E. David Cater University of lowa lowa City, 52242
High Temperature Chemistry of Rare Earth Compounds: Dramatic Examples of Periodicity
It seems clear that the energy required to promote a 4 f electron to the 5d level has a profound and predictable influence on the systematics of reactions involving conversion o f rare earth a toms from combined to free states. The chemistry of the lanthanide elements is generally thought to be characterized by its similarity across the series from La to Lu, rather than by its variability. This results, of course, from the fact that the successively added 4f electrons are relatively uninvolved in bond formation and the main effect is the "lanthanide contraction" as the atomic diameter decreases with increasing atomic number. There is the added occurrence of extra stability of the +2 oxidation state (Sm, Eu, Yb) and the +4 (Ce, Tb) which is correlated with the particularlv stable emotv . . (4f0). . . . . half-filled (4f7). . , .. and comoletelv filled(4f14)subshell. A small periodic variation of some heats of formation and other orooerties accom~aniesthis. so that the characteristics of ~ o & ~ o k from d s La Eu are pakllelled from Gd to Yh, and Lu is analogous to La and Gd (1, 2). However, apart from these variations, one reviewer concluded ( I ) that "chemically, periodicity is not readily distinguishable within the lanthanide series except in the properties associated with differing oxidation states." However, a dramatic variation in properties across the lanthanides does occur in those reactions in which the rareearth atoms pass from a combined to a free state, or vice versa. The combined state may be in the solid metal, a solid compound, or a gaseous molecule. The free state is the state of
gaseous atoms. As three initial examples of this periodicity we may cite the vapor pressures of the metals, the dissociation energies of the monoxides, and the vaporization processes of the monosulfides. In the first example, there is a billion-fold range in vapor pressures of the rare-earth metals at any temperature (3), corresponding to a variation from 102 to 42 kcallmole in their heats of sublimation. Minimum pressures and maximum heats occur a t La, Gd, and Lu; maximum pressures and minimum heats occur at Eu and Yh. In the second example, the dissociation energies of the gaseous monoxide molecules (4.10) which range from 190 for L a 0 to 132 kcallmole or lower (5)for EuO, closely parallel the heats of vaporization of the metals. In the third example, all the monosulfides sublime to MS molecules and simultaneously to M and S atoms, but the mole ratio of MS(g) to M(g) in the vapor varies from 5 (LaS) to 0.05 (SmS), a factor of 100 (6). These periodic variations are the result of the differing relative energies required to promote a 4f electron to the 5d level in the successive gaseous rare-earth atoms, as will be shown below. Thus, even though the f electrons may not participate appreciably in bonding, their energy levels are very important
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Figure 1. Heats of reaction at OK ' versusatomic number for processes in which rare earth atoms are transferred from combined to free states. Processes included are sublimation of the metals and dissociation ofhe molecules MX where X = 0. S. Se. Te, and C2. The dissociation reaction consideredwith lhedicarbbder isMC2(g) = M(g) C&). TO maketha graphmore legible, 100 kcal/mole was added to the heats of sublimation. Sdid points are experimental values: open points depend strongly on estimated quantities. Data taken from Tables 1-4.
+
different structure
Figure 2.Heats of reactionat O°K m 298'K for processes in which he rare & element is transferred from one combined state to another. Processes included are formatim V a n lhe elements of solid sesquioxides, solid m n o 4 f i d e s . sdid dicarbides, gaseous mnoxides, gaseous mnosulfides, and gaseous dicarMdes. and the heats of sublimation of the monosulfides and dicarbides. Solid points are calculated from experimental quantities: open paints depend strongly on estimated quantities. Data taken from Tables 1-4.
