[Bob Sacamano]

Don't second period elements have empty d orbitals? If so why are they not capable of forming expanded octets?

[MrTeo]

Don't second period elements have empty d orbitals?

No, simply because l (the secondary quantum number), which defines the shape of the orbitals, goes from 0 to n-1 (where n is the principal quantum number):

0: s orbitals
1: p orbitals
2: d orbitals
3: f orbitals

as you can see n must be ≥3 to have l=2, that's why 1st and 2nd period elements can't form expanded octets.

[nigel433]

Technically, all atoms DO have an infinity of all sorts of orbitals - but
most are unoccupied all the time, because electrons in them would
have too high an energy.

Through the Periodic Table the "shells" of neutral atoms are filled progressively
as the positive charge on  the nucleus increases. The first shell has one s-orbital
(with two electron places, of course) and no p-orbitals; the second shell
has one more s-orbital and three p-orbitals (eight electron places in total);
the third shell has one s-orbital, three p-orbitals AND some d-orbitals....

"Expanded octet" is a misleading term because it makes it sound as if a
non-octet situation is somehow bizarre. Octets "work" in many simple situations
where the Lewis approach of regarding the valence electrons of one atom as
pairing off one at a time with the valence electrons of the other atom(s)
gives a fairly good explanation of reactivity. But there are also many situations
where "counting to eight" is not good enough.