American Mineralogist, Volume 67, pages 1135-1143, 1982

Quantitative mineralogical analysis of granitoid rocks:a comparison of X-ray and optical techniques

Bnrenr L. De.vrs

Institute of Atmospheric SciencesSouth Dakota School of Mines and Technology

Rapid City, South Dakota 57701

nNo MrcneBr J. WeTewENDER

Department of Geological SciencesSan Diego State UniversitySan Diego, California 92182

Abstract

Five igneous rock specimens from the Peninsular Ranges batholith of southern Californiahave been analyzed for mineral content in a comparative study by X-ray diffraction(reference intensity technique) and optical polarizing microscopy. The X-ray methodutilizes aerosol suspension of pulverized rock samples, followed by collection and analysison glass fiber filters by powder X-ray diffractometry. Under some conditions, a standardwell mount may be used for sample preparation, eliminating the need for sampletransparency and matrix corrections. Optical analysis consists of standard identificationprocedures using polarized light followed by point counting. Excellent agreement betweenthe two methods is observed for quantities of the major components for all rocks except anolivine gabbronorite. Discrepancies in the gabbronorite analyses are primarily due tosample inhomogeneities as well as the use of calculated reference intensity constants forthe several solid solution minerals occurring in this sample. Where both experimentalreference intensity constants and sample measurements are obtained using the aerosolsuspension technique for sample preparation, relatively high accuracy and relatively rapiddata collection may be achieved with the X-rav method.

Introduction and background

Quantitative analysis by X-ray diffraction meth-ods has received increasing attention in recentyears (see the review by Alexander, 1977). Never-theless, problems associated with preferred orienta-tion, extinction, and micro-absorption have stilllimited the application of X-ray diffraction quantita-tive analysis to relatively inaccurate or semi-quanti-tative results. Point counting by microscopy stillremains the basic and most widely used techniquefor direct mineralogical analysis of rock materialswhere particle size is above the 10 pm diameterlevel. However, many X-ray difraction studiesusing specialized calibration techniques have beendescribed in the literature and include examplessuch as that of Parker (1978) for analysis of analcitein pumice, Bidjin and Lahodny-Sare (1976) for astudy of kaolinite and boehmite in bauxite samples,

the calcite study of Garish and Friedman (1973),and the clay mineral work of Cody and Thompson(1976). Additional specialized techniques such asthose described by Henslee and Guerra (1977) usingPVC membranes and Leroux and Powers (1970) forfilms deposited on silver membrane filters, weredesigned for analysis of free SiO2 materials. Manyadditional specialized studies of these types existbut cannot be enumerated here.

In recent years, a general X-ray diffraction tech-nique has emerged, known as the reference intensi-ty method (RIM), which permits quantitative multi-component analysis of crystalline materials withoutthe requirement for preparation of calibrationcurves, and more recently without the need for theadding of an internal standard to the sample. For-mulation of the RIM process was given by Chung(1974a,1974b,1975) and was applied to compoundsused in paint pigments, such as PbO, TiO2, ZnO,

0003-0ux/E2i I I I 2-l | 35$02.00 I 135

l 136 DAVIS AND WALAWENDER: MINERALOGICAL ANALYSrc OF GRANITOID ROCKS

etc., with the compounds reduced to a fine powderand mounted in accordance with the National Bu-reau of Standards' technique (NBS Monograph25,1971). The technique as applied to these compoundsproved highly successful, primarily due to the useof reference intensity constants determined for thesame specific batches of compounds that were usedin the "unknown" mixtures. Most of the early workused an introduced compound, such as Al2O3 as thereference material, but the latest study (Chung,1975) made use of one of the compounds in theunknown mixture as the arbitrary reference. This,of course, was made possible by the previousknowledge of the reference intensity constants forall components of the sample so that transformationof the reference base was possible.

In response to a need for characterization ofcompounds in the atmosphere, a comprehensivestudy was undertaken by one of us (BLD) todevelop a quantitative analysis technique for ambi-ent aerosols. In this case, analysis was made direct-ly on the collecting filter media, usually a high-volume glass fiber filter or one of the membranefilters such as Teflon or Nucleopore. The uniquefilter method of sample preparation was shown byDavis and Cho (1977) to eliminate preferred orienta-tion in calcite aerosols, and it has been presumedthat preferred orientation of other inequant shapedmaterials is similarly eliminated or greatly reduced.These studies are further described by Davis (1980),and Davis and Johnson (1982a,b).

