Thermodynamic properties of Sr-Sb alloys via emf measurements using solid CaF2-SrF2 electrolyte

Electrochimica Acta 305 (2019) 547e554

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Thermodynamic properties of Sr-Sb alloys via emf measurements using solid CaF2-SrF2 electrolyte Nathan D. Smith, Nicole Orabona, Timothy Lichtenstein, Jarrod Gesualdi, Thomas P. Nigl, Hojong Kim* Materials Science and Engineering, The Pennsylvania State University, 406 Steidle Building, University Park, PA, 16802, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 January 2019 Received in revised form 28 February 2019 Accepted 28 February 2019 Available online 2 March 2019

The thermodynamic properties of Sr-Sb alloys were determined by electromotive force (emf) measurements to understand the solution and phase behavior of Sr in Sb. A Sr(s) j CaF2-SrF2 j Sr(in Sb) electrochemical cell was used to measure emf values at 833e1113 K for Sr mole fractions over xSr ¼ 0.03 e0.84. The activity of Sr in liquid Sb was as low as 6.9  1013 at 973 K and xSr ¼ 0.03, implying strong chemical interactions. Six intermetallic compounds were confirmed by X-ray diffraction (XRD): SrSb2, Sr2Sb3, Sr11Sb10, Sr16Sb11, Sr5Sb3, and Sr2Sb. Phase transition temperatures were verified by differential scanning calorimetry (DSC) for xSr ¼ 0.03e0.48. Integrating the thermodynamic properties of the Sr-Sb system from emf, XRD, and DSC measurements, three characteristic transition temperatures were newly defined and an experimentally-determined Sr-Sb phase diagram was constructed up to xSr ¼ 0.50. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Sr-Sb alloys Emf method Sr-Sb phase diagram Thermodynamic properties

1. Introduction Electronegative liquid metals (e.g., Sb and Bi) have been shown to exhibit strong atomic interactions with electropositive alkalineearth elements (Sr and Ba) via electromotive force (emf) measurements of their binary alloys, including the Sr-Bi, Ba-Bi, and BaSb systems [1e3]. Such strong interactions provide these liquid metals with the capability to separate alkaline-earth ions (Sr2þ and Ba2þ) from molten salt solutions electrochemically. For example, liquid Bi metal was demonstrated to deposit Sr and Ba from LiClKCl-SrCl2-BaCl2 solutions at 500  C during cathodic discharge, even though the alkaline-earth ions are typically more stable than other constituent alkali ions (Liþ and Kþ) and would not conventionally be reduced [4]. In practice, the unique separation capability of liquid Bi provides a method to purify molten salts (e.g., LiCl-KCl) by removing alkaline-earth fission products, and might enable the reuse of the salts in an electrorefiner where used nuclear fuels are processed for recycling uranium metal [5,6]. The comparison of the thermodynamic properties of Ba-Sb and Ba-Bi indicates that Ba exhibits stronger atomic interactions (i.e.,

* Corresponding author. E-mail addresses: [email protected] (N.D. Smith), [email protected] (N. Orabona), [email protected] (T. Lichtenstein), [email protected] (J. Gesualdi), [email protected] (T.P. Nigl), [email protected] (H. Kim). https://doi.org/10.1016/j.electacta.2019.02.124 0013-4686/© 2019 Elsevier Ltd. All rights reserved.

lower activity) in liquid Sb than in liquid Bi [2,3]. Assuming a similar trend is found for the Sr-Sb and Sr-Bi systems, liquid Sb can potentially enhance the separation capability for both Sr and Ba species beyond liquid Bi. Understanding fundamental thermodynamic properties is essential in the development of superior electrode materials with an enhanced chemical selectivity; however, thermochemical properties of the Sr-Sb system (e.g., activity) are not available in the literature. Vakhobov et al. [7] determined phase transition temperatures of Sr-Sb alloys using differential thermal analysis and proposed a binary phase diagram by incorporating the results from Shukarev et al. [8]. However, their work included incompatible intermetallic compounds (SrSb3, SrSb, Sr3Sb2) that contradict existing crystal structure databases. To elucidate the strength of chemical interactions in the Sr-Sb system and the relevant phase behavior, this work investigated the thermochemical properties of Sr-Sb alloys via emf measurements at 833e1113 K over a wide range of Sr mole fractions (xSr ¼ 0.03e0.84). Emf measurements directly determine partial molar Gibbs energies of alloy electrodes (the Nernst equation) using a galvanic cell with no external current flowing, and have been widely employed in thermodynamic studies of materials [9,10]. These emf measurements were complemented with thermal and structural characterization to determine thermodynamic properties of Sr-Sb alloys, including the activity, partial molar quantities (chemical potential, entropy, and enthalpy) of Sr in Sb, as well as

