Abstract
The phase of an x-ray diffraction cannot be determined from the intensityof a single two-beam diffraction.Only the amplitude of the crystal structure-factor involved can bemeasured. This fact constitutes the so-called phase proglem in x-raycrystallography and x-ray physics. Solutions to this problem have beendeveloped by taking into consideration the physical and mathematicalaspects of two-beam x-ray diffraction. In addition to those mathematicalmethods. The multiple diffraction techniques have been considered to be apotential technique of extractin the phase information of structurefactors via the interference of the diffracted beams in the crystal. Ithas beeb proven that from the asymmetry of the inter- ference profiles,thephases can be determined for centrosymmetric crystal. While the phases ofreflections from a non-centrosymmetric crystal can be determined form thevariation of the multiple deffraction intensities, It is also known thatmany factors could affect the diffracted intensities,such as absorption,boundary condition, and beam polarixation. It is the puropse of thisdissertation to discuss the poiarization effects on multiple diffraction.The electric field of x-rays can be decomposed into ★ and ★polarizedcomponents. In a two-beam diffraction, the ★ components of incident anddiffracted beams are perpendicular to the plane of incidence and the ★components are in that plane. The different polarizations cannot becorrelated with each other in the two-beam diffraction case. While thedifferent polarizations of the diffracted beams in multiple diffractionwould be coupled to some extent and thus affect the intensity andasymmetry of the diffraction profile. Experimentally we compare themultiple diffraction profiles of GaAs(002), GaAs(222), Ge(111), Ge(222)and Ge(444) using unpolarized and ★-polarized incident beams. The ★-polarised incident beam is generated by using a germanium crystal as themonochromator via the (333) reflection. The oplarization factors in theformulae derived from kinematical and dynamical theories are compared withthe experimental results. According to Chang & Tang (1988), thediffraction intensity can be separated into two parts: thephase-independent kinematical part and the phase-dependent dynamical part.We found that the variations of the calculated intensities of thekinematical part agreed with the experimental results. By substracting thekinematical parts from the diffracted intensities, we determine theinvariant phases via the derived formulae for GaAs(222). The phase valuesare very close to the theoretic ones for both polarized and unpolarizedincident beams.In this work, we also derived the formulae describing the high-orderwnltiple diffraction (N>2) in a many-body quantum approach. It isindicated that the asymmetry of diffraction profiles can provide the phaseinformation about the dominant Structure-factor triplets. Finally,thefornulae derived are applied to x-ray diffraction from superlattices.為了求得晶體之結構, 我們必須知道晶體內原子面的結構因子F, 包括其大小─F─及相位角α, 但是從一般的 X 光繞射強度, 我們只能測得─F─值, 相位α則沒辦法得知。雖然從數學方法, 在電子密度永遼為正值及原子之電子分佈不疊合的假設下, 可以推導出相位角和─F─的關係式, 進而利用機率的估計及大量的計算機時間, 來估算晶體中所有原子面的相位角, 但是對於分子較大晶體如蛋白質等, 其誤差往往很大。不過相位角和─F─的關係實驗的 X 光複繞射現象也可以得到; X 光複繞射是晶體內不原子面之繞射光的干涉, 其繞射強度的變化不僅和幾個原子面的─F─ 有關, 也和這幾個原子面結構因子之相位角之和(稱為不變相位角)有關。對於中心對稱晶體,由 X 光複繞射峰形的不對稱性可以得知其所對應的不變相位; 對於非中心對稱晶體,我們實驗室曾嘗試由複繞射強度變化定量分析其不變相位。影響中心對稱晶體之複繞射峰形不對稱的因素有不變相位的符號, 相關倒晶格點在倒格子空間的相關位置; 但是影響複繞射強度變化的因素很多, 包括不變相位、晶體的散亂度、吸收效應, 晶體的邊界條件及入射光的偏振方向等。本文的主題之一就是探討 X 光的偏振因子對晶體複繞射的影, 包括其強度的變化,繞射峰的半寬度及不變相位的求得。一般的 X 光布拉格繞射, 其電場的分量★和★偏振並不會互相偶合(coupling), 但在複繞射的現象中, 這兩種偏振會有偶合。複繞現象可以從靜力理論及動力理論來探討, 它們推導的繞射強度都和偏振化因子(polar-ization factor)有關; Chang & Tang(1988)從動力理論出發所得到的複繞射強度可分為和相位有關的動力部分及和相位無關的靜力部份, 文中我們證明其靜力部分所含的偏振化因子和前人從靜力理論推導的偏振化因子相同。實驗上, 我們以Ge(333) 做偏振器(Polariner)使得入射光只★有偏振的電場, 以其做GaAs(002), GaAs(111), Ge(111), Ge(222), Ge(444)的複繞射峰形分析, 並且和以無偏振入射光所得的結果做比較, 我們發現不同偏振光對其強度的影響, 和由理論計算的偏振因子對其影響之結果相當吻合, 當中只 Ge(222)樣品的實驗果較差, 我們認為其主要原因是入射在垂直方散角太大所致。所以我認為由動力理論推導的複繞射靜力強度式和直接由靜力理論推導及實驗結果一致,將實驗的繞射強度減去靜力部分所得的動力繞射強度可以正確地計算不變相位。由此我們用兩種偏振入射光做實驗所得的GaAs(222)幾組不變相位,都和理論值接近,最大誤差約為15°。我們也發現由於★偏振的入射光之垂直發散較大,使得其複繞射峰的半寬度變大。本文的第二個主題是用 X 光的多體繞射理論來推導 N 光繞射(N>2)的強度關係式,由這個關係可以分析(3-, 4-, 5-, N-光)繞射的不變相位, 我們並且用這個結果和多光繞射的實驗比對, 結果完全吻合。最後我們將這個關係式用來模擬超晶格的繞射強度, 可以得到由一維結構造成的不對稱衛星峰(Satellite peak), 詳見附錄。