Slip planes in monoclinic <i>β</i> -Ga ₂ O ₃ revealed from its {010} face via synchrotron X-ray diffraction and X-ray topography

Abstract

Abstract Dislocations and their arrays in a {010}-oriented β -Ga 2 O 3 substrate were observed using synchrotron X-ray diffraction (XRD) and X-ray topography (XRT). The XRD measurements used spatially-resolved ω -rocking curves to show that dislocation arrays have a linear contrast with a lower diffraction intensity and a broader full-width at half maximum. Further XRT observations at three different <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo stretchy="true">⃗</mml:mo> </mml:mrow> </mml:mover> </mml:math> vectors resolved these lines as dot contrasts aligned along the four different directions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>100</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>102</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>201</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>001</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> </mml:math> which correspond to the outcrops of threading dislocations that lay in four different slip planes. The Burgers vectors for these dislocation arrays were determined using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo stretchy="true">⃗</mml:mo> </mml:mrow> </mml:mover> </mml:math> ∙ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>b</mml:mi> <mml:mo>⃗</mml:mo> </mml:mover> </mml:math> invisibility criterion. The results indicate there are four slip systems of (1) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>010</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> {001}, (2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>010</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> { <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> 01}, (3) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>201</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> {10 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> }, and (4) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>001</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> {100}. The slip system <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="〈" separators=""> <mml:mrow> <mml:mn>201</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> {10 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> } ha

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