ELECTRON WORK FUNCTION OF LANTHANIDE TRIIODIDES

Dunaev Anatoliy M.; Motalov Vladimir B.; Kudin Lev S.

Т 63 (11)

ИЗВЕСТИЯ ВЫСШИХ УЧЕБНЫХ ЗАВЕДЕНИЙ. Серия «ХИМИЯ И ХИМИЧЕСКАЯ ТЕХНОЛОГИЯ»

2020

IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII V 63 (11) KHIMIYA KHIMICHESKAYA TEKHNOLOGIYA 2020

RUSSIAN JOURNAL OF CHEMISTRY AND CHEMICAL TECHNOLOGY

DOI: 10.6060/ivkkt.20206311.6292 УДК: 544.3

РАБОТА ВЫХОДА ЭЛЕКТРОНА ТРИИОДИДОВ ЛАНТАНОИДОВ A.M. Дунаев, В.Б. Моталов, Л.С. Кудин

Анатолий Михайлович Дунаев*, Владимир Борисович Моталов, Лев Семенович Кудин

Кафедра физики, Ивановский государственный химико-технологический университет, Шереметевский

пр., 7, Иваново, Российская Федерация, 153000

E-mail: [email protected]*, [email protected], [email protected]

Энтальпии десорбции ассоциированных ионов трииодидов лантаноидов LnI4~ и Ln2I7~ (Ln = La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm, and Lu) и энтальпии сублимации молекул LnI3 были найдены при помощи масс-спектрометрического подхода с использованием ячейки Кнудсена. Эти данные были использованы для расчета эффективных значений работы выхода электрона фе для поликристаллических образцов трииодидов лантаноидов LnI3, что было проделано впервые. Методика расчета была основана на изучении термохимических циклов, которые включали атомы, молекулы, ионы и электроны, находящиеся в термодинамическом равновесии с кристаллом LnI3 внутри эффузионной ячейки Кнудсена. Полученные величины для различных лантаноидов имеют весьма близкие значения. Они лежат в интервале от 2,4 эВ до 4,4 эВ со средним значением для всего ряда равным фе = 3,2 ± 0,3 эВ. Эта величина близка к величине работы выхода электрона у трибромидов лантаноидов, изученных авторами ранее. В пределах установленных погрешностей нельзя говорить о проявлении двойной периодичности для величин работы выхода электрона в ряду лантаноидов. Полученные результаты находятся в количественном согласии с теоретическим расчетом ширины запрещенной зоны для трииодидов лантаноидов (работа выхода электрона должна быть больше или равна полуширине запрещенной зоны). Сравнение величин фе с другими классами соединений лантаноидов, таких как оксиды, гексабориды и металлы лантаноидов показало относительно высокую способность к эмиссии электронов, уступающую лишь щелочным и щелочно-земельным металлам.

Ключевые слова: работа выхода электрона, иодиды, лантаноиды, термодинамика, масс-спектрометрия Кнудсена

ELECTRON WORK FUNCTION OF LANTHANIDE TRIIODIDES A.M. Dunaev, V.B. Motalov, L.S. Kudin

Anatoliy M. Dunaev*, Vladimir B. Motalov, Lev S. Kudin

Department of Physics, Ivanovo State University of Chemistry and Technology, Sheremetevskiy ave., 7, Ivanovo, 153000, Russia

E-mail: [email protected]*, [email protected], [email protected]

Desorption enthalpies of LnI4~ and Ln2I7~ associative ions (Ln = La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm, and Lu) and the enthalpy of sublimation of LnI3 molecules were determined by Knudsen effusion mass spectrometric technique. These data were used to calculate the effective values of electron work function pe ofpolycrystalline samples of lanthanide triiodides LnI3 for the

first time. The calculation methodology is based on the study of thermochemical cycles, which include atoms, molecules, ions, and electrons being in thermodynamic equilibrium with the LnI3 crystal inside the effusion cell. The values obtained for different lanthanides turned out to be close. They lie in the range of about 2.4 - 4.4 eV with an average value in the series: pe = 3.2 ± 0.3 eV. The latter value is close to those for previously studied lanthanide tribromides. No secondary periodicity of pe was found within the calculated errors along the lanthanide series. The results obtained are in quantitative agreement with the theoretical calculation of the values of the band gap of lanthanide triiodides. Comparison of pe with other classes of lanthanide compounds such as oxides, hexaborides, and lanthanide metals shows relatively high electron emission ability yielding only to alkali and alkali-earth metals.