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phase transition reactions in the binary Sr-Sb system. 1.1. Electrochemical cell for emf measurements of Sr-Sb alloys

Then, the emf values of Sr-Sb alloys (Ecell) relative to pure Sr(s) can be determined by adding the measured cell potential (EI) and the pre-determined reference potential (EII):

The electrochemical cell for emf measurements of Sr-Sb alloys can described as:

RT Ecell ¼ EI þ EII ¼  lnðaSr Þ: 2F

Sr(s) j CaF2-SrF2 j Sr(in Sb)

(1)

where pure Sr(s) serves as the reference electrode (RE) and each SrSb alloy at a given mole fraction serves as a working electrode (WE). Solid-state CaF2 (97 mol%) was used as the base electrolyte due to its high ionic conductivity (i.e., 1.5  103 S cm1 at 1073 K) and stability over a broad range of temperatures [11,12], with SrF2 (3 mol%) added as the electroactive species. For this cell, the half reactions are: WE: SrF2 þ 2ee ¼ Sr(in Sb) þ 2Fe

(2)

RE: SrF2 þ 2ee ¼ Sr(s) þ 2F

(3)

and the overall cell reaction is: Sr(s) ¼ Sr(in Sb).

(4)

Then, the change in partial molar Gibbs energy of the cell reaction is given by:

DGSr ¼ GSrðin SbÞ  G0Sr ¼ RT lnðaSrðin SbÞ Þ;

(5)

where GSrðin SbÞ is the partial molar Gibbs energy of Sr in Sb, G0Sr is the standard chemical potential of pure Sr(s), R is the universal gas constant, T is the absolute temperature, and aSr(in Sb) is the activity of Sr in Sb, moving forward referred to as aSr. By applying the Nernst equation, the emf of the cell (Ecell) is expressed as:

DGSr

Ecell ¼ 

2F

RT ¼  lnðaSr Þ; 2F

(6)

where F is the Faraday constant. In this study, a less reactive Sr-Bi alloy (xSr ¼ 0.10) was employed as the RE for reliable emf measurements of Sr-Sb alloys, instead of pure Sr which rapidly degraded the electrolyte and the electrodes due to its high reactivity at elevated temperatures. Using the Sr-Bi RE, this electrochemical cell (I) and the cell potential (EI) are:

I : Sr­BiðxSr ¼ 0:10ÞjCaF2  SrF2 jSrðin SbÞ; ! RT aSr EI ¼  ln * 2F aSrðin BiÞ

(7)

where a*Srðin BiÞ is the activity of Sr in Bi at xSr ¼ 0.10. The cell potential of this Sr-Bi alloy (EII) was previously determined relative to pure Sr(s) at 754e1010 K using the following electrochemical cell (II) [1]:

  II : SrðsÞ CaF2  SrF2  Sr­Bi ðxSr ¼ 0:10Þ;  RT  EII ¼  ln a*Srðin BiÞ 2F

(8)

and exhibited a linear variation as a function of temperature according to:

EII ¼ 6:9  105 T þ 0:922 ½V:

(10)

(9)

