Lanthanide contraction

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The lanthanide contraction is the greater-than-expected decrease in atomic radii and ionic radii of the elements in the lanthanide series, from left to right. It is caused by the poor shielding effect of nuclear charge by the 4f electrons along with the expected periodic trend of increasing electronegativity and nuclear charge on moving from left to right. About 10% of the lanthanide contraction has been attributed to relativistic effects. [1]

Contents

A decrease in atomic radii can be observed across the 4f elements from atomic number 57, lanthanum, to 70, ytterbium. This results in smaller than otherwise expected atomic radii and ionic radii for the subsequent d-block elements starting with 71, lutetium. [2] [3] [4] [5] This effect causes the radii of transition metals of group 5 and 6 to become unusually similar, as the expected increase in radius going down a period is nearly cancelled out by the f-block insertion, and has many other far ranging consequences in post-lanthanide elements.

The decrease in ionic radii (Ln3+) is much more uniform compared to decrease in atomic radii.

ElementAtomic electron
configuration
(all begin with [Xe])		Ln3+ electron
configuration		Ln3+ radius (pm)
(6-coordinate)
La 5d16s24f0103
Ce 4f15d16s24f1102
Pr 4f36s24f299
Nd 4f46s24f398.3
Pm 4f56s24f497
Sm 4f66s24f595.8
Eu 4f76s24f694.7
Gd 4f75d16s24f793.8
Tb 4f96s24f892.3
Dy 4f106s24f991.2
Ho 4f116s24f1090.1
Er 4f126s24f1189
Tm 4f136s24f1288
Yb 4f146s24f1386.8
Lu 4f145d16s24f1486.1

The term was coined by the Norwegian geochemist Victor Goldschmidt in his series "Geochemische Verteilungsgesetze der Elemente" (Geochemical distribution laws of the elements). [6]

Cause

The effect results from poor shielding of nuclear charge (nuclear attractive force on electrons) by 4f electrons; the 6s electrons are drawn towards the nucleus, thus resulting in a smaller atomic radius.

In single-electron atoms, the average separation of an electron from the nucleus is determined by the subshell it belongs to, and decreases with increasing charge on the nucleus; this, in turn, leads to a decrease in atomic radius. In multi-electron atoms, the decrease in radius brought about by an increase in nuclear charge is partially offset by increasing electrostatic repulsion among electrons.

In particular, a "shielding effect" operates: i.e., as electrons are added in outer shells, electrons already present shield the outer electrons from nuclear charge, making them experience a lower effective charge on the nucleus. The shielding effect exerted by the inner electrons decreases in the order s > p > d > f.

Usually, as a particular subshell is filled in a period, the atomic radius decreases. This effect is particularly pronounced in the case of lanthanides, as the 4f subshell which is filled across these elements is not very effective at shielding the outer shell (n=5 and n=6) electrons. Thus the shielding effect is less able to counter the decrease in radius caused by increasing nuclear charge. This leads to "lanthanide contraction". The ionic radius drops from 103 pm for lanthanum(III) to 86.1 pm for lutetium(III).

About 10% of the lanthanide contraction has been attributed to relativistic effects. [1] The lanthanide contraction was experimentally observed in aqueous solutions of lanthanides, including radioactive promethium, through X-ray absorption spectroscopy measurements. [7]

Effects

The results of the increased attraction of the outer shell electrons across the lanthanide period may be divided into effects on the lanthanide series itself including the decrease in ionic radii, and influences on the following or post-lanthanide elements.

Properties of the lanthanides

The ionic radii of the lanthanides decrease from 103  pm (La 3+) to 86 pm (Lu 3+) in the lanthanide series, electrons are added to the 4f shell. This first f shell is inside the full 5s and 5p shells (as well as the 6s shell in the neutral atom); the 4f shell is well-localized near the atomic nucleus and has little effect on chemical bonding. The decrease in atomic and ionic radii does affect their chemistry, however. Without the lanthanide contraction, a chemical separation of lanthanides would be extremely difficult. However, this contraction makes the chemical separation of period 5 and period 6 transition metals of the same group rather difficult. Even when the mass of an atomic nucleus is the same, a decrease in the atomic volume has a corresponding increase in the density as illustrated by alpha crystals of cerium (at 77 Kevin) and gamma crystals of cerium (near room temperature) where the atomic volume of the latter is 120.3% of the former and the density of the former is 120.5% of the latter (i.e., 20.696 vs 17.2 and 8.16 vs 6.770, respectively). [8]

