction including critical point are extrapolated and projected into the based Gibbs compositional triangle shown in Figure 8(a) and Figure 9(a) and the critical points are shown in Figure S-6(b); (In all generated isopleth of PG-TRIS-AMPL ternary system, about 4500 compositional data points are calculated to determine the composition regions which can meet the criteria of the HTC approach and go through the invariant reactions.) 3) The transitional enthalpy of all projected compositions at invariant reaction temperature is calculated and projected into Figure 8(a) and Figure 9(a) and the transitional enthalpy of only critical points is projected into 3-D transitional enthalpy space diagram in Figure S-6(c). (In this case, about 246 compositional points have been generated and performed at the first invariant reactions and about 344 compositional points at the second invariant reactions.) Thus, the composition with maximum energy storage could be found in PG-TRIS-AMPL ternary system. The transitional enthalpy of one composition is determined by the difference of enthalpy between the initial and end of invariant reaction. The initial and end status of invariant reaction could be determined by the Gibbs phase rule. For example, the enthalpy as a function of temperature in Figure S-6(d) is calculated for composition of point X-3 in isopleth of x(PG)=0.2 shown in Figure S-6(a). With the increasing of temperature, the enthalpy is gradually increasing. However, there is significantly increasing of enthalpy at 326.5K, at which the invariant reaction (degree of freedom: F=0) occurs with transitional enthalpy 77.1kJ/kg. The point X-3-0 is the initial status of invariant reaction with specific enthalpy about 165.1kJ/kg and the point X-3-1 is the end status of invariant reaction with specific enthalpy about 242.2kJ/kg. At initial point X-3-0, it shows the formation of high temperature phase (AMPL-rich); however, the low temperature phases (AMPL-rich and PG-rich) have been completely consumed at the end point X-3-1. Thus, the initial point X-3-0 can be determined by using Gibbs phase rule, in which the amount of high temperature phase (AMPLrich)

will be used as a variable instead of temperature to maintain the zero degree of freedom for the

equilibrium calculation in POLY module of Thermo-Calc software. Based on this setting, the initial point

X-3-0 will be automatically tracked during the calculation; similar manner is used for end point X-3-1 and others in this case. In Figure S-6(a), the isopleth at constant x (PG) =0.2 and 0.4 are shown as an example. In isopleth at x (PG) =0.2, there are two invariant reactions at 326.5K and 338.4K, respectively. The one at 338.4K is an invariant reaction (++’) with the critical point X-1. The one at 326.5K has an invariant reaction (++) with two critical points X-3 and X-4, respectively. The isopleth at x (PG) =0.4 also shows two invariant reactions at 326.5K and 338.4K, respectively. The one at 338.4K has one invariant reaction (++’) with critical point X-2; the one at 326.5K shows one invariant reaction (++) with critical point X-5. Thus, after the calculation of all isopleth from x(PG)=0 to x(PG)=1 covering the whole PG-TRIS-AMPL ternary system, all the composition points at all invariant reactions including critical points are extrapolated and projected into Gibbs compositional triangle. The projected composition points are composed of region A-C-B-D in invariant reaction at 326.5K shown in Figure 8(a) and region E-G-F-H in invariant reaction at 338.4K shown Figure 9(a) in the main text, the projected critical points are shown in Figure S-6(b) and shown as valley lines in Figure 8(a) and Figure 9(a). Based on Figure S-6(b), the transitional enthalpy of all projected compositions at invariant reaction could be calculated in POLY module of Thermo-Calc software in which the transitional enthalpy is considered as the difference of enthalpy between the initial and end of the invariant reaction. Via reliable thermodynamic database, the transitional enthalpy of all projected composition at invariant reactions could be calculated and shown in Figure S-6(c). The high throughput calculations show that two critical points with maximum transitional enthalpy are observed at 326.5K for point Q11and 338.4K for point Q21, respectively. At 326.5K, critical point Q11 (PG0.33TRIS0.07AMPL0.60) crossed by four compositional lines (A-Q1, B-Q1, C-Q1, and D-Q1 lines) with invariant reaction (++) has the maximum enthalpy change H(max.) = 137.5 J/g; At 338.4K, the critical point Q21 (PG0.58TRIS0.069AMPL0.351) crossed by four compositional lines (E-Q2, F-Q2, G-Q2, and H-Q2 lines) with invariant reaction (++’) has the maximum enthalpy change H(max.) = 52.44 J/g.

