FOR ROCK ANALYSES Cnnnr,Es S. Bacou. Jn.

CHARLESS. BACON,JR.264cally, Y increasesto the right and Z to the left. The right half of theXYZ diagram will be called the XY chart, and the left half will be calledthe XZ chart.The values al, fm, c and alk can be recalculated from the coordinatevalues as follows: l100-x Y-z2x-Y-Z 1002x Y z-10o1 0 0 - x - Y Z,,arK : - 26. Silica (si) is brought onto an equivalent basiswith the Niggli tetrahedral valuesby the following equation:ci: ------Y*:'i"'-l"q!gj"'Jio'----S u m o i t h e m o l e c u l a rn u m b e r s o f a l , f m , c a n d a l k 'si is plotted as a variation diagram against X at the right of the XYZchart using the c-al side as a base. This will be known as the si chart, andis the third unit of the diagram which is to be known hereafter as theXYZ-si diagram.7. The values ti (TiOt, p (PrOu),zr (ZrOz),h (HrO), co2,so3,sor,clz,s, etc. are obtainedin the samemanner as si. They are not usedoften.8. The valuesk and mg are obtained as follows:Molecular number of KzOf,:Molecular numbers of K:O * Na:O (plus Li:O)Molecular number of MsOi l l E :"-M o l e c u l a r n u m b e r s o f F e : O a( X 2 ) * F e O * M n O f M g O9. k and mg may be plotted as ordinates against X at the left of theXZ chart along the alk-c edge (Fig. 4), and become appendagesto theXYZ-si diagram.10. A salt such as NaCl in the analysis of a sedimentary rock is computed as the oxide of the metallic element. In this case the Na-portion ofthe molecular number of NaCl is divided by 2 so as to bring it to the samebasis for calculation as NazO.

NIGGLI-BECKE PROJECTION FOR ROCK ANALYSES265Frc. 4. Mineral distribution in the XYZ-si diagram.Knv ro MrNnn,irr.s e, antigorite, bronzite, brucite, chondrodite, enstatite, epsomite,goethite, hematite, hypersthene, ilmenite, limonite, magnetite, melanterite, olivine, periclase, pyrite, serpentine, siderite, talc, wolframiteactinolite,tremolitediallage, diopside, dolomite, hedenberglteandraditeakermanniteanhydrite, apatite, calcite, collophanite,fluorite,gypsum,perovskite,scheelite, titanite, suvianitephlogopitealmandite, beryl, chamosite, pyropepargasitepolyhalitegehlenite, grossulariteallanite, epidoteacmite, aegirite, carnallite, riebeckitearfvedsoniterN rnr XYZ-sr titexanthopylliteprehnitemeionite, zoisiteglauconitechromite, cordierite, spinelmontmorilloniteanorthite, abazite, heulandite, phillipsiteandesineoligoclasehalite, soda nitermarialite, sodaliteadular, albite, analcite, glaucophane,leucite, microcline, natrolite, nephelite,orthoclase, perthite, sanidine, spodumenealunite, muscovite, paragonite, sericiteandalusite, bauxite, beidellite, corundum, diaspore, halloysite, hydrargillite, kaolinite, kyanite, pyrophyllite,sillimanite, topazThe following example illustrates the method of calculation tabulatedin a convenient form. Note the two subtotals ST which added to AlzOsand CaO give the total T.

