Pauling's Rule Research Articles

Investigation of the electronic, magnetic and optical properties of (Z = Si, Ge) under pressure—a density functional theory study

The structural, electronic, magnetic and optical properties of Co-based Heusler compounds, Co2CrZ (Z = Si, Ge), are studied using first-principle density functional theory. The calculations are performed within the generalized gradient approximation. Our calculated structural parameters at 0 GPa agree well with previous available results. The calculated magnetic moment agrees well with the Slater–Pauling (SP) rule. We have studied the effect of pressure on the electronic and magnetic properties of Co2CrSi and Co2CrGe. With an increase in applied pressure, a decrease in cell volume is observed. Under application of external pressure, the valence band and conduction band are shifted downward which leads to a modification of electronic structure. There exists an indirect band gap along Γ–X for both the alloys. Co2CrSi and Co2CrGe retain 100% spin polarization up to 60 and 50 GPa, respectively. The local magnetic moments of the Co and Si (Ge) atoms increase with an increase in pressure whereas the local magnetic moment of the Cr atom decreases. In addition, the optical properties such as dielectric function, absorption spectra, optical conductivity and energy loss function of these alloys have also been investigated. To our knowledge this is the first theoretical prediction of the pressure dependence of the structural, electronic, magnetic and optical properties of Co2CrSi and Co2CrGe.

Magnetic properties and phase stability of Co2Cr(Ga,Si) Heusler alloys

The phase diagram, magnetic properties and the region over which the Heusler alloys Co2Cr(Ga1−xSix) occur as a single phase have been established. A single phase was obtained in the composition range of x⩽0.5, in which the order–disorder phase transition temperature from the L21 to the B2 phase, TtL21/B2, increased almost linearly with increasing x. The value of TtL21/B2 for the L21-type Co2CrSi Heusler alloy, estimated by linear extrapolation from its concentration dependence, was about 1450K, and therefore higher than that of Co2CrAl and Co2CrGa. The Curie temperature, TC, also increased with increasing x becoming 600K at x=0.5, thus reflecting an increase in the magnetic moment caused by the change in the number of the valence electrons. The concentration dependence of the spontaneous magnetic moment, Ms, measured at 5K increased with increasing x, almost following the generalized Slater–Pauling (S.P.) rule predicted by Galanakis et al.

Electronic and magnetic properties of Co2−xFexCrAl alloys: Ab initio calculations

We performed density functional theory (DFT) calculations within the full‐potential linearized augmented plane wave (FLAPW) method to study the electronic and magnetic properties of Co2−xFexCrAl (x = 0, 0.25, 0.5, 0.75, and 1) alloys. The calculations indicate that Co2−xFexCrAl alloys are half‐metallic within the whole studied range. The local magnetic moments of Fe atoms are found to be anti‐ferromagnetically aligned with those of Cr and Co atoms. This causes a decrease of the total magnetic moments of the alloyed structures from 12 to 8 µB/cell as a function of Fe concentration obeying the Slater–Pauling rule.

ELECTRONIC STRUCTURE AND LINEAR OPTICAL PROPERTIES OF MIXED ALKALI-METAL BOROPHOSPHATES (LiK2BP2O8, Li3K2BP4O14): A FIRST-PRINCIPLES STUDY

LiK 2 BP 2 O 8 and Li 3 K 2 BP 4 O 14 are synthesized by high-temperature solution method with the same elements, while contain different fundamental building units. Li 3 K 2 BP 4 O 14 is a novel P – O – P linking structure which gives a rare example of violation of Pauling's fourth rule. The electronic structures of LiK 2 BP 2 O 8 and Li 3 K 2 BP 4 O 14 are investigated by density functional calculations. Direct gaps of 5.038 eV ( LiK 2 BP 2 O 8) and 5.487 eV ( Li 3 K 2 BP 4 O 14) are obtained. By analyzing the density of states (DOS) of LiK 2 BP 2 O 8 and Li 3 K 2 BP 4 O 14, the P – O – P linking in fundamental building units of Li 3 K 2 BP 4 O 14 crystal is proved theoretically. Based on the electronic properties, the linear optical information is captured.

