One-pulse line intensity for MAS powder, Part 1

AIM: We show that, for simulating a powder sample (樣品), the number of summation steps that the Euler angle α is divided in [0, 2π[ rang must be a 4-fold number so that the results do not depend on the sign of the asymmetry parameter η.

Equipment: Mathematica-5 (or MathReader for reading the notebook if you do not have Mathematica-5).

Method: We simulate the central-line intensities of a spin I = 3/2 for pulse duration t increasing from 0 to 20 μs by steps of 1 μs in a powder rotating at the magic angle, using Mathematica-5 notebook.

The parameters for these simulations are:

• Observed line intensity: central transition
• Nucleus: ²³Na
• Spin: 3/2
• ²³Na Larmor frequency: 105.8731007 MHz
• Proton Larmor frequency: 400 MHz
• Strength of the radio-frequency pulse: 100 kHz
• Initial pulse duration: 0
• Final pulse duration: 20 μs
• Pulse duration increment: 1 μs
• Number of pulse duration increment: 20
• Rotor spinning speed: 15 kHz
• Quadrupole interaction: first- and second-orders
• Quadrupole coupling constant: 8 MHz
• Asymmetry parameter: -1 or 1
• Number maxα of summation steps of the Euler angle α of the rotor: variable
• Number maxβ of summation steps of the Euler angle β of the rotor: 3
• Number maxγ of summation steps of the Euler angle γ of the rotor: 3

(A) Mathematica-5 notebook

1. Download the Mathematica-5 notebook called powder_MAS.nb or the notebook as PDF file powder_MAS.pdf (53 Kb)
2. Save this file into the software Mathematica 5 folder.
3. Open this file with Mathematica-5 and change the value of the asymmetry parameter.
4. Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start the simulation.
5. A file called powderMAS.m is created in Mathematica-5 folder. MS Excel can open this file.

(B) Result

The simulated line intensities are gathered in the following table. The two columns concerning maxα = 4 are identical.