Volume 55, Number 11, November 1978 1 697
in the high temperature chemistry of the elements and their compounds. Figure 1 summarizes the periodic variation and shows the remarkahly parallel behavior of the heats of sublimation of the metals (3, 7) and the dissociation energies of the molecules M O ( 4 , 5 , 8 ) ,MS (6, a), MSe (9, 10) MTe (9, lo), and MC2 (11-14). Note the double periodicity, in which all the heats of reaction have maximum values a t La and Ce, Gd and Th, and Lu, and minima at Eu and Yh. In each case the variation covers ahout a 60 kcal/mole ranse. Figure 2, on the other hand, sh&s the remarkably constant values of the heats of formation of the solid comnounds and the gaseous molecules, and of some heats of suhiimation. Slight trends are observed with random fluctuations of perhaps f 10 kcal/mole. In these processes the rare earth atoms are in combined states both as reactants and products. Figure 3 is a schematic energy level diagram which shows the interrelation among the various heats in Figures 1and 2. Figure 3 is drawn specifically for monosnlfides, but diagrams for the other compounds are quite analogous. Reading up from the bottom of the figure, one sees successively the enthalpy
changes required to convert the solid compound to the solid elements (-AH,), to the gaseous molecules (AH.,b), and to the gaseous atoms (AHat).The dissociation energy is D o= AHat - AHsub. The heat of formation of the gaseous molecules, AH,(MS), is obtainable several ways from the other AH'S. The highest level shown in Figure 3 is that of the gaseous atoms, with the metal atom in the 5d16s2configuration. The next lower level is that of the atoms in their states. For La, Ce, Gd, and Lu these two levels are identical. For the other 5d). elements. the difference betweetithese levels is AUi4f . . .. thr "promotional energy" required to move an rlectron from the4i to thr Sd stare. Table 5 shows that the Sd'tic2cunfiguration is also that of the rare earth aroms in the metallic elp. mmts, except for Ku and Yh. This isan important point and we shal. return to it shorrly. One can see that since thr heats of formation and sublimation in Figure 2 are relatively w n slant, thr heaLs of atomization of the solid nxides, sulfides, and carhidec would also fit the periodic pattern of Figure 1. A11 the data nlotted in the figures are aesemhled in Tahles 1-5. The table's also illustrate"the periodicity of the vapor pressures of the metals and of the oxides and monosulfides,
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Table 1. Thermodynamics o f Hlgh T e m p e r a t u r e A~C(M~O~.S)~ callg atom M (iless than 1 kcal)
La Ce Pr Nd
A&MO,W kcal/mole
-213.6 -214.7 -218.0 -214.2
O x i d e s of
Rare E a r t h E l e m e n t s
~h~0.g)'
(f 3)
kcal/mola (1.2 l o 3)
-3 1 -22 -33 -37
190d 189 179 169
T o t a VaporQ
Pressure 2400K. atm.
PM~PM~ at 2400 K
3X
lo-"
200
1.5 X
lo-'
200
Pm
Srn EU Gd Tb DY Ha Er Tm
Yb Lu
-216.2 -195.6b -215.4 -222.9b -221.6 -223.7 -225.8 -244.3 -216.0 -223.7
-35 -33r~dor-12' -18 -20 -20 -24 -17 -21 less than +7' -6
147" 1326,'0r 112# 170 168 144 147 145 133 less than 85' 166
1X 3 . x lo-' 3 X lo@
2 0.1 10
2 X 1OP 6 X lo-' 6 X lo-' 1.5 X 2X 2 X lo-'
2 2 2 01 0' 2
Note: Data in parenmeses are bared strongly on estimated quantities. 'Ames, et al.. ref. (4).and Brewer and Rorenblan, ref. 124). a All M20sare hexagonal except E U P Swhich is monoclinic, and TbiOo, which is oubic. " Ames. el al.. ref. (4). Ernla. ref. (191,gives chemiluminescenceresults whlch rvppwt ma mass specfrometric work of reh. (4)and (8). Murad and ~ildenbrand.ref. (5).find D'~EUO) = 111.9 i 2.4 kcsilmoie. which leads to AW,,,,. = -1 1.6 i 2.4 kcal/moie. Gole, ref. 119). does not find these resuits tmafiy convinr ing. 'RecslcuUed by Smaen, et al.. ref. ( 8 ) from Am-, et al.. ref. (4)using better tee energy funcilons for the gaseous eiemenb. 'Calculated from data in Ames, et ai., ref. (4). and Goldstein. et al.. ref. (25). Ames, etal.. ref. (4). and Panish, ref. (28). 'Eecau9e of their low dissociafionenergies me YbX(g) mohxksare in tm low a carcentation to beobrervablemrs spectromewicaiiyin most systems. so that only upper or lower limits can be placed on the dissociation energies and related quantiies.
