Analysis of phonon decay processes in corundum structured α − In 2 O 3 and α − Al 2 O 3 by temperature dependent Raman spectroscopy

Temperature dependent Raman spectroscopy was employed on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>α</a:mi> <a:mtext>−</a:mtext> <a:msub> <a:mi>In</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>α</c:mi> <c:mtext>−</c:mtext> <c:msub> <c:mi>Al</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi mathvariant="normal">O</c:mi> <c:mn>3</c:mn> </c:msub> </c:mrow> </c:math> to determine the phonon decay factors associated with the decay of phonons into two and three phonons. Differently oriented corundum structured <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>α</e:mi> <e:mtext>−</e:mtext> <e:msub> <e:mi>In</e:mi> <e:mn>2</e:mn> </e:msub> <e:msub> <e:mi mathvariant="normal">O</e:mi> <e:mn>3</e:mn> </e:msub> </e:mrow> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>α</g:mi> <g:mtext>−</g:mtext> <g:msub> <g:mi>Al</g:mi> <g:mn>2</g:mn> </g:msub> <g:msub> <g:mi mathvariant="normal">O</g:mi> <g:mn>3</g:mn> </g:msub> </g:mrow> </g:math> samples were analyzed by temperature dependent Raman spectroscopy between 80 and 300 K. The shift of the resonance frequency of the Raman active phonon modes <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>A</i:mi> <i:mrow> <i:mn>1</i:mn> <i:mi>g</i:mi> </i:mrow> </i:msub> <i:mo>(</i:mo> <i:mn>1</i:mn> <i:mo>)</i:mo> <i:mo>,</i:mo> </i:math> <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi>E</j:mi> <j:mi>g</j:mi> </j:msub> <j:mo>(</j:mo> <j:mn>4</j:mn> <j:mo>)</j:mo> <j:mo>,</j:mo> <j:mo> </j:mo> <j:mtext>and</j:mtext> <j:mo> </j:mo> <j:msub> <j:mi>E</j:mi> <j:mi>g</j:mi> </j:msub> <j:mo>(</j:mo> <j:mn>5</j:mn> <j:mo>)</j:mo> </j:math> was investigated by a model function including the thermal expansion of the lattice and the decay of the phonons into two and three phonons with lower energy. We obtain the phonon decay factors <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>A</k:mi> </k:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi>B</l:mi> </l:math> representing the decay into two and three phonons, respectively. The findings are in reasonable agreement with the existing literature on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>α</m:mi> <m:mtext>−</m:mtext> <m:msub> <m:mi>Al</m:mi> <m:mn>2</m:mn> </m:msub> <m:msub> <m:mi mathvariant="normal">O</m:mi> <m:mn>3</m:mn> </m:msub> <m:mo>,</m:mo> </m:mrow> </m:math> <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mi>α</o:mi> <o:mtext>−</o:mtext> <o:msub> <o:mi>Ga</o:mi> <o:mn>2</o:mn> </o:msub> <o:msub> <o:mi mathvariant="normal">O</o:mi> <o:mn>3</o:mn> </o:msub> <o:mo>,</o:mo> </o:mrow> </o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mi>α</q:mi> <q:mtext>−</q:mtext> <q:msub> <q:mi>In</q:mi> <q:mn>2</q:mn> </q:msub> <q:msub> <q:mi mathvariant="normal">O</q:mi> <q:mn>3</q:mn> </q:msub> </q:mrow> </q:math> .