Continuous solid-state phase transitions in energy storage materials with orientational disorder – Computational and experimental approach

Energy 91 (2015) 334e349

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Continuous solid-state phase transitions in energy storage materials with orientational disorder e Computational and experimental approach Harpreet Singh a, Anjali Talekar a, Wen-Ming Chien a, Renhai Shi a, Dhanesh Chandra a, *, Amrita Mishra b, Muralidhar Tirumala c, Daryl J. Nelson c a b c

Chemical and Materials Engineering Department, MS 388, University of Nevada, Reno, NV 89557, USA Department of Mechanical Engineering, University, MS 38677, USA Intel Laboratories, Intel Corp., 5200 NE Elam Young Parkway, Hillsboro, OR 97124, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 January 2015 Received in revised form 27 July 2015 Accepted 30 July 2015 Available online 10 September 2015

We report on TES (thermal energy storage) in new CT (continuous phase transitions) in multicomponent tetrahederally configured (orientationally disordered) crystals of NPG-neopentylglycol-C5H12O2, PGpentaglycerine-C5H12O3, and PE-pentaerythritol-C5H12O4. This discovery is applicable in thermal energy storage in many systems which do not require conventional isothermal first-order phase transition energy storage. The above compounds exhibit polymorphs of orientationally disordered phases in which OeH…O bond rotation around the CeC bond stores significant amount of energy; for example, in PE 41.26 kJ/mol are absorbed isothermally during solidesolid transitions. In this paper we show, anisothermal continuous phase transitions (CT), due to compositional changes with changes in temperature, associated with a measurable amount of energy, not reported earlier. The correlation of phase stability regions in pseudo-binaries, calculated from ternary NPGePGePE phase diagrams, is validated by experimental ternary DSC (differential scanning calorimetry) and in-situ x-ray diffraction data. We established equations for determining the CT in a temperature range, and their respective enthalpies of transitions for any composition of the ternaries. Thermodynamic calculations of the Gibbs energies of the solution phases are modeled as substitutional solid solutions, in which the excess Gibbs energies are expressed by the RedlicheKistereMuggianu polynomial. There is excellent agreement between the experimental and CALPHAD calculated data. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Continuous phase transitions Orientationally disordered crystals Pentaerythritol Pentaglycerine Neopentylglycol CALPHAD modeling

1. Introduction A special group of tetrahedral molecular polyalcohol compounds are gaining importance for the storage of thermal energy during the heating or cooling that accompanies phase changes. Pure polyalcohol organic compounds that are tetrahederally coordinated undergo solid-state phase transitions from lowtemperature layered or chained structures to orientationally disordered cubic phases. These materials are referred to as “plastic crystals,” which exhibit orientational disorder in the hightemperature form and store thermal energy in the form of OeH… O bond rotation around the CeC bond. The unique feature of these

* Corresponding author. E-mail address: [email protected] (D. Chandra). http://dx.doi.org/10.1016/j.energy.2015.07.130 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

pure tetrahedral polyalcohols is that the entropy change is ~146.3 J/ K mol during solidesolid phase transitions, as estimated by Richards' and Timmermans' rules of phase transitions [1]. The melting entropy, which is also comparable to metals, is ~8.36 J/ K mol [2], indicating the importance of the solid-state phase transitions in these polyalcohols. Recent developments in encapsulation technologies and heat transfer technologies may allow these systems to be used in practical applications. Typically, the latent heat of solideliquid transitions are used for thermal energy phase change materials, but these pose decomposition problems after a certain number of cycles; moreover, supercooling is generally observed. First-order phase transitions from ordered, low-temperatures phases with rigid OeH…O bonds to disordered, high-temperature plastic phases are known and are used for energy storage. However, important non-isothermal continuous solid-state phase

H. Singh et al. / Energy 91 (2015) 334e349

transitions in multicomponent plastic crystal systems for energy storage purposes have not been previously reported in the literature; we will hereafter refer to these as CT transitions. The CT transitions involve heat storage during compositional changes as the material is heated and are energetic, particularly in ternary polyalcohol systems. More recently, these organic crystals are finding applications in the storage of thermal energy from CSP (concentrated solar power). In CSP systems, focused energy is transferred from a solar tower to low- and high-temperature holding tanks during the day via heat transfer molten salts. Further details may be found on the US DOE website, “Concentrating Solar Power Thermal Energy Storage Basics.” This application does not require a first-order phase transition for storing heat; instead, CT transitions may be used in a certain temperature range that will store a large amount of heat, in addition to the heat capacity of these polyalcohols. We propose new developments and discoveries of thermal energy storage during CT transitions in plastic crystals, in which intermolecular hydrogen bonds break between certain molecules due to composition changes that during heating. Naturally, heat is released during the cooling step of these transitions. The NPG (neopentylglycol-C5H12O2, monoclinic, P21/n), PG (pentaglycerine-C5H12O3, orthorhombic, Pn21a), and PE (pentaerythritol-C5H12O4, body-centered tetragonal, I 4) crystals and their binaries and ternaries store large solid-state phase transition enthalpies (Table 1) [3]. Murrell and Breed [4] and Benson et al. [5,6] have developed practical materials based on these compounds. Barrio et al. [7e10] and Teisseire et al. [11] constructed experimental binary phase diagrams for PEePG, PEeNPG, and NPGePG, thus expanding the available choices of phase transition temperatures for these energy storage materials. Chandra et al. [2,12,13] developed additional binary solid solutions. Recently, Mishra et al. [14,15] and Singh [16] from our group developed various ternary phase diagrams, leading to numerous new materials with different phase transition temperatures. These studies involved a hybrid approach of thermodynamic measurements and computational CALPHAD calculations, resulting in a large number of choices for solid-state thermal energy storage. Crystallographic analyses of these materials were first reported by Nitta and Watanabe [17], and Llewellyn [18] described the lowtemperature BCT structure of PE, which has a layered structure in which the OeH…O intermolecular bonds form square bonds between four molecules. The strength of the H-bond ranges from 10 to 40 kJ/mol in these types of crystals. This strength is considerably less than that of a primary bond, e.g., the bond strength of NaCl is764 kJ/mol [19]. Eilerman et al. [20] reported the BCT structure of PG, which is similar to that of PE. Subsequently, Chandra et al. [21] reported the low-temperature monoclinic structure of NPG, an ̄ important thermal energy storage compound in which the OeH…O bonds form a bimolecular chain with typical square OeH…O intermolecular bonds, leading to a highly anisotropic structure. Continuing their structural work, Nita and Watanabe [17] and Eilerman et al. [20] reported structures of other polyalcohols. The low- and high-temperature structures of NPG are presented in

