Stability of rare-earth-containing high-temperature molecules

Metals, 110 (1985)

Journal of the Less-Common

41

41 - 51

HIGH-TEMPERATURE

STABILITY OF RARE-EARTH-CONTAINING MQLECULES*

K. A. GINGERICH

Department (Received

of Chemistry, January

Texas A&M University,

College Station,

TX 77843 (U.S.A.)

29, 1985)

Summary

The Knudsen effusion mass-spectrometric method has been used to study high-temperature equilibria involving gaseous, rare-earth-containing molecules such as bi-metals, carbides, oxides, and sulfides. Our recent work has especially concentrated on diatomic intermetallic compounds and on gaseous carbides. We summarize our investigations of diatomic intermetallic molecules with strong metal-metal bonds and discuss the bond energies in terms of empirical models of bonding. Our recent work on gaseous carbides has revealed the existence of new classes of gaseous, rare-earth carbides such as (RE)C, or (RE)&, with n = 1 - 8 or M(RE)C, with n = 1 - 4. This complex mode of vaporization is illustrated using the La-Ir-graphite system as example. The atomization energies of the gaseous rare-earth carbides are reviewed.

Introduction

Over the past 15 years a large portion of our mass-spectrometric equilibrium studies at high temperatures has been devoted to the measurement of dissociation energies of rare-earth-containing molecules. This work has led to the thermodynamic evaluation of the first rare-earth boride [l], nitride [ 21, cyanide [3], and polyatomic sulfides [4]. We have also made contributions to the knowledge of the atomization energies of polyatomic rare-earth oxides [ 5,6], but our most systematic and extensive recent investigations have been in the areas of metal molecules [7, 81 and gaseous carbides [9 - 161. In the following we summarize and discuss our results on gaseous rare-earth intermetallic compounds. Then we review the knowledge of the stability of gaseous rare-earth carbides and present and discuss our recent results. *Paper presented at the International land, March 4 - 8, 1985.

Rare

Earth

0022-5088/85/$3.30

0 Elsevier

Conference,

Sequoia/Printed

ETH Zurich,

Switzer-

in The Netherlands

42

Knudsen

cell mass-spectrometric

method

The Knudsen cell mass-spectrometric method is well established and has been described in many reviews [9,17]. It is an important method. for equilibrium vapor studies of high-temperature systems for temperatures up to approximately 3000 K. There is no other method presently available that permits the measurement of bond energies of minor molecular vapor components at such high temperatures. In the Knudsen effusion mass-spectrometric method, a molecular beam of the vapor effusate from the Knudsen cell is sampled and ionized in the ion-source region, usually by electron bombardment. The ions are then accelerated and their mass analyzed. For the identification of the ions and their correlation with the corresponding molecular precursors, their mass-to-charge ratio, isotopic abundance distribution, appearance potential, and intensity profile in the molecular beam are ionization efficiency, usually measured. The measured ion currents are correlated with the corresponding partial pressures using well established instrument calibration procedures. Expressing the partial pressures in terms of reaction equilibrium constants, Keq, allows for the determination of the reaction enthalpies AH0 (13= 0 or 298) by the third-law method, using the equation: AH0” = -RT

In K,, - T[A(Gr”

-He”)/T]

where the bracketed term is the Gibbs energy function. When a large enough temperature range can be covered, the second-law method can also be used, i.e., d In&., d(V)

-AH, =V R

Further details on the instrument, evaluation are given elsewhere [ 91.

Diatomic

intermetallic

rare-earth

experimental

procedure,

and data

molecules

In our systematic work on the dissociation energies of diatomic intermetallic molecules with strong metal-to-metal bonds and their interpretation in terms of empirical models of bonding, the rare-earth molecules with gold or a platinum metal have played a significant role. For the early studies we have used the Pauling correlation of a polar single bond [18] as a guide for our experiments. In this correlation, the bond energy, D(A-B), of a diatomic molecule AB is expressed by: D(A-B)

= l/B[D(A-A)

+ D(B-B)]

+ 96(X* - Xn)’

(in kJ mol-‘)

where D(A-A) and D(B-B) are the “single-bond energies” of the component atoms A and B, respectively, and X, and X, are the respective