Ternary thermodynamic database optimized in this work for high-throughput calculation $ Database file written 2018-09-04 $ From database: PG-TRIS-AMPL ternary system $ From Author: Dr. Renhai Shi (Contact: [email protected]) $ In this file, TR and AD denote TRIS and AMPL, respectively. ELEMENT /ELEMENT VA ELEMENT PG ELEMENT TR ELEMENT AD

ELECTRON_GAS VACUUM TETRAGONAL ORTHORHOMBIC MONOCLINIC

0.0000E+00 0.0000E+00 0.0000E+00! 0.0000E+00 0.0000E+00 0.0000E+00! 1.2015E+02 0.0000E+00 0.0000E+00! 1.2114E+02 0.0000E+00 0.0000E+00! 1.0513E+02 0.0000E+00 0.0000E+00!

FUNCTION UN_ASS 298.15 +0; 300 N ! TYPE_DEFINITION % SEQ *! DEFINE_SYSTEM_DEFAULT ELEMENT 2 ! DEFAULT_COMMAND DEF_SYS_ELEMENT VA /- ! $**********Liquid phase********** PHASE LIQUID:L % 1 1.0 ! CONSTITUENT LIQUID:L :PG,TR,AD : ! PARAMETER G(LIQUID,PG;0) 0 +13043.317-9.943*T-.341*T**2 -2.4454E-04*T**3+2.2991E-07*T**4; 474.10 Y +30613.3842-69.798*T-.4504*T**2+3.3938E-04*T**3-3.011E-07*T**4; 800 N REF0 ! PARAMETER G(LIQUID,TR;0) 0 +8779.813-7.559*T-.2845*T**2 -2.538E-04*T**3+1.52E-07*T**4; 445.40 Y +57998.4642+249.69569*T-1.82099*T**2+.00179*T**3-8.553E-07*T**4; 800 N REF0 ! PARAMETER G(LIQUID,AD;0) 0 -8549.4534-11.975867*T -.118195*T**2-4.95E-04*T**3+2.824083E-07*T**4; 800 N REF0 ! PARAMETER G(LIQUID,PG,TR;0) 0 39084.64-95.98*T; 800 N REF0 ! PARAMETER G(LIQUID,PG,TR;1) 0 -2013.72-3.6*T; 800 N REF0 ! PARAMETER G(LIQUID,AD,PG;0) 0 1850.971; 800 N REF0 ! PARAMETER G(LIQUID,AD,PG;1) 0 -1487.397; 800 N REF0 ! PARAMETER G(LIQUID,AD,PG;2) 0 -2.5*T; 800 N REF0 ! PARAMETER G(LIQUID,AD,TR;0) 0 +1841.32; 800 N REF0 ! PARAMETER G(LIQUID,AD,TR;1) 0 +811.31; 800 N REF0 ! PARAMETER G(LIQUID,AD,TR;2) 0 -3678.32-1.87*T; 800 N REF0 ! PARAMETER G(LIQUID,PG,TR,AD;0) 0 8300-36.5*T; 800 N REF0 ! PARAMETER G(LIQUID,PG,TR,AD;2) 0 15223; 800 N REF0 ! $**********AMPD_2 phase********** PHASE AMPD_2 % 1 1.0 ! CONSTITUENT AMPD_2 :PG,TR,AD : !

