Enthalpy of mixing of liquid Co-Sn alloys.

A literature overview of enthalpy of mixing data for liquid Co-Sn alloys shows large scattering but no clear temperature dependence. Therefore drop calorimetry was performed in the Co-Sn system at twelve different temperatures in 100 K steps in the temperature range (673 to 1773) K. The integral enthalpy of mixing was determined starting from 1173 K and fitted to a standard Redlich-Kister polynomial. In addition, the limiting partial molar enthalpy of Co in Sn was investigated by small additions of Co to liquid Sn at temperatures (673 to 1773) K. The integral and partial molar enthalpies of the Co-Sn system generally show an exothermic mixing behavior. Significant temperature dependence was detected for the enthalpies of mixing. The minimum integral enthalpy values vary with rising temperature from approx. -7820 J/mol at T = 1173 K to -1350 J/mol at T = 1773 K; the position of the minimum is between (59 and 61) at.% Co. The results are discussed and compared with literature data available for this system. X-ray studies and scanning electron microscopy of selected alloys obtained from the calorimetric measurements were carried out in order to check the completeness of the solution process.

Introduction

A growing demand on electrical energy for mobile systems, especially for electrically driven cars, makes the development of devices for an efficient storage of electricity necessary. One of the most promising technologies are the Lithium-Ion Batteries (LIBs) which are currently being further developed, both by basic scientific approaches and technological innovations. The search for new materials includes all possible components, i.e. anode, cathode, and electrolyte. Among those, intermetallic compounds, including many compounds with Sn, have been discussed extensively, especially as material for the anode, to provide a means for efficient Li storage [1-3]. Among the possible candidates are also intermetallic compounds in the system of Li with Co–Sn [4] for which it is hoped that Li can undergo a reversible reaction without drastic volume change that would destroy the anode and the LIB.

In other fields, Co–Sn and (Sn–Co)-based alloys are also under discussion for high-temperature lead-free soft solder alloys at T = (500 to 620) K [5,6] where they might play a certain role for specialized applications. Likewise, Co–Sn alloys are applied in specific high-tech applications. For example, they have been discussed for the production of metallic glasses [7].

Information on thermochemistry and phase relationships of the respective alloy systems forms the basis for a systematic materials design which is desired to avoid complex and time consuming trial and error developing methods. Experimental thermochemical quantities such as the enthalpy of mixing are indispensable for the thermodynamic optimization and calculation of phase diagrams (CALPHAD1) and the calculation of several physical properties, e.g. surface tension, viscosity and wettability. Solidification behavior, interfacial diffusion and reaction as well as microstructure and texture of multi-component alloy systems can be estimated from a proper thermodynamic and kinetic data base.

The purpose of this work is to complete and clarify the information on the enthalpy of mixing of liquid Co–Sn alloys for which the data available in literature are highly inconsistent and to provide a reliable data set. Therefore the integral and partial enthalpies of mixing of molten binary Co–Sn alloys have been measured at several temperatures to obtain both absolute values as well as their temperature dependencies.

Literature survey

The integral and partial enthalpies of mixing for liquid Co–Sn alloys have been measured by several authors. Körber and Oelsen [8] reported values at T = 1773 K, Esin et al. [9] at T = 1850 K, Lück et al. [10] in the temperature range (1671 to 1823) K, and Vassilev et al. [11] between (991 and 1303) K, all using calorimetric methods. The Knudsen effusion method was applied to derive enthalpy data at T = 1573 K by Eremenko et al. [12]. In most cases the authors indicated an S-shaped curve of Δ concentration. However, the reported shape and absolute values of the enthalpy of mixing are contradictory. Körber and Oelsen [8] and Eremenko et al. [12] reported a positive enthalpy of mixing for Sn-rich and negative values for Co-rich liquid alloys. It is noteworthy that the minimum of about 2500 J/mol at about 75 at.% Co is away from the most stable compound Co3Sn2. Esin et al. [9] found a similarly shaped Δ curve but with the endothermic maximum at the Sn-rich side at 10 at.% Co and about 1000 J/mol and with exothermic values in the Co-rich part; the exothermic minimum is at 50 at.% Co and about −4000 J/mol. It has to be pointed out that in the paper by Esin et al. [9] calorimetric measurements are mentioned in the abstract only, and no experimental information or data are given throughout the paper. Values are shown on a graph only without further explanation. Lück et al. [10] measured the enthalpy of mixing at five different temperatures (1671, 1675, 1759, 1780 and 1823 K) and found a significant temperature dependence of Δ with general endothermic behavior above 1675 K. Below this temperature they found an M-shaped curve of Δ concentration with slightly negative values in the composition range between (40 and 60) at.% Co. The most recent experimental determination of the enthalpy of mixing of liquid Co–Sn alloys, though only in a narrow composition range, was performed by Vassilev et al. [11]. They obtained generally exothermic values in the concentration region (0 to 10) at.% Co at T = (991 and 1020) K.

Numerous experimental studies of the limiting partial enthalpy of mixing of Co in liquid Sn, , have been performed over a large temperature range [8,13-16]. Bowersox [17] calculated from solubility data over the temperature range (827 to 1211) K. Most of the available literature data were collected in review articles [18,19]. However, there is no clear trend indicated. Basically, exothermic values are reported [13-16] but endothermic values can also be found in literature [8,17,19]. Several thermodynamic assessments [7,20-22] of the Co–Sn system were presented based on the experimental data by various authors [8-10]. Ivanov [23] has calculated the enthalpy of mixing of liquid Co–Sn alloys based on the associations theory. Under the assumption of tin clusters and Co2Sn type associates in liquid alloys he arrived to calculate a curve by fitting to the experimental values of Körber and Oelsen [8].

Experimental details

The calorimetric measurements were carried out using two different calorimeters. For low temperatures up to T = 1273 K a Calvet-type twin micro-calorimeter system was used, based on a commercial wire wound resistance furnace (HT-1000, SETARAM, Lyon, France) having two thermopiles with more than 200 thermocouples, equipped with an automatic drop device for up to 30 drops; control and data evaluation was performed with Lab View and HiQ. This system was described in detail by Flandorfer et al. [24].

For higher temperatures up to T = 1773 K a commercial Multi High-Temperature micro-calorimeter (MHTC, SETARAM, Lyon, France) was available with one thermopile with 20 thermocouples, a graphite tube resistance furnace, a manual drop device for up to 23 drops; control and data evaluation was performed using the software provided by the company.

The measurements were generally performed in graphite crucibles under Ar flow (99.999 vol.%, purification from oxygen, approx. 30 ml/min). At the end of each series the calorimeters were calibrated by five drops of standard α-Al2O3 provided by NIST (National Institute of Standards and Technology, Gaithersburg, MD). The time interval between individual drops was usually 2400 s and the acquisition interval of the heat flow was 0.5 s. The obtained signals were recorded and integrated. The measured enthalpy (integrated heat flow at constant pressure) iswhere n is the number of moles of the added element i, H denotes molar enthalpies, T is the drop temperature, and T is the calorimeter temperature of the respective measurement in Kelvin. The molar enthalpy difference was calculated using the SGTE data for pure elements [25]. Because of the rather small masses of added component, partial enthalpies can be calculated directly as

The integral molar enthalpy of mixing, Δ, was calculated by summing the respective reaction enthalpies and division by the total molar amount of substance, where n stands for the molar amount of substance which was already present in the crucible:

Co and Sn of high purity (99.99%, Alfa Aesar, Karlsruhe, Germany) were used without further purification. The measurements were carried out by adding solid Co to liquid Sn at twelve different temperatures (673 to 1773) K in intervals of 100 K. In the temperature interval between (673 and 1773) K measurements were performed with very small concentration steps (15 to 25 drops up to xCo ⩽ 0.07) in order to determine the limiting partial enthalpy of mixing of Co in Sn. From 1173 K upwards, measurements were also done with much larger steps in order to determine the integral and partial enthalpies of mixing over a wide concentration range.

In the first case 15 to 25 pieces of Co with masses between (10 and 20) mg were dropped into (7 to 9.5) g of liquid Sn in order to determine the limiting partial enthalpy of mixing of Co in liquid Sn. Measurements for the determination of the integral enthalpy of mixing were carried out starting from T = (1173 to 1773) K. Between (9 and 19) pieces of Co with masses between (20 and 50) mg were dropped into (1.0 to 2.5) g of liquid Sn. The mass of dropped Co pieces was increased throughout each calorimetric run in order to make nearly equal atomic fraction steps. Additional calorimetric measurements were performed dropping Sn into liquid Co at T = 1773 K, slightly above the melting point of Co. However, it was found that the integral enthalpy of mixing values determined by the addition of Sn to liquid Co placed in a graphite crucible were in disagreement with values obtained by dropping Co pieces into Sn-rich solutions. Values at about 50 at.% Co, determined from both sides, differed significantly. We suppose that this was caused by a reaction between sample and graphite crucible and further formation of the ternary compound Co3SnC0.7 [26]. Such measurements using Al2O3 crucibles gave much better agreement at the cross over zone (see table 1 and figure 1). A least square fit based on the entire set of Δ values at T = 1773 K, measured from both sides, is only possible using a Redlich–Kister polynomial with four interaction parameters whereas at all the other temperatures two parameters were sufficient. To present a more consistent data set we did not include enthalpy values obtained by drops of Sn into Co for the mathematical description of the enthalpy of mixing at T = 1773 K.

TABLE 1

Integral and partial enthalpies of mixing of liquid Co–Sn alloys at T = (1773 to 1173) K; standard states: pure liquid components.

