Standard entropy for borides of non-transition metals, rare-earth metals and actinides

Journal

of the Less-Common

STANDARD ENTROPY METALS, RARE-EARTH

Metals,

117

(1986)

287

287

- 291

FOR BORIDES OF NON-TRANSITION METALS AND ACTINIDES*

M. S. BOROVIKOVA Institute uodskaya,

for Superhard Materials 2, Kiev-153 (U.S.S.R.)

of

the

Ukrainian

Academy

of

Sciences,

ul.Autoza-

V. V. FESENKO Kiev

Technological

Institute

of Food

Industry,

ul. Vladimirskaya,

68, Kiev-l

7 (U.S.S.R.)

Summary Using as initial data the most reliable values of standard entropy for 10 compounds, the entropies for 40 compounds of non-transition metals, rareearth metals and actinides have been evaluated by the method of comparative calculation. Taking into account the features of boride structures, two methods, i.e. additive and proportional, have been selected for the entropy calculations. For the range of borides the entropies were calculated from the linear relation of the latter to the number of boron atoms in the boride. For borides of rare-earth metals allowance has been made for magnetic contributions in conformity with the multiplicity of the corresponding ions. Insignificant differences in the electronic contributions to the entropy for borides and metals have been neglected. For dodecaborides only the additive method has been used. This is specified by the most rigid network that provides the same contribution to compound entropy.

1. Results and discussion Boron compounds and alloys in their physical, physicochemical and mechanical properties are rather promising materials for various fields of advanced technology [ 11. Thermodynamic properties of borides, however, have been insufficiently investigated; the knowledge of their thermodynamic properties is essential not only to determine their optimum working characteristics under various conditions but also for the elucidation of the direction of high temperature processes in which borides participate. For this purpose in addition to heats of formation of the borides a knowledge of their entropies is necessary. *Paper presented at the 8th International Symposium on Boron, Nitrides and Related Compounds, Tbilisi, October 8 - 12, 1984. @ Elsevier

Sequoia/Printed

Borides,

Carbides,

in The Netherlands

288 TABLE

1

Standard entropy for borides of non-transition [ 3 - 51 (in joules per mole per kelvin) Boride MgBz

MgB4 MgB 12

metals,

G98

Boride

s;98

36.81 f 0.17 51.04 + 0.25 89.52 It 0.84

LaB, NdB, GdB,

83.16 + 0.21 103.45 + 0.21 126.37 ? 0.21

rare-earth

metals

and actinides

Boride

$98

UB2 UB4 UB12 PuB2

55.13 75.29 112.94 60.65

f + + +

0.13 8.37 12.5 6.21

Considering the lack of standard entropy data published, we have endeavoured to establish the standard entropy by the method of comparative calculation [2]. Usually two methods of calculation are used for this purpose: an additive one, in which a definite entropy increment is attributed to each type of compound forming atoms, and a proportional one, in which the ratio of the same properties for the same type of substances is examined, for instance S~Jax:S~J

= S~eII~x:S,,II

(1)

The results of such calculations are largely determined by the nature of the interaction between the crystal-forming atoms and by the crystal structure. As the interrelation of non-transition metals and rare-earth metals with boron is of a more simple nature than that for transition metals, we consider borides of non-transition metals and rare-earth metals as well as borides of actinides adjoining the latter. Table 1 includes the most reliable values of standard entropy for metal borides, which we used in our calculations. When evaluating the entropy of borides it is necessary to consider the structural features of these compounds. Depending on the atomic ratio of metal to boron, atoms of the latter occupy isolated positions in the crystal lattice, form boric chains of different multiplicity or are bonded into strong networks consisting of octahedra or cube-octahedra [ 11. Typical representatives of the borides with nets made of boron atoms are the hexagonal diborides isostructural with AlB,; they include BeB*, MgB,, ScB2, YB2, DyB,, LuB,, UB2 and PUB,. The proportional method of entropy evaluation is applicable to such boride phases with relatively low boron content. In fact, comparison of Mg-U or Mg-Pu entropy relations as well as relations of their diboride entropies results (within the limits of experimental error) in similar data for each pair of relations: S,“,s(Mg)/S,O,s(U) = 0.650

