# Study of Molecular and Ionic Vapor Composition over CeI3 by Knudsen Effusion Mass Spectrometry

Authors: A. M. Dunaev; V. B. Motalov; L. S. Kudin; M. F. Butman; K. W. Krämer
Journal: Journal of Spectroscopy
 (2016)

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## Abstract

The molecular and ionic composition of vapor over cerium triiodide was studied by Knudsen effusion mass spectrometry. In the saturated vapor over CeI3 the monomer, dimer, and trimer molecules and the negative ions I−, CeI4-, and Ce2I7- were identified in the temperature range of 753–994 K. The partial pressures of CeI3, Ce2I6, and Ce3I9 were determined and the enthalpies of sublimation, ΔsH°(298.15 K) in kJ·mol−1, in the form of monomers (298±9), dimers (415±30), and trimers (423±50) were obtained by the second and third laws of thermodynamics. The enthalpy of formation, ΔfH°(298.15 K) in kJ·mol−1, of the CeI3 (-371±9), Ce2I6 (-924±30), and Ce3I9 (-1585±50) molecules and the CeI4- (-857±19) and Ce2I7- (-1451±50) ions were calculated. The electron work function, φe = 3.3±0.3 eV, for the CeI3 crystal was evaluated.


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## Body

## 1. Introduction

Vaporization thermodynamics of cerium triiodide is the focus of researcher’s attention so far. The first measurements of vapor pressure over CeI3 were carried out by Knudsen effusion mass spectrometry (KEMS) [1] and Knudsen effusion Cahn microbalance [2] techniques. Further KEMS studies were performed by Chantry [3, 4], Struck and Feuersanger [5], and Ohnesorge [6]. In addition the vapor pressure of CeI3 was determined by the torsion method [7], by optical absorption spectra [8], and recently by X-ray induced fluorescence [9]. In spite of the numerous experimental results [1–9], data on the vapor composition over CeI3 are very scanty. Moreover, information on the ionic species in saturated vapor over CeI3 is absent so far.The present work continues our systematic investigations of the molecular and ionic sublimation of lanthanide halides by KEMS; see for example, [10–14]. The composition of the saturated vapor of CeI3 was determined and the thermochemical data of the vapor constituents were refined on the basis of the latest sets of molecular parameters.


## 2. Experimental

A single-focusing magnetic sector type mass spectrometer MI1201 modified for high-temperature studies was used. The combined ion source allowed carrying out successive measurements in two modes; see Figure1 (taken from [15]). In addition to a standard mode of electron ionization (EI) for analysis of neutral vapor species, a thermal ion emission (TE) mode was introduced for the analysis of charged vapor constituents formed inside an effusion cell as a result of thermal ionization. In the latter case, the ions are drawn out from the cell by a weak electric field (104–105 V/m) applied between the cell and the collimator (1). The sample (2) was placed into a molybdenum cell (3) under dry conditions in a glove box and then transferred into the vaporization chamber of the mass spectrometer and evacuated. The lid of the cell had the cylindrical effusion orifice (Ø 0.3 × 0.8 mm). The vaporization-to-effusion area ratio was about 400. A resistance furnace was used for the heating of the cell. Its temperature was measured by a tungsten-rhenium thermocouple calibrated with silver to a ±5 K accuracy in the separate experiment.Figure 1
Scheme of the mass spectrometer (taken from [15]). I—EI mode; II—TE mode. The details are given in text.The vapor species effusing from the cell form a molecular beam, which reaches the ionization chamber (4) and intersects with an electron beam of specified energy. The ionization voltage Ue is set by a computer using a programmable power supply AKIP-1125 in the range of 0–150 V with 10 mV resolution. The tungsten ribbon-type cathode (5) is directly heated by an controllable DC source. The current of the cathode was adjusted to provide a constant emission current of 0.25 A.The ions formed by the collision of molecular species with electrons are extracted from the ionization chamber, focused, and accelerated by a system of electrostatic lenses (6). The electrostatic capacitor mounted after the exit slit of the ion source allows us to study the distribution of ions by the vertical velocity component. The accelerating voltage (3 kV) is applied to the ionization chamber (IE mode) or to the effusion cell (TE mode). The polarity of the high voltage can be reversed with respect to the ground potential. Thus, both positive and negative ions can be analyzed. The ions are separated according to their mass-to-charge ratio in the magnetic field of an electromagnet (7) (90°, 200 mm curvature radius). The magnetic field strength is measured by a Hall probe. The ion current registration system (8, 9) includes a secondary electron multiplier Hamamatsu R595 (8) and a Picoammeter Keithley 6485 with 10 fA resolution and 20 fA typical noise. It allows measuring ion currents down to 10−18 A. The movable shutter (10) operated by a computer (11) allows distinguishing signals caused by the effusing species from those of the background. The special software “HTMSLab” was used to control experimental parameters, collect and process the data, and export the results into the database. Further details on the apparatus and experimental procedure can be found elsewhere [16–18].The cerium triiodide sample was synthesized from cerium metal (99.9%, Metall Rare Earth Ltd.) and iodine (p.a., sublimed, Merck). The elements were sealed in an evacuated silica ampoule and slowly heated to 750°C until the reaction was completed. Afterwards the product was sublimed for purification in a sealed silica ampoule under vacuum at 750°C, that is, slightly below the melting point of CeI3 at 766°C. The bright yellow CeI3 is very hygroscopic. Its synthesis was performed under strictly oxygen-free and anhydrous conditions.