2. Experimental 2.1. Electrochemical cell components and assembly The solid CaF2-SrF2 (97e3 mol%) electrolyte was prepared by ball-milling 350 g of high-purity CaF2 (Alfa Aesar, Stock No. 11055), 17.4 g of high-purity SrF2 (Sigma-Aldrich, Stock No. 450030), and 25 g of polyvinyl alcohol binder (Sigma-Aldrich, Stock No. 341584) in isopropanol for 24 h. The mixture was dried in air for 24 h and approximately 130 g of powder was taken and uniaxially pressed at 30 MPa into a pellet (75 mm  17 mm in diameter and thickness). Seven wells (each with 11.2 mm  12 mm in diameter and depth) were drilled into the pellet with one well in the center and six wells evenly spaced 25.4 mm away from the center (Fig. 1). Similarly, electrolyte caps (19 mm  10 mm in diameter and height) were fabricated from 4 g of the mixture with a 1.1 mm hole drilled through the center. These green pellets were fired in air at 393 K for 12 h to remove moisture, 823 K for 12 h to burn away the binder, and 1273 K for 3 h to sinter. Sr-Sb alloys at specific compositions were fabricated from Sb shot (Alfa Aesar, Stock No. 11348) and Sr ingot (Sigma-Aldrich, Stock No. 343730) using an arc melter (MAM-1, Edmund Bühler GmbH) under argon atmosphere. The Sr-Bi alloy (xSr ¼ 0.10) for the RE was fabricated in the same manner from Sr ingot and Bi pieces (SigmaAldrich, Stock No. 556130). Inductively coupled plasma-atomic emission spectroscopy (ICP-AES, Perkin-Elmer Optima 5300DV) was used to verify the compositions of the arc-melted Sr-Sb alloys with a maximum of 4% error of the measured value (Table 1). As xSr increased, so did the discrepancy between the actual composition and the weighed composition, likely as a result of increased Sr vaporization during the arc melting process. The alloy electrodes were machined into a cylindrical shape (10 mm  7 mm in diameter and thickness) with a centering hole drilled partway through for the tungsten electrical lead. Final assembly of the electrochemical cell was performed in a glovebox under an inert argon environment (O2 < 0.5 ppm) to mitigate the rapid oxidation of the electrodes. The CaF2-SrF2 electrolyte was placed in an alumina crucible (8.2 cm diameter  3.0 cm height). The tungsten wires (1 mm diameter  46 cm length) were insulated with mullite tubes (0.64 cm outer diameter  30.5 cm length) and inserted through the stainless steel test chamber (identical to the design in Ref. [1]), through the CaF2-SrF2 caps, and into the electrodes. The electrolyte caps were installed to minimize the cross-contamination of electrodes through vapor-phase transport during the measurements at elevated temperatures. The test chamber was then sealed, removed from the glovebox, loaded into a crucible furnace, and evacuated to ~1 Pa. The test chamber was heated at 373 K for 12 h, at 543 K for 12 h under vacuum to remove residual moisture and oxygen, purged three times with high purity argon, and finally heated to 1023 K under flowing argon (~10 mL min1) to melt the electrodes for establishment of electrical contact between each electrode, the tungsten wire, and the electrolyte. The cell temperature was measured using a thermocouple (ASTM type-K) located at the center of the electrolyte, and a thermocouple data acquisition system (NI 9211, National Instruments).

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Fig. 1. Schematic (left) and picture (right) of the experimental set-up for emf measurements, comprised of Sr-Sb WEs and Sr-Bi RE at xSr(in Bi) ¼ 0.10 in solid CaF2-SrF2 (97-3 mol%) electrolyte. Table 1 Strontium mole fractions (xSr) of the Sr-Sb alloys used as WEs for emf measurements, as-weighed values and measured values by ICP-AES. Mole fraction, xSr weighed

measured

0.03 0.05 0.08 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.90

0.03 0.04 0.07 0.09 0.14 0.20 0.23 0.30 0.33 0.38 0.43 0.48 0.52 0.57 0.60 0.62 0.69 0.84

facilitate the identification of crystalline phase peaks of Sr-Sb alloys. Differential scanning calorimetry (DSC) was performed using a thermal analyzer (Netzsch Instruments, STA 449 F3 Jupiter) to detect phase transition temperatures of Sr-Sb alloys. About 20e50 mg of each annealed alloy sample was placed in the alumina crucible with a thin tungsten foil interlayer (4.8 mm diameter  0.1 mm thickness) as a reaction barrier between the Sr-Sb alloy and alumina crucible. Thermal analyses were conducted at multiple scan rates of 5e20 K min1 and the phase transition temperature was determined by extrapolating the onset/endpoint temperatures at various scan rates during the heating cycle to 0 K min1 [13]. In determining the liquidus temperature, the endpoint temperature was used in place of onset temperature as the endpoint represents the termination of the liquidus transition during the heating cycle. The Sr-Sb alloys with xSr > 0.20 were found to damage platinum parts of DSC sensor; therefore, a small graphite cap (~5 mm diameter  2 mm height) was placed over samples and only the highest scan rate (20 K min1) was used to protect the instrument. In these cases, liquidus transitions were approximated by the peak location instead of endpoint.

