Enthalpy of mixing of liquid Li-Sb-Sn alloys

MOLLIQ-112036; No of Pages 11 Journal of Molecular Liquids xxx (xxxx) xxx

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Enthalpy of mixing of liquid Li-Sb-Sn alloys Patric Berger, Hans Flandorfer ⁎ Institute of Inorganic Chemistry – Functional Materials, Faculty of Chemistry, University of Vienna, Althanstraße 14, 1090 Vienna, Austria

a r t i c l e

i n f o

Article history: Received 3 July 2019 Received in revised form 3 October 2019 Accepted 29 October 2019 Available online xxxx Keywords: Li-Sb-Sn Drop calorimetry Enthalpy of mixing Liquid alloys

a b s t r a c t The partial and integral molar enthalpies of mixing of liquid Li-Sb-Sn alloys were determined by drop calorimetry at 879 K along ten sections xLi:xSb ≈ 2:3, xLi:xSb ≈ 3:7, xLi:xSn ≈ 1:1, xLi:xSn ≈ 3:5, xLi:xSn ≈ 1:3, xSb:xSn ≈ 4:1, xSb: xSn ≈ 13:7, xSb:xSn ≈ 1:1, xSb:xSn ≈ 1:3 and xSb:xSn ≈ 3:17. A check of enthalpy values at the crossing points of the ten sections proved high accuracy of the measurements. The behavior of the partial and integral enthalpy of mixing along these sections can be grouped into three types, depending on the starting binary systems. For the description of the integral enthalpy over the entire concentration range our experimental ternary data were fitted on the basis of an extended Redlich-Kister Muggianu model for substitutional solutions. Additionally, a comparison of these results to the extrapolation models of Muggianu and Toop is given. The entire system shows a strong exothermic behavior with a minimum of ΔmixH ≈ −65,000 J mol−1 in the binary Li\\Sb near to Li3Sb. From experimental ternary data the phase boundary of the liquid at 879 K was derived. It showed that high melting Li3Sb dominates the solidification behavior of the Li-Sb-Sn system. © 2018 Published by Elsevier B.V.

1. Introduction The intermetallic system Li-Sb-Sn is under consideration regarding Sb\\Sn intermetallic electrodes as anode materials for lithium ion batteries. Especially the non-stoichiometric binary compound SbxSn1-x has been in the focus of many investigations, e.g. [1–4] and shows relatively high rechargeable capacity of 600 mAh g−1 [1] compared to graphite (372 mAh g−1). It exhibits also a better cycling stability in comparison to pure Sb- or Sn-anodes which suffer from degradation by large volume changes upon lithiation/delithiation. SbSn alloys are formation type electrodes, since intermetallic compounds are formed upon lithiation. Sb and Sn are both active materials towards Li, thus, in this case Sb, as well as Sn, form stable intermetallic compounds [5,6]. Trifonova et al. [1] described based on XRD studies the phase formation reaction on lithiation of SbSn: (A) (B) (C) (D)

SnSb + 3 Li+ + 3e− ⇔ Li3Sb + Sn 5 Sn + 2 Li+ + 2 e− ⇔ Li2Sn5 Li2Sn5 + 3 Li+ + 3e− ⇔ 5 LiSn LiSn + x Li+ + x e− ⇔ Li1+xSn

In the first step (A) a fine grained Sn-matrix phase precipitates which acts as buffer of mechanical stress caused by volume changes mentioned above [2]. Usually, by repeated cycling of the electrode the Sn-matrix does not decompose completely but refines to even nanocrystalline texture. ⁎ Corresponding author. E-mail address: hans.fl[email protected] (H. Flandorfer).

In order to describe the theoretical thermodynamic lithiation path as a basic model of future in-situ XRD and kinetic investigations, the knowledge of the Li-Sb-Sn phase diagram is crucial. We currently investigate this phase diagram experimentally at higher temperatures. Batteries, however, usually operate at ambient temperature but very slow solid state diffusion at such temperatures prevents the preparation of equilibrium samples. Phase relations at operation temperatures of Liion batteries can only be obtained by CALPHAD calculation based on extrapolation of high temperature data and thermochemical data like formation enthalpies, heat capacities and enthalpy of mixing. This work provides enthalpy of mixing data for the liquid phase in the ternary LiSb-Sn system at 879 K. 2. Literature review 2.1. Li-Sb The enthalpy of formation of Li\\Sb alloys was first measured in the end 30's by Kubaschewski and Seith [7] in the composition range of 0 b xLi b 0.6. They reported a minimum of ≈−36,000 J mol−1 at approximately 60 at.% Li, related to the formation of Li3Sb2. However, such a compound was never reported to exist in the Li\\Sb system. More information to this point can be found in [5,8]. Shchukarev et al. [9] determined the enthalpy of formation of Li3Sb applying acid calorimetry. Further thermodynamic data of the binary system Li\\Sb have been reported by Weppner and Huggins [10,11] (e.m.f. and coulometric titration), Wang et al. [12] (e.m.f. and coulometric titration), Nikitin et al. [13] (e.m.f.), and Kane et al. [14] (e.m.f.). By using the direct reaction calorimetric method, the enthalpies of formation of Li3Sb and Li2Sb were measured by Terlicka et al. [15] to be −70,030 ± 300 J mol−1 at 942 K

https://doi.org/10.1016/j.molliq.2019.112036 0167-7322/© 2018 Published by Elsevier B.V.

Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036

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and −66,700 ± 500 J mol−1 at 820 K, respectively. They also performed drop calorimetry to determine the mixing enthalpy of a few liquid Li\\Sb alloys in a temperature range between 820 K and 1024 K. Recently, Li and co-workers [8] comprehensively investigated the enthalpy of mixing in the liquid phase of the Li\\Sb system applying drop calorimetry at temperatures between 929 K and 1181 K. They found strongly exothermic mixing behavior with an estimated metastable minimum close to xLi = 0.75. Their results confirmed the one from Terlicka et al. [15] and did not show a significant temperature dependence of the enthalpy of mixing. Beutl et al. [16] determined the enthalpy of formation of Li3Sb to be ≈−70,000 J mol−1 and Li2Sb to be ≈−64,000 J mol−1, both at room temperature. The latest experimental phase diagram was published by Beutl et al. [5]. Thermodynamic assessments of the entire system were published by Li et al. [8] and Zhang et al. [17]. Both authors assumed a liquid associate “Li3Sb” for modelling of the liquid phase.

was reported by Sommer et al. [31]. The liquid phase in the binary Sb\\Sn system was described by Chen et al. [33] using a substitutional solution model, assuming temperature independency of the enthalpy of mixing. Their calculated enthalpies of mixing are in a fairly good agreement with the experimental results given by Witting and Gehring [29], Sommer et al. [31] and Azzaoui et al. [32]. Very recently Schmetterer et al. published a phase diagram work, including an extensive literature review [34] as well as a new phase diagram based on experimental data [35].

