Rapid Modal Analysis of Some 

F elsie Rocks from Calibrated 

X-ray Diffraction Patterns 

GEOLOGICAL SURVEY 8ULLETJN 

Prepared in cooperation with the 

Nevada Bureau of Mines 

Rapid Modal Analysis of Some 

Felsic Rocks from Calibrated 

X-ray Diffraction Patterns 

By D. B. TATLOCK 

GEOLOGICAL SURVEY BULLETIN 1209 

Prepared in cooperation with the 

Nevada Bureau of Mines 

UNITED STATES GOVERNMENT PRINTING OFFICE. WASHINGTON: 1966 
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary 

GEOLOGICAL SURVEY 

William T. Pecora, Director 

For sale by the Superintendent of Documents, U.S. Government Printing, Office 

Washing,t9n, D.C. 20402 - Price 20 cents (paper cover) 
CONTENTS 

Page 

Abstract_________________________________________________________ 1 

IntroducUon------------------------------------------~----------- 1 

Basic aspects of procedure _____________________________ ~____________ 3 

Reproducibility, intensity, and crystallite size----------------,----- 4 

Optimum particle size versus grinding time _________ ,.. ____ -:-________ 6 

Precision test at high scanning speed_____________________________ 9 

Mass absorption and peak intensities ________________ -~_-- __ ~____ 10 

Mass absorption and iron content_______________________________ 12 

Iron, fluorescence, and background intensity______________________ 15 

Possible effects of density di~erences_____ ___ ____ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ 17 

Intensity-concentration curves for quartz analysis_________________ 19 

Rock classification from quartz and iron analysis__________________ 24 

Analysis of altered rhyolitic rocks of the Koipato Group, Nevada_______ 25 

Calibrated versus random patterns_______________________________ 30 

Sample preparation and instrumentation_____________________________ 33 

Sample preparation____________________________________________ 33 

Preparation of powder mounts__________________________________ 34 

Calibration and analytical technique_____________________________ 35 

Standard powders_____________________________________________ 36 

Selection of peaks for measurement______________________________ 36 

Conclusion _____ ----- __________ · ________________ ---~________________ 38 

References cited ________________________________________ ~ _ _ _ _ _ _ _ _ _ _ 39 

ILLUSTRATIONS 

FIGURE 1. Relative intensities from various-sized powder fractions of 

quartZ---------------------------------------------- 5 

2. Relative intensities from various-sized powder fractions of 

calcite, and from quartz at three different angles_________ 7 

3. Relative intensities from whole-rock powders ground for 

various lengths of time________________________________ 8 

4. Calibrated diffraction pattern of a whole-rock powder_______ 11 

5. Comparison of int¢nsity-concentration curves for quartz 

mixed with various constituents________________________ 13 

6. Variation of mass-absorption coefficient of whole-rock powders 

when analyzing for quartz_____________________________ 14 

7. Variation of mass-absorption coefficients of whole-rock powders 

when analyzing fo!r plagioclase_________________________ 16 

8. Comparison of background curves for quartz mixed with 

various constituents_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 17 

m 
IV CONTENTS 

Page 

FIGURE 9. Variation of background intensities with iron content_______ 18 

10. Intensity-concentration curves and background curves for 

quartz mixed with various constituents________________ 20 

11. Intensity-concentration and background curve set for quartz 

determination---------------------------------------- 21 

12. Regression curve of calculated quartz as a function of X-ray 

modal quartz ______ ---- ___ --------------------------- 22 

13. Variation of X-ray modal quartz with normative quartz____ 23 

H. Variation of X-ray modal quartz with thin-section modes____ 24 

15. Relationship of differentiation trends to quartz and iron 

contents--------------------------------------------- 25 

16. Intensity-concentration curves for determining muscovite, 

andalusite, albite, and K-feldspar in altered rhyolitic rocks__ 27 

17. Regression curves of chemically determined oxides as a function 

of oxides calculated from X-ray modes__________________ 31 

18. Calibrated diffraction patterns of altered rhyolitic rocks_____ 32 

TABLES 

TABLE 1. Reproducibility of peak heights on diffraction patterns________ 10 

2. Mass-absorption coefficients (CuKa) of some common oxides 

and normative minerals _________________________ -------_ 12 

3. Total iron, normative quartz and plagioclase, and mass-absorption coefficients (CuKa) of some average igneous rocks______ 15 

4. Calculated minerals, modes determined from diffraction patterns, 

partial chemical analyses, and oxides calculated from X-ray 

modes for altered volcanic rocks of the Koipato Group______ 28 

5. Chemically determined and calculated alkali oxides from some altered rhyolitic rocks _________ ----- ______________ ------ 30 
RAPID MODAL ANALYSIS OF SOME FELSIC ROCKS 

FROM CALIBRATED X-RAY DIFFRACTION PATTERNS 

By D. B. TATLOCK 

ABSTRACT 

The relationships among diffraction, absorption, and fluorescence allow for 

reasonably accurate analysis of quartz and other common felsic minerals in many 

fine-grained rocks, especially altered felsic rocks, from calibrated diffraction 

patterns of finely ground randomly oriented whole-rock powders, even when 

scanned at 2° 28 per minute. balibration is accomplished by adjusting X-ray 

tube power until both peak height and background intensities from standard 

mounts agree consistently with established calibration curves. 

No internal standard is used. Instead, significant differences in mass-absorption coefficients (CuKa) of silicate rock matrices-whole rock less mineral analyzed 

for-are shown to be chiefly a function of iron content. Moreover, iron is the 

only relatively abundant common rock-forming element whose fluorescence 

under copper radiation causes appreciable differences in background. Hence, 

as iron content increases, background intensity increases-thus allowing for an 

estimate of iron content-and so, too, does the absorptive strength of matrices, 

which in turn causes differences in peak heights for a given concentration of any 

mineral to be analyzed for. Modal determinations are made by interpolating 

between sets of peak height and background curves established from standard 

powders, consisting preferably of minerals separated from the suite of rocks 

under study. 

Standardized sample preparation is the most important factor in diffraction 

analysis. The grinding time, p~r given volume of crushed sample, required to 

attain a reasonable compromise between optimum reproducibility and maximum 

intensity of recorded peaks from packed powder mounts is determined experimentally for each group of rocks analyzed. 

Groups of quartz determinations compared with normative quartz and with 

reliable modal counts have standard deviations consistently less than 2.5 weight 

percent. The indicated accuracy of other common felsic mineral determinations 

from artificial powders is good. However, in lieu of direct comparison of optical 

and X-ray modes of natural fine-grained rocks, oxides calculated from X-ray 

modes have been compared with oxides determined chemically from the same 

whole-rock powders. These have standard deviations, in weight percent, of 

1.6 Si02, 1.6 Al20a, 0. 7 K 20, and 0.4 Na20. 

INTRODUCTION 

Chayes (1950) has stated that "the availability of reliable quantitative modal analyses in sufficient number would have immediate 

and profound effect on petrological theory." Probably few geologists 

1 
2 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

would dispute this. And, indeed, few have done more to advance 

techniques of modal analysis than has Chayes. But so far, little has 

been accomplished in developing techniques for the modal analysis of 

very fine grained rocks-rocks commonly termed aphanitic or cryptocrystalline, and those known to be holocrystalline only because of 

aggregate polarization (microcryptocrystalline). Judging from the 

literature, the amount-and probably the accuracy-of modal data 

on common silicate rocks is almost directly proportional to the grain 

size of rocks. Without modal analyses, or at least a knowledge of 

possible relative differences in mineral proportions in rocks of a finegrained suite, it is difficult to select samples for chemical, or other 

more detailed, analysis that will show significant differences in composition as a function of either primary or secondary effects. 

An attempt is made in this paper to show that, in lieu of point 

counting, the recording Geiger-counter X-ray diffraction spectrometer 

can provide reasonably accurate modes of many fine-grained rocks, 

especially altered felsic rocks, from calibrated patterns of whole-rock 

powders. 

Several workers have described application of the Geiger-counter 

diffractometer to quantitative analysis of two-component mixtures, 

or to the determination of one component, usually quartz, in various 

matrices (Klug and Alexander, 1954, p. 410-439; Jenson, 1951 and 

1955). A survey of the literature, however, reveals that the application of X-ray diffraction techniques to the quantitative analysis of 

silicate rocks has been rather limited. Black (1953) used a directcounting technique, without an internal standard, in the analysis of 

bauxite samples on a mass-production basis. Schmalz (1958) employed direct counting, with aluminum as an internal standard, in 

determining 12 common minerals contained in sediments from the 

Peru-Chile Trench. Engelhardt and Haussiihl (1960) have analyzed 

coarse-grained granitic rocks with good accuracy, but only on a limited 

basis. 

Although the stability of recent model spectrometers and the 

reproducibility of peak heights, especially of quartz, have been well 

demonstrated by many investigators-as, for example, Klug and 

Alexander (1954) and W eiskirchner (1960)--the use of quantitative 

diffraction techniques has not been generally employed in petrologic 

studies, owing largely to the adverse effects of absorption and fluorescence. The time required to counteract these effects by accurately 

admixing an internal standard to several hundred samples can be 

prohibitive. In lieu of an internal standard, an attempt is made to 

show that the relationships between diffrac1~ion, absorption, fluorescence, and possibly density do, in fact, permit reasonably accurate 

and rapid estimates of many common felsic minerals, especially quartz, 
BASIC ASPECTS OF PROCEDURE 3 

from recorded patterns of whole-rock powders scanned at 2° 20 per 

minute. The analysis of argillic phases in altrered silicate rocks is 

not included, because quantification of clay minerals involves a 

different and rather specialized approach. 

This paper is an elaboration of an earlier progress report (Tatlock, 

1961). Most of the analytical data presented were obtained during 

a study of fine-grained altered felsic rocks of the Permian and Triassic 

Koipato Group in northwestern Nevada. 

The writer gratefully acknowledges many helpful and fruitful 

discussions with several colleagues, particularly R. A. Gulbrandsen 

on X-ray procedures, R. G. Coleman on mineral-8eparation techniques, 

and E. M. Shoemaker on statistical analysis. The wholehearted 

encouragement and cooperation of R. E. Wallace and N. J. Silber ling 

in the sampling of the volcanic pile of the Koipato Group is greatly 

appreciated. The study was made as part of a cooperative project 

with the Nevada Bureau of Mines. 

BASIC ASPECTS OF PROCE,DURE 

As in all quantitative techniques, diffraction analysis of whole-rock 

powers from automatically recorded patterns requires that all steps 

in sample preparation and instrumentation be a~s nearly standardized 

as possible. 

The technique utilizes the principle that each common rock-forming 

mineral in a holocrystalline silicate rock produces its own characteristic 

diffraction pattern independently of the others and that the relative 

intensities of the patterns are related to the proportions of the minerals 

present. In practice, the average recorded height of one prominent 

reflection from each mineral is usually sufficient for modal estimates, 

provided the instrument has been calibrated with standard powder 

samples to agree with established intensity-concentration curves and 

provided no significant superposition by peaks of other constituents 

is encountered. Corrections must be made, however, for differences 

in mass absorption and background intensity. Furthermore, sample 

powders must be properly prepared and mounted so as to reflect 

reproducible peaks of near-maximum intensity from randomly 

oriented crystallites that have been ground fine enough to reduce 

extinction and microabsorption effects to a negligible level. 

These basic aspects of quantitative diffraction analysis have been 

clearly discussed by Klug and Alexander (1954, especially pp. 92-98, 

129-130, 252, 290-317, 410-439, 586-587, 677) and by Cullity (1956). 

All the quantitative work discussed in this paper has been done 

with two recent-model Philips Geiger-counter X'-ray diffraction 
4 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

spectrometers using copper radiation, nickel filter, and a scanning 

speed of 2° 20 per minute at the following instrument settings: 

Tube: Approximately 44 kv and 14 rna; set by calibration with 

standard powders; 

Counter: 400 cps full-scale deflection, time constant 4 seconds, 

1-degree divergence and antiscatter slits; 0.006 inch 

receiving slit; 

Chart speed: %inch per minute. 

