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Clay Minerals (1967) 7, 79. QUANTITATIVE X-RAY DIFFRACTION ANALYSIS USING CLAY MINERAL STANDARDS EXTRACTED FROM THE SAMPLES TO BE ANALYSED RONALD J. GIBBS Department of Geology, University of California, Los Angeles (Received 2 March 1967) ABSTRACT: In the quantitative X-ray diffraction analysis of a series of samples, the problems arising from the variable compositions and degrees of crystallinity of clay minerals were overcome to a great extent by the use of standards extracted from the samples. Procedures are given for separation of the montmorillonite standard by differential settling of Na-montrnorillonite solvated in an ethanol solution and for isolation of the kaolinite, mica, and chlorite standards by density separation of their Na-forms in thallous formate. Calibration curves were prepared from the X-ray diffractograms obtained for series of known mixtures of Ca-forms of the standards and the internal standard boehmite using both powder and smear-oriented mounting techniques. INTRODUCTION The advancement of quantitative X-ray diffraction clay mineral analysis techniques has been impeded by the problems created through the variable compositions and degrees of crystallinity of clays. Bradley & Grim (1961) reviewed the variety of clay mineral analysis techniques available, discussed the problem of composition and crystallographic variability, and emphasized the importance of selecting, as a standard, a clay with crystallo- graphic properties similar to those of the mineral to be assessed in the sample. The major problem in working with the usual complex mixtures of clays found in nature is the determination of the diffracting power of each of the clay minerals in the sample under study. These diffracting ability factors have often been assumed or calculated (John, Grim & Bradley, 1954) or an approximation has been determined by using, as standards, clays with seemingly 'similar' properties (Schultz, 1960). Freas' (1962) attempt to determine the diffracting ability factors by ascertaining the percentages of clays present in several of the samples to be analysed (and using these samples as standards for calibrating the X-ray analysis) was based on the

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Page 1: QUANTITATIVE X-RAY DIFFRACTION ANALYSIS USING CLAY MINERAL ...minersoc.org/pages/Archive-CM/Volume_7/7-1-79.pdf · QUANTITATIVE X-RAY DIFFRACTION ANALYSIS USING CLAY MINERAL STANDARDS

Clay Minerals (1967) 7, 79.

Q U A N T I T A T I V E X - R A Y D I F F R A C T I O N A N A L Y S I S

U S I N G C L A Y M I N E R A L S T A N D A R D S E X T R A C T E D

F R O M T H E S A M P L E S TO BE A N A L Y S E D

R O N A L D J. G I B B S

Department of Geology, University of California, Los Angeles

(Received 2 March 1967)

ABSTRACT: In the quantitative X-ray diffraction analysis of a series of samples, the problems arising from the variable compositions and degrees of crystallinity of clay minerals were overcome to a great extent by the use of standards extracted from the samples. Procedures are given for separation of the montmorillonite standard by differential settling of Na-montrnorillonite solvated in an ethanol solution and for isolation of the kaolinite, mica, and chlorite standards by density separation of their Na-forms in thallous formate.

Calibration curves were prepared from the X-ray diffractograms obtained for series of known mixtures of Ca-forms of the standards and the internal standard boehmite using both powder and smear-oriented mounting techniques.

I N T R O D U C T I O N

The advancement of quantitative X-ray diffraction clay mineral analysis techniques has been impeded by the problems created through the variable compositions and degrees of crystallinity of clays.

Bradley & Grim (1961) reviewed the variety of clay mineral analysis techniques available, discussed the problem of composition and crystallographic variability, and emphasized the importance of selecting, as a standard, a clay with crystallo- graphic properties similar to those of the mineral to be assessed in the sample. The major problem in working with the usual complex mixtures of clays found in nature is the determination of the diffracting power of each of the clay minerals in the sample under study. These diffracting ability factors have often been assumed or calculated (John, Grim & Bradley, 1954) or an approximation has been determined by using, as standards, clays with seemingly 'similar' properties (Schultz, 1960). Freas' (1962) attempt to determine the diffracting ability factors by ascertaining the percentages of clays present in several of the samples to be analysed (and using these samples as standards for calibrating the X-ray analysis) was based on the

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80 RonaM J. Gibbs

assumption that differential dissolution and measurement of the mono-layer specific surface accurately determine the amounts of kaolinite and montmorillonite, res- pectively, in complex samples. This method, however, is usable only on chlorite-free samples since it assumes the 7 A peak solely represents kaolinite.