2.2. Li-Sn

All measurements were conducted at 879 K along ten sections with constant ratios: xLi:xSb ≈ 2:3, xLi:xSb ≈ 3:7, xLi:xSn ≈ 1:1, xLi:xSn ≈ 3:5, xLi:xSn ≈ 1:3, xSb:xSn ≈ 4:1, xSb:xSn ≈ 13:7, xSb:xSn ≈ 1:1, xSb:xSn ≈ 1:3 and xSb:xSn ≈ 3:17, as shown in Fig. 1. The Li-containing binary starting materials were synthesized by melting the pure components in boron nitride crucibles sealed under vacuum in silica glass using a muffle furnace at 923 K. The Sb\\Sn starting materials were weight and directly sealed under vacuum in silica glass, before melting them over a hydrogen flame. Homogenization was supported by soft shaking. For all measurements, a pure Li wire (Alfa Aesar, 3.2 mm, 99.8%, with oil coating) which was stored in a glovebox under Ar atmosphere (Ar 5.0; O2 b 1 ppm; H2O b 1 ppm), tin rods (Alfa Aesar, 99,9985) and Sb (Alfa Aesar, ingot, 99,999%) were used. The lithium wire was preliminary cleaned outside the glovebox in an ultrasonic bath in n-hexane. The solvent was removed under vacuum in the antechamber of the glovebox. Surface oxidation products at the lithium wire caused by reactions with air were mechanically scraped off before using. Sb was further purified by filtration of the liquid metal through quartz glass wool under vacuum. The calorimetric measurements were performed in a Calvet-type twin calorimeter with two thermopiles including N200 thermocouples each. To ensure isoperibolic conditions a wire wound resistance furnace with high heat capacity was used. A self-constructed auto-sampler with

Kubaschewski and Seith [7] measured the enthalpy of formation of Li\\Sn alloys in the late 1930's. Further thermodynamic studies of the binary system Li\\Sn were done in the early 80's by Wen and Huggins [18] where they performed coulometric titration and EMFmeasurements, respectively in the temperature range from 633 K to 863 K. They reported the existence of six intermediate phases and determined several thermodynamic properties. A few years later Moser and co-workers [19] also conducted EMF-measurements as well as drop calorimetry in a composition range of xLi = 0.01 to 0.5 and xLi = 0.87 to 0.99 between 691 K to 938 K. The molar integral mixing enthalpy curve (ΔmixH vs. xLi) exhibits a triangular shape with an extrapolated minimum of −40,000 J mol−1 close to xLi = 0.80. Later on Gasior et al. [20] postulated a new binary phase Li8Sn3 by means of an additional step in coulometric titration curve of Li into solid Li\\Sn alloys from xLi = 0.47 to xLi = 0.83 in the temperature range of 655–861 K. It has to be mentioned that such a phase could never be prepared or identified by XRD or thermal analysis. Gasior et al. [20] and Gasior and Moser [21] also carried out EMF-measurements in a concentration range of xLi = 0.025 to 0.725 as well as xLi = 0.910 to 0.954 at temperatures between 777 K and 975 K and published partial and integral thermodynamic properties. Yassin and Castanet [22] combined literature data of partial molar limiting enthalpies of mixing of lithium in tin and presented a slight temperature dependent behavior. The integral molar mixing enthalpy was further investigated calorimetrically by Fürtauer and co-workers [23] at 1073 K over the entire concentration range and at 773 K in a composition range of xLi = 0.0 to 0.63 and xLi = 0.92 to 1.0. They obtained a minimum of ≈ −37,000 J mol−1 at xSn = 0.20 at 1073 K and an extrapolated minimum of ≈ −33,000 J mol−1 at xSn = 0.33 for 773 K. Nevertheless, they ascribe the distinction of the minimum values rather to the lack of experimental data in this section at 773 K than by temperature dependence. By now, several assessments of the binary phase diagram based on experimental data and thermodynamic calculations were done by Sangster and Bale [24], Yin et al. [25], Du et al. [26] and Li et al. [6]. The latter authors postulated a liquid associate “Li4Sn” for modelling the liquid phase.

2.4. Li-Sb-Sn To the best knowledge of the authors by now no information to the enthalpy of mixing in the ternary Li-Sb-Sn system is available. 3. Experimental procedure

2.3. Sb-Sn The enthalpy of mixing of liquid Sb\\Sn alloys has been determined several times by calorimetric methods. Kawakami [27] was the first who did measurements at 1073 K. Later on, Kleppa [28] investigated the binary system in the tin-rich corner at 723 K and Wittig and Gehring [29] over the whole concentration range at 973 K. Literature data up to the early 70's were summarized in the work of Hultgren et al. [30]. Calorimetric studies were carried out later by Sommer et al. [31] in the temperature range of 783–1108 K and Azzaoui et al. [32] at 892 K and 913 K respectively. A slight temperature dependence of the enthalpy of mixing with a minimum of −1510 J mol−1 at xSn = 0.535 and 783 K

Fig. 1. Measured sections (A, B, C, D, E, F, G, H, I, J) and alloy compositions in the ternary system Li-Sb-Sn at 879 K. Dashed lines indicate the estimated liquidus. Gray stars show limiting liquidus concentrations for each section, also compare Table 2.

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a capacity of 30 drops was installed to execute drops automatically without any contamination of the atmosphere. In the case of lithium drops, the sample carrier was loaded inside a glovebox (Ar 5.0; O2 b 1 ppm; H2O b 1 ppm) and taken out shortly before the measurement. The whole equipment was controlled by a self-written software based on LabVIEW. Data evaluation was done using HIQ program (detailed description given by Flandorfer et al. [36]). To prevent oxidation all measurements were carried out under a dynamic flow of Ar (Ar 5.0, further cleaned from oxygen) of about 50 ml min−1 which was applied after evacuating and flushing the whole system three times. To getter last traces of oxygen small pieces of a Tifoil were placed next to the crucible. All measurements were done in boron nitride crucibles (major diameter 13 mm, inner diameter 11 mm, length 70 mm). Before usage they were stored in methanol for a couple of days to remove the boric acid at the surface by formation of the volatile methyl ester which was evaporated under vacuum at 1073 K for 2 h. After stabilizing the calorimetric system at 879 K for 12 h, the drops were performed in an interval of 40 min. The heat flow acquisition was 0.5 s. The obtained signals were recorded, integrated and transformed into enthalpy values using the calorimeter constant. To prove the reproducibility of the data most sections were measured twice. The calorimeter constant was determined at the end of the measurement by dropping a certain amount (approximately 50–90 mg) of a NIST Standard sapphire into the calorimeter. Thereby, the integrated signal of the heat effect (ST0→Tc) can be determined, which corresponds to the enthalpy increments of the reference material from the drop temperature (T0) to the calorimeter temperature (Tc). The theoretical enthalpy value (ΔT 0→T cHref) for the NIST sapphire was calculated using the related polynomials provided by the supplier. The calorimeter constant k [J μV−1 s−1] was calculated applying Eq. (1): k¼

Fig. 2. Experimental integral molar enthalpies of mixing of Liquid Li\ \Sb alloys at different temperatures, according to Li et al. [8] and the Redlich-Kister fit indicated as solid line. The corresponding L-parameters are given in Table 1.

