Problem $2$: Aperture grills for cathode ray tubes

There are two types of cathode ray tube $($CRT$).$ In the older technology, color separation is achieved by using a shadow mask: a thin metal plate with a grid of holes that allow only the correct beam to strike a red, green, or blue phosphor. A shadow mask can heat up and distort at high brightness levels $(\text{'}$doming$\text{'}),$ causing the beams to miss their targets, and giving a blotchy image.

To avoid this, shadow masks are made of Invar, a nickel alloy with a near$-$zero expansion coefficient between room temperature and $150C.$ It is a consequence of shadow$-$mask technology that the glass screen of the CRT curves inward on all four edges, increasing the probability of reflected glare.

Sony's "Trinitron" technology overcame this problem and allowed greater brightness by replacing the shadow mask with an aperture grill of fine vertical wires, each about $200m$ in thickness, that allows the intended beam to strike either the red, the green, or the blue phosphor to create the image. The glass face of the Trinitron tube was curved in one plane only, reducing glare.

The wires of the aperture grill are tightly stretched, so that they remain taut even when hot$-$it is this tension that allows the greater brightness. The table summarizes the requirements.

$\backslash$table$[[$Function$,$Aperture grill for CRT$],[$Constraints$,\backslash$table$[[$Wire thickness and spacing specified$],[],[],[$Must carry pre$-$tension without failure$]]],[,$Electrically conducting to prevent charging$],[$Objective$,\backslash$table$[[$Able to be drawn to wire$]]],[$Free variable,Maximize permitted temperature rise without loss of tension$]]$

A$.$ Using the data in the appendixes, identify the material inde $-$ write formulas and eberything

B$.$ Use "ANSYS Granta" software to build the corresponding property chart$($s$).$

C$.$ Create a list of candidate materials and make a short documentation to propose the best material.

Good Luck