A friend of yours has been trying to develop a zero-thermal expansion material.
ID: 3550408 • Letter: A
Question
A friend of yours has been trying to develop a zero-thermal expansion material. She has managed to synthesize a material that has a tetragonal (rectangular parallelepiped with the length equal to width) unit cell. She has measured the a (length and width) parameter and the c parameter (height) from 260 to 500 degrees Celsius at increments of 20 degrees. These values have been saved in the file Lattice_Parameters.mat. The lattice parameters have the units of Angstroms.
Use the plotyy command to plot the cell dimensions as a function of temperature with different scales for the a and c parameters. Add a legend identifying which line corresponds to which parameter. (Make sure the legend does not cover any data.) Calculate the volume for each temperature and create a table with the temperatures in the first column and volumes in the second columns.
*(Lattice_Parameters.mat datas are
a=13.7410000000000 13.6780000000000 13.6210000000000 13.5600000000000 13.4990000000000 13.4410000000000 13.3820000000000 13.3190000000000 13.2600000000000 13.1980000000000 13.1410000000000 13.0580000000000 13
c=6.30200000000000 6.36600000000000 6.42900000000000 6.48400000000000 6.56100000000000 6.62500000000000 6.69000000000000 6.76400000000000 6.82200000000000 6.88300000000000 6.95100000000000 7.01600000000000 7.08000000000000
Explanation / Answer
load('lattice_parameter.mat');
a=lattice_parameter(:,1);
c=lattice_parameter(:,2);
T=260:20:500; %temperature
plot(T,a)
hold on
grid on
plot(T,c,'--k')
hold off
legend('a vs T','c vs T');
xlabel('temperature')
ylabel('parameter')
ylim([5 20])