As expected, when more mass (protons & neutrons) is packed into a space that is subject to "contraction", the density increases consistently with atomic number for the lanthanides (excluding the atypical 2nd, 7th, and 14th) culminating in the value for the last lanthanide (Lu) being 160% of the first lanthanide (La). Melting points (in Kelvin) also increase consistently across these 12 lanthanides culminating in the value for the last being 161% of the first. This density-melting point association does not depend upon just a comparison between these two lanthanides because the correlation coefficient (Pearson product-moment) for density and melting point for these 12 lanthanides is 0.982 and 0.946 for all 15 lanthanides. There is a general trend of increasing Vickers hardness, Brinell hardness, density and melting point from lanthanum to lutetium (with europium and ytterbium being the most notable exceptions; in the metallic state, they are divalent rather than trivalent). Cerium, along with europium and ytterbium, are atypical when their properties are compared with the other 12 lanthanides as evidenced by the clearly lower values (than either adjacent element) for melting points (lower by >10<43%), Vickers hardness (lower by >32<82%), and densities (lower by >26<33%, when exclude Ce, where the density increases by 10% vs lanthanum). The lower densities for europium and ytterbium (than their adjacent lanthanides) are associated with larger atomic volumes at 148% and 128% of the average volume for the typical 12 lanthanides (i.e., 28.979, 25.067, and 19.629 cm3/mol, respectively). [8]

Because the atomic volume of Yb is 21% more than that of Ce, [8] it is understandable that the density for Ce (the 2nd lanthanide) is 98% of that of ytterbium (the 14th lanthanide) when there is a 24% increase in atomic weight for the latter, and the melting point for Ce (1068 K) is nearly the same as the 1097 K for ytterbium and the 1099 K for europium. These 3 elements are the only lanthanides with melting points below the lowest for the other twelve, which is 1193 K for lanthanum. Because europium has a half-filled 4f subshell, this may account for its atypical values when compared with the data for 12 of the lanthanides. Lutetium is the hardest and densest lanthanide and has the highest melting point at 1925 K, which is the year that Goldschmidt published the terminology "Die Lanthaniden-Kontraktion."

Unlike the m. p. data for the lanthanides (where the values increase consistently when the 2nd, 7th & 14th are excluded), the b. p. temperatures show a repeated pattern at 162% and 165% for the 8th lanthanide relative to the 6th and the 15th relative to the 13th (which ignores the atypical 7th and 14th). The 8th and 15th are among the four lanthanides with one electron in the 5d shell (where the others are the 1st and 2nd) and the b. p. values for these four are +/- 2.6% about 3642 K. See the post-lanthanides section for more comments on the 5d-shell electrons. There is also a repeated b. p. pattern at 66% and 71% for the 6th and 13th lanthanides (relative to the preceding elements) that differ by one electron in the 4f shell, i.e., 5 to 6 and 12 to 13.

ElementVickers
hardness
(MPa)		Brinell
hardness
(MPa)		Density
(g/cm3)		Melting
point
(K)		Atomic
radius
(pm)		Boiling
point
(K)
Lanthanum 4913636.16211931873737
Cerium 2704126.7701068181.83716
Praseodymium 4004816.7712081823403
Neodymium 3432657.0112971813347
Promethium ??7.2613151833273
Samarium 4124417.5213451802173
Europium 167?5.26410991801802
Gadolinium 570?7.9015851803546
Terbium 8636778.2316291773396
Dysprosium 5405008.54016801782840
Holmium 4817468.7917341762873
Erbium 5898149.06618021763141
Thulium 5204719.3218181762223
Ytterbium 2063436.9010971761469
Lutetium 11608939.84119251743675

Magnetism of the lanthanides

It has been shown that lanthanide contraction plays a crucial role in determining the magnetic phase diagram of the heavy rare-earth elements, [9] [10] i.e. those from Gadolinium onwards.

