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When I search online for an NaCl unit cell I often find a significant number of images, such as the one I have attached to this post, showing the chloride ions in the "edge" and "body centered" position. I also find many where the chloride ions are on the "corner" and "face-centered" position.

It made me realize that depending on where you cut the cube you could technically illustrate either configuration with accuracy, however, I'm unaware if there is a specific standard for illustrating the NaCl unit cell.

I'm hoping someone on here can chime in and confirm the accepted position of the chloride ion (or lack thereof) and why this designation is the accepted position if such an accepted position exists.

Thank you to everyone who responds with their thoughts on the matter.

  enter image description here

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  • $\begingroup$ For a real particle/crystal it could be either ion on the outside corners. Also I wouldn't expect a real particle/crystal to have absolutely flat faces. $\endgroup$
    – MaxW
    Nov 16, 2023 at 8:51
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    $\begingroup$ The above picture is not the conventional unit cell for NaCl - it is 8 unit cells.See e.g. lampx.tugraz.at/~hadley/ss1/crystalstructure/structures/nacl/… and read the text associated with the picture $\endgroup$
    – Ian Bush
    Nov 16, 2023 at 13:57

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The commonly accepted unit cell is a face center cubic (FCC) chloride structure with all octahedral sites filled with sodium cations. Typically, we construct the framework of the unit cell with the larger ion or, in the case of unit cells with formulas having different stoichiometric quantities, the ion with the charge of greater magnitude.

When using the radius ratio rule, remember that the ratio of radii has equal a quantity less than 1, with the ion whose radius is represented by the numerator is the ion filling the sites in the unit cell scaffold constructed by the ion whose radius is represented by the denominator.

In NaCl, the radii for Na+ and Cl- are 102pm and 175pm, respectively. This gives a cation:anion ratio of 102/175, which equals 0.58, corresponding to octahedral holes.

As a result, we have (1/8)(8)+(1/2)(6) = 4 Cl- ions (each corner is 1/8th in the unit cell, and the centers of the faces have 1/2 in the unit cell) and (1/4)(12)+1 = 4 Na+ ions per unit cell (each edge has 1/4th in the unit cell, and there is one full Na+ ion in the center of the unit cell), for a formula of Na4Cl4 per unit cell.

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  • $\begingroup$ Very insightful. I am too new to the site so the system will not allow me to up vote but I hit the checkmark for whatever that may be worth. Thank you. $\endgroup$
    – Val
    Nov 22, 2023 at 1:10
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NaCl crystallizes in the Fm-3m space group (where the underlying lattice is F, namely face-centered).

Na atoms are usually located (in the structural description) at the 4a Wyckoff site (coordinates: 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0); namely, their positions correspond to the lattice points of the cubic face-centered lattice.

Consequently, Cl atoms are usually located (in the structural description) at the 4b Wyckoff site (coordinates: 1/2,1/2,1/2; 1/2,0,0; 0,1/2,0; 0,0,1/2); namely, their positions correspond to the octahedral voids of the cubic face-centered lattice.

Nonetheless, the 4a and 4b sites have exactly the same site symmetry, so you can interchange the atomic positions. For this reason, it is possible to describe the crystal structure of NaCl in two ways:

(1) Na @ 4a Cl @ 4b => Na atoms located at the cubic face-centered lattice with Cl atoms in the octahedral voids

(2) Na @ 4b Cl @ 4a => Cl atoms located at the cubic face-centered lattice with Na atoms in the octahedral voids

These descriptions are perfectly equivalent, it depends on you and your scope what to choose.

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  • $\begingroup$ Very insightful. I am too new to the site so the system will not allow me to up vote but I hit the checkmark for whatever that may be worth. Thank you. $\endgroup$
    – Val
    Nov 22, 2023 at 1:09

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