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Enthalpies of formation of first-row transition-metal diborides by a new calorimetric method
O-129 J. Chem.
Thermodynamics
19%5, 17, 1003-1016
Enthalpies of formation of first-row transition-metal diborides by a new calorimetric method LETITIA TOPOR and 0. J. KLEPPA The JamesFranck Institute and The Departmentof Chemistry, The University of Chicago,Chicago,Illinois 60637,U.S.A. (Received29 January 1985) The standard enthalpies of formation of the diborides of SC, Ti, and V have been determined calorimetrically at (1400&2) K. Each of these borides was dropped together with solid (platinum or palladium + boron) from room temperature into the calorimeter to generate liquid alloys (platinum or palladium + scandium or titanium or vanadium + boron). In separate experiments alloys of the same composition were formed by dropping the elements. The following values of ArHi are reported: ScB,, -(307.0& 14.8) kJ.mol-‘; TiB,, -(328.4* 10.2) kJ.mol-‘; VB,.,,,, -(206.9& 12.2) kJ.mol-‘. The results are compared with earlier literature values where they exist. However, for ScB, there are no earlier values and for VBs only equilibrium values. The systematic variation of the enthalpy of formation of the diborides from ScB, to MnB, is discussed in relation to the structural parameters and to the change in Me-Me, B-B, and Me-B bonding.
1. Introduction The borides formed by the transition elements form a group of compounds of considerable theoretical and practical interest. It is known, for example, that a change in the number of d-electrons in the transition metal correlates with changes in the boron-metal structures and with changes in the physical and thermodynamic properties of the compounds. (‘) Many of the transition-metal borides find applications in high-temperature technology. This is due to their refractory character, chemical inertness, hardness, and high electrical and thermal conductivity. There is little reliable thermochemical information on the transition-metal borides. This is related to the fact that combustion calorimetry of refractory borides, both in oxygen and fluorine gas, is associated with many experimental difficulties. Because of their chemical inertness, refractory borides cannot be studied by conventional solution calorimetry. In some cases the enthalpy of formation of the boride (e.g. TiBJ has been determined by direct reaction between metal and boron in a calorimeter.‘*’ However, even for reactions which are very exothermic, this method always leaves questions about the completeness of the (solid + solid) reaction, and about corrections which may have to be applied for possible side reactions. 0021-%14/85/l 6’1
11003 + 14 gO2.00/0
0 1985 Academic Press Inc. (London) Limited
L. TOPOR AND 0. J. KLEPPA
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For a number of transition-metal borides the only thermochemical quantitites available have been derived indirectly from equilibrium measurements. An important early example of this approach is the work of Brewer and Haraldsen,‘-l) who studied equilibria between borides, nitrides, and nitrogen gas at very high temperatures. In this way they were able to derive semi-quantitative thermodynamic information on a number of important boride phases. In other studies, thermochemical values have been derived from the equilibrium vapor pressures of the borides and of their constituent atoms. During the past several years we have in this laboratory attempted to find hightemperature calorimetric methods suitable for determining the enthalpies of formation of refractory borides. Initially we obtained such results by hightemperature solution calorimetry, using liquid Mn,,,Ni,,,,‘4’ and pure liquid as the calorimetric solvents. (5.6) In these studies we succeeded in q-w-, determining the formation enthalpies of borides of Mnc5’ Fe, Co, and Ni.(6) Unfortunately this method does not work for most early-transition-metal borides. Very recently we have developed a new high-temperature calorimetric method for thermochemical studies of refractory borides. This method is based on the fact that (platinum or palladium + boron) form low-melting liquid alloys (see phase diagrams in figure l), which also can dissolve a certain amount of a third element. So far we have used this approach to determine the enthalpies of formation of LaB6,(‘) and CrB,,@) two compounds for which no calorimetric enthalpies of formation were available.
/ 1
,/’ / 1’ ,’
1073
.
Pd + Pd,B
1073
673 j2731 ?-i-i-i/i Pd 0.2
110
Pd+,&, ' ' ' 1 ' ' 0.4 0.6 0.8 x
---_-------Pt,B + u-B
B
673
Pt
0.2
0.4
0.6
0.8
B
X
FIGURE 1. Equilibrium phase diagrams for (platinum + boron) and (palladium + boron). (From: Moffatt, W. G. Handbook of Binary Phase Diagrams. General Electric Company: Schenectady, NY. lWlLQAd\ _/I”
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The principle of the new method, as in solution calorimetry, is based on a simple the~odynamic cycle, which we illustrate for the special case of CrB, and Pt: O.l3CrB,(cr, O.l3Cr(cr,
T1)+0.61Pt(cr,
T,)+0.26B(cr,
7”) = Pt,.,,B,.,,Cr,.,,(i,
T1)+0.61Pt(cr,
T2).
T1) = Pt,,,,B0,26Cr0,,3(f,
(1) T,).
(2)
From equations (1) and (2) we get: O.lSCr(cr, T1) + 0.26B(cr, T1) = O.l3CrB,(cr,
?;).
(3)
For Ii = 298.15 K we have ArHk(CrB,)
= ~A~~~(2)-A~~~(l)~/O.l3.
(4)
In liquid-metal solution calorimetry, the compound, and separately its constituent elements, are dissolved in a liquid metal solvent to form an alloy of the same composition. In our new method two solids, which melt at very high temperatures (e.g. CrB,, Tfus= 2473 K; Pt, 7& = 2042 K) generate a liquid alloy in the calorimeter at T, x 1400 K, equation (1). In other experiments an alloy of the same composition is formed at the same temperature from the solid elements, equation (2). The enthalpy of formation is calculated from equation (4). Note that the effects which we measure in the calorimeter are the enthalpies of mixing of two or three solids to form a liquid alloy at calorimeter temperature. Thus the method is not a dissolution method, but a mixing method. Usually we mix the refractory boride with platinum (or palladium) in the initial experiment and thus generate the first amount of liquid alloy. However, the presence of this liquid in the calorimeter is not essential for later experiments, although to some extent it facilitates the mixing process by enhancing the reaction rate. In subsequent experiments we add (boride + platinum) to duplicate the first experiment or, alternatively, (boron + platinum + the third element) in the same mole ratio to keep the liquid-alloy composition unchanged. In the present investigation we report on the use of this method to determine the enthalpies of formation of the diborides of the early first-row transition elements: ScB,, TiB,, and VB,.
2. Ex~~rn~nta~ The calorimetric experiments were carried out at (1400 F 2) K using a Calvet-type microcalorimeter which has previously been operated successfully at temperatures up to 1500 K. The principal features of this equipment were described recently.“-” The measurements were performed in a zirconium-gettered argon atmosphere using a boron-nitride crucible in a manner very similar to that previously described for CrB,.@) (See also figure 2.) It was possible to stir the contents of the crucible by means of a hollow boron-nitride stirrer attached to the end of a 1 m long fusedquartz manipulation tube of 7 mm o.d. All samples were dropped into the calorimeter from room temperature through the central bore of this tube. The platinum and palladium metals were of reference grade (99.99 mass per cent
1006
L. TOPOR AND 0. J. KLEPPA Sample
Silica
Stainless-steel
Zirconium
Boron nitride stirrer and crucible Alloy Alumina Kaowool
c---22 mmFIGURE 2. Schematic diagrams of fused-silica liner with calorimetric cell.