Dropped mole	Measured enthalpy	Partial molar enthalpy				Integral molar enthalpy
n(Sn)	ΔHSignal	xSna	ΔH‾_Sn			xSnb	ΔMixH
10−3 mol	J · mol−1		J · mol−1				J · mol−1
T = 1773 K; starting amount: n(Co) = 24.6900 · 10−3 mol; run 1
0.5561	25,741	0.0110	−23,434	±	530	0.0220	−516	±	12
1.4684	28,444	0.0489	−20,730	±	586	0.0758	−1627	±	43
0.7792	38,717	0.0889	−10,458	±	797	0.1020	−1878	±	65
0.8125	41,751	0.1149	−7423	±	860	0.1278	−2037	±	87
1.7296	44,752	0.1529	−4422	±	921	0.1780	−2174	±	135
1.7657	45,526	0.2008	−3648	±	937	0.2236	−2256	±	180
6.4511	47,317	0.2891	−1858	±	809	0.3546	−2189	±	219
3.0180	47,455	0.3782	−1719	±	897	0.4018	−2154	±	259
n(Co)	ΔHSignal	xCoa	ΔH‾_Co			xCob	ΔMixH
10−3 mol	J · mol−1		J · mol−1				J · mol−1
T = 1773 K; starting amount: n(Sn) = 17.6477 · 10−3 mol; run 2
0.1202	67,863	0.0034	−2683	±	723	0.0068	−18	±	5
0.2819	68,747	0.0145	−1799	±	733	0.0223	−46	±	16
0.3047	67,705	0.0304	−2840	±	721	0.0385	−92	±	28
0.2943	68,637	0.0461	−1909	±	731	0.0537	−121	±	39
0.5090	67,855	0.0663	−2690	±	723	0.0788	−189	±	57
0.5577	67,467	0.0919	−3079	±	719	0.1049	−271	±	76
0.7073	67,264	0.1204	−3282	±	717	0.1359	−375	±	98
0.7648	67,843	0.1515	−2703	±	723	0.1671	−459	±	121
0.7798	67,462	0.1819	−3084	±	719	0.1966	−552	±	142
0.8502	68,325	0.2116	−2220	±	728	0.2266	−615	±	164
0.8735	66,731	0.2408	−3815	±	711	0.2551	−733	±	184
0.9137	66,366	0.2689	−4179	±	707	0.2828	−861	±	203
0.9448	67,422	0.2960	−3124	±	718	0.3093	−944	±	222
1.0338	69,115	0.3227	−1431	±	736	0.3361	−963	±	242
1.0935	66,919	0.3493	−3627	±	713	0.3624	−1068	±	261
1.1566	67,600	0.3752	−2946	±	720	0.3879	−1144	±	279
1.1709	68,933	0.3999	−1613	±	735	0.4118	−1162	±	297
1.3440	68,150	0.4244	−2395	±	726	0.4370	−1215	±	316
1.4852	67,167	0.4498	−3379	±	716	0.4625	−1313	±	334
T = 1773 K; starting amount: n(Sn) = 17.0876 · 10−3 mol; run 3
0.7461	67,827	0.0209	−2668	±	776	0.0418	−112	±	32
0.7702	67,291	0.0617	−3203	±	770	0.0815	−240	±	63
1.5497	68240	0.1168	−2255	±	780	0.1521	−395	±	118
0.7906	67,637	0.1681	−2857	±	774	0.1841	−488	±	143
0.8290	67,444	0.1997	−3051	±	771	0.2152	−585	±	167
0.8576	67,343	0.2301	−3152	±	770	0.2449	−682	±	190
0.8571	67,713	0.2587	−2781	±	774	0.2725	−759	±	211
0.9208	67,110	0.2862	−3385	±	768	0.2999	−858	±	232
0.9454	69,413	0.3130	−1082	±	794	0.3260	−866	±	253
0.9505	68,417	0.3382	−2077	±	782	0.3504	−910	±	272
1.0018	66,728	0.3623	−3767	±	763	0.3742	−1015	±	290
1.1233	69,258	0.3866	−1236	±	792	0.3990	−1024	±	310
1.1537	67,284	0.4107	−3211	±	770	0.4224	−1109	±	328
1.2312	69,290	0.4339	−1204	±	792	0.4455	−1113	±	346
1.2860	68,504	0.4566	−1991	±	783	0.4677	−1148	±	364
1.3598	66,816	0.4785	−3679	±	764	0.4893	−1251	±	380
1.4048	69,017	0.4996	−1478	±	789	0.5099	−1260	±	397
1.5403	68,532	0.5203	−1963	±	784	0.5306	−1290	±	413
T = 1673 K; starting amount n(Sn) = 45.323 · 10−3 mol; run 1
0.3037	62,020	0.0033	−4986	±	722	0.0067	−33	±	5
0.3793	61,510	0.0108	−5496	±	716	0.0148	−78	±	11
0.5062	62,193	0.0202	−4813	±	724	0.0256	−130	±	18
0.5337	62,722	0.0311	−4284	±	730	0.0366	−177	±	27
0.6486	62,596	0.0432	−4410	±	729	0.0497	−234	±	36
0.7221	62,834	0.0568	−4172	±	732	0.0639	−293	±	46
0.7363	62,448	0.0709	−4558	±	727	0.0779	−357	±	57
0.7654	62,826	0.0850	−4180	±	732	0.0921	−416	±	67
0.8185	62,551	0.0994	−4456	±	728	0.1067	−481	±	78
1.0190	62,749	0.1155	−4257	±	731	0.1243	−555	±	91
1.0371	62,530	0.1329	−4477	±	728	0.1415	−632	±	103
1.1581	62,924	0.1507	−4083	±	733	0.1599	−706	±	117
1.2016	63,266	0.1691	−3740	±	737	0.1782	−772	±	130
1.4235	63,684	0.1886	−3323	±	742	0.1989	−837	±	145
1.4590	63,016	0.2090	−3990	±	734	0.2190	−916	±	160
1.4944	62,919	0.2288	−4088	±	733	0.2386	−995	±	175
1.6293	62,972	0.2488	−4034	±	733	0.2589	−1076	±	190
1.6508	63,139	0.2687	−3867	±	735	0.2784	−1150	±	204
1.9049	62,887	0.2890	−4119	±	732	0.2996	−1237	±	219
T = 1673 K; starting amount n(Sn) = 4.6547 · 10−3 mol; run 2
0.2668	61,415	0.0271	−5591	±	1072	0.0542	−303	±	58
0.3692	61,460	0.0872	−5546	±	1073	0.1202	−669	±	129
0.5210	61,815	0.1597	−5191	±	1079	0.1991	−1074	±	214
0.5591	62,522	0.2342	−4484	±	1091	0.2694	−1374	±	291
0.5569	62,160	0.2987	−4846	±	1085	0.3281	−1653	±	355
0.5808	62,917	0.3541	−4090	±	1098	0.3801	−1841	±	412
0.6682	62,714	0.4054	−4292	±	1095	0.4307	−2042	±	468
0.7276	63,346	0.4540	−3660	±	1106	0.4773	−2174	±	520
1.7538	61,438	0.5203	−5568	±	1073	0.5633	−2732	±	611
0.9291	64,644	0.5808	−2362	±	1128	0.5983	−2703	±	653
0.9928	62,732	0.6141	−4275	±	1095	0.6300	−2827	±	688
1.1957	64,855	0.6461	−2151	±	1132	0.6621	−2768	±	726
1.2680	64,518	0.6764	−2488	±	1126	0.6906	−2745	±	760
1.3619	65,806	0.7034	−1200	±	1149	0.7163	−2616	±	792
1.4089	65,812	0.7275	−1194	±	1149	0.7387	−2504	±	820
1.6662	65,760	0.7499	−1247	±	1148	0.7611	−2396	±	848
1.8643	65,535	0.7715	−1471	±	1144	0.7819	−2316	±	874
2.1466	66,363	0.7919	−643	±	1158	0.8019	−2163	±	900
T = 1673 K; starting amount n(Sn) = 21.8652 · 10−3 mol; run 3
0.1302	61,457	0.0030	−5549	±	1206	0.0059	−33	±	7
0.1796	61,413	0.0099	−5593	±	1205	0.0140	−78	±	17
0.1898	60,253	0.0182	−6753	±	1182	0.0223	−135	±	27
0.1830	61,003	0.0263	−6004	±	1197	0.0303	−182	±	36
0.2227	61,359	0.0350	−5647	±	1204	0.0398	−236	±	48
0.2336	62,226	0.0446	−4780	±	1221	0.0495	−282	±	60
0.2433	61,671	0.0545	−5335	±	1210	0.0595	−335	±	72
0.5971	62,406	0.0712	−4600	±	1225	0.0830	−441	±	100
0.7331	62,054	0.0967	−4952	±	1218	0.1104	−576	±	134
0.8605	61,998	0.1254	−5008	±	1217	0.1405	−726	±	170
0.9231	62,348	0.1555	−4658	±	1224	0.1706	−864	±	207
1.0887	62,888	0.1870	−4118	±	1234	0.2035	−993	±	248
1.2702	62,445	0.2211	−4561	±	1225	0.2387	−1151	±	291
1.3374	62,759	0.2556	−4247	±	1232	0.2726	−1288	±	333
1.5574	62,876	0.2905	−4130	±	1234	0.3084	−1428	±	378
1.8793	62,839	0.3278	−4167	±	1233	0.3472	−1582	±	426
1.8973	63,665	0.3647	−3341	±	1249	0.3822	−1676	±	470
2.2379	63,211	0.4006	−3795	±	1241	0.4189	−1802	±	516
T = 1573 K; starting amount n(Sn) = 7.4131 · 10−3 mol; run 1
0.3994	56,697	0.0256	−6501	±	852	0.0511	−332	±	44
0.4261	57,163	0.0757	−6035	±	859	0.1002	−627	±	86
0.4435	57,120	0.1232	−6078	±	859	0.1462	−906	±	125
0.4885	56,683	0.1689	−6514	±	852	0.1916	−1204	±	164
0.4894	55,845	0.2121	−7353	±	840	0.2326	−1516	±	198
0.5001	56,076	0.2515	−7121	±	843	0.2704	−1792	±	230
0.5014	57,133	0.2875	−6065	±	859	0.3047	−1993	±	260
0.5122	56,333	0.3206	−6865	±	847	0.3366	−2216	±	286
0.5298	56,773	0.3516	−6424	±	854	0.3666	−2407	±	312
0.5336	56,684	0.3804	−6514	±	852	0.3942	−2586	±	336
0.5545	54,958	0.4073	−8240	±	826	0.4205	−2831	±	357
0.5591	55,503	0.4326	−7695	±	834	0.4447	−3035	±	377
0.5593	57,039	0.4559	−6159	±	858	0.4671	−3160	±	396
0.6344	57,023	0.4787	−6175	±	857	0.4903	−3292	±	416
0.6932	56,163	0.5019	−7034	±	844	0.5135	−3462	±	436
T = 1573 K; starting amount n(Sn) = 7.4168 · 10−3 mol; run 2
0.4111	56,968	0.0263	−6229	±	828	0.0525	−327	±	43
0.4636	56,361	0.0790	−6837	±	819	0.1055	−691	±	87
0.4713	56,652	0.1295	−6545	±	823	0.1536	−1006	±	126
0.4870	55,894	0.1759	−7304	±	812	0.1982	−1338	±	163
0.4932	56,215	0.2185	−6983	±	817	0.2388	−1623	±	196
0.5091	56,280	0.2577	−6917	±	818	0.2766	−1886	±	227
0.5452	56,006	0.2948	−7192	±	814	0.3131	−2154	±	256
0.5522	56,216	0.3298	−6982	±	817	0.3465	−2389	±	283
0.5732	56,248	0.3622	−6949	±	817	0.3779	−2608	±	309
0.5817	55,983	0.3924	−7215	±	813	0.4069	−2823	±	333
0.5936	56,997	0.4203	−6200	±	828	0.4337	−2976	±	355
0.6009	57,298	0.4462	−5900	±	832	0.4586	−3104	±	376
0.6208	56,295	0.4703	−6902	±	818	0.4821	−3269	±	395
0.6994	58,355	0.4941	−4843	±	848	0.5062	−3342	±	416
0.7019	57,810	0.5172	−5387	±	840	0.5282	−3433	±	435
0.7564	58,305	0.5391	−4892	±	847	0.5499	−3500	±	454
0.7800	59,597	0.5601	−3601	±	866	0.5702	−3505	±	473
0.8671	59,757	0.5805	−3441	±	868	0.5908	−3502	±	492
T = 1573 K; starting amount n(Sn) = 4.3668 · 10−3 mol; run 3
0.1423	56,775	0.0158	−6423	±	936	0.0316	−203	±	30
0.4875	56,528	0.0788	−6670	±	932	0.1260	−834	±	118
0.5201	55,923	0.1672	−7274	±	922	0.2084	−1441	±	193
0.5349	56,180	0.2434	−7017	±	926	0.2784	−1934	±	258
0.5827	56,172	0.3101	−7026	±	926	0.3418	−2381	±	317
0.6672	55,965	0.3719	−7233	±	922	0.4019	−2824	±	372
0.6699	57,357	0.4271	−5840	±	945	0.4522	−3078	±	420
0.9232	58,536	0.4806	−4661	±	965	0.5091	−3242	±	477
0.9242	59,108	0.5322	−4090	±	974	0.5553	−3322	±	524
1.0247	59,842	0.5763	−3356	±	986	0.5973	−3325	±	567
1.0419	60,586	0.6149	−2611	±	999	0.6326	−3263	±	605
1.0535	60,923	0.6476	−2275	±	1004	0.6625	−3182	±	638
1.0567	60,791	0.6752	−2407	±	1002	0.6880	−3124	±	665
1.1800	60,917	0.7001	−2281	±	1004	0.7122	−3058	±	691
