J. Phys. Chem. 1995, 99, 4252-4260
4252
Dissolution of Boron in Lithium Melt Anton Meden* University of Ljubljana, Department of Chemistry, PO Box 537, 61001 Ljubljana, Slovenia
Janez Mavri, Marjan Bele, and Stane Pejovnik National Institute of Chemistry, PO Box 30, 61001 Ljubljana, Slovenia Received: October 27, 1994@
The lithium-boron system has been extensively studied due to the practical importance of Li-B alloys as anode materials for the production of lithium batteries. However, many questions remained unexplained, and the phase diagram has not been determined. Some ambiguities also remained regarding the existence of a LiB3 compound and the dissolution of boron in lithium melt. To resolve these questions an approach using ab initio molecular orbital (MO) calculations on the Hartree-Fock (HF) level of theory is presented. Stability and rules of bonding for lithium-boron clusters were calculated using STO-3G, 3-21G, and 6-31G* basis sets. The calculations enabled a formulation of the rules of bonding in lithium-boron clusters which gave a suggestion as to the possible mechanism of the interaction of ‘molten lithium with crystalline boron. Experimental evidence based on chemical and X-ray diffraction analyses, supporting the results of MO calculations, is also given and a new explanation, which covers all experimental and theoretical data about the processes which occur during the heating of the lithium-boron mixture in the temperature range 300400 “C is presented.
Introduction After the discovery of the metallic lithium-boron alloys’ many studies on their properties have a p ~ e a r e d . ~ -However, ’~ only a few authors have been concerned with the phenomena that are involved in the alloy preparation.6*8s11 According to Wang’ the formation of the alloys Li,B1-, (0.3 < x < 0.9) is accomplished in two steps: the first is the dissolution of crystalline boron in molten lithium in the temperature range between 300 and 400 “C and the second is the formation and solidification of a new crystalline Li-B compound in the temperature range between 400 and 550 “C which is porous and forms the “Li-B alloy” by incorporating the excess lithium into the pores. The first step is characterized by an exothermic effect at 330 “C and the second by an exothermic effect at about 530 “C. The reactions which produce these effects are not well explained and the formula of the solid porous Li-B compound is not certain-Li7B610s11 and Li5B2 are suggested in the literature. From the X-ray powder diffraction data it is obvious that this is the same phase and the formula Li7B6 will be used in the following text, to avoid confusion. Attention in this work has mainly been paid to the first exothermic effect at 330 “C. There are two explanations for this effect in the literature. Wang8 stated that boron is simply exothermally dissolved in the Li melt to form a metallic solution (without chemical reaction), while other authors62l1claimed that a new compound described as LiB3 was formed. These two statements were based on experimental results obtained by two different methods so that actually, they were not controversial. With an in situ powder diffractometer Wang observed a disappearance of crystallinity above the exotherm8 while in other studies6J1differential scanning calorimetry was applied and a “loss” of lithium was detected at the recrystallization. ‘Abstract published in Advance ACS Abstracts, February 15, 1995.
The present work was started with a hypothesis that in the “metallic solution”, provided that it exists, boron atoms or boron clusters are solvated by lithium atoms. Some of the lithium atoms in the solvated clusters may be bound so strongly that they are not incorporated into the lithium crystal lattice during recrystallization, thus remaining dispersed in the metal bound in non crystalline Li-B clusters (the stoichiometry may be LiB3). This would reconcile both the observations and would also be in accordance with the work of Mair,I6 who made an extensive reinvestigation of the Li-B system and found that the reactions leading to well-defined crystalline phases started above 1000 “C. It is, therefore, reasonable that at temperatures of up to 400 “C-the range of main interest in this work-only the products of solvation will occur. We attempted to check the above hypothesis and to clarify the process of dissolution or reaction of boron with lithium melt in the temperature range 300-400 “C in two steps. Using molecular orbital calculations we tried to obtain the estimate of interaction energies of clustering (solvation) of boron with lithium and, possibly, to postulate a mechanism of the dissolution process. Subsequently, some experiments were done to check the conclusions derived from the theoretical calculations. The results of the calculations predicted quite a strong interaction between lithium and boron atoms but too weak an interaction to break the crystal lattice of boron. This was not in accordance with the formation of completely homogeneous “metallic solution” reported in the literature.’ To check if the disagreement is due to too rough assumptions in the calculations, we tried to prepare the homogeneous lithium boron solution as described by Wang.’ The processes in the melt were monitored using chemical analysis and the determination of unit-cell parameters of boron at different stages of “dissolution”, thus trying to follow the degradation of boron crystal lattice. Products of the reaction between Li and B at different temperatures below and above 400 “C were also analyzed by X-ray powder diffraction and a scanning electron microscope to find out whether these end products are “true” solutions.