"
Table 2. Thermodynamics of High Temperature M o n o s u l f l d e s a D ~ S )
of
Rare E a r t h E l e m e n t s Total Vapor
A~~(Ms,s)
A H ~ W
kcallmole
kcallmole
kcal/mole
(i4)
(*3 or 4)
(1.3 or 4)
Pressure at 2150K. atm.
at 2150K
LaS CeS PrS NdS PmS
-108 -109 -110 (-108)
136 140 138 (139)
136b 136 122 112
2 X to-e 7 x lo-' 3 X lo-6 (6 X lo@)
0.2 0.2 0.6 (1.0)
SmS
(-109) -108 -111
(139) 131 147
(6 X lo@) 6 X 10W 4 X lo-'
(20) 12 1.6
EuS GdS TbS DYS HoS ErS T ~ S YbS
85 86 125 (122) (98) 101 (99) (87) less than 3gE
dData on PrS from ref. (30). ~ a t an a ~sSGds assembled by Fries and cater, ref. (81: nDo for mSLusfrom Smaee,et al.. ref. (8). Joneo and Gak.ref. (24. give Ooa(LeS) _( 136.2 -t 0.4 koilmole horn ~~~~~~~~~~~nee experiments. See labie 1, fminote i,
698 / Journal of Chemical Education
Pdhs
and in the ratio of partial pressures of molecules to atoms over solid M z 0 3 and MS. Note that for comparison purposes the enthalpy changes Table 3. Thermodynamics of High Temperature Dlcarbides of Rare Earth Elements A~(Mc~,s)' Lac2 CeC. P,C2 NdC2 PmC2 SmC? EuC) Gdc2 TbC2
!a& HoC~ ErC* TmC* YbC2 LUCZ
AH&c~)*
D~M-C~)~
I 157 i 155 5 150 10 145 i 4
160 i 3 162i2 151 i 3 144 3
(147 i 5) (149 i 5) 149 i 5 161 1 1 5 148 f 8 159 i 5 162 i 7 157 i 8 (161 i 8) (161 i 6)
(I16 i 7) (98 i 8) or 129 i S5 151 3 150 i 3 133 4 133 i 3 135 i 3 119f4 (90 i 10) (156 i 12)
-19f 5 -1555 (-15 5) -12 i 3
*
-la*
1 -9i2 -28 f 8 10) (-20 i -11 i 1 -21 i 1 -19i1 -20 i 2 -18 i 1 (-18 i 5)
have been given at 0 or 298 K. However, these are dl refiadory compounds with melting points in the range 1500-2500 K and appreciable vapor pressures only at very high temperatures. The heats of formation have been obtained by solution calorimetry only for the solid oxides and for CeS. All other enthalpies listed are hased on high temperature vaporization data. The gaseous atoms and molecules can be obtained only by evaporating suitable solid or liquid phases in vacuum at high temperature. Their presence and relative amounts are usuallv detected in the verv low uressure vaoor stream effusine from the small orifice of a"crucihlecalled Knudseu cell (15: 16) into the ion source of a mass wectrometer (17.18).The talntlnted heats of reaction were &rermined fro& the temperature drpendenre of equilihrium constants calculated from
a
*
+
Dab assembled by Filby and Ames. ref. 117). a F 101 am Amer reh 11!-13,and8ao~ccl e t a l . ref (14, "Beldxc .eta1 .ref (78,. haroommnm D'&.C,j ' 129 1 5 kcallmla.~*mmrs%h
Table 4. Thermodynamics of High Temperature Selenldes and Tellurides of Rare Earth Elements D;(MS~)' kcallmole
La Ce Pr Nd Pm Sm
Eu Gd Tb
D;((MT~)" kcallmole
113*3 117f 4 106*6 93 i 3
90 i 4 (92 i 5) (77 i 5) 72 f 4
76 i 4 71i4 102 i 4 (100 10) (78 i 5) 79 f 4 (77 i 5) (65 i 10)
60 i 5 58 i 4 81*4 (79 i 5) (55 i 5) 61+4 (56 i 5) (43 i 10)
*
'a HO Er Tm
...