CHARLES S. BACON, JR.266Rocr Axar,vsrs Calo. Nrccr,r-BncrrPnolrcrroNAnalyst: Dr. Karl WillmannName: GraniteSpec. Grav. 2.663Locality: North side of Echo Lake, Calif.Reference: Unia, CaliJ. Publ., Yol. 17, 1928. Pp. 360-361.Weight per cent Mol. Wt. of oxide:Mol. Number (X10,000)68.416080r4211,345 T 3690: sitipAlzos18.051O21766 "t 3690: 03 T 3690:{m13.611.5CaO2.3956426 T 3690:cNazOK:O3.394.226294.') /448STT.13.16HrOHrOTotal47.92lO9940.78308995 T 3690:alk369027.0Total 100.099.9IKrO/ST:k.45Mgo/Sr:mg.sect fm:X25.L:I",1:)i3:3Rur.os FoR CoMpurrNG RocK CoonorN,q.tnsFRoMTHE MoDES1. Determine the teirahed'ralJactor TF of each mineral in the rock.From the formula or chemical analysis of the mineral find the weightpercentagesof the plottable oxides, i.e., those included in the al, fm, cand alk of the tetrahedron. Minerals such as qlrartz and rutile, lackingin tetrahedral components, are treated later. Divide the weight percentage of each plottable oxide by the molecular weight of the oxide to obtainthe molecular number. The sum of the plottable molecular numbersmultiplied by the specificgravity of the mineral is the TF of the mineral.Thus, orthoclase contains 64.870 SiOz, t8.37o AlzOs and t6.97o KzO byweight. Only the AlzOaand KzO are plotted in the tetrahedron.* The molec* SiOzis plottedin the si-chartat the right of the XY chart.

NIGGLI-BECKE PROJECTION FOR ROCK ANALYSES267ular ratios corresponding to 18.3/6 AlrOa and t6.97o KzO are added(.1794 .t791:.3585) and multiplied by the specificgravity of orthoclase(.3585X 2.56: 0.92).The TF of the common rock forming minerals are given (Table 1) soas to eliminate this step from most modal calculatiops. Man, mineralshave a constant chemical composition and specific gravity, and consequently a definite TF. Other minerals, including important rock-formingsilicates, have variable compositions and specific gravities, and thereforevariable TF. The TF figures used in Table 1 are based upon the statedformulas and specific gravities. For best results the TF of such mineralsshould be based upon individual determinations of composition and specific gravity instead of the averagesused in the table. In casesof smallvolume percentagesof such minerals, variations from the average compositions will nct displacethe rock analysis points appreciably, but whereIarger percentagesare involved accuratevalues of TF should be obtained.*2. Multiply the volume percentageof each mineral by the appropriateTF to obtain the molecular number.3. Reduce the molecular numbers of the minerals with plottable constituents to 10O/6.4. Multiply the reduced molecular numbers of the minerals by thefactors X, Y, Z and si listed in Table 1.5. Make summations for X, Y, Z and si, respectively. The position ofthe rock in the XYZ diagra.mis given by the totals for X,Y, andZ.6. Silica (si) is obtained by multiplying the volume percentage of freequartz by the ia"ctor 4.42 which is obtained in the same manner as thetetrahedral factors.t The molecular number thus obtained is divided bythe sum of the plottable molecular numbers before reduction to t00/p.The result is the si for quartz, to which must be added the si of all theother minerals. The si of a mineral such as zircon is obtained in the samemanner as for quartz.7. Other values such as ti,p, zr, h, etc., are obtained in the same manner as si.The modal calculation of Johannsen's center point granite will serveas an example.* The hornblende field is scattered between the aluminous pargasite and the ferruginousactinolite, and commonly includes some alkali. Johannsen's (1932) average of a numberof analyses of various hornblendes lrom granites was selected as the center point forhornblende. Johannsen's average of dark mica from 34 granites was chosen for the centerpoint of the biotites. Johannsen's average was used for the center point of augite. Thechlorite point corresponds to Dana's (1932) formula of penninite and clinochlore, and fallshalf way between Becke's (1925) amesite molecule and serpentine.Weight percentaget Si iactor:-;# 1XSpec.rylolecutar I\'elgnl100Gruv.:-X2.656:4.12.ou