## 3. Results and Discussion

### 3.1. Neutral Vapor Species

In the IE mass spectra of the saturated vapor over cerium triiodide the Ce+(23), CeI+(16), CeI2+(100), CeI3+(31), Ce2I3+(0.02), Ce2I4+(0.01), Ce2I5+(2.2), I+(22), and Ce3I8+(0.02) ions, as well as the doubly charged Ce++(0.5), CeI++(7), and CeI2++ (3) ions, were registered in the temperature range of 753–994 K. The relative ion currents are given in parentheses for the temperature of 990 K and the energy of ionizing electrons of 40 eV. The mass spectra were found to be constant over the whole evaporation time; see Figure 2.Figure 2
Temperature dependence of the mass spectra of CeI3. Heating and cooling runs are marked by solid and open symbols, respectively.To determine the molecular precursors of the ions, the ionization efficiency curves (IEC) (Figure3) and the temperature dependencies of ion currents (Figure 4) were analyzed. The ionizing electron energy in Figure 3 was corrected by the background signal of HI+ (AE = 10.38 eV [19]). Appearance energies (AE) were determined by vanishing current (VC) and linear extrapolation (LE) methods; average values are given in Table 1. The linear part for the LE method was determined as the segment between two points of inflection on the first-order derivative of the IEC inverse function [20]. The following conclusions were drawn: the ions containing one atom of cerium are formed as a result of direct (CeI3+) and dissociative (Ce+, CeI+, and CeI2+) ionization of the monomer CeI3 molecules with negligibly small contributions from the fragmentation of more complex molecules; the Ce2I3+, Ce2I4+, and Ce2I5+ ions were produced by the dissociative ionization of the dimer Ce2I6 molecules; and the Ce3I8+ ion originated from the trimer molecule Ce3I9.Table 1
Ion appearance energies (eV).
Reaction Ion A E This work [1] [3] [5] [30] CeI3 + ē = Ce+ + 3I + 2ē Ce+ 17.2 ± 0.5 17.7 ± 0.5 16.75 ± 0.15 CeI3 + ē = CeI+ + 2I + 2ē CeI+ 13.1 ± 0.5 13.6 ± 0.5 13.15 ± 0.15 CeI3 + ē = CeI2+ + I + 2ē C e I 2 + 9.8 ± 0.5 9.7 ± 0.5 9.55 ± 0.1 11.2 CeI3 + ē = CeI3+ + 2ē C e I 3 + 9.1 ± 0.5 9.6 ± 0.5 9.05 ± 0.1 10.8 9.71 Ce2I6 + ē = Ce2I5+ + I + 2ē C e 2 I 5 + 9.3 ± 0.5 Ce3I9 + ē = Ce3I8+ + I + 2ē C e 3 I 8 + 9.1 ± 0.5 I + ē = I+ + 2ē I+ 10.7 ± 0.5 ~13.5 10.5Figure 3
Ionization efficiency curves.
(a) (b)Figure 4
Temperature dependence of ion currents in the EI regime.Along with the abovementioned ions I+ was also observed. The determined AE equal to 10.7±0.5 eV (Table 1) points out its origination from atomic iodine (ionization energy IE(I) = 10.4 eV [21]), which can be attributed to the partial decomposition of the sample with the formation of CeI2. Nevertheless the reproducibility of the mass spectra in heating and cooling cycles (Figure 2), the shapes of IECs showing no brakes, and the determined AE values (Table 1) indicate unambiguously the absence of CeI2 in the vapor. This fact agrees with the expected much lower volatility of CeI2 compared to that of CeI3 in the studied temperature range. Therefore it is assumed that the activity of CeI3 in the solid state was unity.The partial pressures of molecules (pj) (see Table 2) were calculated according to the conventional KEMS procedure using the equation(1)pj=k·I·Tσj,where k is the sensitivity constant of mass spectrometer (determined in a separate experiment with Ag; the vapor pressure of silver was taken from [22]), σj is the ionization cross section of thejth molecule at the working energy of the ionizing electrons (calculated from the experimentally determined atomic cross sections, σat [23, 24], by the equation σj=0.75Σσat [25]), Ij=∑i(Iij/(ai·γi)) is the total ion current of the ith ion species formed from thejth molecule, ai is the natural abundance of the measured isotope of the ith ion, γi is the ion-electron conversion coefficient of secondary electron multiplier for the ith ion (γi~M−1/2 [26], where M is the mass of ion), and T is the temperature of the cell.Table 2
Partial pressures (Pa) of the molecules.
CeI3 Ce2I6 Ce3I9 T, K p j · 10 3 T, K p j · 10 4 T, K p j · 10 5 885 54.5 878 3.59 916 0.85 872 47.8 915 26.8 957 7.45 877 55.4 957 182 932 1.83 877 54.7 933 57.0 907 0.41 914 235 906 14.3 905 0.65 957 1080 866 1.62 921 0.84 934 445 829 0.15 945 4.29 906 150 857 1.27 952 5.24 868 29.8 882 5.80 962 12.5 828 4.32 906 17.0 978 29.9 786 0.52 920 39.8 992 58.1 805 1.23 946 134 907 0.51 753 0.081 853 0.76 923 1.08 872 43.5 952 170 943 2.74 957 1210 963 323 969 15.3 857 20.3 978 566 994 54.2 882 59.5 992 1010 906 145 907 23.9 919 274 923 28.8 942 575 883 4.19 854 15.8 857 0.90 951 786 829 0.20 963 1280 811 0.035 979 1970 828 0.081 990 3020 857 0.64 908 150 884 3.77 923 244 917 24.0 883 40.1 943 105 856 15.5 969 343 829 4.06 994 999 811 1.48 826 3.24 856 13.7 883 48.8 918 189 944 551 969 1250 994 2880The temperature dependence of the saturated vapor pressures of the monomer and oligomer molecules was approximated by the equation(2)ln⁡pi=-A×103T+B.The coefficients of equation (2) are given in Table 3.Table 3