Pt, Pd) purchased from Engelhard as 1 mm or 2 mm wire, and as 0.025 mm foil. Before use the platinum and palladium foils were annealed overnight in an inert atmosphere at 1100 K. The boron sample consisted of a crystalline powder, 60 mesh, of the P-rhombohedral form with 99.7 mass per cent of B. Titanium and vanadium were in the form of 6.2 to 6.4 mm rods, of purity: Ti, 99.98 mass per cent; V, 99.5 mass per cent. These materials were purchased from Alfa Products/Ventron. The scandium metal was of distilled quality in the form of 1 to 3 g lumps from Atomergic Chemmetals. Chemical analysis showed 99.5 mass per cent of SC, the principal impurity being about 0.5 mass per cent of Ta. Prior to their use in the calorimeter the Ti and V rods were machined on a lathe to produce very fine chips about 0.02 mm thick. The Sc lumps were reduced to a fine powder by a file, and iron contamination was removed from the powder by a small magnet. The samples of ScB,, TiB,, and VB, were kindly furnished by Professor K. E. Spear of Pennsylvania State University. These compounds had been prepared by
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repeated arc-melting of stoichiometric amounts of high-putty materials; we had available small boride “buttons” of total mass 3 to 5 g. These buttons were crushed in our laboratory, first into a coarse powder in a “diamond” mortar, and then in an agate mortar. Before their use in the calorimeter the powders were sifted through 100 mesh sieves. X-ray and s.e.m. examination showed that the samples of ScB, and TiBz consisted of single-phase material, while “VB,” showed two phases: a major phase VB, and a secondary phase V,B,. Chemical analysis by a.a.s. showed that within experimental error ScB, and TiB, were stoichiometric in composition. while “VB,” had the composition VB1.925f0,010. Before each series of experiments the silica liner was flushed for about 2 h with purified argon. It was then inserted into the calorimeter where it was kept overnight. Calibration was achieved by dropping small pieces of 3 mm diameter high-Puritan copper rod into the calorimeter from room temperature. A 1 per cent correction was applied for the heat pick-up of the copper samples during their drop into the calorimeter. Within a single series of measurements the calibrations were reproducible to f 1 per cent. The enthalpy of pure copper at 1400 K was taken from Hultgren et .l.:(r”’ 44083 J. mol- I. The calorimetric samples, either of (platinum or palladium + scandium diborate or titanium diborate or vanadium diboride + boron), or of the equivalent amounts of (platinum or palladium + scandium or titanium or vanadium + boron), were dropped from room temperature in the form of small cylindrical capsules prepared from Pt or Pd foil. We found that the liquid-alloy composition which we adopted in our recent study of CrB, (see Introduction above) did not dissolve ScB,, TiB,, or VB,,,,,. For these borides we reduced the mole fraction x(Me) of the metal to 0.06, and made use of mole fractions of boron, x(B) = 0.23 (for SC and V) and x(B) = 0.25 (for Ti). The actual choice of the most suitable value of x(B) initially was based on an analysis of the (platinum + boron) and (palladium + boron) phase diagrams (figure 1); following this, we tested different alloy compositions in the calorimeter so as to make sure that the assumed reactions were in fact complete.
3. Results The chemical reaction which occurs when a sample of (platinum + metal diboride + boron) is dropped from room tem~rature (Z’r x 298 K) into the calorimeter (T, x 1400 K) may be written: 0.7lPt(cr,
T,)+O.O6MeB,(cr,
T,)+O.llB(cr,
TI) = Pt,,,,B,.,,Me,.,,(l,
T2).
(5)
In this equation we have arbitrarily set x(B) = 0.23. The reaction which occurs when an equivalent sample of (platinum + metal + boron) is dropped is: 0.71Pt(cr, TI)+0.23B(cr, Combining
1;)+0.06Me(cr,
7”) = Pt,.,,B,.,,Me,,,,(l,
7’,).
(6)
equations (5) and (6) we get O.O6Me{cr, ‘&) + O.l2B(cr,
TI) = OL%MeB,(cr,
7;),
f7l
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L. TOPOR AND 0. J. KLEPPA
TABLE 1. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy Pt,.,,B,.,,%,, at WWk2) K
n(Pt)
Expt no.
mm01
1-l l-2 1-3 l-4 1-5 l-6 l-7 2-1 2-2 2-3 2-4 2-5 2-6
4.6355 4.6030 4.7083 4.6445 4.6714 4.5781 4.6644 4.6819 4.7262 4.7130 4.6201 4.6550 4.5324
n(ScB,)+n(B) mmol
n(Sc) + n(B)
0.3917-tO.7182 0.3889+0.7!33 0.3978 + 0.7296 0.3924+~.7~97 0.3947~0.7238 0.3868 +0.7094 0.3943 co.7234 0.3956+ 1.5166 0.3994+ 1.5310 0.3982 + 1.5267 0.3904+ 1.4966 0.3933 + 1.5079 0.3914+ 1.5006
A,H&/(kJ.mol-t)
= ((37.4&4.8)-(344.4+
A&W
AH,,0
J
kJ.mol-’
128.5 125.4 137.1 139.9 139.2 138.7 137.1 15.1 13.6 18.2 12.9 15.S 13.4 Mean:
~.AfLW
kJ.mol-’
328.1 322.4 344.6 356.5 352.7 358.6 347.7
344.4+ 14.0
14.0)) = -(307.0+
38.2 34.1 45.7 33.0 39.4 34.2 37.4k4.8
14.8)
and also Ar~~(MeB~) where A,&(6)
and A,H,(5)
= W%,,(6) - W&,(3,
(8)
both refer to a reaction which involves 1 MeB,.
TABLE 2. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy %6,Bo,2,Ti,,,6 at (1400 f 2) K Expt no.
WV mm01
n(TiB,) -t n(B)
l-l l-2 l-3 1-4 i-5 l-6 l-7 l-8 l-9 l-10 2-l 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9
4.3006 4.2908 4.1947 4.2621 4.2947 4.1997 4.3837 4.3488 4.3828 4.3180 4.2712 4.3012 4.3818 4.1622 4.2719 4.1694 4.1710 4.1732 4.4031
0.3740+0.8102 0.3731+0.8085 0.3648 + 0.7902 0.37~+0.8031 0.3735 +0.8090 0.3652+0.7912 0.3812+0.8259 0.3782+0.8192 0.3811+0.8258 0.3755+0.8135
mm01
A&/(kJ~mol-‘)
n(Ti) + n(B) mm01
0.3714+ 0.3740+ 0.3810+ 0.3619+ 0.3715+ 0.3626+ 0.3627+ 0.3629+ 0.3829 f
1.5475 1.5584 1.5876 1.5080 1.5478 1.5107 1.5112 1.5120 1S953
= {(13X6*5.6)-(472.0&
AH,, J
- W,(5) kJ. mol- ’
169.02 451.9 173.84 465.9 179.20 491.2 165.83 447.5 181.33 485.5 173.37 474.7 170.94 448.4 184.01 486.5 185.59 487.0 180.73 481.3 49.12 51.81 47.92 49.47 51.28 50.55 51.17 51.14 49.05 Mean: 472.0* 17.3 17.3)f = -(336.4& 18.2)
W,,(6) kJ.mol-’
132.3 138.5 125.8 136.7 138.0 139.4 141.1 140.9 128.1 t35.6f5.6
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TABLE 3. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy Pd0.69B0.25Ti0.06 at (1400+2) K Expt no.
4W mm01
n(TiB,) + n(B) mmol
I-1 I -2 l--3 I.-4 l-5 1 -6 2--l 2--2 2 -3 2--4 2-5 2-b
3.9722 5.6513 5.2941 4.1291 3.9131 4.0785 3.8167 4.0517 3.8289 4.1056 3.9930 3.8934
0.3454+0.7484 0.4914+ 1.0648 0.4604 + 0.9976 0.3591+0.7781 0.3455 + 0.7487 0.3547-tO.7683
n(Ti) + n(B) -~ mm01
AH&, J
@n(5) kJ,mol-’ --_____ -_-.-468.2 486.5 470.4 468.1 451.2 482.7
un(6) kJ.mol-’ _._-.- . -
161.70 239.06 216.57 168.10 155.89 171.22 0.3319+1.3829 53.86 0.3523 + 1.4680 52.20 54.57 0.3330+ 1.3873 0.3570+ 1.4876 54.20 0.3472 + 1.4467 51.96 0.3386+ 1.4107 51.96 Mean: 471.2k 12.5 &Hy(kJ.mol-‘) = {(154.9+6.6)-(471.2k12.5)) = -(316.3+14.1) Weighted mean value: A,Hd(kJ.mol-*) = {( -316.3 x6)+(-336.4~9))/15 = -(328.4+
162.3 148.2 163.9 151.8 149.7 153.5 --_-154.916.b 10.2)
Our experimental results are summarized in tables 1 to 4. Table 1 gives the new results for ScB,, which we studied using (platinum + boron) as the calorimetric medium. Tables 2 and 3 give similar results for TiB,, based on measurements both with (platinum -I- boron) and (palladium + boron), and table 4 lists results for VB 1.925 using (palladium + boron). Decisions regarding the choice of alloy were based on a series of preliminary experiments with different compositions of (platinum + boron) and (palladium + boron): while we had satisfactory TABLE 4. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy P4,,714Bo,226Vo.06 at (lmk2) K Expt
n(W)
110.