Lapham & Jaron (1964) tried to overcome the problem of clay variability in the analysis of illite. A coefficient was devised by measuring the 'total angular peak spread' which, when multiplied by the peak height, gave a comparable number for the Fithian illite and a pegmatitic muscovite. A calculation with these figures shows, however, that by measuring the peak areas of each mineral nearly the same results can be obtained.

In reviewing the techniques available for the quantitative analysis of a series of samples, it became obvious that none of the available techniques had actually overcome the problems of variability of composition and crystallinity of the clay minerals. An appropriate solution seemed to be the extraction of the individual clays from the samples themselves and then using these separated clays as the standards for the series of samples.

The quantitative X-ray diffraction analysis of the clay minerals of the series of samples was based on the use of standards extracted from the samples and of powder and smear-oriented mounting techniques, both of which utilized an internal standard. It was thus possible to combine the advantages of the internal standard method as given by Klug & Alexander (1954) with the advantages of the high sensitivity of the smear-oriented technique (Gibbs, 1965) for clay minerals.

P R E P A R A T I O N AND A NALY SIS OF S A M P L E M A T E R I A L

Size separation

Size separation can be performed before or after any pre-analysis treatment, depending on the particular type of problem under study. In the study of uncon- solidated sediments, size separation before the removal of the organic and iron materials will best reveal any relationship between the material and its transporting media. In the study of consolidated sediments, or when the ultimate degree of mineralogic segregation is desired, size separation should, for best results, be made after the removal of the organic and iron materials.

In this study the ~2/~ particle-size fraction was separated by centrifuge settling (Jackson, 1956) and the 2-20 /~ and ) 2 0 /~ fractions were separated by gravity settling (Jackson, 1956) before treatment. The size interval selected can be varied to suit the needs of the material being studied.

Pre-analysis treatment

The organic material was removed from the sample material by two or three treatments with 35% H~O2 after the material had been wetted with buffered NaOAc (pH 4-8) (Jackson, 1956). Following each treatment the mixture was evaporated to near dryness by boiling before the next addition of H20~. Since the

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Quantitative X-ray analysis 81 samples in this study were calcium carbonate-free, weight loss with this treatment resulted from the destruction of the organic material.

The iron coatings were removed from the sample material (1) to provide complete separation, since the coating acts as a cement in holding dissimilar clay minerals together; (2) to obtain comparable results between samples, since iron coatings have a linear absorption coefficient 10-20 times that of clays (Cullity, 1956) and since the amount and type of coating can vary on different clay minerals within a single sample as well as between samples; and (3) to produce relatively higher diffraction peaks, since the high fluorescent radiation of the coatings considerably increases the background (Bradley & Grim, 1961).

The iron coatings and iron mineral particles were removed from the sample material by the technique of Mehra & Jackson (1960) in which any ferric iron is reduced with sodium dithionite and the ferrous iron is complexed with sodium citrate. Investigation of the peroxide and Na~S204 treatments used showed no detectable alteration of the character of the clay minerals, substantiating the results of Mehra & Jackson (1960) and Follett et al. (1965). The types of iron minerals removed can be readily determined by comparison of the X-ray pattern of the untreated sample with that of the treated sample. Peaks present in the pattern of the untreated sample are revealed, with a high degree of certainty, as being those of the iron minerals. Poor X-ray patterns for the iron minerals were obtained, however, due to the fact that the iron minerals were, to a large extent, amorphous to very poorly crystalline.

Internal standard

Boehmite was selected as the internal standard (Griffin, 1954) because of the following characteristics: (1) a low mass absorption; (2) a medium high intensity, which allows use of small amounts, with a resulting low dilution of the sample; and (3) the ability to produce a wide range of reflections without interfering with those of the minerals under study.

Mounting methods

Powder technique. Specimens analysed using the powder technique were mounted in especially constructed side-loading holders in order to assure random orientation (Niskanen, 1964) using a minimum of about 60 mg of material. Excellent repro- ducibility, no segregation, and no preferred orientation were observed in control r u n s .

Smear-oriented technique. Smear-oriented specimens were mounted by smearing a day paste onto a glass microscope slide with a special spatula, producing a thin, even layer. This method eliminates any segregation of minerals on a size basis which may introduce an error of up to 250% (Gibbs, 1965).