0022-365419512099-4252$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 12, 1995 4253
Dissolution of Boron in Lithium Melt Computational Methods
The GAUSSIAN-8617program package was used throughout. Preliminary calculations were done on a VAX 4000 computer using minimal basis set STO-3G and the counterpoise correction method for basis set superposition errorI8 was applied. The main part of calculations was done on a CONVEX 3860 computer with a 6-31G* basis set. The 3-21G basis set was applied in cases of large clusters due to computational limitations. The counterpoise correction method for basis set superposition error18 was estimated for some clusters. In the case of larger clusters with 6-31G* basis the error in interaction energy was found to be less than 6%. Therefore it was not calculated for smaller ones and is omitted from the tables of results. The calculations were restricted to the clusters in vacuo, and the results were considered as the first approximation of the cluster stability in lithium melt. Since the application of semiempirical methods is questionable due to improper parametrization for lithium, the ab initio methods were applied. The latter imposed a serious limitation on the number of atoms in the clusters under study (the maximum cluster treated was Li20B12 with only two geometrical variables optimized). The general strategy of geometry optimization was to start with small clusters and no symmetry restrictions. In larger clusters symmetry restrictions found by previous calculations and deduced from the crystal structure of boron and lithium were applied. After the geometry optimization the vibrational analysis was done to check if the resulting geometries are true minima on the potential surface. In some cases of larger clusters the vibrational analysis was not performed due to failure of analytical and numeric procedures and also due to very high CPU time requirements of second derivative matrix calculations. Preparation and Analysis of Samples
The preparation of samples was carried out in a BRAUN glovebox in an atmosphere of argon with water and oxygen contents maintained at values lower than 1 and 2 ppm, respectively. Battery-grade lithium (Foot Min. Comp.) and crystalline boron (Merck, p.a.) were used as starting materials. Samples were prepared in two ways. (A) Lithium was preheated in an iron crucible to the desired temperature, and a polycrystalline boron piece was added. (B) The crucible was filled with lithium and boron and then heated slowly to the desired temperature to prevent overheating of the samples due to internal exothermic effects. After the predetermined time at the desired temperature the samples were cooled and prepared for analyses. In the cases where only boron (or boron-rich) particles were desired, the excess lithium was removed, using different procedures. Usually lithium was dissolved in water, the resulting powder was washed with diluted HC1 and dried. Washing was done by repeated sedimentation since the powders contained fine fractions that would block the filter. Since it is known that Li-B compounds may be dissolved in water (for example, and Li2B616), the removal of lithium was also done with nonaqueous methanol and ethanol as well as using the procedure with naphthalene in anhydrous tetrahydrofuran developed by Kilroy and A n g r e ~ .With ~ scanning electron microscopy, X-ray diffraction and chemical analyses it was found that at the temperatures below 400 "C the materials obtained by various procedures do not differ and the samples obtained using water are taken as representative. Chemical analysis was done by atomic absorption spectrophotometry. Powder diffractograms were taken on a Philips PW 1710 X-ray powder diffractometer with Bragg-Brentano
W
W Bq2 (interstice)
812
B6 (planar)
Figure 1. Geometries of the B, clusters optimized on the HFl6-31G" level (Blz(interstit) not optimized). Distances are given in angstroms.
TABLE 1: HF/6-31G* Energies of Optimized B, Clusters, BIZ,Denoted by an Asterisk, Also Calculated on HF/3-21G Level ( E in atomic units, AE and A E h in kcal/mol)a cluster B2( singlet) B;?(triplet) B3 B6(octahedron) Bs(p1anar) B12 B 12 B 12(interstit)~
E
-48.896 -49.027 -73.772 -147.572 -147.694 -295.507 -293.767 -295.301
13 36 07 78 50 79 21 99
AE
AEln
+92.84 +10.49 - 129.24 -276.44 -352.82 -780.19 -684.04 -65 1.05
+46.42 +5.25 -43.08 -46.08 -58.81 -65.02 -57.00 -54.26
a Energy of a single boron atom is of -24.522 04 atomic units using 6-31G* basis and -24.389 76 atomic units using 3-21G basis. Single point (as in crystal).
geometry. Samples containing lithium were sealed in a holder with a thin aluminum window to prevent contamination with air. Unit-cell parameters were determined using a least-squares procedure. Morphology of the samples was studied by a JEOL T220 scanning electron microscope (SEM). Results and Discussion Ab Initio Calculations. Boron clusters: Elaborate studies of different boron clusters can be found in l i t e r a t ~ r e . ' ~ The -~~ geometry of the most stable clusters which were needed for the calculations of interaction energies between lithium and boron clusters were taken from there. The clusters were then reoptimized using given symmetries and the basis sets which we used in the case of lithium-boron clusters to make the results comparable. In the cases where different geometries of the most stable clusters may be found in literature,20-22for example, the geometry of B6, we have reoptimized all geometries and used the most stable one in further calculations. A special case was the B12 cluster where, based on the crystal structure, the icosahedron which is the building unit of the structure was assumed and only the interatomic distance was optimized. Also the B12(interst) cluster simulating the interstitial site in the crystal lattice was determined using crystal structure data23and only a single-point calculation was performed. The energies and geometries of the reoptimized boron clusters are presented in Table 1 and Figure 1, respectively. Vibrational analysis showed all real frequencies for all optimized clusters, except for B6 (octahedron) where four negative frequencies were found, and thus B6 (planar), which is also more stable, was used in subsequent calculations. Energies of other clusters in Table 1 are regarded as true minima on the potential surface. The exception is, of course, B 12(interst), where only a single-point energy was calculated and no vibrational analysis was performed.
Meden et al.
4254 J. Phys. Chem., Vol. 99, No. 12, I995
2.807
6-31 G*
Liz
A A
0 0
@
A
Lis (planar)
;
0
0
3
60
Li4
A
-50
1
I 2s
2t
6p
12
Lis (bipyramid)
12in
Lig
n Figure 2. Cohesive energies per boron atom in B, clusters in kcall mol calculated by various basis sets.