Optical techniques for quantitative evaluation ofmineral constituents in thin section have long beenused by mineralogists and petrologists. It is impor-tant in such an analysis, however, to be sure thatthe volume adjustment of the various species forshape differences is made to the point count dataset. This adjustment is vital in order to make acomparison of the traditional optical analyticaltechnique with the recently developed RIM. Toavoid making such corrections, we have selected aseries of relatively homogeneous even-grained plu-tonic rocks from the Peninsular Ranges batholith ofsouthern California. Classification of these rocksrange from granite through quartz diorite to gabbro-ic species that have been described previously byWalawender (1976) and Walawender and Smith(1980). Further interest was added to the study bycompleting the work independently. Data from onelaboratory was not examined by the workers of theother laboratory until completion of the experimen-tal work and compilation of the final analyticalresults. We feel, therefore, that the present results

give a true evaluation of the X-ray technique if oneconsiders the optical results to be the "standard" ofcomparison. To the authors' knowledge, this studyrepresents the only attempt at a direct and indepen-dent verification of the RIM technique since themethod was successfully applied by Chung.

Brief summary of required X-ray parameters

A complete description of the X-ray theory andmethodology is not possible here. These details canbe obtained by review of the Institute of Atmo-spheric Sciences (IAS) literature cited above. Brief-ly, the raw intensity data can be obtained fromdigital or strip chart output of any properly main-tained powder diffractometer. They should be inte-grated intensities (at least by "triangular" approxi-mation) and must be corrected to constant volumeconditions in cases where the theta-compensatorhas been employed. The intensities representing the"infinite" thickness condition for such a sample isobtained from the relation

rr: Iipfr fWHPS [l - e-zPi'lvta/'wEsinel

where Ii is the raw integrated intensity (counts) forcomponent i, WS is the fraction of the samplematerial in the sample/matrix composite layer, { isthe constant volume factor for diffractometers withtheta-compensating slit systems, lrfi is the massabsorption coefficient experimentally determinedfor the sample material alone, pfi is the massabsorption coefficient for the sample/matrix com-posite, M" is the mass per unit area of sample layerB on the filter substrate, and 0 is the Bragg diffrac-tion angle. This relation corrects the initial intensi-ties for transparency, matrix absorption, and depar-ture from constant volume conditions (if appropri-ate).

The mass absorption coefficient of the filter isobtained from the relation

where I1 is the beam intensity attenuated by thefilter, Is is the initial beam intensity, Ml is the massper unit area of the filter substrate, and gf' is themass absorption coefficient of the filter materialalone. A similar relation is used to obtain the massabsorption coefficient of the sample;

( l )

,i: -# ̂ (+) Q)

pE:-#{" lH] (3)

DAVIS AND WALAWENDER: MINERALOGICAL ANALYSIS OF GRANITOID ROCKS

where I1g is the X-ray beam attenuated by bothfilter and sample material, and other quantities asdefined above. This measured value of the samplemass absorption coefficient is then compared with asimilar quantity calculated from constituent ele-ments, oxides, or mineral components whose massabsorption coefficients are a mass-weighted sum ofelemental values tabulated in the International Ta-bles for X-ray Crystallography (1968, Vol. 3, Table3.2.2a). Significant departures of the measured val-ue from the values calculated from the analyseswould indicate errors in sample processing, orerrors in physical parameters such as the referenceintensity constants, or the presence of amorphouscomponents. For plutonic rocks, we can safelyeliminate the possibility of amorphous constituents.

Reference intensity constants must be availablefor each component expected in the analysis. Theseare intensity ratios IilI(Al2O3) measured experimen-tally from mixed equal-weight proportions of thecomponent (i) and a reference standard, which hasbeen Linde A synthetic Al2O3 in the latest IASinvestigations. Reference intensity constants arealso available in the rcros (Berry, 1970), althoughwe do not recommend their use since the methodsof sample preparation are generally not stated andcertainly not consistent from source to source.Since the sample in the IAS RIM technique hasbeen suspended and collected on a filter, it isimperative that the reference intensity constants bedetermined with an identical procedure, which hasbeen the case for all analyses completed by the IASgroup.r

With these reference intensity constants deter-mined, the final analysis is obtained quickly andsimply by use of the equation

- l

W i :

where W; and k1 are the weight fraction and refer-ence intensity constant, respectively, of the ithcomponent of n components of the mixture.

In the present analyses, the experimental instru-mentation consisted of a Norelco powder diffrac-tometer fitted with theta-compensator and graphitevertical monochrometer, operating with CuKa radi-ation at a scan speed of one-half degree per minute.

tup-to-date list of the current reference intensity valuesobtained by the air suspension method may be obtained from theIAS laboratories on request.

Mass absorption coefficients were measured withan automatic direct-beam transmissometer con-structed in part from components of a Philips small-angle scattering goniometer. In the latter system,the circular filter sample was rotated and translatednormal to the X-ray beam to integrate the countover the entire sample for a 20-sec period. Thedirect beam count was made alternately with thefilter count for an identical period. Direct beamstrength was approximately 2 x l}a counts persecond. No less than 10 separate integrated passeswere made on each filter and filter/sample compos-ite; the average value for the l0 passes was used inEquation (3).

