Q.Graphite and diamond are

Crystalline solids are further split into four families by what holds their constituent particles together, and each family's bonding directly sets its melting point, hardness and conductivity:

• Ionic solids (e.g. NaCl): cations and anions bound by strong electrostatic attraction. High melting point; hard but brittle; non-conducting as a solid (ions are fixed), but conducts well molten or in solution (ions become mobile).
• Covalent (network) solids (e.g. diamond, SiC): atoms bound into one continuous 3D network purely by covalent bonds. Very hard, very high melting point, usually poor thermal/electrical conductors -- though graphite is a notable exception (strong bonding within 2D sheets, weak forces between sheets, giving it softness, slipperiness and in-plane conductivity).
• Molecular solids (e.g. CO2, ice, naphthalene): neutral molecules held by weak van der Waals forces. Soft, low melting point, non-conducting. Sub-divided by the strength of that force: non-polar (dispersion forces only, e.g. naphthalene) < polar (dipole-dipole, e.g. solid CO2) < hydrogen-bonded (e.g. ice, glucose) in order of increasing melting point.
• Metallic solids (e.g. Cu, Fe, brass): metal cations sit at the lattice points, embedded in a mobile 'sea' of delocalised electrons. Hard, high melting point, excellent electrical/thermal conductivity, bright lustre.

Why ionic crystals are hard yet brittle: the strong electrostatic attraction between ions resists any external force trying to shift their relative positions (hardness), but if a shear force does succeed in sliding one plane of ions past the next, like-charged ions are brought face to face; the resulting strong repulsion shatters the crystal rather than letting it bend (brittleness) -- unlike a metal, where the electron sea lets planes of cations slide past each other without ever bringing like charges together.