13 - Lecture notes for Clay Mineralogy

Required reading: Moore and Reynolds, 174-175, 261-297, 359-371
Brindley and Brown, pages 249-267


XRD identification of mixed-layer clay minerals

The terms interlayering, mixed-layer and interstratification all describe phyllosilicate structures in which two or more layer types are vertically stacked in the direction parallel to c*.

Nomenclature - It's important to note that (with exception to regularly ordered 50-50 interstratified clays) there is no "accepted" nomenclature for mixed-layer clays. However, for simple binary mixed systems, an easy short-hand notation can be established that is also relatively unambiguous. The hierarchy is as follows:

  1. Mixed-layer clays are referred to by the two minerals, mineral groups, or layer types involved.
  2. The sequence is given by the cmineral, group, or layer type name with the smallest d-spacing first. Then followed by the second mineral, group, or layer type name (e.g., a mixed layering of illite, which has a 10Å repeat and EG-smectite, which has a 17Å repeat, is named illite-smectite).
  3. The mixed-layer clay mineral name is further qualified by two additional factors:
  4. The proportions of layer types (e.g., 50% illite and 50% smectite).
  5. The ordering scheme of the layer types (i.e., the sequence of layer types can range from random to short-range ordered to long-range ordered).

A shorthand notation to denote the binary mixed-layer system system above would be:

ABXXRY

where:
Definition: Reichweite = "reach back" R is the most distant number of layers that affects the probability of the final layer. When this term is greater than zero, it provides a description of the nearing-neighbor effects.

Examples of R commonly used in the calculation of mixed-layer systems include:

Example of shorthand notation for mixed-layer type.

IS20R0 is an illite-smectite with 20% illite type layers and 80% smectite type layers, that are randomly interstratified.

In the special case where the proportions of each layer type are equal and they are ordered in alternating sequence (ABABABABAB..., i.e., XX = 50 and Y=1) then specific new mineral names are given.

Example:

IS50R1 = rectorite.


How do you recognize the presence of interstratification?

If you examine a crystal structure that repeats its basal reflections at periodic spacing it "obeys" Bragg's Law

n λ = 2dsinθ

where, the d's occur as integral series.

This series is referred to as a rational series of reflections.

One method to assess the rationality of a series is look at the standard deviation of the reflections "normalized" by their order.

An example of chlorite is shown below.

The values of d in the table below have been taken from the CuKα diffractogram above (higher-order reflections are not plotted above).

d (00l) Å

l

l * d

13.939

1

13.939

7.0197

2

14.039

4.6916

3

14.074

3.5243

4

14.097

2.8204

5

14.102

2.3876

6

14.325

2.0020

7

14.014

1.5678

9

14.110

1.4124

10

14.124

mean

14.091

std dev.

0.105

 

 CV

 0.75%

Note the small standard deviation. Bailey (1980, Am. Min. v67 p394) has suggested that any series with a coefficient of variation (CV) of less than 0.75% constitutes a discrete phase.

CV is defined as (100 x stdev) / mean

In the case of the regularly ordered 50/50 mixed-layer clays, the two layer types will combine to form a super structure (equal to the sum of the two layer dimensions). These result in very low angle reflections (i.e., 2 - 3.5° 2θ for Cu Kα radiation).



Statistical treatment of sequences with two layer types

One must consider (1) the composition of the layer types and (2) the probability of a given junction of layer types (i.e., interface).

In a two component system with layer types A and B let,

P A = fraction of A
P B = fraction of B

then,

PA + PB = 1


There are therefore four possible junction probabilities:

PA.B , PB.A, PA.A, PB.B



PABis therefore the junction probability of layer type B following layer type A.

It does not specify the probability of finding an AB pair.

The probability of finding an AB pair is product of the fraction of A and the junction probability of layer type B following layer type A. This is designated,

PAB = PAPA.B


Either an A or a B must follow an A, therefore,


PA.A + PA.B = 1


and either an A or a B must follow a B, therefore,

PB.A + PB.B = 1



and the probability of finding a AB pair is the same as finding a BA pair,

PAB = PBA = PAPA.B = PBPB.A


or

PA.B = PB.A PB / PA


Here we have six variables with four independent equations. Therefore, by giving any two variables the complete system is described.

Usually provided are:

1. The compositional parameter (PA or PB )
2. One junction probability (e.g., PA.A )

Example 1:

Example 2: Using illite-smectite. IS60

Note: This treatment only applies to sequences which are affected by its nearest neighbor. Layer sequences are defined by three particular types, including:

  1. Random
  2. Ordered
  3. Segregated

The random case is specified by equal junction probabilities of any layer being followed by an A, which in turn is equal to the amount of layer type A.

PA.A = PB.A = PA


and likewise, there is are equal junction probabilities of any layer being followed by a B, which in turn is equal to the amount of layer type B.

PB.B =PA.B = PB

The ordered case is specified by the case where,

PA.A = 0, if PA < 0.5


or

PB.B =, 0 if PA > 0.5


The range of PA.A from PA.A= 0 ------> PA.A = PA describes conditions from perfect to random interstratification.

If PA.A > PA, then A and B are separated into completely discrete domains (i.e., a physical mixture).

 Ordering type

 Conditions

 Random

  PA.A = PA

 Ordered

  PA.A = 0, if PA < 0.5

 Segregated

  PA.A = 1, if PA.A > PA

 

The frequency of occurrence for any arrangement of layers into a crystallite is found by using the junction probabilities and compositions. For example the 6-crystallite illite-smectite sequence ISSISI is given by;

PI PI.S PS.SPS.I PI.S PS.I

 When the layer sequence is random, then the fequency of occurrence simplifies to

(PI)nI . (PS)nS

where nI is the number of illite layers and nS is the number of smectite layers (e.g., 3 + 3 = 6 above).

Non-nearest neighbors 

As noted by Reynolds (1980) the nature of non-nearest neighbors is more complicated but follows the same logic.

Here's an example of ordering that considers three next-nearest neighbors in the same 6-crystallite illite-smectite sequence ISSISI as above.

PI PI.S PIS.S PISS.I PSSI. S PSIS.I

In addtion to the single junction probabilities and compositions, ternary junction probabilities are also needed. In our example, these are given as,

Now there are 8 variables and 6 equations, therefore only two junction probabilities will be needed to statisfy the system. One must come from a set containing I as the nearest-neighbor and one comes from a set containing S as the nearest-neighbor

Here are the equations that describe the higher order parameters for a four layer model.

There are 13 equations above and 16 varibles. Consequently 3 values must be given that occur in the last 5 equations. The last 5 equations must consider II and IS as nearest-neighbors. The one additional value must contain SI as nearest-neighbor pairs. Assuming values for PSII.I , PISI.I , and PSSS.I will allow calculation of all proabilities.

Reynolds (1980) notes that calculation of thrice-removed neighbors requires 7 variables to be defined.


Remember! Random ordering and/or non-equal layer proportions produce irrational reflection series.