335

Fig. 1. The crystallographic changes from monoclinic (NPG) to the orientationally disordered crystal (ODIC) FCC (face-centered) structure [21] include increased vibrational motion in the form of asymmetric stretching and bending and libration of the OeH…O bond around the CeC bond, which we simply call “molecular rotation.” The OeH…O bond rotation is just a depiction; bond stretching is actually involved in this high-temperature cubic representation. Nitta and Watanabe [17], Rudman [22], and Smith [23] proposed rotation mechanisms of the OeH…O bonds by removal of the steric hindrances of the H-atoms associated with intramolecular CH2 or CH3 groups. Benson et al. [5] noted the progressive breaking of intermolecular bonds just below and at the phase transition temperature based on a FTIR study. In one of our heated stage optical microscopy studies on a single crystal of PG, microscopic tetrahedral pyramidal features appeared on the surface of the PG crystal below the phase transition temperature. These features progressed steadily, and the sample became polycrystalline, suggesting that high-temperature phases nucleate below the phase transition temperature. In the case of NPG, the low- to high-temperature transformation is associated with a volume change of 40.448 Å3 (651.521 Å3 at 313 K to 691.969 Å3 at 318 K for the b/g transition). This indicates that there is significant free volume for the reorientation of molecules and rotation of the OeH…O bond (Fig. 2). These are important connections involving thermodynamic calculations. The model for the g phase (in Fig. 1) shows the intermolecular bonding of O1eH1…O2, with C2 as the central atom that lies on the cube face (001) corners or mid-plane of this FCC unit cell. The H1eO1eC1 bond rotates as a cone generator whose axis is an extension of C1eC2, and similarly, O2eC6 rotates synchronously about an extension of C6eC7. The O1eH1…O2 bond has an average length of 2.72 Å, and thus, the adjacent molecules may undergo libration. Binary phase diagrams have been developed for all possible combinations of NPGePE, NPGePG, and PGePE [11e17]. The first computational studies of the NPGePGePE ternary system of polyalcohols were developed in our group by Mishra et al. [14]. Singh [16] subsequently performed detailed experiments on the NPGePGePE polyalcohol system using in situ XRD (X-ray diffraction), DSC (differential scanning calorimetry), and NMR. Numerous datasets were obtained, but he could not fully interpret all of the DSC data at that time. Combining Singh's experimental data [16] with work later performed by Mishra [15], we were able to establish ternary phase diagrams of the entire regions that include equations for the phase transition temperatures for various compositions. The motivation for this research is to correlate experimental data with the ternary equilibrium phase diagrams; at this time PEePGeNPG system. We constructed isopleths of the pseudobinaries from the ternary data and correlated to the to the experimentally determined phase boundaries using x-ray diffraction, differential scanning calorimetry, and other methods. To our knowledge t is the first time this correlation has been performed for the ternary system. As mentioned before there are very few

Table 1 Thermodynamic properties of pure orientationally disordered tetrahedral polyalcohols and amines [14]. Materials

a or b phase

TSSTR (K)

DH (a/g) kJ/mol

DS (a/g) J/mol K

g or g
phase

Tfus (K)

DH (g/L) kJ/mol

DS (g/L) J/mol K

PE (C5H12O4) PG (C5H12O3) NPG (C5H12O2) NPA (C5H12O) TRIS (C5H11NO3) AMPL (C5H11NO2)

Tetragonal Tetragonal Monoclinic Triclinic Orthorhombic Monoclinic

461 354 316 242 407.3 357

41.26 23.12 13.63 4.83 32.69 23.54

89.50 65.31 43.55 19.34 80.12 66.69

FCC FCC FCC FCC BCC BCC

533 471 399 328 445 389

5.02 5.43 4.6 4.05 3.34 3.33

9.42 11.53 11.53 12.35 7.51 8.56

336

H. Singh et al. / Energy 91 (2015) 334e349

Fig. 1. (Left) An example of an NPG, low-temperature, b-monoclinic structure, showing atomic positions in the unit cell projected onto the bec plane (view down the z-axis). The lattice parameters of the b phase are a ¼ 5.984 (±0.006) Å, b ¼ 10.912 (±0.01) Å, c ¼ 10.127 (±0.01) Å, and b ¼ 99.84 (±0.03) at 313 K (just below the phase transition temperature). The space group is P21/n (No.14). The b/g transition, where g is the orientationally disordered FCC phase (Right) occurs at 316 K. The 100 plane of the FCC cell is shown with one example of intermolecular bond rotation. Other molecules also exhibit this rotation but are not shown in this figure. The lattice parameter of the FCC g phase is 8.845 Å at 318 K, which is just above the transition temperature [Chandra et al. 2, 21].

polyalcohols or amines available commercially in pure form that have fixed transition temperatures; in this research we have shown possibilities of using several solid solution combinations in the PEePGeNPG system with different phase transition temperatures and transitional enthalpies. In this paper, we report on novel continuous phase (CT) transitions in plastic crystal materials. Ternary polyalcohol solid solutions may be used concentrated solar energies as a secondary storage system, refrigerators, shipping containers, passive solar buildings and others. In these systems, energy is generally stored in a range of temperatures in addition to the first-order transitions that take place a constant temperature. The novelty of these orientationally disordered molecular crystals is their potential for energy storage in renewable energy systems. Because the energy requirements vary depending on the application, a variety of materials with different phase transformation temperatures and energies are needed. Several new thermal energy storage materials have been developed that store heat in the two-phase regions of these crystals. The new information in this paper is correlation of experimental data that was not presented in previous papers [15].

We present global predictions of the phase transition temperatures for a variety of compositions of the NPGePGePE ternary systems are made using thermodynamic calculations coupled with experimental data. The experimental verification is shown for the first time in this study. The methodology used for these systems has broader implications and can be applied to other organic systems. Verification of the enthalpies for localized phase transitions requires experimental thermodynamic data, but their interpretation requires calculations. Therefore, this study may be considered as a validation of the phase diagrams developed by Mishra et al. [14,15]. Additionally, the results of this work serve as a prediction of the thermal properties for these systems. There are two main objectives of this study: (1) to demonstrate novel CT transitions that exhibit significant anisothermally stored thermal energy, as well as first-order phase transitions, that have not been reported earlier, and (2) to calculate and/or measure thermodynamic parameters for ternary phase diagrams, related pseudo-binary isopleths, and equations of phase transitions. In addition, we are currently developing a thermodynamic database for binary and tetrahederally bonded ternary polyalcohols and amines, i.e., plastic crystals that exhibit orientationally disordered crystalline phase transitions. Several examples of ternary isothermal phase diagrams, isopleths, XRD and DSC measurements, equations developed for phase transition temperatures, and measured enthalpies for ternary samples are presented.

2. Experimental methods

Fig. 2. Volume change in pure NPG during the b/g0 (monoclinic, z ¼ 4 / FCC, z ¼ 4) phase transition at ~316 K. There is a ~6.2% increase in volume upon going from the chained structure to the orientationally disordered FCC phase [2].