Influence on the post-lanthanides

The elements following the lanthanides in the periodic table are influenced by the lanthanide contraction. When the first three post-lanthanide elements (Hf, Ta, and W) are combined with the 12 lanthanides, the Pearson correlation coefficient increases from 0.982 to 0.997. On average for the 12 lanthanides, the melting point (on the Kelvin scale) = 1.92x the density (in g/cm^3) while the three elements following the lanthanides have similar values at 188x, 197x, and 192x before the densities continue to increase but the melting points decrease for the next 2 elements followed by both properties decreasing (at different rates) for the next 8 elements. Hafnium is rather unique because not only do density and m. p. temperature change proportionally (relative to lutetium, the last lanthanide) at 135% and 130% but also the b. p. temperature at 133%. The elements with 2, 3, & 4 electrons in the 5d shell (post-lanthanides Hf, Ta, W) have increasing b. p. values such that the b. p. value for W (wolfram, aka tungsten) is 169% of that for the element with one 5d electron (Lu). The high melting point and two other properties of tungsten originates from strong covalent bonds formed between tungsten atoms by the 5d electrons. The elements with 5 to 10 electrons in the 5d shell (Re to Hg) have progressively lower b. p. values such that the element with ten 5d electrons (Hg) has a b. p. value at 52% of tungsten’s (with four 5d electrons).[ citation needed ]

The radii of the period-6 transition metals are smaller than would be expected if there were no lanthanides, and are in fact very similar to the radii of the period-5 transition metals since the effect of the additional electron shell is almost entirely offset by the lanthanide contraction. [4] For example, the atomic radius of the metal zirconium, Zr (a period-5 transition element), is 155 pm [11] (empirical value) and that of hafnium, Hf (the corresponding period-6 element), is 159 pm. [12] The ionic radius of Zr4+ is 84 pm and that of Hf4+ is 83 pm. [13] The radii are very similar even though the number of electrons increases from 40 to 72 and the atomic mass increases from 91.22 to 178.49 g/mol. The increase in mass and the unchanged radii lead to a steep increase in density from 6.51 to 13.35 g/cm3.

Zirconium and hafnium, therefore, have very similar chemical behavior, having closely similar radii and electron configurations. Radius-dependent properties such as lattice energies, solvation energies, and stability constants of complexes are also similar. [3] Because of this similarity, hafnium is found only in association with zirconium, which is much more abundant. This also meant that hafnium was discovered as a separate element in 1923, 134 years after zirconium was discovered in 1789. Titanium, on the other hand, is in the same group, but differs enough from those two metals that it is seldom found with them.

See also

Related Research Articles

Hafnium is a chemical element; it has symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in many zirconium minerals. Its existence was predicted by Dmitri Mendeleev in 1869, though it was not identified until 1922, by Dirk Coster and George de Hevesy. Hafnium is named after Hafnia, the Latin name for Copenhagen, where it was discovered.

<span class="mw-page-title-main">Lanthanum</span> Chemical element with atomic number 57 (La)

Lanthanum is a chemical element; it has symbol La and atomic number 57. It is a soft, ductile, silvery-white metal that tarnishes slowly when exposed to air. It is the eponym of the lanthanide series, a group of 15 similar elements between lanthanum and lutetium in the periodic table, of which lanthanum is the first and the prototype. Lanthanum is traditionally counted among the rare earth elements. Like most other rare earth elements, its usual oxidation state is +3, although some compounds are known with an oxidation state of +2. Lanthanum has no biological role in humans but is essential to some bacteria. It is not particularly toxic to humans but does show some antimicrobial activity.

<span class="mw-page-title-main">Lutetium</span> Chemical element with atomic number 71 (Lu)

Lutetium is a chemical element; it has symbol Lu and atomic number 71. It is a silvery white metal, which resists corrosion in dry air, but not in moist air. Lutetium is the last element in the lanthanide series, and it is traditionally counted among the rare earth elements; it can also be classified as the first element of the 6th-period transition metals.

The lanthanide or lanthanoid series of chemical elements comprises at least the 14 metallic chemical elements with atomic numbers 57–70, from lanthanum through ytterbium. In the periodic table, they fill the 4f orbitals. Lutetium is also sometimes considered a lanthanide, despite being a d-block element and a transition metal.

<span class="mw-page-title-main">Periodic table</span> Tabular arrangement of the chemical elements ordered by atomic number

The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows ("periods") and columns ("groups"). It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks. Elements in the same group tend to show similar chemical characteristics.

In chemistry, a transition metal is a chemical element in the d-block of the periodic table, though the elements of group 12 are sometimes excluded. The lanthanide and actinide elements are called inner transition metals and are sometimes considered to be transition metals as well.