TABLE 2: HF/6-31G* Energies of Optimized Li, Clusters, Lizo, Denoted by Asterisks, Calculated Only on HF/3-21G Level (E in atomic units, AE and AE/n in kcaVmo1)" cluster E AE AEh Li:! Lig
L4 L4 Lis(planar) Lis(bipyramid) Li6 Li7 Lis Li14 Liz0
-14.866 -22.313 -29.753 -29.558 -37.168 -37.195 -44.649 -52.103 -59.556 -103.549 -147.954
92 31 02 34 68 77 76 88 73 00 06
-2.62 - 12.05 - 17.28 -20.26 -7.42 -24.42 -38.62 -52.89 -66.36 - 130.43 -203.18
-1.31 -4.01 -4.32 -5.06 -1.48 -4.88 -6.43 -7.55 -8.29 -9.32 -10.16
Figure 3. Geometries of the Li, clusters optimized on the HFl6-31G* level. Distances are given in angstroms.
1
; 0
1
STO-3G 3-21G 6-31 G*
11 0
10 0
9 -
0
0 A
8 -
Energy of a single lithium atom is of -7.43 1 37 atomic units using 6-31G* basis and -7.381 51 atomic units using 3-21G basis. a
5
7-
4
5 -
I
A comparison of the stability of the calculated clusters is given in the diagram in Figure 2. As a measure of the cluster stability the value of AEln was calculated:
AEln = [E(B,) - nE(B)]ln
Liz0
Li14
(1)
0
4 0
0
A
6 0 0 A
A
$3
3 2 1 -
01
0
B
A
0
'
2
'
3
'
4
5pl
'
5bp
I
6
'
7
'
8
I
14
'
20
n where n is the number of atoms in the cluster, E(B,) is the calculated energy of the cluster, and E(B) is the energy of a single boron atom. Thus AEln is a measure of cohesive energy per boron atom in different clusters while, as usual, AE in all tables respresents the energy of the formation of the cluster if formed in vacuum from isolated atoms. In the diagram in Figure 2 the values of calculations with basis sets STO-3G and 3-21G, (not given in the tables) are presented for comparison. The results in Figure 2 show that already simple basis sets yield correct relative stabilities of the clusters. Moreover, even the absolute values are close to the more reliable results obtained by a larger basis set. From the diagram it can be seen that the absolute value of cohesive energy increases with the number of atoms being -43.08 kcaVmol for B3 which is the smallest stable cluster and -65.02 kcaVmo1 for icosahedral B12. The tendency of forming triangular faces is very strong and, in accordance, the stability of B3 is remarkable. Lithium clusters: Lithium clusters were studed in order to obtain their energies which were later used for estimating the Li-B interactions. Extensive studies of lithium clusters were reported24so the geometries of the most stable clusters were taken from that work. The clusters were then reoptimized using known symmetries and the basis sets used in the present calculations. The vibrational analysis showed nine negative
Figure 4. Cohesive energies per lithium atom in Li, clusters in kcaV mol calculated by various basis sets.
TABLE 3: HF/6-31G* Energies of Optimized Li,B Clusters (E in atomic units, AE and AE/B (Eq 2) in kcaVmol cluster E AE AEIB LiB(singlet) LiB(trip1et) LizB(1inear) Li2B(angular) Li3B Li& (square) Li&(tetrahed) L4B(sq PYr) Li5B(trig bipyr) Li5B (sq bipyr) Li& Li,B(pent bipy) Li7B(oct) Li8B(dodecah) LisB(0Ct)
-3 1.902 90 -31.957 50 -39.341 91 -39.424 88 -46.868 36 -54.339 52 -54.344 64 -54.355 78 -61.805 56 -61.809 90 -69.316 42 -76.740 30 -76.736 76 -84.122 87 -84.198 98
+3 1.70 -2.57 +26.90 -25.16 -32.76 -57.73 -60.94 -67.94 -79.49 -82.21 -129.37 -124.66 -122.45 -94.04 -141.79
+3 1.70 -2.57 +29.52 -22.54 -20.72 -40.45 -43.66 -50.65 -55.06 -57.79 -90.75 -7 1.78 -69.55 -27.68 -75.43
frequencies for Lis (planar) taken from the l i t e r a t ~ r e .There~~ fore the Lis (bipyramid) having all positive frequencies was constructed and optimized. Other Li, clusters also had all positive frequencies. The only exception is Li20 for which vibrational analysis was not performed due to the failure of
-
J. Phys. Chem., Vol. ’99, No. 12, 1995 4255
Dissolution of Boron in Lithium Melt
LizB (linear)
LiB (singlet)
6-31 G* 100
8ol
LiB (triplet)
LizB (angular)
en
a
0
0
L
1
,
0
0
LisB (sq. bipyr.) Q 1 s
A 21
1 t
20
3
4s
4 t 4 s p 5 t p 5sp
6
7b
70 8 d
80
n Figure 6. Cohesive energies per boron atom in Li,B clusters in kcal/ mol calculated by various basis sets. W
Li7B (oct.)
Li7B(pent. bipyr.)
W
LiBB (oct.)
Li8B(dodecah.)
