solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state phy ...

, the Hill limit is a critical distance defined in a

lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an or ...

actinide The actinide () or actinoid () series encompasses at least the 14 metallic chemical elements in the 5f series, with atomic numbers from 89 to 102, actinium through nobelium. Number 103, lawrencium, is also generally included despite being part ...

rare-earth The rare-earth elements (REE), also called the rare-earth metals or rare earths, and sometimes the lanthanides or lanthanoids (although scandium and yttrium, which do not belong to this series, are usually included as rare earths), are a set of ...

atoms. These atoms own partially filled

4f

5f

levels in their

valence shell In chemistry and physics, valence electrons are electrons in the outermost shell of an atom, and that can participate in the formation of a chemical bond if the outermost shell is not closed. In a single covalent bond, a shared pair forms with b ...

and are therefore responsible for the main interaction between each atom and its environment. In this context, the hill limit

r_H

is defined as twice the

radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...

of the

f

-orbital. Therefore, if two atoms of the lattice are separate by a distance greater than the Hill limit, the

overlap Overlap may refer to: * In set theory, an overlap of elements shared between sets is called an intersection, as in a Venn diagram. * In music theory, overlap is a synonym for reinterpretation of a chord at the boundary of two musical phrases * Ove ...

of their

f

-orbital becomes negligible. A direct consequence is the absence of hopping for the f electrons, ie their localization on the ion sites of the lattice. Localized f electrons lead to

paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, ...

materials since the remaining unpaired spins are stuck in their orbitals. However, when the rare-earth lattice (or a single atom) is embedded in a metallic one (

intermetallic compound An intermetallic (also called intermetallic compound, intermetallic alloy, ordered intermetallic alloy, long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elements. Inte ...

), interactions with the conduction band allow the f electrons to move through the lattice even for interatomic distances above the Hill limit.

References

{{reflist Solid-state chemistry Rare earth alloys Electrical conductors

See also

References