268CHARLES S, BACON, JR.VolumeMineralTetrahedralFactor7oQuartz19.9X4.42 OrtboclasePlagioclase (AbroAnro)Biotite38.11 4 5.2 7. sXXX.921.302.MMolecularNumberPlottableMol. NumbersReducedto 100/68828.91 5. 655.5J5.U18.9o/.rsT 121.0S T1 0 0 . 0* si factor.ReducedMol.Nos.MineralFactorsXYZRock 28.915.655.502367507322sT 4.57.88.387374r38.130.6238Checkingthe rnodalcalculotion1. Multiply the volume percentagesof all the minerals in the rock bytheir specific gravities and reduce to 100/p. These are the weight percentagesof the constituents.2. Multiply tbe weight percentagesby the oxide percentage composition of each mineral and enter the values in tabular form as in the example below. It may be difficult to obtain the correct weight percentagesofthe complex silicates, and the use of selected or average percentagesintroduces uncertainties.3. Add the columns vertically to obtain the chemical composition ofthe rock.4. From the chemical composition thus calculated determine X, Y,Z and si according to the method described earlier. These values should

NIGGLI.BECKE PROTECTION FOR ROCK ANALYSES269correspond with those obtained from the mode by the regular method.xChechoJthe Mod,al Calculation. (Johannsen'scenter point granite)/oQuartzOrthoclasePlagioclase (AbroAnrdBiotite19.938.1Yol./6XSpec W t . 7 oGrav.52.797.538.582.5Total62.6Mol. Nos f 10,000:1497alfm:288*613*694:1595: 196c:1155rlk:24219131 0 3 0.4si:234MrNBner, DrsmrnurroN rN THE XYZ-st DreoneutThe mineral distribution in the XYZ-si diagram (Fig. a) is the key toa thorough understanding of the rock positions and to chemico-modalrelationships. Quartz is plotted only as si and has no place in the tetrahedron. The plagioclasefeldspar line with its divisions marking the different members of the isomorphous series is the most important featureof Fig. 4. The division points were calculated from analyses given inWinchell (1927), and Tschermak, G. and Becke, F. (1920). TheZ of allfeldspars is 50. The si ranges from 300 in albite to 100 in anorthite.Located at the same point with the pure albite molecule is orthoclase,nepheline and leucite, but nepheline has an si of only 100 and leucite of200. The biopyriboles are widely scattered toward the fm corner in bothtop and side views, with olivine and orthopyroxenes at fm.Distinctively sedimentary minerals occur at all corners; calcite, gypsum and anhydrite at c, kaolinite and other clay minerals at al, rock saltand soda niter at alk, and the iron ores at fm. Dolomite lies between cand fm.The minerals of the metamorphic rocks are widely distributed between fm and c, and between al and c.I The calculated chemicalcomposition of the rock should be compared with a chemicalanalysis, ii available. Such a comparison frequently sbeds light on the true compositions ofcomplex silicates wbich cannot be determined optically. rf average compositions of the complex silicates are assumed, the calculated weight percentages may differ notably from theactual analyzed values, and then the true nature of the silicates may be determined andt}e modal calculation adjusted.t Printed forms of the XYZ-si diagram and the triangle charts on a single 8iX 11 sheetare available at two dollars per 100 sheets. sample on request. Address the author.

270CIIARLES S. BACON, JR. -3o l*'nF Eu -z-z!Obo(\!-3-8-e-S-3-eaL qf \v 7i l:' !9 A9dtra-:7o? :-3-P-3-3 8-R-e.:.:3I6C/): r,z5l'tr'!;\7l . t vx .:Yl Adaaot 4o'Ea