Figure 5. Geometries of the Li,B clusters optimized on the W/631G* level. Distances are given in angstroms. Boron atoms are darker and smaller.
analytical algorithm and a very long CPU time required to perform vibrational analysis numerically. Li20 was constructed as a fragment of BCC lattice of the metallic lithium and we believe that the energy is close to the global minimum. The results are given in Table 2 and Figure 3 and 4 in the same way as the boron clusters. One can notice that the clustering energies between lithium atoms are almost of an order of magnitude smaller than the clustering energies between boron atoms. Lithium-boron clusters: In the first set of calculations one atom of boron was combined with one to eight lithium atoms in order to find an estimation of the energies of interactions involved and the geometry of the most stable clusters. The results are presented in Table 3 and in Figure 5. Energies of the most stable clusters found were combined with those of lithium clusters and the energies for the processes Li,
+ B -Li,B
nLi
+ E(B))
+
Li,B,
+ mB -Li,B,
where isolated boron atoms combine with a lithium cluster into a mixed cluster. Energies of these interactions AEILi and AEIB were defined as follows:
(2)
The energies AE/B vs number of atoms are presented in Figure 6. It can be seen that the most stable cluster of this type is Li6B with AEIB -90.75 kcal/mol, which suggests that if isolated boron atoms were present in some Li-B compound, they would be octahedrally coordinated with lithium atoms. This is also in accordance with the high stabilities of Li7B(oct) and LisB(oct) which have six octahedrally arranged first neighbors and the remaining atom&) in the “second coordination sphere”. LiSB(oct) with AEIB = -75.43 kcal/mol is remarkably more stable than LisB(dodecah) with AE/B = -27.68 kcal/mol. In
+ B,
where isolated lithium atoms interact with a boron cluster and a mixed cluster is formed and: Li,
where the lithium cluster interacts with a single boron atom forming a mixed cluster were calculated as follows:
AEIB = E(Li,B) - (E(Li,)
the latter cluster all eight lithium atoms are in the dodecahedral “first coordination sphere” of boron and the Li-B distance is forced to be too long to produce electronic states with low energies. Vibrational analysis showed all real frequencies for all clusters except for all the L 4 clusters and Lis(trig bipyr). No further attempts were made to find the most stable form of LiB4 since the results clearly indicate that with n < 6 the clusters where the boron atom is completely surrounded by lithium atoms are not the most stable. A boron atom tends to be on the “surface” of the cluster where it cannot be regarded as “solvated”, while a boron atom in Li6B is positioned inside the cluster. The energy of formation of Li6B from Li6 and a single boron atom (AHB for Li&) may therefore be regarded as an approximation of the energy of the solvation of gaseous boron in lithium melt. In fact, this approximation is likely to underestimate the actual free energy of solvation since only the first solvation sphere is accounted for. Finally, calculations for some clusters with more than one boron atom were done to find out if boron clusters “solvated” with lithium were more stable than “solvated” single boron atoms. Results for representative clusters of this type are given in Table 4 and Figure 7. Cluster stabilities were compared with respect to the energies of the processes:
E(Li,B,)
AELi = E(Li,B,)
AEIB =
- (nE(Li)
+ E(B,))
n - (E(Li,)
m
+ mE(B))
(3) (4)
The AELi and M A 3 are the estimates of cohesive energies per mole of lithium or boron atoms in a given cluster. The AEIB’s of these reactions are shown in Figure 8. They represent an approximation of the energy difference when one boron atom is taken from vacuum, then bound into the B, cluster, and finally
Meden et al.
4256 J. Phys. Chem., Vol. 99, No. 12, 1995
TABLE 4: HF/6-31G* Energies of Optimized Li,B, Clusters, Clusters Denoted by Asterisks, Calculated Only on HF/3-21G Level (E in atomic units, AE, AELi (Eq 3) and AEIB (Eq 4) in kcallmol) E
cluster
-81.260 -111.128 -155.189 -155.028 -162.578 -207.561 -325.345 -323.428 -397.856 -442.277 -302.807
01 46 78 53 64 35 55 22 93 82 53
AE
AEILi
AEIB
- 164.73 -254.45 -392.94 -291.75 -366.25 -613.80 -850.66 -768.74 -1 153.78 -1236.51 -697.61
-35.50 -25.04 -40.10 +61.09 -6.71 -32.62 -17.41 -21.17 -33.55 -27.62 -46.54
-54.91 -76.68 -65.49 -48.62 -60.60 -9 1.24 -69.45 -62.37 -85.28 -86.1 1 -58.13
Single-point calculation (distances taken as typical values from the crystal structure).
100
-
90
-
BO
-
70
-
60
-
A 0
A
a
>a
0
0
‘
I
0
A
A O
A
A A
50
-
A
40
LB3
0
I
I
I
I
t
Lis83
LiB60
LiB6a
Li2B6
Li8fItl
I
l
I
1
Li4612 Lil4B12 Li20812 Lie1 2in
a
Cluster Figure 8. Cohesive energies per boron atom in Li,B, clusters in kcaV mol calculated by various basis sets.
Lis03
LiBe (antipr.)
Li14B12
Li20 0 1 2
LiB,, (interst.)