mmol
mm01
l-1 t-2 1-3 1-4 I-5 1-b l-7 2-1 2-2 2-3 24 2-S
6.5305 5.7166 5.5974 5.6252 5.7117 5.6118 5.6546 5.6543 5.4859 5.3980 5.6915 5.1137
0.5488 + 1.0107 0.48~+0.88~ 0.4704 + 0.8662 0.4727 +0.8706 0.4800+0.8839 0.4716+0.8685 0.4752 +0.8750
4W.,,,)+n(B)
ArH~(kJ.mol-‘)
n(V)+ NW mm01
0.4152 4 1.7897 0.4610+1.7364 0.4536 + 1.7068 0.4783+ 1.8015 0.4381+ 1.6503 = {(266.4&8.0)-(473.3*9.2)}
Wes W,,(5) _____ J kJ.mot-’ _- _ -...-_~----261.08 475.7 230.00 478.8 216.34 459.9 222.23 470.1 234.62 488.8 223.10 473.1 221.90 467.0 123.18 124.67 120.76 132.86 113.28 Mean: 473.3k9.2 = -(206.9+ 12.2)
~A%(6) kJ.mol-’
259.2 270.4 266.2 277.8 258.6 266.4k8.0
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L. TOPOR AND 0. J. KLEPPA
dissolution of the TiB, samples both in (platinum + boron) and (palladium + boron), we had difficulties with ScB, in (palladium + boron). We carried out satisfactory preliminary experiments with V both in (platinum + boron) and in (paliadium + boron), but settled for carrying out the final experiments with (palladium + boron) because of the lower expense. At the bottom of each of the four tables we give the calculated averages of A,H,(5) and A,H,(6) with their standard deviations 6, and S,. Using equation (8) we then calculated A,Hm for ScB,, TiB,, and VB,,,,,. The listed uncertainties in these standard enthalpies of formation were calculated from 6 = (sf + isi)1/‘. In our experiments with ScB, we found A,Hk = -(307.0$- 14.8) kJ. mol-‘. Our measurements yielded two different values of A,H= for TiB,, namely -(336.4f 18.2) kJ *mol-’ obtained from the 9 experiments with (platinum + boron) and -(316.3f 14.0) kJ* mol-’ from the 6 experiments with (palladium + boron). By assigning a weight of 9 to the former average, and a weight of 6 to the latter, we arrive at an overall mean value of ArHk(TiB,) of -(328.4f 10.2) kJ . mol-‘; the stated error limits represent the standard deviation of the mean. From the experiments with VBI,,,, we found A,JY~(VB,,~~~) = -(206.9* 12.2) kJ * mol-i. If, for simplicity, we assume that A,wm varies linearly with the boron content of the boride, we estimate A,Hi(VB,) to be -(206.9x 2.~)/ 1.925 kJ.moi-’ = -215.0 kJ,mol-‘. In figure 3 we present our values for the standard enthalpies of formation of the diborides of SC, Ti, V, Cr. and Mn, along with the other experimental and predicted
I T I I I ScBz Ti& VB2 CrBz MnB2 FIGURE 3. Standard enthalpies of formation A&, and melting temperatures 7&, for ScB,, TiB,, VB,, CrB,, and MnB,. 0, Our values; 0, other calorimetric values: a, reference 12; b, reference 13; c, reference 14; d, reference 2; e, reference 15; A, equilibrium values: TiB2 and CrB2, reference 3, VB2, reference 16; x , predicted values, reference 11. 0, Melting temperatures.
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values.‘“’ For the first three borides the values shown were determined in the present work; for CrB, the given value was taken from a recent publication where we adopted the same experimental approach,@’ while for MnB, we accepted the preliminary value of the enthalpy of formation determined by solution calorimetry in liquid copper and reported in a previous publication from this laboratory.‘6’ Figure 3 also shows the reported melting temperatures for the considered diborides taken from the published phase diagrams.
4. Comparison with earlier results As far as we know, there are no thermochemical values in the literature for the enthalpy of formation of ScB,. Among the other diborides studied in the present work, TiB, has been investigated quite extensively in the past. However, the values of the enthalpy of formation quoted in the literature differ a great deal,‘17, **’ ranging from - 133.9 kJ . mol-1,‘19’ to - 323.8 kJ . mol-‘.“5’ Different techniques have been used: all the calorimetric values are presented in figure 3. In addition. vapor-pressure studies using mass spectrometry have reported values of ArHk of measurements -217.6 kJ.mol-‘,(20’ and - 133.9 kJ . mol- ‘;(19) equilibrium involving TiB, yielded -297.1 kJ.mol-‘,(3’ and -276.1 kJ.mol-‘,‘21’ while reduction of TiO, gave - 293.0 kJ . mol- ’ .(22) Clearly, there is a lack of agreement even among values obtained by the same experimental method. The enthalpies of formation of TiB, listed in the JANAF Thermochemical 16.7) kJ*mol-’ and Tables’23’ and in Hultgren et ~1.‘~~’ are -(279Sf -(279.7&11.3) kJ.mol-‘, respectively The former value was based on an assessment of four different studies, (13*20*21*25) while the latter was based on a single experimental investigation.” 3, Our value, -(328.4+10.2) kJ.mol-‘, is in reasonable agreement with the recent result of Akhachinskij and Chirin:‘2’ A,Hm(TiB 2.056) = -(318.57 + 3.55) kJ . mol-‘, obtained by direct-reaction calorimetry, with the value of Huber,(‘5) -(323.8&3.7) kJ .mol-‘, from oxygen bomb calorimetry, and with the second-law value, -(315.1+ 17.6) kJ.mol-‘. recently derived by Yurick and Spear (r 7’ from equilibrium investigations of (titanium + boron + nitrogen). We consider these three values to be the most reliable ones. Even so, it should be noted that they differ considerably from those tabulated by JANAF and by Hultgren et aL’23,24) and also from a number of other calorimetric values (see figure 3). For VB, the only value reported for the enthalpy of formation has been derived indirectly from a mass-spectrometric study of the enthalpy of vaporization of VB,. Second- and third-law evaluations of these results yielded ArHm = -(214.6+ 15.1) kJ*mol-’ and = -(222.2f 15.9) kJ.mol-‘, respectively. (16) A more precise value, -(203.8+ 10.0) kJ. mol-‘, was reported in the same publication from equilibrium studies of (vanadium + boron + nitrogen).(16) While there are no calorimetric values in the literature for VB, and CrB,, figure 3 shows that there is a good agreement between our calorimetric values for these two diborides and the earlier equilibrium studies.
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5. Discussion Boron combines with most metals and forms a series of binary compounds which range in composition from Me,B to MeB,, and possibly even to MeB,,.“**” While no one metal has the whole range of compounds, there are several which have as many as six or seven distinct boride phases (r.g. Cr, Mn, Re). Two conflicting points of view have been advanced regarding the electronic structure and chemical bonding in transition-metal borides. In some studies it has been assumed that there is electron transfer from boron to the meta1,‘27-29’ while in others it is argued that charge transfer is in the opposite direction.‘30-35’ Recent theoretical studies, as well as discussions based on the important structural parameters, support the view, which now seems to be fairly generally accepted, that in metal-rich borides (from Me,B up to but not including MeB,) there is a transfer of electrons from boron to the metal. On the other hand, in borides rich in boron (from MeB, up to MeB,,) electron transfer is in the opposite direction from the metal to the boron framework. This correlates with the fact that boron-rich compounds are common among the rare earths and early transition metals, but that such borides are rare among the more electronegative late transition metals. Among the first-row transition metals the first five members: SC, Ti, V, Cr, and Mn form diborides while Fe, Co, and Ni do not. Kiessling’27’ made an important contribution to the elucidation of metal-boride structures. He pointed out the tendency of the boron atom to form an increasing number of boron-boron bonds with increasing boron content in the compound. In lower borides (Me,B to Me,B) the boron atoms are isolated. As the boron-to-metal ratio increases, the boron atoms link up with other borons to form chains (single chains in MeB and double chains in Me,B,), two-dimensional networks (MeB, and Me,B,), and three-dimensional boron frameworks (MeB,, MeB,, Metz, and MeB,,).‘35’ Most metal diborides have the AIB, structure, in which the metal and boron atoms are arranged in alternative planar hexagonal layers, with graphite-like boron layers separated by close-packed layers of the metal. If two electrons are transferred from the metal atoms to the boron network, the boron layers become isoelectronic with carbon in graphite. Recent theoretical work’36’ suggests that this may indeed be a reasonable description of the charge structure in the diborides of the early
TABLE 5. Interatomic distances in MeB, borides LI Boride
c/a
cfnm
a/rim
2rhJnm
ScB, TiB, VB, CrB, MnB,
0.1118 0.1064 0.1020 0.1030 0.1010
0.3517 0.3228 0.3050 0.3066 0.3037
0.3146 0.3028 0.2991 0.2969 0.3007
0.328 0.293 0.273 0.260 0.258
a From reference 37.
