Diagonal relationships arise when two elements one period apart and one group apart have similar charge density $\frac{charge}{radius ratio}$ and electronegativity. Li-Mg: Both form nitrides directly, both carbonates decompose on heating, both halides are covalent, both fluorides and phosphates are insoluble. Be-Al: Both form amphoteric oxides/hydroxides, both form covalent bridged chlorides, both carbides give CH4 with water. B-Si: Both are metalloids, both form covalent hydrides and acidic oxides, both form glasses/network solids. The diagonal relationship is much more prominent in Period 2/3 and weakens further down the table.