K$-$L system

Component K melts at $1270\backslash$deg C$,$ and Component L melts at $980\backslash$deg C$.$

There are two intermediate compounds: K$3$L $(17\%$ L$)$ and KL $(48\%$ L$).$

Both K$3$L and KL melt incongruently at $1010\backslash$deg C and $870\backslash$deg C$,$ respectively.

Eutectic e$1$ involves coexistence of KL$-$L$-$Liquid $(80\%$ L$)$ at $680\backslash$deg C$.$

Peritectic p$1$ involves coexistence of K$-$K$3$L$-$Liquid $(37\%$ L$)$ at $1010\backslash$deg C$.$

Peritectic p$2$ involves coexistence of K$3$L$-$KL$-$Liquid $(60\%$ L$)$ at $870\backslash$deg C$.$

K$-$M system

Component K melts at $1270\backslash$deg C$,$ and Component M melts at $1310\backslash$deg C$.$

There is one intermediate compound: KM $(51\%$ M$).$ KM melts congruently at $1480\backslash$deg C$.$

Eutectic e$2$ involves coexistence of K$-$KM$-$Liquid $(30\%$ M$)$ at $1010\backslash$deg C

Eutectic e$3$ involves coexistence of KM$-$M$-$Liquid $(80\%$ M$)$ at $1170\backslash$deg C

L$-$M system

Component L melts at $980\backslash$deg C$,$ and Component M melts at $1310\backslash$deg C$.$

There are two intermediate compounds: L$3$M$2(40\%$ M$)$ and LM $(60\%$ M$).$

L$3$M$2$ melts incongruently at $870\backslash$deg C whereas LM melts congruently at $1280\backslash$deg C$.$

Eutectic e$4$ involves coexistence of L$-$L$3$M$2-$Liquid $(18\%$ M$)$ at $780\backslash$deg C$.$

Eutectic e$5$ involves coexistence of LM$-$M$-$Liquid $(80\%$ M$)$ at $1070\backslash$deg C$.$

Peritectic p$3$ involves coexistence of L$3$M$2-$LM$-$Liquid $(30\%$ M$)$ at $870\backslash$deg C$.$

K$-$L$-$M system

Use the liquidus data in K$-$L$,$ K$-$M and L$-$M diagrams. Plot the liquidus projection of K$-$L$-$M$.$

Ternary Invariant Point I$1$ involves coexistence of KM$-$LM$-$M$-$Liq. $(10\%$ K$,20\%$ L$,70\%$ M$)$ at $960\backslash$deg C

Ternary Invariant Point I$2$ involves coexistence of K$-$K$3$L$-$KM$-$Liq. $(55\%$ K$,25\%$ L$,20\%$ M$)$ at $880\backslash$deg C

Ternary Invariant Point I$3$ involves coexistence of K$3$L$-$KM$-$LM$-$Liq. $(30\%$ K$,35\%$ L$,35\%$ M$)$ at $750\backslash$deg C

Ternary Invariant Point I$4$ involves coexistence of KL$-$K$3$L$-$LM$-$Liq. $(25\%$ K$,50\%$ L$,25\%$ M$)$ at $680\backslash$deg C

Ternary Invariant Point I$5$ involves coexistence of KL$-$LM$-$L$3$M$2-$Liq. $(15\%$ K$,65\%$ L$,20\%$ M$)$ at $620\backslash$deg C

Ternary Invariant Point I$6$ involves coexistence of KL$-$L$3$M$2-$L$-$Liq. $(15\%$ K$,75\%$ L$,10\%$ M$)$ at $530\backslash$deg C

a$)$ Draw the binary diagrams of K$-$L$,$ K$-$M and L$-$M systems. Label the all the fields in the diagrams.

b$)$ Draw the ternary diagram of K$-$L$-$M system. Label the all the primary fields of crystallization in the diagram.

c$)$ Draw the Alkemades lines and form the crystallization triangles in K$-$L$-$M system.

d$)$ Identify the ternary invariant points in K$-$L$-$M system.

e$)$ Find and locate the composition $65\%$ K $25\%$ L$,$ and $10\%$ M$.$

f$)$ Clarify the composition triangle according to the composition that assigned to you go through final

solidification.

g$)$ Indicate the path of solidification by mentioning the phases that precipitate along the path and show the

invariant point where the reactions of final solidification $($the invariant reaction$)$ for your composition.

h$)$ Calculate the weight percentage and indicate the composition of the phases that exist at T$$p

$+$

$($Above the invariant point temp. $)$ and T$$p

$$

$($Below the invariant point temp. $)$ and indicate the amount of

liquid phase for your composition.

i$)$ Draw the projected Isotherms in K$-$L$-$M system.

j$)$ Draw the isothermal sections for $1200,1000,800$ and $600\backslash$deg C$.$