d&nm 0.1816 0.1748 0.1727 0.1714 0.1736
4dnm 0.253 0.238 0.230 0.230 0.231
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DIBORIDES
transition metals SC and Ti; however, for V, and particularly for Cr and Mn, the charge transfer undoubtedly is much less extensive. We present in table 5 a summary of the important structural parameters for the five diborides considered in the present work. 137)Apart from the lattice parameters (I and c, this table also gives the values of the interatomic separations d,, and dr+,; note that dMeeMe= a. Also included in this table are the values of 2ti,, i.e. the accepted atomic diameters of the five pure metals. In order to gain some insight about how the interatomic distances in the compounds change among the members of the studied family, we give in figure 4 plots which show the three ratios dMceMc/2t&, d,_$2r& and dMe-B/(r& + t-g) for the borides from ScB, to MnB,. These ratios illustrate how the observed interatomic distances relate to corresponding distances in a reference structure, which is either the pure elements (Me, B) or a hy~thetical boride in which the metal-boron separation is equal to the sum of the (metal + boron) radii. In analyzing this figure we shall adopt a point of view previously advanced by Spear,‘38) who in a recent publication related the capability of different metals to form diborides to their ability to deform so as to fit into the AlB, structure. Note that when the ratios plotted in figure 4 are about 1.00, that indicates little distortion compared with the adopted reference structure; values larger than 1.00 imply a stretched (and weakened) bond, while values less than 1.00 indicate a compressed (and strengthened) bond. In considering the significance of this graph, it should of
FIGURE
A, &-&G;
4. Structural x , d,,$(&+ri).
parameters for the diborides of SC, Ti, rg has been set equal to 0.087 nm.
V, Cr,
and
Mn. 0,
1014
L. TOPOR
AND
0. J. KLEPPA
course also be kept in mind that there is significant coupling between the plotted ratios: for example, in the diborides of metals with large atoms, the increase in the u-axis of the hexagonal structure is inhibited by the graphitic boron layers. As a result, the B-B bonds stretch while the Me-Me distances are compressed so as to fit the structure. In such a case it is believed that the stability of the diboride in the main will arise from the Me-Me and Me-B bonds, with only little contribution from the B-B bonds. On the other hand, if the metal atom is small for the available space, the Me-Me separation a in the boride will be determined mainly by the B-B contacts. Hence, the stability of the diboride should arise mostly from the B-B and Me-B bonds. Note that among the quantities plotted in figure 4 the ratio dBmB/27$shows only little variation from Ti to Mn; all the values fall within f0.016 of 1.00. However, for ScB, this ratio is 1.04. This reflects the fact that SC is a fairly large atom which causes a significant stretching of the B-B bonds with a corresponding compression of the Me-Me bonds. We mentioned above the possibility of significant ionic bonding between Me and B, particularly for the early transition metals. However, for V, Cr, and Mn the difference in charge between metal and boron becomes smaller.‘36’ Although the influence of the reduced charge difference to some extent is counteracted by the reduced Me-B distance (see table 5), the plot of ~~~-~/(~~~+~~) in figure 4 shows an increase from 1.01 for ScB, to 1.06 for MnB,. This modest increase is of course consistent with some reduction in the strength of the Me-B bond through the series. Apart from this, figure 4 indicates that the structural ratio which most clearly correlates with the large systematic change in A,HL (see figure 3) is dMe.&2r&., which changes from 0.96 in ScB, to 1.16 in MnB,. For example, the low value of this ratio for ScB, suggests considerable strengthening of the SC-SC bonds in the boride compared to the bonds in elementary SC. For Ti, V, Cr, and Mn, on the other hand, the gradual reduction in the size of the atom, in comparison with the space generated by the boron network, gives rise both to an increasing weakening of the Me-Me bonds and to the stretching of the Me-B bonds already referred to. In fact, it seems quite possible that it is the further reduction in the size of the metal atom for Fe, Co, and Ni which prevents each of these metals from forming a stable diboride. In view of figure 4 it is not surprising that the maximum value of ArHz in the considered diboride series is found for TiB,, for which all the structural ratios in this figure fall within the narrow range 1.005 to 1.035. Even so, the enthalpy of formation of ScB,, with d,-,/2r;= 1.04 and dMc.J2r& = 0.96, is not very different. However, for the diborides from TiB, to MnB,, while there is little change in d&2& there is considerable weakening both in the Me-B and Me-Me ratios; this correlates with the dramatic reduction in -At Hk. Finally, we draw attention to the correlation between - A,Hz and the melting temperatures T,,, illustrated by figure 3. Note in particular that a maximum in both of these quantities occurs at Ti. It should be of considerable interest to explore further how the enthalpy of formation of diborides depends on atomic size for atoms even larger than SC.
THERMOCHEMISTRY
OF TRANSITION-METAL
DIBORIDES
1015
Unfortunately, there is no reliable information in the published literature which might throw light on this question. For this reason, we are planning a study of the enthalpy of formation of YB,. As far as we know Y, with 2rG = 0.362 nm, is the largest atom known to form a diboride with the AlB, structure. This investigation has been supported by NSF CHE--8320560 and has also benefited a great deal from the central facilities of The University of Chicago Materials Research Laboratory. The authors are indebted to Professor Karl Spear, who prepared the diborides used, and to Dr A. M. Davis. who carried out the chemical analyses.
REFERENCES 1. Samsonov, G. V.; Goryachev, Yu. M.; Kovenskaya, B. A. J. Less-Common Metals 1976,47. 147. 2. Akhachinskij. V. V.; Chirin, N. A. Thermodynamics of Nuclear Materials, Vol. II. Enthalpy of formation of titanium diboride. Int. Atomic Energy Agency: Vienna. 1975, pp. 467-476. 3. Brewer, L.; Haraldsen, H. J. Electrochem. Sot. 1955, 102, 399. 4. Hong, K. C.; Kleppa, 0. J. J. Chem. Thermodynamics 1978, 10, 797. 5. Kleppa, 0. J.; Sato, S. J. Chem. Thermodynamics 1982, 14. 133. 6. Sato, S.; Kleppa, 0. J. Met. Trans. 1982, 13B, 251. 7. Topor, L.; Kleppa, 0. J. J. Chem. Thermodynamics 1984, 16.993. 8. Topor, L.; Kleppa, 0. J. J. Chem. Thermodynamics 1985, 17. 109. 9. Watanabe, S.; Kleppa, 0. J. J. Chem. Thermodynamics 1983, 15. 633. 10. Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.; Kelley, K. E.; Wagman, D. C. Selected Values of the Thermodynamic Properties of the Elements. ASM: Metals Park, OH. 1973, p. 154. 11. Niessen, A. K.; De Boer, F. R. J. Less-Common Metals 1981, 82. 75. 12. Lowell, C. E.; Williams, W. S. Rev. Sci. Instr. 1961, 32, 1120. 13. Epel’baum, W. A.; Starostina, M. L. Bor Trudy Konf Khim. Bora i Ego Soedinenii lW,97-101. 14. Kirpichev, E. P.; Rubtsov, Yu. J.; Sorokina, T. V.; Prokudina, V. K. Zhur. Fizicheskoi Chim. 1979, 53, 1980. 15. Huber, E. J., Jr. J. Chem. Eng. Data 1966, 77, 430. 16. Spear, K. E.; Schafer, H.; Gilles, P. W. Thermodynamics of Vanadium Borides, High Temperature Technology. Butterworths: London. 1969, p. 201. 17. Yufiak, T. J.; Spear, K. E. Thermodynamics of Nuclear Materials, 1979. Vol. I, Thermodynamics of’ TiBz from Ti-B-N studies. lnt. Atomic Energy Agency: Vienna. 1980, pp. 73-90. 18. Thompson, R. Progress in Boron Chemistry, Vol. 2. Brotherton, R. J.; Steinberg. H.: editors. Pergamon Press: NY. 1970, p. 205. 19. Schissd, P. 0.; Williams, W. S. Bull. Am. Phys. Sot. Ser. II 1959, 4, 5 19. 20. Schis~el, P. 0.; Trulson, 0. C. J. Phys. Chem. 1%2, 66, 1492. 21. Williams, W. S. J. Phys. Chem. 1961, 65, 2213. 22. Samsonov, G. V. J. Appl. Chem. USSR 1955,28, 975. 23. JANAF Thermochemical Data. The Dow Chemical Company: Thermal Lab., Midland, Michigan, 1962, 1965.
24. Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.; Kelley, K. K. Selected Values of the Thermodynamic Properties of Binary Alloys. American Sot. of Metals: Metals Park, Ohio. 1973, D. 344. ‘5. Killer, G. M.; Lyon, T. F.; Linevsky, M. J.; De Santis, V. J. Tech. Rep. No. WADD-TR-60-646. Part IV, General Electric Co.. Evansdale, OH. 1964. 26. Greenwood, N. N.; Parish, R. V.; Thornton, P. &art. Rev. 1966, 20, 441. 21. Kiessling, R. Acta Chem. Stand. 1958, 4, 209. 28. Juretschke, H.; Steinitz, P. I. J. Phys. Chem. Sol. 1958, 4, 118. 29. Cadeville, M. G. J. Phys. Chem. Sol. 1966, 21, 667. 30. Pauling, L. Proc. Roy. Sot. (London) A 1949, 196, 343. A 1954, 224, 336. 31. Longuet-Higgins, H. C.; Roberts, M. de V. Proc. Roy. Sot. (London) 32. Lipscomb, W. N.; Britton, D. J. Chem. Phys. 1960, 33, 275.
1016
L. TOPOR
AND
0. J. KLEPPA
33. Johnson, R. W.: Daane, A. H. J. Chem. Phys. 1963, 38, 425. 34. Samsonov, G. V.; Kovenskaya, B. A. Boron und Refruc~rory Borides. Matkovich. Springer-Verlag: Berlin, Heidelberg. New York. 1977, pp. 5, 19. 35. Post, B. Boron, Metallo-Boron Compounds und Borunes. Adams, R. M.: editor. Publishers: NY. 1964, pp. 301. 313. 36. Armstrong, D. R. Theoret. Chim. Actu (Berl.) 1983, 64. 137. 37. Hoard, J. L.; Hughes, R. E. The Chemistry qf‘Boron and 1~ Compounds. Muetterties. Wiley: New York. 1967, p. 132. 38. Spear, K. E. J. Less-Common Metals 1976, 47, 195.
V. 1.: editor. Interscience
E. L.: editor.
Thermodynamics
19%5, 17, 1003-1016
Enthalpies of formation of first-row transition-metal diborides by a new calorimetric method LETITIA TOPOR and 0. J. KLEPPA The JamesFranck Institute and The Departmentof Chemistry, The University of Chicago,Chicago,Illinois 60637,U.S.A. (Received29 January 1985) The standard enthalpies of formation of the diborides of SC, Ti, and V have been determined calorimetrically at (1400&2) K. Each of these borides was dropped together with solid (platinum or palladium + boron) from room temperature into the calorimeter to generate liquid alloys (platinum or palladium + scandium or titanium or vanadium + boron). In separate experiments alloys of the same composition were formed by dropping the elements. The following values of ArHi are reported: ScB,, -(307.0& 14.8) kJ.mol-‘; TiB,, -(328.4* 10.2) kJ.mol-‘; VB,.,,,, -(206.9& 12.2) kJ.mol-‘. The results are compared with earlier literature values where they exist. However, for ScB, there are no earlier values and for VBs only equilibrium values. The systematic variation of the enthalpy of formation of the diborides from ScB, to MnB, is discussed in relation to the structural parameters and to the change in Me-Me, B-B, and Me-B bonding.
1. Introduction The borides formed by the transition elements form a group of compounds of considerable theoretical and practical interest. It is known, for example, that a change in the number of d-electrons in the transition metal correlates with changes in the boron-metal structures and with changes in the physical and thermodynamic properties of the compounds. (‘) Many of the transition-metal borides find applications in high-temperature technology. This is due to their refractory character, chemical inertness, hardness, and high electrical and thermal conductivity. There is little reliable thermochemical information on the transition-metal borides. This is related to the fact that combustion calorimetry of refractory borides, both in oxygen and fluorine gas, is associated with many experimental difficulties. Because of their chemical inertness, refractory borides cannot be studied by conventional solution calorimetry. In some cases the enthalpy of formation of the boride (e.g. TiBJ has been determined by direct reaction between metal and boron in a calorimeter.‘*’ However, even for reactions which are very exothermic, this method always leaves questions about the completeness of the (solid + solid) reaction, and about corrections which may have to be applied for possible side reactions. 0021-%14/85/l 6’1
11003 + 14 gO2.00/0
0 1985 Academic Press Inc. (London) Limited
L. TOPOR AND 0. J. KLEPPA
1004
For a number of transition-metal borides the only thermochemical quantitites available have been derived indirectly from equilibrium measurements. An important early example of this approach is the work of Brewer and Haraldsen,‘-l) who studied equilibria between borides, nitrides, and nitrogen gas at very high temperatures. In this way they were able to derive semi-quantitative thermodynamic information on a number of important boride phases. In other studies, thermochemical values have been derived from the equilibrium vapor pressures of the borides and of their constituent atoms. During the past several years we have in this laboratory attempted to find hightemperature calorimetric methods suitable for determining the enthalpies of formation of refractory borides. Initially we obtained such results by hightemperature solution calorimetry, using liquid Mn,,,Ni,,,,‘4’ and pure liquid as the calorimetric solvents. (5.6) In these studies we succeeded in q-w-, determining the formation enthalpies of borides of Mnc5’ Fe, Co, and Ni.(6) Unfortunately this method does not work for most early-transition-metal borides. Very recently we have developed a new high-temperature calorimetric method for thermochemical studies of refractory borides. This method is based on the fact that (platinum or palladium + boron) form low-melting liquid alloys (see phase diagrams in figure l), which also can dissolve a certain amount of a third element. So far we have used this approach to determine the enthalpies of formation of LaB6,(‘) and CrB,,@) two compounds for which no calorimetric enthalpies of formation were available.
/ 1
,/’ / 1’ ,’
1073
.
Pd + Pd,B
1073
673 j2731 ?-i-i-i/i Pd 0.2
110
Pd+,&, ' ' ' 1 ' ' 0.4 0.6 0.8 x
---_-------Pt,B + u-B
B
673
Pt
0.2
0.4
0.6
0.8
B
X
FIGURE 1. Equilibrium phase diagrams for (platinum + boron) and (palladium + boron). (From: Moffatt, W. G. Handbook of Binary Phase Diagrams. General Electric Company: Schenectady, NY. lWlLQAd\ _/I”
-.,
THERMOCHEMISTRY
OF TRANSITION-METAL
1005
DIBORIDES
The principle of the new method, as in solution calorimetry, is based on a simple the~odynamic cycle, which we illustrate for the special case of CrB, and Pt: O.l3CrB,(cr, O.l3Cr(cr,
T1)+0.61Pt(cr,
T,)+0.26B(cr,
7”) = Pt,.,,B,.,,Cr,.,,(i,
T1)+0.61Pt(cr,
T2).
T1) = Pt,,,,B0,26Cr0,,3(f,
(1) T,).
(2)
From equations (1) and (2) we get: O.lSCr(cr, T1) + 0.26B(cr, T1) = O.l3CrB,(cr,
?;).
(3)
For Ii = 298.15 K we have ArHk(CrB,)
= ~A~~~(2)-A~~~(l)~/O.l3.
(4)
In liquid-metal solution calorimetry, the compound, and separately its constituent elements, are dissolved in a liquid metal solvent to form an alloy of the same composition. In our new method two solids, which melt at very high temperatures (e.g. CrB,, Tfus= 2473 K; Pt, 7& = 2042 K) generate a liquid alloy in the calorimeter at T, x 1400 K, equation (1). In other experiments an alloy of the same composition is formed at the same temperature from the solid elements, equation (2). The enthalpy of formation is calculated from equation (4). Note that the effects which we measure in the calorimeter are the enthalpies of mixing of two or three solids to form a liquid alloy at calorimeter temperature. Thus the method is not a dissolution method, but a mixing method. Usually we mix the refractory boride with platinum (or palladium) in the initial experiment and thus generate the first amount of liquid alloy. However, the presence of this liquid in the calorimeter is not essential for later experiments, although to some extent it facilitates the mixing process by enhancing the reaction rate. In subsequent experiments we add (boride + platinum) to duplicate the first experiment or, alternatively, (boron + platinum + the third element) in the same mole ratio to keep the liquid-alloy composition unchanged. In the present investigation we report on the use of this method to determine the enthalpies of formation of the diborides of the early first-row transition elements: ScB,, TiB,, and VB,.