1.2007	61,573	0.7228	−1625	±	1015	0.7333	−2953	±	715
1.2462	62,175	0.7428	−1023	±	1025	0.7522	−2816	±	737
1.3156	62,047	0.7608	−1150	±	1023	0.7694	−2701	±	757
1.4264	61,968	0.7775	−1229	±	1021	0.7856	−2598	±	775
1.4268	61,985	0.7926	−1213	±	1022	0.7996	−2507	±	792
T = 1473 K; starting amount n(Sn) = 7.4130 · 10−3 mol; run 1
0.4199	51,379	0.0268	−8150	±	850	0.0536	−437	±	46
0.4247	50,953	0.0779	−8577	±	843	0.1023	−856	±	87
0.4613	50,002	0.1260	−9527	±	827	0.1498	−1314	±	126
0.4812	50,820	0.1720	−8709	±	841	0.1942	−1701	±	163
0.5437	52,258	0.2167	−7271	±	864	0.2392	−2012	±	202
0.5643	50,723	0.2600	−8806	±	839	0.2809	−2384	±	237
0.5826	50,047	0.3001	−9482	±	828	0.3193	−2764	±	269
0.6426	51,315	0.3383	−8214	±	849	0.3572	−3067	±	301
0.6671	51,191	0.3748	−8338	±	847	0.3924	−3355	±	331
0.6694	53,404	0.4082	−6125	±	883	0.4240	−3499	±	360
0.6768	50,717	0.4384	−8812	±	839	0.4528	−3765	±	384
0.6794	51,892	0.4658	−7637	±	858	0.4789	−3950	±	406
0.6958	52,295	0.4911	−7234	±	865	0.5032	−4103	±	428
0.7027	52,087	0.5144	−7442	±	862	0.5255	−4253	±	447
0.7367	49,770	0.5362	−9760	±	823	0.5469	−4501	±	464
0.8020	52,583	0.5575	−6946	±	870	0.5681	−4615	±	483
0.8239	51,111	0.5780	−8418	±	845	0.5879	−4790	±	500
T = 1473 K; starting amount n(Sn) = 7.4966 · 10−3 mol; run 2
0.4396	49,920	0.0277	−9609	±	906	0.0554	−532	±	50
0.4771	50,466	0.0822	−9064	±	916	0.1090	−1016	±	99
0.4836	50,068	0.1332	−9461	±	909	0.1574	−1475	±	143
0.4856	50,047	0.1792	−9482	±	908	0.2010	−1890	±	183
0.4944	50,786	0.2210	−8743	±	922	0.2410	−2233	±	220
0.5175	50,618	0.2599	−8912	±	919	0.2788	−2565	±	255
0.5245	50,576	0.2961	−8953	±	918	0.3134	−2872	±	286
0.5304	50,793	0.3293	−8736	±	922	0.3452	−3144	±	316
0.5733	50,120	0.3608	−9409	±	910	0.3765	−3442	±	344
0.6425	50,945	0.3923	−8584	±	925	0.4081	−3703	±	374
0.6581	51,424	0.4227	−8106	±	933	0.4373	−3921	±	401
0.7069	52,720	0.4515	−6809	±	957	0.4657	−4066	±	429
0.7747	53,291	0.4797	−6239	±	967	0.4936	−4180	±	457
0.7807	50,860	0.5063	−8670	±	923	0.5190	−4405	±	481
0.8111	53,234	0.5309	−6295	±	966	0.5428	−4498	±	505
0.8123	51,793	0.5536	−7736	±	940	0.5644	−4651	±	525
0.8317	53,390	0.5744	−6140	±	969	0.5845	−4720	±	546
T = 1373 K; starting amount n(Sn) = 7.2627 · 10−3 mol; run 1
0.5292	44,610	0.0340	−11,374	±	1459	0.0679	−773	±	99
0.5306	44,054	0.0976	−11,931	±	1441	0.1273	−1484	±	185
0.6176	44,087	0.1575	−11,898	±	1442	0.1876	−2203	±	271
0.6273	43,722	0.2143	−12,262	±	1430	0.2409	−2863	±	347
0.6507	44,216	0.2651	−11,768	±	1446	0.2892	−3430	±	417
0.6804	43,211	0.3114	−12,773	±	1413	0.3336	−4013	±	480
0.6853	43,847	0.3533	−12,138	±	1434	0.3730	−4494	±	536
0.7061	44,086	0.3910	−11,898	±	1442	0.4090	−4919	±	588
0.8114	44,407	0.4273	−11,578	±	1452	0.4456	−5332	±	642
T = 1273 K; starting amount n(Sn) = 21.0679 · 10−3 mol; run 1
0.5190	37,435	0.0120	−15,114	±	520	0.0240	−363	±	13
0.5193	38,339	0.0355	−14,210	±	533	0.0470	−689	±	25
0.5554	38,199	0.0586	−14,350	±	531	0.0703	−1023	±	38
0.5845	38,586	0.0820	−13,963	±	536	0.0937	−1349	±	50
0.5907	38,492	0.1049	−14,058	±	535	0.1162	−1664	±	61
0.5928	38,783	0.1269	−13,766	±	539	0.1376	−1957	±	72
0.6035	38,981	0.1480	−13,569	±	541	0.1584	−2237	±	83
0.6368	39,242	0.1688	−13,308	±	545	0.1793	−2512	±	93
0.6374	39,481	0.1892	−13,069	±	548	0.1992	−2768	±	103
0.6502	38,338	0.2088	−14,212	±	532	0.2185	−3044	±	113
0.6742	38,190	0.2280	−14,359	±	530	0.2375	−3320	±	122
0.6813	33,923	0.2467	−18,626	±	471	0.2559	−3688	±	129
0.6955	32,254	0.2648	−20,295	±	448	0.2737	−4086	±	136
0.7144	29,665	0.2825	−22,885	±	412	0.2912	−4538	±	141
0.7162	27,107	0.2995	−25,443	±	376	0.3079	−5030	±	146
0.7236	25,321	0.3159	−27,228	±	352	0.3239	−5545	±	149
0.7328	26,015	0.3317	−26,535	±	361	0.3395	−6028	±	153
0.7332	26,118	0.3469	−26,432	±	363	0.3543	−6486	±	157
0.7396	26,827	0.3615	−25,722	±	373	0.3686	−6912	±	161
0.7863	25,672	0.3759	−26,878	±	357	0.3832	−7372	±	164
0.7885	25,972	0.3901	−26,578	±	361	0.3971	−7805	±	167
0.7944	26,273	0.4038	−26,276	±	365	0.4105	−8216	±	170
0.8173	26,296	0.4171	−26,253	±	365	0.4237	−8619	±	173
0.8335	27,394	0.4301	−25,156	±	380	0.4365	−8988	±	177
0.8409	26,524	0.4427	−26,025	±	368	0.4489	−9363	±	180
T = 1273 K; starting amount n(Sn) = 21.3158 · 10−3 mol; run 2
0.5216	38,641	0.0119	−13,774	±	462	0.0239	−329	±	11
0.5694	39,592	0.0363	−12,820	±	473	0.0487	−646	±	23
0.5701	39,795	0.0605	−12,616	±	475	0.0723	−943	±	34
0.5712	39,356	0.0835	−13,056	±	470	0.0948	−1237	±	45
0.5978	40,367	0.1060	−12,042	±	482	0.1172	−1505	±	55
0.6123	40,207	0.1281	−12,203	±	480	0.1390	−1769	±	66
0.6235	40,690	0.1496	−11,718	±	486	0.1602	−2014	±	76
0.6487	40,856	0.1707	−11,551	±	488	0.1811	−2251	±	87
0.6649	40,924	0.1913	−11,483	±	489	0.2015	−2481	±	97
0.6801	37,403	0.2114	−15,017	±	447	0.2214	−2793	±	105
0.6970	35,354	0.2310	−17,073	±	422	0.2407	−3147	±	113
0.7130	35,215	0.2501	−17,212	±	421	0.2595	−3496	±	121
0.7171	31,147	0.2685	−21,294	±	372	0.2775	−3928	±	127
0.7207	29,255	0.2861	−23,192	±	349	0.2947	−4388	±	132
0.7347	28,666	0.3031	−23,784	±	342	0.3115	−4848	±	137
0.7412	26,520	0.3195	−25,937	±	317	0.3276	−5341	±	141
0.7701	26,681	0.3355	−25,776	±	319	0.3435	−5826	±	146
0.7732	27,125	0.3511	−25,330	±	324	0.3588	−6279	±	150
0.7802	27,747	0.3661	−24,706	±	331	0.3735	−6702	±	154
0.7828	26,583	0.3805	−25,874	±	318	0.3876	−7133	±	158
0.7881	27,188	0.3944	−25,267	±	325	0.4011	−7535	±	161
0.8008	24,969	0.4077	−27,494	±	298	0.4143	−7974	±	164
0.8089	27,207	0.4207	−25,247	±	325	0.4270	−8349	±	168
0.8348	27,726	0.4333	−24,727	±	331	0.4396	−8709	±	171
0.8390	26,933	0.4457	−25,523	±	322	0.4517	−9072	±	175
T = 1173 K; starting amount n(Sn) = 21.2417 · 10−3 mol; run 1
0.5130	30,295	0.0118	−18,919	±	911	0.0236	−446	±	21
0.5192	30,472	0.0350	−18,742	±	917	0.0463	−873	±	42
0.5413	30,598	0.0577	−18,616	±	920	0.0690	−1294	±	63
0.6180	30,953	0.0812	−18,261	±	931	0.0935	−1741	±	86
0.6203	29,379	0.1052	−19,835	±	884	0.1169	−2208	±	107
0.6286	27,680	0.1281	−21,534	±	833	0.1394	−2700	±	125
0.6500	29,735	0.1504	−19,479	±	894	0.1615	−3130	±	145
0.6608	24,861	0.1721	−24,353	±	748	0.1828	−3670	±	160
0.6740	23,414	0.1931	−25,801	±	704	0.2034	−4229	±	174
0.6839	21,189	0.2134	−28,026	±	637	0.2234	−4824	±	186
0.6867	21,832	0.2329	−27,383	±	657	0.2424	−5377	±	197
0.6995	22,342	0.2516	−26,873	±	672	0.2608	−5900	±	209
0.7222	21,222	0.2699	−27,992	±	638	0.2789	−6442	±	219
0.7541	23,001	0.2879	−26,214	±	692	0.2969	−6935	±	231
0.7586	23,041	0.3056	−26,173	±	693	0.3142	−7406	±	242
0.7619	22,757	0.3224	−26,457	±	684	0.3306	−7864	±	253
0.7644	21,033	0.3385	−28,181	±	633	0.3464	−8342	±	262
0.7769	21,701	0.3540	−27,513	±	653	0.3616	−8789	±	271
0.7879	22,884	0.3690	−26,330	±	688	0.3764	−9195	±	281
0.7892	22,330	0.3835	−26,884	±	672	0.3905	−9596	±	289
0.7962	22,222	0.3973	−26,993	±	668	0.4041	−9984	±	298
0.7985	23,379	0.4107	−25,836	±	703	0.4172	−10,331	±	307
0.7990	22,820	0.4234	−26,394	±	686	0.4297	−10,676	±	315
0.8145	23,852	0.4358	−25,362	±	717	0.4419	−10,990	±	324
0.8181	24,722	0.4478	−24,492	±	744	0.4536	−11,274	±	332
T = 1173 K; starting amount n(Sn) = 21.0598 · 10−3 mol; run 2
0.5448	30,340	0.0126	−18,874	±	918	0.0252	−427	±	23
0.5608	30,520	0.0375	−18,695	±	923	0.0499	−835	±	46
0.5703	30,843	0.0618	−18,371	±	933	0.0737	−1238	±	68
0.5988	30,973	0.0856	−18,241	±	937	0.0975	−1667	±	90
0.6361	29,473	0.1095	−19,741	±	892	0.1214	−2116	±	112
0.5715	30,926	0.1317	−18,288	±	936	0.1419	−2591	±	131
0.6378	24,618	0.1528	−24,596	±	745	0.1636	−3006	±	146
0.6404	23,616	0.1740	−25,598	±	715	0.1844	−3531	±	161
0.6635	22,644	0.1946	−26,570	±	685	0.2048	−4076	±	174
0.6646	21,235	0.2145	−27,980	±	643	0.2243	−4658	±	185
0.6987	22,554	0.2340	−26,660	±	682	0.2437	−5199	±	198
0.7064	19,959	0.2531	−29,255	±	604	0.2624	−5711	±	208
0.7099	21,748	0.2714	−27,466	±	658	0.2803	−6242	±	219
0.7117	21,286	0.2889	−27,928	±	644	0.2974	−6725	±	229
0.7220	22,500	0.3057	−26,714	±	681	0.3139	−7186	±	239
0.7295	23,319	0.3219	−25,895	±	706	0.3299	−7634	±	250
0.7557	21,840	0.3377	−27,374	±	661	0.3456	−8104	±	260
0.7573	22,851	0.3531	−26,363	±	691	0.3607	−8544	±	270
0.7583	21,994	0.3679	−27,221	±	665	0.3750	−8942	±	279
0.7654	22,836	0.3820	−26,378	±	691	0.3889	−9336	±	288
0.7920	22,936	0.3958	−26,279	±	694	0.4027	−9718	±	297
0.7925	22,500	0.4092	−26,714	±	681	0.4158	−10,059	±	305
0.8040	21,995	0.4222	−27,219	±	666	0.4285	−10,398	±	313
0.8159	23,804	0.4347	−25,410	±	720	0.4409	−10,706	±	322
0.8180	23,121	0.4468	−26,093	±	700	0.4528	−10,985	±	330