For identification of montmorillonite and mixed-layer clays, all specimens were glycolated by the vapour method of Brunton (1955) for at least 1.5 hr immediately before analysis and were analysed in a chamber maintained at 50% relative humidity.

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82 RonaM J. Gibbs

X-ray diffraction analysis The specimens were analysed on a standard Norelco wide-angle X-ray dittracto-

meter with Geiger counter using nickel-filtered copper Ka radiation at 35 kV and 20 mA, with divergent, scattering, and receiving slits of 1% 1 ~ and 0-006 in. respectively.

All smear-oriented specimens were run at a scanning speed of �89176 per min and chart speed of �89 in./min which resulted in a precision (rerun error) of 6% of the measured peak area above the background, computed at a 95 % confidence level. These settings were determined with regard to sensitivity, precision, and time. The faster 1~ per min scanning speed resulted in + 10% precision and low sensitivity, while the slower �88176 per rain scanning speed resulted in 4.5% precision and only slightly improved sensitivity over the �89176 per min speed.

The powder-mounted specimens were run at a scanning speed of k~ per min for clay minerals and at �88176 per min for the non-clay minerals in order to obtain a 5 % precision level.

The advantages of fixed counts (highest sensitivity and 3% precision) were far outweighed by the disadvantage of its being too time-consuming in the analysis of a large number of both peaks and samples.

Peak area was measured (using a polar planimeter) since the amount of a mineral present is more closely related to peak area than to peak height (Klug & Alexander, 1954).

P R E P A R A T I O N OF N O N - C L A Y M I N E R A L S T A N D A R D S

Quartz. The standard for quartz was obtained by crushing quartz crystals and treating with HF (Bradley & Grim, 1961) before separating into the 2-5, 5-10, 10-30, and >30 tL particle-size fractions.

Feldspars. The plagioclase and K-feldspar standards were prepared by crushing crystals of albite and K-feldspar, respectively, and separating into 2-5, 5-10, 10-30, and ~30 t~ particle-size fractions.

E X T R A C T I O N OF CLAY M I N E R A L S T A N D A R D S F R O M

SAMPLES TO BE A N A L Y S E D

Selection of material The selection of the material from which the standards are to be obtained can

influence the outcome of results obtained throughout the entire procedure. In order to test for variability of composition and crystallinity of any one of the clays within a series of samples, it is necessary to select sample material representative of the extremes found within the series, such as material obtained as near to or as far away from the sources as possible.

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Quantitative X-ray analysis 83 Size isolation

As a guide for the separation of the clay standards, the distribution of each of the clay minerals found in the samples from which the standards were to be obtained was determined by subdividing the material into <0"2, 0"2-0"5, 0-5-1-0, 1-2, 2-6, 6-12, and ~>12 /~ particle-size fractions, using centrifugal settling (Jackson, 1956) for the < 2 t~ fractions and gravity settling (Jackson, 1956) for the ~>2 p. fractions, The X-ray patterns obtained from these fractions (mounted by a smear-oriented technique) revealed the relative distribution of each clay mineral within each of the size-fraction groups.

Techniques of extraction of standards

To facilitate their extraction, the clay minerals were converted into Na-forms by placing the sample material in a dialysing sack in a 1~ NaC1 solution 20 times its volume for a period of 8 hr, and then by washing it in a like series of water changes until no trace of the chloride ion was detected by the AgNO3 test. Dialysis was used to avoid loss of even the finest size fraction of the clays.

Montmorillonite extraction technique. Preparatory to separating the montmoril- lonite standard, the particle-size fraction which had been previously determined as containing most of the montmorillonite was isolated. In this study almost all of the montmorillonite was contained in the ~0"5 t~ particle-size fraction, with far smaller amounts of illite and kaolinite, and with no chlorite. This size fraction was then purified by removing the kaolinite and illite which, combined, composed about one-third of the total size fraction. This was accomplished by the procedure described below, a variation of the method proposed by Buzagh & Szepesi (1954). This method is based on the fact that Na-montmori l loni te solvated in an ethanol solution has a much lower specific gravity than the kaolinite and illite in the solution and, therefore, can be separated by differential settling.

