Cooperative Jahn–Teller distortion leading to the spin-1/2 uniform antiferromagnetic chains in triclinic perovskites AgCuF3 and NaCuF3

Polycrystalline samples of AgCuF₃, isostructural with NaCuF₃, were synthesized by solid state reaction and characterized by powder X-ray diffraction. The magnetic properties of AgCuF₃ and NaCuF₃ were examined by measuring their magnetic susceptibilities and evaluating their spin exchange interactions. The three-dimensional CuF₃ network of corner-sharing CuF₆ octahedra present in AgCuF₃ and NaCuF₃ shows a cooperative Jahn–Teller distortion such that their magnetic susceptibilities above 50 K are well described by an S = 1/2 Heisenberg uniform antiferromagnetic chain model with average spin exchange of J/k_B ≈ ?300 and ?180 K, respectively. The relative strengths of these interactions are well reproduced by spin dimer analysis based on tight-binding calculations, but not by mapping analysis based on first principles density functional calculations.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

Perspective on “An extended Hückel theory. I. Hydrocarbons”

 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH⁺ ₃ and N⁺ ₂ using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two ²A₁ states, very similar and showing great mixing of the (2a _l ⁻¹) and (3a _l ⁻²5a _l ¹) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH₃. The possible contribution of a ²Π _g (3σ _g ⁻²1π _g ¹) state to the A shake-up peak of N₂ at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH₃ and 37 eV for N₂. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Study of scanning tunneling microscopy images and probable relaxations of the SrTiO3(100) surface by electronic structure calculations

Partial electron density plots were calculated for a model SrTiO₃(100) surface with √5 × √5 ordered oxygen vacancy to examine why the bright spots of the scanning tunneling microscopy (STM) images of SrTiO₃(100) observed in ultrahigh vacuum (UHV) correspond to the oxygen vacancy sites. Possible dependence of the image on the polarity and magnitude of the bias voltage was also discussed on the basis of partial electron density plot calculations. Our study strongly suggests that the UHV STM imaging involves the lowest-lying d-block level of every two Ti³⁺ centers adjacent to an oxygen vacancy, the tip-sample distance involved in the UHV STM experiments is substantially larger than that involved in typical ambient-condition STM imaging, and the Ti⁴⁺ and Ti³⁺ sites of SrTiO₃(100) are reconstructed.     

Structure and magnetic properties of oxychalcogenides A2F2Fe2OQ2 (A = Sr, Ba; Q = S, Se) with Fe2O square planar layers representing an antiferromagnetic checkerboard spin lattice

The oxychalcogenides A2F2Fe2OQ2 (A = Sr, Ba; Q = S, Se), which contain Fe2O square planar layers of the anti-CuO2 type, were predicted using a modular assembly of layered secondary building units and subsequently synthesized. The physical properties of these compounds were characterized using magnetic susceptibility, electrical resistivity, specific heat, (57)Fe Mossbauer, and powder neutron diffraction measurements and also by estimating their exchange interactions on the basis of first-principles density functional theory electronic structure calculations. These compounds are magnetic semiconductors that undergo a long-range antiferromagnetic ordering below 83.6-106.2 K, and their magnetic properties are well-described by a two-dimensional Ising model. The dominant antiferromagnetic spin exchange interaction between S = 2 Fe(2+) ions occurs through corner-sharing Fe-O-Fe bridges. Moreover, the calculated spin exchange interactions show that the A2F2Fe2OQ2 (A = Sr, Ba; Q = S, Se) compounds represent a rare example of a frustrated antiferromagnetic checkerboard lattice.     