Key words: electron work function, lanthanides, iodides, thermodynamics, Knudsen effusion mass spectrometry Для цитирования:

Дунаев A.M., Моталов В.Б., Кудин Л.С. Работа выхода электрона трииодидов лантаноидов. Изв. вузов. Химия и

хим. технология. 2020. Т. 63. Вып. 11. С. 13-20 For citation:

Dunaev A.M., Motalov V.B., Kudin L.S. Electron work function of lanthanide triiodides. Izv. Vyssh. Uchebn. Zaved. Khim.

Khim. Tekhnol. [Russ. J. Chem. & Chem. Tech.]. 2020. V. 63. N 11. P. 13-20

INTRODUCTION

Fast development of modern branches of electronics such as spintronics, laser technologies and electrooptics needs a deep knowledge of electronic structure, which defines in particular the luminescence properties of materials [1]. The key factor in understanding of electronic structure is investigation of emission properties of compounds. Among them the electron work function is one of the most important. It characterizes the minimum energy required to extract an electron from the surface of a solid [2]. From different classes of materials used in microelectronics the lanthanide halides, and especially iodides, are in the focus of attention of scientists all over the world. This interest is caused by specific peculiarities of lanthanide compounds expressed in a wide variety of properties and possibility of their tuning by selection of desired lanthanide atom, dopant etc.

Nowadays lanthanide iodides have found an extensive range of applications in various areas, such for catalytic processes in organic synthesis [3], production of powerful magnets [4], solar cells [5], laser host crystals [6], transparent ceramics [7], and phosphors [8], biomedical applications for the determination of cellular activity [9], in magnetic resonance imaging [10], scintillators for detection of ionizing radiation [11, 12], pyroreprocessing of spent nuclear fuel, and many others [13, 14].

The information on electron work function of lanthanide iodides is absent in literature. Recently we reported the preliminary results of experimental determination of the 9e value for LnI3 (Ln = La, Ce, Pr) [15]. This paper is a continuation of the started work for all other stable lanthanide triiodides. The data

from [15] were revised here because of new experimental measurements obtained and a unified approach used for the thermodynamic functions selection.

EXPERIMENTAL

Apparatus. A single-focusing magnetic sector type mass spectrometer MI1201 modified for Knudsen cell effusion studies (KEMS) was used. The combined ion source allowed to analyze both neutral and charged vapor species under electron ionization (EI) and thermal ion emission (TE) modes, respectively. Detailed description of the apparatus and experimental procedure can be found elsewhere [15-18].

Samples. Eleven thermally stable lanthanide triiodides LnI3 (Ln = La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm, and Lu) were selected as the objects under study. Pm compounds are radioactive. Samarium, europium, and ytterbium triiodides decompose into di-iodides while heating. Sample synthesis and purity control were described elsewhere [19-24].

Calculation method. The method used in this work for calculation of 9e is based on analysis of thermochemical cycles including atoms, molecules, ions, and electrons desorbing from the crystal surface under thermodynamic equilibrium condition. The electron work function in this case is interpreted as electron desorption enthalpy, i.e. quantity of heat liberated at transition of electron from the crystal to the vacuum. The detailed description of the method can be found in [15]. The first application of KEMS to determine the electron work function was realized by the authors [25]. Registration in saturated vapor in the TE mode of positive and negative ions of the same type made it possible to calculate 9e for KOH and CsOH hydroxides based on the Sakha-Langmuir equation. Later, this approach was modified by the au-

thors [25-27] and successfully tested on crystals of alkali halides [26, 27] and lanthanide tribromides [28]. In the latter work it was shown that in the TE mode the associative ions LnX4- and Ln2X7- (X is halogen) are typical for lanthanide trihalides.

