Quantitative Determination of Preferred Orientation

Abstract

Solutions are presented to the problems which usually prevent accurate x-ray determinations of preferred orientation. The relationship between observed and corrected intensities and the angle dependent absorption factors are treated, including the case of displaced and distorted line profiles caused by low absorption in thick specimens. The absorption factors are derived experimentally from measurements of the scattered (Compton) background radiation without recourse to calculations or tables. Two simple methods, either by varying the wavelength λ or the order n of the x-ray reflection, span the region of the pole figure in which data are unreliable or unobtainable if only one wavelength or order is used. Random samples are not required for normalizing the data to ``times random'' units. The intensity for a random sample can be calculated from the corrected data itself and the equation Ihkl=[[double integral operator]Ihkl(α,β) sinαdαdβ]/2π where (α,β) are the coordinates of a point on the usual polar net. It is suggested that textures can generally be represented by Gaussian or superposition of Gaussian orientation distributions.

Ferroelectric 90° Domain Evaluation in Tetragonal Pb(Mg1/3Nb2/3)O3–PbTiO3 Ceramics

“…19 It had also been shown that a Gaussian function could be used to fit the spatial distribution of domain orientation. 20 In our research, a Gauss- 5 0.15). According to the definition of this function, a is a parameter related to the character of spatial distribution as well as to the degree of poling.…”

“…These functions have been used to satisfactorily fit XRD peak profiles and other line profiles 19 . It had also been shown that a Gaussian function could be used to fit the spatial distribution of domain orientation 20 . In our research, a Gaussian function, W (ϕ)= W 0 exp(−ϕ 2 /2σ 2 ), a Cauchy function W (ϕ)=1/1+α 2 ϕ 2 , and the function W (ϕ)=1/(1+α 2 ϕ 2 ) 2 were all used to fit the data.…”

Synthesis of advanced carbon nanomaterials from renewable and waste carbon sources

“…The sharp peaks indicated high crystallinity of all catalysts. Higher intensity of ( 200) peak compared to other peaks for MgO suggested that crystal growth was preferentially oriented along (200) lattice plane [152]. Here we use the ratio of intensity of (200) 1).…”

“…SrO > BaO, indicating that MgO had highest proportion of grains oriented in(200) lattice plane among all alkali-earth metal oxides[152,154]. The decrease of I(200)/IR was attributed to increasing intensity of other…”