Bond Energies In Oxide Systems: Calculated and energies. Experimental Data Stolyarova V. L., Plotnikov E.N., Lopatin S.I. Table 1. Results of the bond energies calculation in the Institute of Silicate Chemistry BaO-TiO 2-SiO 2, CaO-TiO 2-SiO 2, Rb 2O-B2O3 and of the Russian Academy of Sciences Cs 2O-B2O3 systems. in gaseous and solid phases at the

ul. Odoevskogo 24 korp. 2, 199155 Sankt Petersburg, temperature 0 ¥ . Russia Bond energy, KJ/mol System Bond Bond energies in oxide compounds are the main Gaseous Solid factor determining structure and properties of substances. Ba-O[-Ti] 382.0 512.7 In some cases bond energies may be used as the energetic Ba-O[-Ba] 348.5 467.7 parameters in different statistical thermodynamical Ti-O[-Ba] 331.8 450.6 models. Main goal of the present study is to consider the BaO-TiO 2-SiO 2 Ti-O[-Ti] 364.7 497.6 application of the semiempirical Sanderson's method for Ba-O[-Si] 437.6 585.4 calculation of the bond energies in the BaO-TiO 2-SiO 2, Si-O[-Ba] 270.3 334.7 CaO-TiO 2-SiO 2, Rb 2O-B2O3 and Cs 2O-B2O3 systems. Si-O[-Si] 407.9 421.0 The accuracy of this calculation was compared with the Ca-O[-Ti] 377.1 500.1 data obtained by high temperature mass spectrometric Ca-O[-Ca] 322.2 486.8 method. Ca-O[-Si] 441.1 585.1 CaO-TiO -SiO The main equations in Sanderson's method used 2 2 Si-O[-Ca] 287.9 358.2 were the following. Ti-O[-Si] 418.5 574.3 Si-O[-Ti] 294.1 366.7 E=t cEc+t iEi , [1] Rb-O[-Rb] 387.9 527.6 Rb-O[-B] 768.7 988.6 Rb 2O-B2O3

where E is bond energy, t c and t i are coefficients, c and B-O[-Rb] 275.6 339.6

i are covalent and ion bond energies. Coefficients ti, t c B-O[-B] 392.0 488.3 δ δ were calculated using partial charges: t i=( A- B)/2 and B-O[-Cs] 268.4 330.1 tc=1-ti. Covalent bond energies were obtained from the Cs 2O-B2O3 Cs-O[-B] 820.0 954.7 equation: Cs-O[-Cs] 372.9 498.4

1/2 Ec= (E AA EBB ) Rc/R 0, [2] Table 2. Comparison between the calculated values of bond energies in silicon, boron, calcium, titanium, EAA is nonpolar homonuclear bond energy, R c is nonpolar rubidium and cesium oxides in gaseous phase and covalent radii sum, R o is bond length. reference data. The bond energies in the components of the gaseous phase were calculated from the equation: Bond Oxide Bond energy, KJ/mol Calculation Reference Ei=332/R o [3] data

Si–O SiO 2 408.0 315.9±10.5 The bond energies in the components of the solid phase Ca–O CaO 322.2 209.2±42.8 were calculated from the Madelung equation: B–O B O 392.0 449.1±19.2 2 3 Ti–O TiO 364.7 314.8±8.4 E =332Mk/R , [4] 2 i 0 Rb–O Rb O 388.0 232.2±83.5 2 ¡ is Madelung constant, k is repulsion coefficient. Cs–O Cs 2O 372.9 272.3±29.5 Table 1 represents the results of these calculations. Table 3. Comparison of values of bond energies in the The comparison between the data of bond gaseous RbBO 2 and CsBO 2 calculated by the Sanderson energies in the systems studied calculated taking into method and obtained by high temperature mass account the second coordination sphere and the spectrometry experimental values obtained without consideration the Energies, KJ/mol second coordination sphere are given in Table 2. There is Compound Parameter good agreement between experimental and calculated Experiment Calculation results in the frame of the accuracy about 15±2%. D(Rb-BO 2) 540 768 RbBO 2 The values of bond energies in the gaseous Davg (B–O) 641 349 RbBO 2 and CsBO 2 were also obtained by high D(Cs-BO 2) 501 820 CsBO 2 temperature mass spectrometric method using the Davg (B–O) 693 345 following equations: Present study was carried out using financial +

AE(M /MBO 2) ¢ IE(M) + D(M–BO 2); [5] support of the Russian Academy of Sciences according to +

D(M–BO 2) £ AE(M /MBO 2) – IE(M); [6] the Integrated Programme “New principals and methods

0 ¤ Davg (B-O) £ [ at H (MBO 2, gas)– D(M–BO 2)]/2, [7] of the creation of the purposeful synthesis of the substances with the required properties” on the direction where AE i is appearance energy of ion, IE i is the “New principals and methods of synthesis of inorganic ionization energy of atom, D i-i is bond dissociation substances and materials” in the frame of the project “ 0 energy, ¤ at H (MBO 2) is the atomization enthalpy of Features of the structure and energies of chemical bonds compound. Results are presented in Table 3 and of the amorphous phases in oxide systems”. compared with the calculated values of average B–O bond