Oxide Additivity Rule Research Articles

Lattice Energy Determination for Polycrystalline Oxide Ceramics and Single-Crystalline Counterparts

The compositional dependence of lattice energies for polycrystalline specimens of spinel ferrite systems, ZnxCo1−xFe2O4 (x = 0.0–0.6); slowly cooled and quenched systems of CuAlxFe2−xO4 (x = 0.0–0.6); high-energy ball milled mixed ferrite composition, Ni0.5Zn0.5Fe2O4 (0–9 h); garnet system, Y3−xFe5 + xO12 (x = 0.0–0.5); manganite perovskite system, La1−xCaxMnO3 (x = 0.0–1.0); and superconducting systems, Bi1.7−xPb0.3AlxSr2Ca2Cu3O10 (x = 0.0–0.3), Bi1.7−xPb0.3GaxSr2CaCu2O8 (x = 0.0–0.3), and Bi2Sr2CaCu2O8+0−−5 % Ag + addition has been evaluated, making use of mean sound velocity data and employing Kudriavtsev’s approach. It is found that for all the systems, lattice energy decreases, and it is explained based on the change in structural and microstructural parameters as a function of substitution. The lattice energies for single-crystalline counterparts have been computed using four different estimation models based on Kapustinskii method, molecular volume and X-ray density, connectivity indices, and chemical hardness. The observed difference between the two has been discussed in the light of grain and grain boundary contributions and presence of pores and microcracks in polycrystalline materials. A simple model suggested for lattice energy determination for complex oxide compositions based on the oxide additivity rule was found to be quite satisfactory.

Erratum to: On the Relationship Between Structural-Optical Parameters of Y3−x Fe5+x O12 Garnet Ferrites and the Oxide Additivity Rule

The optical parameters refractive index, reflectivity, optical energy band gap, molar refraction, and dielectric and electronic polarizabilities for the polycrystalline Y3−xFe5+xO12 garnet system with x = 0.0, 0.1, 0.3, and 0.5 have been determined from structural parameters. The replacement of large cation Y3+ by smaller cation Fe3+ as well as formation of Fe4+ centers created by native defects is responsible for a decrease in polarizability that followed by decreasing the molar fraction and refractive index. The higher band gap would have a low refractive index. The deviations of measured dielectric and electronic polarizabilities as determined using the Clausius–Mossotti and Lorentz–Lorenz equations from those calculated using the oxide additivity rule are believed to result from garnet structural constraints leading to the “compressed cation” effect.

Ca3WO6: a novel microwave dielectric ceramic with complex perovskite structure

Present work introduces a novel Ca3WO6 microwave dielectric ceramic with a complex perovskite structure. The Ca3WO6 ceramic was prepared by solid state reaction method and can be well densified at above 1,260 °C for 2 h in air. All the XRD patterns can be fully indexed as a single-phase monoclinic structure (space group P21/n). The sharp Raman vibration mode at 810 cm−1 suggests the long range order in the Ca3WO6 structure. The best microwave dielectric properties can be obtained in ceramic sample sintered at 1,275 °C for 2 h with a permittivity ~15.3, a Qf value ~29,200 GHz and a TCF value about −30 ppm/°C. Applying the oxide additivity rule, the calculated permittivity agrees well with the measured value. This kind of ceramic might have some potential value for microwave application for its good microwave dielectric behavior. The (Ca1/2W1/2) complex cations holding the site of Ti4+ in perovskite structure would introduce many new systems in complex perovskite compounds in the future.

Calculation of the Dielectric Properties of Temperate and Tropical Soil Minerals from Ion Polarizabilities using the Clausius–Mosotti Equation

Soil dielectric properties are commonly used to estimate soil water content, however, the relative permittivity of common soil minerals is often unknown or estimated to be 5, similar to quartz (4.6). In this study, the Clausius–Mosotti model is used to estimate mineral relative permittivity from atomic polarizability for common soil minerals. Atomic polarizabilities are used to calculate the average mineral polarizability using the oxide additivity rule. Results of these calculations are compared with measurements found in the literature for rock and mineral samples. Predictions correspond well with measurements on single crystals or obtained using the immersion method to determine relative permittivity (better than 10%). The application of this simple calculation technique allows estimates of relative permittivity to be obtained for minerals for which it is difficult to measure relative permittivity directly, such as soil clay minerals.