Description of the optical technique

Point count techniques, long used by petrolo-gists, are described by Chayes (1956). The proce-dure simply consists of fixing a standard thin sec-tion into a mechanical stage equipped with a 2-axismicrometer control and translating the thin sectionin fixed increments across the stage of a petrograph-ic microscope. At each increment, the grain under-neath the ocular crosshair was identified and re-corded on a point counter device. The final tally ofpoints recorded for each mineral is then equated toa volume percent of that mineral in the thin section.

Our procedure consists of counting an initial 200points and calculating the appropriate weight per-cent for each mineral. An additional 100 points (ir)are then determined and added to the initial count.This total (200 + i1), as weight percent, is comparedto the initial 200 points. If all the major minerals inthe initial count (200) are within 5% of the (200 + il)subtotal, that addition adds no new information andthe (200 * i1) subtotal is considered to approximatethe mode of the thin section. If any of the mineralsin the (200 * i1) subtotal are not within 5Vo of thosein the initial count, an additional 100 points (i) arecounted and added to the previous subtotal. Usingthe 5Vo limit, the (200 + ir + i2) subtotal is comparedto the (200 * it) subtotal. The procedure is repeateduntil the final increment (i.), when added to theprevious subtotal, falls within the 5% limit for eachmajor mineral. The final total, converted to volumepercent, approximates the mode of the thin section.Although 400 points were generally sufficient forthe rock types used in this study, 2 of 10 thinsections required a 500 point total to meet the"diminishing returns" requirement. All thin sec-tions were thus counted to a total of 500 points forconsistency. Duplicate thin sections of each rocktype were counted and the average values, along

t+: (t )l (4)

I 138

with the error factors (+ one-half the differences)are listed in Table 1.

Sample preparation

For the normal RIM procedure, the rock samplesare ground in a carbide ball mill to "flour" consist-ency and the powdered material was suspended inthe simplified aerosol suspension device describedby Davis (1981a). The vertical flow velocity withinthe chamber allows approximately 10 g.m diameterparticles or less to be incorporated into the filter.Best results are obtained when using the WhatmanGF/C (37 or 42.5-mm diam) glass fiber filter. Thesurface is much smoother than that of the heavier"high-volume" type filter and the fine fiber matteaids in creation ofrandom orientation ofthe trappedparticles. No substrate peaks are contributed to thesample spectra, although loadings in excess of 300pg cm-z are necessary for obtaining adequate peakintensities.

For the present study, mass loadings of 3-8 mgcm-2 were accumulated on the filter in an evenlayer by rotation of the Buchner funnel assemblywhile collecting the aerosol. The diameter of thefilter/sample composite is reduced in two stages:

DAVIS AND WALAWENDER: MINERALOGICAL ANALYilS OF GRANITOID ROCKS

First, a cut to 3.65-cm diameter to eliminate theborder areas that have incomplete sample coveragesuch that an accurate Ms can be measured; andsecondly, to obtain a 25-mm diameter disk formounting in the spinning sample pedestal of thediffractometer.

It is possible to bypass the filter mounting of thesample whenever it is apparent that materials withgood cleavages or inequant habit are not present orare only minor components of the sample. Undersuch conditions, that is, when preferred orientationis not expected to be serious, it is possible toeliminate the corrections by mounting the pulver-ized rock material in a normal "well" mount. Thisallows straightforward use of Equation (4) withoutcorrecting for sample transparency or matrix ab-sorption.

In the present study, reference intensity constantmeasurements were made for biotite and horn-blende from the diorite samples because the grainsize of these components was large enough to allowtheir separation. These constants were obtainedfrom pulverized component material treated in thesame manner as the sample material. Prior to sus-pension, the mineral components were mixed with

Table l. Quantitative mineralogic analyses of peninsular ranges batholith rocks by X-ray difraction and polarizing optical microscopy(weight percent)*

CoDpole!tOpttc X-rey ra oprtc opt ic

Q @ t z 2 2 . 7 2 6 , ! ( 2 . 7 )

PtagLoclaeer* 50.4-o 55.1-o (3,2)

L 2 . 2 l 4 . l ( 1 . 6 )

9.6 8 .4 ( r ,2 ) 35 .8 (1 .6 ) 33 .7 (4 .0 ) 37 .3 16 .3 (0 .7 ) f i . ] (3 .0 )57.6-L 57.FL (s.3) 40,7-O (0.1) 33.6-0 (2.3) 5s.7 64,3-0 (2.s) 66.2-L (4,7' 28.0-8 (3.4) 25.2-D (2.4')

- 19 .0 (0 .5 ) 16 .9 (7 .1 ) 2 . .s7 ,O 5 .7 (2 .2 ) 3 .2 (0 .4 ) 0 ,4 (0 .2 ) t . s t3 .o (2 .8 ) 9 .0 (3 .4 )

2 .7 (0 .4 ) r0 .4 r3 .3 (3 .9 )

ls ,4 13 .4 (s ,8 )5 .4 ( r .2 ) 8 .2 (2 .6 ) (3 .2 ) 43 .0 (8 . r )