Average of xCo or xSn before and after the drop.

Per mole of binary mixture.

FIGURE 1

Experimental data of integral enthalpy of mixing of liquid Co–Sn alloys; standard states: pure liquid components.

Random as well as systematic errors of drop calorimetry depend on the calorimeter construction, calibration procedure, signal integration and “chemical errors”, e.g. incomplete reaction or impurities. Considering many calibration measurements done by dropping NIST standard sapphire, the standard deviation can be estimated to be less than ±1% for the HT-1000 and less than ±1.5% for the MHTC instrument. The systematic errors are mainly caused by parasitic heat flows, base line problems at signal integration and dropping and mixing problems. One can estimate that the random error of the measured enthalpy is ±150 J for measurements with our HT-1000 and ±300 J for the MHTC calorimeter. The experimental results of the enthalpy of mixing and the partial enthalpy of mixing together with error values for each drop are represented in the tables 1 and 2.

Selected furnace cooled alloys after calorimetric runs were checked by scanning electron microscopy (SEM) and X-ray diffraction (XRD) to ensure complete dissolution of the dropped component. The powder XRD measurements were done on a Bruker D8 diffractometer at ambient temperature using Ni filtered CuKα radiation (accelerating voltage 40 kV, electron current 40 mA). The diffractometer operates in the θ:2θ mode. The powder was fixed with petroleum jelly on a single crystal silicon sample carrier which was rotated during the measurement. The detection unit was a Lynxeye strip detector. Indexing of the phases was supported by the Inorganic Crystal Structural Database (ICSD). Rietveld refinement of the XRD patterns was done with the Topas3® software provided by Bruker AXS.

The electron microscope Zeiss Supra 55 VP was used for metallographic investigations. The excitation energy of the electron beam was (15 to 20) kV; backscattered electrons were detected in order to visualize the surfaces of the samples. The chemical analyses of the sample phases were performed using the energy dispersive X-ray (EDX) technique with the two characteristic spectral lines Cu_K and Sb_L. Standard deviations for the chemical compositions obtained from EDX were about ±1 at.%.

Results and discussion

The experimental results of 16 measurement series over wide concentration ranges performed at temperatures (1173 to 1773) K can be found in table 1. The values within the shaded fields refer to the two-phase fields (L + CoSn) at T = 1173 K or (L + Co3Sn2) at higher temperatures. Figure 1 shows the experimental data indicating a clear temperature dependence of the integral enthalpy of mixing, with more exothermic values at lower temperatures. As an example, the behavior of the partial and integral enthalpies of mixing crossing a two-phase field (L + CoSn) is shown in figure 2. A kink in the integral enthalpy vs. concentration curve indicates the liquidus limit. Within the two-phase region the curve becomes linear. The intersection of the fitted curve with the linear part corresponds to the limiting liquidus concentration at T = 1173 K. The concentration dependence of the partial enthalpy values exhibits a discontinuity at the phase boundary. The estimated limiting liquidus concentration values at approx. 15 at.% Co at T = 1173 K and 26 at.% Co at T = 1273 K are in good agreement with literature data [7] (15 and 27 at.% Co, respectively).

FIGURE 2

Partial and integral enthalpies of mixing of Co–Sn alloys at T = 1173 K crossing the (L + CoSn) two phase field; standard states: pure liquid components.

In order to prove that all pieces of the solid component dropped into the liquid bath had completely dissolved, selected alloys were investigated by means of SEM–EDX and powder XRD measurements after the calorimeter had cooled down. The results of phase analyses along with BSE images of three exemplary alloys can be found in table 3. No residual pure Co or Sn was found in the investigated samples. The Sn phase in the alloy Co43Sn57 clearly origins from non-equilibrium solidification of the liquid phase and is not a residual of the Sn dropped. The XRD phase analysis fully confirmed the phases that had been found by SEM–EDX.

TABLE 3

SEM–EDX results of Co–Sn samples after calorimetry.

Sample	Temperature of calor. meas. K	Dropped component	Phase 1 (dark)			Phase 2 (gray)			Phase 3 (white gray)			Phase 4 (white)			SEM image
				Co	Sn		Co	Sn		Co	Sn		Co	Sn
				at.%	at.%		at.%	at.%		at.%	at.%		at.%	at.%
Co53Sn47	1773	Co	αCo3Sn2	57.9	42.1	CoSn	49.4	50.6	CoSn2	32.9	67.1
Co43Sn57	1773	Sn	αCo3Sn2	58.2	41.8	CoSn	49.5	50.5	CoSn2	32.7	67.3	(βSn)	1.3	98.7
Co2Sn98	673	Co	CoSn2	31.9	68.1	CoSn3	24.1	75.9	βSn	0.1	99.9

For a mathematical description of the integral enthalpies of mixing as a function of the molar fraction of Co, the experimental data at temperatures (1173 to 1773) K were subjected to a least square fit based on a Redlich–Kister polynomial [27] as proposed by Ansara and Dupin [28]where i and j are equal to 1 and 2 for the elements Co and Sn, and are the binary interaction parameters, with ν = 0, 1, … . These interaction parameters were determined using the experimental Δ values from table 1, and they are listed in table 4. At all temperatures it was possible to describe the course of the values applying only two interaction parameters (νmax = 1). The obtained data were plotted as dashed lines in figure 1. According to our results the minimum of the enthalpy of mixing is shifted towards less exothermic values with increasing temperatures; from about −7820 J/mol at T = 1173 K to about −1350 J/mol at T = 1773 K with the minimum point concentration between about (59 and 61) at.% Co. These observations can be explained based on the so called “association theory” [29] assuming particular interactions within a certain configuration of Co and Sn. The changes of binary interaction parameters with temperature were described using linear equations: L = −75466.9610 + 39.6726 * T and L = −30685.2702 + 15.0835 * T (temperatures in K). A graphical presentation of these fits is shown in figure 3.

TABLE 4

Binary interaction parameters at different temperatures.

T, K	vL (J · mol−1)
1773	0L = −5074.42151L = −2618.7618
1673	0L = −9643.14891L = −6776.9058
1573	0L = −12681.38151L = −6599.7925
1473	0L = −16845.51821L = −8735.1269
1373	0L = −21679.81771L = −11432.1078
1273	0L = −23247.72891L = −10512.1250
1173	0L = −30032.94531L = −12595.8043

L = −75466.9610 + 39.6726T.

L = −30685.2702 + 15.0835T; temperatures in K.

FIGURE 3

Temperature dependencies of binary interaction parameters for the Redlich–Kister polynomial.

The possibility to form such associates in the liquid state was discussed for Co–Sn by Ivanov [23] and Komarnytsky et al. [30]. The first author [23] supposed the existence of an associate with the stoichiometry Co2Sn while the authors of [30] postulated Co3Sn2 as an associate. Both compositions appear as solid phases in Co–Sn although Co3Sn2 is the more stable compound. Generally, the stability of associates is considered to decrease with rising temperature which explains the less exothermic values at elevated temperatures. The competition between the two types of associates could be the reason for the concentration shift of the minimum enthalpy of mixing to higher Co contents. The loss of stability with increasing temperature should be less for Co2Sn than for Co3Sn2. Fitting our experimental data to common association models [29] does not give a clear result which associates are involved. It is possible to well describe the experimental data but the physical meaning is not significant. For a mathematical description, the Redlich–Kister polynomials are preferable because they are much simpler and the number of necessary parameters is lower.