NIGGLI-BECKE PROJECTION FOR ROCK ANALYSESSar,rnNr FBarunBsIrr,usrnarnDrN rrrE XYZ-sr271DraonauXY chart : I gneousrochsThe majority of igneous rocks fall into two main groups, the alkalilime seriesand the alkali series.xThese are distributed in a curved zonefrom alkali feldspar to the fm corner, the alkali-lime serieswith higher Ythan the alkali series(Becke, 1925) (Fig. 5 and Table 2). The alkali-limeseries includes alaskite, granite, granodiorite, quattz diorite, gabbroand peridotite. The alkali seriesincludes alkali granite, nepheline syenite,essexite,theralite and missourite. Two intermediate families, syenite andmonzonite, are included, as well as three branch families anorthosite,lamproite and evisite. The Daly (1910) averagesare used with the exception of the following family types:Essexite of Rongstock, Bohemia (preferred by Becke, 1925)Theralite of Duppau, Bohemia (preferred by Becke, 1925)Lamproite and evisite (Niggli, 1923)Alkali granite (average of 13; Osann, 1900)zolkaoinarolrOAllollol olkli6.r.rirrdYPolorh.rl.rolASodo!a.iarFrc. 6. Niggli's magma families in the XYZ-si diagram.Minerals: aeg aegirine, aug augite, biot biotite, hbl hornblende, oliv olivine. The plagioclase feldsparsare distributed along the line from X 0, Y 50 to X 50, Y 100. The lines converging at fm give the (OrAb)An ratio of most rocks with X under 70.Abbreviations of selected families: AG alkali granitic, AN anorthositic, Ap aplite granitic, D normaldioritic, Ev evistic, G normal gabbroid, GD granodioritic, Gr normal granitic, L lamproitic (Wyomingtype), M monrnouthitic, P peridotitic, QD quartz dioritic, S normal syenitic, T theralitic, U urtitic.The projection for the anorthosite family lies between those for normalgabbro and for calcic plagioclase.Evisite, the soda-amphibolegranite ort Becke's (1925) Pacific andAtlantic suites respectively.

272CHARLES S. BACON, TR.syenite family, known especially from Evisa, Corsica, is drawn stronglytoward the riebeckite point. Lamproite, a family of potash and magnesiarich effusives of lamprophyric character which includes orendite, wyomingite, Ieucite phonolite and others, is drawn toward fm in consequenceof the olivine (and phlogopite) in the rock.Niggli (1923) grouped the magmas or igneous rock families in threeseries,the alkali lime series,the potash series,and the soda series (Fig.6, Table 3). The separation of the two alkali seriesis not apparent in theXYZ-si diagram but can be demonstrated in a k chart (not shown).Feldspars largely control the locations of rocks more alkalic than diorite, and the pyriboles predominantly determine the positions of themore femic igneousrocks. A line from fm through the rock analysis pointto the feldspar line gives the approximate (OrAb) An (orthoclase-albiteanorthite) or the AbAn ratio of the feldspars for rocks more salic thangabbro, the former when both types of feldspars are present, the latterwhen plagioclase is tbe only feldspar.x Rocks with soda-pyriboles haveunusually low Y which gives the analysis points the appearanceof havingAbAn ratios in excessof the true values.or,n.ph,l.ucZolk.- s Illor,n.ph,l.ucol olkYmin.ror.RocxsOuo.lr bto.inC rocltFcldrgor roclr rllho{l quorltoln.Dli ldoo.'lJ[ii'j:,::::.::':[:;::i.'"".,Frc. 7. Modal study of the igneous rocks in the XYZ-si diagram.Mineral abbreviations: ab albite, aeg aegirite, an anorthite, andes andesine, aug augite, biotbiotite, byt bytownite, diop diopside, hbl hornblende, lab labradorite, leuc leucite, neph nepheline,olig oligoclase, oliv olivine, o-pyr orthopyroxene, or orthoclase.Rock abbreviations: D diorite, G gabbro, GD granodiorite, NS nepheline syenite, P peridotite,S syenite.* Nepheline and leucite should be included with orthoclase and albite when present.

