J.R. Gavarri

Monoxyde quadratique PbOα(I): Description de la transition structurale ferroe´lastique

Abstract Lead monoxide PbOα was investigated at low temperature using X-ray and neutron diffraction on powder samples. The tetragonal—orthorhombic symmetry change below 200 K is described. The thermal expansion tensor is connected with the anisotropic temperature factor variation of lead and oxygen atoms in the range 2–300 K. The thermal expansion of Pb-O and Pb-Pb bonds is interpreted and compared with force constant data calculated in previous spectroscopic studies. The layered structure of PbOα can be properly understood by taking into account lone pair interactions involved in Pb-Pb bonds. The principal structural data are: 2 K , C m m a ( Z = 4 ) P b : B 11 = 0.72 A 2 , B 33 = 0.24 A 2 ; O : B 11 = 1.05 A 2 , B 33 = 0.89 A 2 300 K , P 4 / n m m ( Z = 2 ) P b : B 11 = 1.48 A 2 , B 33 = 1.42 A 2 O : B 11 = 1.45 A 2 , B 33 = 2.70 A 2

Oxydes de plomb. I. Structure cristalline du minium Pb3O4, à température ambiante (293 K)

Abstract The structure of Pb 3 O 4 at 293 K has been refined to an R value of 0.06, using 29 neutron diffraction data obtained from a powdered sample. Oxygen atoms are displaced in the quadratic cell (space group P4 2 mbc ; a = 8.811 A and c = 6.563 A) with respect to previous results obtained by several authors. The interatomic Pb IV ue5f8O and Pb II ue5f8O distances are compared with those found in other lead oxides. While the oxygen octahedra around Pb IV atoms are characterized by bondings a little too long, the divalent lead coordination is characterized by bondings a little too short.

Structures isomorphes MeX2O4—Evolution structurale entre 2 K et 300 K de l'antimonite FeSb2O4: Elasticité et ordre magnétique anisotropes

Abstract Neutron diffraction has been used to study the whole structural evolution of the antimony oxide FeSb2O4, from 2 to 300 K. The antiferromagnetic order has been investigated: at 2 K the magnetic moment is M = 3.8 μB. An extrapolated Neel temperature TN = 45 ± 6 K is observed. The function M(T) below TN is similar to that found in the isomorphous NiSb2O4. Magnetostrictive effects are observed. Above 70 K, the thermal expansion tensor is anisotropic with αa ⪡ αc. Using the anisotropic temperature factors Ba (A2), Bc (A2) at 2 and 300 K, anisotropic Debye temperatures are calculated. Then, using simple approximations, mean force constants Fa, Fc are calculated; they allow to evaluate the anisotropic compressibility coefficients χa ∼ 0.857 × 10−11Pa−1, χc ∼ 0.467 × 10−11Pa−1; the value of the Gruneisen constant is γ = 0.33 .

Composés isomorphes MeX2O4: Dilatation thermique anisotrope et ordre magnétique dans MnSb2O4

Abstract Using X-ray diffraction data, the anisotropic thermal expansion coefficients αa and αc of two isomorphic compounds MnSb2O4 and NiSb2O4 are linked to the anisotropic elastic constants of these tetragonal structures and compared to the ZnSb2O4, SnPb2O4 thermal expansion coefficients. The anomalous thermal expansion observed for MnSb2O4 in the 6–115 K range (maximum of αc at 70 K) is related to the ordering of Mn2+ ion magnetic moments. Using neutron diffraction, two kinds of antiferromagnetic order are observed for MnSb2O4 and NiSb2O4. At 6 K the value of the resultant moment is approximately 1.8 μB for NiSb2O4 and 3.8 μB for MnSb2O4. A critical temperature of Tc = 115 K is proposed for MnSb2O4 based on the use of X-ray diffraction data alone.

Les antimonites antiferromagnétiques MnSb2O4 et NiSb2O4

Neutron diffraction has been used to study the variation of antiferromagnetic order in the antimony isomorphous MnSb2O4 (TN ∼ 60 K) and NiSb2O4 (TN ∼ 46 K). The magnetic moments have been related to the Mn2+ and Ni2+ spins and magnetostrictive effects have been interpreted. The influence of the method of synthesis is mentioned: polycrystalline MnSb2O4 has been obtained from hydrothermal synthesis. Orthorhombic distortions are not connected with magnetic interactions but with structural defects.

The chemical bonds in MeSb2O4 (Me = Mn, Ni, Fe, Zn) isomorphous compounds: Thermal expansion, force constants, energies

The various chemical bonds (Meue5f8O, Sbue5f8O) in the MeSb2O4 isomorphous compounds (Me = Mn, Ni, Fe, Zn) are characterized by four quantities: the interatomic distance (rij), the force constant (fij), the thermal expansion (αij = 1r drdT), the bond energy. Using structural evolution data (neutron diffraction) and Raman infrared spectroscopic studies at low temperature (5–300 K), it has been possible to connect the various rij, fij, and αij quantities with bond energies; such energies have been calculated using a simplified pair potential model U(r) = Ar−m ue5f8 Br−n; calculated force constants and thermal expansions have been derived from the derivatives d2Udr2 and d3Udr3. For each MeSb2O4 compound lattice energies (Er) are then proposed. Using a new empirical bond-length-bond-energy method [J. Ziolkowski, J. Solid State Chem. 57, 269 and 291 (1985)] dissociation energies of Meue5f8O and Sbue5f8O bonds have been evaluated for each MeSb2O4 compound. The total calculated dissociation energy D(MeSb2O4 → Me° + 2 Sb° + 40°) is then compared to the lattice energies Er obtained from the first method. The |Er| and D values are respectively about 1080 and 790 kcal · mole−1; the difference is directly linked with the ionic character of Meue5f8O bonds.

