inorganic chemistry - Why do different elements form different types of carbides?

What property of the elements make them form different types of carbides like:

$\ce{Be}$ and $\ce{Al}$ - $\ce{Be2C}$ and $\ce{Al4C3}$ (Methanides) contains $\ce{C^4-}$ ion

$\ce{Na}$ and $\ce{Ca}$ - $\ce{Na2C2}$ and $\ce{CaC2}$ (acetylides) contains $\ce{C2^{2-}}$ ion

$\ce{Li}$ and $\ce{Mg}$ - $\ce{Li4C3}$ and $\ce{Mg2C3}$ (sesquicarbides) contains $\ce{C3^4-}$ ion.

Boron - $\ce{B4C}$ (covalent carbides)

Titanium and tungsten - $\ce{TiC}$ and $\ce{WC}$ (interstitial carbides)

Answer

According to wikipedia,

Carbides can be generally classified by chemical bonding type as follows:

1. salt-like carbides


2. covalent carbides


3. interstitial carbides


4. "intermediate" transition metal carbides.

This type of classification is based on the electronegativity of the element to which the carbon is bonded.

According to this site:-

The most electropositive metals form ionic or saltlike carbides, the transition metals in the middle of the periodic table tend to form what are called interstitial carbides, and the nonmetals of electronegativity similar to that of carbon form covalent or molecular carbides.

Actually credits goes to @jatin who gave me an important hint:-

You might wanna consider diagonal relationship which accounts for similarities between those particular metals.

As you can see that Li and Mg, Na and Ca and Be and Al all form diagonal element pairs. So, they are expected to have similar properties. So, considering their electronegativity, the diagonal element pairs have almost same value (though Li and Mg electronegativity is quite different). So they form similar type of carbide.

(original picture)

As for the intestitial carbides, @bon said that

Insterstitial carbides only form with large cations (Ti and W), as you might expect if the anion (very small) to fit in the spaces in the cation crystal structure.