No echos from isotropic system in saffron

[thanasis]

Hello,

I am trying to get a handle on the basics of saffron. I took the 2p-echo example and tried to simplify it by removing the 14N nucleus and setting the g-tensor to a fully isotropic value (in particular 2.006).

What happens then is that the simulation seems to give an pattern that corresponds to the detuning frequency, and not to the echo itself. Indeed, if I then set the magnetic field precisely to the resonance value, I get two flat lines.

Is there an issue with calculating isotropic systems?

The modified script is:

Code: Select all

% Two-pulse echo transient using chirp pulses (saffron)
%==========================================================================
% Simulates a chirp echo of a nitroxide using saffron

clear; close all;

Exp.Field = 324.9;  % mT

% Spin system
Sys.g = [2.006 2.006 2.006]; % <-- Isotropic g-tensor
% Sys.Nucs = '14N'; % <-- Removed hyperfines
% Sys.A = [11 11 95];  % MHz
Sys.lwpp = 5;  % MHz

% Simulate frequency-sweep spectrum to set pulse excitation bands
pepper(Sys,Exp);

%%

% Define basic experiment parameters
Exp.mwFreq = 9.05;   % GHz <-- Modifying this changes the frequency of the calculate trace
% Exp.Field = 714.4773505*Exp.mwFreq/Sys.g(2)/10;  % mT <-- Uncommenting this gives totally flat patterns

% Define pulses
p90.Type = 'quartersin/linear';
p90.tp = 0.200;              % pulse length, µs
p90.Flip = pi/2;             % flip angle, radians
p90.Frequency = [-120 120];  % excitation band, MHz
p90.trise = 0.030;           % rise time, µs

p180 = p90;
p180.tp = 0.100;   % µs
p180.Flip = pi;    % rad

% Define pulse sequence
tau = 0.2;  % µs
Exp.Sequence = {p90 tau p180 tau+p180.tp};

% Define detection
Exp.DetWindow = [-0.15 0.15];  % µs
Exp.DetPhase = pi;             % rad, for proper phasing of the signal

% Use grid resolution sufficient to get converged echo tails
Opt.GridSize = 30;
Opt.Verbosity = true;

saffron(Sys,Exp,Opt);

[ninowili]

If there is only a single frequency no decay and thus no echo is expected. When exactly on resonance the FID and echo have a frequency of 0. There is thus no evolution in this particular rotating frame.

I assume saffron ignores "Sys.lwpp".

[thanasis]

Thank you Nino,

You are probably right. I have now tried g.Strain to no effect.

So I suppose, to get some inhomogeneous broadening, we need to introduce a slight anisotropy, through g, through A, or some other term. I wonder, however, after what point that becomes too fictitious, especially when our system is intrinsically very isotropic.

[ninowili]

I think it might make sense as a feature request to include a simple gaussian offset-broadening or so in saffron calculations. I assume it ignores g-strain if you say it has no effect.

You can always to it "by hand". ie generate a gaussian distribution of g-values or offsets, calculate them separately, and add the (weighted result).

[thanasis]

Thanks Nino.

That was my first thought. But then, each of the g-values of the distribution would still be isotropic and monodisperse. Calculating each of these separately, would bring us back to the same problem, wouldn't it?

[ninowili]

But that is how an echo forms. Each spin packet evolves with one frequency, and the some of frequencies appears as a decay. After the pi pulse, the packets "evolve backwards"/change place, which leads to constructive interference, i.e. the echo. When discussing inhomogeneous/anisotropic interactions, there will never be an echo for a single spin packet.