2. Ex~~rn~nta~ The calorimetric experiments were carried out at (1400 F 2) K using a Calvet-type microcalorimeter which has previously been operated successfully at temperatures up to 1500 K. The principal features of this equipment were described recently.“-” The measurements were performed in a zirconium-gettered argon atmosphere using a boron-nitride crucible in a manner very similar to that previously described for CrB,.@) (See also figure 2.) It was possible to stir the contents of the crucible by means of a hollow boron-nitride stirrer attached to the end of a 1 m long fusedquartz manipulation tube of 7 mm o.d. All samples were dropped into the calorimeter from room temperature through the central bore of this tube. The platinum and palladium metals were of reference grade (99.99 mass per cent
1006
L. TOPOR AND 0. J. KLEPPA Sample
Silica
Stainless-steel
Zirconium
Boron nitride stirrer and crucible Alloy Alumina Kaowool
c---22 mmFIGURE 2. Schematic diagrams of fused-silica liner with calorimetric cell.
Pt, Pd) purchased from Engelhard as 1 mm or 2 mm wire, and as 0.025 mm foil. Before use the platinum and palladium foils were annealed overnight in an inert atmosphere at 1100 K. The boron sample consisted of a crystalline powder, 60 mesh, of the P-rhombohedral form with 99.7 mass per cent of B. Titanium and vanadium were in the form of 6.2 to 6.4 mm rods, of purity: Ti, 99.98 mass per cent; V, 99.5 mass per cent. These materials were purchased from Alfa Products/Ventron. The scandium metal was of distilled quality in the form of 1 to 3 g lumps from Atomergic Chemmetals. Chemical analysis showed 99.5 mass per cent of SC, the principal impurity being about 0.5 mass per cent of Ta. Prior to their use in the calorimeter the Ti and V rods were machined on a lathe to produce very fine chips about 0.02 mm thick. The Sc lumps were reduced to a fine powder by a file, and iron contamination was removed from the powder by a small magnet. The samples of ScB,, TiB,, and VB, were kindly furnished by Professor K. E. Spear of Pennsylvania State University. These compounds had been prepared by
THERMOCHEMISTRY
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1007
DIBORIDES
repeated arc-melting of stoichiometric amounts of high-putty materials; we had available small boride “buttons” of total mass 3 to 5 g. These buttons were crushed in our laboratory, first into a coarse powder in a “diamond” mortar, and then in an agate mortar. Before their use in the calorimeter the powders were sifted through 100 mesh sieves. X-ray and s.e.m. examination showed that the samples of ScB, and TiBz consisted of single-phase material, while “VB,” showed two phases: a major phase VB, and a secondary phase V,B,. Chemical analysis by a.a.s. showed that within experimental error ScB, and TiB, were stoichiometric in composition. while “VB,” had the composition VB1.925f0,010. Before each series of experiments the silica liner was flushed for about 2 h with purified argon. It was then inserted into the calorimeter where it was kept overnight. Calibration was achieved by dropping small pieces of 3 mm diameter high-Puritan copper rod into the calorimeter from room temperature. A 1 per cent correction was applied for the heat pick-up of the copper samples during their drop into the calorimeter. Within a single series of measurements the calibrations were reproducible to f 1 per cent. The enthalpy of pure copper at 1400 K was taken from Hultgren et .l.:(r”’ 44083 J. mol- I. The calorimetric samples, either of (platinum or palladium + scandium diborate or titanium diborate or vanadium diboride + boron), or of the equivalent amounts of (platinum or palladium + scandium or titanium or vanadium + boron), were dropped from room temperature in the form of small cylindrical capsules prepared from Pt or Pd foil. We found that the liquid-alloy composition which we adopted in our recent study of CrB, (see Introduction above) did not dissolve ScB,, TiB,, or VB,,,,,. For these borides we reduced the mole fraction x(Me) of the metal to 0.06, and made use of mole fractions of boron, x(B) = 0.23 (for SC and V) and x(B) = 0.25 (for Ti). The actual choice of the most suitable value of x(B) initially was based on an analysis of the (platinum + boron) and (palladium + boron) phase diagrams (figure 1); following this, we tested different alloy compositions in the calorimeter so as to make sure that the assumed reactions were in fact complete.
3. Results The chemical reaction which occurs when a sample of (platinum + metal diboride + boron) is dropped from room tem~rature (Z’r x 298 K) into the calorimeter (T, x 1400 K) may be written: 0.7lPt(cr,
T,)+O.O6MeB,(cr,
T,)+O.llB(cr,
TI) = Pt,,,,B,.,,Me,.,,(l,
T2).
(5)
In this equation we have arbitrarily set x(B) = 0.23. The reaction which occurs when an equivalent sample of (platinum + metal + boron) is dropped is: 0.71Pt(cr, TI)+0.23B(cr, Combining
1;)+0.06Me(cr,
7”) = Pt,.,,B,.,,Me,,,,(l,
7’,).
(6)
equations (5) and (6) we get O.O6Me{cr, ‘&) + O.l2B(cr,
TI) = OL%MeB,(cr,
7;),
f7l
1008
L. TOPOR AND 0. J. KLEPPA
TABLE 1. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy Pt,.,,B,.,,%,, at WWk2) K
n(Pt)
Expt no.
mm01
1-l l-2 1-3 l-4 1-5 l-6 l-7 2-1 2-2 2-3 2-4 2-5 2-6
4.6355 4.6030 4.7083 4.6445 4.6714 4.5781 4.6644 4.6819 4.7262 4.7130 4.6201 4.6550 4.5324
n(ScB,)+n(B) mmol
n(Sc) + n(B)
0.3917-tO.7182 0.3889+0.7!33 0.3978 + 0.7296 0.3924+~.7~97 0.3947~0.7238 0.3868 +0.7094 0.3943 co.7234 0.3956+ 1.5166 0.3994+ 1.5310 0.3982 + 1.5267 0.3904+ 1.4966 0.3933 + 1.5079 0.3914+ 1.5006
A,H&/(kJ.mol-t)
= ((37.4&4.8)-(344.4+
A&W
AH,,0
J
kJ.mol-’
128.5 125.4 137.1 139.9 139.2 138.7 137.1 15.1 13.6 18.2 12.9 15.S 13.4 Mean:
~.AfLW
kJ.mol-’
328.1 322.4 344.6 356.5 352.7 358.6 347.7
344.4+ 14.0
14.0)) = -(307.0+
38.2 34.1 45.7 33.0 39.4 34.2 37.4k4.8
14.8)
and also Ar~~(MeB~) where A,&(6)
and A,H,(5)
= W%,,(6) - W&,(3,
(8)
both refer to a reaction which involves 1 MeB,.
TABLE 2. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy %6,Bo,2,Ti,,,6 at (1400 f 2) K Expt no.
WV mm01
n(TiB,) -t n(B)
l-l l-2 l-3 1-4 i-5 l-6 l-7 l-8 l-9 l-10 2-l 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9
4.3006 4.2908 4.1947 4.2621 4.2947 4.1997 4.3837 4.3488 4.3828 4.3180 4.2712 4.3012 4.3818 4.1622 4.2719 4.1694 4.1710 4.1732 4.4031
0.3740+0.8102 0.3731+0.8085 0.3648 + 0.7902 0.37~+0.8031 0.3735 +0.8090 0.3652+0.7912 0.3812+0.8259 0.3782+0.8192 0.3811+0.8258 0.3755+0.8135
mm01
A&/(kJ~mol-‘)
n(Ti) + n(B) mm01
0.3714+ 0.3740+ 0.3810+ 0.3619+ 0.3715+ 0.3626+ 0.3627+ 0.3629+ 0.3829 f
1.5475 1.5584 1.5876 1.5080 1.5478 1.5107 1.5112 1.5120 1S953
= {(13X6*5.6)-(472.0&
AH,, J
- W,(5) kJ. mol- ’
169.02 451.9 173.84 465.9 179.20 491.2 165.83 447.5 181.33 485.5 173.37 474.7 170.94 448.4 184.01 486.5 185.59 487.0 180.73 481.3 49.12 51.81 47.92 49.47 51.28 50.55 51.17 51.14 49.05 Mean: 472.0* 17.3 17.3)f = -(336.4& 18.2)
W,,(6) kJ.mol-’
132.3 138.5 125.8 136.7 138.0 139.4 141.1 140.9 128.1 t35.6f5.6
THERMOCHEMISTRY
OF TRANSITION-METAL
1009
DIBORIDES
TABLE 3. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy Pd0.69B0.25Ti0.06 at (1400+2) K Expt no.