Thermochemical cycles for LnI4- and Ln2I7-anions are shown in Fig. 1a and 1b, respectively. According to the Hess law 9e can be derived from the given cycles by following equations:

9e = AdesH°(LnLf) - 1/4D(LnI3) - 5/4AsH°(LnI3) -

- EA(I) + Adiss#°(LnI4-), (1) 9e = AdesH°(Ln2I7) - 1/4D(LnL) -9/4AH°(LnI3) -

- EA (I) + Adiss#°(Ln2I7-). (2) where 9e is the electron work function; AH°(LnI3) and D(LnI3) the sublimation enthalpy and atomization enthalpy of LnI3 molecule, respectively; EA(I) the electron affinity of iodine atom; AdesH°(LnI4) and AdesH°(Ln2I7) the desorption enthalpies of the LnI4-and Ln2I7- anions, respectively; AdissH°(LnI4-) and A^H^Ln^-) the dissociation enthalpies corresponding to reactions:

LnI4- = LnI3 + I-;

Ln2I7- = 2LnI3 + I-.

b

Fig 1. Thermochemical cycles for LnI4- (a) and Ln2I7- (b) anions

desorbing from LnI3 crystal Рис. 1. Термохимические циклы для анионов LnLf (a) и Ln2I7- (b), десорбирующихся с поверхности кристалла LnI3

RESULTS AND DISCUSSION

The election work function values 9e were obtained from the thermodynamic quantities experimentally determined for the LnI3 molecules in EI mode and for the associative LnI4- and Ln2I7- ions in TE mode. Desorption enthalpies were found in the framework of

approach of the second law of thermodynamics from the slopes of temperature dependencies of ion currents measured in this work in TE mode (Table 1). The sublimation enthalpies of LnI3 (Ln = La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm, and Lu) were taken from [19-24]. The electron affinity of iodine EA(I, 298.15 K) = 301.797 kJ-mol-1 as well as the formation enthalpies of the gaseous iodine AH°(I, 298.15 K) = 106.76 kJ-mol-1 and lanthanide atoms AH°(Ln, 298.15 K) (Ln = La (430); Ce (417.07); Nd (355.81); Pr (327.13); Gd (398.51); Tb (386.06); Dy (285.25); Ho (300.19); Er (313.83); Tm (232.76); and Lu (427.86)) kJ-mol-1 needed for atomization energy determination were taken from the IVTANTHERMO database [29].

In the present study we revise the data from the previous paper [15] according to procedure of determination of formation enthalpies of ions described in recent paper [30]. This procedure allows to reduce the errors in thermochemical values caused by selection of standard. Here we need bring a brief explanation.

The determination by KEMS of the formation enthalpies of LnX4- ions incoming in AdissH° is complicated by the problem of non-equilibrium halogen anions X- forming in the outer surface of the Knudsen cell thus precluding the direct study of the heterophase reaction

LnX4- = LnX3,cr + X-.

To overcome this problem the ion-molecular exchange reactions

LnrefX4- + LnX3 = LnX4- + LnrefX3

were studied.

The reliable AH°(LnX4-) value was obtained for LaBr3 in [31]. Since PrI3 was chronologically first studied for triiodides [21], it was selected as a standard in Ref. [15] using a consecutive transition LaBr3 -PrBr3 - PrI3 in investigating of exchange reaction. However, this two-step transition is relatively long and leads to accumulation of errors. On the other hand, praseodymium has a set of low-lying excited electronic levels impeding precise determination of ther-modynamic functions and additionally increasing errors in the AjH° values. Therefore, to minimize the errors, the better standard LaI3 was applied recently [30] and the revised formation enthalpies for LnI4-ions were used in this work.