43

electronegativities on the Pauling scale. The first term of the equation gives the covalent contribution to the bond energy, to which an “ionic resonance” energy given by the second term, is added. In the case of the rare-earth intermetallic molecules, particularly large ionic contributions are expected for those with gold, since with this element the largest electronegativity differences are obtained. Our measurements of such molecules have yielded the largest values for metal-metal bond energies known at that time [19 211. In Table 1 the presently known measured dissociation energies of diatomic rare-earth elements with gold are listed, together with the corresponding values calculated using the Pauling correlation. The experimental and calculated values have been taken from ref. 7. For all eleven molecules the agreement between the experimental and calculated values is very good, especially if one considers the comparatively large uncertainties in the dissociation energies for many of the homonuclear diatomic rare earths. The Pauling correlation has also been successfully extended to triatomic rare-earth diaurides [22 - 241 by applying it to each of the two bonds when assuming a symmetry linear or bent geometry (see Table 2). This agreement, in turn, supports the assumption from electronic considerations that these molecules are symmetric. The Pauling correlation is only applicable to polar single bonds. For multiply-bonded dimetal molecules an empirical valence-bond approach has been developed [ 25, 261, that is applicable to molecules formed between electronegative and electropositive transition metals. Diatomic intermetallic rare-earth molecules with platinum metals can be interpreted in terms of this model and their dissociation energies predicted by it. In this model description one assumes that each of the two atoms forming the molecule is promoted, if necessary, to a valence state, with between two and four unpaired electrons, that is suitable for multiple bond formation. Electron TABLE

1

Comparison of experimental dissociation molecules with gold and values calculated mol-‘) [7]

energies of diatomic intermetallic rare-earth using the Pauling correlation (values are in kJ

Molecule

DO” (ew.)

Da" (talc.)

AuCe AuDy AuEu AuHo AuLa AuLu AuNd AuPr AuSc AuTb AuY

335 f 254 f 239 + 264 f 355 f 328f17 297 + 305f21 277 f 290 + 304 +

346 250 241 267 348 296 267 290 286 291 305

21 20 10 33 21 21 17 33 8

44 TABLE 2 Comparison of experimental and calculated atomization energies of symmetric rare-earth diaurides, using the Pauling correlation (values are in kJ mol-‘) [ 7 J Molecule

Go (ew.)

Au2 Eu AuzHo AulLu AuzTb

549 533 602 582

+ f f +

17 42 33 42

=Using Do0 = D(M-M) + D(Au-Au)

482 534 592 580 + 192(XM -X&*.

pair bonds are then allowed to form between the two atoms. The bond enthalpy per electron pair per mole is obtained from the valence-state bonding enthalpy per mole of electrons of the corresponding type of electrons in the respective condensed metal [27]. The dissociation energy of the molecule is then obtained from the sum of the electron pair bonding enthalpies minus the respective valence state promotion energies, if any, of the two atoms forming the molecule. This empirical valence-bond model has aided the experimental discovery of the strongest metal-metal bonds known, and many of them have been observed for rare-earth-containing molecules. More recently, Miedema and Gingerich [28,29] have proposed the atomic cell (“macroscopic atom”) model for calculating dissociation energies of diatomic intermetallic molecules. In simplified form, for transition metals of approximately equal atomic size, the dissociation energy, D(A-B), may be expressed by: D(A-B)

= + [D(A-A)

+ D(B-B)]

+ P(A+*)2 - Q(An,S1’3)2

where P and Q are empirical constants, @* is an electronegativity parameter that is related to the work function and nws is the electron density at the boundary of a solid atomic cell. This model may be applied to all transitionmetal combinations and is, in this, more general than either the Pauling correlation or the empirical valence-bond model discussed above. However, it is not yet applicable to the lanthanide series metals, cerium through lutetium, for lack of knowledge of the surface energies at 0 K for these elements. In Table 3 we compare the experimental dissociation energies for inter-metallic rare-earth molecules with platinum metals with the values calculated by the empirical valence-bond model and the atomic-cell model, where applicable. From the comparison it can be seen that the empirical valence-bond model describes the experimental results very well, except for the platinum compounds, for which the experimental values are larger than the calculated ones. The reason for this apparent failure is the fact that the model calculations have been based on an assumed double bond, because platinum has no suitable valence state for formation of a triple

45

TABLE

3

Comparison of experimental dissociation energies of diatomic intermetallic rare-earth molecules with platinum metals and values calculated using the empirical valence bond model or the atomic cell model (values are in kJ mol-‘) Molecule

DO” Cev.)