Phase transitions and microwave dielectric properties in the perovskite-like Ca(Al0.5Nb0.5)O3−CaTiO3 system

Phase transitions and microwave dielectric properties in the (1−x)Ca(Al0.5Nb0.5)O3–xCaTiO3 system were analyzed using x-ray and neutron powder diffraction, transmission electron microscopy, Raman spectroscopy, and dielectric measurements at microwave frequencies (2–8 GHz). Rietveld structural refinements demonstrated that both end compounds exhibit similar octahedral tilted frameworks, while in Ca(Al0.5Nb0.5)O3, tilting is superimposed onto NaCl-type ordering of Al and Nb on the B sites. Accordingly, the room-temperature structures of CaTiO3 and Ca(Al0.5Nb0.5)O3 are described by orthorhombic Pbnm and monoclinic P21/n symmetries, respectively, with similar lattice parameters, √2ac×√2ac×2ac (where ac is the lattice parameter of cubic perovskite). The (1−x)Ca(Al0.5Nb0.5)O3–xCaTiO3 system features both cation ordering and octahedral tilting phase transitions. The Ca(Al0.5Nb0.5)O3 structure remains ordered at least up to 1625 °C. However, the temperature of the order/disorder transition decreases rapidly with increasing Ti content, which correlates with a progressive increase of cation disorder in the specimens. A disordered structure is attained at x=0.5. For the “solid solutions,” the nonlinear dependence of both permittivity ε and the temperature coefficient of the resonant frequency τf on Ti content corresponds to a linear dependence of the macroscopic polarizability on composition; that is, the oxide additivity rule was closely obeyed. Therefore, this rule can be used to predict ε and τf for any intermediate composition from the permittivities and temperature coefficients of permittivity of the end compounds. A zero temperature coefficient of the resonant frequency occurs at the composition x≈0.5 with a relative permittivity of 50 and a Qf value of approximately 30 000 GHz (@4 GHz).

Concentration dependence of the dielectric constant in mixed oxides MxOyMp′Oq

The dielectric constants in mixed oxides ZrO2+Y2O3, Ta2O5+TiO2, Ta2O5+Y2O3, and ZrO2+SiO2 are examined in the context of the oxide additivity rule for molecular polarizability. The experimentally observed concentration dependence of the dielectric constant can be satisfactorily explained by taking account of effective molecular polarizability and molecular volume changes. The simple rule thus enables predictive study of the dielectric constant of oxide alloys.

Dielectric constants of BaO and melilites and the oxide additivity rule

The constant-stress free dielectric constants and dissipation factors of BaO and a series of X_2YZ_2O_7 melilites were measured at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: BaO K = 31.1 Ca_2MgSi_2O_7 K^T_a = 11.83 K^T_c = 7.97 Ca_2CoSi_2O_7 K^T_a = 12.44 K^T_c = 9.00 Ca_2ZnSi_2O_7 K^T_a = 12.03 K^T_c = 8.21 Sr_2CoSi_2O_7 K^T_a = 8.93 K^T_c = 6.87 Ba_2MgGe_2O_7:Nd,Ce = K^T_a = K^T_c= 7.51. The discrepancies between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to ɑ_D(X_2YZ_2O_7) = 2 ɑ_D(XO) + ɑ_D(YO) + 2 α_D(Z0_2) are + 13.6 to + 16.0% for Ca-containing melilites, + 6.1% for Sr_2CoSi_2O_7 and + 1.0% for Ba_(1.92)Nd_(0.04)Ce_(0.04)MgGe_2O_7. The deviations from additivity in the Ca- and Sr-melilites are believed to result from structural misfit between the alkaline earth X ion and the YZ_2O_7 layers which leads to rattling X ions.

Dielectric constants of topaz, orthoclase and scapolite and the oxide additivity rule

The dielectric constants and dissipation factors of topaz, scapolite and orthoclase were determined at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: topaz κ′a =6.61 tan δ=0.0005 κ′b =6.82 tan δ=0.0007 κ′c =6.81 tan δ=0.0007 orthoclase κ′a =4.69 tan δ=0.0007 κ′b =5.79 tan δ=0.0007 κ′c =5.63 tan δ=0.0011 κ′11 =4.72 κ′22 =5.79 κ′33 =5.76 scapolite κ′a =6.74 tan δ=0.0004 κ′c =8.51 tan δ=0.0004 The deviation (Δ) between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of ion polarizabilities according to αD (mineral)=∑αD (ions) for topaz is 2.5%. The large deviations of orthoclase and scapolite from the oxide additivity rule with δ=+7.2 and + 17.6%, respectively, are attributed to “rattling” K ions in orthoclase and “rattling” (Na,K,Ca) ions and disordered O= and Cl- ions in scapolite.

