Andreas Leineweber

ε-Fe3N : magnetic structure, magnetization and temperature dependent disorder of nitrogen

Abstract e-Fe 3 N has been investigated by time-of-flight neutron diffraction (temperature range 4.2–618 K) and SQUID magnetometry (2–700 K, B ≤5 T). A ferromagnetic spin structure is observed with magnetic moments oriented perpendicular to the c -axis of the hexagonal nuclear structure. The magnetic saturation moment of iron is 2.2 μ B at 4.2 K from neutron diffraction and 2.0 μ B from magnetic measurements and decreases in a Brillouin-like manner on heating to T C =575 K. Above 450 K an increasing but reversible disorder of the nitrogen partial structure is observed.

Energetics of binary iron nitrides

Abstract High-temperature solution calorimetry in molten sodium molybdate 3Na 2 O·4MoO 3 was used to determine the energetics of formation of a series of binary iron nitrides: γ′-Fe 4 N, e-Fe 3 N 1+ y ( y =0, 0.10, 0.22, 0.30, 0.33), ζ-Fe 2 N and γ′′-FeN 0.91 . The linear relation Δ H ° f (FeN x )=−65.23 x +13.48 kJ mol −1 was found between the enthalpies of formation from the elements at 298 K of iron nitrides FeN x and their nitrogen content x . Using this linear approximation, the enthalpy of formation of α′′-Fe 16 N 2 has been estimated to Δ H ° f (Fe 16 N 2 )=85.2±46.8 kJ mol −1 .

Theoretical analysis of occupational ordering in hexagonal interstitial compounds: carbides, nitrides and oxides with “ε-type” superstructures

Abstract Different types of N-ordering assigned to the e-phase in the system Fe/N, e-Fe 3 N 1+ x , serve as prototypes for the very common so-called “e-type” occupational ordering of interstitials: in hexagonal interstitial compounds MX y with y ≤0.5 and M in an hcp arrangement with X in octahedral interstices, ordering of X leads to a 3 1/2 ×3 1/2 ×1 superstructure. The relevant space group symmetries of these “e-type” structures are P6 3 22 , P 3 1m and P312 . The variety of theoretically possible structures of “e-type” ordered interstitial compounds is analysed for the general case of partial order and varying composition. It appears advantageous to describe the distribution of the interstitial atoms, i.e. the occupancies of the six octahedral sites within the unit cell, using so-called static concentration waves (SCWs). Their parameters are closely related to the (powder) diffraction patterns of the phases. This relation makes it easy to show which information about the interstitial atom distribution may be extracted from diffraction patterns and which information is lost. In certain cases this may lead to homometric structures of different space group symmetries. Landau theory can eliminate some of the structural ambiguities resulting from the analysis of diffraction patterns. Within its framework the SCW parameters are closely related to order parameters. This allows us to analyse and classify phases and compounds (many transition metal carbides, nitrides or oxides) with “e-type” ordering and possible order–disorder phase transitions.

Crystal structure determination of Hägg carbide, χ-Fe5C2 by first-principles calculations and Rietveld refinement

Abstract X-ray powder-diffraction data recorded using different wave lengths as well as neutron powder diffraction data on Hägg carbide, χ-Fe5C2, were evaluated by Rietveld or Pawley refinements, respectively. Likewise, employing different starting models, first-principles calculations using density functional theory (DFT) involving structure optimisation with respect to energy were performed for χ-Fe5C2. The results from diffraction and DFT imply a crystal structure having a monoclinic C2/c symmetry with a quite regular (monocapped) trigonal-prismatic coordination of C by Fe atoms. The anisotropy of the microstrain broadening observed in the powder-diffraction patterns agrees with the anisotropy of the reciprocal Young’s module obtained from elastic constants calculated by DFT. The anisotropic microstrain broadening can to some degree, be modelled allowing for a triclinic distortion of the metric of χ-Fe5C2 (deviation of the lattice angle γ from 90°) involving reflection spitting, which mimics the hkl-dependently broadened reflections. This distortion corresponds to the most compliant shear direction of the monoclinic χ-Fe5C2. The anisotropic microstrain broadening results from microstress induced e.g. by anisotropic thermal expansion inducing misfit between the grains, in association with the intrinsic anisotropic elastic compliance of χ-Fe5C2. This anisotropic microstrain broadening was likely the origin of previous proposals of triclinic P-1 space-group symmetry for the crystal structure of χ-Fe5C2, which is rejected in the present work.

Preparation of single crystals of LaAl and X-ray structure determination

Single crystals of the compound LaAl have been prepared by the reaction of a mixture of lanthanum and aluminium under nitrogen at 950°C. Previously reported crystal structure data determined by X-ray powder diffraction are now confirmed by an X-ray single crystal structure analysis on LaAl: space group Cmcm, Z=8, a=9.455(1) A, b=7.753(1) A, c=5.791(1) A, R1/wR2=2.4/5.6, N(F2≥2σ(I2))=685, N(var.)=16. The structure of LaAl contains zig-zag chains formed by two crystallographically independent Al atoms with alternating angles Al–Al–Al of 64° and 180°. The chains are connected via lanthanum atoms.

Thermodynamics of Formation of Binary and Ternary Nitrides in the System Ce/Mn/N

Drop solution calorimetry in high-temperature oxide melts has been shown to be very useful to study the energetics of nitride formation. This methodology was used to determine the enthalpies of formation from the elements of binary and ternary nitrides in the Ce/Mn/N system. The resulting values in kJ mol–1 are; δH (CeN) = –340.19 ± 6.80, δ(H (Mn3N1.95, η-Mn3N2 type) = –192.68 ± 7.57, δH (Mn6N5.40, θ-Mn6N5 type) = –430.80 ± 10.93 and δH (Ce2MnN3) = –928.18 ± 9.46. The results show the role of inductive effects in Ce2MnN3 leading to a higher energetic stability compared to binary components. Thermodynamik der Bildung von binaren und ternaren Nitriden im System Ce/Mn/N Hochtemperaturkalorimetrie mit Oxidschmelzen hat sich zur Untersuchung der energetischen Beitrage bei der Nitridbildung bewahrt. Diese Methode wurde zur Bestimmung der Bildungsenthalpien von binaren und ternaren Nitriden im System Ce/Mn/N eingesetzt. Die erhaltenen Werte sind (kJ mol–1): δH (CeN) = –340.19 ± 6.80, δH (Mn3N1.95, η-Mn3N2 type) = –192.68 ± 7.57, δH (Mn6N5.40, θ-Mn6N5 type) = –430.80 ± 10.93 and δH (Ce2MnN3) = –928.18 ± 9.46. Die erhaltenen Daten bestatigen den stabilisierenden Einflus des induktiven Effekts auf die Bindung von Ce2MnN3 im Vergleich mit den binaren Komponenten.