PARAMETER G(AMPD_2,AD;0) 0 -20605.505-.14792*T**2 -1.33333E-04*T**3-1.64183E-08*T**4+5000-14.169*T; 353.72 Y +5596.314-255.2544*T+.75976*T**2-.0015133*T**3+7.24242E-07*T**4+5000 -14.169*T; 8000 N REF0 ! PARAMETER G(AMPD_2,PG;0) 0 +1750.242+7.146*T-.4504*T**2 +3.3939E-04*T**3-3.011E-07*T**4+6288.42+4500; 800 N REF0 ! PARAMETER G(AMPD_2,TR;0) 0 -9096.72+18.645*T-.3729*T**2 +1.912E-04*T**3-1.561E-07*T**4+8850; 445.40 Y +76898.994-15.053*T-1.05591*T**2+.00114*T**3-6.47166E-07*T**4+8850; 800 N REF0 ! $**********BCC_A2 phase********** PHASE BCC_A2 % 1 1.0 ! CONSTITUENT BCC_A2 :PG,TR,AD : ! PARAMETER G(BCC_A2,PG;0) 0 +8329.317-.341*T**2 -2.4454E-04*T**3+2.2991E-07*T**4+90.505; 474.10 Y +25899.3842-59.855*T-.4504*T**2+3.3938E-04*T**3-3.011E-07*T**4+90.505; 800 N REF0 ! PARAMETER G(BCC_A2,TR;0) 0 +5412.813-.2845*T**2 -2.538E-04*T**3+1.52E-07*T**4; 445.40 Y +54631.4642+257.25469*T-1.82099*T**2+.00179*T**3-8.553E-07*T**4; 800 N REF0 ! PARAMETER G(BCC_A2,AD;0) 0 -11330.198-4.74235*T -.1182*T**2-4.95E-04*T**3+2.82408E-07*T**4; 353.72 Y -11329.4534-4.738007*T-.118195*T**2-4.95E-04*T**3+2.82408E-07*T**4; 800 N REF0 ! PARAMETER G(BCC_A2,PG,TR;0) 0 +4457.79-12.48*T; 800 N REF0 ! PARAMETER G(BCC_A2,PG,TR;1) 0 +12614.55-32.66*T; 800 N REF0 ! PARAMETER G(BCC_A2,PG,TR;2) 0 -648.59; 800 N REF0 ! PARAMETER G(BCC_A2,AD,PG;0) 0 -10312.341+30.157*T; 800 N REF0 ! PARAMETER G(BCC_A2,AD,PG;1) 0 -11199.258+24.066*T; 800 N REF0 ! PARAMETER G(BCC_A2,AD,TR;0) 0 +5853.24-9.43*T; 800 N REF0 ! PARAMETER G(BCC_A2,AD,TR;1) 0 -844.46+3.13*T; 800 N REF0 ! PARAMETER G(BCC_A2,AD,TR;2) 0 -3180-4.31*T; 800 N REF0 ! PARAMETER G(BCC_A2,PG,TR,AD;0) 0 6500+9.5*T; 800 N REF0 ! PARAMETER G(BCC_A2,PG,TR,AD;2) 0 6500+23.3*T; 800 N REF0 ! $**********FCC_A1 phase********** PHASE FCC_A1 % 1 1.0 ! CONSTITUENT FCC_A1 :PG,TR,AD : ! PARAMETER G(FCC_A1,PG;0) 0 +8329.317-.341*T**2 -2.4454E-04*T**3+2.2991E-07*T**4; 474.10 Y +25899.3842-59.855*T-.4504*T**2+3.3938E-04*T**3-3.011E-07*T**4; 800 N REF0 ! PARAMETER G(FCC_A1,TR;0) 0 +5412.813-.2845*T**2 -2.538E-04*T**3+1.52E-07*T**4+1198.49; 445.40 Y +54631.4642+257.25469*T-1.82099*T**2+.00179*T**3-8.553E-07*T**4+1198.49;

800 N REF0 ! PARAMETER G(FCC_A1,AD;0) 0 -11330.198-4.74235*T -.1182*T**2-4.95E-04*T**3+2.82408E-07*T**4+1151.94; 353.72 Y -11329.4534-4.738007*T-.118195*T**2-4.95E-04*T**3+2.82408E-07*T**4+1151.94; 800 N REF0 ! PARAMETER G(FCC_A1,PG,TR;0) 0 +6113.87-22.27*T; 800 N REF0 ! PARAMETER G(FCC_A1,PG,TR;1) 0 +4898.21-20.59*T; 800 N REF0 ! PARAMETER G(FCC_A1,PG,TR;2) 0 -2096.48; 800 N REF0 ! PARAMETER G(FCC_A1,AD,PG;0) 0 -12639.514+30.876*T; 800 N REF0 ! PARAMETER G(FCC_A1,AD,PG;1) 0 -2519.161+3.314*T; 800 N REF0 ! PARAMETER G(FCC_A1,PG,TR,AD;0) 0 6800+25.5*T; 800 N REF0 ! $**********MONOCLINIC phase********** PHASE MONOCLINIC % 1 1.0 ! CONSTITUENT MONOCLINIC :PG,TR,AD : ! PARAMETER G(MONOCLINIC,AD;0) 0 -20605.505-.14792*T**2 -1.33333E-04*T**3-1.64183E-08*T**4; 353.72 Y +5596.314-255.2544*T+.75976*T**2-.0015133*T**3+7.24242E-07*T**4; 800 N REF0 ! PARAMETER G(MONOCLINIC,PG;0) 0 +1750.242+7.146*T-.4504*T**2 +3.3939E-04*T**3-3.011E-07*T**4+4389.59; 800 N REF0 ! PARAMETER G(MONOCLINIC,TR;0) 0 -9096.72+18.645*T-.3729*T**2 +1.912E-04*T**3-1.561E-07*T**4+809; 445.40 Y +76898.994-15.053*T-1.05591*T**2+.00114*T**3-6.47166E-07*T**4+809; 800 N REF0 ! PARAMETER G(MONOCLINIC,AD,PG;0) 0 -1496.68+6.63*T; 800 N REF0 ! PARAMETER G(MONOCLINIC,AD,PG;1) 0 2395.3; 800 N REF0 ! PARAMETER G(MONOCLINIC,AD,TR;0) 0 636.78+22.05*T; 800 N REF0 ! PARAMETER G(MONOCLINIC,AD,TR;1) 0 +115.61; 800 N REF0 !

