Balzar Davor
National Institute of Standards and Technology, Boulder, CO 80303-3328.
J Res Natl Inst Stand Technol. 1993 May-Jun;98(3):321-353. doi: 10.6028/jres.098.026.
A method to analyze powder-diffraction line broadening is proposed and applied to some novel high- superconductors. Assuming that both size-broadened and strain-broadened profiles of the pure-specimen profile are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren-Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the "hook" effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from ~1.31 for the minimum allowed Cauchy content to 2 when the size-broadened profile is given solely by a Cauchy function. If the distortion co-efficient is approximated by a harmonic term, mean-square strains decrease linearly with the increase of the averaging distance. The local strain is finite only in the case of pure-Gauss strain broadening because strains are then independent of averaging distance. Errors of root-mean-square strains as well as domain sizes were evaluated. The method was applied to two cubic structures with average volume-weighted domain sizes up to 3600 Å, as well as to tetragonal and orthorhombic (La-Sr)CuO, which exhibit weak line broadenings and highly overlapping reflections. Comparison with the integral-breadth methods is given. Reliability of the method is discussed in the case of a cluster of the overlapping peaks. The analysis of LaCuO and LaMCuO(M = Ca, Ba, Sr) high- superconductors showed that microstrains and incoherently diffracting domain sizes are highly anisotropic. In the superconductors, stacking-fault probability increases with increasing ; microstrain decreases. In LaCuO, different broadening of (00) and (00) reflections is not caused by stacking faults; it might arise from lower crystallographic symmetiy. The analysis of Bi-Cu-O superconductors showed much higher strains in the [001] direction than in the basal plane. This may be caused by stacking disorder along the -axis, because of the two-dimensional weakly bonded BiO double layers. Results for the specimen containing two related high- phases indicate a possible mechanism for the phase transformation by the growth of faulted regions of the major phase.
提出了一种分析粉末衍射线展宽的方法，并将其应用于一些新型高温超导体。假设纯样品轮廓的尺寸展宽和应变展宽轮廓均用沃伊特函数描述，结果表明，对傅里叶系数的分析可得出分离尺寸和应变贡献的沃伦 - 阿韦巴赫方法。尺寸系数分析表明，当尺寸展宽轮廓的柯西含量被低估时会出现“钩”效应。体积加权和表面加权畴尺寸的比值可从最小允许柯西含量时的约1.31变化到尺寸展宽轮廓仅由柯西函数给出时的2。如果畸变系数用谐波项近似，则均方应变随平均距离的增加而线性减小。仅在纯高斯应变展宽的情况下局部应变才是有限的，因为此时应变与平均距离无关。评估了均方根应变以及畴尺寸的误差。该方法应用于平均体积加权畴尺寸高达3600 Å的两种立方结构，以及四方和正交（La - Sr）CuO，它们表现出线展宽较弱且反射高度重叠的情况。给出了与积分宽度方法的比较。在重叠峰簇的情况下讨论了该方法的可靠性。对LaCuO和LaMCuO（M = Ca、Ba、Sr）高温超导体的分析表明，微观应变和非相干衍射畴尺寸具有高度各向异性。在这些超导体中，堆垛层错概率随增加而增加；微观应变减小。在LaCuO中，（00）和（00）反射的不同展宽不是由堆垛层错引起的；它可能源于较低的晶体学对称性。对Bi - Cu - O超导体的分析表明，[001]方向的应变比基面中的应变高得多。这可能是由于沿c轴的堆垛无序，因为存在二维弱键合的BiO双层。含有两种相关高温相的样品的结果表明了一种通过主相缺陷区域生长进行相变的可能机制。
