- Email: [email protected]
Experimental and predicted atomization energies of rare-earth diaurides
-:-::. .. . Vduti~ 1
.-. ,.‘, : ::.
..
13; numb&3
_, : I.. _;. ., ,’ _. .: .: ‘. : .; .,
..
CHEMrCAL
PHYSICS.LETTERS
1 March 1972.
:. -; ._
EXPERIMENTAL AND PREDICTED ‘ATOMIZATION ENERGIES -.OF RARE-EARTH DIAURIDES K.A. GINGEFUCH ;
Deprtment
of Chemidry, TexasA&M Received
:
Urhersity, 21 December
College Station, Texas 77843, CISA 1971.
.Fe atomization energies, aH$,t., of the molecules LuAuz, HoAu2 and TbAu, were determined by means of high-temperature Kundsen-cell mass spectrometry as 143.9 i 8, 131.1 * 8 and 143.3 * 8 kcal mole-‘, respectively. -Themeasuied itoinization energies suggest the structure AuLnAu. They agree with the values calculated after the Pa&g model hi assumingtwo polar singlebonds. The remaining rvesvth metals are also expected to form stable diatuicieswi5hatomization energies ~imi!arto those calculated after the Pauling model.
1. Introduction
vestigation of diatomic, holmiumcontaining molecules [2]. The electron energy used was 20 eV. The gaseous diaurides were identified by their m/e ratio, ionizationefficiency curves, and their appearance potentials. The latter were, within the accuracy of determination, identical with those measured for the corresponding rare-earth atoms. For LuAti2 the calculated abundance was in addition verified experimentally.
Among gaseous intermetaLLic ccmpounds those with gold have been most thoroughly studied [ 11, and found to form particularly stable diatomic molecules. As part of cur continuing program concerning bond-energies of metallic molecules we have been &Ivestigating the Lu-Au system and have found the molecule LuAui in the equilibrium vapor above an I-Lu-~-AU alloy that was contained in a tungsten Kundsen ceil. This molecule appears to be ‘he first po!yatomic inter-metallic compound that has been observed under equilibrium conditions, To test the existence of other gaseous diaurides we have al&investigated an Ie(Ho,‘l%)-~-AU alloy and could identify and.measure the molecules HoAu, and TbAu,. ‘Ihe atomization energies of the gaseous molecules LUAU,, HoAu,, and TbAu, are reported here. The empirical corteIation found between these values and . the values for the dissociation energies of the correspending diatomic amides permits the estimation of the atomization energies of other rare-earth diaurides.
3. Results and discussion The gaseous equilibria involving the diauride molecules which were measured and the third-law results for the corresponding reaction enthalpies are given in table 1. In table 2, the third-law enthalpies for the simultaneously measured exchange reactions of the type LnAu(g) + Au(g) ~Ln(g) + Au2(g), where In= Ho, Lu or Tb and for HoAu(g) t lb(g) = Ho(g) + TbAu(g) are given together with their standard deviations. For all reactions the equihbrium constants were calculated from the measured ion currents, assuming : mutual compensation of ionization cross sections and multiplier gains: Free-energy functions were taken from HuItgren .et aI; [3].‘for kgaseous, elements., For : fhe_diatomic atkides‘the same free-energy func;.,
2 Experimfdal .’
The mass4pectromctric measknents were per- ’ formed under similar conditions as used for ,’the ‘.in-, . .’
263
: -’
.:’ .‘:-.
‘,
‘:-_;
..
,,
..:
,’
_,
-..
Volunie
CHEMICAL. PHYSICS LETI-ERS
13, number 3
Table 1 ‘I’hird-lz.v enthdpies of reactions involving the molecules Lu&, Reaction
LuAu2W
1ogK
T CK):
+
2186 2252 2247 2294 2230 2397 2240 2452
Lu(g) = ~LUAUQJ)
1.711 1.697 1.603 1.627 1.586 1.506 1.691 1.575
1 March 1972,
Ho.&,
-A [(GF -$)/T]
A% 0 kcal
(2.2) (2.1) (2.1)
(2.0) (2.1) (2.0)
-12.3 .-12.8 .. -1l.S -12.3 -11.8 -11.7 -12.6 -12.8 : 10.1 10.1
(2.1) (2.1)
2058 2103
-0.569 -0.543
(2.3) (2.3)
TbAu2 (g) + Tb(g) = 2TbAuCg)
2058 2103
-0.553 -0.479
:z .
