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.

Date of Award	1971
Original language	English