A comparison of our experimental data at T = (973 and 1573) K with available literature data at similar temperatures is shown in figure 4. Jiang et al. [7] modeled the concentration and temperature dependencies of the integral enthalpy of mixing, based on earlier literature data, and found the minimum at T = 1573 K around −1630 J/mol close to 56 at.% Co whereas our data are characterized by a minimum of approx. −3370 J/mol around 61 at.% Co at the same temperature. Our results are in satisfactory agreement with the experimental data by Vassilev et al. [11] at T = 991 K and generally confirm the tendency to an enthalpy minimum on the cobalt-rich side. Figure 5 shows our results for Δ at T = 1773 K compared to literature data also obtained at such high temperatures. The values given by Körber and Oelsen [8] agree in the Co-rich part but become endothermic towards pure Sn. The values given by Esin et al. [9] are quite different but still exothermic at xCo ⩾ 0.2. They report about calorimetric measurements but only show calculations and not their original experimental results. Lück et al. [10] surprisingly show endothermic enthalpy of mixing values in the Co-rich part, contrary to any other results in the literature. At this point it has to be mentioned that it is not clear whether other authors considered the enthalpy effect due to the magnetic transition of cobalt for their evaluations. The enthalpy effect which is approx. (8 to 8.5) kJ/mol was calculated according to the SGTE database and needs to be provided if ferromagnetic Co dissolves in liquid Sn. This has to be considered for the evaluations otherwise the results are less exothermic or even endothermic.

FIGURE 4

Integral enthalpy of mixing of liquid Co–Sn alloys at about T = 991 K (Vassilev et al.[11] at T = 991 K and presented data at T = 973 K) and T = 1573 K (Jiang et al.[7], Eremenko et al.[12] and presented data); standard states: pure liquid components.

FIGURE 5

Integral enthalpy of mixing of liquid Co–Sn alloys at high temperatures (Körber and Oelsen [8] at T = 1773 K, Esin et al.[9] at T = 1850 K, Luck et al.[10] at T = 1780 K and presented data at T = 1773 K); standard states: pure liquid components.

The results of all our measurements up to xCo ⩽ 0.07 performed at temperatures (673 to 1773) K for the determination of the limiting partial enthalpy of Co in Sn are listed in table 2, which comprises the heat effect for each drop and the partial and integral enthalpies of mixing.

TABLE 2

Integral and partial enthalpies of mixing of liquid Co–Sn alloys at T = (1773 to 673) K; standard states: pure liquid components; Co in liquid Sn.