6 . 4 ( r . 1 )

z t .g t2 . 6

lllcrocllD€

!tot l t€

Ituacovlte

EohbleDde

Dlop.tde

EBtetite

Au8lte

Oltvtae

UeBnettte

Sphene

Apatlte

CblotLte

SplDeI

"opaqueer'

2.O (0 .4 )

(o.r)

o -'

(o:2)

0 .9 ( 0 .2 )

8.3 (4 .0 )

o , 7 ( 0 . 4 )tr

tr

1 . 3 ( 0 . 4 )

0 .9 (0 .1 )

22 .2 (2 .0 ) 7 .4 (1 .4 )

23 .2 ' (L .4 ) 22 .4" (3 .5 '

: : ':' ':"

2'.3 .o]r, : :r -

(0.r )

tNolbers lD Pardthese6 ere t I allf f qence La the ffi optlel @unts ed I varlece eErors foE I0RD (Ddts, I98h).**o ' oligoclaeei L = Labredorlte; E - Eytohite (Aag5-9g frcn optlc a*ly6r6; Anos fr@ Fray @ly6{s).

TBdenlte or patgsite vartety,tFoza.

+fFo8o.

as"ryl" liD-I oarysis fru uell Dut.

DAVIS AND WALAWENDER: MINERALOGICAL ANALYS$ OF GRANITOID ROCKS I 139

equal proportions of Linde A synthetic Al2O3 refer-ence standard.

Sources of uncertainty

Davis (1981) describes a variance error propaga-tion procedure which incorporates the standarddeviations of the reference intensity constants,mass absorption coefficients, and other physicalparameters using the reduced multivariate errorexpression for n uncorrelated variables

d f ( X 1 , X 2 , . . . . , X . )

where s2 is the variance propagated from use ofEquations (1) and (4) and other expressions (whereamorphous components are present) involving thevariables X, where the X's stand for ki, p,f , etc.,and s(Xi) represents the estimated standard devi-ation of each parameter. Standard deviations arenot always available, but estimates of them can beobtained by use of range information and from themaximum or minimum error expected. Descriptionand listing of the specific standard deviations for allparameters is beyond the scope of the presentdiscussion. In the absence of amorphous compo-nents, the major sources of uncertainty are thereference intensity constants, k1, and the massloading, Mr. The error from the latter source beginsto be appreciable only below 0.05 mg cm-2 andtherefore errors from this source should be insignifi-cant for the present study. For those componentshaving only one measured value for k; or p,f , thearbitrarily assigned value of o' : 0.10 X; for thevariance error has been used in all calculations. Thehighest measured relative standard deviation (stan-dard deviation divided by the mean) is 0.57 formagnetite based on analyses ofthree separate spec-imens. The variance error process has suggestedfrom past studies that the major components of theanalysis (greater than 50 weight percent) will beknown to within +l0Vo of the stated analyzedamount, whereas minor components (less than 10wt.%) may have uncertainties as high as l00Vo orgreater.

Unfortunately in the current study, referenceconstants were not available for all mineral compo-nents. The values for diopside, enstatite, augite,and olivine were obtained from calculated absorp-tion and intensity data of Borg and Smith (1969).This introduces additional uncertainty into the finalanalyses, and in these cases standard deviations of

l$Vo were assigned to the kr and pf parameters as inthe case where only one measured value is avail-able. We have found that the calculated and mea-sured reference intensity constants agree withinreasonable limits, but that large variations in thisagreement may occur with different mineral spe-cies. The reasons for such disagreement are un-known and obviously suggest the need for addition-al work in the area of reference intensity constantdetermination.

The potential sources of uncertainty in the pointcount method have been considered in detail bymany investigators. Only a brief summary will beattempted herein and the reader is directed toChayes (1956), Solomon (1963), and Frangipane andSchmid (1974). Major sources of uncertainty in-clude:

(1) The average grain size ofthe rock relative tothe traverse increment of the mechanical stage. Theformer value cannot be determined from a thinsection since it represents a random slice throughthe rock. As such. the maximum and minimumgrain sizes can only be approximate. If the traverseincrement is greatly different from the average grainsize of the rock, a significant bias may be encoun-tered.

(2) Direct conversion of areal proportions to vol-ume proportions. This is dependent on the distribu-tion of grains in the rock, and on the ratio of thegrain size of total area of the thin section (Frangi-pane and Schmid, 1974).

(3) Misidentification of a mineral lying under theocular crosshair. This error may be insignificantcompared to the previous sources of uncertainty(Solomon, 1963)

(4) Apparent enlargement of small grains withhigh refractive index (Holmes effect; Chayes, 1956).