of the other two constituent binaries were fitted from experimental values of Li et al. [8] for Li\\Sb, and Sommer et al. [31] for Sb\\Sn. For the latter only values at 968 K were taken since this is the lowest temperature where the system is fully liquid. Our data fits are shown in Figs. 2 and 3 and all interaction parameters applied are listed in Table 1. 4. Results and discussion

ΔT 0 →T c H ref ∙nref

ð1Þ

ST 0 →T c

The calorimeter constant k and the measured integrated signal (ST0→Tc) for each single drop were applied to calculate the enthalpy values (ΔHsignal) using the following equation: ΔH signal ¼ ST 0 →T c ∙k

ð2Þ

The molar enthalpy increment of mixing (ΔmixHi) was then determined by Eq. (3), where the enthalpy increment necessary for melting and heating the dropped material from T0 to Tc (ΔT 0→T cHi), given by the respective polynomials in the SGTE data base [37], is subtracted from the measured enthalpy (ΔHsignal) and divided by the molar amount ni of the dropped element i. Δmix H i ¼

3

ΔHsignal −ΔT 0 →T c H i ∙ni ni

4.1. Experimental data As examples the experimental data of partial and integral molar enthalpies of mixing at 879 K in the ternary system Li-Sb-Sn are listed in Tables 3–5 for all runs along the sections A, E, G and J. Data for all the other investigated sections B, C, D, F, H, and I are given in the Tables S1-S3 in the supplementary material. Tables 3–5 contain all relevant information such as: starting amount, dropped amounts, calorimeter constant, starting values of binary alloys as well as the partial and

ð3Þ

Since the dropped molar amount of the respective element was very small compared to the total molar amount in the crucible the obtained molar enthalpy of mixing approximately corresponds to the partial enthalpy of mixing, Δmix Hi of the respective element at (xi + xi-1)/2. The sum of the partial enthalpies of mixing values over all drops at the respective concentration was divided by the overall molar amount to calculate the integral molar enthalpy of mixing (ΔmixHm). In this formula nbath represents the molar amounts of elements in the bath before starting the drops. P Δmix Hm ¼ Δmix Hbin þ

 Δmix H i ∙ni P nbath þ ni

ð4Þ

The integral enthalpies of mixing for the binary starting alloys in Li\\Sn were calculated using the Redlich-Kister interaction parameters given by Fürtauer et al. [23]. The interaction parameters for binary alloys

Fig. 3. Integral molar enthalpies of mixing of Liquid Sb\ \Sn alloys at different temperatures, according to Sommer et al. [31] For the Redlich-Kister fit only the filled symbols have been used. The corresponding L-parameters are given in Table 1.

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Accordingly, we assumed that the ternary mixing enthalpy could better be described by the asymmetric Toop extrapolation model [39]:

Table 1 Binary and ternary interaction parameters in Li-Sb-Sn. Lij [J mol−1] or Mijk [J mol−1]

v

System

Reference

Li-Sb Li-Sn Sb-Sn Li-Sb-Sn

[8], own data fit. 0L = −194,354 1L = −233,862 2L = −147,816 0 [23] L = −111,137 1L = −124,601 2L = −89,726 1 2 [31], own data fit. 0L = −5764 L = 533 L = 2009 This work M 0 = 28,226 M 1 = 412,812 M 2 = −236,274

xj x Δ H ðx ; 1−xi Þ þ k Δmix Hi;k ðxi ; 1−xi Þ 1−xi mix i; j i 1−xi    2 xj xk ; þ x j þ xk Δmix H j;k x j þ xk x j þ xk

Δmix H Toop ¼

v Lij, [J mol−1] or Mijk [J mol−1], binary or ternary interaction parameters. ν, order and i, j, k, elements.

integral molar enthalpies including an error calculation. Values from semi-liquid regions were shaded in gray. Selected plots of the experimental integral as well as partial molar enthalpies versus the concentration of antimony, lithium or tin, respectively are shown in Fig. 4a–h. All plots for remaining sections B, C, D, F, H, and I can be found in Fig. S1a–l. To ensure reproducibility most of the experiments have been performed at least two times. Furthermore, to prove reliability of our data, values of the integral molar enthalpy of mixing from different sections A–J at their crossovers (intersection-points a–u) are given in Table 6; compare also to Fig. 1. The respective enthalpy values show a maximum deviation of 2900 J mol−1 for intersection-point p what is still within the errors given in Tables 3–5. Most of deviations, however, are well below 2000 J mol−1 and thus the drop calorimetric method applied for our investigations is validated. 4.2. Calculations The integral molar enthalpy of mixing in the ternary is often described by a Redlich-Kister-Muggianu polynomial [38] which is given in Eq. (5): X  ν  ν ν Lij xi −x j þ x j ∙xk ∙ Ljk x j −xk νX ν ν þ xk ∙xi ∙ Lki ðxk −xi Þν ν  ð0Þ ð1Þ ð2Þ þ xi ∙x j ∙xk ∙ M i; j;k ∙xi þ Mi; j;k ∙x j þ M i; j;k ∙xk

Δmix H ijk ¼ xi ∙x j ∙

X

ν

ð5Þ

where i, j and k correspond to Li, Sb, and Sn respectively, νL values are the binary interaction parameter where ν is the order of interaction and Mi,j,k are the so-called ternary interaction parameters. The ternary interaction parameters Mi,j,k were calculated from the experimental values in the fully liquid regions by a least-squares fit based on the empirical Redlich-Kister-Muggianu polynomial in Eq. (5). The necessary binary interaction parameters νL were evaluated from literature data (see above) and are listed in Table 1 together with the obtained Mi,j,k – parameters. The calculated values along sections A, E, G and J are plotted in Fig. 4a, c, e, g using full lines. In order to prove the significance of the ternary interaction the calculated values without ternary interaction were plotted as well in Fig. 4a, c, e, g using pointed lines. They correspond to an extrapolation from binary data according to the symmetric Muggianu model [38]. Notably, the constituent binary systems Li\\Sb and Li\\Sn both show quite strong exothermic enthalpies of formation with minima of −65,800 J mol−1 and −37,000 J mol−1, respectively, see Fig. 2 and [23]. On the other hand, Sb\\Sn shows almost ideal enthalpy of mixing with a minimum of only −1450 J mol−1, see Fig. 3.

