14 - Lecture notes for Clay Mineralogy

Required reading: Moore and Reynolds, 263-276
Brindley and Brown, pages 274 - 300

XRD identification of mixed-layer clay minerals

Recall that mixed-layer clays are identified by the presence of an non-rational series of reflections. This concept of
understanding non-rational series was pioneered by J. Mering (1949) X-ray diffraction in disordered layer structures Acta crystallographica vol:2 pg:371 and has become to be known as Mering's Principles. To learn more, go to Drits and McCarty (1996).

The two variables that determine the nature of the diffraction are:

1. The proportions of layer types
2. The ordering of the sequence.

The position of the irrational reflections occur between the nominal positions of the (00l) peaks of each member of the mixture.

The position of a reflection is fixed by the proportions of end-members.

The designation for a reflection is given by the contributing (00l)'s.

Example: For a randomly mixed-layer I/S (e.g. IS50R0), the composite peak that results from the (002) of the illite and the (003) of the smectite is designated the (002)I/(003)
S or (002)10/(003)17. Remember, the layer with the smaller d-value is listed first. Sometimes, for clarity, the approximate d-spacing value for the respective layer type is appended as a subscript (see above and example below).

In the example below, illite has a repeat of ~10 and the smectite (in the ethylene glycol saturated state) has a repeat of ~17. The position of the discrete reflections of illite and smectite are marked on the diffractogram below with the red and blue lines, respectively.

Peak Widths

Note that the closer the end-members are to a composite peak, the sharper the peak shape becomes. This is exemplified above in the (003)
10/(005)17 reflection for the I/S.

The farther the end-members are from each other; the broader the composite peak shape becomes.

Therefore, in addition to the occurrence of non-rational series, mixed-layer clays can be further identified by the occurrence of peaks with variable peak widths (FWHM).

Example: Regularly ordered I/S 70 R1 (IS70R1). In the example below, note that the composite peaks that result from two closely-spaced higher-order reflections are narrow. This is seen in the (001)
10/(003)27 reflection. Note the (002)10/(006)27 reflection is broad.

Patterns can be thought of as a random mixture of rectorite and illite.

Note positions of where the Rectorite super-structure peaks would be (i.e., 001*, 002*...).

Some smectite layers are followed by more than one illite layer. Because this is R1 (i.e., the reach back or probability of an S following an I is determined by only one layer) there is a random probability for the occurrence of layers beyond one layer.

In the case where the "reach back" involves three nearing-neighbors, a large superstructure is created.

Superstructure of ISII = 10 + 10 + 10 + 17 = 47.

For the special case where ratio of the abundance of layer type A to layer type B is exactly 3:1 (i.e., P A = 0.75) and the ordering scheme is R = 3 (i.e., P ABAA = 1) then this becomes a discrete mineral phase. For ISII this mineral is named tarasovite and it has a basal d-spacing with a 47 repeat.

Example: Regularly ordered I/S 90 R3 (IS90R3). The example below shows the effect of non-nearing neighbor ordering.

Peak at 11.3
is the composite (001)10/(004)47 reflection

Are the discrete clay mineral species we examine really discrete?

Define illite as patterns that meet the following criteria*: * Jan Srodon and Dennis D. Eberl  Illite  Reviews in Mineralogy and Geochemistry, January 1984, v. 13, p. 495-544

The Q-rule ( a broadening descriptor to recognize small amounts of mixed-layering)

Caution: Line broadening also comes from effects of crystallite size, strain, and XRD optics (slit size, misalignment...).

Step 1. Suppose that there is a mixture of two layer types, (e.g., illite and chlorite).

Step 2. Take the ratio of the small d(001) to the large d(001),

e.g., illite (001) /
chlorite (001) = 10/14.2 = 0.704.

Step 3. Multiply this ratio by l : the order of the reflections


1 x 0.704 = 0.074

2 x 0.704 =1.408

Step 4. Determine the deviation of each number from the nearest integer.


1 - 0.704 = 0.294

1.408 - 1 = 0.408

This is easy to set up in a spreadsheet. In Excel the syntax is as follows:

Click here to download Q-rule Excel spreadsheet.

D001A 10 Ratio
D001B 14.2 0.704
Order Order x ratio Q
1 0.704 0.295
2 1.408 0.408
3 2.112 0.112
4 2.816 0.183
5 3.521 0.478
6 4.225 0.225
7 4.929 0.070
8 5.633 0.366
9 6.338 0.338
10 7.042 0.042

Step 5. The Q values predict the relative widths of the mixed-layer type where:

Q = 0.000 - no line broadening at all (only that due to crystallite and instrument effects).
Q = 0.500 - maximum breadth possible.

Step 6. Determine line widths for near-discrete phase and correct for instrumental line broadening (this is done mathematically by analyzing observed peak and a defect free sample with large coherent domains such as NIST
SRM-660 XRD reference material LaB6).

Step 7. Plot Q versus peak width, corrected for by cos
(θ to eliminate angle dependent particle size broadening.  Recall the Scherrer equation;

L =λK/βcosθ  


L = Mean crytallite dimension ()
λ = Wavelength of radiation
K = constant (near unity)
β = FWHM (in radians i.e., measure 2θ then multiply by π/180)
θ = angle of incidence


β (radians) = λK/cosθ

β (2θ) = β (radians)* 180 /π

In the example below from Moore and Reynolds used calculated data, whre they assume a mean defect distance of 10 unit cells with the largest being 50 unit cells.

Step 8. The slope of Q versus corrected width is related to the percentage of layer types in the mixed-layer clay.

If all the peaks have identical widths, then the line will plot vertically and there is only one layer type (i.e., Q is meaningless).

Note: The above  figure is modified from Moore and Reynolds. It is included for use only by the students in this class. Do not reproduce without permission from the authors.

Here is an example for illite/smectite with 90% smectite layers and R0 ordering.

Q versus beta plot