Yb
Figure 3. Energy level diagram for solid and gaseous species in the rare earlh mono~ulfide systems. The highest level shown is for gaseous sulfur atoms and gasWw metal a l m s in an excited state having Uw same elecbonic mnfiguratian as the atom in me solid metal. Far La, Ce. Gd, and Lu this level is identical with m e level for the ground state gaseous atoms. In the symbol 4fnor 4fv', n is 1 for La. 2 for Ce, etc. Thesymbol rh indicates solid rhomblc sulfur, lhe standard State below 368K. The energy levels shown are spaced nearly lhe same for all the rare eanhs except the leva1 M,g S.g.
...
'Bergman. st al.. ref. (4. Nagai, ct al.. ref. (lo),and Ni and Wahlbeck, ref. (27) Bergman, stal.. ref. (4, and ~ a g a ist , al.. ref. (10). see ~ s b l e1. fwmne r.
+
Table 5. Subllmatlon of Rare-Earth Metals Atomic Number 57 58 59 60 61 62 63 64 85 66 67 68 69 70 71
Symbol
La Ce Pr Nd Pm Sm Eu Gd Tb DY Ha Er Tm Yb Lu
Elechonic Configuration metald gasb 4f 5d6e 4f5d6s 0 1 2 3
1 1 1 1
2 2 2 2
0 1 3 4
1 1 0 0
2 2 2 2
5 7 7 8 9 10 11 12 14 14
1 0 1 1 1
2 2 2 2 2 12 12 1 2 0 2 1 2
6 7 7 9 10 11 12 13 14 14
0 0 1 0 0 0 0 0 0 1
2 2 2 2 2 2 2 2 2 2
-
+
5qS Ay4f (kcallmole)
AH;& (kcallmole)
Ay4f 5d) AHw (kcallmole)
Vapor Pressuredat 1300K (ahn)
-43 -14 14 19 19 44 72 -31 1 22 21 21 38 66 -(. . .)
103 101 89 79
(103)' (101)' 103 96
1 X to-" 2 X lo-" 3 X lo-* 5X
48 42 96 94 71 76 82 59 36 102
92 114 (96)' 95 93 97 103 97 102 (102)C
2X 2X 3X 9X 2X 9X 2X 3x 2X 5X
lo@ lo-'" low0 lo-'
lo-' lo-' lo-' lo-''
" Gochneidnsr, ref. (27). "we, ref. (221. 'Vsnder Sluis, ref. (23).Brewer, ref. (20hgives esssmially the same numbere "Honig, ref. (I), mostly taken from Haberman", ref. (3). F o r La. Ce. Gd. Lu. far which AU is negative, only W DIo s given.