Thermodynamic functions O0(7) and H°(T)-H°(0) used in this work were taken from [30] or computed in the "rigid rotator - harmonic oscillator" approximation by StatThermo software [32] with the molecular parameters linearly estimated on the basis of data [33]. The electronic contributions into thermo-

dynamic functions of LnI4- were taken equal to those in corresponding LnI3 [29, 34]. The functions were approximated by polynomials

0O(T) = alnx + bx~2 + cx- + dx + ex2 + fx3, [J mol-1 K-1; x = 10-4T/K]; (3)

H°(7)-H°(0) = 10(ax - 2bx- - c + dx2 + 2ex3 + 3f4), [kJ mol-1; x = 10-4T/K]. (4)

The coefficients of Eq. (3) and (4) are listed in Table S1 in Supplementary materials (http://jour-nals.isuct.ru/ctj/article/view/3037/1884).

Table 1

Experimental data on temperature dependencies of ion currents of associative ions over lanthanide triiodides in the form ln(/-7°'5) vs 1000/T, where I is ion current (arb. un.) and T temperature (K) Таблица 1. Экспериментальные данные по температурным зависимостям ионных токов ассоциативных

------------------— ----------1«/Г.Т°*5\ 1Л1Ш/Т „^П Т ---------г-«., .. Т г-«----------- iTT\

