Plotting a crystal in Mathcad

[naz_or]

Hello guys,

I have a question about ploting a crystal in Mathcad. In general crystal is made by translation of unit cell in a periodical way along x,y,z for some increment a, b, c. The a, b and c determine the size of unit cell, while x, y and z can be at some angle: alpha, beta, gamma (see attached figure).

Lets say that crystal is rock salt (NaCl). Then Na and Cl atoms are positioned within unit cell in some regular manner. The plotting of one unit cell in a form of 3D plot in Mathcad is simple, but I am curious how to create a crystal of desired size? I guess it has to do something with vectors.

Thanks,

Goran

NaCl unit cell NaCl crystal - 3x3 unit cells

[Werner_E]

The plotting of one unit cell in a form of 3D plot in Mathcad is simple,

Really? So lets see what you have done so far and attach your worksheet.

That way we also would see what Mathcad version the question is related to.

[naz_or]

Hi,

Above I've just provided a general description of a problem. What follows is the Mathcad15 file with NaCl crystal as an example.

Thanks!

[Werner_E]

So you do not show the connections/bindings and you do not model the atoms as spheres. That way they won't scale and you would have to manually scale the size down with increasing numer of cells.

While it should be possible to write routines which create the necessary vectors (at least for the orthogonal case, I don't think that Mathcad is the right tool for this task.

BTW, what your sheet shows is not the full unit cell, right? At least not according to the pictures you added in your first post.

[naz_or]

There is no need to present atoms as spheres or to draw bonds between them. The data point present only a position of an atom within a unit cell. This is sufficient for visualisation.

Werner Exinger wrote:

So you do not show the connections/bindings and you do not model the atoms as spheres. That way they won't scale and you would have to manually scale the size down with increasing numer of cells.

While it should be possible to write routines which create the necessary vectors (at least for the orthogonal case, I don't think that Mathcad is the right tool for this task.

BTW, what your sheet shows is not the full unit cell, right? At least not according to the pictures you added in your first post.

1. The scaling is not a problem. In any case this shouldn't go above 5x5 unit cells, so it would be still nicely visible in graph i.e. 3D plot.

2. The unit cell I created and the one in an image provided earlier are esentially the same. Due to simmetry when you perform translation of unit cell I created along the axes at the end you will get the same image.

So, how complicated it is to write routines for vectors that will represent axes? It is important that one can plot them i.e. that these vectors are axes instead of standard X,Y,Z.

[Werner_E · Accepted solution]

Maybe something like the attached could help.

You can control the direction of translation with the three vectors in the sheet.