2058 2103
1.279 1.207
.-
(Cal mole-’ “K-I)
HoAuatii9 + Ho(g) = 2HoAu(g)
HoAuz@) + Tb(g) = Ho&) + ThAu2(g)
and ‘I’IJ&
9.9 9.4 -13.1 -11.6
(0.0) (0.0)
Table 2 Summary of third-law enthalpies of exchange reactions involving gaseous rare-earth monoaurides Reaction
Moo kcal
LuAuW + Au(g) HoAu@ + Au(g) ~A@ + Au(g) HoAuW + Th(g)
= = = =
Lu(g) Ho(g) Tb(g) Ho(g)
25.5 7.5 13.8 6.1
+ Auz(g) + Au2(g) + Au2(g) + TbAu(g)
a) Using D’(Aua) = 53.0 * 1.5 kcd mole-’ b) Using D 1 (HoAu) = 59.7 r 3 kcal mole-’
.,,
.. ;-:
0.8 0.2 0.2 0.2
‘.
78.5 60.5 66.8 65.8
LUAU HoAu TbAu TbAu
a) a) a) bl
[ 11.
For the reaction L.uAu2(g) + Lu(‘g) = 2LuAu(g) a second-law evaluation yielded M!&3ro = - 16.l f 4.9 kcal or AIY~ = -14.0 + 4.9 kcal, in fair agreement with the average value, A$ = -12.3 -COJ, from the third-law evaluation. The error. terms given are standard deviations, Taking the average of the thirdlaw and second-law value, Mt = -13.1.+ 5 kcai is selected where the error term now includes the estimated uncertainties in the free-energy functions, temperature measurements and those intrcduced. by the simphfying assumptions used in arriving at the values for the equilibrium constants. The correspond.. ing values for the reactions involving’HoAr+ and. ‘, .,..‘L%Aui are 10-L *, S,k&,and 9.7 f 5 kc& res edtively., gCombining these values with the values for Do(I+Au), I_
..-
Molecule LnAu
[2].
tions were used as previously [2,4]. Those for TbAu and LUAU have been calculated from estimated molecular parameters in a similar way as those for HoAu [Z] , except that the difference inthe eiectronid contribution between ‘I’hAu and HoAu was chosen the same as that between ,Tb and-Ho [3] . Only approximate estimates have been made for the free-energy functions of gaseous LuAu2, HoAu,, and TbAu2, following procedures adopted by JANAF [5]. They are based on the assumption that these molecules are symmetric and bent and have the same electronic contribution as was assumed for the corresponding monoaurides. We plan to attempt the experimental determination,of the molecular parameters, for these species by matrixiso!afion‘sp,ectroscopy. ...
r * * r
Do0 (LnAu) kcal mole-1
..
./ . : -..
. i
‘,..:.‘.
26?,~;-,.
Sol&
”
iLf;‘nurr+r:3
.’
CHEMIdAL-PHYSICSLETTERS
;
‘.
.1 +rcill972
,
Table.3.. bond energies in in rare-earth monoaurides and diauri~es. The values are in
Comparison of
.G;,i : I
and experimental
kill mole-I
(I..u$~~) = 143.9 +_8 kc?1 mole-’
‘, or h!
,_ :..602.1: t33.5 : ‘.L$&
calculated
kJ mole-l
(HoA~~)=.l31.1
.’ $48.5 f 33.5 kJ mole-’
,
+_.8kcajmole-’
LU
or
HO Tb
,
-_~&~.&(T~Au,) f 143.3 f 8 kcal mole-‘. or ’ 599.6 + 33.5 ;d mole-’ . ‘- I., ’ The enthalpies ‘for reactions of the type LnAu(g) + L.n(g) = 2Lnku(g) are,a ,direct measure of the difference between the bond energy Ln-Au in the diatomic molecule and the bond energy of the diatomic molecule to the. second gold atom. It is surprising that this ,diffeiknce is negative, in cqse of LuAu2, indicating ., a smaller bond energy for the second bond as compared with LUAU; but positive by a similar magnitude for Tbku, and HoAu,, indicating a stronger second bond with Au, as compared TbAu and’Ho’Au,
Nevertheless
talc.