Procedure. Wet 50 mg or less of the separated size fraction of clay material (which had been sodium saturated after removal of the organic and iron materials) with 99 + % ethanol and place it in a closable 50 ml centrifuge tube. Add 48 ml of a 15% ethanol aqueous solution and completely disperse by shaking and/or ultrasonically. The suspen- sion should remain dispersed and should not flocculate. Centrifuge at 1600 g for from 60 to 200 min, depending on the type of material. Remove about 40 ml of the clear sus- pension with a 50 ml pipette, taking care not to disturb the sedimented material. Transfer the removed suspension to a pointed polypropylene tube and begin evaporating it in an oven at 80 ~ C. The polypropylene tube or its more desirable alternative a teflon evaporating dish, overcome the adhesiveness of the montmorillonite to glass. Repeat the treatment and centrifuging three or four times, with diminishing amounts of suspension being removed each time, until separation appears complete.

In order to obtain a sufficient amount of purified montmorillonite for use in this study, four tubes of prepared material were tested simultaneously. The material obtained was 90-95% pure montmorillonite and could have been purified further by additional processing. However, calibration with the other standards can correct for the known impurities with a low error.

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84 RonaM J. Gibbs

Kaolinite extraction technique. Preparatory to separating the kaolinite standard, the particle-size fraction which had been previously determined as containing most of the kaolinite was isolated. I n this study almost all of the kaolinite was contained in the 0.5-4 t~ particle-size fraction, with some mica and chlorite. The separation of the kaolinite was accomplished by the procedure described below, which is based on the principle, noted by R o d d a (1952) and discussed by Kittrick (1961), that the density of many clays is changed in a thallous formate-malonate mixture. In this study the kaolinite s tandard was separated f rom the mica and chlorite by isolating the size fraction having a specific gravity between 2.6 and 2-8 in thallous formate.

Procedure. Place 50 mg or less of the separated size fraction of clay material (which had been sodium saturated after removal of the organic and iron materials) in a closable centrifuge tube. Add 40 ml of an aqueous solution of the thallous formate having a specific gravity of 2-80 and completely disperse ultrasonically. Centrifuge the suspension at 1600 g for 2 rain after which disperse the upper and lower halves, respectively, using a thin spatula. Centrifuging and dispersion should be repeated until separation appears complete, with centrifuging time being increased gradually--in this study, to a maximum of 40 min. Decant the upper two-thirds of the suspension by filtering through a 0"45 /~ molecular filter and wash the purified kaolinite remaining on the filter.

Mica extraction technique. The particle-size fraction which had been previously determined as containing most of the mica extended f rom 1-32/~, with some kaolinite and chlorite. The selection of the 1--4/z particle-size fraction for separation of the mica standard was justified when separation of the 8 -32 /z fraction revealed identical crystallography. In this study the mica standard was isolated in the 2"8-3"0 specific gravity fraction of the 1-4 t~ particle-size fraction by the procedure discussed below, based on the same principle of density separation used for the isolation of the kaolinite standard.

Procedure. From the separated I-4 ~t particle-size fraction of clay material (which had been sodium saturated after removal of the organic and iron materials) remove the ~2.8 and ~3-0 specific gravity fractions using the same thallous formate method outlined for the separation of the kaolinite standard. The remaining 2-8-3"0 specific gravity fraction will prob- ably contain an objectionably high amount of chlorite, which should be broken down, with no detectable alterations to the mica, by boiling in a 10% concentrated HCI solution, converting the chlorite into a non-diffracting material which can be removed as the ,~2.75 specific gravity fraction by the thallous formate method outlined for the separation of kaolinite. Filter the final portion of the decanted suspension through a 045 /~ filter and wash the purified mica remaining on the filter.

Chlorite extraction technique. In this study the particle-size fraction which had been previously determined as containing most of the chlorite extended f rom 2 to 32 t~, with some mica and kaolinite. The selection of the 2-5 tz particle-size fraction for removal of the chlorite s tandard was confirmed when separation of the 5-32 /~ fraction revealed identical crystallography. In this study the chlorite s tandard was isolated in the 3-05-3"3 specific gravity fraction of the 2-5 t~ particle-size fract ion by the procedure discussed below.

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Quantitative X-ray analys& 85 Procedure. From the separated 2-5 /~ particle-size fraction of clay material (which had been sodium saturated after removal of the organic and iron materials) remove the ~305 and the ~3.3 specific gravity fractions using the same thallous formate method outlined for the separation of the kaolinite standard. Filter the final portion of the decanted sus- pension through a 0.45 /~ molecular filter and wash the purified chlorite remaining on the filter.

Post.extraction treatment

For comparability in the X-ray analysis, the clay mineral standards must be converted into Ca-forms by dialysis as used for the pre-extraction conversion to Na-forms, substituting a CaC12 solution.