Electrical Resistivity, Magnetic Susceptibility, X-Ray Photoelectron Spectroscopy, and Electronic Band Structure Studies of Cu2.33−xV4O11

The electronic and physical properties of Cu_2.33V₄O₁₁ were characterized by electrical resistivity, magnetic susceptibility and X-ray photoelectron spectroscopy (XPS) measurements and by tight-binding electronic band structure calculations. Attempts to prepare Cu_2.33−xV₄O₁₁ outside its narrow homogeneity range led to a mixture of Cu_2.33V₄O₁₁, CuVO₃ and β-Cu_xV₂O₅. The magnetic susceptibility data show no evidence for a magnetic/structural transition around 300 K. The XPS spectra of Cu_2.33V₄O₁₁ reveal the presence of mixed valence in both Cu and V. The [Cu⁺]/[Cu²⁺] ratio is estimated to be 1.11 from the Cu 2p_3/2 peak areas, so [V⁴⁺]/[V⁵⁺]=0.56 by the charge balance. Our electronic structure calculations suggest that the oxidation state of the Cu ions is +2 in the channels of CuO₄ tetrahedra, and +1 in the channels of linear CuO₂ and trigonal planar CuO₃ units. This predicts that [Cu⁺]/[Cu²⁺]=1.33 and [V⁴⁺]/[V⁵⁺]=0.50, in good agreement with those deduced from the XPS study.     

Synthesis and characterization of a magnetic semiconductor Na(2)RuO(4) containing one-dimensional chains of Ru(6+)

A new ternary ruthenium oxide Na(2)RuO(4) was prepared and shown to crystallize with a new structure type. Single crystal X-ray diffraction measurements reveal that Na(2)RuO(4) consists of RuO(4) chains made up of RuO(5) trigonal bipyramids by sharing axial corners. Na(2)RuO(4) is a magnetic semiconductor with a variable range hopping behavior, and its molar magnetic susceptibility chi(mol) has a broad maximum at approximately 74 K. The derivative d(chi(mol).T)/dT exhibits a peak at 37.7 K which has been confirmed by heat capacity measurement to be due to long-range antiferromagnetic ordering.     

Comparative electronic band structure study of the intrachain ferromagnetic versus antiferromagnetic coupling in the magnetic oxides Ca3Co2O6 and Ca3FeRhO6

In the (MM'O6)infinity chains of the transition-metal magnetic oxides Ca3MM'O6 the MO6 trigonal prisms alternate with the M'O6 octahedra by sharing their triangular faces. In the (Co(2O6)infinity chains of Ca3Co2O6 (M = M' = Co) the spins are coupled ferromagnetically, but in the (FeRhO6)infinity chains of Ca3FeRhO6 (M = Fe, M' = Rh) they are coupled antiferromagnetically. The origin of this difference was probed by carrying out spin-polarized density functional theory electronic band structure calculations for ordered spin states of Ca3Co2O6 and Ca3FeRhO6. The spin state of a (MM'O6)infinity chain determines the occurrence of direct metal-metal bonding between the adjacent trigonal prism and octahedral site transition-metal atoms. The extent of direct metal-metal bonding in the (Co2O6)infinity chains of Ca3Co2O6 is stronger in the intrachain ferromagnetic state than in the intrachain antiferromagnetic state, so that the intrachain ferromagnetic state becomes more stable than the intrachain antiferromagnetic state. Such a metal-metal-bonding-induced ferromagnetism is expected to occur in magnetic insulators and magnetic metals of transition-metal elements in which direct metal-metal bonding can be enhanced by ferromagnetic ordering. In the (FeRhO6)infinity chains of Ca3FeRhO6 the ferromagnetic coupling does not lead to a strong metal-metal bonding and the adjacent spins interact by the Fe-O...O-Fe super-superexchange, hence leading to an antiferromagnetic coupling.     

Why pressure induces an abrupt structural rearrangement in PdTe2 but not in PtTe2

High-pressure X-ray diffraction measurements were carried out for polymeric CdI₂-type compounds MTe₂ (M=Pt, Pd) to investigate if they undergo a structural phase transition under pressure as does IrTe₂. Up to 27 GPa at room temperature PtTe₂ does not undergo any structural phase transition. In contrast, however, an abrupt change in the inter-atomic distances occurs in PdTe₂ above 15.7 GPa at room temperature, and above 5 GPa at 300 °C, but the volume vs. pressure curve exhibits no discontinuity. To account for the differences between the isostructural compounds PtTe₂, PdTe₂ and IrTe₂, their electronic structures and bonding were analyzed on the basis of first principles electronic band structure calculations.