78.5 f 4 60.5 * 4 66.8 i 4
71 64 71.5
a)
Exp.’
cak.
143.9 * 8 131.1 * 8 143.3 * 8
142 128 143
4
= $[D(Ln-Ln) +D(Au-Au)] + kcal mole-’ per Ln-Au bond.
respectively. Work stiLl in progress
[8] indicates, that the dissociation energy for Tb2 is lower and for I+ is in between fhe reported preliminary values [ I,41 . The electronegativities for Lu, Ho and Tb were taken as 1.3 [7] that for Au as 2.4 f6] . The calculated atomization energies for the LnAu, molecules in table 3 were taken as twice the calculated single-bond
energies..It is noted that the average experimental in--Au bond ener,v of the LnAu, molecules agrees. somewhat
it is note-
wcrthy that in &her c&e the bond energy holding ,.the second Ati atom is iemarkably l$$ and comparable in magnitude with that of the first 4u atom. The bond energies .mekured.are also indicative of a molecular structure Au-h-Au (rather than Au-Au-h). if, for further discussion, we accept the symmetric Jtructure +-inLAu (whidh still needs to be proven by op>icaI spectroscopic methods) then we can assume &at the two &Au links in these mo!ecules have’ the time bond energy; The average energy per L&Au bond in kcal mole-‘,,is thus 72.5 for LuAu2, %;cl- f~.r,I?~Au~‘kd 66.6 for HoAu,. The& values -ar,e iti as good an agreement with the energy of a polar :&ngle bon< calc$ated after ihe Pauling model [6j as ’ haSbeen found-f& the bond,energies of the co&e,.,.sponding,monoaurides’ [2,4;7] . . \ : A conipa&on of~~a$tilated and experimental values . . :’
AHzat. (Au-Ln-Au)
Exp.
a) UsingD(Ln-Au) 23(XLn - XA,,)’
with that in diatomic
respectively.
08 (Ln-Au)
better
the corresponding
with the calculated dissociation
values as .does
energy of the LnAu
molecules. The results presented here indicate that the Pauling model can be applied to gaseous polyatomic ititermetallic compounds, such as those investigated here,
as well as to diatomic molecules. Thus, bond energies ‘of metal diaurides may be predicted accuracy
with reasonable
as being
twice that calculated for a polar single bond. These predictions are expected to hold best for electropositiv%e large metal atoms for which the electronegativity difference is less than lS,,e.g., ‘all rate-earth diaurides and actinide diaurides. In addition one tiay expect that the values calculated will represent reasonably we11the stabilities of gaseous transition-metal diaurides and group-III or group-IV dia&ides. .‘.
:Acknowledgetient .. The abeor is indebted. to the Robert A. Welch Fqtindation for support given ,thiswbTk under.Grant .*_387; -. ; ., ,_..:
Volume 13,numbcr
3
CHEMICAL PHYSICS LETTERS
Referencis [l] K.A.Gingerich. I. Cryst 9 (1971) 31. [2] D.L.Cocke and K.A.Gingerich, J. Phys. Chem. 75 (1971) 3264. [3] R.Hultgren, R.L.Orr and KX.KeUey, Supplement to Selected Values of.Therrimdynamic Properties of Metals and Alloys, University of California, B.erkeley, Calif., Gold (1969), Holmium and Lutetium (1967), and Terbium (1967). [4) K.A.Gingerich, D.L.Cocke, H.C.Finkbeiner and R.J.Seysc, Proc. 19th Ann. Conf. on Mass Spectrometry and Alhed
[5] [6]
[7]
[B]
1 htarch 1972‘
Topics, May 19.71, Atlanta, Georgia. American Society for hkus Spectrometry. pp; 186- 190. JANAF Thermochemical Tables (Dow Chemjcal Co.; hiidlandi Michigan). L.PauBng, The nature of the chemical bond, 3rd Ed. (Cornell Univ. Press, Ithaca, 1960). K.A.Gingerich and H.C.Finkbeiner, Chem. Commun. (1969) 901;J.Chem..Phyr52 (1970)2956;'54(1971) 2621. K.A.Gingerich, R.J.Seyse and H.C.Finkbeines, unpubiislied data.
