小角X射线散射中Porod正偏离的校正

A Positive Deviation from Porod' s Law in SAXS of Porous ZrO_2 Xerogels

当散射体系中除散射体外还存在微电子密度起伏时,实测散射强度将形成对Porod定理的正偏离,从而使散射体的散射失真.提出了一种在长狭缝准直条件下应用模糊强度校正正偏离的方法:作出In[q^3(?)(q)]～q^2曲线,用公式n[q^3I(q)]=InK＇+σ~2q^2拟合大波矢区直线,求出斜率σ~2,作出In[q^(?)(q)]-σ~2q^2～q^2曲线即为无偏离的Porod曲线,由此曲线再还原出无偏离的散射强度,即(?)(q)=exp{In[q^3(?)(q)]-σ~2q^2}/q^3,再以醇热法合成的介孔氧化锆粉体为例进行了讨论.

Small angle X - ray scattering (SAXS) is a useful tool for the study of the structure of porous materials with nano - sized pores. The scattering by an ideal two - phase porous system with sharp boundary obeys Porod' s law. If there are disorder or thermal density fluctuation within solid phase, it will give rise to an additional relatively low scattering mixed with the SAXS intensities of pores and then lead to a positive deviation from Porod' s law. It is therefore necessary to correct the deviation for studying the pore structure. In this paper, a new method of positive deviation correction for the slit - smeared SAXS intensities of porous materials is developed: (1) plotting the ln[q3-I(q)] - q2 curve, which shows a positive deviation from Porod' s law ; ( 2 ) fitting this curve in the high angle region with a positive slope using the equation ln[q3I(q)] = lnK' + σ2 q2, where K' is Porod constant and σ is a parameter in relation to the size of the electron density micro- inhomogeneity; then (3) deducing the σ2; and finally (4) plotting the ln[q3-I(q)] - σ2 q2 - q2 curve, which will show no deviation from Porod's law, and the scattering intensities of the pores can then be obtained by, I'(q) = exp{ln[q3-I(q)]-σ2q2}/q3 . Any information about the pores can be deduced from these data . Based on this method , SAXS investigation using synchrotron radiation as X - ray source with a long - slit collimation system was carried out for the pore structure of ZrO2 xerogels prepared by alcoholicthermal process. The advantages of this method are discussed briefly.