The compositions of the samples that are investigated in this study are shown in the Gibbs triangle in Fig. 3. We prepared our ternary samples along three different compositional paths, namely, the NPG, PG, and PE lines shown in the Gibbs triangle. Three perpendicular lines are drawn from the center of each base to the apex of the Gibbs triangle, and colored dots are used for each line with designated sample numbers (Fig. 3). For example, the NPG Line is drawn by joining point 11 (located on the PGePE baseline) to the apex at point 1. In general, samples were prepared at 20% increments along each direction. For example, 0, 10, 20, 33.3, 40, 60, 80, and 100%NPG correspond to sample numbers 11, 10, 8, 7, 6, 4, 2, and 1, respectively, along the NPG line (see also Table 2 for all compositions). In a similar manner, the sample numbers and compositions are shown for the samples along the PG line and PE line. The results are presented in the order of increasing %NPG, %PG,

H. Singh et al. / Energy 91 (2015) 334e349

337

The sample preparation procedure involved the following steps: (1) Mixtures of the powders were melted in glass test tubes, solidified, and retrieved. These polyalcohols have a tendency to supercool, leading to one or more high-temperature phases that are stable at room temperature. (2) The powders were cooled in sealed containers in a freezer at ~253 K to precipitate the low-temperature phases. (3) Strain-induced transformations were carried out to ensure that all low-temperature phases are in equilibrium, and cylindrical pellets were produced in die of ~1 cm diameter and ~2 cm height. The pellets were then placed in the freezer, after which they were ground using a mortar and pestle. Finally, the samples were placed in sealed glass bottles to avoid the absorption of moisture until being used for the DSC and XRD measurements. 2.2. X-ray diffraction and differential scanning calorimetry

Fig. 3. Gibbs triangle showing the sample numbers and compositions used to perform the XRD and DSC studies. The samples were grouped according to their composition along the NPG, PG, and PE lines, as shown in Table 2.

and %PE (from 0 to 100%) along the NPG, PG, and PE lines, respectively. 2.1. Sample preparation Powder samples of pentaerythritol (PE, C5H12O4, 99.5% purity), pentaglycerine (PG, C5H12O3, 97% purity), and neopentylglycol (NPG, C5H12O2, 95% purity) were procured from Aldrich Chemicals. No further purification was attempted, except for heating to remove moisture. These powders were mixed thoroughly to produce the appropriate ternary compositions of NPGePGePE. In this study, 42 different ternary samples were prepared to determine the phase boundaries. Limited experiments were performed on Sample Nos. 34 to 44 for confirmation of the phase boundaries.

A PANalytical X'Pert, Pro qq X-ray diffractometer equipped with an Anton Paar XRK 900 stage was used to obtain diffraction patterns in the range of 298 Ke~500 K. (The Panalytical Inc. is located in Westborough, MA01581, USA.) At high temperatures, selective vaporization in un-encapsulated samples becomes problematic, particularly for the NPG compounds. The experiments take several hours because the volume of the XRK 900 heating stage is extremely large; therefore, the lower melting point compounds vaporize selectively at temperatures above ~350 K and deposit in cooler areas. To avoid this vaporization, we packed the power samples in epoxy sealed (1 mm) glass capillaries so that in situ XRD powder patterns could be obtained at temperatures above ~350 K. A homemade forced air-heated capillary system was mounted on the X-ray diffractometer, which was coupled with a position sensitive X'Celerator detector for rapid data acquisition. A TA Q100 differential scanning calorimeter was used to identify the phase transitions that took place during heating. Milligram range samples were used for these experiments. 3. Equilibrium thermodynamics 3.1. Thermodynamic calculations e nomenclature

Table 2 Designation of the sample numbers and their respective compositions along the NPG, PG, and PE lines in the Gibbs triangle. Line

% Component

Point on Triangle

Composition e Mol%

NPG Line

%NPG 0 10 30 33.3 40 60 80 100 %PG 0 10 30 33.3 50 70 90 100 %PE 0 20 33.3 40 60 80 100

Sample No. 11 10 8 7 6 4 2 1 Sample No. 33 32 30 7 28 26 24 23 Sample No. 22 20 7 18 16 14 12

NPG 0 10 30 33.3 40 60 80 100 NPG 50 45 35 33.3 25 15 5 0 NPG 50 40 33.3 30 20 10 0

PG Line

PE Line

PG 50 45 35 33.3 30 20 10 0 PG 0 10 30 33.3 50 70 90 100 PG 50 40 33.3 30 20 10 0

PE 50 45 35 33.3 30 20 10 0 PE 50 45 35 33.3 25 15 5 0 PE 0 20 33.3 40 60 80 100

The symbols denoting the crystal structures of the phases of the PEePGeNPG ternary system are chosen based on phase stability considerations and are used in the calculation of the binary and ternary phase diagrams. In the calculated ternary Gibbs triangle the pure components PE, NPG, and PG are represented by A, B, and C, respectively, to obtain simplified expressions. The low-temperature layered BCT (body-centered tetragonal) structure of pure and solid solutions of PE (C5H12O4) and PG (C5H12O3) are designated as a, and the high-temperature phases are designated as g0 (FCC phase) because the crystal structures are the same for these two compounds [17]. Pure NPG and its solid solutions are designated as b (monoclinic), and its BCC high-temperature phase is designated as the g phase. In this ternary system, the regular solution approximation [14,15] was applied to the liquid (L) phase as well as to its primary low-temperature solid solutions, such as a-PE-rich, a-PGrich, and b-NPG-rich. A list of symbols and the phase designations are given below: a Phase e Low-temperature phase of PE (A) and PG (C) (pure and solid solutions); both have body-centered tetragonal (BCT) structures. b Phase e Low-temperature phase of pure NPG (B) and its solid solutions; both have monoclinic structures. g0 Phase e High-temperature, orientationally disordered phase of PE and PG (pure and solid solutions); both have face-centered (FCC) structures.

338

H. Singh et al. / Energy 91 (2015) 334e349 Table 3 Thermodynamic calculations of stable and metastable phase Gibbs energies of the ternary NPG-PG-PE system. No.

Gibbs energy expression

1 2 3 4

0 Ga ¼ 0 PE 0 Gb NPG ¼ 0 0 Ga ¼ 0 PG ðmÞ 0 GbPG ¼ 3403:78 ðmÞ 0 GaNPG ¼ 986:640 ðmÞ 0 GaNPG ¼ 20000  40  T ðmÞ 0 GbPE ¼ 25000  10  T 0 ðsÞ 0 GgPG ¼ 23120  65:29  T  0:236  T 2 þ 1115:333  T  7844109  138:041  T  LnðTÞ 0 g ðsÞ 0 GPE ¼ 41260  89:501  T þ 1:0895  T 2 þ 6794:78175  T  272492:7250  1093:350  T  LnðTÞ 0 ðmÞ GgPE ¼ 41260  89:501  T þ 1:0895  T 2 þ 6794:78175  T  272492:7250  1093:350  T  LnðTÞ ðsÞ 0 GgNPG ¼ 13630  43:22  T þ 0:351  T 2 þ 162198  T  51061568  272:999  T  LnðTÞ 0 ðmÞ 0 GgNPG ¼ 13630  43:22  T þ 0:351  T 2 þ 162198  T  51061568  272:999  T  LnðTÞ þ 1028 0 L ðsÞ GPE ¼ 46280  98:919  T þ 1:3765  T 2 þ 7119:63  T  237151:6225  1180:015  T  LnðTÞ ðsÞ 0 GLNPG ¼ 28550  76:83  T  0:175  T 2 þ 1161:791  T þ 6611:1915  152:5  T  LnðTÞ ðsÞ 0 GLPG ¼ 18315  55:2  T þ 0:425  T 2 þ 2098:38  T  69849:68  349:613  T  LnðTÞ