Incorporation of Al in iron oxyhydroxides: implications for the structure of ferrihydrite

AbstractThe incomplete miscibility of Al into the ferrihydrite structure has been a recurring issue in understanding the environmental geochemistry of this important oxyhydroxide. During co-precipitation from acidic aqueous solution, ferrihydrite has been observed to accept only up to ∼25 at.% Al without the formation of multi-phasic Al and Fe oxyhydroxides. Using basic chemistry and crystal-chemical relationships we propose here that the saturation limit of Al substitution in the structure of Fe oxyhydroxides is controlled by Al – Al avoidance in a manner that conforms to Pauling's distortion rule. Employing this hypothesis, we show that the predicted miscibility limit for Al incorporation is 25 at.% in ferrihydrite and 33 at.% in goethite, in agreement with previous observations. These results indicate that the classical f-phase model for ferrihydrite best represents observations. Incorrect assignment of Fe site occupancy and other shortcomings of the akdalaite/tohdite model for ferrihydrite are also discussed.

Disorder and weak localization effects in Co2MnxTi1−xAl Heusler alloy thin films

The effects of disorder on the structural, magnetic and transport properties of stoichiometric Co2MnxTi1−xAl (0 ⩽ x ⩽ 1) thin films are reported. All the compositions exhibited B2-type structure with the actual composition of each film, as determined by Rutherford backscattering spectroscopy (RBS), being close to the nominal value. The values of saturation magnetization increase with increasing Mn content in the films and are in general agreement with the values obtained using the Slater–Pauling rule and the actual (RBS determined) compositions. Electrical resistivity as a function of temperature shows a change from metallic-type behaviour for x ⩽ 0.25 to a semiconducting type for x > 0.25. At lower temperatures (T < 25 K) metallic compositions show the presence of a resistivity minimum. The resistivity behaviour above low T upturn in metallic compositions follows a T2 dependence that is explained in terms of electron–electron scattering and one-magnon scattering. The presence of a resistivity minimum and the crossover from metallic to semiconducting type resistivity are explained in terms of localization effects originating mainly in the Co antisite disorder in these alloy films.

Cation Disordering by Rapid Crystal Growth in Olivine-Phosphate Nanocrystals

On the basis of Pauling's first rule for ionic bonding, the coordination number of cations with oxygen anions can be determined by comparison of their relative ionic size ratio. In contrast to simple oxides, various site occupancies by multicomponent cations with similar sizes usually occur in complex oxides, resulting in distinct physical properties. Through an unprecedented combination of in situ high-temperature high-resolution electron microscopy, crystallographic image processing, geometric phase analysis, and neutron powder diffraction, we directly demonstrate that while the initial crystallites after nucleation during crystallization have a very high degree of ordering, significant local cation disordering is induced by rapid crystal growth in Li-intercalation metal-phosphate nanocrystals. The findings in this study show that control of subsequent crystal growth during coarsening is of great importance to attain a high degree of cation ordering, emphasizing the significance of atomic-level visualization in real time.

First-principles study of half-metallic properties of the Heusler alloy Ti2CoGe

First-principles calculations have been performed on the electronic structures and magnetic properties of a new Ti2Co-based full-Heusler alloy Ti2CoGe. The calculations predict the Ti2CoGe is a half-metallic ferromagnet at the equilibrium lattice constant with the minority-spin energy gap of 0.60eV. It is found that the total magnetic moment (Mt) and the number of valence electrons (Zt) in Ti2CoGe obey a new Slater–Pauling (SP) rule of Mt=Zt−18 and the rule also can be applied to other Ti2Co-based half-metallic full-Heusler alloys. The Ti2CoGe alloy keeps a 100% polarization at Fermi level and maintains the half-metallic character for lattice constants ranging between 6.05 and 6.67Å.

Partial Nitridation of Sr3Al10SiO20:Eu and Its Effect on Photoluminescence Properties

The first-principles calculation and Pauling's second rule predict that an O2− ion coordinated with two Al3+ and one Si4+, or Si4+-O[3]-2Al3+, is stabilized by cross-substitution to form 2Si4+-N[3]-Al3+ configuration. Motivated by this idea, this work has attempted to synthesize a new phosphor by partial nitridation of Sr3Al10SiO20:Eu2+, which contains one set of Si4+-O[3]-2Al3+ per twenty O2− ions. Synthesis condition of Sr3Al10−xSi1+xO20−xNx:Eu2+ with x = 1 was investigated by variation of Si3N4/SiO2 ratio in the starting materials. Neutron diffraction analysis has shown that nitridation as much as x = 0.6–2 was attained by supply of Si3N4 in excess of the stoichiometry, because Si3N4 is partly oxidized even by firing in reduced atmosphere. Luminescence intensity is increased by seven times at the best by the nitridation, though little change is observed in luminescence spectra and X-ray diffraction patterns. The increased luminescence intensity results mainly from more efficient reduction of Eu3+ by Si3N4.

