THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES
6. Heat capacity of the liquid trihalides 1. LnF 3
THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES 175
Fig. 24. The enthalpy of formation of the lanthanide trichlorides, tribromides and triiodides as a function of the atomic number. Estimated values are indicated by closed symbols.
Fig. 25. The quantity fH◦(LnCl3,cr) − fH◦(Ln3+,aq) as a function of the ionic radius (coordination number 6);, monoclinic and◦hexagonal structure.
6. Heat capacity of the liquid trihalides
176 R.J.M. KONINGS AND A. KOVÁCS
Fig. 26. The quantity fH◦(LnBr3,cr) − fH◦(Ln3+,aq) as a function of the ionic radius (coordination number 6);
◦
hexagonal,⊕, orthorhombic andrhombohedral structure.
Fig. 27. The quantity fH◦(LnI3,cr) − fH◦(Ln3+,aq) as a function of the ionic ra- dius (coordination number 6);⊕, orthorhombic andrhombohedral structure.
most cases a single set of data by Spedding and coworkers (Spedding and Henderson, 1971;
Spedding et al., 1974) is available; only for CeF3and HoF3other measurements have been re- ported. For CeF3the results of King and Christensen (1959) and Spedding et al. (1974) are in excellent agreement, for HoF3the results of Spedding and Henderson (1971) and Lyapunov et al. (2000) disagree up to 6%. We have preferred the results of Spedding and Henderson (1971) for reasons given earlier.
THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES 177
Fig. 28. The heat capacity of the liquid lanthanide trihalides.
Figure 28 shows the trend in the heat capacity of the lanthanide trifluorides. The irregular pattern indicates a large excess term for the compounds with a partially filled lanthanide ion f-shell, suggesting that this is of an electronic nature, which is consistent with the strong ionic nature of these liquids. Not shown in fig. 28 is the value for LaF3derived from the ex- perimental results. It is unrealistically high: 330.07 J·K−1·mol−1. This is probably due to the fact that the experiments only cover a small temperature range (60 K) in which a post-melting effect cannot be excluded, especially in combination with the anomalous rapid increase al- ready noted for the solid phase. Figure 28 shows that the trend in the lanthanide fluorides (and other trihalides) suggests a value of about 135 J·K−1·mol−1for LaF3.
The enthalpies of fusion that have been derived from the enthalpy increment equations for the solid and liquid phase are listed in table 13 and the derived entropies of fusion are plotted in fig. 29. It can be seen that the enthalpies and entropies of fusion for ErF3to LuF3are sig- nificantly lower than those of the other lanthanide trifluorides. Because these four compounds
178 R.J.M. KONINGS AND A. KOVÁCS Table 13
Enthalpy of fusion and heat capacity of the liquid phase for the lanthanide trifluorides
compound Tfus fusH◦ fusS◦ V /Vcra Cp(liq)
/K /kJ·mol−1 /J·K−1·mol−1 /% /J·K−1·mol−1
LaF3 1766 55.87 31.51 29.14 135b
CeF3 1703 56.52 33.19 32.92 130.61b,c
PrF3 1670 57.28 34.30 29.13 130.76b
NdF3 1649 54.75 33.20 30.78 172.82b
PmF3 1605 53.4 33.3 160
SmF3 1571 52.43 33.37 25.58 148.94d
EuF3 1549 52.9 34.2 130
GdF3 1501 52.44 34.94 25.81 115.20b
TbF3 1446 58.44 40.41 151.91d
DyF3 1426 58.42 40.97 25.35 156.92d
HoF3 1416 56.77 40.09 26.57 135.02b
ErF3 1413 27.51 19.47 28.37 146.83d
TmF3 1431 28.90 20.20 140.32d
YbF3 1435 29.74 20.73 29.99 121.70d
LuF3 1455 29.27 20.12 31.95 126.94b
aV=Vliq−VcrwhereVliqis the volume of the liquid phase at the melting point andVcrthe volume of the solid phase at room temperature. Data are taken from Kishenbaum and Cahill (1960), Kishenbaum and Cahill (1962) and Khairulin et al. (2000).
bSpedding et al. (1974).
cKing and Christensen (1959).
dSpedding and Henderson (1971).
Fig. 29. The entropies of fu- sion (◦) and the sum of the tran- sition and fusion entropies (•) of the LnF3compounds.
undergo an orthorhombic to hexagonal transformation before melting, the sum of the tran- sition and fusion entropies are plotted also. This quantity shows a steady but small increase along the lanthanide trihalide series, from which the enthalpies of fusion of PmF3and EuF3 have been estimated.