5 6 7 8 9 10 11 12 13 14 15

ðsÞ ðsÞ ðsÞ

g Phase e High-temperature, orientationally disordered phase of NPG (pure and solid solutions); both have face-centered (FCC) structures. MBa e Metastable phase energy (J/mol), which is equivalent to 0 Ga because 0 Ga ¼ 0 in Equation (16). These types of meta stable B B energies (for different expressions) have numerical values, for example, Nos. 4 (3403.78), 5 (986.64), 10 (1341), and 12 (1028) in Table 3. L Phase e Represents the liquid phases of all three pure components and their solutions. Note: The pure components are designated as A, B and C in the ThermoCalc computer program. The binary phase diagram data of NPGePG, NPGePE, and PGePE were assembled from the literature and our previous work [7,8,11,14,15]. However, we found discrepancies when using the available literature data on PGeNPG [9] and PEePG [10] in evaluating the phase diagram of PEeNPG. To obtain a global picture of the ternary phase diagrams at different temperatures, we first superimposed the binary isothermal phase boundaries at different temperatures on the Gibbs triangle edges, a methodology used by many researchers. In the case of pure PE, the BCT low-temperature a (PE) structure transforms to a FCC structure, g0 (PE), at 461 K, whose lattice parameter, ag0 PE ¼ 8.84 Å, is just above the phase transition temperature. The a(PG)/g0 (PG) transition occurs at ~354 K, and the resulting structure has a lattice parameter of ag0 PG ¼ 8.87 Å. The PEePG binary solid solutions exhibit complete solubility and follow the “Hume-Rothery” rules. This nomenclature is also used in the ternary phase diagrams. In the case of the NPGePE phase diagram, there is a large two-phase region separating the PE-rich a phase and NPG-rich b phase, as shown in Fig. 3. NPG has a bimolecular chained monoclinic [P21/n] structure [21] at room temperature, with lattice parameters of a ¼ 0.5979 nm, b ¼ 1.0876 nm, c ¼ 1.099 nm, and b ¼ 99.78 . This polyalcohol compound exhibits a solid-state phase transition at 316 K from pure bNPG to the gNPG orientationally disordered crystal structure. Just above the phase transition temperature, the lattice parameter of pure gNPG is 8.8 Å (FCC). 3.2. Thermodynamic basis of the calculations The model presented below is composed of energies, such as mechanical mixing, ideal entropy of mixing, and excess energy. According to this approximation, the Gibbs energy of the solution phase f (where, f ¼ a, b, g
, g, and L) can be represented as follows

þ 1341

(the unit of Gibbs energy used throughout this work is J mol1, where mole is a mole of formula unit):

Gf ¼ xoA GfA þ xoB GfB þ xoC GfC þ RTðxA ln xA þ xB ln xB þ xC ln xC Þ þ GEX:f (1) where R is the universal gas constant, T is the temperature in Kelvin, A, B, and C are the pure components, xA, xB, and xC are the mole fractions of pure components PE, NPG, and PG, respectively, and oGA, oGB, and oGC are the Gibbs energies of the pure components. The lattice stability parameter can be described as a function of the temperature T: 0 f

G  0 H;ref : ¼ A þ BT þ CT ln T þ DT 2 þ ET 3 þ FT 7 þ IT 1 þ JT 9 (2)

where oH is the molar enthalpy of the pure component in the stable state. The symbols A through J denote coefficients, which can be calculated using thermodynamic values of the pure components. GEX;f represents the excess Gibbs energy of the phase 4, which can be described using the RedlicheKister formalism:

GEX;f ¼ xA xB LfA;B þ xA xC LfA;C þ xB xC LfB;C þ xA xB xC LfA;B;c

(3)

The binary interaction parameter and ternary interaction parameters in the above can be expressed as

Lfi;j ¼

m X

 n f Li;j xi

 xj



(4)

n¼0

Lfi;j;k ¼ xoi Lfi;j;k þ x1j Lfi;j;k þ x2j Lfi;j;k

(5)

Finally, the binary and ternary interaction parameters can be expressed a power series: n f Lm

¼ a þ bT þ cT lnðTÞ þ dT 2 þ eT 1 þ fT 3 þ gT 7 þ hT 9

(6)

Where a, b, c, d, e, f, g, and h are the excess Gibbs energy parameters. In most cases, only the first two terms of the above equation are used.

H. Singh et al. / Energy 91 (2015) 334e349

3.3. Calculation of Gibbs energies for stable and metastable binary and ternary phases To calculate the ternary phase diagrams, we first provide the compilation of binary thermodynamic parameters for the three systems, and then obtain the parameters for the ternary phases using the PARROT module in the ThermoCalc program. For the phase 4 (4 ¼ a, b, g, g
, L), 0 GfA and 0 GfB are the reference states of pure A, B, and C. A single reference phase is chosen for each component, and the pure component Gibbs energies of other phases are expressed as changes from this reference phase. We chose a for A, b for B, and a for C and set them equal to zero, as shown below. This assumption is made only for the calculation of metastable phases. 0 a GA

¼ 0;

0 b GB

0 a GC

¼ 0 and

¼0

(7)

The binary phase diagrams are calculated first, and the ternary diagram is predicted using the Gibbs energy equations of the binary phases. For the A-B (PEeNPG) system, the Gibbs energies of the other phases in terms of the reference phases can be represented as 0 g` GA

` D0 Ga/g A

D0 Ga/g A

¼

0 a GA

0 L GA

¼

0 a GA

0 g GB

¼ 0 GbB þ D0 Gb/g ¼ D0 Gb/g B B

0 L GB

D0 Gb/g A

þ

¼

0`





0 b GB þ MBa xB MBa þ RTðxB

Gam ¼ xB Gam ¼

339

¼

0 b GB

þ

þ

D0 Gb/L B

¼

¼

D0 Ga/g A

0`

þ

D0 GAa/L

To estimate the values of MAb , MBa ,, and so on, we assume that the a and b phases are ideal solutions. Therefore, the partial molar Gibbs free energies can be expressed as

  GbB ¼ 0 GbB þ RT ln xbB   GaB ¼ 0 GaB þ RT ln xaB

þ

0

(8)

0 a GB

(9)

0 a GB

(11)

¼

0 b GB

þ RTmax

0`

0

0 g GA

0`

¼ 0 GaA þ D0 Ga/g ¼ D0 Ga/g A A ZT

0`

DCPa/g

¼ DHTR  TDSTR þ

¼ RTmax

0

ZT dT  T

0`

DCPg /L dT

ZT T

TF

0 a GA

D0 GAa/L

0 L GA

¼

0 L GA

¼ DHTR  TDSTR þ

þ

¼

TTR

¼ 0 GbB þ MBa

MBg

DCPg/L dT T

xaBðmaxÞ

xbBðmaxÞ xaBðmaxÞ

A

(19)

1

  A ¼¼ 8:314  298  ln 0:899 0:601

0

¼ RTmax

0 0 1   xgBðmaxÞ @ A ¼¼ 8:314  462:7  ln 0:51 ln 0 0:36 xgBðmaxÞ

¼ 1340 J mol1 (13)

0`

þ

0`

D0 GAa/L

DCPa/g dT  T

ZT

(14)

(20b)