Dropped mole	Measured enthalpy	Partial molar enthalpy				Integral molar enthalpy
n(Co)	ΔHSignal	xCoa	ΔH‾_Co			xCob	ΔMixH
10−3 mol	J · mol−1		J · mol−1				J · mol−1
T = 1773 K; starting amount n(Sn) = 108.6870 · 10−3 mol; run1
0.5588	67,578	0.0026	−2904	±	874	0.0051	−15	±	4
0.5967	67,756	0.0078	−2726	±	876	0.0105	−30	±	9
0.6014	68,693	0.0132	−1789	±	888	0.0159	−39	±	14
0.6115	67,557	0.0186	−2925	±	874	0.0213	−55	±	19
0.6183	68,232	0.0240	−2250	±	882	0.0267	−67	±	24
0.6186	69,175	0.0294	−1307	±	895	0.0321	−74	±	28
0.6349	69,655	0.0348	−827	±	901	0.0375	−78	±	33
0.6524	69,265	0.0403	−1217	±	896	0.0431	−85	±	38
0.6585	69,390	0.0458	−1092	±	897	0.0486	−91	±	43
0.6610	69,140	0.0513	−1341	±	894	0.0541	−98	±	48
0.6855	70,168	0.0569	−314	±	907	0.0597	−99	±	53
0.6958	69,693	0.0625	−789	±	901	0.0653	−103	±	58
0.7181	68,425	0.0682	−2057	±	885	0.0710	−115	±	63
0.7249	68,752	0.0739	−1730	±	889	0.0768	−125	±	68
0.7576	69,561	0.0797	−921	±	900	0.0827	−130	±	74
0.7926	69,307	0.0857	−1175	±	896	0.0888	−137	±	79
0.8182	69,335	0.0919	−1147	±	897	0.0950	−144	±	85
T = 1673 K; starting amount n(Sn) = 37.9607 · 10−3 mol; run1
0.1191	61,079	0.0016	−5868	±	792	0.0031	−18	±	2
0.1388	62,442	0.0049	−4504	±	810	0.0067	−34	±	5
0.1461	61,800	0.0086	−5147	±	801	0.0105	−54	±	8
0.1602	61,994	0.0126	−4952	±	804	0.0146	−74	±	12
0.1724	61,797	0.0168	−5149	±	801	0.0190	−97	±	15
0.1999	62,335	0.0216	−4611	±	808	0.0241	−120	±	19
0.2310	62,560	0.0270	−4387	±	811	0.0298	−145	±	24
0.2309	62,575	0.0327	−4371	±	811	0.0355	−170	±	29
0.2349	62,280	0.0384	−4667	±	808	0.0413	−196	±	33
0.2379	62,250	0.0441	−4697	±	807	0.0470	−223	±	38
0.2600	61,300	0.0501	−5646	±	795	0.0532	−258	±	43
0.2695	61,961	0.0563	−4985	±	803	0.0595	−290	±	48
0.3346	61,532	0.0633	−5415	±	798	0.0672	−332	±	54
0.3747	62,667	0.0715	−4279	±	813	0.0757	−368	±	61
0.3935	62,884	0.0801	−4062	±	815	0.0845	−403	±	68
T = 1573 K; starting amount n(Sn) = 22.5465 · 10−3 mol; run1
0.1614	56,190	0.0036	−7008	±	1139	0.0071	−50	±	8
0.1614	56,214	0.0106	−6983	±	1140	0.0141	−99	±	16
0.1859	56,078	0.0181	−7119	±	1137	0.0221	−155	±	25
0.1895	56,168	0.0261	−7030	±	1139	0.0300	−211	±	34
0.2005	55,746	0.0342	−7451	±	1130	0.0383	−273	±	44
0.2322	56,376	0.0431	−6822	±	1143	0.0478	−338	±	54
0.2386	55,589	0.0525	−7609	±	1127	0.0573	−410	±	65
0.2397	55,371	0.0619	−7827	±	1123	0.0666	−484	±	76
T = 1573 K; starting amount n(Sn) = 22.0460 · 10−3 mol; run 2
0.1356	56,112	0.0031	−7086	±	812	0.0061	−43	±	5
0.1496	55,734	0.0094	−7464	±	806	0.0128	−93	±	10
0.1575	55,485	0.0162	−7713	±	803	0.0197	−146	±	16
0.1689	54,875	0.0233	−8322	±	794	0.0270	−207	±	22
0.1700	56,353	0.0306	−6845	±	815	0.0342	−257	±	28
0.1710	55,711	0.0378	−7487	±	806	0.0414	−311	±	33
0.1740	54,657	0.0450	−8541	±	791	0.0486	−372	±	39
0.3593	57,683	0.0559	−5515	±	835	0.0631	−451	±	51
T = 1473 K; starting amount n(Sn) = 21.2186 · 10−3 mol; run 1
0.1520	50,633	0.0036	−8897	±	606	0.0071	−63	±	4
0.1805	50,140	0.0113	−9390	±	601	0.0154	−141	±	9
0.1923	49,596	0.0198	−9934	±	594	0.0241	−228	±	14
0.1965	49,597	0.0285	−9932	±	594	0.0329	−315	±	20
0.1998	50,703	0.0372	−8826	±	607	0.0416	−392	±	25
0.2000	50,323	0.0459	−9206	±	603	0.0502	−471	±	30
0.2102	49,586	0.0546	−9943	±	594	0.0590	−559	±	35
0.2168	51,048	0.0635	−8481	±	611	0.0680	−634	±	41
T = 1473 K; starting amount n(Sn) = 22.3699 · 10−3 mol; run 2
0.1652	50,622	0.0037	−8908	±	836	0.0073	−65	±	6
0.1692	50,011	0.0110	−9519	±	826	0.0147	−136	±	12
0.1843	50,112	0.0187	−9417	±	828	0.0227	−210	±	19
0.2143	49,759	0.0272	−9770	±	822	0.0317	−299	±	26
0.2143	51,283	0.0362	−8247	±	847	0.0406	−372	±	34
0.2147	49,489	0.0450	−10,040	±	817	0.0494	−460	±	41
0.2213	50,198	0.0538	−9331	±	829	0.0582	−543	±	48
0.2244	49,450	0.0626	−10,079	±	817	0.0670	−632	±	55
T = 1373 K; starting amount n(Sn) = 66.7256 · 10−3 mol; run 1
0.1943	45,469	0.0015	−10,516	±	1069	0.0029	−31	±	3
0.2073	44,684	0.0044	−11,300	±	1051	0.0060	−65	±	6
0.2157	46,022	0.0076	−9963	±	1082	0.0092	−97	±	10
0.2198	46,097	0.0108	−9887	±	1084	0.0124	−129	±	13
0.2207	46,574	0.0140	−9410	±	1095	0.0156	−159	±	17
0.2338	44,988	0.0173	−10,997	±	1058	0.0190	−196	±	20
0.2425	45,942	0.0207	−10,042	±	1080	0.0225	−231	±	24
0.2446	46,769	0.0242	−9216	±	1100	0.0260	−263	±	28
0.2469	44,785	0.0277	−11,199	±	1053	0.0295	−303	±	32
0.2486	45,027	0.0312	−10,958	±	1059	0.0330	−341	±	35
0.2535	45,409	0.0347	−10,575	±	1068	0.0365	−379	±	39
0.2680	45,617	0.0384	−10,367	±	1073	0.0402	−417	±	43
T = 1273 K; starting amount n(Sn) = 75.7459 · 10−3 mol; run 1
0.2448	37,021	0.0016	−15,529	±	743	0.0032	−50	±	2
0.2516	38,058	0.0049	−14,491	±	764	0.0065	−98	±	5
0.2528	37,536	0.0082	−15,013	±	754	0.0098	−147	±	7
0.2548	38,407	0.0114	−14,142	±	771	0.0131	−193	±	10
0.2570	37,896	0.0147	−14,654	±	761	0.0164	−242	±	12
0.2659	38,659	0.0181	−13,890	±	776	0.0198	−289	±	15
0.2743	37,973	0.0215	−14,577	±	763	0.0232	−339	±	18
0.2751	38,210	0.0250	−14,339	±	767	0.0267	−389	±	20
0.2816	37,668	0.0284	−14,882	±	756	0.0302	−441	±	23
0.2893	38,116	0.0320	−14,433	±	765	0.0338	−493	±	26
0.2905	37,614	0.0356	−14,936	±	755	0.0373	−546	±	28
0.2970	38,313	0.0391	−14,237	±	769	0.0410	−597	±	31
0.3002	38,349	0.0428	−14,200	±	770	0.0446	−649	±	34
0.3013	38,113	0.0464	−14436	±	765	0.0482	−701	±	37
0.3138	38,489	0.0501	−14,060	±	773	0.0519	−754	±	40
0.3150	38,064	0.0538	−14,485	±	764	0.0557	−808	±	43
0.3170	38,384	0.0575	−14,165	±	771	0.0594	−860	±	45
0.3202	38,566	0.0612	−13,983	±	774	0.0631	−912	±	48
0.3298	37,834	0.0650	−14,716	±	760	0.0669	−968	±	51
0.3400	38,532	0.0689	−14,017	±	774	0.0708	−1023	±	54
T = 1273 K; starting amount n(Sn) = 75.0990 · 10−3 mol; run 2
0.2377	36,335	0.0016	−16,215	±	730	0.0032	−51	±	2
0.2517	37,612	0.0048	−14,938	±	755	0.0065	−101	±	5
0.2556	37,515	0.0081	−15,035	±	753	0.0098	−151	±	7
0.2570	37,435	0.0115	−15,114	±	752	0.0132	−202	±	10
0.2620	37,778	0.0149	−14,771	±	759	0.0166	−252	±	12
0.2692	37,736	0.0183	−14,814	±	758	0.0200	−303	±	15
0.2721	36,967	0.0217	−15,583	±	742	0.0235	−357	±	18
0.2762	37,310	0.0252	−15,239	±	749	0.0270	−410	±	20
0.2921	37,426	0.0288	−15,124	±	752	0.0306	−466	±	23
0.2946	37,167	0.0325	−15,383	±	746	0.0343	−522	±	26
0.2998	38,233	0.0362	−14,317	±	768	0.0380	−575	±	29
0.3035	37,378	0.0399	−15,171	±	751	0.0417	−632	±	31
0.3035	37,512	0.0436	−15,037	±	753	0.0454	−687	±	34
0.3092	37,868	0.0473	−14,681	±	760	0.0492	−742	±	37
0.3098	37,784	0.0510	−14,765	±	759	0.0529	−797	±	40
0.3181	38,061	0.0548	−14,488	±	764	0.0567	−851	±	43
0.3272	38,267	0.0586	−14,282	±	769	0.0605	−906	±	46
0.3315	37,156	0.0625	−15,394	±	746	0.0644	−966	±	49
0.3384	38,207	0.0664	−14,343	±	767	0.0683	−1022	±	52
T = 1173 K; starting amount n(Sn) = 75.0215 · 10−3 mol; run 1
0.2342	29,714	0.0016	−19,500	±	894	0.0031	−61	±	3
0.2352	30,007	0.0047	−19,207	±	903	0.0062	−120	±	6
0.2458	29,954	0.0078	−19,260	±	901	0.0094	−182	±	8
0.2520	29,772	0.0111	−19,442	±	896	0.0127	−246	±	11
0.2543	30,305	0.0144	−18,909	±	912	0.0160	−309	±	14
0.2593	30,162	0.0177	−19,053	±	907	0.0194	−372	±	17
0.2633	30,221	0.0210	−18,994	±	909	0.0227	−436	±	21
0.2674	29,793	0.0244	−19,422	±	896	0.0261	−502	±	24
0.2688	30,464	0.0278	−18,750	±	917	0.0295	−565	±	27
0.2994	30,463	0.0314	−18,751	±	916	0.0332	−636	±	30
0.3042	30,184	0.0351	−19,030	±	908	0.0370	−707	±	34
0.3090	30,583	0.0389	−18,632	±	920	0.0408	−778	±	37
0.3152	30,345	0.0428	−18,870	±	913	0.0447	−851	±	41
0.3237	30,361	0.0466	−18,853	±	913	0.0486	−925	±	44
0.3260	30,629	0.0506	−18,586	±	921	0.0525	−997	±	48
0.3274	30,301	0.0545	−18,913	±	912	0.0564	−1071	±	51
0.3372	30,816	0.0584	−18,399	±	927	0.0604	−1144	±	55
0.3373	30,607	0.0624	−18,607	±	921	0.0644	−1218	±	59
T = 1173 K; starting amount n(Sn) = 76.6077 · 10−3 mol; run 2
0.2400	29,907	0.0016	−19,307	±	902	0.0031	−60	±	3
0.2465	30,544	0.0047	−18,670	±	921	0.0063	−120	±	6
0.2549	29,790	0.0079	−19,424	±	899	0.0096	−183	±	9
0.2564	30,052	0.0112	−19,162	±	907	0.0129	−246	±	12
0.2648	30,535	0.0145	−18,680	±	921	0.0162	−309	±	15
0.2719	30,898	0.0179	−18,316	±	932	0.0196	−371	±	18
0.2807	30,477	0.0214	−18,737	±	919	0.0231	−437	±	21
0.2841	30,509	0.0249	−18,705	±	920	0.0267	−503	±	24
0.2918	30,331	0.0285	−18,883	±	915	0.0303	−571	±	28
0.2922	30,189	0.0321	−19,026	±	911	0.0338	−639	±	31
0.2990	30,265	0.0357	−18,949	±	913	0.0375	−708	±	34
0.3003	30,770	0.0393	−18,444	±	928	0.0411	−774	±	38
0.3003	30,283	0.0429	−18,931	±	914	0.0447	−842	±	41
0.3044	29,826	0.0465	−19,388	±	900	0.0483	−913	±	44
0.3114	30,532	0.0501	−18,682	±	921	0.0520	−981	±	48
0.3235	30,472	0.0539	−18,742	±	919	0.0557	−1052	±	51
0.3248	30,263	0.0576	−18,951	±	913	0.0595	−1123	±	54
0.3293	30,466	0.0614	−18,749	±	919	0.0633	−1194	±	58
0.3315	30,608	0.0652	−18,607	±	923	0.0671	−1265	±	61
0.3341	30,979	0.0690	−18,235	±	935	0.0709	−1333	±	65
T = 1073 K; starting amount n(Sn) = 80.0034 · 10−3 mol; run 1
0.1727	21,806	0.0011	−24,165	±	1090	0.0022	−52	±	2
0.1753	21,917	0.0032	−24,053	±	1096	0.0043	−104	±	5
0.1815	21,581	0.0055	−24,390	±	1079	0.0066	−159	±	7
0.1829	21,266	0.0077	−24,705	±	1063	0.0088	−215	±	10
0.1837	22,140	0.0100	−23,831	±	1107	0.0111	−268	±	12
0.1838	22,876	0.0122	−23,095	±	1144	0.0133	−320	±	15
0.1869	21,733	0.0145	−24,238	±	1087	0.0156	−375	±	17
0.1870	22,729	0.0167	−23,242	±	1137	0.0178	−428	±	20
0.1877	22,169	0.0190	−23,802	±	1109	0.0201	−481	±	22
0.1880	21,993	0.0212	−23,978	±	1100	0.0224	−535	±	25
0.1893	22,865	0.0235	−23,106	±	1143	0.0246	−587	±	27
0.1895	22,190	0.0257	−23,781	±	1110	0.0269	−641	±	30
0.1896	21,638	0.0280	−24,333	±	1082	0.0291	−695	±	32
0.1908	22,684	0.0302	−23,287	±	1134	0.0313	−748	±	35
0.1918	22,205	0.0325	−23,766	±	1110	0.0336	−801	±	37
0.1919	21,925	0.0347	−24,046	±	1096	0.0358	−855	±	40
0.1932	22,249	0.0369	−23,722	±	1113	0.0381	−908	±	42
0.1950	21,937	0.0392	−24,034	±	1097	0.0403	−962	±	45
0.1952	22,677	0.0414	−23,294	±	1134	0.0426	−1014	±	47
0.1969	22,365	0.0437	−23,606	±	1118	0.0448	−1067	±	50
T = 1073 K; starting amount n(Sn) = 79.9663 · 10−3 mol; run 2
0.1656	21,689	0.0010	−24,282	±	1087	0.0021	−50	±	2
0.1695	22,066	0.0031	−23,905	±	1105	0.0042	−101	±	5
0.1702	20,901	0.0052	−25,070	±	1047	0.0063	−153	±	7
0.1741	21,864	0.0074	−24,107	±	1095	0.0084	−205	±	9
0.1743	21,936	0.0095	−24,035	±	1099	0.0106	−256	±	11
0.1748	21,957	0.0116	−24,014	±	1100	0.0127	−308	±	14
0.1787	22,026	0.0138	−23,945	±	1103	0.0149	−360	±	16
0.1833	21,895	0.0160	−24,076	±	1097	0.0171	−413	±	19
0.1858	22,209	0.0182	−23,762	±	1113	0.0193	−466	±	21
0.1867	22,255	0.0204	−23,716	±	1115	0.0216	−519	±	24
0.1873	22,466	0.0227	−23,505	±	1125	0.0238	−572	±	26
0.1891	22,044	0.0249	−23,927	±	1104	0.0261	−626	±	29
0.1900	22,236	0.0272	−23,735	±	1114	0.0283	−679	±	31
0.1906	22,485	0.0294	−23,486	±	1126	0.0305	−732	±	34
0.1924	22,015	0.0317	−23,956	±	1103	0.0328	−786	±	36
0.1948	22,241	0.0339	−23,730	±	1114	0.0351	−840	±	39
0.1952	22,044	0.0362	−23,927	±	1104	0.0373	−894	±	41
0.1953	22,407	0.0385	−23,564	±	1122	0.0396	−947	±	44
0.1984	22,337	0.0407	−23,634	±	1119	0.0419	−1001	±	46
0.2017	22,280	0.0430	−23,691	±	1116	0.0442	−1056	±	49
T = 973 K; starting amount n(Sn) = 79.2747 · 10−3 mol; run 1
0.1453	13,098	0.0009	−29,715	±	919	0.0018	−54	±	2
0.1504	13,933	0.0028	−28,880	±	977	0.0037	−109	±	4
0.1531	12,854	0.0047	−29,960	±	902	0.0056	−166	±	5
0.1552	13,999	0.0066	−28,814	±	982	0.0076	−222	±	7
0.3167	12,200	0.0095	−30,613	±	856	0.0115	−342	±	10
0.1604	13,424	0.0125	−29,389	±	942	0.0135	−400	±	12
0.1666	13,529	0.0145	−29,285	±	949	0.0155	−460	±	14
0.1669	13,649	0.0165	−29,165	±	957	0.0175	−519	±	16
0.1682	13,718	0.0186	−29,096	±	962	0.0196	−578	±	18
0.1686	13,829	0.0206	−28,984	±	970	0.0216	−637	±	20
