Contour plot of Landau energy density

Question

Hexe 2023-12-12

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https://ww2.mathworks.cn/matlabcentral/answers/2059754-contour-plot-of-landau-energy-density

回答： Yash 2023-12-22

Hi! I have the Landau energy density for ferroelectric where X,Y,Z are components of polarization and Y is a polar axis.

Using this code I obtain a standart plot of 2 minima.

clear all

X = -0.1:0.001:0.1;

Y = -0.1:0.001:0.1;

Z = -0.1:0.001:0.1;

ax = 0.132;

az = 0.214;

a0 = 3.5e7;

b = 7.5e11;

axz = -0.011;

Tc = 322;

T = 200;

F = (X.^2)*ax + (Y.^2)*a0*(T - Tc) + (Z.^2)*az + (Y.^4)*b + (X.*Z)*axz;

figure(1)

plot(Y,F)

I need to obtain a contour plot with states of polarization (for example in XY-plane). Here it will be just 2 minima, because only one axis Y is polar and has a fourth power in the potential. The contour should look similar like in the attached picture but only with 2 minima. I would be very grateful for the ideas and recommendations expressed.

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Answer 1

Yash 2023-12-22

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Hello Hexe,

To obtain a contour plot with the states of polarization, you can use the 'contour' function in MATLAB. This function will help you generate a contour plot with any number of contour levels, representing the states of polarization in the XY-plane. You can adjust the number of contour levels to achieve the desired level of detail in the plot.

You can refer to the documentation of the 'contour' function to know how to use it in your code: https://www.mathworks.com/help/matlab/ref/contour.html

Hope this helps!