MAg

0

¼ RTmax

0 0 1   xgBðmaxÞ A ¼¼ 8:314  462:7  ln 0:64 ln@ g 0:49 xBðmaxÞ

¼ 1028 J mol1

0`

DCPa/g dT T

(15)

(20c)

TTR

(16)

Using the above, the Gibbs energy of the a phase can be written as

xbBðmaxÞ

A as 0 Gb ¼ 0; B

(20a)

00 `

DCPa/g dT T

Similar expressions can be obtained for the Gibbs energies of the stable phases of components B and C (not shown). The Gibbs energies for the metastable (m) phases in the binary systems are calculated using the stable phases, as performed in previous calculations by Chellappa et al. [24]. For example, for component B in the a-phase (BeC system), the following equation can be used to calculate the metastable phases: 0 a GB

xaBðmaxÞ 1

1

TF

D0 Ga/g A ZT

xbBðmaxÞ

¼ 997:68 J mol1

TTR

ZT

ln@

ln@

(12)

TTR

þ DHF  TDSF þ

¼ RTmax ln@

0 MBa

For component A, the Gibbs energies of the stable phases are 0 g GA

(18)

Where, GbB and GaB are the Gibbs energies of B in the b and a phases, respectively. At equilibrium, i.e., when GbB ¼ GaB , it is reasonable to assume that the temperature is that corresponding to maximum solubility. At T ¼ Tmax,

(10) D0 Gb/L B

ln xB þ xC ln xC Þ þ GEX;a (17)

0 D0 GAa/L

þ xC 0 GaC þ RTðxB ln xB þ xC ln xC Þ þ GEX;a

0 MCb

¼ RTmax ln@

xaCðmaxÞ `

xbCðmaxÞ

¼ 3403:78 J mol1

1

  A ¼ 8:314  298  ln 0:399 0:101 (20d)

The assumption that the a and b phases are ideal solutions is used only to describe the metastable pure Gibbs energies 0 GaB and 0 Gb . The nature of the non-ideality of the a phase can still be C expressed using a sub-regular solution model for GEX;a. The above calculations are performed for the binary system PGeNPG, where PG is denoted by C and NPG is denoted by B.

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4. Results and discussion 4.1. Calculated thermodynamic parameters of the NPGePGePE system Calculated and optimized phase diagrams for the three systems, namely, PG-ePE, PEeNPG, and PGeNPG, from this study are presented in this section. The PEePG binary system is composed of a liquid phase (L), FCC solid solution (g0 ), and tetragonal solid solution (a). There is complete solubility between the PEeNPG phases according to the Hume-Rothery rules. The optimized interaction parameters for these binary systems were established using the experimental data of Barrio et al. [9]. The interaction parameters for the PEePG system are as follows: GEX,a ¼ 0; GEX,L ¼ 0; GEX,g’ ¼ xCxB (72.3e522.7 (xB  xC)) The PEeNPG binary system is more complex and has five different phases: a liquid phase (L), a PE-rich FCC solid solution (g0 ), a NPG-rich FCC solid solution (g), a PE-rich tetragonal solid solution (a), and a NPG-rich monoclinic solid solution (b). PEeNPG contains one eutectic, one eutectoid, and one peritectic reaction. The binary phase diagram was optimized using a temperature-dependent Henrian solution model and experimental results from Chandra et al. [2,12,13,15]. The optimized parameters for PEeNPG are GEX,a ¼ xAxB (20, 000  40T); GEX,b ¼ xAxB (25,00010T); 0 GEX,g ¼ xAxB (1341); GEX,g ’ ¼ xAxB (1028); GEX,L ¼ xAxB (2471.8). The NPGePG system is simpler than the PEeNPG system and contains four phases with one eutectoid reaction: a NPG-rich monoclinic solid solution (b), a PG-rich tetragonal solid solution (a), a NPG-rich FCC solid solution (g), and a PG-rich FCC solid solution (g). The solution phases for the NPGePG binary system were modeled using regular and sub-regular solution models as well as experimental data from Barrio et al. [9], Hildebrand [25], and R. Chellappa and D. Chandra [24]. The NPGePG binary solution exhibits a demixing region in the solid state. The optimized parameters are GEX,b ¼ xBxC (16, 600  49.9T); GEX,a ¼ xBxC ((25, 30077.8T) 1495 (xC  xB)); GEX,g ¼ xBxC (13, 200 þ 36.2T); GEX,L ¼ xBxC (1940 þ 7.52T). Finally, the PEePGeNPG ternaries were calculated to obtain isothermal and pseudo-binary isopleth sections for the construction of the ternary phase diagram over the entire composition range, which is shown in the following section. The calculated ternary parameters are shown in Table 3. An example of a calculated isothermal ternary section at 450 K is plotted along with respective binaries to illustrate that phase boundaries on the binary edges of the ternary diagram coincide with the phases observed at 450 K of the binaries in Fig. 4. With regard to the binary phase equilibria, the following phases are observable: (aþb), (aþg), (aþg0 ), (bþg0 ), (Lþg), and (Lþg0 ). In the ternary system, one can expect similar binary phase equilibria, as well as three-phase equilibria in the tie triangles, such as (aþbþg), (aþbþg0 ), and (Lþaþg0 ), among others. These three-phase regions are found in the “tie triangle” in the ternary phase diagrams. Lowtemperature phases can equilibrate with the liquid phases in the ternary system. In the binary systems, only the g phases are in equilibrium with the liquid phases. However, in the ternary systems, the liquid phases can be in equilibrium with the lowtemperature phases, e.g., (aþL) and (bþL). 4.2. Validation of the thermodynamically modeled phase diagrams using experimentally determined parameters Isothermal sections of the PEePGeNPG ternary system were calculated at various temperatures [7] over the entire compositional range using the CALPHAD approach [15]. Then, several

pseudo-binary isopleths were constructed to compare the calculations with data from the experimental studies on the ternary system. The experimental data are particularly important for obtaining the enthalpies of continuous solid-state phase transitions in the PEePGeNPG ternary system, while the calculated isopleth gives phase boundaries and stable phases in a certain temperature range. Newly optimized parameters from this work were used to construct isothermal ternary diagrams and pseudo-binary isopleths. The thermal energies stored during continuous phase transitions in a ternary system are reported for the first time in this paper. Isothermal sections of the ternary phase diagrams were calculated at specific temperatures, and pseudo-binary isopleths were constructed because it is easier to interpret DSC/XRD data (where the x-axis is the localized composition range and the y-axis is the temperature) from these isopleths. We show the correspondence of these data with the calculated isopleths for the mid-range compositions, i.e., one composition per PE, PG, and NPG line, and then compile the thermodynamic data along with isopleths. We will first discuss the methodology and results from the samples that lie on the NPG line in detail, and then summarize the results for the samples along the PG and PE lines in following sections. 4.3. Comparison of the phase transition data from calculated isopleths with the DSC/XRD data for samples along the NPG line Thermodynamically calculated NPG-PG-PE ternary isotherms obtained at 298 K, 368 K, 423 K, and 458 K are shown in Fig. 5(a)e(d). In situ XRD data for ternary solid solutions of Sample No. 4 are shown in Fig. 5(e). A pseudo-binary isopleth is calculated on Line A-B, as shown in the isotherm of 298 K (Fig. 5(a)), which shows that the low-temperature a (BCT) þb (monoclinic) phases are stable at 298 K. Between 308 K and 383 K the aþg phases are stable. The data at 423 K show the presence of Bragg peaks from a single g (FCC) phase. At 448 K, in addition to the g phase, the pattern exhibits a broad hump corresponding to the liquid phase. The liquid phase finally appears at 458 K in the XRD pattern; however, the hump from the liquid phase is suppressed because the scan was downscaled to accommodate all of the data in a single plot. The DSC data are indexed using the calculated isopleth, which exhibits an onset temperature of ~308 K for the b/g phase transition, as shown in Fig. 5(f) for Sample No. 4. The transitions are summarized as follows: 295 K