Magnetic properties and spin polarization of Co 2Mn(Si xSn 1− x) alloys containing two L2 1 phases

Bulk Co 2Mn(Si x Sn 1− x ) (0 < x < 1) alloys have been prepared and their crystal structure, magnetization and spin polarization have been measured. X-ray diffraction pattern and scanning electron micrograph revealed the alloy phase separate into two L2 1 phases, Co 2MnSi and Co 2MnSn for x ≥ 0.25. The saturation magnetization values corresponded to the value predicted by the Slater–Pauling (S–P) rule. Spin polarization measurements using point contact Andreev reflection (PCAR) technique showed that the quaternary alloys exhibited higher intrinsic spin polarization than the parent ternary compositions. The highest spin polarization of 0.67 ± 0.01 was obtained for the Co 2Mn(Si 0.5Sn 0.5) alloy. These studies show that isovalent substitution for Sn with Si in Co 2MnSn results in enhanced intrinsic spin polarization in spite of the phase separation.

Disentangling the Mn moments on different sublattices in the half-metallic ferrimagnet Mn3−xCoxGa

Ferrimagnetic Mn3−xCoxGa compounds have been investigated by magnetic circular dichroism in x-ray absorption (XMCD). Compounds with x&amp;gt;0.5 crystallize in the CuHg2Ti structure. A tetragonal distortion of the cubic structure occurs for x≤0.5. For the cubic phase, magnetometry reveals a linearly increasing magnetization of 2x Bohr magnetons per formula unit obeying the generalized Slater–Pauling rule. XMCD confirms the ferrimagnetic character with Mn atoms occupying two different sublattices with antiparallel spin orientation and different degrees of spin localization and identifies the region 0.6&amp;lt;x≤0.8 as most promising for a high spin polarization at the Fermi level. Individual Mn moments on inequivalent sites are compared to theoretical predictions.

Half-metallic full-Heusler compound Ti 2NiAl: A first-principles study

Full-Heusler compound Ti 2NiAl with Hg 2CuTi-type structure is demonstrated to be a new half-meltal ferromagnet by first-principles calculations. The compound has a complete (100%) spin polarization around the Fermi level in the total density of state. The band structure calculations show that the majority spin is strongly metallic, while the minority spin shows an insulating behavior. The compound has a total magnetic moment of −3.0 μ B per formula on first-principles calculations which complies well with the Slater–Pauling (SP) rule. Though having different atomic surroundings, the profiles of atom-projected density of states of Ti( A) and Ti( B) are similar. The half-metallic character is retained when the lattice constant ranging from −12.8% to +4.9%.

PDF analysis of ferrihydrite and the violation of Pauling's Principia

AbstractThe risk of overfitting pair distribution function (PDF) data for highly defective material (Farrow et al., 2007) is illuminated with the example of the nanocrystalline hydrous ferric oxyhydroxide, ferrihydrite. Two structural models have been published by Michel et al. (2007, 2010) using this method, both of which contradict the standard ‘ferrihydrits’ model established by X-ray diffraction (Drits et al., 1993), and confirmed by single-crystal electron nanodiffraction (Janney et al., 2001) and neutron diffraction (Jansen et al., 2002). Although PDF data are reproduced equally well with the two regression models, neither model is realistic: the first (fhyd6) violates Pauling's 2nd rule, and the second (ferrifh), Pauling's 3rd rule.

Partial Nitridation of Sr3Al10SiO20:Eu and Its Effect on Photoluminescence Properties

The first principle calculation and Pauling's second rule predicted that an O2- ion coordinated with two Al3+ and one Si4+, or Si4+-O[3]-2Al3+, is stabilized by cross-substitution to form 2Si4+-N[3]-Al3+ configuration. Motivated by this idea, this work has attempted to synthesize a new phosphor by partial nitridation of Sr3Al10SiO20:Eu2+, which contains one set of Si4+-O[3]-2Al3+ per 20 O2- ions. Synthesis condition of Sr3Al10-xSi1+xO20-xNx:Eu2+ with x=1 was investigated by variation of Si3N4/SiO2 ratio in the starting materials. Neutron diffraction analysis has shown that nitridation as much as x=0.6-2 was attained by supply of Si3N4 in excess of the stoichiometry, because Si3N4 is partly oxidized even by firing in reduced atmosphere. Luminescence intensity is increased by 7 times at the best by the nitridation, though little change is observed in luminescence spectra and X-ray diffraction patterns. The increased luminescence intensity results mainly from more efficient reduction of Eu3+ by Si3N4.