All samples were mounted in aluminum holders as flat-surfaced 

powder cakes measuring 1X2X0.16 em. 

The details of sample preparation, instrumentation, calibrationr 

and selection of lines for measurement are described at the end of 

this paper. 

REPRODUCIBILITY, INTENSITY, AND OR YSTALLITE SIZE 

The stability of, and reproducibility attainable with, recent-model 

spectrometers by automatic recording is generally excellent. Instrument stability can be checked, after a thorough warm-up period, by 

running a series of peak-height measurements on a single finely 

ground powder mount without disturbing the mount or the controls 

of the X-ray generator and circuit panel. The two Philips spectrometers used in the present study invariably record, from an undisturbed finely ground quartz-bearing sample, a mean deviation of 

less than one-tenth inch from the average of four or more runs across 

the 4.26-A quartz line at a scanning speed of 2° 20 per minute. This 

is largely a test of the stability of X-ray production and of the pulseintegrating circuit, as all effects due to the sample powder are kept 

constant. 

In quantitative work, however, effects due to the sample powder 

are of paramount importance. Maximum peak intensity, at fixed 

instrument settings, as well as peak-height reproducibility is required. 

Reproducibility of peak heights on several mounts of the same sample 

powder is dependent chiefly on random orientation of crystallites, 

and random orientation is most nearly achieved in powders of 

extremely fine crystallite size (Birks, 1945). Moreover, maximum 

peak intensity, also, is dependent on fine crystallite size. 

Alexander, Klug, and Kummer (1948) and Klug and Alexander 

(1954, p. 292) have demonstrated statistically the relationship between 

peak intensity, reproducibility, and crystallite size. They prepared 

four quartz-powder fractions containing crystallites of 15-50, 5-50, 

5-15, and <5 microns mean dimensions. The peak intensities of 

10 different samples of each fraction were measured under as nearly 

identical conditions as possible. Figure 1 shows that the reproducibility of intensity measurements from the finer fractions ( <15 
REPRODUCIBILITY, INTENSITY, AND CRYSTALLITE SIZE 5 

100 • 

>- 1-

(i) 80 

z 

IJJ 

1-

z 

w 

> 

t= 

c( 

...J 

w 

a:: 60 

40~----~----------~------------~-----------~~ <5 5-15 5-50 15-50 

QUARTZ POWDER FRACTIONS, IN MICRONS 

FIGURE 1.-Maximum, minimum, and mean relative intensities from measurements on 10 different mounts of each of four quartz-powder fractions 

at 3.34 A. Modified from Alexander, Klug, and Kummer (1948). 

microns) is considerably better than from the coarser fractions. It 

shows also that the average observed intensity is greltter for the finer 

fractions, an effect which is attributed to a reduction in extinction in 

sample powders made up of very small crystallites (Brindley, 1945; 

Klug and Alexander, 1954, p. 129, 295). 

It can be said, therefore, that reproducibility of peak heights for 

quartz is dependent on random orientation of crystallites, and that 

random orientation is most nearly achieved in sample powders of very 

fine particle size; fine particle size reduces extinction and microabsorption effects (Brindley, 1945) to a negligible level and, hence, 

allows for near-maximum peak intensity. 

More recently, however, several investiga,tors (N agelschmidt, 

Gordon, and Griffin, 1952; Gordon and Harris:, 1955; Brindley and 

Udagawa, 1959) have shown that diffracted intensity for quartz 

particles ground smaller than about 2 microns is appreciably diminished owing probably to a thin layer of "amorphous" material on the 

particle surfaces, developed during grinding, which contributes to 

X-ray absorption. Weiskirchner (1960) has found a similar reduction 

78'9-859-6~ 
6 X-RAY MODAL ANALYSJiS OF FELSIC ROCKS 

in intensities from calcite and quartz (fig. 2), and Engelhardt and 

Haussi.ihl (1960) from adularia, muscovite and quartz, if crystallite 

sizes are less than about 2 microns. All investigators agree, however, 

that for crystallites larger than 30 to 40 microns the phenomenon of 

extinction severely reduces intensities. 

In quantitative diffraction analysis, therefore, to attain both 

optimum reproducibility and near-maximum intensity, experimental 

work on sized fractions of pure minerals indicates that sample powders 

should have a maximum crystallite size of less than 40 microns and a 

minimum size greater than 2 microns. Obviously, however, any 

attempt to size-fraction a whole-rock powder to fit this optimum 

size range will render the sample unrepresentative. Quantitative 

analysis of a multicomponent mixture requires that all the sample 

be analyzed, not merely a given size fraction. Since a wide range in 

particle size is inevitable in preparing whole-rock powders, a compromise between maximum peak intensity and peak-height reproducibility must be attained. 

OPTIMUM PARTICLE SIZE VERSUS GRINDING TIME 

Considering the grinding equipment generally available io geologic 

laboratories at the present time, the only practical way to prepare 

a large number of whole-rock sample powders in a reasonable time 

is with power mortars. During grinding, a wide range in particle 

sizes is produced-a range greater than the optimum 2 to 40 microns 

suggested by the work of W eiskirchner (1960) and others. The 

maximum optimum particle size can, of course, be controlled by 

prolonged grinding, but during the process a very fine fraction, 

submicron in size and certainly less than the minimum optimum 

size of 2 microns, is inevitably produced. Any attempt to eliminate 

this very fioe material by size-fractioning will amost certainly render 

the sample unrepresentative. 

It should be pointed out that, strictly speaking, particle size and 

crystallite size are different. A particle may be made up of one or 

more crystallites. In sample powders prepared from such coarsegrained rocks as granites, particles are commonly single crystallites, 

whereas in powders of very fine grained rocks, particles may consist 

of several minute crystallites. The finer the crystallite size, the 

better the reproducibility of diffraction patterns, but ultimately 

always at the expense of intensity of peak heights. 

To attain a compromise between intensity and reproducibility in 

the processing of a large number of samples, an attempt was made 

to relate grinding time per given amount of whole-rock sample to 

both peak height reproducibility and peak intensity (fig. 3). About 

30 grams of microcrystalline nonporphyritic altered rhyolite was 
100 

~ u; 

z 

IJJ 

1- 80 

z 

IJJ 

> 

-I 

~ 

LLt 

a: 

60 

OPTIMUM PARTICLE. SIZE VEHSUS GRINDING TIME 7 

d 

1 

/ 

I 

I 

;:r---o---

<2 2-4 4-5 5-10 10-20 ;20-30 30-40 40-50 

POWDER FRACTIONS, IN MICRONS 

FIGURE 2.-Mean relative intensities from various-sized powder fractions of 

calcite measured at 3.03 A and quartz at 1.82 A, 3.34 A, and 4.26 A. Modified 

from Weiskirchner (1960). 

crushed in a hardened steel mortar to pass a 1-mm sieve. Sixteen 

splits of about 1 cc were obtained with the aid of a microsplitter. 

Each split was ground in a power mortar for periods ranging from 2 

to 120 minutes as indicated in figure 3. Ten powder cake mounts 

of each ground split were scanned, always in the same direction, at 

2° 20 per minute across the quartz, albite, microcline, and muscovite 

lines at 4.26 A, 3.20 A, 3.25 A, and 10.00 A, respectively. The 

maximum, minimum, and mean relative intensities recorded from the 

10 runs of each of the 16 splits are plotted in :figure 3. The curves 

show that reproducibility improves with increase in grinding time, 

but at the expense of intensity-except for quartz whose intensity 

remains nearly constant. The curves are at near-maximum intensity 

between 10 and 30 minutes of grinding time. Muscovite shows the 

most abrupt drop in intensity with prolonged grinding. 

The experiment was repeated on two other microcrystalline altered 

felsic rocks, but this time only 11 splits were prepared, and only 6 

mounts of each split were scanned. The rocks contained the same 

constituents as the sample used in preparing figure 3, but in different 

proportions. Both showed variations in mean relative intensities 

nearly identical to those shown in figure 3. 
8 

110 

100 

90 

110 

100 

90 0 

z 

::> 

0 80 ,. 0::: 

(!l 

~ 

() 

c:( 110 m 

w 

> g 100 

c:( 

>- 1-

U5 

90 

z 

w 

1- 80 ~ 

UJ 

> i= 110 c:( 

-' w 

0::: 100 

90 

80 

70 

60 

50 

X-RAY MODAL ANALYSIIS OF FELSIC ROCKS 

Quartz ""' 40 percent 

4.26A 

--- ---------

Low albite = 25 percent 

3.20A 

--

Microcline = 20 percent 

3.25A 

------~ 

20 

, __ --...._ 

' ' " " 

Muscovite = 15 percent 

10.00A 

- _ _....... ....... 

40 60 80 100 

GRINDING TIME, IN MINUTES 

120 

FIGURE 3.-Maximum, minimum, and mean relative peak intensities recorded 

from 10 different mounts of each of 16 whole-rock powders ground from 2 to 

120 minutes and scanned at 2° 20 per minute. The 16 powders were split, 

before final grinding, from a single crushed sample of microcrystalline altered 

rhyolite that had passed a 1-mm sieve. All splits about 1 cc. 

Similar experiments performed on three medium-grained granitic 

rocks indicated that only quartz could be determined quantitatively 
PRECISION TEST AT mGH SCANNING SPEED 9 

with reasonable accuracy. Satisfactory reproducibility of feldspar 

and mica peaks was attained only after a minimum of 40 minutes of 

grinding (1 cc of crushed sample), at which point intensities had 

decreased 50 percent. 

Summarizing, quantitative diffraction analysis of whole-rock 

powders is most satisfactory when performed on microcrystalline rocks 

in which the crystallite size of all constituents is less than about 100 

microns. Crushed samples of rocks of this grain size, or finer, can be 

readily ground in a power mortar to the maximum optimum crystallite 

size of 40 microns in 15 to 30 minutes. Longer grinding will improve 

reproducibility but at the expense of intensity, especially of mica. 

Coarse-grained rocks are less amenable to diffraction analysis because 

of grinding difficulties that prevent a reasonable compromise between 

intensity and reproducibility of peak heights. 

PRECISION TEST AT HIGH SCANNING SPEED 

A typical test of reproducibility by automatic recording made during 

the course of routine diffraction analysis of altered rhyolites is shown 

in table 1 and figure 4. A sample of about 20 grams was chipped from 

a hand specimen of extremely fine grained sparsely porphyritic altered 

rhyolite and crushed in a hardened steel mortar to pass a 1-mm sieve. 

The crushed sample was split-with a microsplitter-into four parts 

and each of the four parts was split to about, but not more than, 1 cc. 

The four l-ee splits of crushed sample were then ground for 18 minutes, 

each in a different mullite power mortar but all of the same model. 

The largest particles observed under the microscope after grinding 

were less than 40 microns; it is estimated that at least 70 percent of 

the powder was less than 20 microns. 