S&s(MgB,)/S,“,,(UB,)

S,o,,(U)/S&,s(Pu) = 0.893

S,“,s(UB,)/S,“s(PuB,)

= 0.653 = 0.909

289

TABLE Standard

2 entropy

for

borides

of non-transition

metals,

rare-earth

metals

and actinides

in joules per mole per kelvin

Boride

S&8

BeBo.2

9.2 8.8 57.3 11.7 31.4 38.5

BeBo.5 PUB BeB2 AlB2 ScB2

+ 1.2 + 1.2 ?r 4 f 1.2 f 2.1 f 2.1

DY&

50.0 ? 2.1 82.8 + 1.7

LuB2

56.1

=‘f34

58.6 + 6.3

YB2

+ 1.2

Boride

fj&

LaB4 CeB4

75.3 89.9 92.0 96.2 89.9 96.2 75.3 79.5 36.0 60.7

fiB4

NdB4 SmB4 GdB4 ThB4 PuB4 BeB6 MtZB6

+ 6.3 +_6.3 I? 6.3 + 6.3 * 6.3 + 6.3 f 6.3 + 6.3 * 8.4 f 2.1

Boride

S&S

cd&,

65.7 79.5 90.4 67.8 97.9 101.6 97.9 104.6 83.7 87.8

SrB6 BaB6 YB6 Cd%6 PrB6

SmB6 GdBb ThB6 PuB6

+ 2.1 + 2.1 * 2.1 + 4.2 + 4.2 +-4.2 t 4.2 + 6 + 8.4 + 8.4

Boride

S&S

AlBlz ScBlz

83.7 f 8.4 96 f 13 109 + 13 130+13 138213 138 + 13 134 * 13 138 f 13 121 + 13 313 f 13

YB12 TbBn

DyBlz HoB12 ErB 12 FmB12 YbBlz LuB12

On the other hand, the boron network in the diborides has a definite rigidity. Therefore, this network is assumed to make a constant contribution to the entropy. The change in entropy in transition from one metal to another is determined by the nature of the metal. The boron contribution to the entropy can be determined from the additive formula SMeBx = Swe + “SB

(2)

where x is the number of boron gram-atoms in a gram-formula of the boride. The entropy for the pure metal rather than the increments usually recommended for substances with predominantly ionic bonds is chosen as SMe. Then for magnesium, uranium and plutonium diborides, xSB (J mol-’ K-‘) equals 3.30 ?I 0.21, 4.85 + 0.13 and 4.35 + 6.27 respectively. The difference of 1.55 J mol-’ K-’ between the diborides of magnesium and uranium, the metals being at different ends of the periodic system, is insignificant. For the calculation of the entropy of the diborides, two methods have been used: (1) comparison of standard entropies for pure metals and (2) the additive formula. The value of xSB taken for the diborides of beryllium and aluminium was the same as that for magnesium diboride, while the average value of 4.08 + 0.17 (from the diborides of magnesium and uranium) has been taken for the diborides of scandium, yttrium, dysprosium and lutetium. Results of the calculation and an evaluation of the error are given in Table 2. Beryllium unlike magnesium forms borides with isolated boron atoms, by the BeB0.2 and BeBO.,. The entropy for the latter has been determined comparative method using the entropy of BeC,., (8.16 J mol-’ K-r) while the entropy for BeBos2 has been calculated as the average value between those for pure beryllium and BeCO.s. Of the metals considered only plutonium forms a monocarbide. Entropy for this compound has been evaluated by the comparative method assuming that the entropy ratio for isostructural monoborides and monocarbides of plutonium is the same as for the diboride and the dicarbide of uranium. The entropy data for carbides have been taken from ref. 6.