ð6Þ

The so calculated values are as well plotted in Fig. 4a, c, e, g using dashed lines. All plots for the remaining sections B, C, D, F, H and I, can be found in Fig. S1a–l. The calculations of the ternary integral enthalpy of mixing in Li-SbSn for the entire system are presented as isoenthalpy plots in Fig. 5a and b. In Fig. 5a only the isoenthalpy curves calculated using the R.K.Muggianu model are shown whereas in Fig. 5b the same curves are shown together with the extrapolations according to Muggianu (pointed lines) and Toop (dashed lines). The shaded areas in both figures indicate semi-liquid or solid regions. The limiting concentrations of the Sn/Sb-rich liquid were obtained from discontinuities in the partial enthalpy of mixing curves, see Fig. 4. 4.3. Discussion The behavior of the partial and integral enthalpy of mixing along the sections A–J can be grouped into three types, depending on the binary starting alloys. Sections A–C start from Li\\Sn and all of them show similar curves for the partial and integral enthalpy of mixing. As an example, section A starting at Li0.5Sn0.5 is shown in Fig. 4a (integral enthalpy) and 4b (partial enthalpy). In order to explain the mixing behavior, the following needs to be considered for the binary system Li\\Sb [8]: the partial enthalpy Δmix H Sb of Sb in pure Li is ≈−240,000 J mol−1 and corresponds to the formation of strong liquid associates “Li3Sb”. Such associates are also formed dropping Sb to Li50Sn50 but the Δmix H Sb (approx. −145,000 J mol−1) is lower, since Li is already diluted by Sn. This very strong exothermic mixing reaction for the first Sb-drops leads to a steep fall of the integral enthalpy values. At approx. 10 at.% Sb, the partial values suddenly rise, end up at zero and steadily increase up to Δmix H Sb is ≈20,000 J mol−1. At this point we need to mention that Li et al. [8] found that Δmix HSb is constant ≈28,000 J mol−1 in the two-phase region Li3Sb + L. Thus, it can be concluded that this binary two-phase field largely extends into the ternary and is crossed by section A. On the contrary to the binary, Δmix H Sb in the ternary Li3Sb + L phase field is not constant but rises as described above. This is, however, no contradiction because partial values of state functions can vary in a two-phase field of a ternary system. At approx. 37 at.% Sb, there is a second discontinuity ending up in a plateau at approx. zero partial enthalpy of mixing. This is again in accordance to the binary Li\\Sb system [8] where Δmix H Sb is close to zero in the Sb-rich liquid. The measured values between those of the continuous parts of the curve can be explained by kinetics of the dissolution process at phase boundaries. Accordingly, we took the mean values of the concentrations before and after the discontinuity as the phase boundary. The same trend can be observed for sections B and C. There are only two differences, i)Δmix HSb at the beginning is less exothermic towards section C and ii) the phase boundaries are shifted to lower Sb-concentrations.

Table 2 Assumed limiting liquidus concentrations at the sections A–J. Section

A

B

C

D

E

F

G

H

I

J

Liquid/semi-liquid Semi-liquid/liquid

xSb = 0,13 xSb = 0,42

xSb = 0,11 xSb = 0,38

xSb = 0,07 xSb = 0,31

xLi = 0,09 xLi = 0,35

xLi = 0,14 –

xLi = 0,23 –

xLi = 0,36 –

xLi = 0,41 –

– –

xSn = 0,36 –

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5

Table 3 Partial and integral molar enthalpies of mixing of Sb dropped into liquid Li-Sn alloys at 879 K; gray shaded values represent semi-liquid regions; standard states: liquid alloys. (xaSb: Average of xSbbefore and after the drop).

Dropped mole nSb [10−3 mol]

Drop enthalpy ΔHsignal [J]

Partial molar enthalpy Δ mix [J mol−1

Integral molar enthalpy Δ mixH [J mol−1]

Section A1: starting amount: nLi=8.0795 · 10−3mol; nSn=8.0789 · 10−3 mol, calibration: 4 pieces of NIST-sapphire, calibration constant k=(0.5150±0.0017·10−3) JµV −1 s−1

0.0000

0.0000

−27,785 ± 1300

0.6004

−66,683

0.0000 0.0179

−146,415 ± 1652

0.0358

−32,035 ± 1359

0.6005

−63,667

0.0525

−141,376 ± 1635

0.0692

−35,817 ± 1414

0.6047

−62,370

0.0848

−138,487 ± 1616

0.1005

−39,273 ± 1464

0.6174

−47,200

0.1155

−111,797 ± 1503

0.1304

−41,683 ± 1509

0.6354

8627

0.1448

−21,769 ± 1260

0.1592

−41,025 ± 1544

0.6376

20,312

0.1727

−3490 ± 1316

0.1862

−39,819 ± 1578

0.6411

25,873

0.1989

5009 ± 1338

0.2116

−38,417 ± 1611

0.6524

28,026

0.2238

7612 ± 1325

0.2359

−36,997 ± 1642

0.6549

31,047

0.2474

12,059 ± 1335

0.2589

−35,523 ± 1672

0.6551

31,787

0.2697

13,176 ± 1339

0.2805

−34,103 ± 1700

0.6976

34,266

0.2913

13,773 ± 1269

0.3022

−32,661 ± 1727

0.7021

35,500

0.3124

15,218 ± 1267

0.3227

−31,252 ± 1751

0.7028

37,859

0.3324

18,522 ± 1276

0.3421

−29,827 ± 1775

0.7179

40,817

0.3514

21,511 ± 1263

0.3608

−28,369 ± 1797

0.7197

36,287

0.3696

15,075 ± 1239

0.3785

−27,167 ± 1818

0.7337

31,166

0.3870

7130 ± 1192

0.3955

−26,225 ± 1836

0.7415

31,267

0.4037

6818 ± 1180

0.4118

−25,333 ± 1854

0.7425

26,261

0.4196

23 ± 1157

0.4273

−24,666 ± 1870

0.7468

25,868

0.4347

−707 ± 1148

0.4421

−24,048 ± 1884

0.7547

25,052

0.4492

−2152 ± 1133

0.4563

−23,492 ± 1898

0.7650

25,772

0.4631

−1657 ± 1121

0.4699

−22,944 ± 1912

0.7718

27,172

0.4765

−138 ± 1117

0.4830

−22,381 ± 1924

0.7784

26,369

0.4893

−1468 ± 1104

0.4956

−21,873 ± 1936

0.7878

28,924

0.5016

1367 ± 1101

0.5077

−21,315 ± 1947

0.8157

28,087

0.5136

−912 ± 1060

0.5196

−20,820 ± 1957

Section A2: starting amount: nLi=15.7038 · 10−3 mol; nSn = 15.7049 · 10−3 mol, calibration: 5 pieces of NISTsapphire, calibration constant k = (0.5151 ± 0.0106·10−3) JµV −1 s−1

