$($a$)$ Explain the heat treatment methods of: $$

$($i$)$ annealing, 

$($ii$)$ normalizing, $$

$($iii$)$ quenching, $$

$($iv$)$ tempering, and $$

$($v$)$ austempering. 

$($b$)$ Explain how tempering can be used to improve the strength of the quenched alloy. 

$($c$)$ Explain the effect of annealing temperature and annealing time on grain size. 

$($d$)$ Explain, using the diagram below, how to obtain bainite, pearlite, and martensite. Compare the hardness and tensile strength of these materials and discuss their suitable applications. $(25$ Marks$)$

Temperature C 800 700 600 500 400 Y unstable 300 200 100 0 y unstable M M 10 4 y+Martensite Martensite 1 sec y stable 10 10 sec Start (0%) fine pearlite Upper bainite 10 course Finish medium (100%) pearlite pearlite 50% transformed I min a + Fe, C 10 Time (sec, log scale) 723C 15 min 1 hr 10 lower bainite 4 Pearlite 10 Bainite 10 hr 10