1000/Г LnI4 Ln2I7 1000/Г LnI4 Ln2I7 1000/Г LnI4 Ln2I7 1000/Г LnI4 Ln2I7

LaÏ3 PrI3 TbI3 1.127 -17.64 -22.71

1.023 -15.14 -19.73 1.058 12.11 8.05 1.083 -13.73 -18.59 ErI3

1.023 -15.36 -19.82 1.070 11.70 7.65 1.083 -13.98 -18.97 1.065 -16.27 -20.74

1.061 -17.46 -21.71 1.097 10.47 5.93 1.112 -14.94 -20.32 1.018 -14.83 -18.79

1.061 -17.31 -21.76 1.061 11.92 7.76 1,168 -16.82 -22.57 1.049 -15.62 -19.83

1.092 -19.17 -23.63 1.044 12.37 8.48 1.239 -19.78 1.086 -17.01 -21.45

1.092 -18.98 -23.53 1.024 13.03 9.24 1.321 -23.04 1.136 -18.61

1.136 -21.27 1.033 12.73 8.94 1.284 -21.74 1.171 -19.87

1.137 -21.37 1.049 12.33 8.34 1.200 -18.61 1.117 -18.04

1.081 -17.77 -22.48 1.001 13.75 10.32 1.144 -16.42 -21.96 1.054 -15.85 -20.20

1.081 -17.80 -22.23 0.971 14.42 11.59 1.093 -13.99 -19.09 1.000 -14.10 -17.77

1.055 -16.49 -21.23 0.954 15.02 12.46 1.050 -12.43 -16.94 1.034 -15.15 -19.41

1.054 -16.49 -21.10 0.990 13.86 10.89 1.112 -14.38 -19.45 TmI3

1.041 -15.89 -20.46 1.014 13.13 9.82 DyI3 1.228 -20.72

1.041 -15.95 -20.59 1.113 9.89 5.51 1.012 -16.25 -20.51 1.182 -18.58 -24.68

1.010 -14.76 -19.45 1.066 11.65 7.47 1.030 -17.07 -21.67 1.137 -16.86 -22.54

1.010 -14.91 -19.27 1.039 12.43 8.57 1.030 -16.96 -21.60 1.103 -15.49 -20.93

0.979 -13.89 -17.62 1.006 13.33 9.87 1.067 -18.47 -23.52 1.065 -14.37 -19.57

0.979 -14.08 -17.47 1.052 12.15 7.94 1.067 -18.37 -23.38 1.061 -14.02 -19.17

CeI3 1.103 9.92 5.34 1.103 -19.81 1.086 -15.02 -20.50

1.067 -12.14 -17.85 1.074 11.34 7.04 1.071 -18.10 -23.26 1.116 -16.16 -21.95

1.090 -12.92 -18.97 1.028 12.88 8.96 1.029 -16.76 -21.22 1.152 -17.65 -23.65

1.138 -14.75 -21.31 1.014 13.25 9.71 0.984 -15.52 -19.29 1.196 -19.67

1.188 -16.60 -23.62 NdI3 0.984 -15.80 -19.38 LuI3

1.252 -18.94 1.074 -15.34 -19.79 0.994 -16.22 -19.95 1.062 -17.04 -22.15

1.328 -22.77 1.127 -17.20 -22.11 0.994 -16.42 -20.16 1.114 -18.96 -24.59

1.284 -20.89 1.176 -18.68 1.031 -17.21 -21.88 1.088 -17.98 -23.34

1.221 -17.66 1.153 -17.93 1.073 -18.68 -23.74 1.049 -16.60 -21.45

1.152 -14.83 -21.64 1.095 -16.13 -20.64 1.124 -20.62 1.067 -17.26 -22.29

1.160 -14.72 -21.74 1.058 -14.76 -18.87 HoI3 1.105 -17.95 -23.66

1.113 -12.79 -19.12 1.031 -13.84 -17.75 1.070 -16.62 -21.21 1.126 -19.02 -25.01

1.073 -11.31 -17.16 1.010 -13.16 -16.86 1.099 -17.69 -21.83 1.155 -20.06

1.027 -14.86 GdI3 1.041 -15.26 -19.35 1.143 -19.65

1.042 -10.32 -15.68 1.061 -23.05 -16.60 1.003 -14.11 -17.72 1.163 -20.34

1.082 -11.82 -17.72 1.061 -22.95 1.024 -14.42 -18.35 1.182 -21.03

1.121 -13.37 -19.72 1.041 -21.93 -15.93 1.015 -13.52 -17.71 1.224 -22.54

1.183 -15.74 -22.83 1.019 -20.65 -14.98 0.989 -13.73 -17.43 1.258 -23.87

1.252 -18.38 1.036 -21.75 -15.70 1.024 -14.66 -18.56 1.209 -22.14

1.290 -20.26 1.026 -20.64 -15.09 1.070 -15.79 -20.22 1.244 -23.45

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1.340 -22.89 1.014 -20.09 -14.56 1.117 -17.48 -22.30 1.198 -21.76

1.314 -22.19 1.005 -19.33 -14.12 1.093 -16.68 -21.14 1.108 -18.42 -24.20

1.285 -20.45 0.991 -17.52 -12.36 1.054 -15.28 -19.63 1.072 -17.13 -22.48

0.976 -16.68 -12.45 1.007 -14.24 -18.06 1.032 -15.95 -20.79

0.968 -16.44 -11.98 1.030 -14.73 -18.55 1.034 -15.95 -20.81

Analysis of the found 9e (Table 2, Fig. 2) shows a reasonable agreement of values calculated from the equations (1) and (2), but we give preference to the values obtained by the equation (1) as more precise. One can see that obtained values through the lanthanide series are close to each other within the given errors with the exception for GdI3, whose value is apparantly somewhat higher. It can be explained by feature of band structure of lanthanide triiodides. Electron work function is linked with other parameters of band structure by following equation [35]

9e = Eg/2 + x, (5)

where Eg is the band gap and x is the electron affinity of the crystal. Theoretically calculated band gap values of lanthanide iodides published recently by Rogers et al. [36] can be used for checking our results (Fig. 2). According to (5) > Eg/2. This expression is fulfilled for all examined compounds except HoI3. However, it is known that x can take a negative value [37]. Here one can see the maximum at GdI3 agrees well with our data.

Comparison of our results with data from [28] reveals closeness of electron work function values of lanthanide tribromides and triiodides. It indicates that the nature of lanthanide atom is primary factor defining 9e of lanthanide trihalides.

The calculated average value of electron work function for lanthanide iodides 9e = 3.2±0.3 eV is

quite low and points out high electron emission ability of this class of compounds. Among the compounds used as cathode materials 9e of lanthanide iodides is a little bit higher than those of LaB6 (2.8 eV) [40], CeBix® (cerium hexaboride based cathode) (2.65 eV) [38], but lower than those of transition metals carbides (HfC (3.58 eV), NbC (3.53 eV), ZrC (4.0 eV), TaC (4.2 eV), TiC (3.8 eV)) and tungsten (4.55 eV) [39]. At the same time, it is considerably higher than those of alkali and alkali-earth metals (from 1.95 to 2.93 eV) [2] and BaO (~1 eV) [39].