D,”

Valence-bond CeIr CeOs

CePd CePt CeRh CeRu EuRh IrLa IrY LaPt LaRh LuPt PdY PtY RhSc RhY aTaken bTaken

581 t 25 503 + 33 318f17 551 f 25 546 + 25 527+25 232 * 34 573 f 12 453 f 16 496 + 21 525f17 398 * 34 237 + 15 470212 440+12 442 + 11

565 536 326 423 544 544 252 565 451 423 540 356 251 316 387 424

Reference

(talc.)

modela

Atomic-cell

537 522 573 470 339

555 467 452

modelb 7 7 7 7 7 7 7 I 7 8 7 7 31 8 7 7

from ref. 30. from ref. 29.

bond as do almost all rare-earth metals. Apparently, platinum also forms bonds that are comparable in strength to what would be expected for a triple bond. For the atomic-cell model the calculated dissociation energies are higher than the experimental values for the platinum compounds, but they are still in fair agreement. Noteworthy is the large discrepancy for PdY in the case of the atomic-cell model, indicating a weakness of the model when comparatively large promotion energies for suitable valence states are involved in both component atoms. It can be projected that the empirical valence-bond model will be applicable for predicting all not yet known dissociation energies of diatomic intermetallic molecules between a rareearth metal and a platinum metal other than platinum itself.

Gaseous rare-earth carbides Since the first thermodynamic study of molecular carbides by Chupka [33] some 25 years ago, this class of gaseous molecules has been extensively investigated, especially the carbides of the rare-earth metals. General reviews have been given by De Maria and Balducci [34] and by Gingerich [9]. In their initial work Chupka et al. pointed out the pseudooxygen character of the &-radical, and showed the similarity of the M-O

et al.

with the corresponding M-C2 bonding enthalpies. This pseudo-oxygen concept was extended to the gaseous rare-earth tetracarbides by Balducci et al. [35]. In their systematic studies of the rare-earth carbides, De Maria and co-workers showed that the dicarbide is always the most abundant gaseous molecular species in the equilibrium vapor over the corresponding followed by the tetracarbide. Table 4 rare-earth carbide-graphite system, shows examples of equilibrium partial-pressure ratios, P(MC,)/P(M) and P(MC&P(M), at the specified temperatures. TABLE

4

Partial pressure graphite systems

ratios

Metal

T(K)

SC

2319 2504 2561 2500 2500 2500 2500 2500 2500 2500 2320

Y La Ce Pr Nd Gd DY Ho Er Eu

/‘(M&)/P(M)

and

P(MCJ)/P(M)

over

rare-earth

metal

carbide--

Reference 2.6 x 1O-3 1.2 x 10-l 1.2 1.0 3.7 1.5 3.1 6.2 5.8 1.1 1.3

x x x x x x x

10-l 10-l 10-l 1O--3 10-a 10-Z 10-S

6.6 1.3 2.4 4 x 1.3 7.5

x 10-6 x 10-S x lo-* 10-2 x 10-4 x 10-S

1 x 10-d 1 x 10-e

36 37 38 39 39 39 39 39 39 39 40

The first gaseous rare-earth monocarbide, CeC, was measured by Gingerich [41], and the first tricarbide, La&, by Stearns and Kohl [38]. The experimental work on ternary gaseous rare-earth carbides has been pioneered by Guido and Gigli [42] for a molecule containing one metal atom, CeSiC, and by Gingerich [43] for molecules containing two different metals, RhCeCz and PtCeC,. Since 1976, Gingerich and co-workers have extended these mixed-metal carbide studies to a number of rare-earth metals, including molecules of the type M(RE)C, (n = 1 - 4). They have also identified many complex binary rare-earth carbides of the type (RE)C, (n = 1 - 8) and (RE),C, (n = 1 - 8). Space does not permit a detailed review of the gaseous carbides. We select, therefore, the lanthanum-containing gaseous carbides as an example. Lanthanum dicarbide, LaC2, was the first rare-earth carbide studied in the pioneering work of Chupka et al. [33]; LaCa and La& were first found by Stearns and Kohl [38]. Our thorough study of the equilibrium vapor above the La-Ir-graphite system at high temperatures revealed the existence of numerous additional lanthanum-containing species, in accordance with Brewer’s paradox [44]. This is illustrated in Table 5. The data have not been corrected for fragmentation. It is estimated that all the ion currents listed represent to more than 90% ionization from the

47 TABLE

5

Relative ion currents, 2829 Ka.