.-. ,.‘, : ::.
..
13; numb&3
_, : I.. _;. ., ,’ _. .: .: ‘. : .; .,
..
CHEMrCAL
PHYSICS.LETTERS
1 March 1972.
:. -; ._
EXPERIMENTAL AND PREDICTED ‘ATOMIZATION ENERGIES -.OF RARE-EARTH DIAURIDES K.A. GINGEFUCH ;
Deprtment
of Chemidry, TexasA&M Received
:
Urhersity, 21 December
College Station, Texas 77843, CISA 1971.
.Fe atomization energies, aH$,t., of the molecules LuAuz, HoAu2 and TbAu, were determined by means of high-temperature Kundsen-cell mass spectrometry as 143.9 i 8, 131.1 * 8 and 143.3 * 8 kcal mole-‘, respectively. -Themeasuied itoinization energies suggest the structure AuLnAu. They agree with the values calculated after the Pa&g model hi assumingtwo polar singlebonds. The remaining rvesvth metals are also expected to form stable diatuicieswi5hatomization energies ~imi!arto those calculated after the Pauling model.
1. Introduction
vestigation of diatomic, holmiumcontaining molecules [2]. The electron energy used was 20 eV. The gaseous diaurides were identified by their m/e ratio, ionizationefficiency curves, and their appearance potentials. The latter were, within the accuracy of determination, identical with those measured for the corresponding rare-earth atoms. For LuAti2 the calculated abundance was in addition verified experimentally.
Among gaseous intermetaLLic ccmpounds those with gold have been most thoroughly studied [ 11, and found to form particularly stable diatomic molecules. As part of cur continuing program concerning bond-energies of metallic molecules we have been &Ivestigating the Lu-Au system and have found the molecule LuAui in the equilibrium vapor above an I-Lu-~-AU alloy that was contained in a tungsten Kundsen ceil. This molecule appears to be ‘he first po!yatomic inter-metallic compound that has been observed under equilibrium conditions, To test the existence of other gaseous diaurides we have al&investigated an Ie(Ho,‘l%)-~-AU alloy and could identify and.measure the molecules HoAu, and TbAu,. ‘Ihe atomization energies of the gaseous molecules LUAU,, HoAu,, and TbAu, are reported here. The empirical corteIation found between these values and . the values for the dissociation energies of the correspending diatomic amides permits the estimation of the atomization energies of other rare-earth diaurides.
3. Results and discussion The gaseous equilibria involving the diauride molecules which were measured and the third-law results for the corresponding reaction enthalpies are given in table 1. In table 2, the third-law enthalpies for the simultaneously measured exchange reactions of the type LnAu(g) + Au(g) ~Ln(g) + Au2(g), where In= Ho, Lu or Tb and for HoAu(g) t lb(g) = Ho(g) + TbAu(g) are given together with their standard deviations. For all reactions the equihbrium constants were calculated from the measured ion currents, assuming : mutual compensation of ionization cross sections and multiplier gains: Free-energy functions were taken from HuItgren .et aI; [3].‘for kgaseous, elements., For : fhe_diatomic atkides‘the same free-energy func;.,
2 Experimfdal .’
The mass4pectromctric measknents were per- ’ formed under similar conditions as used for ,’the ‘.in-, . .’
263
: -’
.:’ .‘:-.
‘,
‘:-_;
..
,,
..:
,’
_,
-..
Volunie
CHEMICAL. PHYSICS LETI-ERS
13, number 3
Table 1 ‘I’hird-lz.v enthdpies of reactions involving the molecules Lu&, Reaction
LuAu2W
1ogK
T CK):
+
2186 2252 2247 2294 2230 2397 2240 2452
Lu(g) = ~LUAUQJ)
1.711 1.697 1.603 1.627 1.586 1.506 1.691 1.575
1 March 1972,
Ho.&,
-A [(GF -$)/T]
A% 0 kcal
(2.2) (2.1) (2.1)
(2.0) (2.1) (2.0)
-12.3 .-12.8 .. -1l.S -12.3 -11.8 -11.7 -12.6 -12.8 : 10.1 10.1
(2.1) (2.1)
2058 2103
-0.569 -0.543
(2.3) (2.3)
TbAu2 (g) + Tb(g) = 2TbAuCg)
2058 2103
-0.553 -0.479
:z .