0.0000

0.0000

−27,783 ± 1300

0.6635

−66,882

0.0000 0.0103

−136,152 ± 3228

0.0207

−30,025 ± 1367

0.6152

−66,330

0.0299

−143,166 ± 3463

0.0391

−32,154 ± 1431

0.7008

−68,443

0.0492

−133,012 ± 3102

0.0593

−34,271 ± 1493

0.6270

−66,702

0.0680

−141,725 ± 3410

0.0766

−36,252 ± 1552

0.6443

−65,129

0.0852

−136,438 ± 3269

0.0938

−38,114 ± 1608

0.6920

−63,260

0.1027

−126,760 ± 2988

0.1115

−39,850 ± 1661

0.6632

−33,289

0.1197

−85,541 ± 2193

0.1279

−40,691 ± 1695

0.6626

−13,974

0.1358

−56,434 ± 1598

0.1436

−40,975 ± 1716

0.6808

2525

0.1514

−31,638 ± 1211

0.1593

−40,805 ± 1731

0.6561

17,148

0.1665

−9208 ± 1713

0.1738

−40,260 ± 1753

0.6301

23,336

0.1805

1692 ± 1985

0.1872

−39,576 ± 1778

0.6741

24,884

0.1942

1570 ± 1902

0.2012

−38,870 ± 1802

0.6651

26,669

0.2078

4754 ± 1983

0.2145

−38,145 ± 1827

0.6681

27,869

0.2209

6365 ± 2010

0.2274

−37,413 ± 1851

0.6753

31,227

0.2337

10,896 ± 2091

0.2400

−36,624 ± 1877

0.6733

31,710

0.2461

11,750 ± 2112

0.2522

−35,848 ± 1901

0.6780

32,597

0.2581

12,734 ± 2124

0.2641

−35,077 ± 1925

0.6450

32,694

0.2695

15,340 ± 2236

0.2750

−34,326 ± 1949

0.6314

34,296

0.2802

18,972 ± 2336

0.2854

−33,560 ± 1974

0.6708

34,971

0.2908

16,785 ± 2219

0.2962

−32,804 ± 1997

0.6531

36,462

0.3012

20,481 ± 2326

0.3063

−32,035 ± 2020

Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036

6

P. Berger, H. Flandorfer / Journal of Molecular Liquids xxx (xxxx) xxx

Table 3 (continued)

0.6833

36,701

0.3115

18,368 ± 2231

0.3166

−31,286 ± 2043

0.6561

37,055

0.3214

21,127 ± 2334

0.3263

−30,548 ± 2065

0.6027

37,756

0.3306

27,302 ± 2565

0.3349

−29,810 ± 2088

0.6772

36,560

0.3396

18,637 ± 2246

0.3443

−29,125 ± 2109

Table 4 Partial and integral molar enthalpies of mixing of Li dropped into liquid Sb-Sn alloys at 879 K; gray shaded values represent semi-liquid regions; standard states: liquid alloys. (xaLi: Average of xLibefore and after the drop). Dropped mole nLi [10−3 mol]

Drop enthalpy ΔHsignal [J]

Partial molar enthalpie Δmix [J mol−1]

Integral molar enthalpy ΔmixH [J mol−1]

Section E1: starting amount: nSb = 8.3686 · 10−3 mol; nSn = 25.1152 · 10−3 mol. Calibration: 5 pieces of NISTsapphire. Calibration constant k = (0.5029 ± 0.0117·10−3) JμV−1 s−1

0.0000

0.0000

−1036 ± 100

0.5638

−30,314

0.0000 0.0083

−75,594 ± 2588

0.0166

−2271 ± 143

0.6261

−31,178

0.0254

−71,617 ± 2362

0.0343

−3523 ± 185

1.1150

−63,553

0.0494

−78,819 ± 2001

0.0644

−5869 ± 244

0.7055

−41,606

0.0734

−80,795 ± 2440

0.0825

−7317 ± 289

0.8068

−48,393

0.0924

−81,801 ± 2329

0.1023

−8928 ± 335

0.8447

−53,092

0.1123

−84,671 ± 2354

0.1222

−10,606 ± 382

1.3140

−100,224

0.1368

−98,094 ± 2347

0.1514

−13,519 ± 451

0.9825

−79,344

0.1618

−102,581 ± 2645

0.1721

−15,683 ± 507

0.9583

−76,788

0.1816

−101,950 ± 2650

0.1912

−17,680 ± 558

1.0387

−85,997

0.2011

−104,611 ± 2651

0.2110

−19,807 ± 612

1.0938

−92,292

0.2209

−106,195 ± 2651

0.2308

−21,978 ± 666

1.0962

−88,255

0.2403

−102,329 ± 2559

0.2497

−23,952 ± 715

1.1018

−93,254

0.2588

−106,457 ± 2652

0.2678

−25,939 ± 764

1.1415

−93,707

0.2767

−103,912 ± 2569

0.2856

−27,838 ± 810

1.1732

−96,204

0.2944

−103,826 ± 2549

0.3031

−29,694 ± 855

1.2150

−98,552

0.3117

−102,938 ± 2506

0.3203

−31,500 ± 898

1.2459

−100,084

0.3287

−102,149 ± 2473

0.3370

−33,243 ± 940

1.2512

−99,210

0.3451

−101,112 ± 2446

0.3531

−34,884 ± 979

1.2770

−105,195

0.3609

−104,195 ± 2505

0.3686

−36,553 ± 1018

1.3907

−107,118

0.3767

−98,844 ± 2333

0.3848

−38,145 ± 1054

Section E2: starting amount: nSb = 8.3709 · 10−3 mol; nSn = 25.1098 · 10−3 mol. Calibration: 4 pieces of NISTsapphire. Calibration constant k = (0.5016 ± 0.0077·10−3) JμV−1 s−1

0.0000

0.0000

−1036 ± 100

0.5649

−32,728

0.0000 0.0083

−79,753 ± 2216

0.0166

−2343 ± 137

1.0235

−57,718

0.0309

−78,215 ± 1596

0.0453

−4557 ± 182

0.8454

−50,938

0.0565

−82,073 ± 1810

0.0678

−6382 ± 223

0.8695

−50,049

0.0788

−79,379 ± 1744

0.0898

−8107 ± 261

0.8885

−56,250

0.1005

−85,131 ± 1813

0.1113

−9924 ± 300

0.8948

−68,345

0.1216

−98,204 ± 2007

0.1319

−11,972 ± 342

0.9147

−75,429

0.1419

−104,280 ± 2081

0.1520

−14,110 ± 385

0.9229

−72,863

0.1617

−100,767 ± 2020

0.1714

−16,090 ± 424

0.9730

−80,597

0.1811

−104,650 ± 2037

0.1909

−18,172 ± 465

0.6215

−50,969

0.1968

−103,834 ± 2462

0.2028

−19,440 ± 496

1.0433

−81,543

0.2125

−99,978 ± 1914

0.2222

−21,392 ± 532

1.0485

−87,081

0.2314

−104,870 ± 1985

0.2407

−23,377 ± 569

1.1268

−95,678

0.2501

−106,733 ± 1964

0.2596

−25,454 ± 607

1.2817

−125,355

0.2698

−107,673 ± 2080

0.2800

−27,721 ± 650

Section G1: starting amount: nSb = 21.4646 · 10−3 mol; nSn = 11.5570 · 10−3 mol. Calibration: 5 pieces of NISTsapphire. Calibration constant k = (0.5002 ± 0.0028·10−3) JμV−1 s−1

0.0000

0.0000

−1234 ± 100

0.6987

−35,645

0.0000 0.0104

−72,856 ± 1364

0.0000

−2718 ± 128

0.7031

−36,229

0.0307

−73,372 ± 1360

0.0207

−4161 ± 155

0.7967

−40,669

0.0516

−72,889 ± 1232

0.0407

−5715 ± 182

0.8183

−43,788

0.0731

−75,351 ± 1221

0.0624

−7297 ± 208

0.8932

−47,774

0.0948

−75,326 ± 1144

0.0837

−8942 ± 233

0.8976

−45,213

0.1165

−72,216 ± 1122

0.1059

−10,443 ± 256

0.9019

−47,414

0.1373

−74,414 ± 1131

0.1271

−11,933 ± 279

0.9019

−48,911

0.1571

−76,074 ± 1140

0.1474

−13,393 ± 301

0.9077

−48,130

0.1761

−74,870 ± 1128

0.1668

−14,769 ± 322

Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036

P. Berger, H. Flandorfer / Journal of Molecular Liquids xxx (xxxx) xxx

7

Table 4 (continued)