Volume 55, Number 11, November 1978
/ 699
the mass spectrometric data. Partial pressures and equilihrium constants so determined are typically uncertain by a factor of two or three, chiefly because of temperature uncertainties and gradients in the high temperature apparatus and because it is necessary to use estimated ionization cross-sections in interpreting the mass spectrometric data. These uncertainties, compounded with estimated molecular parameters used for the long extrapolation to room temperature or zero K, give rise to several kilocalories (a few percent) uncertainty in the data of Tables 14 and Figures 1and 2. Such uncertainties, however, are much smaller than the periodic effects being discussed. Quite recently, analysis of the chemiluminescence spectra observed when excited molecules are formed in molecular heam reactions hi15 providt!d lower limits ro dissociation energiesof several of the moleculei ofTaI~Ivs1 and !( I Y , 2 O ) , as is noted in the fwtnotes there. These values in eeneral aeree w with the mass spectrometrically determined ones. The W-shaped curves for all the processes shown in Figure 1 are explained by consideration of the energy required to oromote one 4f electron to the 5d level in the rare earth atom. ~ a h e r m a n na d Daane (3) in 1964 proposed that if all the rare earths had the same electronic confieuratiou in the metallic state, and if all had the same conf&uration as free atoms (different. uerhaus from that of the solid state). then one should expect that the heats of suhlimation would be rather constant from La to Lu with only a small, systematic variation due to the lanthanide contraction. Thus, they reasoned, the large observed variation of heats of suhlimation was related to differences in electronic configuration in the comhined andlor free states of the successive atoms. Using more recently available information we may pursue the argument further. Table 5 gives the electronic configurations for the rare earth atoms in the solid (metallic) (21) and gaseous (22) ground states. Also listed are the promotional energies AU(4f 5d) given hv Vander Sluis and Nueent .(23). In the metallic state the 6s a i d 5d electrons are itinerant and populate the metallic conduction band. The 4f electrons are localized and hound to the metal ions on their lattice sites. Except for Eu2+,andYb2+, the rare earth ions are trivalent in the metals (21). Those elements, La, Ce, Gd, and Lu, for which the 4f 5d transition energy is negative (the 5d state is at lower energy than the 4f), have a 4fn-'5d1 configuration in both the combined (metallic) and free states. Here n = 1for La, 2 for Ce, etc. Their heats of suhlimation are virtually constant, being, respectively, 103, 101, 96, 102 kcallmole (with uncertainties o f f 2 or 3 kcall mole). 5d transition For the other elements, for which the 4f energy is positive (the 4f is the lower energy state), the elements except Eu and Yh also have the 4fn-'5d1 confwration in the combined state, hut the gaseous atoms have transferred the d electron to the lower energy 4f shell, giving a 4fn5dO configuration. These elements have heats of suhlimation 5d varying from 48 (Sm) to 94 (Th) kcallmole. If the 4f promotional energy is added to the heats of suhlimation for the latter group, the re~ultis the (hypothetical)energy change fnr valmrizing the metal atums to an excited g a s e o ~stare ~ s in which they have the same electronic state as in the solids. As seen in ~ a h l 5, e this energy change is much more nearly constant for all elements than is AH,b(M). Eu and Yh are somewhat anomalous with n o d electron and high preference for the +2 state. Consequently they behave in many ways more like alkaline earths (group IIA) than like lanthanides. That the variation of about 60 kcallmole in heat of suhlimation is the factor directly leading to the 109-fold variation in vapor pressure, can be seen as follows. The vapor pressure is related to the change in Gihbs free energy accompanying the vaporization process by the equation -RT In P = AG; = AH; - TAS; (1) By far the largest contribution to the entropy change for sublimation is the translational entropy of the gas, and this is only slightly dependent on molecular weight. Therefore the
-
-
-
-
700 1 Journal of Chemical Education