$**********ORTHORHOMBIC phase********** PHASE ORTHORHOMBIC % 1 1.0 ! CONSTITUENT ORTHORHOMBIC :PG%,TR,AD : ! PARAMETER G(ORTHORHOMBIC,PG;0) 0 +1750.242+7.146*T-.4504*T**2 +3.3939E-04*T**3-3.011E-07*T**4+4948.8; 800 N REF0 ! PARAMETER G(ORTHORHOMBIC,TR;0) 0 -9096.72+18.645*T-.3729*T**2 +1.912E-04*T**3-1.561E-07*T**4; 445.40 Y +76898.994-15.053*T-1.05591*T**2+.00114*T**3-6.47166E-07*T**4; 800 N REF0 ! PARAMETER G(ORTHORHOMBIC,AD;0) 0 -20605.505-.14792*T**2 -1.33333E-04*T**3-1.64183E-08*T**4+460; 353.72 Y +5596.314-255.2544*T+.75976*T**2-.0015133*T**3+7.24242E-07*T**4+460; 800 N REF0 ! PARAMETER G(ORTHORHOMBIC,PG,TR;0) 0 +489.63+16.776*T; 800 N REF0 ! PARAMETER G(ORTHORHOMBIC,PG,TR;1) 0 +0.0; 800 N REF0 ! PARAMETER G(ORTHORHOMBIC,AD,TR;0) 0 +1552.99+17.28*T; 800 N REF0 ! PARAMETER G(ORTHORHOMBIC,AD,TR;1) 0 +1525.84; 800 N REF0 !

PARAMETER G(ORTHORHOMBIC,AD,TR;2)

0 -4510.85; 800 N REF0 !

$**********TETRAGONAL phase********** PHASE TETRAGONAL % 1 1.0 ! CONSTITUENT TETRAGONAL :PG,TR,AD : ! PARAMETER G(TETRAGONAL,PG;0) 0 +1750.242+7.146*T-.4504*T**2 +3.3939E-04*T**3-3.011E-07*T**4; 800 N REF0 ! PARAMETER G(TETRAGONAL,TR;0) 0 -9096.72+18.645*T-.3729*T**2 +1.912E-04*T**3-1.561E-07*T**4+10608.94; 445.40 Y +76898.994-15.053*T-1.05591*T**2+.00114*T**3-6.47166E-07*T**4+10608.94; 800 N REF0 ! PARAMETER G(TETRAGONAL,AD;0) 0 -20605.505-.14792*T**2 -1.33333E-04*T**3-1.64183E-08*T**4+497.06; 353.72 Y +5596.314-255.2544*T+.75976*T**2-.0015133*T**3+7.24242E-07*T**4+497.06; 800 N REF0 ! PARAMETER G(TETRAGONAL,PG,TR;0) 0 +2370.25-24.04*T; 800 N REF0 ! PARAMETER G(TETRAGONAL,PG,TR;1) 0 +0.0; 800 N REF0 ! PARAMETER G(TETRAGONAL,AD,PG;0) 0 +7043.611-1.173*T; 800 N REF0 ! PARAMETER G(TETRAGONAL,AD,PG;1) 0 +2062.326; 800 N REF0 ! LIST_OF_REFERENCES NUMBER SOURCE !