Coefficients of (2).
Species T, K A B CeI3 753–994 33.35 ± 0.36 34.84 ± 0.41 Ce2I6 811–994 44.93 ± 0.62 43.10 ± 0.69 Ce3I9 905–994 49.62 ± 1.43 42.43 ± 1.52 The standard deviation is given with a “±” sign.The partial pressuresof the molecules of cerium triiodide from different references are compared in Figure 5. As one can see, all experimental vapor pressure values are scattered within about one order of magnitude. Temperature dependencies from the work of Hirayama et al. [2], Villani et al. [7], and Ohnesorge [6] lie below those obtained in this work. The fraction of the dimer molecules measured in this work and in [6] is about the same whereas the absolute pressures differ considerably. The vapor pressure of trimer molecules was determined in this study for the first time.Figure 5
Temperature dependencies of the saturated vapor pressure: (1)p(CeI3) from [9], (2) our data, (3) [2], (4) [7], and (5) [6]; (1′)p(Ce2I6) from [9], (2′) our data, and (5′) [6]; (2′′)p(Ce3I9) our data.The enthalpies and entropies of sublimationof cerium triiodide in the form of monomer and oligomer molecules were determined from the temperature dependencies of the partial pressures of the saturated vapor species using the procedure for experimental data processing according to the second and third laws of thermodynamics; see Table 4. The thermodynamic functions required for calculations were taken from [22] for CeI3,cr and evaluated in this work for the monomer and oligomer molecules in the state of an ideal gas (see Appendix).Table 4
Enthalpies,ΔsH° (kJ·mol−1), and entropies, ΔsS° (J·mol−1·K−1), of sublimation of cerium triiodide.
ΔT, K T, K N 1 II law2 III law3 Ref. Δ s , v H °(T) Δ s , v S °(T) Δ s H °(298) Δ s H °(298) Δ s , v S °(T) C e I 3 , c r , l = CeI3,g 753–994 893 38 277 ± 3 194 ± 3 292 ± 4 294 ± 10 191 ± 10 This work ? 933 ? 292 ± 21  307 ± 21   [1] 870–1015 945 32 284 ± 4 197 ± 4 301 ± 4 298 ± 10 189 ± 10 [2] 810–953 877 50 274 ± 2  288 ± 2   [5] 854–1017 936 29 284 ± 1 164 ± 1 278 ± 1 307 ± 10 189 ± 10 [6] 910–1031 970 81 284 ± 3 192 ± 6 301 ± 3 303 ± 10 189 ± 10 [7] 1000 1    291 ± 10 187 ± 10 [8] 1072–1136 1094 5 201 ± 11 119 ± 10 272 ± 11 296 ± 10 155 ± 10 [8] 1080–1400 1250 ? 299 ± 1 119 ± 1 290 ± 1 301 ± 10 123 ± 10 [9] 297  [22] 322  [27] 280  [28] 300 ± 5  [29] Δ s H °(298.15 K) = 298±94  2 C e I 3 , c r , l = Ce2I6,g 811–994 893 30 374 ± 6 262 ± 6 395 ± 25 409 ± 30 278 ± 30 This work 825–953 898 50 377 ± 5  400 ± 15   [5] 854–1017 936 17 354 ± 1 219 ± 1 379 ± 25 428 ± 30 276 ± 30 [6] 1080–1400 1250 ? 251 ± 1 138 ± 1 413 ± 1 421 ± 30 148 ± 30 [9] Δ s H °(298.15 K) = 415±30  3 C e I 3 , c r = Ce3I9,g 907–994 949 16 413 ± 12 257 ± 13 443 ± 40 423 ± 50 236 ± 50 This work Δ s H °(298.15 K) = 423±50 1Number of measurements. 2The original errors are given for the literature data, the standard deviations for this work. 3The uncertainties are mainly determined by those in thermodynamic functions. 4The uncertainty of the recommended values was calculated by Student’s method (monomer) and accepted as the third law ones (others).As it is seen from Table4, the values of ΔsH°(298.15) and ΔsS°(T) obtained in this work by the second and third laws are in a fair agreement for both monomer and oligomer molecules. The same can be said about the results for the monomer molecules from [2, 7]. The data of the work [9] are in notably worse agreement, whereas those of [6, 8] do not agree within the given uncertainties. At the same time, the third law values for all the data are in a good consent with each other. The temperature trend of the third law values ΔsH°(298.15) is given in Figure 6, from which one can see that the data of this work and [2, 9] do not show a pronounced temperature dependence as compared to those of [6, 7]. Taking into account this analysis, the recommended values were selected and emphasized in bold in Table 4. The early estimates [27, 28] made for monomers differ considerably from the recommended value, while the assessments given in [22, 29] agree with the experimental data.Figure 6
Temperature dependencies of the third lawΔsH°(298.15 K) values: (1) monomer from [9], (2) our data, (3) [2], (4) [7], and (5) [6]; (1′) dimer from [9], (2′) our data, and (5′) [6]; (2′′) trimer our data.The standard formation enthalpies, ΔfH°(298.15 K), are equal to -371±9 kJ·mol−1 (CeI3), -924±30 kJ·mol−1 (Ce2I6), and -1585±50 kJ·mol−1 (Ce3I9) and were calculated from the recommended ΔsH°(298.15 K) values. The formation enthalpy of crystalline cerium triiodide, ΔfH°(CeI3,cr; 298.15 K) = −669 kJ·mol−1 [22], was used.