Ion

I+

La+ Ir+ Lair+ LaIrC+ LaIr&+ LaIrCj+ LaIrC4+

1.00 2.95 1.46 3.8 2.2 7.9 3.9

I ‘, over the La-Ir-graphite

x 10-2 x 1O-2 x 10-s x 10-4 x 10-e x 10-b

aData correspond to the most bMeasured at 2835 K.

system

IOn

I+

LaC’ LaC2+ Lacs+ LaCa+ LaCS+ LaC6+ LaC,+ LaCs+

2.26 1.36 1.00 7.15 9.0 4.8 5.7 4.6

abudant

isotope

x 1O-2 x 10-2 x lo- 2 x lo@ x lo--4 x 10-b x 10mm6

measured

with 20 V electrons

IOn

I+

La2C+ La2 C2+ La2Cs+ La2 C4+ LazCs+ La2C6+

1.5 4.6 3.9 3.4 6.5

La2 CT+ La*Cs+

and are not corrected

x x x x x 1.3 x 3.0 x 4.6 x

at

10-s lo-’ 10-s 10-4 1O-s 10-4 lo-6b lo@

for fragmentation.

parent neutral, and therefore relative partial pressures of the latter. Only in the case of LaC+ is the ion current measured to approximately 99% due to a fragment ion, predominantly from La&. This is also in agreement with the conclusion by Stearns and Kohl [38]. It can be seen from the Table that the molecules La& [33, 381, LaC, [38], and LaC4 [38], that had previously been observed by others, are the most abundant molecular lanthanum carbides. The additional equilibrium species discovered by us have a concentration of the order of 0.1% or less of the saturated vapor. Among the monolanthanum carbides, La&, an alternation in the relative ion currents or partial pressures is discernible, in that they mirror the saturated vapor composition over graphite. Here reference is made to the similar behavior of the cerium carbides [45], in which case the relative ion currents for the carbon species had also been reported for 2733 K [45]: C+, 1; C,+, 5.3 X 10-l; C;, 9.09; C,‘, 1.6 X lo-*; C:, 3.2 X lo-*; C6+, 1.6 X 10-4; C,+, 8.1 X lops. Up to C5 the molecules with an odd number of atoms have a larger partial pressure than the molecules with the preceding even number of atoms. The presence of the platinum metal is not expected to alter markedly the relative concentrations of the rare-earth carbide species MC,,. For the dilanthanum carbides it is interesting to note that those with an even number of carbon atoms appear to be favored. The most abundant mixed carbide is LaIrC2, containing the C2 radical. Mixed rare-earth carbides and complex binary rare-earth carbides of metals other than lanthanum have also been observed and measured by us. carbides are The atomization energies of gaseous, rare-earth-containing listed in Table 6 for the binary carbides, and in Table 7 for the ternary carbides. For none of these carbides has the molecular and electronic structure yet been determined by optical spectroscopy. Therefore, assumptions have to be made concerning the low-lying electronic states and their multiplicities, the geometry, the equilibrium separation between the atoms, and

48 TABLE

6

of binary Atomization energies, De’, ref. 9 supplemented by new values

gaseous

rare-earth

carbides

(in kJ mol-

‘),

from

Molecule

Do”

Reference

Molecule

DOa

Reference

CeC CeCz CeC3 CeC4 CeCS CeC6 Cez C

14 14 14 14 14 14 15 15 15 15 15 15

LaCa La&2

4992 * 60 1670 + 40 2339 + 27 3060 ?r 21 3703 + 50 4395 * 50 5658 f 60 1238 + 34 2519 + 43 1238?21 2562 * 30 1264 f 21 2575 + 30 1185 + 14 1779 f 22 2455 f 22 3139 k 29 3777 t 34 1242 f 25

13 16 16 16 16 16 16

ErC2 EuCz Cd& Hoc2 Hoc4

441 f. 12 1268.2 + 2.7 1833 + 11 2512+9 3111415 3748 + 14 1047 _+ 26 1690 * 25 2332 * 28 3076 + 25 3654 5 32 4347 f 36 1155217 2418 + 33 1163 + 43 1142 + 21 1255? 25 1155 + 25 2476 * 34

LaCz LaC3 LaC4 LaCs LaC6 LaC7

1265 * 1819+7 2527 + 3121 + 3795 + 4320 f

12 12 12 12 12 13

Ce2C2 Ce2C3 Ce2C4 Ce2C5 Ce2C6

DYCZ DyC4

TABLE

5 7 45 45 60

La&3 La2C4 La2C5 La2C6 La2%

LuC* LuC4 NdC, NdC,, PrCz PrC4 scc2 scc3

scc4 scc5 scce TbC2 TmCz yc2 yc3 yc4

YC5 YC6

_

1114f21 1257 f 15 1805 I30 2530 * 24 308lf 35 3781+60

10 10 10 10 10

46 46 46 46 46

7

Atomization

energies,

Molecule

DO”