300 K

417 K 425 K

426 K

a þ b ! a þ b þ g ! a þ gðCTÞ ! g ! L þ g ! *L þ g 0 430

K

0 470

K

þ g ! L þ g ! L  Sample No:4 * this transition cannot be interpreted from the DSC/XRD data and is therefore proposed from the calculated isopleth plots. The phase transitions determined by the in situ XRD patterns (Fig. 5(e)) match the data in the isopleth for Sample No. 4. Further increases in the temperature result in the formation of the Lþg phase and finally the liquid phase; however, the peak is not observed in its entirety because the experiment was terminated slightly below the complete melting temperature. Thermodynamic DSC data are plotted in Fig. 6(a) along the NPG line. The labeling of these DSC data comes partially from the experimental data and partially from the calculated isopleths for the three-phase regions. The (red) hatched areas represent broad endotherms, which we propose are CT transitions occurring due to compositional changes from low to high temperatures. These represent a non-isothermal solid-state energy storage process, not previously reported for these types of materials. Nearly all of the ternary samples in Fig. 6(a) exhibit these broad transitions, which

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Fig. 4. Calculated ternary phase diagram of NPG-PG-PE at 450 K showing equilibrium stable phases. Binary phase diagrams containing a line at 450 K that correlates well with the binaries in the ternary perimeter phases are superimposed.

Fig. 5. (a)e(d) CALPHAD-computed NPG-PG-PE ternary phase diagram isotherms from 298 to 450 K. The composition point of Sample No. 4 (20e20e60 mol %) is marked on each ternary diagram. The isopleth shown in (f) is along the Line AB in the ternary at 298 K. (e) XRD patterns of the ternary solid solutions of PE/PG/NPG for Sample No. 4 taken in the range of 298e458 K. The temperature scale of the DSC data corresponds to the scale of the isopleth shown in (f) between 0.4 PG and 0.6NPG.

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Fig. 6. (a) DSC data for Samples No. 11 to 1 show CT transitions marked by cross hatching in red along the NPG line in the Gibbs triangle. Phase designations determined from XRD data as well as from calculated isopleths are also marked. (b) The phase transformations of Sample No. 11 (PG/PE: 50/50) in (a) are also shown in the middle of the composition line (NPG line) of the calculated binary PE-PG phase diagram [14,15]. (c) The pseudo-binary isopleth of Sample No. 6 (NPG/PG/PE: 40/30/30), which is calculated from the ternary phase diagram, shows phase stabilities and transformations comparable to the DSC results of (a). (d) The isopleth for Sample No. 2 (NPG/PG/PE: 80/10/10). Note that the strong endotherm at ~500 K for sample No. 6 is due to bursting of the DSC pan. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

are useful for thermal energy storage. The thermodynamic properties of these transitions are summarized in Table 4. The DSC scan shown in Fig. 6(a) for Sample No. 11 (PG:PE 50:50), for which the NPG concentration is zero, exhibits a broad peak representing a continuous phase transition (red hatched area). A calculated pseudo-binary phase diagram of PGePE (from ternary data) is shown in Fig. 6(f). On the right-hand side, the DSC pattern shows a broad peak that matches the aþg0 CT region in the PG-PE phase diagram. Continuous transitions are also observed for the 40 and 80%NPG samples (Nos. 6 and 2), and are consistent with the isopleths shown in Fig. 6(c) and (d). The phase transitions in Samples No. 6 and 2 can be summarized as 298 K

300 K

412 K

0

416 K

a þ b ! a þ b þ g ! a þ gðCTÞ ! a þ g þ g ðCTÞ ! a 0 420

K

0 450

K

0 485

K

þ g ! g ! L þ g ! L  Sample No:6

295 K

305 K

398 K 432 K

a þ b ! a þ b þ g ! a þ gðCTÞ ! g ! L  Sample No:2 The CT enthalpies for Samples No. 6 and 2 are 33.14 and 12.6 J/g, respectively. The melting temperature decreases as the NPG content increases in the ternaries. 4.4. Development of the equations for the phase transition temperatures and enthalpies (NPG line) A summary of all of the thermodynamic phase properties obtained from the samples examined along the NPG line, particularly the enthalpies of continuous transitions, is given in Table 4. The CT transitions are shown in the red hatched areas of the DSC scans (Fig. 6(a)) and are also given in Table 4. Table 4 is organized in the order of increasing amount of NPG along the NPG line, starting from 0%NPG (Sample No. 11) and ending at 100%NPG (Sample No. 1; see Fig. 3). The transition temperatures

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Table 4 Phase transition temperatures and enthalpies for the compositions along the NPG line.

from two- to three-phase regions were not possible to interpret from our DSC and XRD patterns either due to the Bragg peak positions or because the transition temperatures were too close. A decreasing trend in the aþg CT energies from to 12.76 J/g was observed as the concentrations increased from 10 to 80%NPG. For example, the amount of NPG is fixed at 80% for Sample No. 2, and that of PE and PG is fixed at 10% each (Fig. 6(d)). However, the amount of each of the a or g phases varies with the temperature due to changes in the curvature of the solvus line between the (aþg) and g0 phases in the PG-rich region. Noting that the variation of the composition is very small (only 0.2 mol fraction of PE), the energy absorbed is also very small (12.76 J/g) in the aþ g CT from ~300 to 400 K. In Fig. 7(a), the transition temperature equations are developed for the various phase changes based on the data from samples with increasing NPG concentration from 0 to 100%NPG. The equations for any transition in the plots are shown in the accompanying table (middle of the figure). The low-temperature transitions of aþb/aþbþg are nearly independent of composition (based on data from five samples, as listed in Table 4), whereas the aþg/aþgþg0 and aþg/g transitions have higher phase transition temperatures and are composition dependent. The g0 /L transition temperatures decrease as the amount of NPG increases in

the ternaries. This decreasing trend of the liquid phase transition temperature can be justified based on the melting temperature of pure NPG, NPGMP ¼ 399 K, compared with those of the other two compounds, PGMP ¼ 471 K and PEMP ¼ 533 K. The enthalpies of the CT transitions, plotted in Fig. 7(b), are important for practical applications, such as energy storage devices. Plastic crystal powders may be encapsulated and used in renewable thermal energy storage systems. The energies associated with the transitions along the NPG line (Samples No. 11 to 1) are shown in Fig. 7(b). In estimating the enthalpies of these transitions, we grouped the aþg/aþgþg0 /aþg0 /g0 transitional enthalpies (between 30 and 40%NPG) together because we could not deconvolute their DSC peaks, particularly in the CT regions. The continuous transition regions of aþg CT transitions are high in energy (43.4 J/g) compared with those of aþg0 CT transitions (10.936 J/g). These enthalpies are well below the solid-state transitions of pure NPG or binary-phase PG/PE (50/50). The liquid phase energies (shown as blue circles) exhibit a hyperbolic shape with an energy minimum at ~50%NPG, which is lower than that of the solid-state transitions. The solideliquid phase transition in metals or inorganic solids typically has a higher latent heat. Therefore, one can infer that the solid-state transitions (Fig. 7(b)) have higher enthalpies than those of the liquid phase formation.

