Conduction of heat takes place:

Conduction of heat refers to the transfer of thermal energy through a material without the movement of the material itself. This process occurs primarily at the atomic or molecular level and is fundamentally based on the vibrations and collisions of particles.

When heat is conducted through a solid, atoms or ions vibrate more vigorously as they gain energy. These vibrations are transmitted from one atom to adjacent atoms, leading to a transfer of energy through direct contact.

The option mentioning conduction from ion to ion within the substance is misleading because heat transfer occurs through collisions and interactions of particles, not specifically through ions, and is not limited to a single mechanism or direction. The second choice involving a difference in densities is related more to convection and is not a method of heat conduction. Heat conduction does not operate in straight lines like rays from the sun, as suggested in the third choice, because heat transfer is a result of particle interaction and can take place through any arrangement of particles in contact.

Therefore, the statement that 'none of the above' accurately reflects that the provided options do not accurately describe the process of heat conduction, validating the choice of option D.