Figure 7. Geometries of the Li,B, clusters optimized on the HF/63 1G* level. Distances are given in angstroms. Boron atoms are darker and smaller.
solvated with lithium. Results obtained with the STO-3G basis set differ much more in this case than in previous examples, implying that they have poor quantitative value. Still, these results are correct measure for the relative stability of the clusters. Vibrational analysis was performed for the clusters up to LiB6 and showed all real frequencies in all cases. For other clusters computational failures of analytical as well as numeric algorithms were encountered, and the results of vibrational analysis are not available. It is however believed that the clusters mentioned have energies close to the real minima and are valid for further comparisons since they were constructed with the rules of bonding found in previously calculated Li-B clusters. From the results shown above it can be concluded that boron atoms in Li,B, clusters tend to form boron-boron bonds with
rules of bonding being similar to that in the clusters with boron atoms only. Lithium atoms are then coordinated to the boron clusters so that triangular boron faces are capped with lithium atoms. A good example of this statement is L&(OCt) where lithium is attached to one of the faces of the boron octahedron. This geometry is much more stable than LiB6(antipr), where lithium is sandwiched between two triangles of boron atoms. Considering the cohesive energy of boron in different clusters, it can be seen that boron is most strongly bound in Li&, Li14B12, and Li20B12. The differences between these three clusters are small and the precision of the calculations and the way of approximatino does not allow a definite conclusion about the optimal solvation of boron in lithium melt. It is, however, interesting that the “advantage” of forming strong boron- boron bonds is lost due to the less-efficient “solvation” with lithium atoms in the case of larger Li-B clusters. The importance of efficient solvation of boron atoms with lithium is also indicated if the stability of the clusters is compared from the point of view of Wade25and Mingos26rules which relate the cluster stabilities to the number of the valence electrons. Using the rules, LisB6 and Lila12 would be expected to be most stable among the calculated clusters. In both cases boron atoms form closo polyhedra with n vertices (8 and 12) and, according to the rules, the most stable electronic configuration is achieved with 34 and 50 valence electrons per cluster respectively (all boron electrons plus n i2 additional). The results in Table 4 show that these two clusters are among the most stable ones, the most stable being where the electron count is optimal as well as the efficiency of solvation-the whole “surface” of the cluster is covered with lithium atoms. In the case of Lila12, further solvation to Li20B12 still slightly increases the stability of boron atoms in the cluster. It is possible that the cluster stability would increase if the boron atoms rearranged into some other type of cluster with a different optimum number of valence electrons. It was not possible to check this possibility since it means full optimization of large clusters, and this could not be accomplished in real time. In the literature, the experimental data for cohesive energy of boron in the crystal differ from 97.227to 133.985 kcaVmol,28 which is considerably higher than the AE/B values of the four most stable clusters (85.25-91.24 kcdmol). This was contrary to our expectations since the difference to the newer value in literature of almost 134 kcaVmol is too large. This comparison suggests that the boron atoms (and icosahedral clusters) are so strongly bound in the crystal lattice of elemental boron that it is not possible to dissolve them in the surrounding lithium melt.
J. Phys. Chem., Vol. 99, No. 12, 1995 4257
Dissolution of Boron in Lithium Melt Also the comparison of the stability and cohesive energy of lithium atoms in the clusters with the overall composition LiB3 gave results which were not in accordance with the starting hypothesis which states that LiB3 could exist in the form of stable solvates. From the following two reactions it can be seen that LQ312 is the most stable among the three calculated “LiB;’ clusters:
-
2LiB3 2Li,B6
Li,B6
AE = -36.78
Li,B,,
AE = -118.14
25001
3 ‘3-
2000
2
1500
1
V
v
+
z
1000 500
kcdmol
‘5
kcdmol
15
25
35 45 2-THETA (deg )
55
2500r
According to the starting hypothesis, lithium atoms should be bound more strongly in solvates than in metallic lithium. The cohesive energy of lithium atoms in all three “LiB;’ clusters (Table 4), and especially in the most stable one (17.41 kcai/ mol) is, however, too low to prevent the incorporation of lithium into the crystal lattice (the cohesive energy of a lithium atom in metal is 37.02 kcal/moPg). Therefore, these clusters would not remain stable at the solidification of lithium and no “loss” of lithium would be detected by DSC. It would be very difficult to estimate how good the approximation is which was used in the calculations (only the first solvation sphere taken into account, clusters calculated in vacuo, no estimate of the entropy contribution at real temperatures, only clusters with less than 12 boron atoms considered, no larger “LiB3” clusters than Li812, geometrical constraints used, etc.) so it might be possible that an improved approximation would raise the cohesive energy of boron in solvated clusters enough to reach the values from literature. On the other hand, the basis set in the calculations was reasonable large and this possibility does not seem probable. At this point several important questions appeared: Is it really possible to prepare a homogeneous “metallic solution” of boron in lithium? If not in a solvated cluster form, in what form does LiB3 exist? Does it exist at all? And on the other hand, is the approximation used in the calculations too inaccurate and are the results useless? The only relevant way to answer these questions was an experiment. Our approach was based on the literature data1j2%6,8 and the analyses were designed to give as clear answers as possible. Experimental Results: X-ray Diffraction, Chemical Analysis, and SEM. First we tried to prepare the homogeneous metallic solution following the procedure described by Wang.’S8 Samples were heated and stirred at a temperature of 380 “C (f10“C) using procedure B) from 5 min to several weeks. If powder diffraction data were taken on the overall bulk samples, in all cases only lithium peaks were detected-the same result as reported by Wang.8 It means that Li7B6 is not formed at these temperatures, and Wang’s conclusion* that boron is dissolved in lithium is also logical. But when lithium is removed, the product is not amorphous boron as would be expected if boron was dissolved. Powder pattem of the residues, which are very similar to each other (representative shown on Figure 9b), show broad diffraction peaks, which can, however, be indexed with a somewhat enlarged unit cell of crystalline boron. From the results of chemical and X-ray diffraction analyses and also from the observation of the morphology of the residues, performed by a scanning electron microscope (SEM), it can be concluded that the residues after 1 h of heating at 380 O C do not change any more. SEM observations reveal that the particles diminish only at the very first stages of the process and after 1 h their average size reaches the value of about 10 pm and then their shape and size remain apparently the same.