Two powder-cake mounts of each of the four finely ground wholerock powders were prepared. Each of the 8 mounts was scanned 

from 34° to 6° 28 at a scanning speed of 2° 28 per minute on each of 

two spectrometers. Both instruments were calibrated with standard 

powder mounts containing 30 and 70 percent qm!rtz to agree with an 

established intensity-concentration curve. Figure 4 shows that the 

4.26 A peak of quartz exhibits slightly better reproducibility than do 

the muscovite and feldspar peaks. This is chiefly because quartz has 

no preferential cleavage and, hence, in finely ground powders tends to 

orient randomly. The reproducibility of the muscovite and feldspar 

peaks, considering the tendency of these minerals to orient preferentially, is better than might be expected owing largely to fine grinding 

and to the original extremely fine crystallite size of these minerals in 

the natural rock. Also, minute mica plates tend to be held more 

nearly at random by the high percentage of interspersed quartz and 

feldspar crystallites in the sample powder. 
10 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

TABLE L-Reproducibility of peak heights on 16 diffraction patterns 

[Recorded from two mounts of each of four whole-rock powders scanned at 2° 28 per minute on each of two calibrated Philips diffractometers. The four powders were split originally from a single crushed sample of altered rhyolite, then ground for 18 minutes. Peak heights are in inches X10] 

Powder Quartz Muscovite K-feld~ar Albite 

split No. 4.26A 10.00A 3.25 3.20A 

Peak height above background, diffraction 

unit A __________ ------------------------- 1a 47 21 61 59 

b 46 21 61 59 2a 48 23 57 54 b 45 20 57 56 

3a 47 20 57 58 b 48 20 59 56 4a 46 25 58 58 b 47 23 58 56 

Peak height above background, diffraction 

unit B ____ ------------------------------- 1a 49 22 62 58 b 46 20 61 62 2a 48 20 57 56 

b 47 22 61 55 

3a 47 19 55 57 

b 49 21 54 57 

4a 48 25 59 58 

b 47 24 58 55 

Average of units A and B ____________ ------------ 47.2 21.6 58.4 57.1 Range in peak heights _____________________ ------------ 45-49 19-25 54-62 54-62 

Standard deviation _____________________________________ 1.1 1.9 2.3 2.0 Relative deviation percent _____________________________ 2.3 8.8 3.9 3.5 

Range in weight percent of constituent as determined from peak heights ____________________________________ 40-43 16--19 15-17 27-31 

Weight percent determined from average peak height ___ 41 17 16 28 

Reproducibility at a scanning speed of 1° per minute was not 

measurably better than at 2° per minute. The phenomenon of 

"undershoot" (Klug and Alexander, 1954, p. 305-308) is not a problem 

so long as reproducibility is readily attainable. 

The relatively high degree of reproducibility attainable from 

several powders of a given sample scanned on two different spectrometers does not necessarily guarantee accuracy. Accuracy requires 

that peaks as near maximum intensity as possible be recorded for a 

given concentration at a fixed setting of the instrument. That the 

pattern (fig. 4) is near maximum intensity (and hence, the sample 

powder near optimum crystallite size) is suggested by the fact the 

sum of the four chief constituents as read from their respective 

intensity-concentration curves (figs. 11 and 16) is 102 percent (table 1), 

comparing favorably with a total of about 98 percent as calculated 

from chemical analyses of similar rocks (table 4). 

MASS ABSORPTION AND PEAK INTENSITIES 

Although the reproducibility of peak heights on automatically 

recorded diffraction patterns of whole-rock powders has been shown 

to be within the limits required for reasonably accurate modal analysis, 

it remains necessary to correct for differences in the mass-absorption 

coefficients of the various constituents. 
MASS ABSORPTION AND PEAK IN~rENSITIE.S 11 

70 Potassium feldspar ±2.0 

60 

±1.0 Quartz 

50 >-

1-

U5 

z 

w 

1- ±1.7 Muscovite ~ 40 w 

> 

f= 

<( 

......J 

w 

a:: 30 

20 

10 

lOA 6A 4A 3A 

10 15 20 25 30 

DEGREES 28 

FIGURE 4.-Calibrated diffraction pattern of a whole-rock powder (altered 

rhyolite) scanned at 2° 28 per minute, showing the mean deviation of quartz, 

muscovite, and feldspar peak heights measured from eight different mounts 

made from four different powders of the same sample and scanned on each of 

two Philips diffractometers. 

In comparing diffraction patterns of whole--rock powders ranging 

from felsic to mafic in composition, absorption effects are present 

that usually prevent a direct comparison of the peak heights of any 

given mineral as a function of its weight concentration. Specifically, when a mixture contains both a weak and a strong absorber, 

peaks of the weakly absorbing component appear weaker and those of 

the strongly absorbing component stronger, than expected from a 

linear relationship for each component (Klug and Alexander, 1954, 
12 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

p. 92, 411). In multicomponent mixtures, sample powders may be 

regarded as consisting of just two components, the mineral to be analyzed for, and the sum of the other minerals which may be designated 

the matrix (Klug and Alexander, 1954, p. 412). The effects of absorption differences on quartz-peak intensities is shown in figure 5, which 

compares theoretical intensity-concentration curves for quartz mixed 

with, in order of increasing absorptive strength, (1) magnesite, (2) 

albite, (3) a hypothetical felsic matrix, ( 4) a hypothetical mafic matrix, 

and (5) magnetite. These have mass-absorption coefficients of 20, 

34, 48, 75, and 238, respectively, compared with 35 for quartz 

(table 2). The expression for the theoretical curves is given by Klug 

and Alexander (1954, p. 411-415): 

It Xt"t* 

Cit)o XtCu1 *-.u2*) +.u2* 

where (11) 0 is the intensity from the pure component to be analyzed 

for; 11 is the intensity of the component when mixed with the matrix; 

xl is the weight fraction of the component; JL1 * is the mass-absorption coefficient of the component; and JL2 * is the Inass-absorption 

coefficient of the matrix. In almost all silicate rocks, theoretical 

intensity-concentration curves for quartz will fall between the quartzalbite and the quartz-mafic matrix curves of figure 5. 

TABLE 2.-Mass-absorption coefficients (CuKa) of some common oxides and 

normative minerals 

[Calculated from Internationale Tabellen zur Bestimmung von Kristallstruckturen, Gebriider Borntraeger, Berlin, 1935] 

Oxides MAC 

Si02--------------------------- 35 

Al20a-------------------------- 32 

FeO Fe20a-------------------------- 231 ___________________________ 255 ~no __________________________ 223 ~go__________________________ 30 

CaO ___________________________ 127 

Na20-------------------------- 26 

][20--------------------------- 121 

H20--------------------------- 11 

Ti02--------------------------- 127 

P20s--------------------------- 39 

Iron 002--------------------------- ___________________________ 324 11 

Minerals 1\lA C 

Orthoclase______________________ 49 

Albite__________________________ 34 

Anorthite______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 52 

N ephelite_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 32 

Acmite _________________________ 102 

CaSiOa------------------------- 79 ~gSiOa------------------------ 33 

FeSiOa------------------------- 155 ~g2Si04---- _---- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 32 

Fe2Si04------ ___________________ 190 ~agnetite__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 238 

Ilmenite ________________________ 189 

Apatite________________________ 89 

Calcite___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7 4 

MASS ABSORPTION AND IRON CONTENT 

The usual procedure for countering absorption effects in multicomponent mixtures is to add an internal standard (Klug and 

Alexander, 1954, p. 426), but the admixing of the reference material 

is time consuming, dilutes the sample, and increases the number of 

measurements required. A more direct procedure may be employed, 

similar in part to the diffraction-absorption technique of Leroux, 

Lennox, and Kay (1953), and to that of Black (1953) in his analysis 
MASS ABSORPTION AND IRON CONTENT 13 

....... ·::> -... 

~ 80 

~ 

~ 

<( 

LLJ 

a.. 

N 

1-

0:: 

<( 

:::> 60 0 

<( 

10 

N 

-i 

1-

<( 

E 40 (/) 

z 

w 

1-

~ 

LLJ 

> 

~ <( 

..J 

LLJ 20 0:: 

0 20 40 60 80 100 

QUARTZ (X), WEIGHT PERCENT 

FIGURE 5.-Comparison of theoretical intensity-concentration curves for quartz 

mixed with (1) magnesite, (2) albite, (3) felsic matrix, (4) mafic matrix, and (5) 

magnetite. Experimental measurements for some quartz-albite (open circles) 

and quartz-magnetite (solid circles) mixtures are shown. Dashed curve (5a) is 

quartz-magnetite curve eorrected for density differenees. 

of bauxite samples. The procedure is based on the premise that 

iron is the element chiefly responsible for appreciable differences in 

mass absorption in silicate rocks, and also that iron is the only 

relatively abundant cornmon rock-forming element whose fluorescence 

under copper radiation effects appreciable differences in background, 

thus allowing for measurement of iron content. 

That iron is, indeed, the element responsible for appreciable 

differences in absorption in silicate rocks is suggested by the massabsorption coefficients (MAC) of some common oxides and normative 

minerals listed in table 2. Although MnO and Ti02 have high 

coefficients, their effect on average mass absorption is small owing to 

their low concentrations in average rocks. The high coefficients of 

789-35~66--3 
14 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

CaO and K20 tend to balance one another in rocks ranging frmn 

felsic to mafic. 

As stated earlier, sample powders of silicate rocks may be regarded 

as consisting of just two components, the mineral to be analyzed for, 

and the sum of the other minerals which may be designated the 

matrix. Regardless of which of the chief felsic minerals is analyzed 

for in rocks ranging from felsic to mafic, the MAC's of matrices, 

excluding iron, will remain nearly constant; with iron included, the 

MAC's of matrices will show a regular variation with iron content. 

To demonstrate the relationship of iron to absorption differences, 

it will be assumed that the weight concentrations of quartz and 

plagioclase are to be determined in rocks ranging from felsic to mafic 

in composition. The mass-ab&orption coefficients of quartz-free 

matrices and of plagioclase-free matrices of 18 average igneous rocks 

(Nockolds, 1954), as well as G-1 granite and W-1 diabase (Fleischer 

and Stevens, 1962), have been calculated, both with and without 

iron (table 3), from the MAC's of oxides and normative minerals in 

table 2. In analyzing for quartz, table 3 and figure 6 show that the 

~ 70 :J 

s 

1-

z 

w 

~ 60 LJ.. 

w 

0 

(.) 

z 

0 

t 50 0:: 

0 

C/) 

en 

< 

C/) 

C/) 

~ 40 

Matrix not co~tai~ing iron 00 

0 0 

00 0 

Quartz 

2 3 4 5 6 7 8 9 10 

IRON, IN WEIGHT PERCENT, IN WHOLE ROCK 

FIGURE 6.-Variation of mass-absorption coefficients of matrices-whole rock 

less normative quartz-of average igneous rocks (Nockolds, 1954) as a function 

of iron content (solid circles) and without iron (open circles). Plotted values 

are those of rocks listed in table 3. 
IRON, FLUORESCENCE, AND BACKGROUND INTENSITY 15 

1fAC's of the matrix portion-whole rock less normative quartzof average igneous rocks, exclusive of iron, are nearly constant, 

ranging from 42 for nlkali grnnite to 4 7 for tholeiitic andesite and 

tholeiitic basalt. With iron included in the matrices, however, the 

MAC's range from 48 for alkali granite to 76 for tholeiitic andesite. 

TABLE 3.-Total iron, normative quartz and plagioclase, and mass-absorption co- efficients (CuKa) of quar-tz-free and plagioclase-free matrices, both with and without 

iron, of some average igneous rocks 

[Adapted from Nockolds, 1954. Total Fe is 0.70 (Fe,Os)+0.78 (FeO)] 

Quartz Plagioclase 

------------ MAC of MAC of plagioRock name quartz-free clase-free 

Total Norm. matrix matrix Fe quartz Norm. An MAC 

MAC plag. con- plag. 