### 3.2. Charged Vapor Species

In the TE mass spectra in the temperature range of 747–960 K the I−(0.44), CeI3-(0.18), CeI4-(100), and Ce2I7-(0.08) ions were identified with the relative ion currents given in parentheses forT = 846 K.Additional experiments with the CeI3-PrI3 binary system were performed to determine the enthalpy of formation of CeI4- ions. The enthalpy of exchange ion-molecular reaction (5) was found to be 1±5 kJ·mol−1. The enthalpy of formation of PrI4-ΔfH°(298.15 K) = -860±23 kJ·mol−1 was used as reference value. It was obtained by recalculation of the data (-865±25 kJ·mol−1) [13] with the thermodynamic function used in this work. The experimental equilibrium constants of reaction (3) and reaction (4) investigated over pure CeI3 are listed in Table 5:(3)CeI3,g+PrI4-,g=CeI4-,g+PrI3,g,(4)Ce2I7-,g=CeI4-,g+CeI3,cr,lTable 5
Experimental data for reactions (3) and (4).
Reaction (3) Reaction (4) T (K) ln ⁡ K P ° T (K) ln ⁡ K P ° 889 0.35 868 6.39 865 0.39 862 6.61 835 0.30 898 5.92 846 0.49 932 5.43 907 0.41 960 4.94 934 0.39 924 5.49 966 0.38 892 5.94 956 0.37 846 6.67 929 0.34 906 0.22 856 0.34 806 0.38 854 0.30 884 0.38 902 0.30 950 0.40 976 0.30The reaction enthalpies were calculated by the second and third laws of thermodynamics; see Table6. The evaluation of the thermodynamic functions of the CeI4- and Ce2I7- ions is described in Appendix.Table 6
Enthalpies (kJ·mol−1) of reactions (3) and (4).
ΔT, K T, K N 1 II law2 III law3 Ref. Δ r H °(T) Δ r H °(298.15 K) Δ r H °(298.15 K) C e I 3 , g + PrI4-,g = CeI4-,g + PrI3,g 806–976 897 17 0 ± 3 1 ± 3 1 ± 5 This work  C e 2 I 7 - , g = CeI4-,g + CeI3,cr,l 842–960 896 12 -99±5 - 113 ± 6 - 75 ± 40 This work 1Number of measurements. 2The original errors are given for the literature data, the standard deviations for this work. 3The uncertainties are mainly determined by those in thermodynamic functions.One can see that the agreement for the enthalpy of reaction (3) obtained by the second and third laws is good. ΔfH°(CeI4-, 298.15 K) = -857±19 kJ·mol−1 was recommended. This value is in agreement with those -850±33 kJ·mol−1 obtained by Chantry from the enthalpy of the reaction CeI4-,g = I-,g + CeI3,g and recalculated with our sublimation enthalpy and thermodynamic functions. The selected formation enthalpy of the Ce2I7- ion is -1451±50 kJ·mol−1 (third law) and was obtained for the first time.


### 3.3. Thermodynamic Properties Derived from IECs

The enthalpies of ion-molecular reactions were calculated from the differences of the measuredAE values given in Table 1; see Table 7. On their basis the standard formation enthalpies of the ions were determined; see Table 8. The accurate values of ΔfH°(Ce+, 298.15 K) = 957±0.1 kJ·mol−1 [22] and ΔfH°(I, 298.15 K) = 106.76±0.04 kJ·mol−1 [22] and the formation enthalpies of the CeI3, Ce2I6, and Ce3I9 molecules obtained in this work (see above) were used as references. The comparison of our results with the data obtained by photoelectron spectroscopy [30], computation [31], and assessment [32] shows that all data are in agreement within the given errors; see Table 8.Table 7
Ion-molecular reactions (kJ·mol−1).
Reaction This work [1] [3] [5] [30] [31] C e I + , g = Ce+,g+Ig 391 ± 10 396 ± 50 347 ± 50   393 C e I 2 + , g = CeI+,g+Ig 323 ± 10 376 ± 50 347 ± 50 C e I 3 + , g = CeI2+,g+Ig 66 ± 10 10 ± 50 48 ± 50 39 62 ± 50 C e I 3 , g + Ce2I5+,g = Ce+,g + 2Ig+Ce2I6,g 750 ± 10 C e I 3 , g + Ce3I8+,g = Ce+,g + 2Ig+Ce3I9,g 768 ± 20Table 8
Ion formation enthalpies (kJ·mol−1).
Ion This work [1] [3] [32] [31] CeI+ 673 ± 10 669 ± 50 717 760 671 C e I 2 + 467 ± 10 399 ± 50 476 C e I 3 + 497 ± 10 496 ± 50 535 C e 2 I 5 + - 131 ± 10 C e 3 I 8 + - 811 ± 20Analysis of the ion-molecular reaction enthalpies confirmed the weakness of the first cerium iodine bond in comparison with the other two. Probably, it explains the lower enthalpy of the formation ofCeI2+ (467±10 kJ·mol−1) compared to CeI3+ (497±10 kJ·mol−1).The formation enthalpy of gaseous CeI3 (-371±9 kJ·mol−1) obtained from the vapor pressure measurement is in a good agreement with those calculated from the appearance energies (-376±50 kJ·mol−1) and with the value (−381 kJ·mol−1) assessed by Sapegin et al. [33] (Table 9). The coincidence of the formation enthalpy values of CeI3,g, as determined from the thermodynamic and threshold approaches, points out a negligible contribution from the excitation and kinetic energy of the fragments. The atomization energy derived from ΔfH°(CeI3, 298.15 K) = -371±9 kJ·mol−1 was found to be 1109±10 kJ·mol−1. It yields the average bond strength equal to 370±10 kJ·mol−1.Table 9
Formation enthalpies ofCeI3,g(kJ·mol−1).
This workfrom IEC This workfrom ΔsH° [1] [9] [33] >−376 ± 50 −371 ± 9 −436 ± 50 −349 −381