Dielectric constants of apatite, epidote, vesuvianite, and zoisite, and the oxide additivity rule

The dielectric constants and dielectric loss values of 4 Ca-containing minerals were determined at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: vesuvianitel κ′_a=9.93 tan δ=0.006 κ′_c=9.79 tan δ=0.005 vesuvianitel κ′_a=10.02 tan δ=0.002 κ′_c=9.85 tan δ=0.003 zoisite1 κ′_a =10.49 tan δ=0.0006 κ′_b =15.31 tan δ=0.0008 κ′_c=9.51 tan δ=0.0008 zoisite2 κ′_a =10.55 tan δ=0.0011 κ′_b =15.45 tan δ=0.0013 κ′_c=9.39 tan δ=0.0008 epidote κ′_(11)= 9.52 tan δ=0.0008 κ′_(22)=17.1 tan δ=0.0009 κ′_(33)= 9.37 tan δ=0.0006 fluorapatite1 κ′_a =10.48 tan δ=0.0008 κ′_c = 8.72 tan δ=0.0114 fluorapatite2 κ′_a =10.40 tan δ=0.0010 κ′_c=8.26 tan δ=0.0178 The deviation (δ) between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α_D (mineral)=∑ α_D (oxides) for vesuvianite is ∼ 0.5%. The large deviations of epidote and zoisite from the additivity rule with Δ=+ 10.1 and + 11.7%, respectively, are attributed to “rattling” Ca ions. The combined effects of both a large F thermal parameter and possible F-ion conductivity in fluorapatite are believed to be responsible for Δ=+2–3%. Although variation of oxygen polarizability with oxygen molar volume (V_o) is believed to affect the total polarizabilities, the variation of V_o in these Ca minerals is too small to observe the effect.

Dielectric constants of crystalline and amorphous spodumene, anorthite and diopside and the oxide additivity rule

The dielectric constants and dissipation factors of LiAlSi_2O_6, CaAl_2Si2O_8 and CaMgSi_2O_6 in both the crystalline (α-spodumene, anorthite, and diopside) and amorphous forms were determined at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: spodumene κ'_(11)=7.30 tan δ= 0.0007 κ′_(22)=8.463 tan δ= 0.0002 κ′_(33) =11.12 tan δ= 0.0007 anorthite κ′_a^*=5.47 tan δ= 0.0009 κ′_b^*=8.76 tan δ= 0.0010 κ′_c^*=7.19 tan δ= 0.0013 diopside κ′_(11)=9.69 tan δ= 0.0016 κ′_(22) = 7.31 tan δ= 0.0007 κ′_(33)=7.29 tan δ= 0.00019 LiAlSi_2O_6 κ′=8.07 tan δ= 0.047 amorphous CaAl_2Si_2O_8 κ′=7.50 tan δ= 0.0024 amorphous CaMgSi_2O_6 κ′=8.89 tan δ= 0.0021 amorphous The dielectric properties of a spodumene glass, progressively crystallized at different conditions, were also determined. As the crystallization temperature was increased from 720 to 920° C, κ′ increased from 6.22 to 6.44. The dissipation factor, tan δ, remained constant at 0.020. Similarly, as the crystallization time at 750° C increased from 0.5 hr to 6.0 hr, κ′ increased from 6.28 to 6.35. The deviations of the measured dielectric polarizabilities as determined from the Clausius-Mosotti equation from those calculated from the sum of oxide polarizabilities according to α_D(mineral, glass) = σ α D(oxides) are +7.4% for α-spodumene, +1.2% for diopside, and +28.0, +19.6 and +15.9% for amorphous spodumene, anorthitie and diopside compositions, respectively. Positive deviations in α-spodumene and anorthite are consistent with lower than normal apparent cation bond valence sums and are believed to be evidence for loosely bonded “rattling” Li and Ca ions. Diopside, with Ca and Mg ions having normal bond valence sums, exhibits no abnormal deviation from additivity. Larger positive deviations in amorphous SiO_2, LiAlSi_2O_6, CaAl_2Si_2O_8 and CaMgSi_2O_6 are postulated to arise from a combination of loosely bonded cations and disordered O= ions where the oxygen dielectric polarizability increased from its normal value of 2.0 A^3 in well-behaved oxides to 2.2–3.0 A_3 in the amorphous phases.