35 Matrix Total tent Matrix Total 

less Fe matrix less Fe matrix 

·-------------------- G-1 granite _________________ 1. 37 28.6 43 48 33.7 16 37 42 48 Alkali granite _______________ 1. 43 32.2 42 48 32.1 9 36 42 48 

Calc-alkali rhyolite _________ 1. 45 33.2 43 49 30.1 17 37 42 48 Calc-alkali granite. _________ 1.00 29.2 43 51 31.8 18 37 43 51 Adamellite __________________ 2.62 24.8 43 53 39.4 28 39 43 55 Granodiorite ________________ 2.96 21.9 42 53 48.9 34 40 42 58 

Calc-alkali trachyte ________ 3.35 -------- 44 54 38.5 25 39 48 65 Tonalite. ____________ ------- 3. 61 24.1 42 56 53.8 39 41 40 63 

Calc-alkali syenite.--------- 3. 73 2.0 44 55 43.0 23 38 50 68 Dacite _________ ------------- 3.90 19.6 43 56 57.4 41 41 41 68 Peralkallne granite __________ 4. 70 26.2 41 59 34.6 0 34 42 63 Monzonite __________________ 5.36 -------- 46 61 45.1 35 40 51 78 

Latite _______ ---------------- 5. 78 .5 46 62 47.0 41 41 50 81 

Mangerite. ________ --------- 6.47 2.0 44 63 53.0 40 41 49 87 

Andesite _______________ ----- 6. 71 5. 7 45 65 58.1 47 42 47 92 

Diorite. ___ ----------------- 7.33 .3 45 65 54.1 48 43 48 93 W -1 diabase ________________ 7. 79 4.1 47 69 47.6 64 46 47 89 

Gabbro ____________ --------- 7.95 -------- 47 69 53.1 64 46 48 95 

Tholeiitic basalt. ___________ 9.07 3.5 47 74 44.8 58 44 50 96 

Tholeiitic andesite __________ 9.93 3.2 47 76 45.3 40 41 52 102 

Similarly, in analy~ing for plagioclase (table 3 nnd fig. 7), the 

MAC's of the matrices-whole rock less normntive plagioclase, 

excluding iron-range from 42 in granite and rhyolite to 52 in tholeiitic 

andesite; the iron-free mntrix curve very nearly parallels thnt of the 

normative plagioclaseB (fig. 7). With iron included in the matrices, 

the mass-absorption coefficients range from 48 in granites to 102 in 

tholeiitic andesite. lienee, in annlyzing for quartz nnd plagioclnse, 

iron is shown to be the element chiefly responsible for nppreciable 

differences in mass nbsorption in the matrix com.ponent of the common 

silicate rocks, and thereby the element that effects differences in 

quartz and plagioclase peak intensities for a given quartz or plagioclase concentration. Similar effects from iron can be theoretically 

demonstrated in analyzing for any of the major silicate rock-forming 

minerals. 

IRON, FLUORESCENCE, AND BACKGROUND INTENSITY 

When analyzing for quartz and plagioclase in the more common 

silicate rocks, iron has been shown to be the element chiefly respon-
16 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

100 

~ 90 :::.::: 

::l 

8 

fz 80 w 

u 

u: 

LL.. 

w 70 0 

u 

z 

0 • • • 

i= 60 a.. 

0: • C/) 

0 • III 

c( 50 

C/) 

C/) 

c( 

:i: 

40 

0 ° Q · 0 iron . t conta1n1n o Matnx. no 0 o 

.. ----~- 0 oPiagioc\aS~-..--..---

_.._ _ • _,-. li~----·...... • __ .... -..--

• 

2 3 4 5 6 7 8 9 10 

IRON, IN WEIGHT PERCENT. IN WHOLE ROCK 

FIGURE 7.-Variation of mass-absorption coefficients of matrices-whole rock 

less normative plagioclase-of average igneous rocks (Nockolds, 1954) as a 

function of iron content (solid circles) and without iron (open circles). Dashed 

curve shows variation of MAC's of normative plagioclase. Rocks are those 

of table 3. 

sible for appreciable differences in absorption. Iron, also, is the only 

relatively abundant common rock-forming element whose fluorescence 

(Klug and Alexander, 1954, p. 95) under copper radiation effects 

appreciable differences in background. 1 The greater the iron content 

of a holocrystalline whole-rock powder, the greater the background 

intensity of its diffraction pattern. Experimentally determined background curves for quartz-albite and quartz-magnetite mixtures, using 

copper radiation, are shown in figure 8 along with two theoretical 

curves representing felsic and mafic matrices that contain 1.9 and 10.0 

percent iron. The relationship between iron content and background 

intensity allows for an estimation of the total iron in a sample by 

reading the background at a given angle 20 after the diffraction unit 

has been calibrated with standard mounts to agree with established 

intensity-concentration and background curves (figs. 10 and 11). In 

figure 9 the total iron-0.70 (Fe20 3) +0.78(Fe0)-calculated from 

t Manganese fluorescence (CuKa) effects differences in background that are about half as great as those 

due to iron. Manganese content, however, seldom exceeds a few tenths of a percent in common silicate 

r-ocks (Nockolds, 1954). 
POSSIBLE EFFECTS OF DENSITY DIFFERENCES 17 

IRON IN QUARTZ-MAGNETITE MIXTURES, IN WEIGHT PERCENT 

70 60 80 ~~o 40 30 20 10 0 

w 

z 

::i 

N 

1-

0:: 60 4 <( 

::::> 

0 

<( 

\!) 

(\1 

-i 

1-

<( 

>- 40 1-

u; 

z 

w 

1-

~ 

::::> 

0 

0 

z 

0:: 

20 -~ 

Cl 2 ~ 

(.) 

<( 

co 

0 20 40 60 80 100 

QUARTZ, IN WEIGHT PERCENT 

FIGURE 8.-Comparison of background curves for mixtures of quartz and (1) 

albite, (2) felsic matrix, (3.) mafic matrix, t4) magnetite (CuKa; nickel filter). 

Background measured at 4.26 A quartz line. Variation in curves is chiefly a 

function of iron content. That portion of the quartz-magnetite curve outlined 

near the lower right corner is the mirror image of the curve in figure 9. 

chemical analyses of altered rhyolitic, andesitic, and basaltic rocks, 

and graywackes, has been plotted against background iiltensities at 

the 4.26 A quartz line as recorded on diffraction patterns of splits of 

the chemically analysed powders. The background intensity is the 

average of measurements on both sides of the selected line as shown 

in figure 4 (Carl, 1947). The curve was constructed from background 

intensities recorded on weighed mixtures of quartz and pure magnetite, and is actually the mirror image of that portion of the quartznlagnetite curve outlined in the lower right corner of figure 8. The 

standard deviation of iron determined by background intensity from 

that determined chemically is about 0.45 weight percent. 

POSSIBLE EFFJB:CTS OF DENSITY DIFFERENCES 

Theoretically, in correeting for absorption differences, the density 

of components should have no effect on the position of calculated 

intensity-concentration curves. This has been shown experimentally 
18 

<: 

\0 

(\J 

«i 

..... 

28 

<: 20 

>-

..... 

u; 

z 

w 

..... 

z 

0 

z 

:::::l 

0 

a:: 

(!) 

::.::: 

<..> 

<: 

m 

16 

12 

I 

o/ o / 

I 

I 

/ 

I 

X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

• 0 

0 0 

0 

t 

I 

G-1 

2 

• 

• • • • 0 

0 • i 

W-1, diabase 

EXPLANATION 

• 

Altered basalts 

• 

Graywackes 

0 

Felsic tuffs and keratophyre& 

0 

Altered rhyolites 

4 6 8 

TOTAL IRON, IN WEIGHT PERCENT 

• 

10 

FIGURE 9.-Background intensities, to nearest tenth of an inch, recorded from 

diffraction patterns of splits of 31 chemically analyzed powders plotted against 

total iron content. Curve was determined experimentally from quartz-magnetite mixtures. 

by Klug and Alexander (1954, p. 414) for quartz mixed with BeO 

(very low mass absorption, high density) and with KCl (high mass 

absorption, very low density). Referring again to figure 5, the theoretical curve for quartz-albite mixtures is almost linear and very 

nearly coincides with some experimentally determined points, as one 

might expect from the similar mass-absorption coefficients of quartz 

and albite. In contrast, experimental quartz-magnetite points (fig. 

5, solid circles) depart radically from the theoretical curve. This 

departure probably arises chiefly from microabsorption effects (H. L. 

Klug, written commuuication, 1963; Brindley, 1945; and Engelhardt, 

1959), which result largely from the gross difference in linear-absorp-
INTENSITY-CONCENTJRATION CURVES FOR QUARTZ ANALYSIS 19 

tion coefficients (mass-absorption coefficient times density) between 

quartz and magnetite (93 and 1234, respectively). Microabsorption 

effects can be rendered negligible only if the product.of linear-absorption coefficient and particle diameter is extremely small-smaller than 

can be attained easily by routine grinding procedures. If the product 

is b~rge, as in magnetite powders, the ~-ra.y reflection process is 

confined mainly to a surface layer of particles (Brindley, 1945, p. 350), 

in which case the difference in specific gravity between quartz and 

magnetite may affect the position of the experimental curve because 

of the greater volume percent-and hence, greater percent of surface 

exposed to radiation-of quartz relative to its weight percent when 

mixed with a denser material. The relationship is expressed by: 

Q qpm 

Qpm+mpq 

where Q is volume percent of the component to be analyzed for; q is 

weight percent of the component; pq is specific gravity of the component; m is weight percent of matrix; and pm is specific gravity of 

matrix. It is interesting to note, though possibly fortuitous, that if 

allowance is made for both density and mass-absorption differences, a 

theo:retical quartz-magnetite curve (fig. 5, dashed curve) will nearly 

coineide with the experimental points. A correction for density 

differences necessitated by microabsorption e:ffects is probably not 

required when analyzing for felsic minerals in silicate rocks unless the 

iron content of the matrix exceeds about 20 percent. 

INTE:NSITY-CONCENTRATION CURVES FOR QUARTZ ANALYSIS 

Regardless of possible discrepancies between theoretical and experimental intensity-concentration curves, as displayed by the quartzmagnetite curves of figure 5, direct analysis for quartz remains possible 

by reference to curves prepared from synthetic mixtures. 

To compensate for the absorption and fluorescence effects of iron, 

four intensity-concentration curves and their corresponding background curves were established from prepared powders of quartz 

mixed, in order of increasing absorptive strengths, with (a) natural 

pinite (very fine muscovite-pyrophyllite mixture), (b) biotite-actinolite greenstone, (c) chlorite, and (d) magnetite; the letters correspond 

with the curve sets in figure 10. The curves are based on the diffraction intensity of copper radiation from the (100) plane of quartz 

(Weiskirchner, 1960) and the background intensity in the immediate 

vicinity of the same line (4.26 A or 20.8° 28) at a scanning speed of 

2° 28 per minute. The inteHsity of the X-ray source was adjusted to 

give almost full deflection of the recording pen at the 70 percent 

quartz level as this was the maximum quartz content expected in 

the rocks under study. 
20 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

80 80 

q:, 

(\J 

Co 70 70 

c) 

~ 

<( 

1.0 60 (\J 

..; 

60 d 

1- ~ <( ::J 

Cl 50 

z 

:::> 

(.) 

50 ~ 1.0 

(\J 

0 ..; 0::: 

G 

~ 40 40 1-

<( 

(.) 

<( 

m Cl 

z 

:::> w 30 > 30 0 

0::: 0 (!) 

m :X:: <( (.) 

..... 20 I 

<( 

20 m 

~ 

lLJ 

I 

:X:: 10 10 <( 

w 

0.. 

0 10 20 30 40 50 60 70 80 

QUARTZ, IN WEIGHT PERCENT 

FIGURE 10.-Intensity-concentration curves and corresponding background 

curves for quartz mixed with matrix materials having different mass-absorption coefficients resulting chiefly from differences in iron content. Construction of interpolation curve is illustrated. 

Differences in the mass-absorption coefficients of matrices of common silicate rocks have been shown to be chiefly a function of iron 

content (fig. 6), and iron content is expressed by background intensity 

(fig. 9). As iron content increases, background intensity increases, 

and so, too, does the absorptive strength of the matrix, which has the 

effect of depressing the peak height, or intensity-concentration, curve. 