3
2000-
b
0’
1500.
U
v i
1000-
500 -
h v5
A 15
25
35
45
55
2-THETA(deq )
Figure 9. Comparison of powder diffractograms of pure boron (a) and sample heated 24 h in lithium melt at 380 “C (b). Data collection using automatic 10 mm divergence slit, 0.1 mm receiving slit and f i e d 1” antiscatter slit.
TABLE 5: Lithium Content in Boron Residues, Washed with Diluted Acid temp (“C) time (h) wt % Li 380 380 380 380 400
400 400 400
0.15 0.5 1 334 0.5 3 20 (1st run) 20 (2nd run)
1 6 4
6 3
6 4 8
Chemical analysis (Table 5, first four samples) of the acidwashed powder residues revealed that the powder is boron which contains 3-6 wt % lithium with low reproducibility. A possible reason for this is a high mobility of lithium atoms in the channels of the boron framework so that the majority of lithium is washed out when the lithium atoms, moving in the framework, reach the surface. Nevertheless, it could be concluded that lithium is present inside the particles of the residues. Analysis of powder diffractograms (Table 6, first four samples) supported the findings of SEM observations and chemical analyses. The unit cell of the residues increases at the first stages and then remains constant in the limits of standard deviations which are quite high, due to broadened overlapping peaks. The unit-cell volume increase of the final stages is about 5% compared to boron. Also the full width of diffraction peaks at half-maximum (fwhm), which is related to the internal distortion and strain in the crystallites (the size itself, observed by SEM, is too large to contribute to the broadening), changes only in the first stages of the process. Two qualitative indications were also evaluated in order to detect an eventual increase of the amount of amorphous phase in the residues. This could be ascribed to the amount of dissolved boron in the melt. One is the background level which is directly dependent on the amount of amorphous phase in the sample. The other is the integrated intensity of the first four resolved peaks. Because of possible changes of relative intensities, the sum of all four integrated intensities measured
Meden et al.
4258 J. Phys. Chem., Vol. 99, No. 12, 1995
TABLE 6: Unit-Cell, Background, and Peak-Width Parameters of the Residues, Washed with Diluted AcidC temp ("C) time (h) a (4 c (A) v (A3) bi? (CPS) FW* (028) 2468(4) 40 0.20 10.938(4) 23.82(3) r.t. (boron) 0 (boron) 380 380 380 380 400 400 400
0.15 0.5 1 334 0.5 3 20
10.96(1) 10.99(1) 11.08(2) 11.10(2) 11.03(1) 11.21(8) d
24.01(3) 24.18(4) 24.35(5) 24.35(5) 24.28(8) 24.57(7) d
2498(8) 2529( 12) 2589(15) 2598( 15) 2473( 10) 2673(45) d
50 45 50 50 80 90 180
0.22 0.25 0.28 0.27 0.28 0.32 d
IC [arb u] 505 470 497 520 475 408 312 d
Background intensity is given in counts per second at 14" 28. Average peak width at half-maximum of the first four peaks. Sum of Integrated intensities of first four peaks. Not determined due to very distorted peaks. e Numbers in parentheses denote standard deviations. is given to achieve better reproducibility. This is a relative measure of the amount of crystalline phase in the sample. These two values remain relatively constant from the very beginning of the process to the last stages and are not very different from the values of pure boron, thus indicating that the amount of amorphous phase is not rising with time and confirming that the process in lithium melt under 400 "C is not the dissolution of boron. Also more detailed comparison of the diffraction patterns of boron (Figure 9a) and the residue (Figure 9b), which is in progress now, preliminary analysis indicates that the crystal structure of the residue is in fact a distorted structure of boron containing some lithium as found by chemical analysis. The reason for not observing boron peaks in the presence of bulk lithium is the dilution of boron in the sample and the broadness of the peaks which are hidden in the background. These peaks can be detected in the presence of lithium only if the sample is cooled without stirring and the bottom part of the specimen, where the concentration of boron particles is high, is taken. If the temperature used for the preparation of the samples was raised to 400 "C or above, Li7B6 started to form. This compound can easily be detected by X-ray powder diffraction since it has two characteristic strong diffraction peaks. After 24 h at 400 "C (with a precision of f 1 0 "C using procedure B) and without stimng, peaks started to rise from the background and after one week Li7B6 was clearly formed. At 420 "c,also without stirring, Li& formed within 24 h. The formation of this new phase was also detected through the solidification of the specimen in the crucible. If was dissolved in water, methanol, or ethanol and the resulting powder washed, the product was purely amorphous boron, while after the dissolution of lithium, using the procedure by Kilroy and A n g r e ~ Li7B6 ,~ was preserved. At 400 "C it was also possible to follow the formation of Li7B6 with the effects of its occurrence to the residues (Tables 5 and 6 , last four and three samples, respectively). SEM analysis showed a gradual diminishing of the residue particles with time, which is in accord with the X-ray diffraction analysis, which shows progressive distortion of the crystallites (fwhm increasing), and increasing amount of amorphous phase which is the product of the reaction of Li7B6 with water (increasing background and diminishing integrated intensity of the peaks). These effects are detected even before the presence of Li7B6 could be detected by X-ray powder diffraction. Experiments on a transmission electron microscope indicated that this is probably due to low concentration and very small particles of Li7B6 at the initial stages of the reaction. The above results show that it is not possible, as suggested by the molecular orbital calculations, to prepare a homogeneous metallic solution of boron in lithium melt either below or above 400 "C. Below this temperature nondissolved particles always remain in the melt and these particles react with excess lithium at 400 "C and above to give However, some questions