CeSiCa RhCeCz a PtCeCz a CeCRha CeCRua LaIrC LaCzIra

1046 f 1674 f 1695 f 10312 1109 * 1027 f 1779+25

De’,

42 50 50 40 40 30b

of ternary

gaseous

rare-earth-containing

Reference

Molecule

Do0

42 43 43 47 47 50 50

LaC# LaC4 IF RhScCb RhScC:! b YIrCb IrYCz b RhYCz

2344 2966 1001 1617 996 1678 1672

“Values based on linear geometry aa written. bAverage value resulting from various assumed

carbides

(in kJ

mol-‘f

Reference f 35 k 35 + 40h f 50b +33b f 33b f 50b

50 50 48 48 49 49 48

geometries.

the force constants, in order to calculate the thermal functions needed in the evaluation of the bond energies from the mass-spectrometric data. Thus, as sufficient experimental and also theoretical knowledge on electronic and

49

molecular constants will become available for a specific molecule, it will be possible to re-evaluate and improve the respective atomization energies in Tables 6 and 7 on the basis of new available experimental data. In favorable cases indirect information as to the probable geometry of a new molecule can be obtained if reliable second- and third-law evaluations can be performed. The molecules LaC, and LaC, serve as an example (Table 8). For both molecules, the linear chain structure, with the lanthanum atom at the end of the carbon chain, appears favored on the basis of best second- and third-law agreement, and also in terms of the smallest standard deviation in the third-law reaction enthalpy. To the extent that the various estimated parameters differ from the unknown true values, a trend is developed with temperature in the estimated Gibbs energy functions which is reflected in an increased standard deviation for the third law enthalpy. The measurements shown in Table 8 were performed in continuation of the work reported in ref. 12 under the same experimental conditions and using the same electronic contribution, bond lengths, and force constants as reported there. TABLE

8

Second-law and third-law = 3 or 5, assuming different Reaction

enthalpies geometries

for

the

reaction

La(g) + nC(graph)

AH”298 (kJ mol-l)a

Temperature range (K)

2nd.law

3rd.law

= LaC,(g),

Assumed of LaC,

n

structure

La(g) + 3C(graph)

= LaC3(g)

2444 - 2798

311.1 + 9.6 306.7 + 9.6 315.9 + 9.6

318.8 + 1.3 353.1 + 2.1 388.3 f 2.9

La-C3 (linear) C-La-C2 (linear) C-La-C2 (bent)

La(g) + 5C(graph)

= LaC,(g)

2527 - 2798

445.2 f 17.6 440.2 + 17.6 449.8 + 17.6

449.8 f 1.7 478.2 f 2.1 516.3 f 2.9

La-Cs (linear) Cz-La-C3 (linear) Cz-La-C3 (bent)

aError

terms correspond

to the standard

deviation.

Conclusion We have shown that the Knudsen cell mass-spectrometric method is a powerful tool to study equilibrium vapors over rare-earth-containing condensed systems. This has been illustrated for two classes of these molecules. The method has allowed the recognition of many intermetallic, diatomic, rare-earth-containing molecules as forming strong metal bonds. For such molecules various empirical models have been developed that allow quite reliable predictions of the dissociation energies of previously unknown molecules. These models thus provide a bridge between experiment and ab initio calculations. The latter cannot yet predict reliable bond

50

energies, but they give a deeper insight into the nature of bonding and electronic structure. Thus, our recent ab initio calculations on PdY [32] revealed that both atoms, Pd and Y, react in their respective closed 4d” and 5s2 shell when forming the rather weak bond (Table 3) by electron transfer of 4d electrons from Pd to Y and back donation of 5s electrons from Y into the empty 5s and 5p orbit& of Pd. The net transfer is to the yttrium atom in the opposite direction as expected from the respective electronegativities, but in the direction predicted by Brewer’s acid-base concept [27 J. This results in a small dipole moment with the negative end at yttrium. For rare-earth carbides we have shown that Knudsen effusion mass spectrometry, employing high temperatures combined with high detection sensitivity, revealed a previously unrecognized complexity of the vapor above certain rare-earth-graphite systems. For the interpretation of the bond energies in carbides, the pseudo-oxygen concept for the C2 radical and the bond-additivity rule have been successfully used. A wide open field remains for spectroscopists and theoreticians to elucidate the electronic and molecular structure of these molecules.

Acknowledgments The author is indebted to the many able co-workers who have contributed to the results summarized here and whose names appear in the literature quoted. This work has been supported by the National Science Foundation and the Robert A. Welch Foundation.

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