Using this relationship, the quartz content of a rock powder can be 

determined from any combination of peak height (above background) 

and background by interpolating between established sets of intensityconcentration and background curves. The greater the mass-absorption coefficient of the matrix-as a function of iron, and expressed 

by background-the greater the quartz content for a given peak 

height. For example, in figure 10, at a peak height above background 

of 40, the quartz content of a powder having the absorption characteristic of curve set a would be 35 percent, of curve-set b 43 percent, of 
INTENSITY-CONCENTRATION CURVES FOR QUARTZ ANALYSIS 21 

curve set c 51 percent, and of curve set d 58 percent. This relationship 

es·tablishes a so-called interpolation curve, the construction of which is 

illustrated in figure 10. A series of interpolation curves is shown in 

figure 11, in conjunction with an intensity-concentration and background curve set. Actually, any one of the sets of curves in figure 10 

showing peak height and corresponding background intensity could be 

used in conjunction with the interpolation curves in preparing figure 

11. To illustrate how the weight percent of quartz is determined from 

figure 11, assume a peak height above background of 50 and a background of 20; both are read in the same units on the ordinate scale. 

By following the dashed lines, the quartz content for this combination 

of peak height and background intensities is shown to be 53 percent. 

The intensity-concentration and background curve set of figure 

11 was developed specifically for determining t,he quartz content of 

extremely fine grained altered volcanic rocks of the Koipato Group, 

<::. 

N 00 70 

ci 

~ 

< 

~ 60 

..t 

1-

<( 

~ 20 

Q 

LLJ 

::c 

~ 10 LLJ 

0.. 

70 

0 10 20 30 40 50 60 70 80 

QUARTZ, IN WEIGHT PERCENT 

FIGURE 11.-lntensity-concentration and background curve set, with interpolation curves, for determining weight percent of quartz in silicate rocks 

containing 0 to 72.4 percent iron. 
22 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

of Permian and Early Triassic age, in northwestern Nevada. A 

regression curve for quartz calculated from 27 chemically analyzed 

Koipato rhyolitic rocks (table 4) as a function of X-ray modal quartz 

determined from diffraction patterns of splits of the analyzed powders 

is shown in figure 12. The standard deviation is 2.2 weight percent. 

The curve set of figure 11, although established for analysis of a 

given suite of rocks, has been found to give reliable determinations 

of quartz in almost all common holocrystalline silicate rocks, both 

fresh and altered, regardless of rock type or source area. Figure 13 

shows the weight percent of quartz determined from diffraction 

patterns of splits of 26 chemically analyzed samples plotted against 

calculated quartz. The samples consist of 11 granitic rocks (granodiorite and quartz monzonite), 6 felsic graywackes, 4 altered felsic 

tuffs, and 3 quartz keratophyres from various sources in California 

and Nevada, as well as G-1 granite and W-1 diabase. The percentage of calculated quartz in the granitic rocks agrees very closely 

with the percentage of quartz determined from modal counts made on 

stained slab surfaces. The tuffs, graywackes, and keratophyres 

70 

60 

0 

LLJ 50 

~ ....I 

::::::1 

0 

....I 

c( 40 

0 

N 

1-

0::: 

c( 30 ::::::1 

0 

20 

10 

20 30 40 50 60 70 

QUARTZ, X-RAY MODAL 

FIGURE 12.-Regression curve of calculated quartz as a function 

of X-ray modal quartz determined from splits of 27 chemically 

analyzed samples of rhyolitic rocks from the Koipato Group, 

Nevada. 
INTENSITY-CONCENTRATION CURVES FOR QUARTZ ANALYSIS 23 

• 50 

EXPLANATION 

• 

Granitic rocks 

40 0 

0 G-1, granite 

@ 

LLJ Graywackes @ > 

i= @ 0 o• <: • ~ 0 @ 

a:: 30 Tuffs and keratophyres 

0 

z 

N 0 

f- @ a:: 

<: • :::::> 20 

0 • 

10 

0 10 20 30 40 50 

QUARTZ, X-RAY MODAl..., 

FIGURE 13.-Weight percent of quartz determined from diffraction 

patterns of splits of 26 chemically analyzed powders plotted against 

normative quartz. 

could not be reliably counted. The standard deviation of the X-ray 

modal quartz from the calculated quartz is 2.4 weight percent. Considering only the 12 granitic rocks, the standard deviation is 1.2 

weight percent. · 

A comparison of quartz determined from diffraction patterns with 

thin-section modal quartz is shown in figure 14. Both the X-ray 

and thin-section determinations were made by Rowland W. Tabor, 

of the U.S. Geological Survey, on specimens of mica schist and 

fine-grained gneiss from the Cascade Range, Washington. The open 

circles are thin-section determinations considered to be less than 

satisfactory owing to uneven distribution of quartz lenses, difficulties 

in distinguishing quartz from plagioclase, obscuring by alteration 

products, or badly plucked sections. In fine-grained altered rocks 

of this type, modal quartz determined by X-ray is probably more 

accurate than that determined from thin-section point counts. The 

standard deviation of the X-ray modal quartz from the thin-section 

quartz is 4.3 percent, without density corrections. For the seven 
24 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

more reliably counted specimens the standard deviation is 2.2 

percent which is about the same as the standard deviations calculated 

for quartz in rhyolitic rocks of the Koipato Group (fig. 12) and the 

rocks of figure 13. 

50 

-l 

<( 

0 

0 40 ~ 

z 

0 

1-

() 

w 30 (f) 

z 

:J: 

1-

N' 

1- 20 a:: 

<( 

::::> 

0 

10 

• 

0 

EXPLANATION 

• 

High quality thin section mode 

0 

Low quality thin section mode 

10 

0 

0 • 

20 30 40 

QUARTZ, X-RAY MODAL 

0 

50 60 

FIGURE 14.-Weight percent of quartz determined from 18 powder diffraction 

patterns of schists and fine-grained gneisses plotted against modal quartz 

determined from thin-section counts. 

ROCK CLASSIFICATION FROM QUARTZ AND IRON ANALYSIS 

Many igneous rocks can be tentatively classified merely on the 

basis of their quartz and total-iron contents as determined from 

calibrated diffraction patterns (figs. 9 and 11). This is shown in 

figure 15 where theoretical differentiation trends have been drawn 

through plots of normative quartz versus iron for some average rocks 

of Nockolds (1954); the rocks are listed in table 3 of this paper. 
RHYOLITIC ROCKS OF THE KOIPATO GROUP, NEVADA 25 

30 

• 

1 • Peralkaline granite LLI 

> i= • <( G-1, granite ~ • 0:: 

0 20 z • 

N" 

f0:: 

<( 

:;) 

0 

10 

0 0 

0 2 4 6 8 10 

TOTAL IRON, IN WEIGHT PERCENT 

FIGURE 15.-Relationship of theoretical differentiation trends to quartz and iron 

contents of rocks listed in table 3 . 

.ANALYSIS OF .ALTERED RHYOLITIC ROCKS OF THE 

KOIP.ATO GROUP, NEVADA 

It has been shown that reasonably accurate weight concentrations 

of quartz and total iron can be readily detern1ined from calibrated 

powder diffraction patterns of almost all the common holocrystalline 

silicate rocks (figs. 9, 12, 13, and 14). Quantitative detern1inations 

of most other common constituents from diffraetion patterns are not 

universally reliable, however, owing largely to :intensity and spacing 

differences brought about by compositional variations within mineral 

species. Also, the innately fine crystallite sizes of some minerals, 

especially the feldspars, in many microcryptocrystalline rocks, commonly reflect broadened peaks of less than maxilmum intensity (Klug 

and Alexander, 1954, p. 586). 

Nevertheless, in studying rocks of a given type from a given limited 

area, relative differences in the proportions of the chief felsic constituents are readily determined from calibrated diffraction patterns. 
26 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

And, going a step further, reasonably accurate quantitative determinations can be obtained by establishing intensity-concentration curves 

for each of the chief felsic minerals from artificial powder mixtures 

consisting of constituents separated from the rocks under study. 

-This has been done in analyzing more than 800 samples of rhyolitic 

rock from the Kiopato Group, of Permian and Early Triassic age, in 

northwestern Nevada. The rhyolitic pile consists of flow, pyroclastic, 

detrital, and intrusive rocks which crop out sporadically over an area 

of about 3,000 square miles and probably originally aggregated at 

least 1,000 cubic miles. All the rocks are holocrystalline although 

extremely fine grained, rendering modal analysis by microscopic 

methods impossible. Furthermore, the pile is pervasively altered; 

the alteration is reflected chiefly in wide differences in the proportions 

of quartz, muscovite, K-feldspar, albite, andalusite, and pyrophyllite. 

Various combimations of these minerals make up more than 95 percent 

of the average rock. Feldspar and andalusite-pyrophyllite are everywhere mutuaHy exclusive. Quartz is ubiquitous and generally the 

most abundant constituent. 

Intensity-concentration curves for determining the weight percentages of m.uscovite, microcline, monoclinic K-feldspar, albite, and 

andalusite in rhyolites of the Koipato Group are shown in figure 16. 

Background curves were not established for these minerals, because 

significant differences in mass absorption in the rhyolites is small 

owing to their generally low iron content. All the artificial powders 

from which peak intensities were measured to establish the intensityconcentration curves were made up of constituents separated from 

rocks of the Koipato Group, usually by centrifuging 20 to 50 micron 

powders in heavy liquids of appropriate specific gravity. Therelatively 

smooth loci of experimental points determined, in increments of 5 or 10 

weight percent, from the artificial powders suggest that the precision 

of the quantitative diffraction technique is satisfactory. The accuracy 

of the technique, however, can be checked only indirectly as there 

is no way possible to measure the absolute weight fraction of each 

constituent in a fine-grained altered rock. 

Table 4 compares X-ray modal analyses, determined from 

diffraction patterns of splits of chemically analyzed whole-rock 

powders, with modes calculated from the chemical analyses. The 

modes have been calculated in a manner similar to the calculation 

of the CIPW norm except that MgO and the available FeO remaining 

after ilmenite and magnetite are allotted to biotite or chlorite or both 

in lieu of pyroxene. The K20 remaining after biotite and the Al20a 

after biotite, chlorite, and plagioclase are apportioned between 

K-feldspar and muscovite by simultaneous equations, which gives: 
RHYOLITIC ROCKS OF THE KOIPATO GHOUP, NEVADA 27 

A-K 

m=-2-

f=K-m 

where m is muscovite molecules, f is K-feldspar molecules, A is 

available Ah03, and K is available 1(20. 

50 100 

I I :X:: 40 :X:: () () 

~ ~ 

ttl~ ttl~ 0 IJJO IJJ:;, > . >· 0;:: 30 OLO 60 ttl!- ttl!- ~~ ~~ 

1-o 1-o 

~z Iz -:::> 20 £!:::> 40 LLIO IJJQ I a:: J:a:: :x::t!l ::.::" ~ ~ IJJ 10 IJJ a.. 20 a.. 

0 10 20 30 40 0 10 20 30 40 

MUSCOVITE, IN WEIGHT PERCENT ANDALUSITE, IN WEIGHT PERCENT 

100 100 

I 1 :X:: 80 ::r:: 80 () (.) 

~ ~ 

ttl~ IDe( 

IJJO LO IJJN >"! oM 60 ~~ 60 !Ill- ml- ~·:( c(c( 

1-0 1-0 Iz IZ C!':::> 40 (!):::) 40 ~0 UiO IO:: :x:a:: (!) (!) 

::r:: ::r:: ~ 20 <( IJJ IJJ 20 a.. a. 

