Hyperfine parameters

Isomer shift (δ, mm/s)

The isomer shift comes from the interaction between the nucleus and the electrons around it. It moves the whole spectrum left or right. Strictly, it is only called the isomer shift when the source and the sample are at the same temperature. Otherwise centre shift is the better term, although the two are often used interchangeably.

The shift depends on how many s electrons are found at the nucleus itself. When Fe(III) gains an electron to become Fe(II), the extra 3d electron shields the s electrons and pushes them slightly outwards, so fewer reach the nucleus. For iron-57 this gives a larger isomer shift.

The isomer shift is given relative to a calibration, usually metallic iron (α-Fe) at room temperature, which is defined as 0 mm/s. It is very sensitive to the oxidation state. At room temperature, high-spin Fe(III) usually lies between about 0.2 and 0.5 mm/s and high-spin Fe(II) between about 0.9 and 1.3 mm/s.

Shading shows s electrons, dots show 3d electrons. The extra 3d electron in Fe(II) shields the s electrons, so fewer reach the nucleus and δ is larger.

Quadrupole splitting (ΔE_Q, mm/s)

The iron-57 nucleus is spherical in its ground state, but slightly elongated in the excited state that absorbs the gamma rays. When the electric field around the nucleus is uneven, because of the iron's own electrons or the atoms around it, the energy of the excited state depends on how the elongated nucleus is oriented. The excited state splits into two levels, so there are two transitions and the single line splits into two.

This pair of lines is called a doublet. The isomer shift is the midpoint of the two lines and the quadrupole splitting is the distance between them. A perfectly symmetric environment gives no splitting.

The quadrupole splitting also depends on the oxidation state. High-spin Fe(II) usually has a large splitting (often above 1.5 mm/s), while high-spin Fe(III) usually has a smaller one (often below 1 mm/s). Plotting δ against ΔE_Q is a quick way to tell the two apart.

In an uneven electric field the elongated excited state splits into two levels, so there are two transitions instead of one.

Hyperfine field (B_hf, T)

When the iron atoms in a mineral are magnetically ordered, the nucleus feels a strong magnetic field. This splits the spectrum into six lines, called a sextet. The larger the field, the further apart the lines. In a powder, where the crystals point in all directions, the six lines have areas in the ratio 3:2:1:1:2:3.

The total area stays the same, so as the lines spread out each one becomes shallower (the plot below rescales to fill its space, so this does not show). Metallic iron has a field of about 33 T and hematite about 52 T, which is why spectrometers are usually run from −12 to +12 mm/s. A narrower range would cut off the outer lines.

The six lines come from the nucleus itself. A magnetic field splits the ground state into two levels and the excited state into four, and six transitions between them are allowed.

A magnetic field splits both nuclear states. Six transitions are allowed, so the single line becomes a sextet. The numbers link each transition to its line.

Quadrupole shift (ε, mm/s)

In a sextet, the quadrupole interaction no longer splits lines into pairs. Instead it shifts the two outer lines one way and the four inner lines the other, so the sextet becomes slightly lopsided. This is the quadrupole shift. It is related to the quadrupole splitting by ε = (ΔE_Q/2)(3cos²θ − 1)/2, where θ is the angle between the magnetic field and the main axis of the electric field.

The quadrupole shift is usually small compared with the hyperfine field, but it can help identify minerals. Goethite, for example, has a clearly negative ε. Take care when reading papers, because some report 2ε instead of ε, and some call it quadrupole splitting.

Linewidth (FWHM, mm/s)

Each line has a width, usually given as the full width at half maximum (FWHM). The natural linewidth of iron-57 is 0.097 mm/s, and because both the source and the sample contribute, the narrowest line you can measure is about 0.19 mm/s. Thick samples, the instrument and a spread of slightly different iron environments all make lines broader.

Relative area (%)

When a spectrum is fitted with several sites, the share of the total area in each site gives an estimate of how much of the iron is in that environment, for example the Fe(II) to Fe(III) ratio. Different environments can absorb with different efficiency (the recoil-free fraction), so the estimate is approximate, especially at room temperature.

Bringing it all together

A real site has all of these parameters at once. Choose a doublet or a sextet, then move the sliders or try one of the examples.

Most real spectra contain more than one site, each with its own parameters, and the measured spectrum is their sum. Fitting a spectrum means finding the set of sites that best adds up to the data. The guide on line shapes looks at the choices involved.

The hyperfine parameters at a glance
Parameter	Unit	What it shows in the spectrum	What it tells you
Isomer shift δ	mm/s	Position of the whole spectrum	Oxidation and spin state
Quadrupole splitting ΔE_Q	mm/s	Gap between the two lines of a doublet	Oxidation state and the symmetry of the surroundings
Hyperfine field B_hf	T	Spread of the six lines of a sextet	Magnetic ordering, and which mineral
Quadrupole shift ε	mm/s	Lopsidedness of a sextet	Symmetry of the surroundings in a magnetic phase
Linewidth (FWHM)	mm/s	Width of each line	Sample quality and how varied the iron environments are
Relative area	%	Share of the total absorption	Roughly how much iron is in each environment

The information here is a starting point only. For more detail, see the books and reviews below.