<span class="mw-page-title-main">Ytterbium</span> Chemical element with atomic number 70 (Yb)

Ytterbium is a chemical element; it has symbol Yb and atomic number 70. It is a metal, the fourteenth and penultimate element in the lanthanide series, which is the basis of the relative stability of its +2 oxidation state. Like the other lanthanides, its most common oxidation state is +3, as in its oxide, halides, and other compounds. In aqueous solution, like compounds of other late lanthanides, soluble ytterbium compounds form complexes with nine water molecules. Because of its closed-shell electron configuration, its density, melting point and boiling point are much lower than those of most other lanthanides.

<span class="mw-page-title-main">Stable nuclide</span> Nuclide that does not undergo radioactive decay

Stable nuclides are isotopes of a chemical element whose nucleons are in a configuration that does not permit them the surplus energy required to produce a radioactive emission. The nuclei of such isotopes are not radioactive and unlike radionuclides do not spontaneously undergo radioactive decay. When these nuclides are referred to in relation to specific elements they are usually called that element's stable isotopes.

<span class="mw-page-title-main">Atomic radius</span> Measure of the size of an atom

The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Four widely used definitions of atomic radius are: Van der Waals radius, ionic radius, metallic radius and covalent radius. Typically, because of the difficulty to isolate atoms in order to measure their radii separately, atomic radius is measured in a chemically bonded state; however theoretical calculations are simpler when considering atoms in isolation. The dependencies on environment, probe, and state lead to a multiplicity of definitions.

<span class="mw-page-title-main">Ionization energy</span> Energy needed to remove an electron

In physics and chemistry, ionization energy (IE) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, positive ion, or molecule. The first ionization energy is quantitatively expressed as

<span class="mw-page-title-main">Electron configuration</span> Mode of arrangement of electrons in different shells of an atom

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s2 2s2 2p6, meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively.

A period 6 element is one of the chemical elements in the sixth row (or period) of the periodic table of the chemical elements, including the lanthanides. The periodic table is laid out in rows to illustrate recurring (periodic) trends in the chemical behaviour of the elements as their atomic number increases: a new row is begun when chemical behaviour begins to repeat, meaning that elements with similar behaviour fall into the same vertical columns. The sixth period contains 32 elements, tied for the most with period 7, beginning with caesium and ending with radon. Lead is currently the last stable element; all subsequent elements are radioactive. For bismuth, however, its only primordial isotope, 209Bi, has a half-life of more than 1019 years, over a billion times longer than the current age of the universe. As a rule, period 6 elements fill their 6s shells first, then their 4f, 5d, and 6p shells, in that order; however, there are exceptions, such as gold.

<span class="mw-page-title-main">Praseodymium</span> Chemical element with atomic number 59 (Pr)

Praseodymium is a chemical element; it has symbol Pr and the atomic number 59. It is the third member of the lanthanide series and is considered one of the rare-earth metals. It is a soft, silvery, malleable and ductile metal, valued for its magnetic, electrical, chemical, and optical properties. It is too reactive to be found in native form, and pure praseodymium metal slowly develops a green oxide coating when exposed to air.

<span class="mw-page-title-main">Group 3 element</span> Group of chemical elements

Group 3 is the first group of transition metals in the periodic table. This group is closely related to the rare-earth elements. It contains the four elements scandium (Sc), yttrium (Y), lutetium (Lu), and lawrencium (Lr). The group is also called the scandium group or scandium family after its lightest member.

<span class="mw-page-title-main">Group 4 element</span> Group of chemical elements

Group 4 is the second group of transition metals in the periodic table. It contains the four elements titanium (Ti), zirconium (Zr), hafnium (Hf), and rutherfordium (Rf). The group is also called the titanium group or titanium family after its lightest member.

<span class="mw-page-title-main">Neutron capture</span> Atomic nuclear process

Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, which are repelled electrostatically.

Core electrons are the electrons in an atom that are not valence electrons and do not participate in chemical bonding. The nucleus and the core electrons of an atom form the atomic core. Core electrons are tightly bound to the nucleus. Therefore, unlike valence electrons, core electrons play a secondary role in chemical bonding and reactions by screening the positive charge of the atomic nucleus from the valence electrons.

A block of the periodic table is a set of elements unified by the atomic orbitals their valence electrons or vacancies lie in. The term seems to have been first used by Charles Janet. Each block is named after its characteristic orbital: s-block, p-block, d-block, f-block and g-block.