Results

The diffractograms of an original sample and the clay minerals separated from it are shown in Fig. 1.

The technique of clay mineral separation suggested by Loughnan (1962), using an e thanol-bromoform separating solution, resulted in incomplete separation due to flocculation.

C A L I B R A T I O N A N D I N T E R P R E T A T I O N

Calibration curves were prepared by analysing series of known mixtures of the standards and an internal standard. Each series of calibration mixtures (Table 1) was prepared by thoroughly mixing known percentages of the standard with an amorphous material having an absorption coefficient similar to that of the samples under study. Boehmite was added to each mixture as the internal standard in an amount equal to 10% of the weight of the mixture.

Each calibration mixture was mounted for X-ray diffraction by both powder and smear-oriented techniques. In the analysis of the series of mixtures prepared with the clay mineral standards, the smear-oriented technique proved generally superior to the powder-mounted technique, giving greater sensitivity and better precision for the lower percentages and comparable sensitivity and precision for the higher percentages.

TABLE 1. Calibration mixtures

Particle-size fraction for which Mineral standard ~ standard in mixtures series of mixtures were prepared

Quartz 2, 5, 10, 20, 35, 50, 70, 90 % 2-5 ~, 5-10 tt, 10-30 ~t, > 30/t Plagioclase 2, 5, 10, 20, 35, 50, 70, 90~ 2-10/~, 10-30/x, > 30/t K-feldspar 2, 5, 10, 20, 35, 50, 70, 90% 2-10 tt, 10-30/x, >30/t MontmoriUonite 5, 10, 20, 30, 40, 60, 80% <0"5 tt Mica 2, 5, 10, 20, 30, 40, 60 % 1-4 tt, 8-32/z Kaolinite 2, 5, 10, 20, 30, 40, 60, 90% 0.5-4/~ Chlorite 2, 5, 10, 20, 30, 40, 60, 90% 2-5 ~, 5-32/t

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86 Ronald J. Gibbs Working calibration curves (as in Figs. 2 and 3) prepared from the X-ray dittracto-

grams were used to determine the percentage of each mineral in the samples by comparing the ratios of each mineral's peak area to the boehmite peak area with the calibration curves of the respective minerals.

S Chlorite

Mica

I I I I I

28 26 2 4 22 20 18 16 14 12 10 8 6 4 2O

FIO. I . D i f f r ac to~ams o f original sample and separated clay minerals.

Kaolinite

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Quantitative X-ray analysis

I 0 0 -

8 0 -

6 0 - o"

4 0 -

2 0 -

/ /

o//

.2

f / / I I I I 2 3 4

Peak area ratio of 4-26~, quartz 6-10 ~ boehrnite

FIG. 2. Calibration curve for quartz.

87

Non-clay minerals

Quartz calibration technique. The calibration curves for the quartz series (obtained by measuring the 4.26 A peak area) indicate a slight decrease of intensity with increase in particle size (Fig. 2).

Feldspar calibration technique. Calibration curves were obtained for the plagioclase series by measuring the area of the 4"02 A peak, which was free of interference, and, for the K-feldspar series by measuring the area of the 3.24 A peak, which was usable even though interference of nearby peaks necessitated estimating base level.

In order to determine if the feldspar standards sufficiently resembled the feld- spars of the actual sample material, the 15-30 tk size fraction of each of a series of eight samples covering the full sampling range was isolated. The percentage of plagioclase and K-feldspar was then determined by the standard staining method (Jackson, 1956) and using a binocular microscope. This independent method eliminates the unknown factors of similarity of types of feldspars and the changes which occur during crushing. The standards were of composition similar to the feldspars of the samples, but produced consistently lower (30%) X-ray diffraction intensities than the 15-30 t~ test fraction due, probably, to the crushing.

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88 Ronald J. Gibbs

In this study, therefore, the calibration of the feldspars was based on the latter method, with the calibration curves being prepared from X-ray diffractograms of unstained portions of the samples mixed thoroughly with 10% boehmite.

Clay minerals

The calibration curves for montmorillonite, mica, kaolinite, and chlorite were adjusted by 9, 11, 10, and 10%, respectively, to correct for the impurities deter- mined from the calibration curves of the other clay minerals.

Montmorillonite calibration technique. The calibration curves for the mont- morillonite series were obtained by measuring the area of the glycolated 17 A peak.