Fig. 7. (a) Analyses of the phase transition temperatures using selected binary/ternary compositions from DSC data for Samples No. 11 to 1 along the NPG line. The numbering is in reverse order because we start from the base of the triangle and finish at the apex. The equations for the variation in temperature as function of %NPG composition are also listed in Table 4. (b) The enthalpies of the continuous phase transitions along the NPG line.

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4.5. Comparison of the phase stabilities obtained from experimental data with isopleth data along the PG and PE lines 4.5.1. Phase transitions in samples along the PG line In a similar manner to that carried out for the NPG line, we now briefly summarize the phase transitions occurring along the PG line, i.e., Sample Nos. 23e33. Calculated ternary isotherms for Sample No. 7 at 308, 423, and 463 K are shown in Fig. 8(a)-(c), respectively. Fig. 8(d) displays the corresponding Gibbs triangle for reference. The calculated isopleth shows increasing PG concentrations from 0 to 0.7 mol fraction of PG (Line AB in Fig. 8a) in Fig. 8(e). In situ, capillary XRD analyses of the ternary Sample No. 7 showing structural phase transitions as a function of temperature from 298 K to 473 K is displayed in Fig. 8(f). The progression of thermal events in samples with increasing PG content starting from 0%PG (No. 33) to 100%PG (No. 23) are presented in the DSC scans in Fig. 9(a), in which the hatched regions mark the CT areas. The DSC plots for the binary (No. 33; PE/ NPG: 50/50) reveal four phase transitions, which were confirmed by Guinier XRD experimental data (Fig. 9(b)). The partial binary phase diagrams (Fig. 9(c)) indicate that there are two large CT regions, namely, the aþg and g0 þL regions. The DSC plot (Sample

No. 33) does not show a broad hump, which indicates continuous transitions. The reason for this result is that the g0 /a transition is exothermic in this two-phase region (PE/NPG: 50/50), based on the inverse lever rule of phase diagrams for this composition. In other words, the high-temperature phase transforms to the lowtemperature phase with the release of heat. This is an exception to the higher-concentration NPG compositions found in the PEeNPG phase diagram. Further details on this matter are the subject of separate manuscript currently in preparation. In the DSC scan, as the temperature is ramped up the exothermic continuous transition events are not observable, which is related to the amount of phase transformed as well. The DSC data for ternary Samples No. 32 and No. 28 (Fig. 9(a)) also exhibit CT transition regions that can be compared with the transitions shown in the isopleths in Figs. 9(d) and 8(e), respectively. These isopleths also show higher temperature transitions that will not be discussed here. All of these phase transitions and their temperatures are listed Table 5 as well as their associated enthalpies, particularly for CT transitions. Finally, phase transitions in the pure PG exhibit a first-order solid-state transition a/g0 at ~354 K, with the liquid phase appearing at ~471 K. These are summarized below for Sample No. 23:

Fig. 8. (a)e(c) Ternary isothermal sections generated at 413, 423, and 463 K for Sample No. 7 (the mid-point of the Gibbs triangle). (d) Gibbs triangle with sample numbers. (e) Isopleth with superimposed XRD data points. (f) XRD patterns of the ternary solutions taken in the range of 298e478 K. (g) DSC data for Sample No. 7. The temperature axis of the plot corresponds to that of the isopleth.

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Fig. 9. (a). DSC data for Samples No. 33 to 23 along the PG line (Fig. 2), with phase designations marked based on XRD data (purple dots) as well as from calculated isopleths. (b) Experimental [2] high-resolution Guinier XRD data taken at various phase transitions in the temperature range of 200e481 K, (c) Calculated PE-PG phase diagram [14,15] with the composition line of Sample No. 33 (NPG/PG/PE: 45/10/45). (d) Pseudo-binary isopleth of Sample No. 32 (NPG/PG/PE: 50/0/50) showing calculated phase stabilities. (e) Isopleth for Sample No. 28 (NPG/PG/PE: 25/50/25). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

~354 K ~471 K a / g0 / L DHNPG (a / g0 ) ¼ 192.7 J/g ¼ 46.02 cal/g ¼ 23.15 kJ/mol ¼ 5529 cal/mol

4.5.2. Phase transitions in samples along the PE line DSC data for Samples No. 22 to No. 12 are shown in Fig. 10(a). The DSC scan of the sample with 0%PE (No. 22; PG/NPG: 50/50) match that of Barrio's experimental PG-NPG phase diagram [9], shown in Fig. 10(b). Samples No. 20 and No. 16 show CT transitions, which can be correlated with the isopleth data shown in Fig. 10(c) and (d) because there are compositional changes leading to CT transitions in the aþg region (298e410 K). The phase transitions in pure PE are given below: ~461 K ~541 K a / g0 / L DHNPG (a / g0 ) ¼ 302.46 J/g ¼ 72.48 cal/g ¼ 41.73 kJ/mol ¼ 9868 cal/mol 4.6. Development of equations for the phase transition temperature and enthalpies (PG and PE lines) The energies associated with phase transitions along the PG line, Samples No. 33 to 23, reveal aþg CT transitions that increase in energy with the PG concentration from 10% to 50%PG. However, the

aþg/aþgþg0 /aþg0 /g0 transition energy decreases slightly with increasing PG concentration. The liquid phase exhibits a hyperbolic shape with increasing PG concentration and has a minimum at 50%PG. The plots and equations of the phase transition temperatures and enthalpies for the PG line are shown in Fig. 10. The energies associated with the phase transitions along the PE line, i.e., Samples No. 22 to No. 12, show aþg/aþgþg0 /aþg0 /g0 CT transitions that increase in energy with the PE composition from 40 to 80%PE (Fig. 11). The liquid phase behavior was rather different from the other ternary samples, showing low energies of liquid phase formation for the 60 and 70%PE compositions. 4.7. Complexities in the deconvolution of the high-temperature g or g0 peaks and the low-temperature a phase Bragg peaks in twophase regions The tetrahedral molecules in the low-temperature BCT a phase of PE are bonded in a nearly planar and layered manner via hydrogen bonds in the (002) plane and van der Waals bonds between the layered planes. When this crystal is heated to 461 K, there is sufficient energy to break the intermolecular OeH…O bonds in the structure, resulting in an orientationally disordered structure [17]. The rearrangement and rotation of the OeH…O bonds in the high-temperature structure leads to indeterminate positions of the O and H atoms in these crystals. Only one or two