<span class="mw-page-title-main">Kainosymmetry</span>

Kainosymmetry describes the first atomic orbital of each azimuthal quantum number (ℓ). Such orbitals include 1s, 2p, 3d, 4f, 5g, and so on. The term kainosymmetric was coined by Sergey Shchukarev. Pekka Pyykkö referred to such orbitals as primogenic instead. Such orbitals are much smaller than all other orbitals with the same ℓ and have no radial nodes, giving the elements that fill them special properties. They are usually less metallic than their heavier homologues, prefer lower oxidation states, and have smaller atomic and ionic radii.

The actinoid contraction or actinide contraction is the greater-than-expected decrease in atomic radii and ionic radii of the elements in the actinoid series, from left to right.

References

  1. 1 2 Pekka Pyykko (1988). "Relativistic effects in structural chemistry". Chem. Rev. 88 (3): 563–594. doi:10.1021/cr00085a006.
  2. ↑ Chistyakov, V. M. (1968). "Biron's Secondary Periodicity of the Side d-subgroups of Mendeleev's Short Table". Journal of General Chemistry of the USSR. 38 (2): 213–214. Retrieved 6 January 2024.
  3. 1 2 Housecroft, C. E.; Sharpe, A. G. (2004). Inorganic Chemistry (2nd ed.). Prentice Hall. pp. 536, 649, 743. ISBN   978-0-13-039913-7.
  4. 1 2 Cotton, F. Albert; Wilkinson, Geoffrey (1988), Advanced Inorganic Chemistry (5th ed.), New York: Wiley-Interscience, pp. 776, 955, ISBN   0-471-84997-9
  5. ↑ Jolly, William L. Modern Inorganic Chemistry, McGraw-Hill 1984, p. 22
  6. ↑ Goldschmidt, Victor M. "Geochemische Verteilungsgesetze der Elemente", Part V "Isomorphie und Polymorphie der Sesquioxyde. Die Lanthaniden-Kontraktion und ihre Konsequenzen", Oslo, 1925
  7. ↑ Driscoll, Darren M.; White, Frankie D.; Pramanik, Subhamay; Einkauf, Jeffrey D.; Ravel, Bruce; Bykov, Dmytro; Roy, Santanu; Mayes, Richard T.; Delmau, Lætitia H.; Cary, Samantha K.; Dyke, Thomas; Miller, April; Silveira, Matt; VanCleve, Shelley M.; Davern, Sandra M. (May 2024). "Observation of a promethium complex in solution". Nature. 629 (8013): 819–823. Bibcode:2024Natur.629..819D. doi:10.1038/s41586-024-07267-6. ISSN   1476-4687. PMC   11111410 . PMID   38778232.
  8. 1 2 3 "Atomic volumes" (PDF).
  9. ↑ Hughes, I. D.; Däne, M.; Ernst, A.; Hergert, W.; Lüders, M.; Poulter, J.; Staunton, J. B.; Svane, A.; Szotek, Z.; Temmerman, W. M. (2004). "Lanthanide contraction and magnetism in the heavy rare earth elements". Nature. 446 (7136): 650–653. doi:10.1038/nature05668. ISSN   1476-4687. PMID   17410171.
  10. ↑ Mendive-Tapia, Eduardo; Staunton, Julie B. (2017-05-11). "Theory of Magnetic Ordering in the Heavy Rare Earths: Ab Initio Electronic Origin of Pair- and Four-Spin Interactions". Physical Review Letters. 118 (19): 197202. arXiv: 1610.08304 . Bibcode:2017PhRvL.118s7202M. doi:10.1103/PhysRevLett.118.197202. PMID   28548504.
  11. ↑ "Zirconium | Zr (Element) - PubChem".
  12. ↑ "Hafnium".
  13. ↑ Nielsen, Ralph H.; Updated by Staff (2013-04-19), "Hafnium and Hafnium Compounds", in John Wiley & Sons, Inc. (ed.), Kirk-Othmer Encyclopedia of Chemical Technology, Hoboken, NJ, USA: John Wiley & Sons, Inc., pp. 0801061414090512.a01.pub3, doi:10.1002/0471238961.0801061414090512.a01.pub3, ISBN   978-0-471-23896-6 , retrieved 2022-11-25
  14. ↑ "Lanthanide Contraction - Chemistry LibreTexts". 2 October 2013.
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