Dielectric constants and crystal structures of CaYAlO 4, CaNdAlO 4, and SrLaAlO 4, and deviations from the oxide additivity rule

The structures of CaYAlO 4, CaNdAlO 4, and SrLaAlO 4 have been refined using single-crystal X-ray diffraction data. These compounds possess the full symmetry of the K 2NiF 4 structure type, I4 mmm , with lattice parameters a = 3.6451(1) and c = 11.8743(6)Å for CaYAlO 4, a = 3.6847(3) and c = 12.124(2)Å for CaNdAlO 4, and a = 3.7564(1) and c = 12.6357(5)Å for SrLaAlO 4. Inspection of the interatomic distances reveals stretching of the AlO bond, from an average of 1.878 to 1.901 to 1.935 Å, as smaller cations (CaY) are replaced by larger cations (CaNd) and (SrLa) in the MM′ sites between the two dimensional aluminate sheets. The dielectric constants (κ′) and dielectric loss values of CaYAlO 4, CaNdAlO 4, and SrLaAlO 4 were measured at 1 MHz using a two-terminal method with empirically determined edge corrections. The results are CaYAlO 4 κ′ a = 21.44 ± .02 tan δ a = 0.0008 κ′ c = 16.12 ± .04 tan δ c = 0.0008 CaNdAlO 4 κ′ a = 19.65 ± .1 tan δ a = 0.0002 κ′ c = 17.65 ± .1 tan δ c = 0.0004 SrLaAlO 4 κ′ a = 16.81 ± .1 tan δ a = 0.0006 κ′ c = 20.02 ± .1 tan δ c = 0.0008. The deviations of measured dielectric polarizabilities, as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α D( MM′AlO 4) = α D( MO) + 0.5 α D( M′ 2O 3) + 0.5 α D(Al 2O 3), are + 1.7% for CaYAlO 4, −2.0% for CaNdAlO 4, and −5.9% for SrLaAlO 4. The deviations from additivity are believed to result from K 2NiF 4 structural constraints leading to “rattling” M and M′ ions in CaYAlO 4 and “compressed” M and M′ ions in CaNdAlO 4 and SrLaAlO 4.

Dielectric constants of YVO 4, Fe-, Ge-, and V-containing garnets, the polarizabilities of Fe 2O 3, GeO 2, and V 2O 5, and the oxide additivity rule

The dielectric constants and dissipation factors of Y 3Fe 5O 12, YVO 4, NaCa 2Mg 2V 3O 12, and a variety of Ge garnets were determined at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: Y 3Fe 5O 12 κ′ = 15.70 tan δ = 0.0009 Ca 3Ga 2Ge 3O 12 κ′ = 9.73 tan δ = 0.0007 Ca .90Y 1.88Mg 2.27Ge 3O 12 κ′ = 10.35 tan δ = 0.0006 CaY 1.96Nd .04Zn 2Ge 3O 12 κ′ = 11.32 tan δ = 0.0006 Nd 2.95Mg 1.48In .68Ga 1.54Ge 1.32O 12 κ′ = 11.86 tan δ = 0.0009 NaCa 2Mg 2V 3O 12 κ′ = 10.32 tan δ = 0.0007 YVO 4 κ a ′ = 9.68 tan δ a = 0.0010 κ c ′ = 16.59 tan δ c = 0.0278 The dielectric polarizabilities of Fe 2O 3, GeO 2, and V 2O 5 derived from the dielectric constants of the above compounds are 10.5, 5.5, and 15.8 Å 3, respectively. The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α D(mineral) = Σα D(oxides) for the above garnets is ≈0.5%.

Dielectric constants of tephroite, fayalite and olivine and the oxide additivity rule

The dielectric constants and dissipation factors of synthetic tephroite (Mn2SiO4), fayalite (Fe3SiO4) and a forsteritic olivine (Mg1.80Fe0.22SiO4) were measured at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: tephroite, κ′a= 8.79 tan δa = 0.0006 κ′b = 10.20 tan δb = 0.0006 κ′c= 8.94 tan δc= 0.0008 fayalite, gk′a = 8.80 tan δa = 0.0004 gk′b= 8.92 tan δb = 0.0018 gk′c = 8.58 tan δc = 0.0010 olivine, gk′a = 7.16 tan δa = 0.0006 gk′b = 7.61 tan δb = 0.0008 gk′c = 7.03 tan δc = 0.0006 The low dielectric constant and loss of the fayalite indicate an exceptionally low Fe3+ content. An FeO polarizability of 4.18 A3, determined from αD(FeO) = [αD (Fe2SiO4)-αD(SiO2)]/2, is probably a more reliable value for stoichiometric FeO than could be obtained from FexO where x = 0.90–0.95. The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to αD(M2M′X2) = 2αD(MX) + αD(M′X2) is ∼+2.8% for tephroite and +0.2% for olivine. The deviation from additivity in tephroite is discussed.