entropy changes for suhlimation of the metals are very nearly equal, so that the TAS term varies by a few kilcalories at most. This is greatly overshadowed by the large differences in Ah'. For example, the 54 kcal difference in heats of suhlimation of the adjacent elements Gd and Eu compares to a 4 kcal difference in TAS a t 1300 K (24), and the observed vapor pressure of Eu is 108 greater than that of Gd. In explaining ;he periodicity in the disswiation energies, we ma\' follow the argument uf Ames. Walsh. and Whit[, ( 4 ) who first published tee dissociation energies of all the gasedui monoxides. The gaseous monoxides are all modeled as M2+02-, at least to a first approximation, with the combined metal atoms all in the 4f-'5d1 state. One would then expect that the sum of Di(M0) and AU(4f 5d) should be constant. Tables 1-4 show that this quantity is indeed rather constant, with Yh eivine an anomalouslv low value. The model is thus acceptahye an; the periodic variation in Di(M0) is the result of the euernv levels in the gaseous rare-earth atoms. Similar arguments ;in he made forthe other diatomic MX molecules and for MC7. In contrast, the heats of formation and suhlimation shown in Figure 2 are for processes which involve the transfer of the rare earth element from one combined state to another. The f electrons have little direct role in bonding. Thus, in each of these processes it is expected that the enthalpy differences across the series should not he much affected by the differing ~romotionalenereies. because the similaritv of bondine" " eovkrns the heats orre&tion. Indeed, these d o not show the pronounced periodicity of Figure 1. Finally, consider the vaporization processes of the solid compounds, to see how the ~romotionalenerev affects the relative importance of vaporizkion to m o l e c u l e s ~ dto atoms. For the monosulfides the reaction giving gaseous molecules and the corresponding relation of & t o i h e partial pressure are
-
~
The equation for vaporization to atoms is The relative importances of reactions (2) and (3) are determined by the relative values of the AG's. The argument is similar to that for the vapor pressures of the metals. The entropy changes for all the iarekarths for reaction (2) are nearly equal. Again, for reaction (3) the entropy changes are nearly equal, although all are larger than for reaction (2). Thus the relative sizes of the AG's are in the same order as those of the m s . Reference to Tables 1 4 and Figures 1and 2 shows that for the monosulfides the oartial oressures of the molecules over all the MS(s) should be comparable (equal heats of suhlimation) hut the partial pressures of the atoms should vary widely (large differences in heats of atomization). Thus the ratio P~/Phns should varv svstematicallv, .. as indeed it does. Because of the interrelationbf-Ah':,, and Di shown in Figure 3, those monosulfides having the largest dissociation energies are the ones with the largest concentration of molecules in the vapor. Although no vapor pressure measurements have been made for ThS-LuS, a parallel trend is confidently expected there. The case for the oxides can be argued similarly, and the same ~ e r i o d i cvariation occurs as exoected. as indicated in ahl lei 1-4. Effects of background oxygen in the mass spectrometer and small deviations from stoichiometry in the solids a t high temperatures make the measurement of the ratio of molecules to atoms more difficult for the oxides than for the sulfides, hut the overall picture is the same. That the present discussion is somewhat overlv sim~listic is seen from-the fact that the quantities predicted to be constant by these arguments do in fact vary by 10%or so. Further there appears tobe a diffrrence of the order of 10 kral,mde between the first half and last half of the rare earth scqumre in w m r of the heats of reaction and in D,\MX) A1'(.1f
+
-
5 d ) . A discussion of this ( 8 , l I ) is beyond the scope of this paper. In conclusion, it seems clear that the energy required to promote a 4f electron to the 5d level has a profound and predictable influence on the systematics of reactions involving conversion of rare earth atoms from combined to free states. On the other hand, for reactions in which the rare earth atoms are transferred from one combined state to another. onlv verv small periodic effects are observed. Literature Cited 111 I21 131 I41 151 161 171
Moe1ler.T.. J.CHEM. EDUC.47.417 119701. Ternstrom.T., J.CHEM. EDUC., 53,629 11976). Hahermann,C.E.,and 0aane.A. H., J. Cham. Phys., 41,2818119641. Ames.1.. I.., Wahh, P. N..snd White,D.. J . Phys Chem., 71.2707 (19671. Murad, E..and Hiidenbrand, D. L., J Chem. Phys., 65,3250 (1976). Fries,d.A.,and CaLer.E. D., J . Chem Phvs.. 68,3978 (19781. Honig, R. E.,and I