2.2. Emf measurements

3. Results and discussion

Emf measurements were performed by measuring the potential difference between the RE (Sr-Bi, xSr ¼ 0.10) and each WE sequentially in 180 s intervals during thermal cycles using a potentiostatgalvanostat (Autolab PGSTAT302N, Metrohm AG). Emf data were collected throughout a cooling and reheating cycle between 1113 K and 833 K in 25 K increments. The cell temperature was held constant at each increment for 1.5 h to reach thermal and electrochemical equilibria and ramped at ±5 K min1 between increments. In each increment, the last data approached a steady state thermally (dT/dt < 0.05 K s1) and electrochemically (dE/dt < 0.01 mV s1), and these data were considered for thermodynamic analyses.

3.1. Emf measurements of Sr-Sb alloys Using the electrochemical cell (Type I in Eq. (7)), the cell potentials (EI) of Sr-Sb alloys (xSr ¼ 0.03e0.84) were recorded over a temperature range of 833e1113 K, shown in Fig. 2 for xSr ¼ 0.20,

2.3. Structural and thermal analyses of Sr-Sb alloys Crystal structures of the Sr-Sb alloys were characterized using an X-ray diffractometer (XRD, PANalytical Empyrean). Samples were prepared by grinding Sr-Sb alloys into a fine powder using a mortar and pestle in an Ar-filled glovebox. For equilibrium phase determination, Sr-Sb alloys were annealed at ~15 K below their solidus temperatures for 24 h with the exception of xSr ¼ 0.43 which reacted with its stainless steel container during annealing. The powder samples were coated with mineral oil in order to minimize the oxidation of the alloys during the measurements. A broad amorphous background from mineral oil was present in XRD patterns at low angles (10 < 2q < 20 ) and was subtracted to

Fig. 2. Emf measurements as a function of time during the heating cycle using the electrochemical cell: Sr-Bi (xSr ¼ 0.10) j CaF2-SrF2(s) j Sr-Sb (xSr ¼ 0.20, 0.38, 0.43).

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0.38, and 0.43 during the heating cycle. The stability of the RE was maintained within a 5 mV potential difference between the identical REs during the cooling-heating cycle, and the WEs showed high stability over long periods of time (>3 h) (Fig. 2). The cell potentials of WEs approached steady-state values within the 1.5 h hold during the heating cycle, but continued to change during the cooling cycle, requiring a longer time for equilibration. For this reason, the cell potentials during the heating cycle were used for further analysis. Using Eq. (9), the emf values of Sr-Sb alloys versus pure Sr(s) were plotted as a function of temperature (Fig. 3). For mole fractions xSr ¼ 0.03e0.23, emf values changed linearly as a function of temperature in the liquid (L) state (Fig. 3a). At low temperatures, these mole fractions exhibited discontinuities in each slope (dEcell/ dT) due to first-order liquidus transition reactions: [L ¼ L þ Sb] for xSr ¼ 0.03e0.09 and [L ¼ L þ SrSb2] for xSr ¼ 0.14e0.23. Below the liquidus temperature in these two-phase regions, the emf values merged onto the same curve due to the invariant activity (Gibbs phase rule). Below ~860 K, two separate curves in the L þ S (solid) regions again merged into the same curve due to the eutectic transition reaction: [L ¼ Sb þ SrSb2], also suggesting the eutectic composition to be between xSr ¼ 0.09 and 0.14. However, the emf