Dielectric constant of MgAl 2O 4 spinel and the oxide additivity rule

The dielectric constants and dielectric loss values of five natural and three synthetic spinel single crystals were determined at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: Mg 1.02Al 1.98Fe 0.01O 4 K' = 8.355 tanδ = 0.0005 Mg 1.00Al 1.98Fe 0.02O 4 k' = 8.322 tanδ = 0.0007 Mg 1.00Al 1.99Fe 0.02O 4 k' = 8.203 tanδ = 0.0007 Mg 1.01Al 1.98O 4 k' = 8.352 tanδ = 0.0005 Mg 0.97Al 2.01Fe 0.01O 4 k' = 8.302 tanδ = 0.0005 Mg 1.00Al 2.00O 4 k' = 8.325 tanδ = 0.0008 Mg 1.00Al 2.00O 4 k' = 8.176 tanδ = 0.0005 Mg 0.415Al 2.39O 4 k' = 8.572 tanδ = 0.0011 The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α D(mineral) = Σα D(oxides) for this group of spinels ranges from + 1.1 to + 3.2%, well above the agreement value of 0.5–1.0% found for well-behaved oxides. Possible reasons for these discrepancies are discussed.

Dielectric constants of yttrium and rare-earth garnets, the polarizability of gallium oxide, and the oxide additivity rule

The dielectric constants (κ′) and dielectric loss values of 10 rare-earth gallium garnets and 1 rare-earth aluminum garnet were measured at 1 MHz using a two-terminal method with empirically determined edge corrections. The results are: κ′(Dy3Al5O12)=11.07±0.05; κ′(Ho3Ga5O12) =12.38±0.05; κ′(Dy3Ga5O12)=12.36±0.06; κ′(Tb3Ga5O12) =12.40 ±0.03; κ′(Gd3Ga5O12) =12.18±0.10; κ′(Eu3Ga5O12) =12.46±0.05; κ′(Sm3Ga5O12) =12.55±0.03; κ′(Nd3Ga5O12) =12.59±0.12; κ′(Y3Sc2Ga3O12) =12.94±0.03; κ′(Sm3Sc2Ga3O12) =13.67±0.04; and κ′(La2.66Lu2.66Ga2.66O12) =14.40±0.03. The dielectric polarizability of Ga2O3 derived from the dielectric constants of these and other Ga compounds is 8.80±0.14 Å3. The agreement between measured dielectric polarizabilities as determined from the Clausius–Mosotti equation and those calculated from the sum of oxide polarizabilities according to αD(mineral) =ΣαD (oxides) for six aluminum garnets and twelve gallium garnets is ∼1%.

Dielectric constant of Y-stabilized zirconia, the polarizability of zirconia and the oxide additivity rule

The dielectric constant of the Y-stabilized zirconia, Zr .894Y .095Hf .011O 1.95, was determined to be 28.6 ± 0.2 at 1 MHz using a two-terminal method and empirically determined edge corrections. The dielectric polarizability of ZrO 2 derived from dielectric constants of several Zr compounds is 7.30 Å 3. The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α D (mineral) = Σ α D (oxide) for zircon and three Y-stabilized zirconia samples is ∼0.5%.

Dielectric constants of chrysoberyl, spinel, phenacite, and forsterite and the oxide additivity rule

The dielectric constants and dielectric loss values of BeAl2O4 (chrysoberyl), MgAl2O4 (spinel), Be2SiO4 (phenacite), and Mg2SiO4 (forsterite) were measured at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: chrysoberyl, κ′ a =9.436, κ′ b =9.071, κ′ c =8.269; spinel, κ′ a =8.18; phenacite, κ′ a =6.28, κ′ c =6.06; and forsterite, κ′ a =6.867, κ′ b =7.392, κ′ c =6.739. The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to αD(M2M′X4) = 2αD(MX)+αD(M′X2) is ~ 1.0%.

Mineral Dielectric Constants and the Oxide Additivity Rule

The 1 MBz dielectric constants of a variety of synthetic aluminate garnets: Y_3Al_5 O_(12), Ho_3Al_5 O_(12), Y_(2.93)Nd_(.07)Sc_2Al_3 O_(12) and Gd_(2.95)Nd_(.05)Sc_(1.98)Cr_(.02)Al_3 0_(12) and several silicates: CaB_2Si_2 O_8 (danburite), Ca_3Al_2Si_3 O_(12) (grossular) and Mg_2Al_4Si_5 O_(18) (cordierite) were determined using the two-terminal method with edge corrections. These data and polarizabilities derived from the published single crystal dielectric constants of simple oxides were used to compare compound polarizabilities obtained from the Clausius-Mosotti equation and the oxide additivity rule.