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Such situations are commonly observed in powders, and the spectra are therefore called "powder-pattern spectra".In crystals, the number of EPR lines is determined by the number of crystallographically equivalent orientations of the EPR spin (called "EPR center").Since the source of an EPR spectrum is a change in an electron's spin state, the EPR spectrum for a radical (S = 1/2 system) would consist of one line.

In practice, EPR samples consist of collections of many paramagnetic species, and not single isolated paramagnetic centers.

If the population of radicals is in thermodynamic equilibrium, its statistical distribution is described by the Maxwell–Boltzmann equation: ≈ 0.998, meaning that the upper energy level has a slightly smaller population than the lower one.

In general, the g factor is not a number but a second-rank tensor represented by 9 numbers arranged in a 3×3 matrix.

The principal axes of this tensor are determined by the local fields, for example, by the local atomic arrangement around the unpaired spin in a solid or in a molecule.

In practice, it is usually the frequency that is kept fixed.

A collection of paramagnetic centers, such as free radicals, is exposed to microwaves at a fixed frequency.

Choosing an appropriate coordinate system (say, x,y,z) allows one to "diagonalize" this tensor, thereby reducing the maximal number of its components from 9 to 3: g are the components of the magnetic field vector in the coordinate system (x,y,z); their magnitudes change as the field is rotated, so does the frequency of the resonance.

For a large ensemble of randomly oriented spins, the EPR spectrum consists of three peaks of characteristic shape at frequencies g: the low-frequency peak is positive in first-derivative spectra, the high-frequency peak is negative, and the central peak is bipolar.

Experimentally, this equation permits a large combination of frequency and magnetic field values, but the great majority of EPR measurements are made with microwaves in the 9000–10000 MHz (9–10 GHz) region, with fields corresponding to about 3500 G (0.35 T).


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