Reproducibility tests reports by Chayes and Fair-bairn (1953) indicate that, for the major minerals ina given thin section, the variation in modes deter-mined by several observers was essentially thesame as that reported on replicates from one ob-server. These results seem to suggest that forgranitoid rocks such as those used in this study, thevolume percentages of the major minerals could bedetermined to within approximately 5% of theamount present.

Results

Table 1 presents the mineralogical analyses forthe five Peninsular Ranges rock samples. Valuesare in weight percent and include estimated uncer-

dXi

lz.stxJj (5)

l l,t0

tainties from the difference measurements in theoptical counts and from the variance error routineof the RIM. For sample WD-l, we completed ananalysis by the RIM procedure using a standard"well" mount for comparison with results from thefilter preparation. This column is marked W inTable 1. Although the major components agree wellin quantity with those obtained from the filtersample, the higher biotite component and appear-ance of chlorite in the well mount results suggestthe enhancement of these intensities from phyllosil-icate particle orientation in the well mount.

Table 2 presents the physical parameters requiredfor the analysis and includes the source informationfrom which average compositions of the oxides ofthe mineral components were obtained and used for

DAVIS AND WALAWENDER: MINERALOGICAL ANALYSIS OF GRANITOID ROCKS

oxide reduction. In addition to the X-ray diffractionand polarizing optical analyses, atomic absorptionand X-ray fluorescence analyses were available orcompleted for the samples during the study. There-fore, a direct comparison of the oxide reduction forboth optical and X-ray analyses can be made withthe elemental analyses (also converted to oxides)obtained from X-ray fluorescence and atomic ab-sorption. These reductions and analyses are givenin Table 3.

Table 4 presents the mass absorption coefficientdata as measured directly from the loaded filtersand as calculated from the optical, X-ray, andchemical analysis procedures.

In first examining Table 1, we note excellentagreement between the values for components of

Table 2. Physical constants required for reference intensity analysis

Conponent hkr u .' Ir{I

Conposition for Oxide Reduction**

quartz

0I igoclase

Andesine

Labradorite

Bytounite

Microc I ine

siot i te*

Biot i te

lfuscovite

Hornblende*

Hornblende

Edenitic Hornblende

Diopside

Enstatite

Augite

Ol iv ine

Magnetite

Chlor i te

Spinel

Sphene

101

f

+++

7oz * l2s00I

001

002

l r 0

l l 0

221

3 1 0

LL2

3 l l

002

2 . 8 4 3 4 . 9

I . 5 5 3 8 . 1

1 . 6 5 4 2 . 2

1 . 6 8 4 5 . 9

L . t I + J - a

0 . 2 8 4 1 . 3

1 . 4 7 8 8 . 9

2 . 1 3 9 6 . 5

0 . 2 7 4 5 . 4

0 . 8 0 7 7 . 8

0 . 6 7 8 7 . 9

s 9 . I

t . o s f t 6 8 . 0

o .aq t i 45 .6

l . l4+ f 79 .6

r .29 f t 6s . s

2 . 6 2 2 3 2 . 0

0 . 4 6 6 5 . 3

31.2

98. I

Pure Si02

I V ; 1 4 ; 1 - 1 4

IV ; l 5 ; l - 14

IV ; 16 ; l - 14

IV ; l 7 ; l - 15

I V ; 5 ; 9 - 1 6

I IT i l 2 i l - 7 , 9 , l ! , 12 , L4

I I ; 5 ; l 2 - 1 5

I I ; 40 ; 17 , 19 , 20 , 24 -27 , 29 , 36 , 38

I I ; 4 1 ; 3

I I ; 5 ; I 0 , 1 2 , 1 3 , 1 6 - 2 4

I I ; 2 ; 1 - 5

I I ; l 7 ; l 5

I i 2 i l O

V ; 1 2 ; 1 - 3 , 5 , 6

I I I ; 25 ; L -3 , 12 -20 , 24 -30

V ; l l ; I

I i L2 i 2 -7

'Relat ive to A1203-115 standard (L inde 600 mesh).**Volune;

Table; Sa:nple Number -- Dee" et g!: (1963).+All peaks between d=3.19 and d=3.2 i are included in the reference

the plagioclase fe ldspars. These include ZOz,2ZO, 040, and 002 for rDostGoodyear and Duffin (f954), Bolg and Snith (f969)1.