The powder-mounted technique was not usable for the X-ray analysis for mixtures of 30% or less montmorillonite without excessive error because of in- sufficient sensitivity.

Mica calibration technique. The calibration curves for the mica series were obtained by measuring the area of the 10 A peak.

The powder-mounted technique was not usable for the X-ray analysis for mixtures of 20% or less mica without excessive error due to insufficient sensitivity. A negligible precision decrease from 6 to 8% for the smear-oriented coarser (8-32/L) fraction was attributed to possible particle-size segregation.

i00

80

"E=

60

N 4o

20

r

I I I 2

PeGk oree ratio of 7.15~ kaolinite 6-10 ~, boehmite

FIG. 3. Calibration curve for kaolinite.

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Quantitative X-ray analysis 89 Kaolinite and chlorite calibration techniques. The calibration curves were ob-

tained by measuring the area of the 7 A peak for the kaolinite series and of the 7"2 A and 4-7 A peaks for the chlorite series.

Direct application of the calibration curves obtained by measuring only the 7-7"2 A peak is not possible when both kaolinite and chlorite are present in a single sample because of mutual interference of the diffraction patterns. When both minerals are present, the chlorite can be determined by measuring the 4-72 A peak. However, since this peak has a generally much lower sensitivity, a preferable course of action was taken in which the double peak at 3"5-3"6 A of kaolinite and chlorite was used to determine the proportion of the clays in a sample. The 7-7-2 A peak was then subdivided for direct application of the calibration curves obtained for the kaolinite and chlorite standards.

To obtain calibration curves for use with the 3"5-3"6 A peaks, a series of known mixtures of the two clays was prepared and analysed and the peak height above the background of each peak was measured. The lack of linearity of the calibration curve obtained (Fig. 4) is due to peak flank interferences. It will be observed in Fig. 4 that chlorite has nearly twice the diffracting ability of an equal portion of kaolinite.

The powder-mounted technique was not usable for the X-ray analysis for mixtures of 15% or less of either kaolinite or chlorite without excessive error due to insufficient sensitivity. A negligible precision decrease from 6 to 8% for the smear-oriented coarser (5-32 t0 fraction of chlorite was attributed to possible particle-size segregation.

Non-calibrated minerals

Any remaining or unaccounted for percentage of a sample can be ascribed to

o . c

t~ a0 to to

E 0.~

f,,

Q.

0"1

A / s f t /

I I n n t t l l l t i r i ~ a n n l t I iO

Weight ratio kaolinite chlorite

FIG. 4. Calibration curve for chlorite-kaolinite mixtures.

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90 RonaM J. Gibbs a mineral or minerals not calibrated for or, if the minerals calibrated for account for the entire diffractogram, the remaining percentage can (1) be considered amorphous material or (2) be adjusted by increasing (or decreasing) the known percentages, proportionately, to total 100%. In this study, non-calibrated gibbsite and amphibole were present in some samples; for other samples, the known percentages were adjusted to 100% by proportionate increasing (or decreasing) of 2 or 3% per sample usually, the greatest total discrepancy being 10%.

R E M A R K S

In the quantitative analysis of clay minerals the problems arising f rom their variable compositions and degrees of crystallinity have been overcome to a great degree in this study by the use of clay mineral standards extracted from the samples to be analysed, as introduced here. Further study of the extraction of standards from the samples to be analysed and, also of the use of an internal standard in smear- oriented mounting is warranted. The testing of these techniques in the quantitative analysis of a wide variety of materials should be encouraged.

R E F E R E N C E S

BRADLEY W.F. & GRIM R.E. (1961) The X-ray Identification and Crystal Structures o/ Clay Minerals (G. Brown, editor). Mineralogical Society, London.

BRUgrON G. (1955) Am. Miner. 40, 124. BtrZAGH A. & SZEPESX K. (1954) Acta chim. hung. 3/4, 287. CULLITY B.D. (1956) Elements of X-ray Diffraction. Addison-Wesley, Reading, Massachusetts, FOLLIEa"r E.A.C., MCI-~RDY W.J., MITCHELL B.D. & SMITH B.F.L. (1965) Clay Miner. 6, 23. FREAS D.H. (1962) Bull. geol. Soc. Am. 73, 1341. GIBBS R.J. (1965) Am. Miner. 50, 741. GRIFFIN O.G. (1954) A new internal standard for the quantitative X-ray analysis of shales and

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