### 3.4. Electron Work Function

The mass spectrometric approach for the work function determination is based on the use of thermochemical cycles including desorption enthalpies of ions and sublimation enthalpies of molecules as described elsewhere [34]. The desorption enthalpy of the CeI4- ions, ΔdesH°(851 K) = 350±8 kJ·mol−1, and the Ce2I7- ions, ΔdesH°(902 K) = 430±18 kJ·mol−1, were obtained from the temperature dependence of their ion currents; see Figure 7. The electron work function was calculated in accordance with the following expressions:(5)φe=-14DCeI3+54·ΔsH°CeI3+EAI+ΔdissH°CeI4-+ΔdesH°CeI4-,(6)φe=-14DCeI3+94·ΔsH°CeI3+EAI+ΔdissH°Ce2I7-+ΔdesH°Ce2I7-,where EA(I) is the electron affinity of iodine [22],D(CeI3) is the dissociation enthalpy of the CeI3 molecule, ΔdissH°(CeI4-) is the enthalpy of the CeI4- = I− + CeI3 reaction (Table 6), and ΔdissH°(Ce2I7-) is the enthalpy of the Ce2I7- = I− + 2CeI3 reaction.Figure 7
Temperature dependencies ofCeI4- and Ce2I7- ion currents.Theφe values equal to 3.3±0.3 eV and 3.5±0.5 eV were obtained from (5) and (6), respectively. They turned out to be close to φe(LaI3) = 3.5±0.3 eV [14].