$Determined fron urineral separation of LQD and llqD sanples,ficalculated f"on data of Borg and Srnith (f969).

intensity constant forspecies [see

DAVIS AND WALAWENDER: MINERALOGICAL ANALYSIS OF GRANITOID ROCKS

Table 3. Analyses* expressed as oxides (weight percent)

l 14 l

lilD-2

Opttc X-ray 0pt lc opttc X-ray Optlc X-ray Opttc X-tay

Sto2 58.0

A 1 2 0 3 1 6 . 3

N62o 5.6

K z O 1 . 1

C a O 2 . 7

F e o 1 . 0

Fe203 O.7

MeO 4.0

MDO

Tlo2

BaO

sio

820 (LoI) 0.3

66.9 68 .6

4 , 7 4 . 3

3 . 8 4 . 3

3 . 6 II r .z*

0 . 7 |

0 .04 0 .05

0 , 6 0 . 7

0 . 6 ( 0 . 6 )

27 .5 19 .3

4 . 0 2 . 8

0 . 5 0 . 8

t0 .2 11 .4

2 . s 4 . 3

4 , 6 3 . 9

- 0 , 1

_ 0 . 5

76.2

0 . 7

8 , 3'I

i 10 .6*I)

3 . 6

0 . 2

7 4 . 1 7 3 . 0

r3 .4 r3 .2

3 , 6 3 . 2

3 . 4 3 . 4

7 . 7 2 . 9

1 . 0 r . 2

0 . 9 0 . 9

0 . 4 1 . 3

0 .0r 0 .02

0 , 2 0 . 2

0 .01 c .05

o . 2 0 . 0 2

0 . 3 0 . 5

47 .3 44 .9

1 . 5 1 . 0

0 . 1 0 . 4

7 . 6 9 . 5

5 . 0 r 0 . 4

0 . 8 3 . 4

23.5 L7 .4

0 . 1 0 . 2

0 .05 0 .4

0 .01 0 .01

0 . 7 1 . 0

4 3 . 0

1 . 0

0 . 0 5

1 3 . 3

II r . lo*I

t 7 . o A

0 . 3

6 4 . r

L6.9

5 . 9

3 . 2

3 . 6

0 . 5

0 . 60 . 1 0 . 5

7 2 . 2

L4.6

4 . 0

4 . 2

2 . 0'II r .o*)

0 . 5

0 .05

0 . 3

5 9 . 5 5 6 . 8

3 , 1 6 . 5

8 . 8 4 . 6

3 . 1 lt . r *

L . 2 |)

0 . 1 0 . 2

o ,4 1 .1

0 .01

0.03

0 . 5

' I ron expreseed a6 Fe2o3.

, rReduced fron Elderal cmPo6ltlons in rroptlcl and tt-ray"i lndependent amly6es Dy x-ray fluotescence spectr@etEy h trIRFn, and by AtoEic

Aboorpt lon spectro6copy ln "MS!.

aTheee two vslues were erroneous.ly lnterch&ged tn Table 2 of walaretrdet (1976) and have be6 corrected here.

three of the samples. For samples LQD, MQD, andWD-2, the agreement between the optical and X-rayresults are well within the difference enors andvariance errors listed. This agreement is not onlywith respect to the numerical values of the mineraltypes present, but with regard to the specific miner-al "sub-species" determined independently by wellestablished optical and X-ray techniques. In the X-ray analysis, trace amounts of sphene, apatite,chlorite, and spinel were not observed primarilybecause of the extensive coverage of the various

Table 4. Measured and calculated mass absorption coefficients*

Silp1eCheuical

X-raI Analysis

peaks of the plagioclase spectra throughout thescanning interval. In the cases of some of the minorcomponents, the reference intensity used was notthe value given in Table 2, which is based on thestrongest peak of the pattern, but rather one basedon a peak of lesser magnitude, the reference intensi-ty value of which was scaled down from a knowl-edge of the relative calculated or observed intensi-ties of the pure component spectrum. Magnetite isan example where interference by plagioclase peakswas extensive, and in the case of W-113 correctiondue to the overlapping plagioclase peak was madebased on the calculated intensities given for bytow-nite by Borg and Smith (1969). In the opticalanalysis, magnetite, ilmenite, and other metallicoxides or sulphides were simply listed as"opaques",

The computation procedure used in the IASlaboratory (on a CDC Cyber 170) includes reductionof all mineralogical components to oxides based onaverage compositions of these components ob-tained from the tabulated analyses given in Deer etal. (1963). This results in what may be termed a"probably" oxide analysis. For the oxide reduc-tions of Table 3, no modification of the compositionfiles in the computer was completed as an attemptto adjust for unusual amphibole or pyroxene com-

LQD

IreD

llD-1

l{D-2

l{-rr3

4 3 , 6

44.1

46.3

1 t , 2

4 9 . 6

5 3 . 4

4 6 . 4

5 8 . 8

42,9

4 5 . 8

63,4

4 3 . I

s 2 , 4

'Ltni ts of -2 gr-1. cuKa radiat ion, calculated values obtained

fr@ elqental nass ebsgrpt ion coeff ic ients.