regarding the observations remained unexplained: Why do boron pieces disintegrateinto small particles? Why is the crystal structure of boron distorted and the unit cell enlarged? Why and how is lithium present in the boron-like residues? What is the reason for the exothermic effect at about 330 "C? The answers were suggested by considering the crystal structure of boron23which contains many large interstitial holes in the boron framework (the distance from the center of y e intersitial site to the surrounding boron atoms is about 2.1 A). It is possible that lithium atoms are incorporated into these holes. This possibility was already mentioned by Emst," who, on the basis of differential scanning calorimetry (DSC) experiments, regarded the inclusion of lithium into the interstitial sites as only a first step prior to the formation of a new solid phase-"LiB3 compound". In his report" the presence of "a new solid phase" was detected only by a mechanical stirrer, and we (and also Wang8) could not confirm the presence of a new crystalline phase by powder diffraction. If this new phase was amorphous, then it could only (a) be preserved during the reaction of lithium with water and subsequently chemically analyzed or (b) react with water to give another LiB, phase or amorphous boron. Since the residue after the reaction with water had a boronlike framework and contained lithium, we think that the "LiB3 compound" is actually boron, saturated with lithium. There are 34 sufficiently large holes above the icosahedral faces (Figure 1, B12 interstice) per primitive rhombohedral unit cell of /?-rhombohedral boron containing 105 boron atoms.23 If all the holes were filled with lithium atoms, the formula of this phase would be LiB3.088. Although this is very close to LiB3, we think that naming boron, saturated with lithium, as a "compound' may not be correct since it has more in common with solid solutions (especially with the interstitial ones) than with, for example, well defined intercalate compounds. If lithium is incorporated into the interstitial holes neighboring boron atoms have to accommodate it. This (a) enlarges the unit cell and (b) produces a local disorder and microstrains in the crystal lattice. Therefore a significant shift of diffraction peaks to higher angles and their broadening occur. Both effects were observed in powder diffractograms (Figure 9, Table 4), and we believe that the enlargement of the unit cells at the surface of the boron piece, where lithium is first incorporated, produces an internal stress that results in repetitive breaks and final disintegration of the boron piece into small particles. If this process was interrupted after a very short time (some minutes at 380 "C) or the preparation was done at low temperatures (below 300 "C), the gradual diminishing of the particles in the residues could be followed. The exothermic effect, which was observed at about 330 "C if the mixture of lithium and boron is heated and was ascribed to the formation of LiB311 or to the dissolution of boron,8 can also be explained with the incorporation of lithium atoms into the interstitial holes. If the lithium atom is more stable (larger
Dissolution of Boron in Lithium Melt cohesive energy) in the hole than in the liquid lithium, its inclusion into the hole will produce an exothermic effect. The energy of the lithium atom included into the interstitial site was estimated using molecular orbital calculations as AELi for LiB&t) (Table 4). According to this approximation lithium, in the interstitial site is bound with 46.54 kcdmol which is, as expected, more than the cohesive energy of lithium atoms in lithium melt (less than 37.02 kcdmol). The difference is about 10 kcdmol of lithium and this value agrees quite well with the one observed for the first exothermic effect6 (18 f 4 kI/ mol of boron which is roughly between 10 and 16 kcdmol of lithium). This good agreement might be incidental, but it could also mean that the approximation in the molecular orbital calculations is not too bad and the exothermic effect is really due to inclusion of lithium into the holes of boron framework. Inclusion of lithium into the boron framework is also supported by all the available experimental evidence we have about the processes in the Li-B mixture below and slightly above 400 “C. It is, therefore, believed that the explanation of the processes observed by the inclusion of lithium into the interstitial holes of the boron structure is correct and that the molecular orbital calculations are at least qualitatively valid despite the fact that many approximations have been used. Conclusions