Evaluation of the structural model for ferrihydrite derived from real-space modelling of high-energy X-ray diffraction data

AbstractA new structural model for ferrihydrite that challenges the standard ferrihydrite model established by X-ray diffraction and confirmed by neutron diffraction and single-crystal electron nanodiffraction was recently proposed by Michel et al. (2007a) from the simulation of the pair distribution function obtained by Fourier transformation of diffraction data measured at λ = 0.137 Å. The new ferrihydrite model is isostructural to akdalaite (Al10O14(OH)2), a mineral having the Baker-Figgis δ-isomer of the Al13-Keggin structure as its structural motif. The new model is unrealistic because: (1) it is completely periodic (i.e. defect-free); (2), it has 20% tetravalent octahedral iron (VIFe4+), 20% divalent tetrahedral iron (IVFe2+), and some IVFe–O distances equal to or larger than the VIFe3+–O distances, thus violating Pauling's 2nd rule; (3) it does not describe X-ray diffraction and EXAFS spectroscopic data; and, (4) it is inconsistent with electron microscopy results and contradicts previous X-ray scattering studies.

A First-Principles Study of the Electronic and Structural Properties of γ-TaON

The geometric and electronic structure of the recently found new polymorph of tantalum oxynitride, gamma-TaON, and its structural stability were studied quantum-chemically at the density functional level. Results obtained by complementary quantum-chemical techniques with wavefunctions either expanded in atom-centered functions or in plane waves were compared, having employed pure density-functional functionals within the generalized gradient approximation as well as density-functional/Hartree-Fock hybrid methods. In particular, several plausible anion distributions were investigated and, in accordance with Pauling's second rule, it was found that the configuration in which nitrogen occupies crystallographic sites with highest coordination numbers is the most stable one. Theoretically generated local structural parameters were used to improve the accuracy of the experimentally derived information. The bonding situation in the most stable configuration was investigated by an analysis of the density of states.

Entropy Evaluation of the Superprotonic Phase of CsHSO4: Pauling's Ice Rules Adjusted for Systems Containing Disordered Hydrogen-Bonded Tetrahedra

The entropy of the superprotonic transition (phase II → phase I) of CsHSO4 is evaluated both experimentally and theoretically. Calorimetric measurements reveal a value of 14.75(22) J mol-1 K-1. Under the assumption that the entropy is entirely configurational, arising from both sulfate group orientational disorder and disorder in the hydrogen-bond network, we evaluated several structural models of CsHSO4 for their consistency with the measured entropy. For a structure in which hydrogen-bond disorder is independent of sulfate-group orientational disorder, simple methods of calculating the number of structural configurations are inadequate. Thus, the configurational entropy of the superprotonic, disordered phase of CsHSO4 is evaluated using an approach similar to that employed by Pauling to describe the residual entropy of ice at 0 K. Analogous to ice and the so-called ice rules, superprotonic CsHSO4 is assumed to obey a set of structural rules. Key among these are that there is only one proton per sulfate tetrahedron and only one proton per hydrogen bond. Defects are argued to make a negligible contribution to the transition entropy. The transition entropy obtained from this model, 14.9 J mol-1 K-1, is in excellent agreement with the measured value. Such a match between theoretical and experimental values suggests that of all published Phase I structures, the structure proposed by Jirak2 more correctly describes the arrangements of the sulfate tetrahedra and protons attached to them. The assumption of a low defect concentration implies that the jump in proton conductivity at the transition is due to an increase in the mobility of charge carriers rather than their concentration.

