Is there a specific number of repeated unit cells require to classify a structure as a lattice. If there is no specific number, based on what criteria we call any given structure a lattice?
There is no specific number of repeated unit cells required to classify a structure as a lattice. A lattice is defined by its regular and repeating arrangement of points in space, typically represented by a set of translation vectors. The concept of a lattice focuses on the underlying periodicity and symmetry of the structure rather than the exact number of unit cells. As long as the arrangement of points exhibits translational symmetry and repeats indefinitely in all directions, the structure can be considered a lattice. The size and shape of the unit cell may vary, but the essential feature is the repetition of the pattern throughout space.
Maybe of interest, some tiny crystal structures.
https://news.cornell.edu/stories/2006/06/researchers-discover-how-focus-tiniest-very-small
https://www.newswise.com/articles/discovering-how-to-focus-on-tiniest-of-the-very-small
https://phys.org/news/2016-02-smallest-lattice-worldwide.html
https://phys.org/news/2012-09-chemists-smallest-molecules-ice-crystal.html
https://www.eurekalert.org/news-releases/951593
https://www.science.org/doi/abs/10.1126/science.1225468
Regards,
Joachim
Thank you Samira Akter Tumpa and Joachim Pimiskern for your reply.
In my case I am asking with respect to additively manufactured TPMS structures. I have 3D printed TPMS structures with varying number of unit cell from 2 to 10. So structure with 2 unit cell can be classify as lattice structure?
In order to refer to a structure as a lattice, it is necessary to have a minimum of one repeated unit cell. The unit cell is the basic building block that is repeated throughout the lattice to create the overall structure. It contains all the essential features of the lattice, such as the arrangement of atoms, ions, or molecules, and their connectivity. By replicating the unit cell in all three dimensions, a lattice is formed, exhibiting long-range order and periodicity. The repeated unit cells allow for the extension of the lattice in space, creating an infinite and repeating pattern characteristic of a crystalline structure.
In general, a lattice is a repetitive arrangement of unit cells in a structure. The number of repeated unit cells required to classify a structure as a lattice depends on the specific characteristics and properties being considered. In the case of additively manufactured TPMS (Triply Periodic Minimal Surface) structures, the classification as a lattice may also depend on the specific requirements or definitions within the context of TPMS structures. If a structure with two unit cells exhibits the essential characteristics of repetition and periodicity, it can be considered a lattice structure within the given context. However, the classification might be subject to further criteria or considerations specific to TPMS structures. Therefore, it is important to consult relevant literature, guidelines, or experts in the field for a more precise determination in the context of TPMS structures.
If you mean a crystal LATTICE, i.e. translational symmetry, the cell should be repeated By infinite number . Of course this abstract concept differs from real crystalline STRUCTURES . As to the latter, their least sign is an elementary cell representing a certain arrangement and (approx) spacing of atoms.
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