Tuning superconductivity in high entropy nitrides

The recently investigated nitrogen (N) incorporation into TiNbMoTaW high entropy alloy films leads to a domelike superconducting transition temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>T</a:mi> <a:mi>C</a:mi> </a:msub> </a:math> vs nitrogen concentration <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>x</b:mi> </b:math> (with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>x</c:mi> <c:mo>=</c:mo> <c:mtext>N</c:mtext> <c:mo>/</c:mo> <c:mi>M</c:mi> </c:mrow> </c:math> representing the ratio between atomic fractions of nitrogen and metal atoms, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>M</d:mi> <d:mo>=</d:mo> <d:mi>Ti</d:mi> <d:mo>+</d:mo> <d:mi>Nb</d:mi> <d:mo>+</d:mo> <d:mi>Mo</d:mi> <d:mo>+</d:mo> <d:mi>Ta</d:mi> <d:mo>+</d:mo> <d:mi mathvariant="normal">W</d:mi> </d:mrow> </d:math> ) in the respective high entropy nitride <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mrow> <f:mo>(</f:mo> <f:mi>TiNbMoTaW</f:mi> <f:mo>)</f:mo> </f:mrow> <f:mrow> <f:mn>1.0</f:mn> </f:mrow> </f:msub> <f:msub> <f:mi mathvariant="normal">N</f:mi> <f:mi>x</f:mi> </f:msub> </f:mrow> </f:math> , with a large <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>T</h:mi> <h:mi>C</h:mi> </h:msub> </h:math> enhancement. In this study, we report on the effect of N insertion into NbTaHfTiZr films, which show a lower valence electron concentration and a lower configuration entropy than those of TiNbMoTaW. The <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>T</i:mi> <i:mi>C</i:mi> </i:msub> </i:math> vs <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>x</j:mi> </j:math> dependence in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:msub> <k:mrow> <k:mo>(</k:mo> <k:mi>NbTaHfTiZr</k:mi> <k:mo>)</k:mo> </k:mrow> <k:mrow> <k:mn>1.0</k:mn> </k:mrow> </k:msub> <k:msub> <k:mi mathvariant="normal">N</k:mi> <k:mi>x</k:mi> </k:msub> </k:mrow> </k:math> exhibits a different course, in which <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>T</m:mi> <m:mi>C</m:mi> </m:msub> </m:math> first decreases from <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mo>∼</n:mo> <n:mn>6.5</n:mn> <n:mspace width="0.28em"/> <n:mi mathvariant="normal">K</n:mi> </n:mrow> </n:math> at <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mi>x</q:mi> <q:mo>=</q:mo> <q:mn>0</q:mn> </q:mrow> </q:math> to <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:msub> <r:mi>T</r:mi> <r:mi>C</r:mi> </r:msub> <r:mo>≈</r:mo> <r:mn>1</r:mn> <r:mspace width="0.28em"/> <r:mi mathvariant="normal">K</r:mi> </r:mrow> </r:math> at <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mrow> <u:mi>x</u:mi> <u:mo>=</u:mo> <u:mn>0.25</u:mn> </u:mrow> </u:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"> <v:mrow> <v:mi>x</v:mi> <v:mo>=</v:mo> <v:mn>0.42</v:mn> </v:mrow> </v:math> , and then starts to increase and reaches a maximum of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"> <w:mrow> <w:mo>∼</w:mo> <w:mn>8.6</w:mn> <w:mspace width="0.28em"/> <w:mi mathvariant="normal">K</w:mi> </w:mrow> </w:math> at <z:math xmlns:z="http://www.w3.org/1998/Math/MathML"> <z:mrow> <z:mi>x</z:mi> <z:mo>=</z:mo> <z:mn>0.81</z:mn> </z:mrow> </z:math> followed by a decline to <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML"> <ab:mrow> <ab:mo>∼</ab:mo> <ab:mn>6.7</ab:mn> <ab:mspace width="0.28em"/> <ab:mi mathvariant="normal">K</ab:mi> </ab:mrow> </ab:math> when <db:math xmlns:db="http://www.w3.org/1998/Math/MathML"> <db:mi>x</db:mi> </db:math> approaches the stoichiometric value 1. In this case, the transition of the initial high entropy alloy bcc structure to the fcc structure of high entropy nitrides proceeds slowly and leads to a wide <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML"> <eb:mi>x</eb:mi> </eb:math> range in which <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML"> <fb:msub> <fb:mi>T</fb:mi> <fb:mi>C</fb:mi> </fb:msub> </fb:math> is suppressed. The analysis shows that the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML"> <gb:msub> <gb:mi>T</gb:mi> <gb:mi>C</gb:mi> </gb:msub> </gb:math> vs <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML"> <hb:mi>x</hb:mi> </hb:math> course and the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML"> <ib:msub> <ib:mi>T</ib:mi> <ib:mi>C</ib:mi> </ib:msub> </ib:math> enhancement in high entropy nitrides depend on the valence electron concentration of the initial high entropy alloy, as higher values accelerate the tendency to form a fcc structure and are less sensitive to the localization of otherwise mobile electrons in metallic high entropy alloys due to their bonding to N atoms. However, other parameters, such as the atomic size difference of the metallic constituents and their affinity towards nitrogen, also have to be considered.