Tuesday, January 25, 2011

"The Rare Earth Question: What do the f-orbitals have to do with anything?"


Answered by Graduate Fellow Ashley Driscoll

The Lanthanides are usually placed on the bottom of the periodic table with the Actinides for the sake of space.  This sometimes leads to confusion about how they relate to the rest of the elements and their electronic structure.  Another way to view the periodic table is this:

(From (1), pg. 140.) 

Two important points about the periodic table:
·       Elements of the same Group in the table (same column) have similar chemical properties because their outer-most electron shells are similar (the outer-most electrons are the ones involved in reactions)
·       As you go down the rows of the table (n increases ↓ the table from 1 to 7) the difference in energy between electron shells decreases (from (1), pg. 140):
                   
The first 5 orbitals have very large differences in energy (1s, 2s, 2p, 3s and 3p).  Starting with the 4s orbital, the energy differences between the orbitals decrease and this affects how the orbitals are filled.  The arrow scheme on the right in the figure shows how electrons fill in the orbitals of lowest energy and this follows a pattern of 1s, 2s then 2p, 3s, 3p then 4s (increasing number and s orbitals are filled before p orbitals). 
This order changes once we get to the 3d orbitals of the transition metals (the order of orbital filling can be followed in the periodic table in the first picture by going across the rows from left to right).  Now 3d is filled before 4p, and 4d is filled before 5p (so the lowest number is now not always filled first).  Electrons fill in the available orbitals according to Hund’s Rule by first adding a single electron to each possible slot all with the same spin direction, then the remaining electrons add with the opposing spin to create spin pairs.
The Lanthanides change the orbital filling order again by introducing the f-orbitals.  The f-orbitals have 7 suborbitals each of which holds two electrons.  This requires in 14 electrons needed to fill the suborbitals and results 14 lanthanide elements.  The lanthanide elements are also called rare earth elements, which is a bit of a misnomer because they are relatively abundant in the earth’s crust (1, 2).  The lanthanides have similar chemical properties, with most of the lanthanides forming a +3 (trivalent) ionic configuration (2).  Cerium (Ce) will form the +4 ions, and Europium (Eu), Ytterbium (Yb) and Samarium (Sm) will form +2 ions (2).    The similar ionic states cause the elements to have similar chemical properties, which means they will have similar chemical reactivities.  This has two consequences, the elements occur together in mineral deposits, but that they are difficult to separate (2). 

To purify the lanthanides to their metals, they are first reacted with chlorine (La – Gd) or fluorine (Tb – Tm) to from a neutral complex, such as LaCl3.  This complex is then reacted with calcium (Ca) at temperatures of 1000 °C to form the metal (2).  Fluorine is used for the Tb – Tm elements because reacting them with chlorine makes a complex that is too volatile to process (2).  To form the metal of Yb, the oxidized from Yb2O3 is reacted with La at high temperature (2).  If Yb were reacted with chlorine like other lanthanides, and then reacted with calcium, it would only form YbCaCl2 and not lose the other two chlorine atoms (2).   
Another feature of the lanthanides is the reduction of the ionic radius of the elements as you go across their row in the periodic table.  This is termed the Lanthanide Contraction, and is the result of two effects. Lanthanide contraction in graph form, data from (2):


The first is due to electron shielding.  Remember that the identity of an element is determined by its atomic number (i.e. the number of protons in the nucleus), and as the atomic number increases, we are increasing the positive charge in the nucleus.  With each additional proton comes an electron to maintain a neutral charge.  Electron shielding means that the electrons in an outer orbital feel less than the full charge of the nucleus because all of the electrons of the inner orbitals act as moving screens that reduce net effective charge felt by electrons as you move away from the nucleus.  For example, hydrogen (H) does not have a screening effect because the one electron orbiting the nucleus does not have any other electrons to shield it from the nucleus.  But lithium (Li), which like hydrogen has one valence electron but has a filled 1s orbital, does experience a screening effect.  The one valence electron in the 2s orbital feels less of the positive charge of the nucleus than the 1s electron of hydrogen because the full 1s orbital of Li shields the charge of the nucleus.  This continues as orbitals are filled throughout the periodic table.
The ability of electron orbitals to shield the positive charge of the nucleus decreases s > p > d > f  (1).  For the lanthanides, we’ve seen that the order of filling electron orbitals is a little less straightforward, and a 3d orbital fills before a 4s orbital, and 5s and 5p fill before a 4f.  A quick note, the order of filling the orbitals has to do with energy and filling the lowest energy orbital first.  The relative positions of the orbitals to the nucleus is a bit different; the 4f orbital is between the 5s and 5p orbitals and the nucleus (1, 2).  The 4f orbital acts as a poor shield for the filled 5s and 5p orbitals and so their electrons feel a bit more of the effect of the nucleus and this causes the radius of the atom to be smaller. 
The second is the relativistic effect.  This takes into account when the speed of electrons orbiting the nucleus is fast enough that, due to the theory of relativity, they have an increased mass compared to their mass if they were stand still, or rest mass.  This becomes important for the heavier elements of the periodic table (from about hafnium (Hf) and above) because the increased positive charge in the nucleus causes the electrons orbiting nearest the nucleus to experience greater attraction, which causes them to orbit faster (2).  This makes the radius of the electron orbit smaller, because the radius of an orbit is inversely proportional to mass (so the increased mass from the increased orbiting speed causes the orbital to be a bit smaller) (2).  This effect then carries out over the next shell of orbital electrons and all the way to the outer orbitals because of the strong positive charge concentrated in the nucleus.  This accounts for about 15% of the lanthanide contraction (2). 






With m0 = rest mass
 c = speed of light
v = velocity
m = mass of electron in motion
From (2)



Reference and Figures:
(1)   Gilbert, Thomas R., Rein V. Kirss and Geoffrey Davies.  Chemistry – The Science in Context.  New York: W.W. Norton & Company, Inc., 2004.
(2)   Cotton, F. Albert, Geoffrey Wilkinson, Carlos A. Murillo and Manfred Bochmann.  Advanced Inorganic Chemistry, 6th Edition.  New York: John Wiley & Sons, Inc., 1999.

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