values from various mole fractions were rather scattered below this eutectic transition possibly due to the sluggish solid-state diffusion toward equilibrium. Mole fraction xSr ¼ 0.38 exhibited a solidus transition at ~996 K [L þ Sr2Sb3 ¼ SrSb2 þ Sr2Sb3] (Fig. 3b). For high-melting mole fractions (xSr ¼ 0.43e0.84), the temperature-dependent emf traces were relatively simple with no observable phase transitions, possibly due to the absence of transition reactions or the sluggish solid-state transformation kinetics. In addition, the emf values of xSr ¼ 0.43e0.52 and xSr ¼ 0.60e0.62 overlapped each other, indicating the two-phase behavior of [Sr2Sb3 þ Sr11Sb10] and [Sr16Sb11 þ Sr5Sb3], respectively. The phase constituents of these alloys were determined based on XRD analyses (see Section 3.2). The highest mole fraction xSr ¼ 0.84 possesses two equilibrium phases of Sr2Sb and Sr(s), resulting in its emf values near zero due to the presence of pure Sr(s). Overall, the emf measurements of Sr-Sb alloys were internally consistent, indicated by the decrease in emf values with the increase in xSr. It is noted that the emf measurements for high mole fractions (xSr > 0.52) were less reliable during the thermal cycles with an instability up to 100 mV. Such erratic behavior is postulated to occur due to the combination of (i) increased reactivity with high Sr content, (ii) high melting temperatures of these alloys that can result in unstable electrical contact between the WE and the electrolyte, as well as (iii) the formation of non-equilibrium phases which are further discussed below.

3.2. Intermetallic compounds in the Sr-Sb system via XRD Prior to thermodynamic analyses, the intermetallic compounds in Sr-Sb alloys were examined using XRD to clarify the phase constituents in the emf measurements and to resolve existing conflicts in the literature. Shukarev et al. reported four intermetallic compounds (SrSb3, SrSb, Sr3Sb2, and Sr2Sb) [8] which were used for constructing the binary Sr-Sb phase diagrams by Vakhobov et al. [7] and Okamoto [14]. However, of these four compounds, only the Sr2Sb compound exists in the crystal structure database which also includes five additional compounds: SrSb2, Sr2Sb3, Sr11Sb10, Sr16Sb11, and Sr5Sb3 [15e24]. The XRD patterns of annealed Sr-Sb alloys (xSr ¼ 0.04e0.69) were in good agreement with the standard patterns of six reported crystal structures (Fig. 4), and the detected phases are summarized in Table 5 for each mole fraction. The presence of SrSb2 (xSr ¼ 0.33), in place of SrSb3 (xSr ¼ 0.25), also supports the emf results in Fig. 3a where the identical two-phase behavior (L þ SrSb2) is obvious for xSr ¼ 0.14e0.33. It is noted that higher mole fractions (xSr  0.38) often possessed more than two phases, indicating the presence of metastable, non-equilibrium phases even after annealing. In equilibrium, mole fractions of xSr ¼ 0.69 and xSr ¼ 0.84 possess two solid phases (Sr2Sb, Sr) and the emf traces would overlap each other; however, the measured emf traces were substantially different from each other (Fig. 3b) due to the formation of a metastable Sr5Sb3 compound in xSr ¼ 0.69 (Table 2). 3.3. Thermodynamic properties of Sr-Sb alloys The linear fits of Ecell vs. T were analyzed to calculate the changes in partial molar entropy ðDSSr Þ and enthalpy (DH Sr Þ using the Nernst and Gibbs-Helmholtz relations:

Ecell ¼  Fig. 3. Emf values of Sr-Sb alloys (Ecell) as a function of temperature vs. pure Sr(s) for (a) xSr ¼ 0.03e0.33 and (b) xSr ¼ 0.38e0.84.

DGSr 2F

¼

DHSr 2F

þT

DSSr 2F

(11)

N.D. Smith et al. / Electrochimica Acta 305 (2019) 547e554

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Fig. 4. XRD patterns for selected Sr-Sb alloys (a) xSr ¼ 0.04e0.52 and (b) xSr ¼ 0.57e0.69, with the reported XRD pattern denoted (*) [15e24].

Table 2 Crystal structures identified by XRD patterns at each mole fraction, where the equilibrium phases are marked in bold. xSr

Phases detected

0.04, 0.20 0.33 0.38 0.52 0.57 0.62 0.69

Sb, SrSb2 SrSb2 SrSb2, Sr2Sb3, Sr11Sb10 Sr2Sb3, Sr11Sb10 Sr11Sb10, Sr16Sb11, Sr5Sb3 (hex) Sr16Sb11, Sr5Sb3 (hex), Sr2Sb Sr5Sb3 (hex), Sr2Sb, Sr

linear fitting parameters are summarized in Table 3. For curved, non-linear behavior in Ecell vs. T, the data in the two-phase region were fit to the following general fitting equation [25,26]:

Ecell ¼ A þ BT þ CT lnðTÞ

(14)

where A, B, and C are fitting parameters, reported in Table 4. Using the Nernst equation in Eq. (6), the activity of Sr in Sb was calculated for each alloy at 923 K, 973 K, and 1073 K as well as the  E partial molar excess Gibbs energy GSr according to: E

DSSr

DH Sr

    vDGSr vEcell ¼ ¼ 2F vT vT P P . 1 0    v DGSr T A ¼ 2F vðEcell =TÞ : ¼ T vð1=TÞ vT P 2@

GSr ¼ RTðlnaSr  lnxSr Þ (12)

(13)

P

when Ecell vs. T is linear, DSSr and DH Sr are temperatureindependent and can be estimated from the slope and the intercept at 0 K, respectively. The calculated partial molar quantities and

(15)

The resulting values are listed in Table 5, and are depicted graphically as a function of xSr at 973 K with the intermetallic compounds detected by XRD (Fig. 5). At 973 K, the emf values decrease as xSr increases in the singlephase liquid, and remain constant in the two-phase regions due to invariant activity, with the exception of [Sr2Sb þ Sr] region due to the formation of a metastable phase at xSr ¼ 0.69 (Fig. 5a and b). The E

activity of Sr in Sb is as low as 1.1  1012 at xSr ¼ 0.04; GSr as low as 197 kJ mol1, both indicating stronger chemical interactions of Sr with liquid Sb than liquid Bi (i.e., aSr(in

Bi) ¼ 1.9  10

11

E

, GSr

Table 3 Linear fits to emf (Ecell) versus temperature (T) for xSr ¼ 0.03e0.84, and the changes in partial molar entropy (DSSr ) and enthalpy (DHSr ). The standard errors in the parentheses represent the 95% confidence interval of the fit. xSr

T (K)

vEcell/vT (mV K1)

v(Ecell/T)/v(1/T) (mV)

DSSr (J mol1 K1)

DHSr (kJ mol1)

adj-R2

0.03 0.04 0.07 0.09 0.14 0.20

886e1090 888e1092 908e1087 882e1089 882e1087 860e933 933e1089 928e979 979e1082 904e1082 877e1082 833e983 858e933 933e1088 836e934 934e1086 858e1111 859e1113

174 (4) 142 (2) 73 (3) 66 (2) 3 (4) 435 (9) 6 (1) 484 (21) 38 (2) 543 (16) 573 (14) 11 (1) 318 (37) 157 (4) 305 (7) 129 (6) 378 (14) 33 (21)

1006 (4) 1017 (2) 1057 (3) 1052 (2) 1076 (4) 1462 (8) 1062 (1) 1510 (20) 1074 (2) 1565 (16) 1596 (14) 1001 (0) 1246 (34) 1096 (4) 1230 (6) 1066 (6) 1248 (14) 21 (21)

33.6 27.3 14.2 12.7 0.5 83.9 1.1 93.4 7.4 104.8 110.6 2.1 61.3 30.3 58.8 25.0 72.8 6.4

194.1 196.2 203.9 202.9 207.6 282.1 205.0 291.4 207.3 302.0 308.0 193.1 240.4 211.6 237.4 205.7 240.8 4.0

0.996 0.999 0.986 0.994 0.073 0.999 0.764 0.996 0.987 0.994 0.995 0.981 0.960 0.996 0.998 0.989 0.987 0.136

0.23 0.30 0.33 0.38 0.43 0.52 0.57 0.84

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Table 4 Non-linear fits of the temperature dependence of emf data in two-phase region. The data were fit to Ecell ¼ A þ BT þ CT lnðTÞ. The standard errors in the parentheses represent the 95% confidence interval of the fit. xSr

two-phase region

T (K)

A

B

C

0.03e0.09 0.38 0.60 0.62

L þ Sb L þ Sr2Sb3 Sr16Sb11 þ Sr5Sb3 Sr16Sb11 þ Sr5Sb3

860e888 984e1137 857e1111 857e1111

140.9 (143.2) 3.40 (0.30) 4.80 (0.34) 3.52 (0.29)

1.256 (1.275) 0.037 (0.002) 0.029 (0.003) 0.019 (0.007)

0.16 (0.16) 0.0047 (0.0003) 0.0036 (0.0003) 0.0023 (0.0003)

Table 5 Measured emf, natural log of the activity of Sr in Sb, and the excess partial molar Gibbs energy for mole fractions xSr ¼ 0.03 to xSr ¼ 0.84. xSr

0.03 0.04 0.07 0.09 0.14 0.20 0.23 0.30 0.33 0.38 0.43 0.52 0.57 0.60 0.62 0.69 0.84

Ecell (V)

Bi) ¼ 0.05).