## 3.1. Neutral Vapor Species

In the IE mass spectra of the saturated vapor over cerium triiodide the Ce+(23), CeI+(16), CeI2+(100), CeI3+(31), Ce2I3+(0.02), Ce2I4+(0.01), Ce2I5+(2.2), I+(22), and Ce3I8+(0.02) ions, as well as the doubly charged Ce++(0.5), CeI++(7), and CeI2++ (3) ions, were registered in the temperature range of 753–994 K. The relative ion currents are given in parentheses for the temperature of 990 K and the energy of ionizing electrons of 40 eV. The mass spectra were found to be constant over the whole evaporation time; see Figure 2.Figure 2
Temperature dependence of the mass spectra of CeI3. Heating and cooling runs are marked by solid and open symbols, respectively.To determine the molecular precursors of the ions, the ionization efficiency curves (IEC) (Figure3) and the temperature dependencies of ion currents (Figure 4) were analyzed. The ionizing electron energy in Figure 3 was corrected by the background signal of HI+ (AE = 10.38 eV [19]). Appearance energies (AE) were determined by vanishing current (VC) and linear extrapolation (LE) methods; average values are given in Table 1. The linear part for the LE method was determined as the segment between two points of inflection on the first-order derivative of the IEC inverse function [20]. The following conclusions were drawn: the ions containing one atom of cerium are formed as a result of direct (CeI3+) and dissociative (Ce+, CeI+, and CeI2+) ionization of the monomer CeI3 molecules with negligibly small contributions from the fragmentation of more complex molecules; the Ce2I3+, Ce2I4+, and Ce2I5+ ions were produced by the dissociative ionization of the dimer Ce2I6 molecules; and the Ce3I8+ ion originated from the trimer molecule Ce3I9.Table 1
Ion appearance energies (eV).
Reaction Ion A E This work [1] [3] [5] [30] CeI3 + ē = Ce+ + 3I + 2ē Ce+ 17.2 ± 0.5 17.7 ± 0.5 16.75 ± 0.15 CeI3 + ē = CeI+ + 2I + 2ē CeI+ 13.1 ± 0.5 13.6 ± 0.5 13.15 ± 0.15 CeI3 + ē = CeI2+ + I + 2ē C e I 2 + 9.8 ± 0.5 9.7 ± 0.5 9.55 ± 0.1 11.2 CeI3 + ē = CeI3+ + 2ē C e I 3 + 9.1 ± 0.5 9.6 ± 0.5 9.05 ± 0.1 10.8 9.71 Ce2I6 + ē = Ce2I5+ + I + 2ē C e 2 I 5 + 9.3 ± 0.5 Ce3I9 + ē = Ce3I8+ + I + 2ē C e 3 I 8 + 9.1 ± 0.5 I + ē = I+ + 2ē I+ 10.7 ± 0.5 ~13.5 10.5Figure 3
Ionization efficiency curves.
(a) (b)Figure 4
Temperature dependence of ion currents in the EI regime.Along with the abovementioned ions I+ was also observed. The determined AE equal to 10.7±0.5 eV (Table 1) points out its origination from atomic iodine (ionization energy IE(I) = 10.4 eV [21]), which can be attributed to the partial decomposition of the sample with the formation of CeI2. Nevertheless the reproducibility of the mass spectra in heating and cooling cycles (Figure 2), the shapes of IECs showing no brakes, and the determined AE values (Table 1) indicate unambiguously the absence of CeI2 in the vapor. This fact agrees with the expected much lower volatility of CeI2 compared to that of CeI3 in the studied temperature range. Therefore it is assumed that the activity of CeI3 in the solid state was unity.The partial pressures of molecules (pj) (see Table 2) were calculated according to the conventional KEMS procedure using the equation(1)pj=k·I·Tσj,where k is the sensitivity constant of mass spectrometer (determined in a separate experiment with Ag; the vapor pressure of silver was taken from [22]), σj is the ionization cross section of thejth molecule at the working energy of the ionizing electrons (calculated from the experimentally determined atomic cross sections, σat [23, 24], by the equation σj=0.75Σσat [25]), Ij=∑i(Iij/(ai·γi)) is the total ion current of the ith ion species formed from thejth molecule, ai is the natural abundance of the measured isotope of the ith ion, γi is the ion-electron conversion coefficient of secondary electron multiplier for the ith ion (γi~M−1/2 [26], where M is the mass of ion), and T is the temperature of the cell.Table 2
Partial pressures (Pa) of the molecules.
CeI3 Ce2I6 Ce3I9 T, K p j · 10 3 T, K p j · 10 4 T, K p j · 10 5 885 54.5 878 3.59 916 0.85 872 47.8 915 26.8 957 7.45 877 55.4 957 182 932 1.83 877 54.7 933 57.0 907 0.41 914 235 906 14.3 905 0.65 957 1080 866 1.62 921 0.84 934 445 829 0.15 945 4.29 906 150 857 1.27 952 5.24 868 29.8 882 5.80 962 12.5 828 4.32 906 17.0 978 29.9 786 0.52 920 39.8 992 58.1 805 1.23 946 134 907 0.51 753 0.081 853 0.76 923 1.08 872 43.5 952 170 943 2.74 957 1210 963 323 969 15.3 857 20.3 978 566 994 54.2 882 59.5 992 1010 906 145 907 23.9 919 274 923 28.8 942 575 883 4.19 854 15.8 857 0.90 951 786 829 0.20 963 1280 811 0.035 979 1970 828 0.081 990 3020 857 0.64 908 150 884 3.77 923 244 917 24.0 883 40.1 943 105 856 15.5 969 343 829 4.06 994 999 811 1.48 826 3.24 856 13.7 883 48.8 918 189 944 551 969 1250 994 2880The temperature dependence of the saturated vapor pressures of the monomer and oligomer molecules was approximated by the equation(2)ln⁡pi=-A×103T+B.The coefficients of equation (2) are given in Table 3.Table 3
Coefficients of (2).
Species T, K A B CeI3 753–994 33.35 ± 0.36 34.84 ± 0.41 Ce2I6 811–994 44.93 ± 0.62 43.10 ± 0.69 Ce3I9 905–994 49.62 ± 1.43 42.43 ± 1.52 The standard deviation is given with a “±” sign.The partial pressuresof the molecules of cerium triiodide from different references are compared in Figure 5. As one can see, all experimental vapor pressure values are scattered within about one order of magnitude. Temperature dependencies from the work of Hirayama et al. [2], Villani et al. [7], and Ohnesorge [6] lie below those obtained in this work. The fraction of the dimer molecules measured in this work and in [6] is about the same whereas the absolute pressures differ considerably. The vapor pressure of trimer molecules was determined in this study for the first time.Figure 5
Temperature dependencies of the saturated vapor pressure: (1)p(CeI3) from [9], (2) our data, (3) [2], (4) [7], and (5) [6]; (1′)p(Ce2I6) from [9], (2′) our data, and (5′) [6]; (2′′)p(Ce3I9) our data.The enthalpies and entropies of sublimationof cerium triiodide in the form of monomer and oligomer molecules were determined from the temperature dependencies of the partial pressures of the saturated vapor species using the procedure for experimental data processing according to the second and third laws of thermodynamics; see Table 4. The thermodynamic functions required for calculations were taken from [22] for CeI3,cr and evaluated in this work for the monomer and oligomer molecules in the state of an ideal gas (see Appendix).Table 4
Enthalpies,ΔsH° (kJ·mol−1), and entropies, ΔsS° (J·mol−1·K−1), of sublimation of cerium triiodide.
ΔT, K T, K N 1 II law2 III law3 Ref. Δ s , v H °(T) Δ s , v S °(T) Δ s H °(298) Δ s H °(298) Δ s , v S °(T) C e I 3 , c r , l = CeI3,g 753–994 893 38 277 ± 3 194 ± 3 292 ± 4 294 ± 10 191 ± 10 This work ? 933 ? 292 ± 21  307 ± 21   [1] 870–1015 945 32 284 ± 4 197 ± 4 301 ± 4 298 ± 10 189 ± 10 [2] 810–953 877 50 274 ± 2  288 ± 2   [5] 854–1017 936 29 284 ± 1 164 ± 1 278 ± 1 307 ± 10 189 ± 10 [6] 910–1031 970 81 284 ± 3 192 ± 6 301 ± 3 303 ± 10 189 ± 10 [7] 1000 1    291 ± 10 187 ± 10 [8] 1072–1136 1094 5 201 ± 11 119 ± 10 272 ± 11 296 ± 10 155 ± 10 [8] 1080–1400 1250 ? 299 ± 1 119 ± 1 290 ± 1 301 ± 10 123 ± 10 [9] 297  [22] 322  [27] 280  [28] 300 ± 5  [29] Δ s H °(298.15 K) = 298±94  2 C e I 3 , c r , l = Ce2I6,g 811–994 893 30 374 ± 6 262 ± 6 395 ± 25 409 ± 30 278 ± 30 This work 825–953 898 50 377 ± 5  400 ± 15   [5] 854–1017 936 17 354 ± 1 219 ± 1 379 ± 25 428 ± 30 276 ± 30 [6] 1080–1400 1250 ? 251 ± 1 138 ± 1 413 ± 1 421 ± 30 148 ± 30 [9] Δ s H °(298.15 K) = 415±30  3 C e I 3 , c r = Ce3I9,g 907–994 949 16 413 ± 12 257 ± 13 443 ± 40 423 ± 50 236 ± 50 This work Δ s H °(298.15 K) = 423±50 1Number of measurements. 2The original errors are given for the literature data, the standard deviations for this work. 3The uncertainties are mainly determined by those in thermodynamic functions. 4The uncertainty of the recommended values was calculated by Student’s method (monomer) and accepted as the third law ones (others).As it is seen from Table4, the values of ΔsH°(298.15) and ΔsS°(T) obtained in this work by the second and third laws are in a fair agreement for both monomer and oligomer molecules. The same can be said about the results for the monomer molecules from [2, 7]. The data of the work [9] are in notably worse agreement, whereas those of [6, 8] do not agree within the given uncertainties. At the same time, the third law values for all the data are in a good consent with each other. The temperature trend of the third law values ΔsH°(298.15) is given in Figure 6, from which one can see that the data of this work and [2, 9] do not show a pronounced temperature dependence as compared to those of [6, 7]. Taking into account this analysis, the recommended values were selected and emphasized in bold in Table 4. The early estimates [27, 28] made for monomers differ considerably from the recommended value, while the assessments given in [22, 29] agree with the experimental data.Figure 6
Temperature dependencies of the third lawΔsH°(298.15 K) values: (1) monomer from [9], (2) our data, (3) [2], (4) [7], and (5) [6]; (1′) dimer from [9], (2′) our data, and (5′) [6]; (2′′) trimer our data.The standard formation enthalpies, ΔfH°(298.15 K), are equal to -371±9 kJ·mol−1 (CeI3), -924±30 kJ·mol−1 (Ce2I6), and -1585±50 kJ·mol−1 (Ce3I9) and were calculated from the recommended ΔsH°(298.15 K) values. The formation enthalpy of crystalline cerium triiodide, ΔfH°(CeI3,cr; 298.15 K) = −669 kJ·mol−1 [22], was used.