In the literature it was suggested using a diffraction experiment that crystalline boron is dissolved in lithium melt below 400 “C forming a homogeneous “metallic solution”.8 Other sources,6~11interpreting the DSC data, claim that a LiB3 compound is formed at 330 “C. Both statements can hold simultaneously only if LiB3 is amorphous-existing in a “molecular” or solvated cluster form. This possibility was studied with ab initio quantum chemical calculations of lithium-boron clusters. Some simple rules of bonding in Li-B clusters were found: (i) boron atoms tend to form strong boron-boron bonds; (ii) these bonds are arranged so that a boron framework of side-sharing triangles is formed. (iii) Lithium atoms are bound on the triangular faces of the boron network to form equal-sided pyramids. Triangular bipyramids with two lithium atoms on the opposite sides of one boron triangle are not favored. In most stable clusters the cohesive energies of boron atoms are quite high (about 90 kcdmol) but still considerably lower than the experimental cohesive energy of boron in crystal (nearly 134 kcdmo126),implying that a complete dissolution of boron in lithium melt is not probable. Furthermore, the cohesive energies of lithium atoms in L a 1 2 (about 17 kcaymol) which is the most stable cluster with stoichiometry LiB3 are lower than that of the atoms in solid lithium (about 37 kcaYmol). Therefore, LiB3 which might exist in the lithium melt in the form of solvated clusters cannot exist in a dispersed form in the crystalline lithium after the solidification since lithium atoms from the clusters would incorporate themselves into the lithium crystal lattice. Present ab initio results are in disagreement with the possible dissolution of boron in molten lithium as well as with the existence of the “compound “LiB3” in the solvated cluster form. Validity of the calculations which used a number of approximations was experimentally checked. With carefully controlled preparation of the samples and use of X-ray diffraction, chemical and SEM analyses it was proven that it is impossible to completely dissolve boron in molten lithium below and above 400 “C. Below 400 “C the polycrystalline piece of boron is readily disintegrated into the crystallites of an average size of about 10 pm, which remain dispersed in
J. Phys. Chem., Vol. 99, No. 12, 1995 4259 the melt. These crystallites contain lithium, their structure is similar to that of boron but rather distorted and the unit cell is larger. Above 400 “C these particles obviously react with excess lithium to give a new solid-phase Li&. These experimental findings as well as the results of the molecular orbital calculations inspired a new explanation covering all available experimental and theoretical data related to the processes which take place in the lithium-boron mixture at temperatures slightly above 400 “C. The basic idea behind this explanation is the inclusion of lithium atoms into the interstitial holes of P-rhombohedral boron. According to the molecular orbital calculations, the inclusion is accompanied by the release of energy since lithium atoms are more stable in the interstitial holes of the boron framework than in the lithium melt. This is in accordance with the observed exothermic effect at about 330 “C. The inclusion of lithium atoms in the holes can also modify the local structure of boron, resulting in microstrains and a disorder together with an enlargement of the unit cell which were found by X-ray powder diffraction. It is believed that the internal strain, which is due to lithium first being included into the surface layers of the boron pieces, produces repetitive breaks and thus the inclusion process is also responsible for the disintegration of the pieces of boron. It is proposed that the “compound” LiB3, suggested on the basis of thermochemical analysis,8s11is actually boron saturated with lithium. Although the composition of boron particles, saturated with lithium, was found to be about LiB38J1which is close to the theoretical composition if all sufficiently large holes are occupied by lithium atoms (LiBs,os8),the name “compound” may not be correct since the phase in question is more similar to solid solutions than to well-defined compounds. Experimental evidence, presented in this work also requires a modification of the conditions to obtain the compound Li&. According to Wang,* the dissolution of boron in lithium melt must be accomplished to enable the formation of the compound Li7B6 (originally claimed to be Li5B4). On the other hand, Emst” stated that LiB3 has to be formed first and then it reacts with the excess lithium to form Li&. If these statements are rephrased, it can be said that a new solid crystal lattice of Li7B6 is formed from boron particles, saturated with lithium and the surrounding lithium melt. Finally we can conclude that the results of molecular orbital calculations are in, at least qualitative, accordance with experimental findings and were quite helpful in designing experiments and especially in explaining the experimental results. Acknowledgment. The authors are indebted to Prof. D. HadZi for critical reading of the manuscript. The financial support of the Ministry for Science and Technology of the Republic of Slovenia is gratefully acknowledged. References and Notes (1) Wang, F. E. U.S.Patent 4,110,111, 1978. (2) Wang, F. E.; Mitchell, M. A,; Sutula, R. A.; Holden, J. R.; Bennet, L. H. J . Less-Common Met. 1978,61,237. (3) James, S. D.; De Vries, L. E. J . Electrochem. SOC.1976,123,321. (4) Mitchell, M. A.; Sutula, R. A. J . Less-Common Met. 1978,57,161. (5) Sorokin, B. P.; Gavrilov, P. I.; Levakov, E. V. Zh. Neorg. Khim. 1977,22,595. (6) Dallek, S.; Emst, D. W.; Larrick, B. F. J. Electrochem. SOC. 1979, 126,866. (7) Kilroy, W. P.; Angres, I. J. Less-Common Met. 1979,63,123. (8) Wang, F. E. Metall. Trans. 1979,IOA, 343. (9) De Vries, L. E.; Jackson, L. D.; James, S. D. J . Electrochem. SOC. 1979,126,996. (10) Szwarc. R.: Walton. R. D.: Dallek., S.:. Lanick. B. F. J . Electrochem. so.: 1982,129,’ 11‘6s. (11) Emst, D. W. J. Electrochem. SOC. 1982,129,1513.
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