4W mm01
n(TiB,) + n(B) mmol
I-1 I -2 l--3 I.-4 l-5 1 -6 2--l 2--2 2 -3 2--4 2-5 2-b
3.9722 5.6513 5.2941 4.1291 3.9131 4.0785 3.8167 4.0517 3.8289 4.1056 3.9930 3.8934
0.3454+0.7484 0.4914+ 1.0648 0.4604 + 0.9976 0.3591+0.7781 0.3455 + 0.7487 0.3547-tO.7683
n(Ti) + n(B) -~ mm01
AH&, J
@n(5) kJ,mol-’ --_____ -_-.-468.2 486.5 470.4 468.1 451.2 482.7
un(6) kJ.mol-’ _._-.- . -
161.70 239.06 216.57 168.10 155.89 171.22 0.3319+1.3829 53.86 0.3523 + 1.4680 52.20 54.57 0.3330+ 1.3873 0.3570+ 1.4876 54.20 0.3472 + 1.4467 51.96 0.3386+ 1.4107 51.96 Mean: 471.2k 12.5 &Hy(kJ.mol-‘) = {(154.9+6.6)-(471.2k12.5)) = -(316.3+14.1) Weighted mean value: A,Hd(kJ.mol-*) = {( -316.3 x6)+(-336.4~9))/15 = -(328.4+
162.3 148.2 163.9 151.8 149.7 153.5 --_-154.916.b 10.2)
Our experimental results are summarized in tables 1 to 4. Table 1 gives the new results for ScB,, which we studied using (platinum + boron) as the calorimetric medium. Tables 2 and 3 give similar results for TiB,, based on measurements both with (platinum -I- boron) and (palladium + boron), and table 4 lists results for VB 1.925 using (palladium + boron). Decisions regarding the choice of alloy were based on a series of preliminary experiments with different compositions of (platinum + boron) and (palladium + boron): while we had satisfactory TABLE 4. Enthalpy changes according to equations (5) and (6) leading to the formation of the liquid alloy P4,,714Bo,226Vo.06 at (lmk2) K Expt
n(W)
110.
mmol
mm01
l-1 t-2 1-3 1-4 I-5 1-b l-7 2-1 2-2 2-3 24 2-S
6.5305 5.7166 5.5974 5.6252 5.7117 5.6118 5.6546 5.6543 5.4859 5.3980 5.6915 5.1137
0.5488 + 1.0107 0.48~+0.88~ 0.4704 + 0.8662 0.4727 +0.8706 0.4800+0.8839 0.4716+0.8685 0.4752 +0.8750
4W.,,,)+n(B)
ArH~(kJ.mol-‘)
n(V)+ NW mm01
0.4152 4 1.7897 0.4610+1.7364 0.4536 + 1.7068 0.4783+ 1.8015 0.4381+ 1.6503 = {(266.4&8.0)-(473.3*9.2)}
Wes W,,(5) _____ J kJ.mot-’ _- _ -...-_~----261.08 475.7 230.00 478.8 216.34 459.9 222.23 470.1 234.62 488.8 223.10 473.1 221.90 467.0 123.18 124.67 120.76 132.86 113.28 Mean: 473.3k9.2 = -(206.9+ 12.2)
~A%(6) kJ.mol-’
259.2 270.4 266.2 277.8 258.6 266.4k8.0
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L. TOPOR AND 0. J. KLEPPA
dissolution of the TiB, samples both in (platinum + boron) and (palladium + boron), we had difficulties with ScB, in (palladium + boron). We carried out satisfactory preliminary experiments with V both in (platinum + boron) and in (paliadium + boron), but settled for carrying out the final experiments with (palladium + boron) because of the lower expense. At the bottom of each of the four tables we give the calculated averages of A,H,(5) and A,H,(6) with their standard deviations 6, and S,. Using equation (8) we then calculated A,Hm for ScB,, TiB,, and VB,,,,,. The listed uncertainties in these standard enthalpies of formation were calculated from 6 = (sf + isi)1/‘. In our experiments with ScB, we found A,Hk = -(307.0$- 14.8) kJ. mol-‘. Our measurements yielded two different values of A,H= for TiB,, namely -(336.4f 18.2) kJ *mol-’ obtained from the 9 experiments with (platinum + boron) and -(316.3f 14.0) kJ* mol-’ from the 6 experiments with (palladium + boron). By assigning a weight of 9 to the former average, and a weight of 6 to the latter, we arrive at an overall mean value of ArHk(TiB,) of -(328.4f 10.2) kJ . mol-‘; the stated error limits represent the standard deviation of the mean. From the experiments with VBI,,,, we found A,JY~(VB,,~~~) = -(206.9* 12.2) kJ * mol-i. If, for simplicity, we assume that A,wm varies linearly with the boron content of the boride, we estimate A,Hi(VB,) to be -(206.9x 2.~)/ 1.925 kJ.moi-’ = -215.0 kJ,mol-‘. In figure 3 we present our values for the standard enthalpies of formation of the diborides of SC, Ti, V, Cr. and Mn, along with the other experimental and predicted
I T I I I ScBz Ti& VB2 CrBz MnB2 FIGURE 3. Standard enthalpies of formation A&, and melting temperatures 7&, for ScB,, TiB,, VB,, CrB,, and MnB,. 0, Our values; 0, other calorimetric values: a, reference 12; b, reference 13; c, reference 14; d, reference 2; e, reference 15; A, equilibrium values: TiB2 and CrB2, reference 3, VB2, reference 16; x , predicted values, reference 11. 0, Melting temperatures.
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values.‘“’ For the first three borides the values shown were determined in the present work; for CrB, the given value was taken from a recent publication where we adopted the same experimental approach,@’ while for MnB, we accepted the preliminary value of the enthalpy of formation determined by solution calorimetry in liquid copper and reported in a previous publication from this laboratory.‘6’ Figure 3 also shows the reported melting temperatures for the considered diborides taken from the published phase diagrams.
4. Comparison with earlier results As far as we know, there are no thermochemical values in the literature for the enthalpy of formation of ScB,. Among the other diborides studied in the present work, TiB, has been investigated quite extensively in the past. However, the values of the enthalpy of formation quoted in the literature differ a great deal,‘17, **’ ranging from - 133.9 kJ . mol-1,‘19’ to - 323.8 kJ . mol-‘.“5’ Different techniques have been used: all the calorimetric values are presented in figure 3. In addition. vapor-pressure studies using mass spectrometry have reported values of ArHk of measurements -217.6 kJ.mol-‘,(20’ and - 133.9 kJ . mol- ‘;(19) equilibrium involving TiB, yielded -297.1 kJ.mol-‘,(3’ and -276.1 kJ.mol-‘,‘21’ while reduction of TiO, gave - 293.0 kJ . mol- ’ .(22) Clearly, there is a lack of agreement even among values obtained by the same experimental method. The enthalpies of formation of TiB, listed in the JANAF Thermochemical 16.7) kJ*mol-’ and Tables’23’ and in Hultgren et ~1.‘~~’ are -(279Sf -(279.7&11.3) kJ.mol-‘, respectively The former value was based on an assessment of four different studies, (13*20*21*25) while the latter was based on a single experimental investigation.” 3, Our value, -(328.4+10.2) kJ.mol-‘, is in reasonable agreement with the recent result of Akhachinskij and Chirin:‘2’ A,Hm(TiB 2.056) = -(318.57 + 3.55) kJ . mol-‘, obtained by direct-reaction calorimetry, with the value of Huber,(‘5) -(323.8&3.7) kJ .mol-‘, from oxygen bomb calorimetry, and with the second-law value, -(315.1+ 17.6) kJ.mol-‘. recently derived by Yurick and Spear (r 7’ from equilibrium investigations of (titanium + boron + nitrogen). We consider these three values to be the most reliable ones. Even so, it should be noted that they differ considerably from those tabulated by JANAF and by Hultgren et aL’23,24) and also from a number of other calorimetric values (see figure 3). For VB, the only value reported for the enthalpy of formation has been derived indirectly from a mass-spectrometric study of the enthalpy of vaporization of VB,. Second- and third-law evaluations of these results yielded ArHm = -(214.6+ 15.1) kJ*mol-’ and = -(222.2f 15.9) kJ.mol-‘, respectively. (16) A more precise value, -(203.8+ 10.0) kJ. mol-‘, was reported in the same publication from equilibrium studies of (vanadium + boron + nitrogen).(16) While there are no calorimetric values in the literature for VB, and CrB,, figure 3 shows that there is a good agreement between our calorimetric values for these two diborides and the earlier equilibrium studies.