Evolution structure entre 2 et 300 K de l'oxyde MnSb2O4: Proprie´te´se´lastiques et magne´tiques anisotropes

Neutron diffraction on a powdered sample has been used to determine the structure of MnSb 2 O 4 at 2 and 300 K. The existence of antiferromagnetic order is confirmed: at 2 K the value of the magnetic moment of Mn 2+ ions is 4.3 ± 0.2 μ B . The structural variation of this antimony oxide above the Ne´el temperature is interpreted in terms of elementary physical models (Debye hypothesis, Gru¨neisen relations). The anisotropic Debye temperatures are calculated. The anisotropic compressibility coefficients χ a , χ c , are evaluated from a model. The compliance factors are s 11 + s 12 = 1.16 ± 0.05 × 10 −11 , s 13 = −0.42 ± 0.01 × 10 −11 , and s 33 = 1.29 ± 0.08 × 10 −11 Pa −1 . The anisotropic Gru¨neisen constants are obtained as γ a = 0.47 ± 0.02, γ c = 0.54 ± 0.02. These quantities permit a better interpretation of the magnetostrictive effects in MnSb 2 O 4 .

Composes isomorphes MeX2O4E2: I. Etude vibrationnelle de MnSb2O4 entre 4 et 300 K: champ de force et tenseur élastique

Abstract A vibrational study of the tetragonal antimony oxides (Mn, Ni, Zn) Sb2O4E2 in which E is a lone pair has been carried out using Raman and infrared spectroscopy between 4 and 300 K. A force field calculation has been performed using previous results (J. P. Vigouroux et al., Spectrochimi. Acta A 38, 393, 1982) and a new structural evolution approach using models and results of X-ray and neutron diffraction experiments (R. Chater and J. R. Gavarri, J. Solid State Chem. 59, 123, 1985). This approach delivers mean force constants Fa, Fc, elastic constants Cij, and Gruneisen parameters. Using these results it has been possible to propose initial force constants which have been refined. For MnSb2O4 the following results are obtained: (1) In MnO6 octahedra, the six Mnue5f8O bond force constants are about 60 N m−1. (2) In SbO3E tetrahedra, the three Sbue5f8O force constants are about 200 N m−1 while Oue5f8Sbue5f8O angle force constants are in the range 50–70 N m−1. (3) SbE · · · SbE interactions are evaluated in the three Mn, Zn, Ni isomorphous compounds: the interaction is strongly connected with the Sbue5f8Sb distances found in these structures. It is shown that the force field calculation is in agreement with the results of the structural evolution approach: the values Fa = 49 N m−1, Fc = 70 N m−1 can be compared qualitatively with the various averaged force constants.

Nucleation and stability of defect clusters: New energetic model in the case of substituted wustites

Abstract For wustite Fe1−z O (z < 0.08) an energetic model accounts for the stability of cubic defect clusters (m/n) which are partly ordered in the crystal. The Gibbs energy GT (N) associated with clusters, including their distorted envelope, is expressed as a sum of a volume term in N 3 and of surface terms in N 4; N is the number of bonds characteristic of the cluster size. In the case of a (10/4) type cluster, this energy is negative and minimum for Nm ranging between 4 and 5, when the volume and surface energies range between specific values. Using simple assumptions, a volume energy −0.80 eV per vacancy is found in accordance with the value of stabilization energy calculated by theorists for the (10/4) cluster. The substitution of Fe2+ by Ca2+ should lead to a decrease of cluster size; this has been recently suggested by neutron diffraction studies.

Évolution structurale sous pression de NiSb2O4: Compressibilités anisotropes et ordre magnetique

The structural evolution of NiSb2O4 under pressure (4000 atm) and at low temperature has been investigated using neutron diffraction on a polycrystalline sample. The tetragonal cell parameters have been refined at 2, 63, and 240 K and high pressure. The anisotropic compressibility factors obtained at 240 K are χa = −(1a) × dadp ∼ 0.60 × 10−11 Pa−1 and χc = −(1c) × dcdp ∼ 0.35 × 10−11 Pa−1. These quantities have been compared with those predicted from the compressibility calculation model which is used to fit calculated thermal expansion functions to experimental thermal expansion coefficients. The models and physical assumptions we proposed to evaluate several elastic constants of polycrystal-line materials have been shown to approximate well the elastic properties, especially when large single crystals are not available, i.e., when direct analysis is not possible. The magnetic moments at 2 K have been refined at p = 0 kbar and p = 3.6 kbar. At low pressure, the C magnetic mode is confirmed; at high pressure, although this C mode is predominant, a small G component is observed. The mean magnetic moment is M = 2.2μB at both pressures.