lr42 DAVIS AND WALAWENDER: MINERALOGICAL ANALYSIS OF GRANITOID ROCKS

positions. The file does separate, however, individ-ual feldspar ranges into the six "member" classifi-cation commonly used by petrologists and mineral-ogists. With regard to samples LQD, MQD, andWD-2 discussed above, the comparison of the ox-ides also shows generally very good agreement. Anexception to this is in the somewhat higher ironoxide content of the XRF analysis compared tooptic and X-ray oxide reduction values for sampleMQD.This anomaly is also reflected in the comput-ed mass absorption data of Table 4. In the case ofWD-2, the analysis by X-ray fluorescence showsquite good agreement with the X-ray data andreasonable agreement with the optic data. Thehigher silica and lower alumina content observedfor the optic analysis in WD-2 is the result ofclassification of the feldspar as oligoclase ratherthan labradorite. The optic/X-ray discrepancy forthis sample with regard to the plagioclase type wasresolved by determination of the difference20(13l)-20(131) and use of the Smith and Yoder(1956) procedure for determination of An content.The An value thus determined for WD-2 is 32Vo(sodic andesine). With this reassignment the oxideanalysis would move closer to that observed by theoptical technique and further from agreement withthe X-ray fluorescence analysis.

Agreement in the results of optic and X-rayanalysis of WD-l is generally good, with the excep-tion of the assignment^of the mica quantities. Inthese analyses, the l0A spacing, similar for bothbiotite and muscovite. was used as the referencepeak and assignment to a specific mica species isvery difficult because of the weak nature of otherpeaks in the diffraction spectra or their masking byplagioclase. Only slight diffractometer misalign-ment can cause serious errors in spacing measure-ment in this region of 20 and the lack of suitableinternal standards in this regon precludes accuratemeasurement. Therefore it is safer to rely on theoptical data in this case. Except for this minordifference, the optic and X-ray data for WD-l arealso in good agreement as demonstrated by themineralogical comparison and the oxide compari-SONS.

For samples LQD, MQD, WD-l, and WD-2, thecorrectness of the optic and X-ray analysis is sub-stantiated by the mass absorption coefficient data ofTable 4. Those samples containing the higher pro-portions of basic constituents are readily apparentin the table. Samples LQD and WD-l are similar inthis respect in their absence of significant "mafic"

constituents, whereas values for MQD and WD-2indicate moderate iron contents (as also demon-strated in the XRF analyses, Table 3).

More serious discrepancies in analyses are obvi-ous for sample W-113. In this analysis, measuredreference intensity constants were not available forenstatite, olivine, and the specific variety of amphi-bole which is different from the common horn-blende parameters presently in use in the RIMcomputer files. Consequently, the reference intensi-ty constant for the common hornblende was used inthe analysis and calculated reference intensity con-stants for the other two minerals were determinedfrom the data of Borg and Smith (1969). From Tablel, we see that for W-113 the amphibole and ortho-pyroxene contents represent the major differencesin the optic and X-ray results. Although thesedifferences could be the result of uncertainties inthe reference intensity constant assignments, it isalso possible that sample inhomogeneities are re-sponsible for the observed discrepancies. Largeoikocrystic amphiboles, which are common in thisrock unit (Walawender, 1976), may not have beenincorporated into the thin section slices but werepresent in the remainder of the block crushed forthe X-ray sample. The larger volume of rock used inthe X-ray technique could thus be more repre-sentative of the actual modal proportions.

Conclusions

Remarkably good agreement between the tradi-tional optical point count analysis and X-ray difrac-tion quantitative analysis by means of the referenceintensity method is demonstrated in the study of thegranitoid rocks of the Peninsular Ranges batholith.The best agreement is noted for those samples forwhich measured reference intensity constants havebeen obtained by the aerosol suspension technique,and poorer agreement is observed where such dataare not available but reliance was made on calculat-ed data. The reduction of the mineralogical analysisto oxides perrnits additional comparison betweenthe two methods as well as with standard chemicalanalytical results. The results of this study suggestto us the need for more widespread use of the RIMprocedure in quantitative anlaysis of rock speci-mens.

Successful use of the technique ordinarily re-quires the suspension of pulverized rock materialinto an aerosol and collection and analysis onspecial filter substrates. Exceptions to this require-ment might be those materials not containing signif-

icant amounts of micas, carbonates. or other com-ponents subject to strong preferred orientation. Thefilter-sample preparation procedure is very simpleand requires no elaborate laboratory apparatus. TheX-ray scanning can be accomplished on any powderdiffractometer and with the additional X-ray trans-mission measurements provides a means for analy-sis of both crystalline and amorphous components.These studies have demonstrated that with the useof good reference intensity. constants, uncertaintieson the order of only a few percent may be associat-ed with the analyses for even minor components.Much larger errors are possible, however, whenanalyzing coarse- or uneven-grained rocks andwhen using calculated reference intensity con-stants, especially for those minerals showing exten-sive solid solution properties.

AcknowledgmentsThis work was supported by the Environmental protection

Agency under Cooperative Agreement CR-806769-01, and by theState of South Dakota. The point counts for samples LQD andMQD were made by A. Bryce Cunningham, San Diego StateUniversity.

