Energy Change Regularities of Crystal Lattice of Lanthanide Borohydrides

Thermodynamic characteristics of lanthanides’ borohydrides are defined by tensimetric, calorimetric and semiempirical methods. Lanthanides’ borohydride crystal energy lattice is defined by compiled Born-Haber cycle and their change regularity within the whole lanthanide’s row is determined.


Introduction
In such cases, it is difficult to identify crystal compounds stability criteria. For example, energy cycle analysis for carbide, silicide and other compounds formation process [3][4][5][6]. Small values of carborundum kJ/mole is due to big energy expenditures and atomization of silicon and carbon crystals but not due to weak binding energy in carborundum (Nat. = -1255,2 kJ/mole).

Objectives
In continuation of series of research on thermal and thermodynamic characteristics of complex hydride compounds [7][8][9][10], the present work is devoted to enthalpy formation (∆ f H 0 298 ) and crystal lattice energy (U k ) identification of complex borohydrides -Ln(BH 4 ) 3 (Ln-lanthanides) and their change regularity determination.

Material and Methods
Limited literatures are available which cover issues of crystal lattice energy determination of complex hydride compounds. Only works [11,12] where: V -number of ions in one formula unit; Z -cation or anion charge, and, r -their radius.
While making calculations by equation (1), where V=4ion numbers in one formula unit, lanthanide cations Ln radius values are used with coordination number 8, specific for studying compounds and determined according to X-ray structure investigation of lanthanide borohydride [13][14][15][16].
Unknown value for thermochemical radius of where: Ln -lanthanides; parentheses -gaseous, square brackets -solid state of substance; S -sublimation enthalpy, D -dissociation enthalpy, δ -formation enthalpy and Еsensitivity to component system's electrons.
( -calculated, -literature data).    Lanthanide borohydride enthalpy formation -atomic number diagram curve (Fig.2) is complicated with tetrad-effect development. Sharp borohydrides' enthalpy formation value increase for cerium sub-group elements is observed as far as cainosimmetric 4f orbital are filled by electrons (f 2 -f 6 ). Sharp decrease of enthalpy formation value for europium borohydride is due to partial filling of 4f orbital by one electron and considerable influence of orbital motion moments of lanthanides' ion.
For yttrium subgroup borohydrides, starting from gadolinium, symbasis, almost linear increase of enthalpy formation values for lanthanides' borohydrides is observed with increase of 4f-electrons number.
From Born-Haber cycle, U к value of lanthanide borohydride is identified by the following equations:    Figure 3 within the group. It is necessary to notice that almost rectilinear character of this diagram is obtained according to Kapustinskiy equation which assumes purely ion nature of binding and considers only lanthanides' ion cation size change.

Conclusions
Thus, obtained results allowed to reveal the following features in thermochemical characteristics change of borohydrides: a) with lanthanides atom nucleus increase charge:  sybasis change and increase of enthalpy formation values and crystal lattice energy of lanthanides borohydrides is observed;  diagrams of these curves have identical character with tetrad-effect development and with clear separation of lantanides' subgroups;  characteristics deviation for europium and ytterbium compounds from general regularities due to their partial and full fillings by 4f orbital electrons of these elements atoms, extra stability in crystal field and spin-orbital interaction of 4-f-electrons. b) K U values difference calculated by thermochemical cycle and Kapustinskiy formula indicates on certain fraction of covalent nature of chemical binding in borohydrides, by dominating character of ion binding.

c)
K U values coincidence, calculated by different methods for europium and ytterbium borohydrides indicates on purely ion character binding in compounds of these metals.