0 10 20 30 40 0 10 20 30 40 

ALBITE, IN WEIGHT PERCENT POTASSIUM FELDSPAR, 

IN WEIGHT PERCENT 

FIGURE 16.-Intensity-concentration curves for determining muscovite, andalusite, albite, and K-feldspar in altered rhyolitic rock8 of the Koipato Group, 

Nevada. Dots and circles are average experimentally· determined points used 

in establishing the curves. 
28 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

TABLE 4.-Calculated minerals, modal minerals determined from diffraction patterns, 

[All are in weight percent. Analyses are of 

Calculated minerals X-ray modal minerals 

Sample 

Q M Kf Ab Sub- Other Q M Kf 

total 

---- -- 1.----------- 38.6 7.1 21.1 31.4 98.2 ------------------------------ 41 11 18 10 ____________ 44.8 13.6 38.9 1. 6 98.9 ---------------------.. -------- 43 13 42 46.---------- 54.4 20.0 22.2 1.1 97.7 An, l.L.-------------------- 53 18 27 

58.---------- 57.2 27.6 3.3 9.4 97.5 Hm, 1.0 _____________________ 57 28 

58F. _ ------- 58.6 20.2 7.2 12.1 98.1 Hm, 1.3.-------------------- 56 25 4 61B. _ ------- 27.1 1. 7 67.6 96.4 Kaolinite, 2.3 .. ------------- 30 2 61W _ -------- 22.7 23.5 31.7 18.3 96.2 Cc, 2.3 ______________________ 23 22 32 

67----------- 68.0 13.3 15.0 2. 7 99.0 ------------------------------ 64 14 21 

79.---------- 52.2 23.9 14.5 4. 7 95.3 Hm, 1.0 _____________________ 50 13 32 

98.---------- 54.8 23.9 16.1 .5 95.3 Chlorite, 2.9. _ -------------- 52 23 22 152.--------- 50.6 17.6 27.8 2.6 98.6 ------------------------------ 53 17 29 

153.--------- 46.7 18.3 8. 9 12.1 86.0 Bio, mt, an, 12.0. _ ---------- 44 20 12 

349.--------- 16.3 1.1 64.5 81.9 Hm, chi, il, an, 17.7--------- 14 ------ ------

387---------- 36.4 9. 8 50.0 2. 6 98.8 ------.... ---------------------- 39 15 44 

388.--------- 48.5 15.4 32.8 1.6 98.3 ------------------------------ 47 22 29 

392.--------- 50.3 24.4 9.5 14.2 98.4 ------------------------------ 48 38 4 

562.--------- 44.0 9.6 7.2 14.2 75.0 Bio, an, mt, cc, 24.8 _________ 40 25 5 576 __________ 47.5 13.8 1. 1 37.2 99.6 ------------------------------ 49 19 

577---------- 34.1 17.6 22.2 23.1 97.0 cc, mt, 2.9 ___________________ 33 27 17 578 __________ 36.8 8.1 28.9 24.6 98.4 ------------------------------ 38 9 26 

579.--------- 47.0 16.8 32.8 1.1 97.7 ------------------------------ 45 17 37 580 __________ 36.4 8.1 26.1 27.3 97.9 ------------------------------ 36 11 25 581 __________ 59.6 4.8 27.8 6.3 98.5 ------------------------------ 62 32 582 __________ 32.5 22.5 30.6 8.4 94.0 hm, 3.7---------------------- 35 31 22 

583.--------- 32.6 20.1 34.5 8.4 95.6 hm, 2.2.--------------------- 33 19 36 584 __________ 33.9 17.7 28.9 15.2 95.7 hm, 1.6 ______________________ 35 16 29 585 __________ 32.2 14.4 45.6 6.3 98.5 ------------------------------ 35 10 46 ---------- ------ Average ___ 43.1 15.3 21.7 15.5 ------ ------------------------------ 42.8 17.2 21.9 

Q M A Py Ka D Q M A 

369 3 _________ ---------- ---------- ---------- ---------- ---------- ---------- 47 14 

420 __________ ---------- ---------- ---------- ---------- ----------- ---------- 45 5 30 

429 __________ ---------- ---------- ---------- ---------- ---------- ---------- 40 15 40 

464 __________ ---------- ---------- ---------- ---------- ---------- ---------- 42 4 42 495B _________ ---------- ---------- ______________________________ ---------- 56 18 24 

Ab 

---

28 

12 

12 

65 

20 

15 

67 

---io·--

15 

30 

20 

25 

25 

5 

5 

7 

15 

7 ---

14.2 

Py 

20 

10 

2 

10 

1 

Average _______________________ ---------------------------------------- ------ ------ ------ --------

1 3(Fe) is a constant used in estimating the total of minerals in excess of quartz, mica, and alkali feldspar in Koipato rocks. 2 From U.S. Geological Survey rapid rock analyses (U.S.G.S. Bu11.1036-C) by I. H. Barlow, S.D. Botts, 

W. W. Brannock, G. Chloe, P. L. D. Elmore, M. D. Mack, and H. H. Thomas. 

Quartz calculated in this manner agrees with CIPW normative 

quartz to within one percent in the rocks listed in table 4. The 

standard deviation of X-ray modal quartz from calculated quartz is 

2.2 weight percent (fig. 12), and of albite 3.5 weight percent. 2 The 

standard deviations of the muscovite and K-feldspar values are large, 

probably owing chiefly to the apportioning of K20 and Al20 3 in the 

calculated minerals by means of ideal formulas which are not attained 

in the natural minerals. Chemical analyses of the rocks that contain 

andalusite are not amenable to calculation unless a weight concentration for quartz is assumed. 

2 A regression curve for calculated albite as~ function of X-ray modal albite would be tne same as that for 

Na20 (fig. 17C) since the CaO content of the rocks averages less than 0.2 percent, occurring chiefly in traces 

of calcite. 
RHYOLITIC ROCKS OF THE KOIPATO GHOUP, NEVADA 29 

partial chemical analyses, and oxides calculated from X-ray diffraction modes 

altered volcanic rocks of the Koipato Group, Nevada] 

X-ray modal minerals- Partial chemical analyses 2 

Continued 

Other Total 3(Fe)t Total Si02 Al20a K20 NS20 Fe Fe 

------------ ----------- o. 7 2 0.8 77.1 12.6 4.4 3. 7 

----------- .7 2 .7 77.2 12.4 8.1 .2 

----------- .7 2 .6 79.0 12.2 6.1 .1 

----------- 1.0 3 1.0 78.2 12.4 3.8 1.1 

----------- 1.0 3 .9 80.7 11.1 3.6 1.4 

----------- 1.1 3 .7 75.4 14.6 .2 8.0 Cc _______ 1.0 3 1.0 66.3 17.9 8.1 2.2 

----------- .3 1 .4 85.2 8.5 4.0 .2 

----------- 1.6 5 1.1 75.9 12.9 5.3 .6 

----------- 1.1 3 1.2 77.3 12.7 5.5 .1 

----------- .3 1 .4 78.5 12.4 6.8 .3 Bio, 5 ____ 1.3 4 1. 7 73.3 13.7 4.5 1.4 rhl__ ____ }6.4 Mt _______ 19 6. 2 64.3 14.8 .2 7.6 Hm ______ 

----------- . 7 2 .6 75.0 13.4 9.6 .3 

----------- .7 2 .9 77.7 11.9 7.3 .2 

----------- 1.3 4 1.1 77.0 13.3 4.4 1. 7 Bio, 10 ___ 1.6 5 1.8 71.1 13.5 3.9 1. 7 

----------- .7 2 .5 80.0 12.3 1.6 4.4 

----------- 1.1 3 1.1 72.3 15.2 5.8 2. 7 

----------- . 7 2 .6 76.2 13.2 5.8 2.9 

----------- .3 1 .4 77.0 12.9 7.5 .1 

----------- 1.0 3 .9 75.9 13.4 5.4 3.2 

----------- .3 1 .2 84.5 8.4 5.4 .8 

----------- 2.2 7 3.0 68.2 15.5 7.8 1.0 

----------- 1.7 5 2.3 69.8 15.4 8.2 1.0 

----------- 1.7 5 1.7 70.8 14.7 7.0 1.8 

----------- .7 2 .6 72.6 15.1 9.4 .8 ------ ----------- 1.18 ------ 1.2 ------ ------ ------ ------

Ka D 

12 ________ 7 ------ ------ 74.2 21.2 .4 <.1 

----------- 10 ------ ------ 66.7 30.3 .6 .1 

----------- ------ ------ ------ 70.5 27.2 .4 <.1 2 _________ ------ ------ ------ 66.6 31.6 .1 <.1 

l_-- ------ ------ ------ ------ 73.0 22.6 2.3 .2 --------- ----------- ------ ------ ------ 74.6 15.3 4.8 1.6 

Analyses calculated 

from X-ray modes 

Sub- Si02 

total 

.A.l20a K20 Na20 

--------- 97.8 76.8 13.0 4.3 3.3 

97.9 76.1 12.7 8.6 <.5 

97.4 78.6 11.9 6. 7 <.5 

95.5 77.9 13.1 3.3 1.4 

96.8 78.1 12.7 3.6 1. 4 98.2 75.5 13.4 <.5 7. 7 94.5 67.4 18.3 8.0 2.4 

97.9 83.9 9.3 5.2 <.5 

94.7 76.6 10.9 6. 7 <.5 

95.6 76.5 12.9 6.4 <.5 

98.0 79.5 11.9 6.9 <.5 

92.9 73.3 14.1 5.0 1.8 

86.9 62.2 14.5 <.5 7.9 

98.3 74.2 13.9 9.2 <.5 

97.1 75.8 13.8 7.5 <.5 

96.4 74.7 17.3 5.2 1.2 

90.2 69.2 15.9 4.9 1.8 

98.3 78.2 13.2 2.2 3.5 

96.0 69.9 17.4 6.1 2.4 

98.1 76.1 13.1 5.5 3.0 

97.5 76.6 13.4 8.3 <.5 

97.9 74.4 13.7 5.5 3.0 

99.1 86.1 6.9 5.4 .6 92.5 66.6 16.9 7.4 .6 94.4 69.7 15.3 8.3 .8 

94.3 71.3 14.4 6.8 1.8 

97.9 74.1 13.7 9. 0 .8 

------ ------ ------ ------ ------

95.8 74.4 19.7 1.6 <.5 

97.7 68.2 29.2 .6 <.5 

98.1 64.2 :32.9 1.7 <.5 

98.3 66.9 31.6 .5 <.5 

98.1 74.0 :22.8 2.2 <.5 -----------

------ 74.0 15.7 5.1 1.5 

Sample 

_____________ 1 

------------10 

____________ 46 ____________ 58 __________ 58F __________ 61B 

----------61W 

____________ 67 

____________ 79 

------------98 

-----------152 

___________ 153 

___________ 349 

___________ 387 

----------_388 ~----------392 ___________ 562 ___________ 576 ___________ 577 ___________ 578 ___________ 579 ___________ 580 ___________ 581 ___________ 582 ___________ 583 ___________ 584 ___________ 585 

----Average 

__________ 369 3 

___________ 42 ___________ 42 ___________ 46 

0 

9 

4 ________ _495B 

----Average 

3 Calculated minerals: Samples 369, 420, 429, 464, 495B consist chiefly of Si02 and Al20s in the form of 

quartz (Q), andalusite (A), muscovite (M), pyrophyllite (Py), kaolinite (Ka), and dumortierite (D); not amenable to calculation. 

