Incorrect Diamond Crystal Symmetry

[rchaklashiya]

When we try to run an EPR simulation averaging the four possible orientations of P1 center in diamond, we get a different result when we manually average these four orientations vs when we use the diamond space group via Exp.CrystalSymmetry = ‘Fd3m’ or 227. The results differ in both peak position and in peak height ratio. However, when we modify the manual orientations slightly by changing their theta euler angle from the correct 109.47 degrees to the incorrect 90 degrees, the peak positions match up perfectly with the CrystalSymmetry case, though the peak height ratios continue to be incorrect (2:1 rather than the correct 3:1).
See these images here:

diamondeprissuepic1.png (240.68 KiB) Viewed 7353 times

diamondeprissuepic2.png (262.25 KiB) Viewed 7353 times

As well as this matlab code here:

Diamond_EPR_Simulation_4_Orientations.m

(3.26 KiB) Downloaded 745 times

We think that there is an issue with the ‘Fd3m’ space group as defined in Easyspin, and are wondering if anyone has seen this issue before or can verify this.
Please let us know. Thanks!

[Stefan Stoll]

This does not look like a bug, but rather like a misunderstanding of the crystal frame.

In EasySpin (like in X-ray crystallography in general), by convention the principal axes a,b,c in a cubic space group such as diamond's Fd-3m (#227) are defined along the 4-fold symmetry axes of the corresponding point group ([001], [010], [100]).

From literature (e.g. Cox/Newton/Baker 1994) it is known that the principal axis of the P1 center 14N hyperfine tensor with the largest value is along a 3-fold axes ([111] etc) due to a unique elongated N-C bond.

Here is one way how to correctly specify the P1 center. First, choose a local molecular frame for the P1 center. We are free to choose this any way we want, but it's simplest if we define it such that the local z axis is along the unique N-C bond along [111]. The x and y axis are perpendicular to z, but can otherwise be arbitrary, since all tensors are axial. In this chosen molecular frame, the g and A tensors are diagonal, and we don't have to provide gFrame or AFrame - this makes this particular choice quite convenient.

Code: Select all

P1.S = 1/2;
P1.Nucs = '14N';
P1.g = [2.002203 2.002181];
P1.A = [81.318 114.032];  % MHz

Next, we have to tell EasySpin how the chosen P1 molecular frame is oriented within the diamond crystal/space group frame. Note that the latter frame is hard-wired and follows the standard convention, i.e. axes are taken to be along [100], [010] and [001]. Now, since the [111] axis is tilted with respect to the crystal frame, we need to provide the appropriate tilt angles in Exp.MolFrame:

Code: Select all

ma = 54.73561;  % magic angle, degrees
Exp.MolFrame = [45 ma 0]*pi/180;  % orientation of P1 molecular frame in diamond crystal frame
Exp.CrystalSymmetry = 'Fd-3m';  % diamond space group, #227

For simulating the spectrum of a single diamond, specify its orientation in the spectrometer in Exp.SampleFrame. For example, use all-zero if the crystal frame aligns with the lab frame.

Code: Select all

Exp.SampleFrame = [0 0 0];   % degrees

Hope this helps!