0.3384	14,151	0.0236	−28,663	±	993	0.0257	−754	±	24
0.1731	13,473	0.0267	−29,341	±	945	0.0278	−815	±	26
0.1740	13,921	0.0288	−28892	±	977	0.0298	−875	±	28
0.1753	14,916	0.0309	−27897	±	1046	0.0319	−932	±	30
0.3576	14,495	0.0340	−28,318	±	1017	0.0361	−1051	±	35
0.1812	14,556	0.0372	−28,258	±	1021	0.0382	−1111	±	37
0.1834	14,331	0.0393	−28,483	±	1005	0.0404	−1172	±	39
T = 973 K; starting amount n(Sn) = 79.9983 · 10−3 mol; run 2
0.1310	13,990	0.0008	−28,823	±	910	0.0016	−47	±	1
0.1370	13,626	0.0025	−29,187	±	887	0.0033	−97	±	3
0.1386	13,597	0.0042	−29,217	±	885	0.0051	−147	±	5
0.1390	13,396	0.0059	−29,418	±	872	0.0068	−198	±	6
0.1393	13,302	0.0076	−29,511	±	866	0.0085	−248	±	7
0.1413	13,916	0.0094	−28,897	±	905	0.0102	−298	±	9
0.1422	13,457	0.0111	−29,356	±	876	0.0120	−349	±	11
0.1432	13,978	0.0128	−28,835	±	910	0.0137	−400	±	12
0.1542	13,592	0.0146	−29,222	±	884	0.0156	−454	±	14
0.1577	14,139	0.0165	−28,674	±	920	0.0175	−509	±	16
0.1607	14,267	0.0184	−28,547	±	928	0.0194	−564	±	17
0.1643	14,066	0.0204	−28747	±	915	0.0214	−621	±	19
0.1652	13,884	0.0224	−28,929	±	903	0.0234	−678	±	21
0.1687	14,025	0.0244	−28,788	±	913	0.0254	−736	±	23
0.1687	13,790	0.0264	−29,023	±	897	0.0274	−794	±	25
0.1752	13,881	0.0284	−28,932	±	903	0.0294	−853	±	26
0.1789	13,568	0.0305	−29,245	±	883	0.0315	−915	±	28
0.1820	13,828	0.0326	−28,986	±	900	0.0337	−977	±	30
T = 973 K; starting amount n(Sn) = 41.8931 · 10−3 mol; run 3
0.0707	13,788	0.0008	−29,107	±	902	0.0017	−49	±	2
0.0762	13,662	0.0026	−29,232	±	894	0.0035	−102	±	3
0.0507	13,756	0.0041	−29,138	±	900	0.0047	−137	±	4
0.0839	13,745	0.0057	−29,149	±	899	0.0067	−195	±	6
0.0596	13,835	0.0074	−29,059	±	905	0.0081	−235	±	7
0.1084	14,336	0.0093	−28,558	±	938	0.0106	−308	±	10
0.1056	16,048	0.0118	−26,846	±	1050	0.0131	−374	±	12
0.0959	15,148	0.0142	−27,746	±	991	0.0153	−436	±	14
0.0813	15,248	0.0162	−27,646	±	998	0.0172	−487	±	16
T = 973 K; starting amount: n(Sn) = 92.2513 · 10−3 mol; run 4
0.0449	13,806	0.0002	−29,213	±	912	0.0005	−14	±	1
0.0698	14,078	0.0009	−28,941	±	929	0.0012	−36	±	1
0.0985	13,481	0.0018	−29,538	±	890	0.0023	−68	±	2
0.1149	13,584	0.0029	−29,435	±	897	0.0035	−104	±	3
0.1167	14,183	0.0042	−28,836	±	936	0.0048	−140	±	4
0.1246	13,489	0.0055	−29,530	±	891	0.0061	−180	±	6
0.1474	13,901	0.0069	−29,117	±	918	0.0077	−225	±	7
0.1537	14,602	0.0085	−28,417	±	964	0.0093	−272	±	9
0.1655	14,590	0.0102	−28,429	±	963	0.0111	−322	±	10
0.1674	16,034	0.0120	−26,985	±	1059	0.0129	−370	±	12
0.1828	14,831	0.0138	−28,188	±	979	0.0148	−424	±	14
0.1858	15,692	0.0158	−27,327	±	1036	0.0168	−477	±	16
T = 873 K; starting amount: n(Sn) = 84.2413 · 10−3 mol; run 1
0.1616	13,351	0.0010	−26,386	±	1072	0.0019	−51	±	2
0.1619	14,862	0.0029	−24,875	±	1193	0.0038	−98	±	4
0.1631	11,729	0.0048	−28,008	±	942	0.0057	−152	±	6
0.1884	13,191	0.0068	−26,546	±	1059	0.0079	−210	±	8
0.1911	12,975	0.0091	−26,762	±	1042	0.0102	−270	±	11
0.1989	13,183	0.0113	−26,555	±	1058	0.0125	−331	±	13
0.2021	12,745	0.0137	−26,992	±	1023	0.0148	−394	±	16
0.2053	13,117	0.0160	−26,621	±	1053	0.0172	−457	±	18
0.2061	14,703	0.0184	−25,034	±	1180	0.0195	−516	±	21
0.2068	13,009	0.0207	−26,728	±	1044	0.0219	−579	±	23
0.2109	14,636	0.0231	−25,101	±	1175	0.0243	−639	±	26
0.2129	14,379	0.0255	−25,358	±	1154	0.0267	−700	±	29
0.2232	16,381	0.0279	−23,356	±	1315	0.0292	−758	±	32
0.2278	15,861	0.0305	−23,876	±	1273	0.0317	−818	±	35
0.2564	15,516	0.0331	−24,221	±	1246	0.0346	−887	±	39
T = 873 K; starting amount: n(Sn) = 84.2145 · 10−3 mol; run 2
0.1682	11,688	0.0010	−28,049	±	942	0.0020	−56	±	2
0.1788	15,709	0.0030	−24,028	±	1266	0.0041	−107	±	5
0.1818	12,191	0.0052	−27,546	±	983	0.0062	−165	±	7
0.1829	12,194	0.0073	−27,543	±	983	0.0084	−224	±	9
0.1860	13,875	0.0095	−25,862	±	1118	0.0105	−280	±	11
0.1874	14,088	0.0116	−25,649	±	1136	0.0127	−336	±	14
0.1894	13,789	0.0138	−25,948	±	1112	0.0149	−393	±	16
0.2117	15,049	0.0161	−24,688	±	1213	0.0173	−453	±	19
0.2158	14,048	0.0186	−25,689	±	1132	0.0198	−516	±	22
0.2162	15,946	0.0210	−23,791	±	1285	0.0223	−575	±	25
0.2190	16,589	0.0235	−23,148	±	1337	0.0248	−632	±	28
0.2241	15,538	0.0260	−24,199	±	1253	0.0273	−693	±	32
0.2293	16,618	0.0286	−23,119	±	1340	0.0298	−752	±	35
0.2309	16,649	0.0311	−23,088	±	1342	0.0324	−812	±	38
0.2420	15,963	0.0338	−23,774	±	1287	0.0351	−875	±	42
T = 873 K; starting amount: n(Sn) = 32.6032 · 10−3 mol; run 3
0.0331	12,431	0.0005	−27,598	±	1103	0.0010	−28	±	1
0.0342	11718	0.0015	−28,311	±	1040	0.0021	−58	±	2
0.0501	12,258	0.0028	−27,770	±	1088	0.0036	−100	±	4
0.0615	12,408	0.0045	−27,620	±	1101	0.0055	−152	±	6
0.0698	13,065	0.0065	−26,963	±	1159	0.0076	−209	±	8
0.1020	13,005	0.0091	−27,024	±	1154	0.0106	−292	±	12
0.0978	13,900	0.0121	−26,129	±	1233	0.0136	−368	±	16
0.1016	14,239	0.0151	−25,790	±	1263	0.0166	−446	±	19
0.1034	14,034	0.0181	−25,994	±	1245	0.0197	−526	±	23
0.1193	14,028	0.0214	−26,001	±	1245	0.0232	−617	±	28
0.1210	15,153	0.0249	−24,876	±	1344	0.0267	−704	±	32
0.1312	14,116	0.0286	−25,912	±	1252	0.0305	−803	±	37
0.1339	15,598	0.0324	−24,431	±	1384	0.0343	−896	±	42
0.1441	15,969	0.0364	−24,060	±	1417	0.0384	−995	±	48
0.1712	14,936	0.0408	−25,093	±	1325	0.0433	−1116	±	55
T = 773 K; starting amount: n(Sn) = 85.0400 · 10−3 mol; run 1
0.1583	10,307	0.0009	−26,522	±	1031	0.0019	−49	±	2
0.1723	10,735	0.0029	−26,093	±	1074	0.0039	−102	±	4
0.1747	12,433	0.0049	−24,396	±	1244	0.0059	−151	±	7
0.1788	12,334	0.0069	−24,494	±	1234	0.0080	−202	±	9
0.1830	12,459	0.0090	−24,370	±	1247	0.0101	−254	±	12
0.1872	12,841	0.0112	−23,987	±	1285	0.0122	−305	±	15
0.2041	12,598	0.0134	−24,230	±	1261	0.0146	−362	±	18
0.2058	13,681	0.0158	−23,147	±	1369	0.0169	−416	±	21
0.2059	13,455	0.0181	−23,373	±	1346	0.0193	−471	±	24
0.2207	13,141	0.0205	−23,687	±	1315	0.0217	−530	±	27
0.2375	12,887	0.0218	−23,942	±	1289	0.0244	−593	±	31
T = 773 K; starting amount: n(Sn) = 80.1196 · 10−3 mol; run 2
0.2260	10,226	0.0014	−26,691	±	1027	0.0028	−75	±	3
0.2389	11,288	0.0043	−25,629	±	1134	0.0058	−151	±	6
0.2429	11,966	0.0073	−24,951	±	1202	0.0088	−225	±	10
0.2461	13,358	0.0103	−23,559	±	1341	0.0118	−296	±	14
0.2513	13,874	0.0133	−23,044	±	1393	0.0148	−366	±	18
0.2554	12,938	0.0164	−23,979	±	1299	0.0179	−440	±	22
0.2693	13,711	0.0195	−23,206	±	1377	0.0211	−515	±	27
0.2733	13,052	0.0228	−23,865	±	1311	0.0244	−593	±	31
0.2760	11,691	0.0260	−25,226	±	1174	0.0277	−676	±	35
0.2773	12,206	0.0293	−24,711	±	1226	0.0309	−756	±	39
0.2897	12,613	0.0326	−24,304	±	1267	0.0343	−838	±	43
0.2995	13,774	0.0360	−23,143	±	1383	0.0378	−919	±	48
0.3056	12,218	0.0395	−24,699	±	1227	0.0413	−1006	±	52
0.3280	12,869	0.0432	−24,049	±	1292	0.0450	−1096	±	57
0.3359	12,919	0.0469	−23,998	±	1297	0.0489	−1187	±	62
0.3362	14,253	0.0507	−22,664	±	1431	0.0526	−1272	±	67
0.3479	12,521	0.0546	−24,396	±	1257	0.0565	−1367	±	72
0.3532	13,001	0.0585	−23,916	±	1306	0.0604	−1460	±	77
0.3575	13,685	0.0624	−23,232	±	1374	0.0643	−1551	±	83
T = 773 K; starting amount: n(Sn) = 77.7405 · 10−3 mol; run 3
0.1288	9111	0.0008	−27,717	±	914	0.0017	−46	±	2
0.1350	10,003	0.0025	−26,825	±	1004	0.0034	−92	±	3
0.1630	10,469	0.0044	−26,359	±	1051	0.0055	−147	±	5
0.1721	11,857	0.0066	−24,971	±	1190	0.0076	−201	±	8
0.1725	11,545	0.0087	−25,284	±	1159	0.0098	−257	±	11
0.1772	12,724	0.0109	−24,104	±	1277	0.0121	−310	±	14
0.1836	12,180	0.0132	−24,649	±	1222	0.0144	−367	±	16
0.1840	12,367	0.0155	−24,462	±	1241	0.0166	−423	±	19
0.1962	12,617	0.0179	−24,211	±	1059	0.0191	−487	±	22
0.1999	13,931	0.0203	−22,897	±	1398	0.0215	−543	±	26
0.2058	12,868	0.0228	−23,960	±	1291	0.0241	−604	±	29
0.2081	13,517	0.0253	−23,312	±	1356	0.0266	−663	±	33
0.2113	12,794	0.0279	−24,034	±	1284	0.0292	−725	±	36
0.2184	12,592	0.0292	−24,237	±	1264	0.0318	−789	±	40
0.2209	13,079	0.0332	−23,750	±	1312	0.0345	−852	±	43
0.2216	13,330	0.0358	−23,498	±	1338	0.0371	−914	±	47
T = 773 K; starting amount: n(Sn) = 36.1807 · 10−3 mol; run 4
0.0337	8830	0.0005	−28,045	±	922	0.0009	−26	±	1
0.0372	9753	0.0014	−27,122	±	1018	0.0020	−54	±	2
0.0386	10,166	0.0025	−26,709	±	1061	0.0030	−82	±	3
0.0486	10,813	0.0037	−26,062	±	1129	0.0044	−117	±	5
0.0440	11,600	0.0050	−25,275	±	1211	0.0056	−147	±	6
0.0443	12,508	0.0062	−24,367	±	1306	0.0068	−177	±	8
0.0478	11,609	0.0074	−25,266	±	1212	0.0081	−210	±	9
0.0514	12,513	0.0088	−24,362	±	1307	0.0095	−244	±	11
0.0476	13,097	0.0101	−23,778	±	1367	0.0107	−274	±	13
0.0588	13,485	0.0115	−23,390	±	1408	0.0123	−311	±	15
0.0754	12,968	0.0134	−23,907	±	1354	0.0144	−360	±	18
0.0768	13,716	0.0154	−23,158	±	1432	0.0164	−408	±	21
0.0780	13,747	0.0175	−23,128	±	1435	0.0185	−456	±	24
0.0819	12,740	0.0196	−24,134	±	1330	0.0207	−508	±	27
T = 673 K; starting amount: n(Sn) = 77.3911 · 10−3 mol; run 1
0.1459	9050	0.0009	−24,855	±	906	0.0019	−47	±	2
0.1487	9126	0.0028	−24,780	±	914	0.0038	−94	±	3
0.1567	9536	0.0048	−24,369	±	955	0.0058	−143	±	5
0.1643	10,133	0.0068	−23,773	±	1014	0.0079	−193	±	7
0.1708	10,411	0.0090	−23,495	±	1042	0.0101	−244	±	10
0.1715	9410	0.0111	−24,496	±	942	0.0122	−297	±	12
0.1719	10351	0.0133	−23,555	±	1036	0.0144	−348	±	14
0.1727	10,108	0.0155	−23,797	±	1012	0.0166	−399	±	16
0.1774	9889	0.0177	−24,017	±	990	0.0188	−452	±	18
0.1780	10,253	0.0199	−23,653	±	1026	0.0210	−504	±	21
0.1783	9764	0.0221	−24,142	±	977	0.0232	−558	±	23
0.1783	9639	0.0243	−24,267	±	965	0.0254	−611	±	25
0.1796	9735	0.0265	−24,171	±	974	0.0276	−664	±	27
0.1806	9712	0.0287	−24,194	±	972	0.0298	−717	±	29
0.1829	9834	0.0309	−24,071	±	984	0.0320	−771	±	31
0.1831	9806	0.0331	−24,100	±	982	0.0342	−824	±	34
0.1877	10,178	0.0353	−23,728	±	1019	0.0365	−878	±	36
0.1915	9921	0.0376	−23,985	±	993	0.0388	−933	±	38
0.1926	10,402	0.0399	−23,503	±	1041	0.0410	−986	±	41
0.1934	9569	0.0422	−24,336	±	958	0.0433	−1042	±	43
0.1937	9845	0.0445	−24,061	±	985	0.0456	−1097	±	45
0.1965	10,380	0.0468	−23,526	±	1039	0.0479	−1151	±	47
0.1967	10,419	0.0491	−23,486	±	1043	0.0502	−1205	±	50
0.1995	10,249	0.0514	−23,657	±	1026	0.0525	−1260	±	52
0.2054	10,621	0.0537	−23,285	±	1063	0.0549	−1315	±	55
T = 673 K; starting amount: n(Sn) = 37.4399 · 10−3 mol; run 2
0.0252	9598	0.0003	−24,352	±	1090	0.0007	−16	±	1
0.0263	10,106	0.0010	−23,845	±	1148	0.0014	−33	±	2
0.0284	10,173	0.0018	−23,778	±	1156	0.0021	−51	±	2
0.0287	9540	0.0025	−24,411	±	1084	0.0029	−70	±	3
0.0314	9646	0.0033	−24,304	±	1096	0.0037	−90	±	4
0.0354	9862	0.0042	−24,089	±	1120	0.0047	−113	±	5
0.0356	9027	0.0051	−24,924	±	1025	0.0056	−136	±	6
0.0359	10,349	0.0061	−23,601	±	1176	0.0066	−158	±	7
0.0575	10,126	0.0073	−23,825	±	1150	0.0081	−194	±	9
0.0637	9219	0.0089	−24,732	±	1047	0.0097	−236	±	11
0.0760	9007	0.0107	−24,944	±	1023	0.0117	−285	±	13
0.0852	9452	0.0128	−24,499	±	1074	0.0139	−340	±	15
0.0854	9405	0.0150	−24,545	±	1068	0.0162	−394	±	18
0.0864	9051	0.0173	−24,899	±	1028	0.0184	−450	±	20
T = 673 K; starting amount: n(Sn) = 76.1605 · 10−3 mol; run 3
0.0306	8859	0.0002	−25,092	±	1100	0.0004	−10	±	1
0.0306	8800	0.0006	−25,150	±	1093	0.0008	−20	±	1
0.0323	9493	0.0010	−24,458	±	1179	0.0012	−31	±	2
0.0393	9383	0.0015	−24,567	±	1165	0.0017	−43	±	2
0.0441	8627	0.0020	−25,324	±	1071	0.0023	−58	±	3
0.0586	9541	0.0027	−24,410	±	1184	0.0031	−76	±	4
0.0609	8848	0.0035	−25,103	±	1098	0.0039	−96	±	5
0.0820	9288	0.0044	−24,662	±	1153	0.0049	−123	±	7
0.0829	8750	0.0055	−25,200	±	1086	0.0060	−150	±	8
0.0848	8944	0.0066	−25,007	±	1110	0.0071	−177	±	10
0.0863	8979	0.0077	−24,972	±	1115	0.0082	−205	±	11
0.0908	10443	0.0088	−23,508	±	1296	0.0094	−233	±	13
0.0964	9748	0.0100	−24,203	±	1210	0.0106	−263	±	15
0.1011	9197	0.0113	−24,754	±	1142	0.0119	−295	±	16
0.1036	9482	0.0126	−24,469	±	1177	0.0133	−327	±	18

