14 - Lecture notes for Clay Mineralogy

XRD identification of mixed-layer clay minerals

Recall that mixed-layer clays are identified by the presence of an non-rational series of reflections.

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 composit 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 ~10Å and the smectite (in the ethylene glycol saturated state) has a repeat of ~17Å. 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 refelection 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 = 10Å + 10Å + 10Å + 17Å = 47Å.

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 _A·B·A·A = 1) then this becomes a discrete mineral phase. For ISII this mineral is named tarasovite and it has a basal d-spacing with a 47Å repeat.

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



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

• d-spacing of the (001) = 10 +/- 0.05 Å.
• d-spacing of (060) = 1.50 +/- 0.01 Å.
• (002) intensity greater than (001)/4 (suggests aluminus octahedral sheet, Fe causes decrease).
• Calculate the "illite ratio" (I_r) where:.
• The I_r index uses the intensities of the first and third order basal reflections. If expandable smectitic layers are present, then the relative intensities will be influenced by mixed-layering. An I_r greater than 1 indicates smectitic layers.

e.g.,

1 x 0.704 = 0.074

2 x 0.704 =1.408

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

e.g.,

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:

• Enter respective layer type A and B (001) d-values into cells B1 and B2
• Let cell C2 = B1/B2
• Let cell B4 = A4 * $C$2
• Let cell C4 = ABS(ROUND(B4,0)-B4)
• Copy formulas from row 4 to the rows below.

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 cosQ to eliminate angle dependent particle size broadening).

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 2 figures are from Moore and Reynolds. They are included for use only by the students in this class. Do not reproduce without permission from the authors.