NIGGLI-BEOKEPROJECTIONFOR ROCKANALVSES273The families of Joha,nnsen's(rg20) quantitative mineralogicalclassification of the igneousrocks may be plotled fike any othermod:*es,but dueto the chemical overlap of his families they are not reproducedhere, asthis would require numerous additional charts.The distribution of the rocks as controlled by the readingmineral constituents is illustrated in Fig. 7. The average biopyriboles (biotitepyroxene-amphibole) were calcurated for 31 nephelinesyenites, 10 syenites,.58 granites,68 granodiorites,16 diorites, and,42gubbro, (Johannsen, 1932, 1937,1938). The XyZ-si of these average tropyribolesandthe fields which the points represent are given below:XYZsIFieldNepheline e, hornblende, biotitehornblende, biotite, augite, diopsidehornblende, biotite, augitebiotite, hornblendehornblende, orthopyroxene, clinopyroxene,biotite84 augite, orthopyroxene, hornblende, olivineT.inesfrom thesepoints to the proper pragioclasesgivethe linear distributions of the families, the leucocratic members near the feldspar line,themelanocratic members at the other end. Biotite granites ur. di.tribrrt"dbetween biotite and albite-oligoclase,whereas hoinbrende graniteshavebigher Y and lie between hornbrende and the same feldspar. rh. riebeckite granites have lower y than the biotite granites. Granodiorites,diorites and gabbros lie between the biopyriboles and the plagioclasesAb76An36,AbroAnsoand AbsoAnz0respectively. olivine arrd ortho-rhombicpyroxene draw the points for olivine gabbros and norites towardthe fmcorner. Peridotites and related rocks lie in the triangular area definedbybiotite, augite and the fm corner.The field of the igneousrocks is limited by lines connecting fm, augite,anorthite, albite, aegirite and fm.XY chart: SedimentaryrocksThe field of the sedimentary rocks in the Niggii tetrahedron hasashape very unlike that of the igneous rocks, due rargely to the considerable quantities of lime and alumina in sedimentary io.tr (Fig. g, Table4).

CHARLES S. BACON, JR.n1Ac ol, grD, o nhydmolillfm60J--:l-oRcd irud'r!lnonl --]o5l PSH.BLOG SStlIDLol olkloolooninarolrRocxsO---ORoctr@lin.ou.of ro6a l06lltll.lttFrc. 8. Distribution of the sedimentary rocks in the XYZ-si diagram'gl glauconitMineral abbreviations: anhyd anhydrile, baux bauxite, cal calcite, cbam chamosite, dol dolomite,gyp gypsum, kaol kaolinite, mont montmorillonite'BLDG.LS building limRock abbreviations: ALK.EVAP. alkali evaporites, ARG.LS. argillaceous limestones,shale, Mt' Diablcalcareouscalc.sH.shales,calcareousstones, BLDG.SS. building sandstones, CALC.SH.MC SH Mesozoic and CenozoCalif ., CL clay, D L diorite laterite, Gr L granite laterite, L laterite, LS limestones,shales, P SH Paleozoic shales, SS sandstones.Limestones, if pure, lie at the c corner. Most limestonesare magneslan'with a little alumina present, and their positions in the diagram are al-outside of the igneous field, nearer the al-c edge'Sandstonesare distinguished by higher c values than any igneousrocksexcept anorthosites.Iron ores lie close to fm. Rock salt and other alkali evaporites lie nearalk.XY chart: MetamorPhicrocksMetamorphic rocks do not occupy an area distinguishable from thoseof igneous and sedimentary rocks. The mineral combinations in meta-

NIGGLr-BECKEPROJECTIONFOR ROCRANALYSES275"Wo,ool olkctrdrktfoolooYmo orr oD.tOO ZOOOlond,lt l@l300 400 5006antrottRocKso""l' "e i:::::."i','.,Frc. 9. Metamorphic rocks and processes, and weathering in the XyZ-si d.iagram.Mineral abbreviations: ab albite, act actinolite,

XY chart: Metamorphic rocks XY chart: Metamorphic and weathering processes. XZ chart: Ignmus rocks. . XZ chart'. Sedimentary rocks XZ chafi Metamorphic rocks and processes, and weathering si chart: Igneous rocks. . . si chart: Sedimentary rocks . . si chart: Metamorphic rocks and processes, and weathering k chart