モワレ縞

Moire fringe

格子の周期が少し異なるd₁、d₂の格子を平行に重ねると、元の格子に平行でD=d₁・d₂/(d₂-d₁)倍に拡大された元の格子に平行な格子縞が現れる。これを平行モワレ縞という。　周期dの格子を二枚、角度αだけ回転して重ねると、元の格子と90°異なる方向にD=d/α倍に拡大された格子が元の格子と90°異なる方向に現れる。これを回転モワレ縞という。　モワレを利用した観察の応用として、刃状転位を含む格子に完全な格子を少し回転させて重ねると、90°異なる方向に拡大された転位像が現れる。

Moire fringe⇒図1
(1a) モワレ縞を示す明視野像。試料: 雲母、加速電圧: 200kV。
(1b) 同じ周期の結晶格子AとBが僅かな方位のずれを伴って重なったときにつくられる大きい周期の縞(回転モアレ縞)の模式図。

Moire fringe⇒図2
(2) 刃状転位を含む結晶格子A’と同じ周期の完全な結晶格子Bが僅かな方位のずれを伴って重なったときにつくられる、90°異なる方向に拡大された転位像の模式図。

When a lattice with a spacing d₁ and another lattice with a spacing d₂, where d₂-d₁<d₁ or d₂, are superposed in parallel, an enlarged lattice with spacing D = d₁・d₂/(d₂-d₁) that is parallel to the original lattice appears. The lattice fringes are called "parallel Moire fringe." When two lattices with the same spacing d are superposed with a rotation by angle α, an enlarged lattice with spacing D = d/α emerges in a direction perpendicular (90°different) to the original lattice. The lattice fringes are called "rotation Moire fringe." An example of applications of Moire fringes is observation of an edge dislocation. When a perfect lattice is superposed on a lattice containing an edge dislocation, where the latter lattice is rotated a little with respect to the former at the dislocation, an enlarged dislocation image appears in a direction perpendicular to the original dislocation.

(1a) Bright-field image of mica showing Moiré fringes, taken at an accelerating voltage of 200 kV.
(1b) Schematic of rotation Moiré fringes. The fringes with an enlarged spacing appear when crystal lattices A and B which have the same spacing are superposed with a small orientation change.

(2) Schematic of an enlarged dislocation image. An enlarged dislocation image is formed when a perfect lattice (B) is superposed on a lattice containing an edge dislocation (A’) with a small orientation change. It should be noted that the enlarged image is perpendicular to the original dislocation.