Average of xCo before and after the drop.

Per mole of binary mixture.

Crossing the liquidus line into a two-phase field (L → L + CoSn2 or L → L + CoSn) is usually indicated by a kink in the integral enthalpy of mixing and a discontinuity in the partial values; see figure 2. Interestingly, the enthalpy curves at low temperatures don not show any clear kink or jump, respectively, as it was expected with respect to the phase diagram given e.g. in reference [7]. For instance, we did not find any significant effect at T = 673 K, the lowest of our experimental temperatures, as shown in figure 6, although CoSn2 has clearly been formed (see EPMA results given in table 2); the partial enthalpy of mixing (about −24 kJ/mol) does not change abruptly although we should have crossed the liquid phase boundary. The reason might be that the heat effect, caused by mixing of one mole of liquid Co into the liquid alloy (partial enthalpy of mixing), is approximately equal to the heat effect for crystallization of approximately one mole Co and its reaction with the corresponding amount of liquid Co3Sn97 forming one mole solid CoSn2. Based on the data collected in table 3 of reference [11], an average value of −16.6 kJ/mol can be calculated for the enthalpy of formation of Co0.33Sn0.67, referred to Co(s, fcc) and Sn(l) which makes −49.8 kJ referred to one mole of CoSn2 at T = 673 K. According to the SGTE database for the elements [25] the crystallization enthalpy of one mole Co at T = 673 K can be calculated as ∼23.3 kJ. The enthalpy necessary to provide the corresponding amount of Co(s) and Sn(l) from liquid Co3Sn97 is roughly estimated to be 1.5 kJ/mole Co. With these numbers, the calculation of the molar partial effect for dropping Co to liquid Co3Sn97 and formation of CoSn2 gives −25 kJ. This agrees quite well with the values observed experimentally and shown in figure 6 and would explain the missing of any clear kink or discontinuity in the enthalpy curves. A similar behavior could be observed at T = 773 K where still CoSn2 should crystallize first from the liquid at less than 3 at.% Co [7].

FIGURE 6

Partial and integral enthalpies of mixing of Co–Sn alloys at T = 673 K, standard state: pure liquid components.

The limiting partial enthalpies of mixing of pure Co into liquid Sn, , were determined at temperatures (673 to 1773) K by extrapolation of the partial molar enthalpies close to pure Sn applying a linear function. Our data are compared with experimental values from literature and are generally in good agreement with the exothermic values published in references [13-16] but not with endothermic results of references [8,17] (table 5). The collected data of calorimetric measurements of were plotted vs. temperature in figure 7. Our experimental -values become less negative at temperatures above 973 K. At lower temperatures (673 to 973) K values which are constant or even decreasing with temperature are observed. According to Kaptay [31,32] some thermodynamic quantities can show exponential temperature dependence. Therefore, the obtained curve of with temperature requires a precise theoretical analysis. It is noteworthy that Torgersen et al. [13] suggested the temperature variation of to be attributed to the existence of Co clusters or CoSn units in the liquid at low temperatures. Our results qualitatively confirm the assumption of short range order effects in liquid Co–Sn alloys.

TABLE 5

The limiting partial enthalpies of Co in liquid Sn at different temperatures; standard state: Co(l).

Temperature, K	ΔH‾Co∞, J · mol−1			Source
673	−24,600	±	2000	Present work
773	−27,000	±	2000	Present work
873	−28,100	±	1900	Present work
874	−27,800a			[13]
874	−28,000a			[14]
973	−29,100	±	1500	Present work
1073	−24,200	±	1400	Present work
1095	−21,800a	±	600	[16]
1173	−19,200	±	1200	Present work
1173	−17,000a			[14]
1173	−18,900a			[15]
1273	−15,100	±	1200	Present work
1373	−11,200	±	1700	Present work
1473	−9200	±	1200	Present work
1573	−7300	±	1300	Present work
1673	−5300	±	1800	Present work
1773	−3000	±	1000	Present work

All values have been rounded to the nearest hundred

Value has been recalculated according to the given reference state.

FIGURE 7

Limiting partial enthalpy of Co in liquid Sn against temperature referred to liquid Co; standard states: pure liquid components.

Conclusions

Enthalpy of mixing values published in literature generally show large variations. A temperature dependence was suggested but not proved consistently up to now. Summarizing the literature values at different temperatures does not give a stringent picture of temperature dependence. In this work the enthalpy of mixing was determined using drop calorimetry in T = 100 K steps in the temperature range T = (663 to 1773) K. The new values obtained are generally exothermic and show a clear temperature dependence of the integral and partial enthalpy of mixing with less exothermic values on rising temperature. The limiting partial enthalpy of Co in Sn is nearly constant at temperatures T = (673 to 973) K. Then the values rise and approach an exothermic value of about −1350 J/mol at T = 1773 K. Co–Sn seems to be an interesting alloy system for further studies concerning the phenomena of short range order formation in liquid intermetallic alloys.