Last Update 09/ 02/ 2015
The figure obtained by default or after a click on button I on the right side shows a projection of solid sodium chloride, kitchen salt ions. The buttons numbered I to X select presentations of solid or aqueous ions with x and y screen coordinates displayed on the bottom of the figure after mouse moving. In this text each figure will be numbered according to the number of the button used to enable the figure.
Chloride anions and sodium cations in a cube of 564 pm (or 5.64 A) of edge dimension named unit cell are illustrated in figure I. Here the sodium cation occupies the center of the cube with coordinates x = 149 and y = 146 and also the center of each edge of the unit cell. The chloride ions are on the vertices and on the center of each cube face. In this general orientation of the unit cell the ions are not eclipsed, it means all the 27 ions can be individually observed without any superposition. This text will represent sodium cations by Na and chloride anions by Cl, without any explicitly electrical charge announcement. Another correct and equivalent presentation of solid sodium chloride changes the position of each Na with a Cl and vice-versa, in this case Na would be on the vertices and center of faces and Cl at center of edges and center of the cubic unit cell.
Figure II shows 25 ions of the unit cell in a projection on a plane perpendicular to the cube diagonal or to the triad axis. The Cl above and the Cl below Na at coordinates x = 149 and y = 146 were not represented. The symbol Na in red was used 6 times, whenever eclipsed with Cl.
Figure III shows 30 ions, 6 Cl coordinated on the octahedron vertices in red around Na centered on x = 149 and y = 146. On the other hand, 6 Na coordinated on the octahedron vertices in green are at same distances from the Cl centered at x = 275 and y = 215. Undergraduate students form the Crystallography class of the Universidade Federal de Viçosa during 2012 obtained a projection like this as homework with the aid of gira program.
Figure IV shows 28 ions with Cl eclipsed under Na in red on coordinates x = 100 and y = 97 and also with Na eclipsed under Cl on x = 167 and y = 79. This way, 3 Cl will occupy a plane above Na centered on x = 149 and y = 146 and other 3 Cl on a parallel plane below the centered Na. On the green octahedron Cl is centered at x = 246 and y = 243 and is coordinated to 6 Na at equal distances from the centered Cl, 3 Na on a plane above this Cl and 3 on a parallel plane below the Cl centered on the octahedron.
Figure V shows only the red octahedron with 6 Cl and Na centered on coordinates x = 149 and y = 146 together with the green octahedron with 6 Na and Cl centered on x = 275 and y = 215.
Figure VI shows only the red octahedron with 6 Cl and Na centered on coordinates x = 149 and y = 146 together with the green octahedron with 6 Na and Cl centered on x = 246 and y = 243.
Figure VII shows the green octahedron with 6 Na and Cl centered on coordinates x = 246 and y = 243.
Figure VIII shows the red octahedron with 6 Cl and Na centered on coordinates = 149 and y = 146.
Figure IX shows 6 water molecules with a possible symmetry where hydrogen occupies the vertices of a green octahedron with aqueous Cl centered on coordinates x = 246 and y = 243.
Figure X shows 6 water molecules with a possible symmetry where oxygen occupies the vertices of a red octahedron with aqueous Na centered on coordinates x = 149 and y = 146.
Exercises
1) Define the 4 fold symmetry axes of solid NaCl giving the coordinates of two points belonging to each axis on figure I.
2) If there are at least two 4 fold axes on the red octahedron on figure V with Na centered at coordinates x = 149 and y = 146 parallel to two 4 fold axes on the green octahedron with Cl centered on x = 275 and y = 215, respectively, what can be concluded on the spatial orientation of plane faces of both octahedrons, respectively?
3) What can be concluded on the orientation of the triad axes of one octahedron related to the 3 fold axes of the other octahedron on figure VI, respectively?
4) Justify why hydrogen atoms are on the vertices of the octahedron on figure IX and oxygen atoms are on the vertices of the octahedron on figure X?
5) Why the coordinates of Na centered on the red octahedron in figure V and VI are equal and on the same figures the coordinates of Cl centered on the green octahedron are different, respectively?
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