2058 2103
1.279 1.207
.-
(Cal mole-’ “K-I)
HoAuatii9 + Ho(g) = 2HoAu(g)
HoAuz@) + Tb(g) = Ho&) + ThAu2(g)
and ‘I’IJ&
9.9 9.4 -13.1 -11.6
(0.0) (0.0)
Table 2 Summary of third-law enthalpies of exchange reactions involving gaseous rare-earth monoaurides Reaction
Moo kcal
LuAuW + Au(g) HoAu@ + Au(g) ~A@ + Au(g) HoAuW + Th(g)
= = = =
Lu(g) Ho(g) Tb(g) Ho(g)
25.5 7.5 13.8 6.1
+ Auz(g) + Au2(g) + Au2(g) + TbAu(g)
a) Using D’(Aua) = 53.0 * 1.5 kcd mole-’ b) Using D 1 (HoAu) = 59.7 r 3 kcal mole-’
.,,
.. ;-:
0.8 0.2 0.2 0.2
‘.
78.5 60.5 66.8 65.8
LUAU HoAu TbAu TbAu
a) a) a) bl
[ 11.
For the reaction L.uAu2(g) + Lu(‘g) = 2LuAu(g) a second-law evaluation yielded M!&3ro = - 16.l f 4.9 kcal or AIY~ = -14.0 + 4.9 kcal, in fair agreement with the average value, A$ = -12.3 -COJ, from the third-law evaluation. The error. terms given are standard deviations, Taking the average of the thirdlaw and second-law value, Mt = -13.1.+ 5 kcai is selected where the error term now includes the estimated uncertainties in the free-energy functions, temperature measurements and those intrcduced. by the simphfying assumptions used in arriving at the values for the equilibrium constants. The correspond.. ing values for the reactions involving’HoAr+ and. ‘, .,..‘L%Aui are 10-L *, S,k&,and 9.7 f 5 kc& res edtively., gCombining these values with the values for Do(I+Au), I_
..-
Molecule LnAu
[2].
tions were used as previously [2,4]. Those for TbAu and LUAU have been calculated from estimated molecular parameters in a similar way as those for HoAu [Z] , except that the difference inthe eiectronid contribution between ‘I’hAu and HoAu was chosen the same as that between ,Tb and-Ho [3] . Only approximate estimates have been made for the free-energy functions of gaseous LuAu2, HoAu,, and TbAu2, following procedures adopted by JANAF [5]. They are based on the assumption that these molecules are symmetric and bent and have the same electronic contribution as was assumed for the corresponding monoaurides. We plan to attempt the experimental determination,of the molecular parameters, for these species by matrixiso!afion‘sp,ectroscopy. ...
r * * r
Do0 (LnAu) kcal mole-1
..
./ . : -..
. i
‘,..:.‘.
26?,~;-,.
Sol&
”
iLf;‘nurr+r:3
.’
CHEMIdAL-PHYSICSLETTERS
;
‘.
.1 +rcill972
,
Table.3.. bond energies in in rare-earth monoaurides and diauri~es. The values are in
Comparison of
.G;,i : I
and experimental
kill mole-I
(I..u$~~) = 143.9 +_8 kc?1 mole-’
‘, or h!
,_ :..602.1: t33.5 : ‘.L$&
calculated
kJ mole-l
(HoA~~)=.l31.1
.’ $48.5 f 33.5 kJ mole-’
,
+_.8kcajmole-’
LU
or
HO Tb
,
-_~&~.&(T~Au,) f 143.3 f 8 kcal mole-‘. or ’ 599.6 + 33.5 ;d mole-’ . ‘- I., ’ The enthalpies ‘for reactions of the type LnAu(g) + L.n(g) = 2Lnku(g) are,a ,direct measure of the difference between the bond energy Ln-Au in the diatomic molecule and the bond energy of the diatomic molecule to the. second gold atom. It is surprising that this ,diffeiknce is negative, in cqse of LuAu2, indicating ., a smaller bond energy for the second bond as compared with LUAU; but positive by a similar magnitude for Tbku, and HoAu,, indicating a stronger second bond with Au, as compared TbAu and’Ho’Au,
Nevertheless
talc.