As the intent of the diffraction analysis of the Koipato rhyolitic 

rocks was to determine significant compositional differences that would 

indicate the type, intensity, and pattern of alteration in various parts 

of the volcanic pile, and in lieu of direct compariBon of calculated and 

X-ray modes, it seems reasonable to compare the chief oxide values 

calculated from X-ray modes with those of oxides determined chemically. Regression analyses have been made of chemical oxides as a 

function of calculated oxides, using the 32 sets of oxide values shown 

in table 4 as well as the 35 sets of alkali oxides of table 5. Regression 

curves and their corresponding equations for Si02, Al203, K20, Na20, 

and difference in alkali oxides are shown in figure 17A-E. Minimum 

differences in the weight percentages of the calculated oxides that are 
30 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

TABLE 5.-Chemically determined and calculated alkali oxides from some rhyolitic 

rocks of the Koipato Group, Nevada 

{Samples were analyzed by I. H. Barlow and P. L. D. Elmore by flame photometer methods described in 

U.S. Geol. Survey Bulletin 1036-C] 

Chemical Calculated Chemical Calculated 

Sample Sample 

K20 Na20 K20 Na20 K20 Na20 K20 Na20 

---- ------ 114C. ----------- 7.3 0.64 6.1 0.8 348A __ ---------- 3.4 3.0 3.1 4.1 

123_ ------------- 12.6 1.3 11.9 1.2 349A ____________ .11 10.0 .2 11.2 

123A ___ --------- 10.8 2.0 9.8 2.0 414 ______________ 4.6 4.5 4.6 4.5 

134B _____ ------- .16 4.9 .2 4.2 457-------------- 11.6 .24 11.9 .2 159D ____________ 7.0 .66 5.1 .9 513 _____________ - 4.9 .27 4.8 .2 

160 ______ -------- 6.8 1.2 5.9 1.4 513A __ ---------- 9.0 1.0 8.3 .8 164M ____________ 3.4 .30 2.9 .5 516 ______ -------- 5.2 2.8 5.6 2.3 

1640------------ .22 5.3 .2 4.2 529 ________ ------ .16 7.4 .2 7.3 

172 _______ ------- 4.2 .12 4. 7 .2 529A __ ---------- 2.6 6.3 2.6 6.2 220 _________ ----- 5.3 1.8 5.6 1.2 529B __ ---------- 8.2 1.2 7.1 1.4 

220A_- _ --------- 6.4 2.0 7.9 1.2 530 __________ ---- 10.5 .24 10.5 .2 221 _______ ------- 8.8 .22 10.0 .2 533 __ ------------ 5.4 1.2 5.1 1.7 

255 _______ ------- 8.2 .87 7.5 .7 533A __ ---------- 6.4 2.4 6.2 2.4 

255A __ ---------- .58 6.0 1.3 4.6 548A __ ---------- 5. 7 3. 7 5.6 3.9 

280 ____ ---------- 3.8 4.4 4.9 4.8 581A ____ -------- 7.0 1.5 5.2 1.8 

318 _______ ------- .12 5.8 .2 5.4 601B __ -------- __ .10 5.6 .2 5.6 

318A __ ---------- 3.1 2.6 2.9 2.3 661 __________ ---- 13.0 .54 11.9 .2 

336B __ ---------- .39 7.6 .2 7.6 

significant at 95 percent confidence over the range of the data are 

about 2.5 percent Si02, 3.5 percent Al20 3,

3 1.6 percent K20, 0.8 percent 

Na20, and 1.8 percent difference in alkali oxides. This means that if, 

for example, two samples differ in X-ray-determined Si02 by 2.5 

percent or more, one may expect a real difference in their chemical 

Si02 content with about 95 percent confidence. Considering the 

extreme range in K20, Na20, and Al20 3 in the Koipato rhyolitic rocks, 

the minimum differences that are significant at 95 percent confidence 

are generally adequate for allowing detection of significant changes in 

chemical composition as a function of differences in phase proportions 

across altered zones. 

Calibrated diffraction patterns of three of the samples listed in 

table 4 are shown in figure 18. 

CALIBRATED VERSUS RANDOM PATTERNS 

The recording of calibrated diffraction patterns is well worth the 

slight extra time and effort involved in sample preparation and 

instrumentation, even if no immediate quantitative use is made of 

them. They provide permanent records that can be compared 

directly with calibrated patterns recorded at a later time. Slight 

relative differences that might not ordinarily be discerned in rocks, 

especially altered rocks, commonly become apparent by comparing 

suites of calibrated patterns. 

In studying altered mafic volcanic piles, it has been possible to 

select from calibrated whole-rock patterns, samples that show the 

a Based on assumed normal bivariate distributions; AhOa and Na20 are skewed. 
90 

85 

-I 

~ 80 

~ 

I.LI 

I 75 (..) 

§ 70 (/) 

65 

60 

35 

30 

-I 

<( 

~ 25 

:E 

I.LI 

I 20 (..) 

q; 15 

<: 

...J 

<( 

10 

5 

10 

~ 8 

~ 

w 

I 6 (..) 

0 

~ 4 z 

0 

CALIBRATED VERSUS RANDOM PATTERNS 31 

/ 

/ 12 /. . /-

/ / 

/ / 10 / .. /·. -I . / <( / . . /.• / ~ 8 / ·: . / 

/ ·./ :2 v: . / I.LI :- ·v t5 6 / . / /. •/ / . ··/ ./ / 0 

/ ·~ ~4 / ... / 

/ ':'. 1/ . / A / / / . 2/ . ,/ D / 65 70 75 80 85 90 

Si02, X-RAY 0 2 4 6 8 10 12 

K20, X-RAY 

/" / /. 

/ 1 12 

/. / . / :::::i 

/ 

-1 

<( --110 / / 

/. ::s:::<( / ,/• // -I(.) / . <(_ 

/: 

.. "/' / / I z ~ 8 :/ / / 

-

-W /. . . / WI /: "/ u<-:6 ·/· . . / 

/ . . Z(f) ,_/ .. ww . / ' . -/ "/ l 0:::0 / . /. .. / B w- 4 / .. L.L..x •/ L.L..O /.. ~) .. / / Ci 10 15 20 25 30 35 2 / • , / 

E 

Af203, X-RAY 

0 2 4 6 8 10 12 

DIFFERENCE IN ALKALI OXIDES, X-RAY 

EXPLANATION 

A. Si02 (Chemical) =0.91 Si02 (X-ray)+ 7.29 

B. AI203 (Chemical) ==0.91 Al203 (X-ray)+ 1.03 

C. Na20 (Chemical)=: 0.99 Na20 (X-ray)+ 0.08 

D. K20 (Chemical)= 1.03 K20 (X-ray)- 0.20 

E. ~:;.Alkali oxides (Chemical)= 0.97 6 (X·ray) + 0.20 

c 

2 4 6 8 10 12 

Na20, X-RAY 

FIGURE 17.-Regression curves and equations of chemically determined oxides 

as a function of oxides calculated from X-ray modes (A-D); difference in 

alkali oxides (E). Dashed curves are 95 percent confidence limits. Data 

from analyses of rhyolitic rocks of the Koipato Group, Nevada (see tables 4 

and 5). 
80 

Q 

4.26A 

l >- 1-

U5 60 

z 

LLJ 

1-

~ 

LLJ 

> 

i= 

::s 40 LLJ 

c:: 

20 

Sample 579 Background 

10 15 20 

DEGREES 2 8 

II II 

/Ill 

Kf 

3.25A 

I I I I 

-80-

-60-

c 

7.00A 

l 

Ab 

3.20A 

,-- ' --~:-l 

4.26A l 

Ab 

-80-

-60-

M 

10.00A 

A 

5.57A 

A 

-40-

M 

Kf 

Background 

Sample 495-B Background 'Sample ~49 .l ' ' I I 

25 30 10 15 20 25 30 10 15 20 25 

DEGREES 2 8 DEGREES 2 8 

FIGURE 18.-Calibrated diffraction patterns of samples 579, 349, and 495-B, whose partial chemical analyses and X-ray modes 

ft.re listed in table 4. A1 andalusite; Ab1 albite; C, chlorite; Kf, mi9rocline; M, muscovite; Q, quartz. 

C/.j 

t-.:) 

~ ~ 

~ 

~ 0 

t::1 

~ 

~ 

~ 1<1 

[/). 

r;.l 

0 

l'lj 

~ 

~ c 

ttl 

0 

~ 
SAMPLE PREPARATION AND INSTRUMENTATION 33 

greatest probable differences in phase composition through a given 

altered zone. Chemical analyses of the selt:1cted "end member" 

samples provide a working range throughout which the chemical 

composition of intermediate samples can be estimated from calibrated patterns. 

Similarly, in working with young salle volcanic rocks ranging from 

glassy to holocrystalline to hydrothermally s~ltered, the following 

relative differences in phases are readily apparent from calibrated 

patterns: (1) Patterns of glassy rocks commonly show only incipient 

cristobalite or sanidine peaks; (2) holocrystalline varieties may show 

well-defined quartz lines-with or without a high-temperature silica 

polymorph-, and commonly two distinct alkali feldspar patterns 

are developed; (3) in altered types, zeolites, a single low-temperature 

feldspar, mica and clay minerals, or differences in iron content are 

readily distinguished. 

Any relative differences in calibrated patterns are considerably more 

meaningful than are differences on randomly recorded patterns. 

SAMPLE PREPARATION AND INSTUUMENTATION 

SAMPLE PREPARATION 

A representative sample aggregating, if possible, 2cc or more, 

depending on grain size and texture, is chipped from a hand specimen 

and crushed-not ground-in a hardened steel nwrtar to pass a 1-mm 

sieve. The crushing is most easily accomplished in increments-that 

is, by pouring the fines through the sieve and the remainder back into 

the mortar and further crushing the remaining coarse material, 

repeating the crushing and pouring until the entire sample has passed 

the sieve. The crushed sample is split, preferably with a microsplitter, to about-but not more than~lcc. The crushed split is 

than ground in a power mortar, such as the :Fisher mortar grinder 

with alumina mortar and pestle and plastic scraper, until the largest 

particles are less than 40 microns. It has been found in practice 

that 1 cc of material split from a crushed rock sample that has passed 

a 1-mm sieve is both representative of the original sample and readily 

ground to < 40 microns. A split smaller than 1 cc is apt to be unrepresentative; a larger split requires a correspondingly longer grinding 

time. For most microcyrstalline silicate rocks about 15 to 30 minutes 

of grinding is required to reduce 1 cc of crushed ( < 1 mm) sample to 

less than 40 microns, depending on such variables as the speed of the 

grinder and the weight of the pestle head. In order to standardize 

the grinding procedure for a given suite of san:Lples, particle size as a 

function of grinding time should be checked under the microscope and 

also on the diffractometer by checking peak-height reproducibility 

from several different mounts of each of several sample powders. 
:34 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

It must be emphasized that in quantitative diffractometric analysis 

accuracy is dependent on both reproducibility and maximum peak 

intensity. Reproducibility is dependent on random orientation of 

crystallites which is most nearly achieved in sample powders of very 

fine particle size. Fine particle size also reduces extinction and most 

microabsorption effects to a negligible level and, hence, allows for 

near-maximum peak intensity. 

PREPARATION OF POWDER MOUNTS 

The procedure for mounting the sample powder is essentially that 

described by McCreery (1949), which minimizes preferred orientation and at the same time produces a plane surface and a powder 

layer thick enough to allow for maximum diffracted intensities (Klug 

and Alexander, 1954, p. 252). The sample holder, or cell, is a rectangular sheet of aluminum about 3.5X4X0.16 centimeters with a 

rectangular hole 1 X2 centimeters through the sheet. The sample 

number is penciled on the side of the cell which will face the X-ray 

beam, and this side is covered with a clean glass slide held firmly in 

place with masking tape or a spring-binder paper clip. The cell, 

with glass slide attached, is placed glass down on a flat surface and 

an excess of the sample powder is poured into the cavity. The powder is thoroughly tamped with the edge of a small spatula-blade 

about 1 centimeter wide-so as to fill the cavity evenly and to minimize 

flowing of the powder along the glass face plate. The powder is then 

gently compressed with the flat blade of the spatula; a slight surplus, 

or hump, on the back of the powder cake is preferable to a depression. The back is then covered across the width of the aluminum 

cell with l-inch masking tape reinforced on the sticky side with a piece 

of file card, slightly larger than the cavity, which covers the powder. 

The backing over the powder cake is pressed :firmly, further compressing the powder. The cell is picked up, the glass face plate 

gently removed, and the masking tape on the back is cut off with 

scissors flush with the edges of the aluminum holder. Five or six 

packed cell mounts can be prepared in 15 minutes after a little practice. 

