Colossal dielectric response of H f x Z r 1 − x O 2 nanoparticles

We observed a colossal dielectric response of small (5–10 nm) oxygen-deficient <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="normal">H</a:mi> <a:msub> <a:mi mathvariant="normal">f</a:mi> <a:mi>x</a:mi> </a:msub> <a:mi mathvariant="normal">Z</a:mi> <a:msub> <a:mi mathvariant="normal">r</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mo>−</a:mo> <a:mi>x</a:mi> </a:mrow> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> nanoparticles ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>x</g:mi> <g:mo>=</g:mo> <g:mn>1</g:mn> <g:mo>–</g:mo> <g:mn>0.4</g:mn> </g:mrow> </g:math> ), prepared by solid-state organonitrate synthesis. The effective dielectric permittivity of the pressed <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi mathvariant="normal">H</h:mi> <h:msub> <h:mi mathvariant="normal">f</h:mi> <h:mi>x</h:mi> </h:msub> <h:mi mathvariant="normal">Z</h:mi> <h:msub> <h:mi mathvariant="normal">r</h:mi> <h:mrow> <h:mn>1</h:mn> <h:mo>−</h:mo> <h:mi>x</h:mi> </h:mrow> </h:msub> <h:msub> <h:mi mathvariant="normal">O</h:mi> <h:mn>2</h:mn> </h:msub> </h:mrow> </h:math> nanopowders has a pronounced maximum at <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mn>38</n:mn> <n:mo>–</n:mo> <n:mn>88</n:mn> <n:msup> <n:mspace width="0.16em"/> <n:mo>∘</n:mo> </n:msup> <n:mi mathvariant="normal">C</n:mi> </n:mrow> </n:math> , the shape of which can be fitted by the Curie-Weiss type dependence modified for the diffuse ferroelectric-paraelectric phase transition. The maximal value of the dielectric permittivity increases from <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mn>1.5</q:mn> <q:mo>×</q:mo> <q:msup> <q:mrow> <q:mn>10</q:mn> </q:mrow> <q:mn>3</q:mn> </q:msup> </q:mrow> </q:math> (for <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:mi>x</r:mi> <r:mo>=</r:mo> <r:mn>1</r:mn> </r:mrow> </r:math> ) to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mrow> <s:mn>1.5</s:mn> <s:mo>×</s:mo> <s:msup> <s:mrow> <s:mn>10</s:mn> </s:mrow> <s:mn>5</s:mn> </s:msup> </s:mrow> </s:math> (for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mrow> <t:mi>x</t:mi> <t:mo>=</t:mo> <t:mn>0.4</t:mn> </t:mrow> </t:math> ) at low frequencies ( <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mrow> <u:mo>∼</u:mo> <u:mn>4</u:mn> </u:mrow> </u:math> Hz), being much smaller, namely, changing from 7 (for <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"> <v:mrow> <v:mi>x</v:mi> <v:mo>=</v:mo> <v:mn>1</v:mn> </v:mrow> </v:math> ) to 20 (for <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"> <w:mrow> <w:mi>x</w:mi> <w:mo>=</w:mo> <w:mn>0.4</w:mn> </w:mrow> </w:math> ) at high frequencies ( <x:math xmlns:x="http://www.w3.org/1998/Math/MathML"> <x:mrow> <x:mo>∼</x:mo> <x:mn>500</x:mn> </x:mrow> </x:math> kHz). The frequency dispersion of the dielectric permittivity maximum position is almost absent; meanwhile, the shape and width of the maximum changes in a complex way with increase in frequency. The temperature dependencies of the dielectric permittivity and resistivity are almost mirrorlike turned over with respect to each other, which means that all their features, such as position and shape of maxima, plateau, minima, and inflexions, almost coincide after the mirror reflection with respect to the temperature axis. These correlations of resistivity and dielectric permittivity are well described in the Heywang barrier model applied together with the variable range hopping conduction model in semiconducting ferroelectrics. Ferroelectriclike behavior of the small oxygen-deficient <y:math xmlns:y="http://www.w3.org/1998/Math/MathML"> <y:mrow> <y:mi mathvariant="normal">H</y:mi> <y:msub> <y:mi mathvariant="normal">f</y:mi> <y:mi>x</y:mi> </y:msub> <y:mi mathvariant="normal">Z</y:mi> <y:msub> <y:mi mathvariant="normal">r</y:mi> <y:mrow> <y:mn>1</y:mn> <y:mo>−</y:mo> <y:mi>x</y:mi> </y:mrow> </y:msub> <y:msub> <y:mi mathvariant="normal">O</y:mi> <y:mn>2</y:mn> </y:msub> </y:mrow> </y:math> nanoparticles is expected from the Landau-Ginzburg-Devonshire approach and density functional theory calculations. Obtained results may be useful for developing silicon-compatible functional nanomaterials based on <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML"> <eb:mrow> <eb:mi mathvariant="normal">H</eb:mi> <eb:msub> <eb:mi mathvariant="normal">f</eb:mi> <eb:mi>x</eb:mi> </eb:msub> <eb:mi mathvariant="normal">Z</eb:mi> <eb:msub> <eb:mi mathvariant="normal">r</eb:mi> <eb:mrow> <eb:mn>1</eb:mn> <eb:mo>–</eb:mo> <eb:mi>x</eb:mi> </eb:mrow> </eb:msub> <eb:msub> <eb:mi mathvariant="normal">O</eb:mi> <eb:mn>2</eb:mn> </eb:msub> </eb:mrow> </eb:math> nanoparticles.