L. TOPOK AND 0. J. KLEPPA
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5. Discussion Boron combines with most metals and forms a series of binary compounds which range in composition from Me,B to MeB,, and possibly even to MeB,,.“**” While no one metal has the whole range of compounds, there are several which have as many as six or seven distinct boride phases (r.g. Cr, Mn, Re). Two conflicting points of view have been advanced regarding the electronic structure and chemical bonding in transition-metal borides. In some studies it has been assumed that there is electron transfer from boron to the meta1,‘27-29’ while in others it is argued that charge transfer is in the opposite direction.‘30-35’ Recent theoretical studies, as well as discussions based on the important structural parameters, support the view, which now seems to be fairly generally accepted, that in metal-rich borides (from Me,B up to but not including MeB,) there is a transfer of electrons from boron to the metal. On the other hand, in borides rich in boron (from MeB, up to MeB,,) electron transfer is in the opposite direction from the metal to the boron framework. This correlates with the fact that boron-rich compounds are common among the rare earths and early transition metals, but that such borides are rare among the more electronegative late transition metals. Among the first-row transition metals the first five members: SC, Ti, V, Cr, and Mn form diborides while Fe, Co, and Ni do not. Kiessling’27’ made an important contribution to the elucidation of metal-boride structures. He pointed out the tendency of the boron atom to form an increasing number of boron-boron bonds with increasing boron content in the compound. In lower borides (Me,B to Me,B) the boron atoms are isolated. As the boron-to-metal ratio increases, the boron atoms link up with other borons to form chains (single chains in MeB and double chains in Me,B,), two-dimensional networks (MeB, and Me,B,), and three-dimensional boron frameworks (MeB,, MeB,, Metz, and MeB,,).‘35’ Most metal diborides have the AIB, structure, in which the metal and boron atoms are arranged in alternative planar hexagonal layers, with graphite-like boron layers separated by close-packed layers of the metal. If two electrons are transferred from the metal atoms to the boron network, the boron layers become isoelectronic with carbon in graphite. Recent theoretical work’36’ suggests that this may indeed be a reasonable description of the charge structure in the diborides of the early
TABLE 5. Interatomic distances in MeB, borides LI Boride
c/a
cfnm
a/rim
2rhJnm
ScB, TiB, VB, CrB, MnB,
0.1118 0.1064 0.1020 0.1030 0.1010
0.3517 0.3228 0.3050 0.3066 0.3037
0.3146 0.3028 0.2991 0.2969 0.3007
0.328 0.293 0.273 0.260 0.258
a From reference 37.
d&nm 0.1816 0.1748 0.1727 0.1714 0.1736
4dnm 0.253 0.238 0.230 0.230 0.231
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transition metals SC and Ti; however, for V, and particularly for Cr and Mn, the charge transfer undoubtedly is much less extensive. We present in table 5 a summary of the important structural parameters for the five diborides considered in the present work. 137)Apart from the lattice parameters (I and c, this table also gives the values of the interatomic separations d,, and dr+,; note that dMeeMe= a. Also included in this table are the values of 2ti,, i.e. the accepted atomic diameters of the five pure metals. In order to gain some insight about how the interatomic distances in the compounds change among the members of the studied family, we give in figure 4 plots which show the three ratios dMceMc/2t&, d,_$2r& and dMe-B/(r& + t-g) for the borides from ScB, to MnB,. These ratios illustrate how the observed interatomic distances relate to corresponding distances in a reference structure, which is either the pure elements (Me, B) or a hy~thetical boride in which the metal-boron separation is equal to the sum of the (metal + boron) radii. In analyzing this figure we shall adopt a point of view previously advanced by Spear,‘38) who in a recent publication related the capability of different metals to form diborides to their ability to deform so as to fit into the AlB, structure. Note that when the ratios plotted in figure 4 are about 1.00, that indicates little distortion compared with the adopted reference structure; values larger than 1.00 imply a stretched (and weakened) bond, while values less than 1.00 indicate a compressed (and strengthened) bond. In considering the significance of this graph, it should of
FIGURE
A, &-&G;
4. Structural x , d,,$(&+ri).
parameters for the diborides of SC, Ti, rg has been set equal to 0.087 nm.
V, Cr,
and
Mn. 0,
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course also be kept in mind that there is significant coupling between the plotted ratios: for example, in the diborides of metals with large atoms, the increase in the u-axis of the hexagonal structure is inhibited by the graphitic boron layers. As a result, the B-B bonds stretch while the Me-Me distances are compressed so as to fit the structure. In such a case it is believed that the stability of the diboride in the main will arise from the Me-Me and Me-B bonds, with only little contribution from the B-B bonds. On the other hand, if the metal atom is small for the available space, the Me-Me separation a in the boride will be determined mainly by the B-B contacts. Hence, the stability of the diboride should arise mostly from the B-B and Me-B bonds. Note that among the quantities plotted in figure 4 the ratio dBmB/27$shows only little variation from Ti to Mn; all the values fall within f0.016 of 1.00. However, for ScB, this ratio is 1.04. This reflects the fact that SC is a fairly large atom which causes a significant stretching of the B-B bonds with a corresponding compression of the Me-Me bonds. We mentioned above the possibility of significant ionic bonding between Me and B, particularly for the early transition metals. However, for V, Cr, and Mn the difference in charge between metal and boron becomes smaller.‘36’ Although the influence of the reduced charge difference to some extent is counteracted by the reduced Me-B distance (see table 5), the plot of ~~~-~/(~~~+~~) in figure 4 shows an increase from 1.01 for ScB, to 1.06 for MnB,. This modest increase is of course consistent with some reduction in the strength of the Me-B bond through the series. Apart from this, figure 4 indicates that the structural ratio which most clearly correlates with the large systematic change in A,HL (see figure 3) is dMe.&2r&., which changes from 0.96 in ScB, to 1.16 in MnB,. For example, the low value of this ratio for ScB, suggests considerable strengthening of the SC-SC bonds in the boride compared to the bonds in elementary SC. For Ti, V, Cr, and Mn, on the other hand, the gradual reduction in the size of the atom, in comparison with the space generated by the boron network, gives rise both to an increasing weakening of the Me-Me bonds and to the stretching of the Me-B bonds already referred to. In fact, it seems quite possible that it is the further reduction in the size of the metal atom for Fe, Co, and Ni which prevents each of these metals from forming a stable diboride. In view of figure 4 it is not surprising that the maximum value of ArHz in the considered diboride series is found for TiB,, for which all the structural ratios in this figure fall within the narrow range 1.005 to 1.035. Even so, the enthalpy of formation of ScB,, with d,-,/2r;= 1.04 and dMc.J2r& = 0.96, is not very different. However, for the diborides from TiB, to MnB,, while there is little change in d&2& there is considerable weakening both in the Me-B and Me-Me ratios; this correlates with the dramatic reduction in -At Hk. Finally, we draw attention to the correlation between - A,Hz and the melting temperatures T,,, illustrated by figure 3. Note in particular that a maximum in both of these quantities occurs at Ti. It should be of considerable interest to explore further how the enthalpy of formation of diborides depends on atomic size for atoms even larger than SC.
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Unfortunately, there is no reliable information in the published literature which might throw light on this question. For this reason, we are planning a study of the enthalpy of formation of YB,. As far as we know Y, with 2rG = 0.362 nm, is the largest atom known to form a diboride with the AlB, structure. This investigation has been supported by NSF CHE--8320560 and has also benefited a great deal from the central facilities of The University of Chicago Materials Research Laboratory. The authors are indebted to Professor Karl Spear, who prepared the diborides used, and to Dr A. M. Davis. who carried out the chemical analyses.
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V. 1.: editor. Interscience
E. L.: editor.