Question Topics :
Q1. Burgers vector.
See Picture, slide 5, Lecture#6. The crystal is sliping (top portion is sliding wrt to lower portion) in the direction of the slip vector creating certain amount of displacement (indicated by the pink shade). All points across the plane of slip have been displaced from each other by this amount. Hence, this is the magnitude of slip and is called the Burgers vector. Since it is a vector it has a direction too and it is always in the direction of the slip vector. For edge dislocation this becomes perpendicular and for screw parallel to the dislocation line.
For more details you can refer to the Book, Mechanical Metallurgy By George E. Dieter.
Q2. Frenkel defect.
Slide 4, first figure. The smaller atom is supposed to be at the vacant position (the red encirled area) but for some reason it has moved to a position, known as an interstitial site, which is in between two bigger atoms. In the process it has created a vacancy in the lattice and this pair is the Frenkel
Hardenability of steels can be defined as the ability to harden through formation of the martensite phase throughout the cross section when subjected to rapid cooling.
permeability is the measure of a material's ability to support formation of magnetic field in it.
Suceptibility is the degree of magnetization when a magnetic field is applied.
Higher order symmetry like 8, 10, 12 etc are not allowed in crystallography as any shape with these symmetry will not fill the space completely.
Its no different from Fe-C. Fe3C forms at a C content of 6.67% and this point can be taken as 100% Fe3C and hence the diagram can also be represented as Fe-Fe3C. Steels generally have C content much below 6.67% and cast irons can contain up to 4.5%. Therefore, practically there is no need to go beyond 6.67% C.
The max solubility of C in Fe is about 2% in austenite at 1147 C. Beyond this C exists in its free form as graphite which you get in cast irons. At 6.67% C it is only Fe3C which is a hard and brittle intermetallic compound. Therefore, beyond 6.67% you don't get anything useful at least not steels.