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Table 5 Phase transition temperatures and enthalpies for the compositions along the PG and PE lines.

characteristic peaks of the FCC-HT structure, g(111) (strong) and g(200) (extremely weak), can be observed, whereas the remainder of the Bragg peaks cannot be observed due to orientational disorder (OD). One more class of this type of material exists, which is an amine derivative. The high-temperature crystal structure of this amine is BCC, and the XRD patterns exhibit only g(110) (strong) and g(200) (extremely weak) Bragg peaks. However, the g(111) and g(110) phase Bragg peaks are in close angular range to those of the major low-temperature a phase, and thus, high-resolution XRD instruments are necessary to observe the former. Thus, the X-ray results obtained from our position-sensitive detector can only positively identify the g(111) peak and a weak g(200) phase peak for a single-phase sample. To illustrate the complexity of analyzing the XRD pattern, we used a high-resolution Seeman Bohlin focusing Guinier camera with a high-temperature attachment [2] and obtained in situ powder film patterns (Fig. 9(b)) by increasing the temperature of the NPG/PE: 50/50 sample (No. 33) from 290 K to 481 K. We observed 13 patterns at different temperatures and estimate a maximum of ±5 K error in the temperature. The g(111) peak overlaps with the a(101) in the aþg region. The lattice of the OD cubic phase expands relatively more than that of the lowtemperature a phase in this temperature range; therefore, the Bragg peaks of the g phase shift toward lower angles, whereas the a phase peaks do not shift significantly. Even in the case of the Guinier patterns, one can see the overlapping of the OD g(111)

phase peak between 322 K and 391 K. Returning to our standard in situ X-ray diffractometer pattern shown in Fig. 8(b), there is overlap of the a and g phase Bragg peaks in the two phase regions, and thus, it is difficult to isolate the g phase peaks. We were able to interpret these diffraction patterns by using our previous experience with high-resolution Guinier film. 5. Summary and conclusions Pure, tetrahederally configured polyalcohols with orientational disorder exhibit higher solidesolid phase transitional entropies/ enthalpies compared with their solideliquid transitions. Ternary systems also follow the phase change rules of Timmermans and Richard. In this study, we observed energetic continuous solid-state phase CT transitions in ternary polyalcohol systems. The binary or ternary polyalcohol orientationally disordered crystals are able to store energy in this manner due to the unique nature of the rotation/oscillation of OeH…O bonds in these molecules. Computed thermodynamic data of complex phase transitions taking place in ternary samples have been verified experimentally for the first time for these types of materials, and there is a remarkable agreement between the calculated and experimentally determined parameters. DSC and in situ XRD data of ~35 samples of different compositions revealed the structural transitions in these systems. Due to the superposition of the Bragg peaks of the orientationally disordered g phase and a or b phases in the XRD patterns, their

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Fig. 10. (a) DSC data for Samples No. 22 to 12 along the PE line with phase designations marked based on XRD data and calculated isopleths. (b) Calculated phase diagram [14,15] of NPG-PG showing the line of Sample No. 22 (PG/NPG: 50/50). (c) Pseudo-binary isopleth obtained from the ternary of NPG/PG/PE: 40/40/20 (Sample No. 20) showing calculated phase stabilities as function of temperature. (d) Isopleth of Sample No. 16 (NPG/PG/PE:20/20/60).

deconvolution is not possible for the three-phase (tie triangle) region. In this paper, we have reported on novel CT transitions in plastic crystal materials. These materials may be significant for thermal energy storage in ternary polyalcohol solid solutions and may see use in applications such as concentrated solar energies as a secondary storage system. In these systems, energy is generally stored in a range of temperatures in addition to the first-order transitions that take place a constant temperature. The novelty of these orientationally disordered molecular crystals is their potential for energy storage in renewable energy systems. Because the energy requirements vary depending on the application, a variety of materials with different phase transformation temperatures and energies are needed. Several new thermal energy storage materials have been developed that store heat in the two-phase regions of these crystals. Several two-phase continuous aþg transitions have been observed for the NPGePGeTRIS ternary system. For the samples along the NPG line with concentrations ranging from 0 to 80%NPG, the aþb/aþ b þg transition temperatures remain the same at

~298 K, whereas for aþg/aþgþg0 , there is a slight increase in the temperature as the NPG concentration is increased. For the other transitions, aþg/g, aþg0 /g0 , and g0 /L, the transition temperatures decrease with increasing NPG concentration. A sharp decrease in the enthalpies of the solid-state aþg or aþg CT transitions (from ~76 to ~13 J/g) was observed as the NPG concentration increased from 10 to 40%NPG. The solid-state transformational enthalpies for the aþgCT/aþgþg0 /aþg0 /g0 transitions decrease by ~22 J/g upon going from 10 to 40%NPG, and a further decrease for the CT transitions of aþgCT or aþg0 CT down to minimum of 12.76 J/g. In general, there is a decreasing trend in the enthalpies from 54.68 to 12.76 J/g as the NPG concentration increases from 10 to 80%NPG due to the nature of the isopleths and their compositional changes for different samples. The g0 or Lþg0 /L transitions exhibit a hyperbolic trough with a minimum at ~50%NPG. Along the PG line, as the PG concentration increases, the transition temperatures for a/aþg and aþb/aþbþg remain the same (~298 K), whereas those of aþg/aþgþg0 , aþg0 /g0 , and g0 /L decrease linearly (~500e475 K). The enthalpies for the

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Fig. 11. (a) Analyses of the phase transition temperatures using selected binary/ternary compositions from DSC data for Samples No. 50 to 24 along the PG line. The equations for the temperature dependence of the PG composition are also listed in the middle of Table 5. (b) Enthalpies of the continuous phase transitions and compositions along the PG line (Fig. 2). (c)e(d) Temperature and enthalpy curves for the compositions along the PE line (Samples No. 22-12).

compositions (10e80% PG) show a gradual increase up to ~50%PG followed by a small decrease (ranging from ~42 to ~54 J/g) for the solid-state phase transitions. In contrast, the g0 or Lþg0 /L transitions exhibit the opposite trend with a minimum at ~50% PG (from ~12 to 32 J/g). Along the PE line, as the PE concentration increases, the transition temperatures for aþb/aþbþg and aþg/aþgþg0 show a similar linear trend with a slight increase in transition temperatures (from ~298 to 302 K), whereas the aþg0 /g0 and g0 /L transitions display an increase in their phase transition temperatures. The enthalpy for the aþg/aþgþg0 /aþg0 /g0 transition exhibits an initial decrease from ~85 to ~55 J/g (20e40% PE), and then an increase to ~85 J/G when the concentration is increased from 40 to 80%PE. The liquid phase transition shows a sinusoidal type behavior (0e~40 J/g), which has not been previously observed. Acknowledgments The authors would like to gratefully acknowledge the financial support of the Intel Corporation for this study. Finally, D. Chandra wants to acknowledge all the graduate students work, and interactions with Intel Corporation scientists/engineers, and earlier work with Dave Benson, and (late) Dick Burrows of NREL, gratefully acknowledges Prof. Klaus Yvon, Uni. of Geneva, for his valuable comments on this manuscript. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2015.07.130.

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