78.5 f 4 60.5 * 4 66.8 i 4
71 64 71.5
a)
Exp.’
cak.
143.9 * 8 131.1 * 8 143.3 * 8
142 128 143
4
= $[D(Ln-Ln) +D(Au-Au)] + kcal mole-’ per Ln-Au bond.
respectively. Work stiLl in progress
[8] indicates, that the dissociation energy for Tb2 is lower and for I+ is in between fhe reported preliminary values [ I,41 . The electronegativities for Lu, Ho and Tb were taken as 1.3 [7] that for Au as 2.4 f6] . The calculated atomization energies for the LnAu, molecules in table 3 were taken as twice the calculated single-bond
energies..It is noted that the average experimental in--Au bond ener,v of the LnAu, molecules agrees. somewhat
it is note-
wcrthy that in &her c&e the bond energy holding ,.the second Ati atom is iemarkably l$$ and comparable in magnitude with that of the first 4u atom. The bond energies .mekured.are also indicative of a molecular structure Au-h-Au (rather than Au-Au-h). if, for further discussion, we accept the symmetric Jtructure +-inLAu (whidh still needs to be proven by op>icaI spectroscopic methods) then we can assume &at the two &Au links in these mo!ecules have’ the time bond energy; The average energy per L&Au bond in kcal mole-‘,,is thus 72.5 for LuAu2, %;cl- f~.r,I?~Au~‘kd 66.6 for HoAu,. The& values -ar,e iti as good an agreement with the energy of a polar :&ngle bon< calc$ated after ihe Pauling model [6j as ’ haSbeen found-f& the bond,energies of the co&e,.,.sponding,monoaurides’ [2,4;7] . . \ : A conipa&on of~~a$tilated and experimental values . . :’
AHzat. (Au-Ln-Au)
Exp.
a) UsingD(Ln-Au) 23(XLn - XA,,)’
with that in diatomic
respectively.
08 (Ln-Au)
better
the corresponding
with the calculated dissociation
values as .does
energy of the LnAu
molecules. The results presented here indicate that the Pauling model can be applied to gaseous polyatomic ititermetallic compounds, such as those investigated here,
as well as to diatomic molecules. Thus, bond energies ‘of metal diaurides may be predicted accuracy
with reasonable
as being
twice that calculated for a polar single bond. These predictions are expected to hold best for electropositiv%e large metal atoms for which the electronegativity difference is less than lS,,e.g., ‘all rate-earth diaurides and actinide diaurides. In addition one tiay expect that the values calculated will represent reasonably we11the stabilities of gaseous transition-metal diaurides and group-III or group-IV dia&ides. .‘.
:Acknowledgetient .. The abeor is indebted. to the Robert A. Welch Fqtindation for support given ,thiswbTk under.Grant .*_387; -. ; ., ,_..:
Volume 13,numbcr
3
CHEMICAL PHYSICS LETTERS
Referencis [l] K.A.Gingerich. I. Cryst 9 (1971) 31. [2] D.L.Cocke and K.A.Gingerich, J. Phys. Chem. 75 (1971) 3264. [3] R.Hultgren, R.L.Orr and KX.KeUey, Supplement to Selected Values of.Therrimdynamic Properties of Metals and Alloys, University of California, B.erkeley, Calif., Gold (1969), Holmium and Lutetium (1967), and Terbium (1967). [4) K.A.Gingerich, D.L.Cocke, H.C.Finkbeiner and R.J.Seysc, Proc. 19th Ann. Conf. on Mass Spectrometry and Alhed
[5] [6]
[7]
[B]
1 htarch 1972‘
Topics, May 19.71, Atlanta, Georgia. American Society for hkus Spectrometry. pp; 186- 190. JANAF Thermochemical Tables (Dow Chemjcal Co.; hiidlandi Michigan). L.PauBng, The nature of the chemical bond, 3rd Ed. (Cornell Univ. Press, Ithaca, 1960). K.A.Gingerich and H.C.Finkbeiner, Chem. Commun. (1969) 901;J.Chem..Phyr52 (1970)2956;'54(1971) 2621. K.A.Gingerich, R.J.Seyse and H.C.Finkbeines, unpubiislied data.