## 3.2. Charged Vapor Species

In the TE mass spectra in the temperature range of 747–960 K the I−(0.44), CeI3-(0.18), CeI4-(100), and Ce2I7-(0.08) ions were identified with the relative ion currents given in parentheses forT = 846 K.Additional experiments with the CeI3-PrI3 binary system were performed to determine the enthalpy of formation of CeI4- ions. The enthalpy of exchange ion-molecular reaction (5) was found to be 1±5 kJ·mol−1. The enthalpy of formation of PrI4-ΔfH°(298.15 K) = -860±23 kJ·mol−1 was used as reference value. It was obtained by recalculation of the data (-865±25 kJ·mol−1) [13] with the thermodynamic function used in this work. The experimental equilibrium constants of reaction (3) and reaction (4) investigated over pure CeI3 are listed in Table 5:(3)CeI3,g+PrI4-,g=CeI4-,g+PrI3,g,(4)Ce2I7-,g=CeI4-,g+CeI3,cr,lTable 5
Experimental data for reactions (3) and (4).
Reaction (3) Reaction (4) T (K) ln ⁡ K P ° T (K) ln ⁡ K P ° 889 0.35 868 6.39 865 0.39 862 6.61 835 0.30 898 5.92 846 0.49 932 5.43 907 0.41 960 4.94 934 0.39 924 5.49 966 0.38 892 5.94 956 0.37 846 6.67 929 0.34 906 0.22 856 0.34 806 0.38 854 0.30 884 0.38 902 0.30 950 0.40 976 0.30The reaction enthalpies were calculated by the second and third laws of thermodynamics; see Table6. The evaluation of the thermodynamic functions of the CeI4- and Ce2I7- ions is described in Appendix.Table 6
Enthalpies (kJ·mol−1) of reactions (3) and (4).
ΔT, K T, K N 1 II law2 III law3 Ref. Δ r H °(T) Δ r H °(298.15 K) Δ r H °(298.15 K) C e I 3 , g + PrI4-,g = CeI4-,g + PrI3,g 806–976 897 17 0 ± 3 1 ± 3 1 ± 5 This work  C e 2 I 7 - , g = CeI4-,g + CeI3,cr,l 842–960 896 12 -99±5 - 113 ± 6 - 75 ± 40 This work 1Number of measurements. 2The original errors are given for the literature data, the standard deviations for this work. 3The uncertainties are mainly determined by those in thermodynamic functions.One can see that the agreement for the enthalpy of reaction (3) obtained by the second and third laws is good. ΔfH°(CeI4-, 298.15 K) = -857±19 kJ·mol−1 was recommended. This value is in agreement with those -850±33 kJ·mol−1 obtained by Chantry from the enthalpy of the reaction CeI4-,g = I-,g + CeI3,g and recalculated with our sublimation enthalpy and thermodynamic functions. The selected formation enthalpy of the Ce2I7- ion is -1451±50 kJ·mol−1 (third law) and was obtained for the first time.