There are no literature data on electron work function of lanthanide iodides. Handbook of Fomenko [39] contains the data on lanthanide oxides. 9e values of lanthanide metals are given in [41]. However, both these works bring a very scattered data collected from different sources, e.g. the 9e value for La2O3 lies into a range from 2.5 to 4.2 eV thus precluding precise comparison. This fact can be explained by a strong dependence of the 9e values determined by usual thermoionic or photoelectron methods from structural features (type of face and the type of lattice) whereas in our approach the efficient work function was found. The average value 9e for lanthanide oxides is about 3.0 eV [39] that is similar to our data for LnI3. Recently Wang et al. [41] published theoretical research on lanthanide hexaborides LnB6.

Table 2

Thermochemical data and of lanthanide iodides

Molecule Ion T AdeH°(T) AsH°(298.15 K) D°(298.15 K) AdiSSH°(298.15 K) 9e(LnI3)

K kJ-mor1 eV

LaI3 LaI4- 950 396±18 305±4 1119±4 257±19 3.4±0.3

La2I7- 959 419±17 456±44 2.6±0.5

CeI3 CeI4- 841 350±8 294±4 1110±5 258±21 3.0±0.2

Ce2I7- 901 430±18 453±45 2.9±0.5

PrI3 PrI4- 962 264±8 293±6 1048±8 256±22 2.4±0.3

P^If 962 369±8 467±47 2.7±0.5

NdI3 NdI4- 917 278±4 293±3 993±5 274±24 3.0±0.3

Nd2I7- 938 374±7 492±46 3.4±0.5

Gdl3 GdI4- 982 448±32 285±5 1058±6 266±22 4.4±0.4

Gd2I7- 982 621±27 470±45 5.4±0.6

TbI3 TbI4- 864 329±7 280±3 1050±4 265±21 3.2±0.2

Tb2I7- 904 404±29 474±45 3.3±0.6

Dyl3 DyI4- 960 281±14 280±3 943±4 280±23 3.2±0.3

Dy2I7- 971 395±14 492±46 3.8±0.5

HoI3 HoI4- 951 267±19 281±3 962±4 277±23 3.0±0.3

Ho2I7- 951 3 3 9±16 493±46 3.1±0.5

ErI3 ErI4- 932 279±4 278±4 975±5 283±24 3.1±0.3

E^If 958 352±14 500±46 3.3±0.5

TmI3 TmI4- 883 333±9 276±3 897±5 268±21 3.7±0.2

Tm2I7- 899 378±15 475±45 3.5±0.5

LuI3 LuI4- 884 291±5 278±10 1075±10 277±24 2.9±0.3

Lu2I7- 928 374±12 466±47 2.9±0.5

e

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Fig. 2. Electron work function of lanthanide triiodides calculated from the cycles with LnI4- (eqn. (1), filled squares) and Ln2I7-(eqn. (2), open circles). The filled triangles are the фс values for LnBr3 from [28]. The line is half of band gap for LnI3 from [36] Рис. 2. Работа выхода электрона трииодидов лантаноидов, рассчитанная из циклов для ионов LnI4- (ур. (1), заполненные квадраты) и Ln2I7- (ур. (2), пустые кружки). Заполненные треугольники соответствуют величинам фс для LnBr3 из [28]. Линия указывает на полуширину запрещенной зоны LnI3 из [36]

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CONCLUSION

Analysis of the electron work function of lanthanide triiodides LnI3 (Ln = La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm, and Lu) determined by Knudsen effusion mass spectrometry reveals relatively high electron emission ability for this compounds, that can be used for production of various electron sources and vacuum devices. The average 9e value is close to those of lanthanide oxides, hexaborides and pure lanthanide metals. Thus, the emission ability of LnI3 yields only to those of alkali and alkali-earth metals, but the latter are more hygroscopic and chemically active.

ACKNOWLEDGEMENT

This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of Government order (№ FZZW-2020-0007).

Работа поддержана Министерством науки и высшего образования Российской Федерации в рамках Государственного задания (№ FZZW-2020-0007).

REFERENCES