6.2. LnCl3
For the liquid lanthanide trihalides data from enthalpy-increment measurements and heat ca- pacity (DSC) measurements are available, as summarised in table C.1 of Appendix C, the rec- ommended values are given in table 14. The majority of the results have been reported by two
THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES 179 Table 14
Enthalpy of fusion and heat capacity of the liquid phase for the lanthanide trichlorides
compound Tfus fusH◦ fusS◦ V /Vcra Cp(liq)
/K /kJ·mol−1 /J·K−1·mol−1 /% /J·K−1·mol−1
LaCl3 1133 55.0b 48.54 19.1 157.7b
CeCl3 1090 53.6c 49.17 18.0 161.05c
PrCl3 1060 49.9b 47.12 21.0 155.3b
NdCl3 1032 49.2b 47.67 21.8 149.5b
PmCl3 994 48.7 49 147
SmCl3 950 47.6 50.1 24.5 144.4d
EuCl3 894 45.0 50.3 142
GdCl3 875 40.6b 46.40 26.4 139.7b
TbCl3 855 19.5b 22.80 21.0 144.47b
DyCl3 924 25.5b 27.75 0.3 144.77b
HoCl3 993 32.6b 32.83 1.3 148.67b
ErCl3 1049 32.6d 31.08 4.9 141.00b
TmCl3 1095 35.6d 32.51 141
YbCl3 1138 37.6 33 140
LuCl3 1198 39.5 33 141
aData taken from Iwadate et al. (1995) and Wasse and Salmon (1999b).
bDworkin and Bredig (1963a, 1963b, 1971).
cWalden and Smith (1961).
dGaune-Escard et al. (1994, 1996).
different research groups: Dworkin and Bredig (1963a, 1963b, 1971) using drop calorime- try and Gaune-Escard et al. (Gaune-Escard et al., 1996; Rycerz and Gaune-Escard, 2002a, 2002b) using differential scanning calorimetry. The early results of Dworkin and Bredig (1963a, 1963b) were reported without details and could not be recalculated, in contrast to the later results. In general, the reliability of the results of both studies is limited since the measurements cover small temperature ranges. For NdCl3and GdCl3the studied temperature range is larger than 50 K, and the agreement is excellent; for PrCl3and DyCl3it is less than 25 K for the DSC measurement and the agreement is poor.
The trend in the heat capacity of the lanthanide trichlorides is shown in fig. 28. It is clear that the variation in the values is much less pronounced than in case of the trifluorides, the (apparent) electronic excess term being small. This suggests that the structure of the liquid trichlorides is different, i.e., less ionic. The structure of the liquid trichlorides has been studied extensively in recent years (Iwadate et al., 1995; Wasse and Salmon, 1999a, 1999b; Hutchin- son et al., 1999; Wasse et al., 2000) by X-ray and neutron diffraction. The results of these studies indeed show that intermediate range order exists in the liquid trichlorides through the formation of molecular species of the type LnCl3n−nand eventually Ln2Cl6n−n, yielding a loose ionic network. With decreasing cation size from La to Lu, the ionic character of the liquid re- duces further, which is evidenced by the decrease of the electrical conductivity of the liquid trichlorides along the lanthanide series (Wasse and Salmon, 1999a).
As is shown in fig. 30 the variation inCp(liq)of the hexagonal trichlorides can be corre- lated to the volume change between the solid (at room temperature) and the liquid: the heat
180 R.J.M. KONINGS AND A. KOVÁCS
Fig. 30. The heat capacity of liquid lanthanide trichlo- rides as a function of the volume changeV /Vcr.
Fig. 31. The entropies of fusion of the LnCl3compounds.
capacity is low when the volume change is large, indicating that part of the variation inCp(liq) arises from variation inClat. Thus the heat capacity of SmCl3is estimated from the known V, that of PmCl3and EuCl3is interpolated. For the monoclinic trichlorides DyCl3, HoCl3 and ErCl3the volume change is quite small, which is due to the fact that these compounds undergo a solid-solid transformation before melting. The values for these compounds have been estimated from the trend suggested in fig. 28.