The pressure applied in the packing of powder mounts has no significant effect on diffracted intensities (Weiskirchner, 1960; Schmalz, 

1958). Also, finely ground powders mounted in a rotating sample 

holder showed no better reproducibility than those mounted in a 

stationary holder (Schmalz, 1958). The mounting of sample powders as a slurry on glass slides is not recommended for quantitative 

work because this method is conducive to preferred orientation and is 

likely to yield diffracted rays of low intensity owing to inadequate 

sample thickness. 
SAMPLE PREPARATION AND INSTRUMENTATION 35 

CALIBRATION AND ANALYTICAL T:ECHNIQUE 

The X-ray source and circuit panel are allowed a warm-up period 

of about 30 minutes during which time a sample for qualitative analysis may be scanned. During this time, also, the slits and filter are 

checked. Several powder mounts are prepared. When the instrument has attained equilibrium, the circuit-panel rate meter is zero 

set and then calibrated so that the recording pen ranges from exactly 

zero to 60 at 100 cps full-scale deflection on 60 cycles. The desired 

counting rate and time constant are then set; all settings on the circuit panel remain constant from here on. The recording pen is allowed 

to run continuously, because turning the chart drive switch on and 

off occasionally affects the calibration. Only the motor that rotates 

the goniometer is ever shut off during the course of analyzing several 

samples. 

To calibrate for analysis, the X-ray power source (kilovolt and milliamp dials) is adjusted until both the peak height and background 

intensities recorded at the 4.26 A quartz line from two or more standard quartz-bearing powder mounts agree consistently with established 

calibration curves. The standard powder mounts used in the present study contain 30 and 70 percent quartz, tJmd were used in preparing the curve set of figure 9. A final check on calibration is made 

by measuring background at 4.26 A on a pure magnetite sample. 

Both peak height and background calibration is assured by following 

this procedure. Calibration usually requires 10 to 15 minutes after 

the instrument warm-up period. The calibration should be checked 

periodically with a standard mount, but in practice, intensity remains 

remarkably constant. 

Scanning of the 4.26 A quartz line from the stu,ndard mounts should 

be always in the same direction and should start at least 1° 28 ahead 

of the measured line to assure that full background intensity has been 

attained. 

If a second instrument or a different nickel filter and slit set is used, 

or if the X-ray beam take-off angle is altered, the intensity-concentration and background curve sets may have to be modified. Slight 

differences in thickness of nickel filters and width of receiving slits 

will effect differences in spread between background and peak-height 

intensity; any significant differences will show up immediately during 

calibration. Similarly, if a slower scanning speed or time constant 

is employed, curve sets must be modified, although background will 

remain the same for any scanning speed or time: constant. 

For routine analysis of silicate rocks, powders are scanned from 

40 ° to 6 ° 28, as almost all the major minerals in common holocrystalline silicate rocks, both fresh and altered, have prominent measur-
36 X-RAY MODAL ANALYSJS OF FELSIC ROCKS 

able reflections in this range. For many felsic rocks, scanning from 

32° to 6° is sufficient. The main peaks are rescanned, always in the 

same direction. The powder mount is then rotated 180°, making 

essentially a new mount, and the main peaks are again scanned 

twice in the same direction, beginning at least 1 ° ahead of the line to 

be measured. If, from four runs, the mean deviation, especially of 

the quartz peak, exceeds 0.2 inches, one or more new powder mounts 

should be prepared. Large deviations in peak heights are usually 

caused by preferred orientation of crystallites-owing to insufficient 

grinding and poor mounting-rather than by instrument deficiencies. 

In analyzing rhyolitic rocks of the Koipato Group, the chief constituents, as determined frmn the intensity-concentration curves, invariably totaled from 85 to 105 percent. The total iron, 4 quartz, andalusite, 

and usually the muscovite determinations were considered absolute; 

the feldspars were adjusted proportionally so that the total of all 

constituents was 100 percent. 

Analysis of the Koipato rhyolitic rocks, after a standardized routine 

was established, was accomplished at an average rate of about 40 

samples per day by one worker using two diffractometers and four 

automatic grinders. 

STANDARD POWDERS 

Standard powders should, if possible, be prepared from constituents 

contained in the rocks under study. A pure separation of most minerals can be made by centrifuging 20- to 50-micron n1aterials in heavy 

liquids of appropriate specific gravity. The pure mineral and the 

selected matrix material are then weighed on 4- by 5-inch glazed paper 

on an analytical balance in the desired proportions to total 1 to 2 

grams. Enough standards should be made, in increments of about 5 

percent, to fill the expected range of each constituent in the rocks under 

study. 

To be certain that the pure mineral and the matrix material for 

each standard powder are thoroughly mixed, the weighed portions are 

stirred with a small spatula on the glazed paper and then sieved 

(<I mm), care being taken to retain all the powder. The stirring 

and sieving is repeated 3 or 4 times. The mixture is then ground in 

a power mortar for about 15 minutes to meet the size requirements 

discussed in the section on sample preparation. 

SELECTION OF PEAKS FOR MEASUREMENT 

Most of the major minerals in common holocrystalline silicate rocks, 

both fresh and altered, have prominent reflections in the range 40° to 

4 The total iron in rocks of the Koipato Group, determined from background intensity, is multiplied by a 

constant of three for estimating the total of the minor constituents. (See table 4.) 
SAMPLE PREPARATION AND INSTRUMENTATION 37 

6° 2fJ. A few preliminary scans of sample powders from the rocks 

under study will show which lines are best for m.easurement. 

Quartz.-For quartz, the 4.26 A line (20 .8 ° 2fJ), the second strongest 

quartz line, is best for quantitative determinations, as it is not significantly superposed by peaks of other common rock-forming minerals. 

Moreover, using copper radiation and 1-degree sllits, a standard 20-mm 

sample mount is almost completely covered by the X-ray beam at 

the 4.26 A line, affording a better sampling of the powder surface 

than at higher angles. The only common interference is from the 

weak 4.25 A K-feldspar line, which, when reflected from finely ground 

randomly oriented powders, has no significant effect on the 4.26 A 

quartz line unless the K-feldspar content exceeds about 40 percent, 

and the quartz content is very low. (See charts by Mc0reery,1949, 

reproduced in Klug and Alexander, 1954, p. 303.) There is some 

evidence, however, that certain low-temperature adularia-type feldspars may reflect a strong peak at 4.25 A. The ratio of the 4.26 A 

and 1.8·2 A (50.1 ° 2fl) quartz lines may be used- to check this possible 

effect. 

The 3.34 A quartz line, commonly used in analyzing for quartz in 

two-component mixtures, is nearly five times a8 strong as the 4.26 A 

line and is therefore usually offscale relative to pHaks of other minerals 

when analyzing felsic rocks. Furthermore, the 3.34 A line nearly 

coincides with strong mica and sillimanite lines and lesser alkali 

feldspar lines. The 3.34 A line is of use, however, in analyzing 

unaltered mafic rocks or trachytes in which 1quartz may occur in 

low concentrations. 

Feldspar.-Plagioclase and K-feldspar are estimated from the 

composite peaks at about 3.20 A (27.9° 2fJ) and 3.25 A (27.4° 2fJ), 

respectively. Owing to compositional variations and to extremely 

small original crystallite size in some rocks, whieh reduces intensities, 

universally reliable determinations of feldspars cannot be made. 

Furthermore, in scanning from high to low angles, a 3.20 A plagioclase 

peak will effectively increase the K-feldspar peak at 3.25 A and 

vice versa. Also, the 3.20 A plagioclase peak must be corrected 

for slight effects from muscovite. 

However, when analyzing a given group of rocks from a common 

source area, empirically derived correction faetors can be applied 

which allow for reasonably accurate feldspar determinations. Many 

altered felsic rocks commonly contain only one feldspar (tables 4 

and 5) whose concentration can be determined rather accurately. 

If only K-feldspar is present (fig. 18, sample 5'79), its "triclinicity" 

can be determined from the difference between the 131-131 spacings 

(Goldsmith and Laves, 1954). If only sodic plagioclase is present 
38 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

(fig. 18, sample 349) its anorthite content can be determined from the 

difference between the 220-131-131 spacings (Smith and Yoder, 1956). 

Micas.-At angles smaller than about 18° 28, using 1° slits, the 

primary X-ray beam covers an area larger than the standard 20-mm 

sample, and intensity measurements from the sample decrease; no 

interference is encountered from irradiated portions of aluminum 

sample holders, however. Regardless of intensity loss, mica is generally most reliably measured at the 10.00 A line when only one mica 

is present in a sample. If a sample contains both biotite and muscovite, the muscovite may be measured, though less reliably, at the 5.00 

A line which is about half as strong as the 10.00 A line; biotite has 

only a very weak peak at 5.00 A. The ratio of the two line intensities 

allows for an estimation of both biotite and muscovite in the same 

sample. 

Chlorite and kaolinite.--These are measured at the 7.00 A line 

(12.4° 28). If both are present in the same sample, the ratio of the 

7.00 A and 4.67 A lines allows for an estimation of each mineral proprovided standards are prepared from chlorite and kaolinite contained 

in the rocks under study. 

Some other common minerals.-Andalusite is reliably measured at 

5.57 A (15.9° 28); no interference has been encountered at this line. 

Pyrophyllite is estimated at the 9.25 A line (9.6° 28); sillimanite at 

5.39 A (16.4° 28); amphibole and cordierite at about 8.50 A (10.4° 28); 

and calcite at about 3.03 A (29.4° 28). 

No attempt has been made in the present study to estimate the 

weight concentrations of pyroxenes and olivines from diffraction 

patterns of whole-rock powders. Schmalz (1958), however, has used 

the 1.63 A line (56.4° 28) for determining augite. 

CONCLUSION 

Calibrated diffraction patterns of whole-rock powders, even when 

scanned at 2° 28 per minute, provide a reasonably accurate, rapid, 

and inexpensive means of determining the weight concentrations of 

many of the chief silicate minerals and of total iron in fine-grained 

felsic rocks. The technique is especially well suited to the analysis 

of altered felsic volcanic rocks. Although the intensity -concentration 

curves shown, except for quartz and total iron, apply only to rhyolitic 

rocks of the Koipato Group, the technique can be applied to other 

fine-grained rocks if appropriate curves are established from artificial 

powders prepared from minerals contained in the rocks under study. 

The quartz and iron curves appear to be almost universally applicable. 

Intensity-concentration and background curve sets can be readily 

modified for use with direct counting techniques or slower scanning 

speeds. 
REFERENCES CITED 39 

Corrections for differences in mass-absorption coefficients between 

the mineral to be analyzed for and the matrix-sum of all other constituents-are based on differences in the iron content of samples; 

iron content is measured from background intensity. As the admixing 

of an internal standard is not required, the ra,pidity of analysis is 

considerably increased. 

The accuracy of the technique is dependent on the reproducibility 

of peak heights. Reproducibility is dependent chiefly on random 

orientation of crystallites in sample powders ground fine enoughless than 40 microns-to reduce extinction andl microabsorption effects to a negligible level, thus allowing for maximum intensity of 

peaks at fixed instrument settings. 

The most likely sources of analytical error are: (1) the sample 

itself, owing chiefly to inadequate grinding and poor mounting of 

the powders-errors associated with the sample are more serious 

than those due to the instrument; (~)compositional variations within 

mineral species; (3) poor calibration of X-ray beam intensity with 

standard powder mounts; (4) counting rate no:~ properly calibrated 

initially; zero set is off; (5) slits and filter not centered; and (6) 

instability of the electronic circuitry. 

The success of the technique as applied to altered rhyolitic rocks 

of the Koipato Group is due to several favorablle factors common to 

many altered volcanic piles: (1) the samples analyzed constitute a 

large group always containing the same major components, though 

occurring in a wide range of proportions; (2) alll the rocks are bolocrystalline; (3) the fine grain of the rocks simplifies sampling from 

hand specimens and allows for unusually uniform crystallite sizes in 

finely ground powders; and (4) absorption characteristics are 

essentially constant for most of the rocks. 

Limited experimental work indicates that several other relatively 

abundant common minerals, including chlorites, amphiboles, and 

pyrophyllite, can be determined with reasonable accuracy, provided 

intensity-concentration curves are established from standard powders consisting of minerals separated from the rocks under study. 

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40 X-RAY MODAL ANALYSIS OF FELSIC ROCKS 

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0