The application of x-ray diffraction line profile analysis to the study of anti-phase domains in lithium ferrite

Abstract

X-ray diffraction patterns of lithium ferrite LiFe,0. quenched from just below the temperature of its order-disorder transition were found to exhibit sharp lattice lines (h,k,2 of similar parity) and superlattice lines (h,k,1l, of-mixed parity) whose breadths normally exceeded those of the lattice lines. Similar diffraction patterns were also obtained from specimens of lithium ferrite into which partial disorder a: introduced by the substitution of a small fraction of cr°* ions for Fe* ions (i.e. Life, Cr 0g, x < 2). The behaviour of these diffraction patterns is explained by assuming that the crystallites contain many small ordered regions which are generally referred to as anti-phase domains. In the present work a more precise picture of the antiphase domains in these materials is developed through quantitative analysis of the X-ray line profiles. Line positions are determined by the centroid method whilst line breadths are determined Fey the aid of Fourier, variance and two new methods of analysis. One of the new methods, namely that based on the variation of the function (truncated integrated intensity X range) versus range, is shown to have similar merits and limitations to variance for the analysis of broadened lines as well as being an ~ accurate method for evaluating integrated intensities. The second new method, referred to as pseudo-variance, is a modification of variance in which the range dependence of the latter is corrected for the hyperbolic term. Prior to interpretation of the line profile parameters, consideration is given to the propagation of systematic errors. The influence of the K& satellite group on the parameters is eliminated by exploiting its intensity distribution with the aid of the centroid-range function. Justification for the background intensity levels obtained from variance analysis is given and the effects of non-linear range dependent terms on the measured variance slopes and intercepts are discussed. In the Fourier transform analysis, errors, particularly those resulting from profile truncation, are reduced by correction procedures. It is shown that good agreement is obtained between values for the Wilson parameter 3*"(0)/3(0) . determined from Fourier analysis and pseudo-variance. The conclusion is reached that the most reliable interpretation of the diffraction broadening is achieved with the parameters measured from the latter two methods of analysis. Measurements of long range order parameters and lattice parameters indicate that the specimens prepared are slightly nonstoichiometric. Except for one special case, this did not appear to affect the breadths of the lattice lines which are accounted for by the emission profile, the instrumental aberrations and a small diffraction broadening contribution which seems to be independent of the stoichiometry and state of order of the specimens. Because of inconsistencies in the crystal structure of lithium ferrite proposed by Braun (1952), a redetermination is carried out with account being taken of non-stoichiometry. The new proposed structure is shown to be consistent with intensity results obtained from three specimens and previous published cation-anion distances. The mean domain thicknesses obtained from the superlattice lines of the quenched and cr>+ ion substituted lithium ferrite specimens are best accounted for by anti-phase domain boundaries on the {110} planes. Evidence is presented to demonstrate that these are low energy boundaries. For some specimens, values of the domain thickness distribution f(t) at t =0, as estimated from pseudovariance, are shown to be in very good agreement with those values predicted from the anti-phase domain model developed by Wilson in 1943. For other specimens an approximate agreement is found. The time and temperature dependence of domain growth in unsubstituted specimens of lithium ferrite indicate a rate process similar to grain growth in metals and a growth mechanism which is probably diffusion controlled. Agreement is obtained between measured and calculated values for the activation energy of the growth process. Anti-phase domains in the cr?* ion substituted specimens of lithium ferrite appear to exist in a state of thermal equilibrium. This 3+ condition is explained by assuming that all the Cr~ ions lie on the domain boundaries and that domain growth is prevented by the immobility of these ions which arises from their crystal field stabilization energy. Finally, a theory is developed which enables the complete domain thickness distribution to be evaluated from Fourier transform results. A practical evaluation of the distribution in some of the specimens is carried out. These and other results suggest that the domain thickness distribution approximates to a Gaussian curve during the earlier stages of domain growth and to a Cauchy curve during the later stages.