![]() Graph2 - ln(Intensity) vs time, and fit of points 19 - 99 using linear equation f(t) = C-t/T2 Graph5 - ln(Intensity) vs time, and fit using linear equation for the entire data set: f(t) = C-t/T2 Graph1 - ln(Intensity) vs time, and fit using equation f(t) = ln(I1*exp(-t/T2f)+I2*exp(-t/T2s)) Graph0 - intensity vs time, and biexponential fit f(t) = I1*exp(-t/T2f)+I2*exp(-t/T2s) Please find attached Igor Pro experiment file with all generated data and graphs. And then I applied two above mentioned methods of calculating T2 values. To check the methodology, I generated test data (100 points, wave called Intensity). Could you please tell me, which variant of calculating T2 values is true? Please find attached two pictures which show the difference between two mentioned methods of calculating T2 values. Finally, I fit these 3 points with equation y1 = C1 - t/T2_1 and find the parameters C1 and T2_1. Let's call these new values as ln(I)1, ln(I)2, ln(I)3. After that, I subtract these extrapolated ln(I) values from first three experimental ln(I) values. Then, using equation y2 = C2 - t/T2_2, I find ln(I) values for time values corresponding to the first part of points (i.e., for example, first 3 points). And the second variant is the following: first, I fit the second part of points with equation y2 = C2 - t/T2_2, i.e., for example, 7 points as you can see in the attached pictures. The first variant is just to fit each part of data points with linear equation with corresponding initial guesses. And here I have two variants of how to do this fitting. Then I consider that the data set is described by two T2 components (T2_1 and T2_2). In obtained semilog graph, I need to divide points into two parts: first part of points will be fitted by linear equation y1 = C1 - t/T2_1, and the second part of points will be fitted by linear equation y2 = C2 - t/T2_2. I take natural logarithm of intensity values, and thus the vertical axis in the graph is now in ln(I). Then I fit y = C - t/T2 to the entire data set, assuming that the data set is described only by one T2 value. In order to ensure that the experimental points have biexponential behavior and not monoexponential (or conversely), I use semilog graph. In most cases (I have a number of experiments), both mono- and biexponential fits are good. I fit the experimental data points with mono- and biexponential equations. The purposes are 1) to determine whether the experimental points obey monoexponential dependence or biexponential dependence, and 2) to calculate T2 (in case of monoexponential behavior), T2_1 and T2_2 (in case of biexponential behavior). In the second case, I1 and I2 are intensities which represent fractions of two T2 components - T2_1 and T2_2. The experimental points obey mono- or biexponential dependence: I = I0*exp(-t/T2) or I = I1*exp(-t/T2_1) + I2*exp(-t/T2_2). I have experimental nuclear magnetic resonance data that describe T2-relaxation of the nuclei in the sample of interest. Wide-Angle Neutron Spin Echo Spectroscopy.
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