0.9120

−49,831

0.1944

−76,483 ± 1133

0.1855

−16,127 ± 342

0.9192

−54,269

0.2120

−80,883 ± 1152

0.2034

−17,531 ± 362

0.9595

−53,173

0.2293

−77,259 ± 1097

0.2207

−18,854 ± 380

0.9768

−53,605

0.2463

−76,721 ± 1080

0.2379

−20,130 ± 398

1.0517

−58,865

0.2634

−77,813 ± 1032

0.2547

−21,467 ± 415

1.0589

−59,743

0.2803

−78,261 ± 1029

0.2720

−22,763 ± 431

1.1843

−63,069

0.2975

−75,098 ± 936

0.2886

−24,065 ± 446

1.1843

−69,180

0.3147

−80,258 ± 966

0.3063

−25,429 ± 461

1.2361

−74,291

0.3315

−81,942 ± 949

0.3232

−26,825 ± 476

1.2405

−80,770

0.3479

−86,956 ± 975

0.3399

−28,280 ± 490

1.2405

−82,973

0.3635

−88,732 ± 985

0.3559

−29,709 ± 504

1.2794

−89,412

0.3785

−91,731 ± 984

0.3711

−31,184 ± 518

1.3269

−92,736

0.3934

−91,732 ± 963

0.3860

−32,642 ± 531

1.4148

−108,978

0.4083

−98,871 ± 968

0.4008

−34,299 ± 545

1.6597

−127,527

0.4241

−98,680 ± 889

0.4158

−36,136 ± 557

1.7361

−136,235

0.4407

−100,316 ± 878

0.4325

−37,995 ± 569

These effects can be explained by the lower Li-content towards section C and the lower amount of Li3Sb in the two phase region. Sections D–H represent drops of Li into binary Sb\\Sn alloys of different starting compositions. The interactions of Sb and Sn in the liquid are very weak and range from zero to less than −2000 J mol−1. The addition of Li, which shows strong interactions with both, Sb and Sn, naturally results in highly exothermic partial enthalpy of mixing which ranges from Δmix H Li = −65,000 to −85,000 J mol−1. This trend is in accordance to the stronger interaction of Li with pure Sb ( Δmix H Sb ≈−90,000 [8]) compared to this with pure Sn (Δmix H Sb ≈−57,000 [23]). In section E, see Fig. 4c (integral enthalpy) and 4d (partial enthalpy) descending Δmix HLi values can be observed until they suddenly fall down to ≈−103,000 J mol−1 at ≈13 at.% Li and stay constant at this level throughout the experiment. Again, this discontinuity can be assigned to the transition of the liquid phase boundary fully liquid to semi-liquid (Li3Sb + L). In the ternary two phase field Δmix H Li of ≈−103,000 J mol−1 is slightly lower than Δmix HLi ≈−120,000 J mol−1 in the binary Li3Sb + L phase field (evaluated graphically from Fig. 5 in Li et al. [8]). The Sn-content of the liquid mixture at the phase boundary Li3Sb + L should rise from sections H to D. This can be proved regarding sections D to F where the plateau in section D is at Δmix H Li ≈−100,000 J mol−1 and at Δmix HLi ≈−110,000 J mol−1 in section F. The plateaus in sections G and H are not sufficiently expressed to attribute the significant partial enthalpy value. All sections E to H end up in the two-phase field Li3Sb + L whereas D crosses again the phase boundary forming a Sb-poor liquid phase; see supplementary material. Sections I and J start with drops of Sn into liquid binary Li\\Sb alloys. The first drops in section J show low endothermic mixing effects with Δmix H Li ≈3000 J mol−1. Assumedly, this is because liquid Li\\Sn associate “Li4Sn” is considered to be less stable than this of Li\\Sb, “Li3Sb”. At approx. 36 at.% Sn the values fall suddenly to ≈−4000 J mol−1 which corresponds to the entry into the two-phase field Li3Sb + L. Immediately afterwards Δmix H Sn rises slightly because the Sn-content of the equilibrium liquid phase rises as well. At the beginning of section I the partial mixing enthalpy of Sn is slightly exothermic, ≈−4000 J mol−1, contrary to section J. This is comparable to Δmix H Sn ≈−4000 J mol−1 in the binary Sb\\Sn system [31] and shows that associate formation is minor at higher Sb-contents. Section I never crosses the two-phase

field Li3Sb + L, the partial enthalpy approximates to zero and the integral enthalpy continuously rises towards pure Sn. The integral enthalpy values calculated based on the Redlich-KisterMuggianu (R-K-M) equation (Eq. (5)) are shown as solid lines in Fig. 4a, c, e, g and Fig. 5a, b. The ternary interaction parameters have been evaluated by a least square fit based on our experimental data of only fully liquid alloys. The extrapolated integral enthalpy according to the Muggianu model (Eq. (5) without ternary interaction terms) is indicated as pointed line in Fig. 4a, c, e, g and Fig. 5b. In the same figures the extrapolated integral enthalpy according to the Toop model is drawn as dashed line. In section A, which is a representative of sections A–C, the measured values fall very steeply at the beginning before drops enter into the twophase region Li3Sb + L. The respective sharp kink before the linear slope cannot be fully reproduced by calculations. At the reentry of the system into the fully liquid phase field the R-K-M calculation has a trend to less exothermic values until it ends up at zero for pure Sb. This is caused by the mathematical characteristics of the function and compromises for the best fit of the entire system. The Muggiano extrapolation is able to describe this section rather well at the first part but is too exothermic in the Sb-richer part. The Toop model fails to describe the experimental data except for the last drops. The calculated enthalpy values within the two-phase field Li3b + L belong to the metastable liquid mixture at the given temperature of 879 K. All the three calculation models can describe the experimental values in sections B and C in a similar way (see Fig. S1a–l). Dropping pure Li into Sb\\Sn alloys (sections D to H) the mixing effect is exothermic before the two-phase boundary is crossed. The extension of the fully liquid phase rises from xLi = 0.09 in section D to xLi = 0.41 in section H with rising Sb-content, see also Table 2. The integral mixing enthalpy of Sb-poor liquid can be better described with the RK-M calculation whereas for Sb-rich liquid the Toop model seems to be preferable. This is in agreement with the situation in sections A to C where the Sn-rich liquid cannot be well described with the Toop model contrary to the Sb-rich liquid which appears after crossing the two-phase field Li3Sb + L. Sections E and G in Fig. 4c and e are representatives of this behavior. The R-K-M calculations of the integral enthalpy of mixing along sections I and J, where Sn was dropped into a Li\\Sb bath, well correspond

Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036

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P. Berger, H. Flandorfer / Journal of Molecular Liquids xxx (xxxx) xxx

Table 5 Partial and integral molar enthalpies of mixing of Sn dropped into liquid Li-Sb alloys at 879 K; gray shaded values represent semi-liquid regions; standard states: liquid alloys. (xaSn: Average of xSnbefore and after the drop).

