コラム近似

column approximation

[目次：理論(電子の散乱／回折／結像)]

結晶下面の一点での電子波の形成に及ぼす結晶上面での領域はフレネルゾーンを使って推定できる。第一フレネルゾーン半径Rは√(λｔ)で与えられる。ここでλは電子線の波長、tは試料の厚さである。λ＝0.0026nm、t＝100nmとすると直径２Rは～0.5nmとなる。第三フレネルゾーンまで取っても直径は～1.5nmである。すなわち結晶下面のある点の電子波の振幅を計算する場合、2nm以下のコラムの中で電子波の透過と回折を考えればよいことになる。”乱れ”のある結晶を取り扱う場合、結晶をこのような大きさのコラムに分けて、このコラム内では完全結晶とし、コラム間に”乱れ”に対応する”ずれ”があるとして扱う。これをコラム近似という。

"Column approximation" is an approximation method to calculate the amplitudes of transmitted and diffracted waves at the bottom of a crystal, which assumes the crystal to be composed of columns. The top specimen plane, which affects the formation of an electron wave at a point on the crystal bottom plane, is deduced by Fresnel zones. The radius of the first Fresnel zone, R, is given by √(λt), where, λ is the wavelength of the electron and t is the specimen thickness. When it is assumed that λ = 0.0026 nm and t = 100 nm, the diameter of the Fresnel zone, 2R, is ～0.5 nm. If Fresnel zones are taken up to the third zone, its diameter is ～1.5 nm. That is, when the amplitude of an electron wave at a certain point on the crystal bottom plane is calculated, it is enough to consider transmission and diffraction of the electron wave in a column of 2 nm or less. When a distorted crystal is treated, the amplitudes of the transmitted and diffracted waves are calculated inside such columns, in each of which the crystal is assumed to be a perfect, and between which the crystals are shifted each other corresponding to the distortion.