On cooling the cubic perovskite SrZrO₃ (space group Pm3m) from high temperature, it undergoes a phase transition to the tetragonal space group I4/mcm. At the phase transition, the c cell parameter doubles and a increases by √2. The strain et is related to the difference in a and c parameters scaled back to those of the cubic cell. With appropriate normalization,

e = (2/3)((c-a)/acub) where acub is the cell parameter expected for an undistorted material at that temperature, and is expected to be proportional to n'. The table below contains unit-cell parameters at various temperatures from ref. [9] that were later analyzed in ref. [10]. Plot the temperature evolution of the cell parameters. By assuming a sensible functional form, predict acub for each temperature below 1360 K. Comment on your graph. (b) Comment on a plot of e0.5 versus T. (c) From a suitable plot, show that the data are consistent with the transition being close to tricritical in character and determine the transition temperature Te T(K) 1160 1180 1200 1220 1240 1260 1280 1300 1320 1340 a () 4.1394 4.1405 4.1416 4.1428 4.1441 4.1455 4.1469 4.1485 4.1500 4.1517 c (A) 4.1514 4.1520 4.1524 4.1529 4.1532 4.1535 4.1539 4.1542 4.1542 4.1537 T(K) 1360 1380 1400 1420 1440 1460 1480 1500 acub () 4.1536 4.1546 4.1555 4.1565 4.1575 4.1585 4.1594 4.1604