Dropped mole nSn [10−3 mol]

Drop enthalpy ΔHsignal [J]

Partial molar enthalpie Δmix [J mol−1]

Integral molar enthalpy ΔmixH [J mol−1]

Section J1: starting amount: nLi = 5.3234 · 10−3 mol; nSb = 7.9860 · 10−3 mol. Calibration: 4 pieces of NISTsapphire. Calibration constant k = (0.5152 ± 0.0068·10−3) JμV−1 s−1

0.0000

0.0000

−36,836 ± 1000

0.6548

17,837

0.0000 0.0234

3525 ± 1538

0.0469

−34,943 ± 1072

0.6646

17,046

0.0685

1933 ± 1499

0.0902

−33,268 ± 1137

0.6988

18,833

0.1109

3238 ± 1460

0.1317

−31,603 ± 1197

0.7049

17,864

0.1508

1627 ± 1429

0.1699

−30,142 ± 1251

0.7099

18,263

0.1875

2013 ± 1426

0.2051

−28,779 ± 1301

0.7136

19,819

0.2213

4060 ± 1447

0.2375

−27,436 ± 1348

0.7215

20,057

0.2527

4085 ± 1436

0.2678

−26,185 ± 1391

0.7284

20,022

0.2819

3775 ± 1422

0.2960

−25,031 ± 1431

0.7742

20,903

0.3099

3285 ± 1352

0.3237

−23,917 ± 1467

0.7803

21,008

0.3366

3211 ± 1344

0.3495

−22,882 ± 1501

0.8130

20,029

0.3619

921 ± 1274

0.3744

−21,973 ± 1530

0.8334

15,987

0.3862

−4531 ± 1179

0.3979

−21,315 ± 1555

0.8430

16,563

0.4090

−4065 ± 1175

0.4201

−20,682 ± 1577

0.8705

18,686

0.4307

−2248 ± 1169

0.4413

−20,008 ± 1599

0.8813

18,528

0.4512

−2690 ± 1153

0.4612

−19,390 ± 1619

0.8931

18,447

0.4706

−3058 ± 1136

0.4800

−18,820 ± 1637

0.8985

20,585

0.4888

−803 ± 1161

0.4976

−18,209 ± 1655

0.9295

19,568

0.5061

−2662 ± 1108

0.5147

−17,682 ± 1670

0.9382

19,891

0.5227

−2513 ± 1102

0.5307

−17,180 ± 1684

0.9894

22,085

0.5386

−1391 ± 1074

0.5465

−16,648 ± 1697

1.0174

23,110

0.5541

−999 ± 1058

0.5617

−16,124 ± 1709

1.0274

23,387

0.5689

−950 ± 1051

0.5761

−15,627 ± 1721

1.0321

23,995

0.5828

−464 ± 1054

0.5896

−15,145 ± 1731

1.0542

25,132

0.5960

127 ± 1046

0.6025

−14,664 ± 1741

1.0902

26,314

0.6087

423 ± 1026

0.6150

−14,188 ± 1750

Section J2: starting amount: nLi = 5.3652 · 10−3 mol; nSb = 8.0483 · 10−3 mol. Calibration: 5 pieces of NISTsapphire. Calibration constant k = (0.5158 ± 0.0049·10−3) JμV−1 s−1

0.0000

0.0000

−36,374 ± 1000

0.6422

16,479

0.0000 0.0228

1946 ± 1449

0.0457

−34,624 ± 1066

0.6522

17,759

0.0669

3514 ± 1445

0.0880

−32,932 ± 1127

0.6600

17,763

0.1076

3201 ± 1428

0.1272

−31,381 ± 1183

0.6637

17,508

0.1452

2665 ± 1417

0.1633

−29,971 ± 1234

0.6691

16,843

0.1801

1458 ± 1396

0.1968

−28,712 ± 1281

0.7264

19,576

0.2136

3234 ± 1321

0.2303

−27,380 ± 1324

0.7306

20,402

0.2458

4212 ± 1325

0.2613

−26,109 ± 1364

0.7524

19,469

0.2760

2162 ± 1274

0.2907

−24,984 ± 1401

0.7562

20,639

0.3043

3578 ± 1283

0.3179

−23,886 ± 1435

0.7779

21,236

0.3309

3587 ± 1254

0.3439

−22,841 ± 1466

0.7828

19,540

0.3560

1249 ± 1226

0.3681

−21,952 ± 1494

0.7954

15,632

0.3795

−4061 ± 1160

0.3909

−21,306 ± 1518

0.8479

18,004

0.4022

−2480 ± 1114

0.4135

−20,608 ± 1540

0.8641

18,185

0.4242

−2670 ± 1096

0.4349

−19,955 ± 1560

0.8879

18,446

0.4450

−2940 ± 1069

0.4552

−19,342 ± 1579

0.8894

19,865

0.4647

−1379 ± 1082

0.4742

−18,715 ± 1596

0.9174

21,558

0.4833

−214 ± 1067

0.4925

−18,073 ± 1612

0.9239

20,798

0.5010

−1203 ± 1052

0.5096

−17,503 ± 1627

0.9394

22,142

0.5178

−143 ± 1048

0.5259

−16,927 ± 1641

1.0080

24,031

0.5341

127 ± 994

0.5422

−16,340 ± 1653

1.0118

24,597

0.5498

596 ± 996

0.5575

−15,775 ± 1665

Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036

P. Berger, H. Flandorfer / Journal of Molecular Liquids xxx (xxxx) xxx

9

Table 5 (continued)

1.0266

23,916

0.5647

−417 ± 975

0.5720

−15,272 ± 1675

1.0300

24,620

0.5788

189 ± 979

0.5856

−14,780 ± 1685

1.0806

27,099

0.5923

1364 ± 955

0.5990

−14,258 ± 1693

1.1397

26,972

0.6056

−49 ± 904

0.6122

−13,790 ± 1700

Fig. 4. Integral and partial enthalpy of mixing for sections A, E, G and J determined at 879 K, together with fitted and extrapolated curves. Circles indicate the first, squares the second measurement. Lines indicate data calculated with the R.K.-Muggianu model (solid line), the Muggianu model (pointed lines) and the Toop model (dashed lines). Vertical pointed lines for 4 a, c, e and g indicate assumed phase boundaries. Vertical dashed lines for 4 b, d, f and h indicate the approximate range of liquidus limits.

Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036

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Table 6 Experimental values of the integral molar enthalpy of mixing at the intersection-points a to u according to Fig. 1. Intersection

a b c d e f g h i j k l m n o p q r s t u

Integral molar enthalpy of mixing ΔmixH [J mol−1]

Composition

A

B

C

D

E

F

G

H

I

J

xLi

xSb

xSn

Li0.5Sn0.5 + Sb

Li37.5Sn62.5 + Sb

Li0.25Sn0.75 + Sb

Sb0.15Sn0.85 + Li

Sb0.25Sn0.75 + Li

Sb0.5Sn0.5 + Li

Sb0.65Sn0.35 + Li

Sb0.8Sn0.2 + Li

Li0.3Sb0.7 + Sn

Li0.4Sb0.6 + Sn

0.460 0.338 0.221 0.311 0.200 0.182 0.158 0.334 0.250 0.240 0.230 0.176 0.144 0.286 0.200 0.303 0.259 0.218 0.105 0.348 0.255

0.080 0.099 0.117 0.172 0.200 0.272 0.369 0.333 0.375 0.360 0.385 0.412 0.428 0.428 0.467 0.453 0.482 0.509 0.582 0.522 0.596

0.460 0.563 0.662 0.517 0.600 0.546 0.473 0.333 0.375 0.400 0.385 0.412 0.428 0.286 0.333 0.244 0.259 0.273 0.313 0.130 0.149

−37,000 −19,500

−38,100 −31,700 −20,800

−30,200 −28,800 −17,200 −14,700 −12,600 −30,500

−30,600 −18,700 −16,200 −13,900 −32,200 −22,900

−19,600 −18,700 −11,700

−21,900 −21,000

−20,900 −15,800 −13,000

−15,700

−24,600

−25,200 −16,500

−17,900

−22,400 −9000

to the experimental values. Section J, shown in Fig. 4g (integral enthalpy), crosses the liquid phase boundary at xSn = 0.36 whereas all alloys at measured compositions along section I (see Fig. S1k) are fully liquid. The Muggianu model (R-K-M without ternary interactions) results in too exothermic values in both sections. The Toop model yields too less exothermic values in case of section J but can satisfactorily describe all integral enthalpy values in section I. This confirms the trend that the Toop model is the more suitable the higher the Sb-content of the liquid phase.

−23,900 −20,500 −17,300 −8900

−26,800 −19,400 −29,400 −21,300

−31,300 −22,600

The isoenthalpy plots according to the R-K-M calculations in Li-SbSn at 879 K are shown in Fig. 5a. It has to be mentioned at this point that only experimental results from the fully liquid regions (unshaded) have been considered for the evaluation of the ternary interaction parameters. Accordingly, the enthalpy values within the semi-liquid or solid regions (shaded) correspond to the metastable liquid phase. The entire system shows negative integral enthalpy of mixing where the minimum is located in the metastable binary Li\\Sb region with ΔmixH ≈ −65,000 J mol−1 at xLi ≈ 0.75. This corresponds to the very

Fig. 5. a.) Isoenthalpy plot calculated according to the Redlich Kister Muggianu fit; b.) Isoenthalpy plot calculated according to the Redlich Kister Muggianu fit (solid line), Muggianu extrapolation (pointed lines) and Toop extrapolations (dashed lines).

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strong compound forming tendency at Li3Sb in the liquid as well as in the solid state. Solid Li3Sb has a melting point of 1580 K [5], much higher than all other constituent binary compounds which melt way below 1073 K. Accordingly, Li3Sb dominates the Li-Sb-Sn phase diagram with a wide extend of the primary crystallization of the solid compound and the highly negative enthalpy of mixing into the ternary. In addition to that, Li\\Sn shows strong compound forming and a negative minimum of the mixing enthalpy at ≈Li0.8Sn0.2 [6,23]. The combination of both influences determines the course of the vertices of the isoenthalpy curves from −65,000 J mol−1 to zero at pure Sn. The respective enthalpy valley first proceeds from Sn straight forward to Li3Sb but bends towards the enthalpy minimum in Li\\Sn before ending in Li3Sb. The calculation according to the Toop model fails in the description of this enthalpy valley giving less exothermic values compared to R-K-M, see Fig. 5b. In the Sb-rich part, however the Toop model describes our experimental data very well, see discussion above. The R-K-M calculation shows acceptable but larger deviations in this region because the ternary interactions depends on the squares of the molar concentrations of the components. The fit to the steep enthalpy valley at the Sb-poor side and the overshoot at the Sbrich side are mutually dependent. The extrapolation based on the Muggianu model (R-K-M without ternary interactions) results in too less exothermic enthalpy along the valley from Sn to Li3Sb and gives on the other hand too exothermic values in the other regions. Authors contribution P. Berger prepared the samples, performed the experiments and analyzed the data. P. Berger and H. Flandorfer discussed the results. P. Berger drafted the manuscript, H. Flandorfer did proofreading. H. Flandorfer conceived the idea for the project and supervised the work. Acknowledgement This work was supported by the DFG (Deutsche Forschungsgemeinschaft) project FL-730/1-2 within the priority program SPP 1473, “WeNDeLIB”. We thank Mr. P. Wibner for doing preliminary experiments. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2019.112036. References [1] A. Trifonova, M. Wachtler, M. Winter, J.O. Besenhard, Sn-Sb and Sn-Bi alloys as anode materials for lithium-ion batteries, Ionics 8 (2002) 321–328, https://doi. org/10.1007/Bf02376044. [2] I. Rom, M. Wachtler, I. Papst, M. Schmied, J.O. Besenhard, F. Hofer, M. Winter, Electron microscopical characterization of Sn/SnSb composite electrodes for lithium-ion batteries, Solid State Ionics 143 (2001) 329–336, https://doi.org/10.1016/S01672738(01)00886-4. [3] A.T. Tesfaye, Y.D. Yucel, M.K.S. Barr, L. Santinacci, F. Vacandio, F. Dumur, S. Maria, L. Monconduit, T. Djenizian, The electrochemical behavior of SnSb as an anode for Liion batteries studied by electrochemical impedance spectroscopy and electron microscopy, Electrochim. Acta 256 (2017) 155–161, https://doi.org/10.1016/j. electacta.2017.10.031. [4] J.O. Besenhard, M. Wachtler, M. Winter, R. Andreaus, I. Rom, W. Sitte, Kinetics of Li insertion into polycrystalline and nanocrystalline ‘SnSb’ alloys investigated by transient and steady state techniques, J. Power Sources 81 (1999) 268–272, https://doi. org/10.1016/S0378-7753(99)00199-8. [5] A. Beutl, D. Cupid, H. Flandorfer, The Li-Sb phase diagram part I: new experimental results, J. Alloys Compd. 695 (2017) 1052–1060, https://doi.org/10.1016/j.jallcom.2016. 10.230. [6] D. Li, S. Fürtauer, H. Flandorfer, D.M. Cupid, Thermodynamic assessment and experimental investigation of the Li-Sn system, Calphad 47 (2014) 181–195, https://doi. org/10.1016/j.calphad.2014.09.002. [7] O. Kubaschewski, W. Seith, Bildungswärmen von Nichteisenmetall-Legierungen, Z. Metallkd. 30 (1938) 7–9. [8] D. Li, A. Beutl, H. Flandorfer, D.M. Cupid, The Li-Sb phase diagram part II: calorimetry and thermodynamic assessment, J. Alloys Compd. 701 (2017) 186–199, https://doi. org/10.1016/j.jallcom.2016.12.399.

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Please cite this article as: P. Berger and H. Flandorfer, Enthalpy of mixing of liquid Li-Sb-Sn alloys, Journal of Molecular Liquids, https://doi.org/ 10.1016/j.molliq.2019.112036