The SialonsMLn[Si4−xAlxOxN7−x] withM = Eu, Sr, Ba andLn = Ho-Yb – Twelve Substitution Variants with theMYb[Si4N7] Structure Type

The oxonitridoalumosilicates (so-called sialons) MLn[Si4−xAlxOxN7−x] with M = Eu, Sr, Ba and Ln =Ho, Er, Tm, Yb were obtained by the reaction of the respective lanthanoid metal, the alkaline earth carbonates or europium carbonate, resp., AlN, “Si(NH)2” and MCl2 as a flux in a radiofrequency furnace at temperatures around 2100 °C. The compounds MLn[Si4−xAlxOxN7−x] are relevant for the investigation of substitutional effects on the materials properties due to their ability of tolerating a comparatively large phase width up to x ≈ 2.0(5). The crystal structures of the twelve compounds were refined from X-ray single crystal data and X-ray powder data and are found to be isotypic to the MYb[Si4N7] structure type. The compounds crystallize in space group P63mc (no. 186, hexagonal) and are made up of chains of so-called starlike units [N[4](SiN3)4] or [N[4]((Si,Al)(O,N)3)4], respectively. These units are formed by four (Si,Al)(N/O)4 tetrahedra sharing a common central nitrogen atom. The structure refinement was performed utilizing an O/N-distribution model according to Paulings rules, i.e. nitrogen was positioned on the four-fold bridging site and nitrogen and oxygen were distributed equally on both of the two-fold bridging sites, resulting in charge neutrality of the compound. The Si and Al atoms were distributed equally on their two crystallographic sites, referring to their elemental proportion in the compound, due to being poorly distinguishable by X-ray methods. The chemical compositions of the compounds were derived from electron probe micro analyses (EPMA).

Prediction of Anion Distributions Using Pauling's Second Rule

Pauling's second crystal rule is shown to be able to predict in a general and simple way the distribution of anions in mixed oxyanion systems such as oxynitrides and oxyhalides with diverse compositions and structure types. Results are presented in a plot correlating the charge of the anions obtained from the observed occupancies in crystallographic positions with the calculated bond strength sums for these sites.

Single‐Crystal X‐ray Diffraction and Electron Microprobe Analysis of the Structurally related J‐Phases Nd4[Si2O5N2]O2, Nd4[Si2−xAlxO5+xN2−x]O2 with x ≈ 0.4 and SrxHo4−x[Si2−yAlyO5+(x+y)N2−(x+y)]O2 with x ≈ 0.2 and y ≈ 0.4

AbstractThe oxonitridosilicate Nd4[Si2O5N2]O2, and the oxonitridoaluminosilicates Nd4[Si2−xAlxO5+xN2−x]O2 with x ≈ 0.4 and SrxHo4−x[Si2−yAlyO5+(x+y)N2−(x+y)]O2 with x ≈ 0.2 and y ≈ 0.4 were obtained by the reaction of the lanthanide metals, silicon diimide “Si(NH)2” and additional SiO2, AlN and SrCO3, respectively. The reactions were performed in a radio‐frequency furnace at temperatures between 1800 and 2100 °C. The crystal structures of the three compounds were determined by single‐crystal X‐ray diffraction (P21/c, no. 14, Z = 4; Nd4[Si2O5N2]O2: a = 7.8577(8) Å, b = 10.7793(12) Å, c = 11.0163(12) Å, β = 110.759(11)°, R1 = 0.0752; Nd4[Si2−xAlxO5+xN2−x]O2: a = 7.842(2) Å, b = 10.710(2) Å, c = 11.074(2) Å, β = 110.32(3)°, R1 = 0.1078; SrxHo4−x[Si2−yAlyO5+(x+y)N2−(x+y)]O2: a = 7.5704(5) Å, b = 10.4744(8) Å, c = 10.8502(11) Å, β = 109.856(7)°, R1 = 0.0825). The compound SrxHo4−x[Si2−yAlyO5+(x+y)N2−(x+y)]O2 crystallizes isotypically with the mineral cuspidine (Ca4[Si2O7]F2), the neodymium compounds crystallize in a cuspidine‐related structure type. The structure refinements were performed utilizing an O/N distribution model according to Paulings rules and according to powder neutron diffraction data obtained from La4Si2O7N2 and Lu4Si2O7N2 by Takahashi et al., i.e. nitrogen was positioned on the bridging site, mixed O/N‐occupation was assumed on the terminal sites and oxygen was positioned on the isolated site resulting in charge neutrality of the compounds. The Si and Al atoms were refined equally mixed on the two possible positions. The structures consist of bitetrahedral units [(Si,Al)2(O,N)7], lanthanide and alkaline earth cations and isolated oxygen anions. The chemical compositions of all three compounds were determined by electron probe micro analyses (EPMA).