The entropies of fusion almost constant in the hexagonal LnCl3 series LaCl3–GdCl3, as shown in fig. 31. From this trend we estimate fusS◦=47 J·K−1·mol−1 for PmCl3 and SmCl3. In the series TbCl3to TmCl3the entropy of fusion increases towards a constant value fusS◦=33 J·K−1·mol−1which we have taken for YbCl3and LuCl3. This observation is not in agreement with the experimental DTA data by Goryushkin et al. (1990) who observed a steady increase from TbCl3to LuCl3. We consider their data, however, not accurate enough.
6.3. LnBr3and LnI3
There are only a few measurements of the heat capacity of the liquid tribromides and triio- dides and most of them have been made by Dworkin and Bredig (1963a, 1963b, 1971) using drop calorimetry. Rycerz and Gaune-Escard (1999a) measured the heat capacity of LaBr3(l)
THERMODYNAMIC PROPERTIES OF THE LANTHANIDE(III) HALIDES 181 Table 15
Enthalpy of fusion and heat capacity of the liquid phase for the lanthanide tribromides and triiodides
compound Tfus fusH◦ fusS◦ V /Vcra Cp(liq)
/K /kJ·mol−1 /J·K−1·mol−1 /% /J·K−1·mol−1
LaBr3 1061 54.39a 51.26 144.3a
CeBr3 1005 51.88a 51.62 149
PrBr3 965 47.28a 48.94 154.8a
NdBr3 955 45.61a 47.76 154.92a
PmBr3 930 48.6 52 155
SmBr3 913 47.5 52 149
EuBr3 978 50.9 52 144
GdBr3 1043 38.07 35.98 139.46a
TbBr3 1102 41.9 38 144
DyBr3 1152 46.4b 40.31 149
HoBr3 1192 50.21a 41.98 149
ErBr3 1196 50.2 42 149
TmBr3 1228 51.6 42 149
YbBr3c
LuBr3 1298 51.8 42 144
LaI3 1045 55.45a 53.26 151.77a
CeI3 1033 51.88a 50.22 155
PrI3 1011 53.14a 52.56 155
NdI3 1059 40.94a 38.66 155.74a
PmI3 1090 43.6 40 155
SmI3 1123 47.2 42 155
EuI3c
GdI3 1204 53.97a 44.83 155.85a
TbI3 1229 57.48a 46.77 157.50a
DyI3 1251 56.5b 45.16 155
HoI3 1267 57.0 45 155
ErI3 1288 58.0 45 155
TmI3 1294 58.2 45 155
YbI3c
LuI3 1323 59.5 45 155
aDworkin and Bredig (1963b, 1971).
bCordfunke and Booij (1997).
cDecomposes before melting.
in a very limited temperature range (1070–1090 K), obtaining a somewhat different value (151.12 J·K−1·mol−1). The results (fig. 28) show that the variation inCp(liq)along the lan- thanide series becomes less prominent going from F to I, indicating that the character becomes increasingly less ionic and more molecular. The heat capacity of the liquid tribromides have therefore been assumed to show a slight trend, those of the triiodides to be approximately constant (table 15).
The enthalpies of fusion of some hexagonal tribromides and orthorhombic triiodides have been measured by drop calorimetry (Dworkin and Bredig, 1963a, 1971). The en-
182 R.J.M. KONINGS AND A. KOVÁCS
tropies of fusion derived from these values is about 50 J·K−1·mol−1 for the first group, and 52 J·K−1·mol−1 for the second, except for NdI3. This compound, however, undergoes a solid state transition, as discussed before, and the sum of the entropies of transition and fusion is close (54 J·K−1·mol−1). For the orthorhombic tribromides no experimental data are available, and we have assumed the entropy of fusion to be close to that of the isostruc- tural triiodides. The few data for the hexagonal/rhombohedral tribromides suggest an increase with increasing atomic number, whereas the few data for the hexagonal/rhombohedral triio- dides suggest a constant value. This may be an indication that the high temperature phase behaviour for GdBr3and TbBr3is more complex. It should be noted that Goryushkin and coworkers (Goryushkin and Poshevneva, 1992, 1996; Goryushkin et al., 1999; Poshevneva et al., 2002) reported enthalpies and entropies of fusion of LuI3, HoI3, ErI3, and SmI3that are very different (fusS◦=22.6±3.0 J·K−1·mol−1for SmI3, 18±4 J·K−1·mol−1for HoI3, 23±2 J·K−1·mol−1for ErI3and 82±20 J·K−1·mol−1 for LuI3). But since the results for the trichlorides by the same authors are in poor agreement with other experimental determi- nations, they have not been considered for the recommended values.
7. Heat capacity of the gaseous trihalides