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Another of the hard unit cells

Dear Reader,

After my success with the sodium nitrate I will now present tripotassium hexacyanoferrate(III) which is an example of a monoclinic cell. Again we have to start with drawing a box to make our cell. The lengths of the cell are 7.047, 10.400  and 8.384 Å. Two of the angles (alpha and gamma) are 90 degrees while the beta angle is 107.29 degrees.

This will give us a box which is more complex than an orthorhombic box.

We start by adding iron atoms, the fractional coordinates of the iron atoms are 0 0 0 and 0 0.5 0.5 which means we have two iron atoms in the unit cell.

We next have to add the potassiums at the following fraction coordinates 0.000 0.000 0.500, 0.000 0.500 0.000, 0.5025 0.7700 0.6252, 0.5025 0.7300 0.1252, 0.4975 0.2700 0.8748 and 0.4975 0.2300 0.3748.

We should now understand that we will have six potassium atoms to go with our two irons.

Next we add the cyanide carbons

These are at the following fractional coordinates

0,1875 0,9480 0,2102
0,1887 0,945 0,886
0,8795 0,8317 0,9712
0,8795 0,6683 0,4712
0,8113 0,445 0,614
0,8125 0,448 0,2898
0,8125 0,0520 0,7898
0,8113 0,0550 0,1140
0,1205 0,1683 0,0288
0,1205 0,3317 0,5288
0,1887 0,5550 0,3860
0,1875 0,5520 0,7102

We should understand that they are all fully inside the cell so we have 12 cyanide carbons.

Next we do the cyanide nitrogens

0,8004 0,7335 0,9515
0,2974 0,9120 0,8160
0,2962 0,9180 0,3361
0,8004 0,7665 0,4515
0,7026 0,4120 0,6840
0,7038 0,4180 0,1639
0,1996 0,2665 0,0485
0,7026 0,0880 0,1840
0,7038 0,0820 0,6639
0,1996 0,2335 0,5485
0,2974 0,5880 0,3160
0,2962 0,5820 0,8361

Now lets have a look at what we have done, from the side we can see how one of the angles (beta) is a long way from ninety degrees.

Side view of unit cell

Now we will have a look from a different angle.

The front view of the cell

Here are the x,y,z coordinates of the atoms on a conventional 90 degree and 90 degree set of x y and z axis. I have marked on bold the iron atoms which are at the corners of the cell.

46
XYZ file   for : K3Fe(CN)6
K 0.28089 -3.45899 -5.16955
K -5.00083 0.38661 -3.78117
K 5.38365 0.38134 -3.21339
K 0.10193 4.22694 -1.82501
K -2.32040 -2.87755 -1.40161
K 2.82526 -0.96562 -0.24795
K -2.82526 0.96562 0.24795
K 2.32040 2.87755 1.40161
K -0.10193 -4.22694 1.82501
K -5.38365 -0.38134 3.21339
K 5.00083 -0.38661 3.78117
K -0.28089 3.45899 5.16955
Fe -4.91135 -3.45635 -5.45344
Fe 5.47313 -3.46163 -4.88566
Fe 0.19141 0.38398 -3.49728
Fe -5.09031 4.22958 -2.10890
Fe 5.29417 4.22430 -1.54112
Fe -5.29417 -4.22430 1.54112
Fe 5.09031 -4.22958 2.10890
Fe -0.19141 -0.38398 3.49728
Fe -5.47313 3.46163 4.88566
Fe 4.91136 3.45635 5.45344
C 4.80935 -2.73005 -3.21574
C 0.69724 -1.37587 -2.85930
C -1.59727 0.07097 -2.84632
C 0.66992 1.11497 -1.76490
C -3.38358 3.91480 -1.26682
C 4.72002 2.46500 -0.96219
C -4.72002 -2.46500 0.96219
C 3.38358 -3.91480 1.26682
C -0.66992 -1.11497 1.76490
C 1.59728 -0.07097 2.84632
C -0.69724 1.37587 2.85930
C -4.80935 2.73005 3.21574
N 0.98970 -2.42716 -2.50303
N 4.41252 -2.27534 -2.24005
N -2.64379 -0.14067 -2.41469
N -2.39058 3.70212 -0.72368
N 4.38940 1.41403 -0.63999
N 0.95847 1.56933 -0.75174
N -4.38940 -1.41403 0.63999
N 2.39058 -3.70212 0.72368
N -0.95846 -1.56933 0.75174
N -4.41252 2.27534 2.24005
N 2.64379 0.14067 2.41469
N -0.98969 2.42716 2.50303

If you want a free program (free to academic users only) then I would suggest ORTEP which I have provided a link for on the right hand side of this blog.

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2 Responses

  1. I dont understand what “Fractional coordinates” means. Plz help me understand…

  2. I will get back to you as soon as I can, I will try to help you understand.

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