the early nuclear plants (commisioned between 1950-1970) uses Beryllium as control rods. the more recent nuclear plants use beryllium-coated steel as control rods, because it's more economic and almost equally effective, except one has to use more rods of the same dimension for steel in the same reactor to sustain the same extent of moderating the nuclear fission chain reaction.

I thought they use steel rods. I remember reading that from a book. I attached the book info here. i got that book from my departmental library. constant-thinker, you may like to read up to know more.

Nuclear Politics - The History of Nuclear Power in Britain
Harmondsworth: Pelican, 1986 Soft Cover. Very Good/No Jacket. First Edition. Trade Pb. 200pp. Slight reading crease, o/w as new. Follows the British atomic power industry from its birth in the shadow of the atom bomb up to the Windscale/Sellafield investigation (1977) and subsequent reported concerns, and the Sizewell inquiry. (Environment, Technology, Nuclear, Atomic, Economics, Politics, Energy)
ISBN: 0140224939

Boron Carbide pellets inside of tubes, of which alloy I'm not sure. These are used in commercial Boiling Water Reactors.

Europium is by far the best neutron absorber.

Europium is by far the best neutron absorber.

Close.  Europium is the second best thernal neutron absorber.  It is beat out by Gadolinium, which is about an order of magnitude better (4500 vs 48 000 barns by my calculation).  If you want to waste the money to separate out the ¹⁵⁷Gd, then you gain another order of magnitude (250 000 barns).  

Good point, Europium is very reactive. Also, I didn't know Gd was a neutron absorber; I get my information in this field from a book written in 1961, so I guess they didn't know Gadolium was a control rod material.

does anybody know the composition of the zirconium alloy use for radioactivity shielding in nuclear reactors?

The material that is used to enclose the fuel rods is called zircaloy. It is an alloy of zirconium with mainly tin and some chromium and nickel. There are different versions of the alloy and the exact composition varies for each. The alloy is used for its heat- and corrosion-resistant properties. But it is not used as radiation shielding. It is just used to mechanically contain the fuel rods and keep them separated from the water.
On the contrary, it was picked because zirconium has a very low neutron capture cross section. It does not interfere with the neutron balance and allows most of the neutrons to actually hit the uranium and cause fisison. The proper neutron balance is maintained by the control rods and by the amount of boric acid in the cooling water.