Academic Articles & Supplements

Ferro-ionic States and Domains Morphology in (Hf,Zr)O_2 Nanoparticles

Eugene Eliseev, Anna Morozovska

Author

Eugene Eliseev, Anna Morozovska

Title

Ferro-ionic States and Domains Morphology in (Hf,Zr)O_2 Nanoparticles

Description

code to perform calculations, presented in prerint arXiv:2410.04476

Ferro-ionic States and Domains Morphology in
Hf
x
Zr
1-x
O
2
Nanoparticles

Eugene A. Eliseev and Anna N. Morozovska

Unique polar properties of nanoscale hafnia-zirconia oxides HfxZr1-xO2 (HZO) are of great interest for condensed matter physics, nanophysics and advanced applications. These properties are connected (at least partially) to the ionic-electronic and electrochemical phenomena at the surface, interfaces and/or internal grain boundaries. Here we calculated the phase diagrams, dielectric permittivity, spontaneous polar and antipolar ordering, as well as the domain structure morphology in HZO nanoparticles covered by ionic-electronic charge originating from the surface electrochemical adsorption. We revealed that the ferro-ionic coupling supports the polar long-range order in the nanoscale HZO, induces and/or enlarges the stability region of the labyrinthine domains towards smaller sizes and smaller environmental dielectric constant at low concentrations of the surface ions. The ferro-ionic coupling causes the transition to the single-domain ferro-ionic state at high concentrations of the surface ions

Definitions

Parameters of Landau-Ginsburg-Devonshire model: x-dependences


Phase diagrams and Loops without domains


Phase diagrams and Loops with domains included


colors scheme for different phases


Figures

Tyical hysteresis Loops at fixed values of
ε
e
,x
,
R
and
n
1,2
(for Figure 1b)


phase diagram in coordinates (R, x) and physical properties at fixed
n
1,2
(Figure 2)


phase diagram in coordinates
(
ε
e
,x
) at fixed
R
and
n
1,2
(Figure 3)


phase diagram in coordinates
(
n
i
,x
) at fixed
R
and
ε
e
(Figure 4)


NC-criterium at map
(
n
i
,x
) at fixed
R
and
ε
e
(Figure 7)


phase diagram in coordinates
(
n
i
,x
) at fixed
R
and
ε
e
, single-domain aproxymation (NO DOMAINS taken into account)


Loops for different values of
(
n
1,2
,x
) at fixed
R
and
ε
e
(supplement Figure)


Loops for different values of
(
ε
e
,x
) at fixed
R
and
n
1,2
(supplement Figure)


Cite this as: Eugene Eliseev, Anna Morozovska, "Ferro-ionic States and Domains Morphology in (Hf,Zr)O_2 Nanoparticles" from the Notebook Archive (2024), https://notebookarchive.org/2024-10-6hf91wv

Ferro-ionic States and Domains Morphology in HfxZr1-xO2 Nanoparticles

Definitions

​Parameters of Landau-Ginsburg-Devonshire model: x-dependences 

Phase diagrams and Loops without domains

Phase diagrams and Loops with domains included

colors scheme for different phases 

Figures

Tyical hysteresis Loops at fixed values of εe,x, R and n1,2 (for Figure 1b)

phase diagram in coordinates (R, x) and physical properties at fixed n1,2 (Figure 2)

phase diagram in coordinates (εe,x) at fixed R and n1,2 (Figure 3)

phase diagram in coordinates (ni,x) at fixed R and εe (Figure 4)

NC-criterium at map (ni,x) at fixed R and εe (Figure 7)

phase diagram in coordinates (ni,x) at fixed R and εe, single-domain aproxymation (NO DOMAINS taken into account)

Loops for different values of (n1,2,x) at fixed R and εe (supplement Figure)

Loops for different values of (εe,x) at fixed R and n1,2 (supplement Figure)