3.4. Thermal analyses and Sr-Sb phase diagram

E

GSr (kJ mol1)

ln aSr

¼ 176 kJ mol1 at xSr(in

923 K

973 K

1073 K

923 K

973 K

1073 K

923 K

973 K

1073 K

1.167 1.147 1.124 1.112 1.078 1.061 1.063 1.064 1.067 1.011 0.953 0.949 0.899 0.874 0.878 0.819 0.010

1.175 1.154 1.128 1.116 1.079 1.057 1.039 1.036 1.038 1.012 0.944 0.940 0.880 0.845 0.853 0.807 0.012

1.193 1.168 1.135 1.122 1.079 1.056 1.033 0.982 0.981 0.945 0.928 0.927 0.843 0.812 0.820 0.784 0.015

29.3 28.8 28.3 28.0 27.1 26.7 26.7 26.7 26.8 25.4 24.0 23.9 22.6 22.0 22.1 20.6 0.3

28.0 27.5 26.9 26.6 25.7 25.2 24.8 24.7 24.8 24.1 22.5 22.4 21.0 20.2 20.4 19.3 0.3

25.8 25.3 24.6 24.3 23.3 22.8 22.3 21.2 21.2 20.5 20.1 20.1 18.2 17.6 17.7 17.0 0.3

197 197 197 196 193 192 194 196 197 188 177 178 169 165 166 155 1

197 197 196 196 192 191 189 190 191 187 175 176 165 159 161 153 1

197 197 196 195 191 189 186 179 179 174 172 173 158 152 154 148 1

For selected mole fractions (xSr ¼ 0.03e0.48), thermal analyses from continuous heating cycles were conducted to complement the transition temperatures detected in emf measurements with 25 K increments. Representative thermograms are presented in Fig. 6 at a heating rate of 20 K min1, demonstrating three characteristic transitions (IeIII) and liquidus transitions (*) summarized in Table 6 for each mole fraction. Based on the emf, DSC, and XRD measurements, the first transition reaction was identified as the eutectic reaction [I: L ¼ Sb þ SrSb2] at 845 K; the second as the peritectic reaction [II: L þ Sr2Sb3 ¼ SrSb2] at 996 K, correcting the incompatible transitions of [I: L ¼ Sb þ SrSb3] at 873 K and [II: L þ SrSb ¼ SrSb3] at 953 K, respectively [7]. The DSC measurements also identified an additional transition (III) at 1133 K, which could be a eutectic transition [L ¼ Sr2Sb3 þ Sr11Sb10]. Transition temperatures and the relevant phase behavior were translated into the experimentally-determined Sr-Sb phase diagram (Fig. 7). Here, the transition temperatures from emf

E

Fig. 5. (a) Measured emf values (Ecell), (b) natural log of activity (ln aSr), and (c) excess partial molar Gibbs energy (GSr ), as a function of xSr at 973 K.

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measurements were also estimated based on the discontinuities in the slope (dEcell/dT) and agreed within 15 K, indicating reliable emf measurements in this study. 4. Conclusions

Fig. 6. Thermogram for Sr-Sb alloys xSr ¼ 0.03e0.48 at a scan rate of 20 K min1, where characteristic transition reactions are marked by Roman numerals (IeIII) and liquidus transitions by *. Table 6 Summary of the transition temperatures (Ttrs) from DSC measurements and proposed transition reactions (IeIII). xSr

Ttrs (K)

0.03 0.04 0.07 0.09 0.14 0.20 0.23 0.30 0.33 0.38 0.43 0.48

847 848 845 847 844 847 844 843 843 e e e

reaction (type) Ttrs (K)

L ¼ Sb þ SrSb2 (eutectic) 845 (3)

I (1) (1) (2) (1) (1) (1)

II

III

liquidus

e e e e e e e e 1000 995 993 e

e e e e e e e e e e 1131 1134

901 (2) 896 (1) 880 (1) 872 (3) e 915 (7) 977 1026 1077 1164 e e

L þ Sr2Sb3 ¼ SrSb2 (peritectic) 996 (4)

L ¼ Sr2Sb3 þ Sr11Sb10 (eutectic) 1133 (2)

Fig. 7. Experimentally-determined Sr-Sb phase diagram up to xSr ¼ 0.50, based upon emf, DSC, and XRD measurements.