## 3.3. Thermodynamic Properties Derived from IECs

The enthalpies of ion-molecular reactions were calculated from the differences of the measuredAE values given in Table 1; see Table 7. On their basis the standard formation enthalpies of the ions were determined; see Table 8. The accurate values of ΔfH°(Ce+, 298.15 K) = 957±0.1 kJ·mol−1 [22] and ΔfH°(I, 298.15 K) = 106.76±0.04 kJ·mol−1 [22] and the formation enthalpies of the CeI3, Ce2I6, and Ce3I9 molecules obtained in this work (see above) were used as references. The comparison of our results with the data obtained by photoelectron spectroscopy [30], computation [31], and assessment [32] shows that all data are in agreement within the given errors; see Table 8.Table 7
Ion-molecular reactions (kJ·mol−1).
Reaction This work [1] [3] [5] [30] [31] C e I + , g = Ce+,g+Ig 391 ± 10 396 ± 50 347 ± 50   393 C e I 2 + , g = CeI+,g+Ig 323 ± 10 376 ± 50 347 ± 50 C e I 3 + , g = CeI2+,g+Ig 66 ± 10 10 ± 50 48 ± 50 39 62 ± 50 C e I 3 , g + Ce2I5+,g = Ce+,g + 2Ig+Ce2I6,g 750 ± 10 C e I 3 , g + Ce3I8+,g = Ce+,g + 2Ig+Ce3I9,g 768 ± 20Table 8
Ion formation enthalpies (kJ·mol−1).
Ion This work [1] [3] [32] [31] CeI+ 673 ± 10 669 ± 50 717 760 671 C e I 2 + 467 ± 10 399 ± 50 476 C e I 3 + 497 ± 10 496 ± 50 535 C e 2 I 5 + - 131 ± 10 C e 3 I 8 + - 811 ± 20Analysis of the ion-molecular reaction enthalpies confirmed the weakness of the first cerium iodine bond in comparison with the other two. Probably, it explains the lower enthalpy of the formation ofCeI2+ (467±10 kJ·mol−1) compared to CeI3+ (497±10 kJ·mol−1).The formation enthalpy of gaseous CeI3 (-371±9 kJ·mol−1) obtained from the vapor pressure measurement is in a good agreement with those calculated from the appearance energies (-376±50 kJ·mol−1) and with the value (−381 kJ·mol−1) assessed by Sapegin et al. [33] (Table 9). The coincidence of the formation enthalpy values of CeI3,g, as determined from the thermodynamic and threshold approaches, points out a negligible contribution from the excitation and kinetic energy of the fragments. The atomization energy derived from ΔfH°(CeI3, 298.15 K) = -371±9 kJ·mol−1 was found to be 1109±10 kJ·mol−1. It yields the average bond strength equal to 370±10 kJ·mol−1.Table 9
Formation enthalpies ofCeI3,g(kJ·mol−1).
This workfrom IEC This workfrom ΔsH° [1] [9] [33] >−376 ± 50 −371 ± 9 −436 ± 50 −349 −381


## 3.4. Electron Work Function

The mass spectrometric approach for the work function determination is based on the use of thermochemical cycles including desorption enthalpies of ions and sublimation enthalpies of molecules as described elsewhere [34]. The desorption enthalpy of the CeI4- ions, ΔdesH°(851 K) = 350±8 kJ·mol−1, and the Ce2I7- ions, ΔdesH°(902 K) = 430±18 kJ·mol−1, were obtained from the temperature dependence of their ion currents; see Figure 7. The electron work function was calculated in accordance with the following expressions:(5)φe=-14DCeI3+54·ΔsH°CeI3+EAI+ΔdissH°CeI4-+ΔdesH°CeI4-,(6)φe=-14DCeI3+94·ΔsH°CeI3+EAI+ΔdissH°Ce2I7-+ΔdesH°Ce2I7-,where EA(I) is the electron affinity of iodine [22],D(CeI3) is the dissociation enthalpy of the CeI3 molecule, ΔdissH°(CeI4-) is the enthalpy of the CeI4- = I− + CeI3 reaction (Table 6), and ΔdissH°(Ce2I7-) is the enthalpy of the Ce2I7- = I− + 2CeI3 reaction.Figure 7
Temperature dependencies ofCeI4- and Ce2I7- ion currents.Theφe values equal to 3.3±0.3 eV and 3.5±0.5 eV were obtained from (5) and (6), respectively. They turned out to be close to φe(LaI3) = 3.5±0.3 eV [14].


## 4. Conclusions

New experimental data on the saturated vapor composition of CeI3 have been obtained by a Knudsen effusion mass spectrometer. The monomer, CeI3, dimer, Ce2I6, and trimer, Ce3I9, molecules, as well as the [I(CeI3)n]− ions (n=0–2), have been observed in the temperature range of 747–994 K. The Ce3I9 molecules and the Ce2I7- ions were detected for the first time. The sublimation enthalpies of the monomer and oligomer molecules were calculated by the second and third laws of thermodynamics. Critical analysis of all available data allowed us to recommend the following enthalpies of sublimation: ΔsH°(298.15 K) in kJ·mol−1: 298±9 (monomer), 415±30 (dimer), and 423±50 (trimer) and to calculate the formation enthalpies, ΔfH°(298.15 K) in kJ·mol−1: -371±9 (CeI3), -924±25 (Ce2I6), -1585±50 (Ce3I9), -857±19 (CeI4-), and -1451±50 (Ce2I7-). The electron work function for cerium triiodide (3.3±0.3 eV) has also been evaluated.



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