The fitting of the temperature dependencies of the dielectric permittivity and resistivity of (Hf, Zr)O_2 nanoparticles
Author
Eugene Eliseev, Anna Morozovska
Title
The fitting of the temperature dependencies of the dielectric permittivity and resistivity of (Hf, Zr)O_2 nanoparticles
Description
code used to perform the fitting of the experimental results, presented in ArXive publication https://doi.org/10.48550/arXiv.2508.04697
Category
Academic Articles & Supplements
Keywords
ferroelectric nanoparticles, resistivity, Landau-Ginsburg-Devonshire model
URL
http://www.notebookarchive.org/2025-08-7fidfp8/
DOI
https://notebookarchive.org/2025-08-7fidfp8
Date Added
2025-08-16
Date Last Modified
2025-08-16
File Size
462.01 kilobytes
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Rights
CC BY 4.0
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The fitting of the temperature dependencies of the dielectric permittivity and resistivity presented in the paper “A colossal dielectric response of HfxZr1-xO2 nanoparticles” [https://doi.org/10.48550/arXiv.2508.04697]
The fitting of the temperature dependencies of the dielectric permittivity and resistivity presented in the paper “A colossal dielectric response of nanoparticles” [https://doi.org/10.48550/arXiv.2508.04697]
Hf
x
Zr
1-x
O
2
Eugene A. Eliseev and Anna N. Morozovska
We observed a colossal dielectric response of small (5 - 10 nm) oxygen-deficient HfxZr1-xO2 nanoparticles (x = 1 0.4), prepared by the solid-state organonitrate synthesis. The effective dielectric permittivity of the pressed HfxZr1-xO2 nanopowders has a pronounced maximum at 38 - 88oC, which shape 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 1.5·103 (for x = 1) to 1.5·105 (for x= 0.4) at low frequencies (~4 Hz); being much smaller, namely changing from 7 (for x = 1) to 20 (for x = 0.4) at high frequencies (~500 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 mirror-like turned over in 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 in 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. The ferroelectric-like behavior of the dielectric permittivity is explained by the Landau-Ginzburg-Devonshire approach.
Experimental data
Experimental data
data plots
data plots
Test of temperature dependence of R and ϵ at 4 Hz
Test of temperature dependence of R and ϵ at 4 Hz
Test of temperature dependence of R and ϵ at 500 kHz
Test of temperature dependence of R and ϵ at 500 kHz
data plot of R vs. 1/(T*ϵ)
data plot of R vs. 1/(T*ϵ)
data fit with Heywang barrier model for dependences of ρ on 1/(T ϵ) (Figure 8)
data fit with Heywang barrier model for dependences of ρ on 1/(T ϵ) (Figure 8)
Dielectric permittivity: fitting of the experimental results
Dielectric permittivity: fitting of the experimental results
Static permittivity vs. temperature: experimental data for different samples
Static permittivity vs. temperature: experimental data for different samples
Fit
Fit
x=0.4, frequency 4 Hz (Figures 9d and S3h)
x=0.4, frequency 4 Hz (Figures 9d and S3h)
x=0.4, frequency 500 kHz (Figures S4d and S4h )
x=0.4, frequency 500 kHz (Figures S4d and S4h )
x=0.5, frequency 4 Hz (Figures 9c and S3g)
x=0.5, frequency 4 Hz (Figures 9c and S3g)
x=0.5, frequency 500 kHz (Figures S4c and S4g )
x=0.5, frequency 500 kHz (Figures S4c and S4g )
x=0.6, frequency 4 Hz (Figures 9b and S3f)
x=0.6, frequency 4 Hz (Figures 9b and S3f)
x=0.6, frequency 500 kHz (Figures S4b and S4f )
x=0.6, frequency 500 kHz (Figures S4b and S4f )
x=1.0, frequency 4 Hz (Figures 9a and S3e)
x=1.0, frequency 4 Hz (Figures 9a and S3e)
x=1.0, frequency 500 kHz (Figures S4a and S4e )
x=1.0, frequency 500 kHz (Figures S4a and S4e )
Figure S5: alternative fitting functions
Figure S5: alternative fitting functions
Fitting functions for Static Permittivity
Fitting functions for Static Permittivity
x=0.4 at 4 Hz (Figures S5d and S5h)
x=0.4 at 4 Hz (Figures S5d and S5h)
x=0.5 at 4 Hz (Figures S5c and S5g )
x=0.5 at 4 Hz (Figures S5c and S5g )
Full experimental curve
Full experimental curve
low temperature Curie-Weiss fit
low temperature Curie-Weiss fit
high temperature Curie-Weiss fit
high temperature Curie-Weiss fit
Pseudo-Lorentzian Fit
Pseudo-Lorentzian Fit
Pseudo-Ising Fit
Pseudo-Ising Fit
All the fits combined (Figures S5c and S5g )
All the fits combined (Figures S5c and S5g )
x=0.6 at 4 Hz (Figures S5d and S5f )
x=0.6 at 4 Hz (Figures S5d and S5f )
x=1.0 at 4 Hz (Figures S5a and S5e )
x=1.0 at 4 Hz (Figures S5a and S5e )
Cite this as: Eugene Eliseev, Anna Morozovska, "The fitting of the temperature dependencies of the dielectric permittivity and resistivity of (Hf, Zr)O_2 nanoparticles" from the Notebook Archive (2025), https://notebookarchive.org/2025-08-7fidfp8
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