Why does Samarium have such a large c-axis lattice constant? (>26 Å) Are there significantly larger lattice constants of the elements?

Figure 1.2 on page 12 of *The Structure of Rare-earth Metal Surfaces* linked below shows a repeating stack of hexagonal layers arranged as A B A B C B C A C... and several sources give the c-axis lattice constant for Samarium of over 26 angstroms!


**Question(s):**


1. Why does Samarium have such a large c-axis lattice constant?
2. Are any significantly larger lattice constants seen in pure crystal forms of the elements?


I understand that the short answer to #1 may simply be that this just so happens to be the lowest energy configuration, but something about this "long" range order in a crystal of a single type of atom somehow feels unusual.


As the image shows, for many elements we see A B and A B C stacking of hexagonal layers in the form of fcc and bcc structures (cf. [this answer](https://chemistry.stackexchange.com/a/153327/16035)).


Has the reason for this been studied? And explained?




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* [The Structure of Rare-earth Metal Surfaces](https://books.google.com/books?id=7fxpDQAAQBAJ&pg=PA5&hl=en&source=gbs_selected_pages&cad=2#v=onepage&q&f=false) By Stephen David Barrett, Sarnjeet S. Dhesi (2001)
* [The Crystal Structure of Samarium](https://journals.iucr.org/q/issues/1954/08-09/00/a01231/a01231.pdf) A. H. Daane, R. E. Rundle, H. G. Smith AND F. H. Spedding, Acta Cryst. (1954). 7, 532


[![enter image description here](https://i.stack.imgur.com/LblIV.png)](https://i.stack.imgur.com/LblIV.png)



> 
> Fig 1.2 Conventional unit cells for the crystal structures based on the hexagonal lattice.
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This is the answer to the question



> 
> 2. Are any significantly larger lattice constants seen in pure crystal forms of the elements?
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and provides *arguably* the largest single linear parameter of a unit cell for an element, $\pu{45.46 Å}.$


Loa et al. [[1](https://doi.org/10.1038/nmat3342)] reported the Ba-IVc host-guest phase stable in the range from 18 to 21 GPa and possessing a supercell ([ICSD #186822](https://www.ccdc.cam.ac.uk/structures/Search?Doi=10.1038%2Fnmat3342&DatabaseToSearch=Published)) with the following parameters:


\begin{align}
a &= \pu{33.99 Å} &\quad \alpha &= 90.00^\circ \\
b &= \pu{45.46 Å} &\quad \beta &= 90.00^\circ \\
c &= \pu{13.41 Å} &\quad \gamma &= 90.00^\circ \\
V &= \pu{20720.94 Å^3} \\
Z &= 768
\end{align}



> 
> [![Figure 1 | Basic host–guest motif of the Ba-IV crystal structures](https://i.stack.imgur.com/yqQqH.png)](https://i.stack.imgur.com/yqQqH.png)  
> 
> **Figure 1 | Basic host–guest motif of the Ba-IV crystal structures.**
> The red lines indicate the basic host unit cell.
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This is far from “*ordinary*” crystal structures, as authors explain:



> 
> […] the crystal structure lacks translational symmetry along one direction (along $b$) so that neither a crystallographic unit cell nor a space group can be assigned.
> Nonetheless, the supercell not only indexes all the reflections, both sharp and diffuse, but also has the size of the smallest possible unit cell of fully ordered variants of this structure ([Supplementary Information](https://static-content.springer.com/esm/art%3A10.1038%2Fnmat3342/MediaObjects/41563_2012_BFnmat3342_MOESM13_ESM.pdf)).
> It is therefore appropriate to discuss the Ba-IVc structure in terms of a representative unit of that size, containing 768 atoms.
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> 
> […]
> 
> 
> Our final model of the full Ba-IVc host–guest crystal structure is illustrated in Fig. 3, with the guest substructure being of particular interest.
> All of the chains of guest atoms take one of only two different positions along the chain direction (the $c$ direction), which we will call the up and the down positions hereafter.
> In Fig. 3, the up and down chains are coloured yellow and blue, respectively, and
> from the relative arrangement of the two types of chain an intricate
> two-dimensional pattern emerges (Fig. 3c).
> The pattern consists of intertwined S-shaped units, each comprising 12 adjacent chains of the same type, up or down.
> At first glance, the pattern in Fig. 3c looks well ordered, but it contains two different configurations of these S-shaped units that are mirror images of each other, and the tiling includes an element of randomness.
> It is this tiling of relatively large building blocks with a certain degree of randomness that leads to the unusual diffraction patterns with sharp and diffuse
> reflections.
> We find it rather striking to observe such structural patterning in an elemental crystal, reminiscent in some ways of Escher’s drawings of plane-filling patterns.
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> 
> [![Figure 3 | Schematic view of the crystal structure of Ba-IVc](https://i.stack.imgur.com/OZXQ2.png)](https://i.stack.imgur.com/OZXQ2.png)  
> 
> **Figure 3 | Schematic view of the crystal structure of Ba-IVc.**
> **a,b,** Views of a 768-atom representative unit along the crystallographic $c$ and $b$ directions, respectively.
> Host atoms in alternate layers perpendicular to $c$ are shown dark and pale grey.
> Guest atoms in the up and down positions are coloured yellow and blue, respectively.
> Light blue and light yellow backgrounds highlight the pattern formed by the up and down guest chains.
> The red square in a indicates the basic Ba-IV unit cell.
> **c,** Pattern representing the up and down guest chains and decomposition into zigzag and square-wave rows.
> **d,e,** Side views along the $b$ direction of the zigzag and square-wave rows.
> **f,** Displacements of the guest atoms perpendicular to the chain direction.
> The reﬁned atomic displacements are shown ×5 magniﬁed.
> The chains at the corners of the S-shaped building blocks, marked ×, show a clear zigzag displacement pattern.
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### Reference


1. Loa, I.; Nelmes, R. J.; Lundegaard, L. F.; McMahon, M. I. Extraordinarily Complex Crystal Structure with Mesoscopic Patterning in Barium at High Pressure. *Nature Mater* **2012**, 11 (7), 627–632. DOI: [10.1038/nmat3342](https://doi.org/10.1038/nmat3342).


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