ReferencesAlexander, L. E. (1977) Forty years of quanritative difiraction

analysis. Advances in X-ray Analysis, 20, l-13.Berry, L. G. (Editor) (1970) Establishment of a reference intensi-

ty. In Inorganic Index to the Powder Diffraction File: JointCommittee on Powder Diffraction Standards, 1970 (PDl5-2I).

Bidjin, D. and Lahodny-Sare, O. (1976) A rapid X-ray difractionmethod for the quantitative determination of Boehmite andKaolinite in Bauxites. Travaux du Comite International pourL'Etude des Bauxites, Oxydes, Hydroxydes, d'Aluminium,13.35r -356.

Borg, I. Y. and Smith, D. K. (l%9) Calculated X-ray powderpatterns for silicate minerals. Geological Society of America,No. 122.

Chayes, F. (1956) Petrographical modal analysis. John Wiley andSons, Inc., New York.

Chayes, F. and Fairbairn, H. W. (1951) A rest of precision ofthin section analysis by point counter. American Mineralogist,36,7MJ12.

Chung, F. H. (1974a) Quantitative interpreration of X-ray dif-fraction patterns of mixtures. I: matrix-flushing method forquantitative multi-component analysis. Journal of AppliedCrystallography, 7, 519-525.

Chung, F. H. (1974b) Quantitative interpretarion of X-ray dif-fraction patterns of mixtures. II: adiabatic principle of X-raydiffraction analysis of mixtures. Journal of Applied Crystallog-raphy,7,526-531.

Chung, F. H. (1975) Quantitative interpretation of X-ray ditrrac-tion patterns of mixtures. III: simultaneous determination of a

I 143

set of reference intensities. Journal of Applied Crystallogra-phy, E, 17-19.

Cody, R. D. and Thompson, G. L. (1976) Quantitative X-raypowder diffraction analysis of clays using an orienting internalstandard and pressed disks of bulk shale samples. Clays andClay Mineralogy, 24, 224-231.

Davis, B. L. (1980) "Standardless" X-ray diffraction quantita-tive analysis. Atmospheric Environment, 14, 217 -220.

Davis, B. L. (l9El) A study of the errors in X-ray quantitativeanalysis procedures for aerosols collected on filter media.Atmospheric Environment, 15, 291-296.

Davis, B. L. and Cho, N-K. (1977) Theory and application of X-ray diffraction compound anlaysis to hi-volume filter samples.Atmospheric Environment, I l, 73-85.

Davis, B. L. and Johnson, L. R. (1982a) On the use of variousfilter substrates for quantitative particulate analysis by X-raydiffraction. Atmospheric Environment, 16, 27 3-282.

Davis, B. L. and Johnson, L. R. (l9E2b) Sample preparation andmethodology for X-ray quantitative analysis of thin aerosollayers deposited on glass fiber and membrane filters. Ad-vances in X-ray Analysis , 25, 295-300.

Deer, W. A., Howie, R. A., and Zussman, J., 1963: RockForming Minerals (Vols. I-V). John Wiley and Sons, NewYork.

Frangipane, M. and Schmid, R. (1974) Pointcounting and itserors: a review. Schweizerische Mineralogische und Petro-graphische Mitteilungen, 54, 19-31.

Garish, E. and Friedman, G. M. (1973) Quantitative analysis ofcalcite and Mg<alcite by X-ray difraction; effect of grindingon peak height and peak area. Sedimentology,20, 437-444.

Henslee, W. W., and Guerra, R. E. (1977) Direct quantitativedetermination of silica by X-ray diffraction on PVC membranefiIters. Advances in X-ray Analysis, 20,139-152.

International Tables for X-ray Crystallography (196E) Vol. III,Physical and Chemical Tables (K. Lonsdale, ed.). Birming-ham, Kynoch Press.

Leroux, J. and Powers, C. J. (1970) Direct X-ray diffractionquantitative analysis of quartz in industrial dust films deposit-ed on silver membrane filters. Occupational Health Review,21,26-34.

NBS Monograph 25; (1971) Standard X-ray difiraction powderpatterns, Washington, D.C. United States Government Print-ing Ofrce

Parker, R. J. (1978) Quantitative determination of analcime inpumice samples by X-ray diffraction. Mineralogical Magazine,42. 103-106.

Smith, J. R. and Yoder, H. S., Jr. (1956) Variation in X-raypowder diffraction patterns of plagioclase feldspars. AmericanMineralogist, 4l, 6i2.

Walawender, M. J. (1976) Petrology and emplacement of the LosPintos pluton, southern California. Canadian Journal of EarthSciences, 13, 1288-1300.

Walawender, M. J. and Smith, T. E. (1980) Geochemical andpetrologic evolution of the basic plutons of the PeninsularRanges batholith, southern California. Journal ofGeology, E8,233-2M.

Manuscript received, December 9, I98I;.acceptedfor publication, July 6, 1982.

DAVIS AND WALAWENDER: MINERALOGICAL ANALYSB OF GRANITOID ROCKS