290

For the majority of rare-earth metafs, non-tr~sition metals and actinides, cubic hexaborides are the most stable boride phases. Their structure is determined mostly by the network of boron atoms, influence of the metal being less significant. This may be due to the fact that the voids between the boron octahedra are sufficiently large and metal atoms (ions) arranged within them are free of significant deformation [l]. Therefore, the supposition of additive entropy for hexaborides is much more valid than for the other borides. This should be most clearly shown in hexaborides of rare-earth metals. Considering the radii of trivalent ions of these metals to be changed insign~icantly, the lattice entropy for rare-earth metal hexaborides as usual [7] can be set equai to the non-magnetic contribution (19.83 J moT’ K-‘) while the magnetic one can be evaluated as

s

magn

=

R In(W + 1)

where J is the total quantum number and R is the universal gas constant. The insignificant difference between the electronic contributions to the entropy of the borides of rare-earth metals and that of the metals can be neglected. The entropy for yttrium hexaboride has been calculated by the two methods: from eqn. (2) when xSB is the same as for LaB6 (26.27 J moI-’ K-‘) and from the entropy ratio for the metals, oxides and nitrides of lanthanum and yttrium (1.285) when setting this value equal to the ratio SLaB,/ &?B,The same approach has been used in evaluation of the entropy for hexaborides of alkali earth metals, thorium and plutonium. For the comparative method, entropy ratios for metals and hexaborides La/Ba, Y/Sr and Ca/Sr have been compared. For the hexaborides of thorium and plutonium comparison has been made using cerium and samarium which are their electronic analogs. Because the structure of MgB, is much different from that of other compounds considered, the entropy value for MgB6 was obtained both using eqn. (2) and by interpolation from the relation of this value to the number of atoms in the boride. The averaged results are given in Table 2. Tetrabo~des except for MgB4 have a hexagonal structure of the UB4 type. The entropy for these compounds has been calculated using the entropy for YB4 which is determined by interpoIation according to the linear relation of the entropy to the number of boron atoms in the YB,, YB,, YB6 series. The difference in entropy between YB,, and YB6 is (8.4 + 2.1) J mol-’ K-‘, assuming this difference for compounds of the other metals we obtamed the data given in Table 2, To evaluate the entropy for plutonium tetraboride, the difference between the entropies of UB2 and of LJB4 was assumed to be (25 f 8) J mol-’ K-‘. Of all the boron compounds dodecaborides appear to have the most rigid boron network because the structure of these compounds is strongly stabilized by a cube-octahedron made of boron atoms. Therefore, the supposition of a constant contribution to the entropy by the boron network is valid. For cahzulations according to eqn. (2)? the entropy for cubic UBll has been

291

taken because the majority of dodecaborides have the structure of this compound. For the evaluation of the entropy for tetragonal A1B12, the entropy for MgB,, has been used. The results are given in Table 2.

References 1 G. V. Samsonov, T. I. Serebryakova and V. A. Neronov, Borides, Atomizdat, Moscow, 1975 (in Russian). 2 V. A. Kireyev, Methods of Practical Calculations in Thermodynamics of Chemical Reactions, Khimiya, Moscow, 1975 (in Russian). 3 V. P. Glushko (ed.), Handbook of Thermal Constants for Materials, VINITI, Moscow, 10th edn., 1979 (in Russian). 4 S. P. Gordiyenko, V. V. Fenochka and G. Sh. Viksman, Thermodynamics of Lantanide Compounds, Naukova Dumka, Kiev, 1979 (in Russian). 5 V. P. Glushko (ed.), Handbook of Thermal Constants for Materials, VINITI, Moscow, 8th edn., 1978 (in Russian). 6 A. S. Bolgar, A. G. Turchanin and V. V. Fesenko, Thermodynamic Properties of Carbides, Naukova Dumka, Kiev, 1973 (in Russian). 7 S. P. Gordiyenko, V. V. Fenochka and V. V. Fesenko, Rare-Earth Metals and Their Refractory Compounds, Naukova Dumka, Kiev, 1971 (in Russian).