This study has determined the thermochemical properties of the Sr-Sb system (xSr ¼ 0.03e0.84), including activities, partial molar entropies, partial molar enthalpies, and excess partial molar Gibbs energies at 833e1113 K. Phase relations were corroborated by XRD and DSC measurements, verifying six intermetallic compounds: SrSb2, Sr2Sb3, Sr11Sb10, Sr16Sb11, Sr5Sb3, and Sr2Sb, and resulting in an experimentally-determined Sr-Sb phase diagram up to xSr ¼ 0.50. For more complete understanding of the Sr-Sb system at higher mole fractions, additional work is necessary, including computational thermodynamic modeling over the entire range of Sr compositions. The atomic interaction of Sr with liquid Sb was found to be stronger than that with liquid Bi, based on the lower Sr activity at 1.1  1012 in liquid Sb (xSr ¼ 0.04) compared to the activity in Bi at 1.9  1011 (xSr ¼ 0.05) at 973 K. The stronger interactions of liquid Sb for both Sr and Ba than liquid Bi suggest the possibility for enhanced separation capability of liquid Sb for both Sr and Ba from molten salt solutions. Author contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Acknowledgements This work was supported by the US Department of Energy, Office of Nuclear Energy’s Nuclear Engineering University Program (Award No. DE-NE0008425) and Integrated University Program Graduate Fellowship (Award No. DE-NE0000113). References [1] N.D. Smith, T. Lichtenstein, J. Gesualdi, K. Kumar, H. Kim, Electrochimica acta thermodynamic properties of strontium-bismuth alloys determined by electromotive force measurements, Electrochim. Acta 225 (2017) 584e591, https://doi.org/10.1016/j.electacta.2016.12.051. [2] T. Lichtenstein, N.D. Smith, J. Gesualdi, K. Kumar, H. Kim, Thermodynamic properties of Barium-Bismuth alloys determined by emf measurements, Electrochim. Acta 228 (2017) 628e635, https://doi.org/10.1016/ j.electacta.2016.12.141. [3] T. Lichtenstein, J. Gesualdi, T.P. Nigl, C.T. Yu, H. Kim, Thermodynamic properties of barium-antimony alloys determined by emf measurements, Electrochim. Acta 251 (2017) 203e211. [4] T. Lichtenstein, T.P. Nigl, N.D. Smith, H. Kim, Electrochimica Acta Electrochemical deposition of alkaline-earth elements ( Sr and Ba ) from LiCl-KClSrCl2-BaCl2 solution using a liquid bismuth electrode, Electrochim. Acta 281 (2018) 810e815, https://doi.org/10.1016/j.electacta.2018.05.097. [5] J. Bruno, R.C. Ewing, Spent nuclear fuel, Elements (2006), https://doi.org/ 10.2113/gselements.2.6.343. [6] M.F. Simpson, Projected salt waste production from a commercial pyroprocessing facility, Sci. Technol. Nucl. Install. (2013) 945858, https://doi.org/ 10.1155/2013/945858. [7] A.V. Vakhobov, Z.U. Niyazova, B.N. Polev, Phase diagram of the system Sr-Sb, Inorg. Mater. 11 (1975) 306e307. [8] S.A. Shukarev, M.P. Morozova, K. Hou-yu, No title, Zh. Obshch. Khim. 27 (1957) 1737. [9] H. Ipser, A. Mikula, I. Katayama, Overview: the emf method as a source of experimental thermodynamic data, Calphad Comput. Coupling Phase Diagrams Thermochem. (2010), https://doi.org/10.1016/j.calphad.2010.05.001. [10] J.N. Pratt, Applications of solid electrolytes in thermodynamic studies of materials: a review, Metall. Trans. A 21 (1990) 1223e1250, https://doi.org/ 10.1007/BF02656541. [11] J. Delcet, A. Delgado-Brune, J.J. Egan, Coulometric titrations using CaF2 and BaF2 solid electrolytes to study alloy phases, in: Y.A. Chang, J.F. Smith (Eds.),

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