THE AMERICAN MINERALOGIST. VOL. 48, MARCH-APRIL' 1963
Co-Ni-Fe DIARSENIDES: COMPOSITIONS AND CELL DIMENSIONS1
EucnNB H. Rosreoour, [/. S. Geologi,calSuraey, Washington,D. C.2 Assrnect Analyses of natural Co-Ni-Fe diarsenides have indicated two distinct compositional groups: the rammelsbergites (and pararammelsbergites), which are nickel-rich, and the loellingite-safflorite series, which are nickel-poor. The synthetic diarsenides show extensive sotd solution at 800o C. A solvus interrupts the FeAsrNiAsp series near the NiAsz end and extends into the ternary solid solution toward CoAs:. This solvus probably interrupts the NiAsrCoAsz series at temperatures well below 800o C. and hence explains the separation of rammelsbergites lrom the loellingite-saffiorite series in nature. At 800. c., synthetic rammelsbergite appears to be stoichiometric with the formula NiAsz,oo.Loellingite is homogeneous from FeAsz to FeAsr,ee..[Iomogeneous cobalt saffiorite was made with the compositions CoAsr,es and CoAsr,sa and appears to have monoclinic symmetry, in contrast to rammelsbergite and Ioellingite which are orthorhombic. Although the cell edges of the co, Ni, Fe diarsenides vary as complex functions of the composition, the cell volumes vary as a linear function. The cell edges of nine analyzed specimens of loellingite and saffiorite show fair agree- ment with synthetic diarsenides of equivalent composition, after corrections are made for the eftect of nickel and sulfur on the cell edges.
INrnopuctroN In the course of an investigation of part of the system Co-Ni-Fe-As (Roseboom,1957, 1958, 1959), the cell edgesand compositionranges of synthetic triarsenides and diarsenideswere determined. The triarsenides (skutterudites) were discussedin a previous paper (Roseboom, 1962)' The data on the synthetic diarsenidesand their correspondenceto data for the natural diarsenidesare the subject of the present paper. The arsenid.es,of Co, Ni and Fe exhibit a wide range of solid solution' Figure 1 illustrates the nomenclature and the approximate extent of Co, Fe and Ni substitution in the diarsenidesand triarsenides.The most re- cent and complete classifi.cationof the diarsenidesof Co, Ni and Fe is that of Holmes (1947) which will be followed in this paper. In this classifi- cation, the nickel-rich diarsenidesare the dimorphs, rammelsbergiteand pararammelsbergite. The iron-rich diarsenides are called loellingite. Cobalt-iron diarsenideswith a Co: Fe ratio of about 1: 1 are called saffiorite. Holmes arbitrarily placed the boundary between saffioritesand loellingites at 70 mol per cent FeAsz. In addition to the Co, Ni and Fe substitutions, various workers have reported diarsenides with less arsenic than that required by the theo-
I Publication authorized by the Director, U. S. Geological Survey. 2 This work was begun at Harvard University as part of a Ph.D. thesis and continued at the Geophysical Laboratory, Carnegie Institute of Washington' 271 EUGENE H, ROSEBOOM
retical composition.For this reasonthe range of arseniccontent in some synthetic diarsenideswas also investigated. No work was done on pararammelsbergite, the low-temperature di- morph of rammelsbergite.Yund (1961) has investigatedthe pararam- melsbergite-rammelsbergitetransition in detail.
Ansaxrc CoNrnNr on SyNrnrrrc DrensBNrtrs Synthesis. The materials used and details of the experimental tech- niques have beendiscussed in a previous paper (Roseboom, 1962).In addi- tion, spectrographicanalyses are given by Swansonet al. (1960) of CoAs2, FeAs2,NiAs2 and (Co6.5Fe65)As2 synthesized by Roseboom. The maximum arsenic content of Ni diarsenide and Fe diarsenide was investigated by means of "tube-in-tube,' runs. In these runs, iron or nickel was placed in a small open tube within the larger sealedtube. The larger tube contained sufficient arsenic to maintain a vapor phase in equilibrium with solid arsenic.The amount of arsenicthat reactedwith the iron or nickel was determined from the increasein weight of the inner tube. The samplewas regroundand the processrepeated until a constant compositionwas obtained. Homogeneityof the phasewas confirmedby means of the ore microscope. The maximum arsenic content of Co diarsenide could not be deter-
CoAs3_x CoAsa SKUTTERUDITE SAFFLORITE
NiAs 3-x FeAs3-x/ NiAs, FeAs2 RAMMELSBERGITEA LoELLTNGITE PARARAMMELSBER GITE A B Ftc. 1 (A). The extent of Co, Ni, and Fe substitution in synthetic skutterudite solid solution at 800'C. is shown by shading Almost atl analyzed natural skutterudites fall in or close to the shaded area. Fro. 1 (B). The approximate extent of Co, Ni and Fe substitution in the natural diarsen- ides is shown by shading. At 800'c. the solid solutions cover all of the triangle except for an area approximately that shown by dashed lines. CO.NI-FE DIARSENIDES 273 mined in this mannerbecause it is not stablein the presenceof crystalline arsenic. Instead, samples of different arsenic content were annealed and the products examined to see whether or not any cobalt skutterudite (CoAsa-x) was present.When cobalt skutterudite appearedin the sample, the arsenic content of the sample was greater than the maximum arsenic content of Co diarsenide. The minimum arsenic content of Co, Ni and Fe diarsenideswere de- termined in the same way as the maximum arsenic content of Co diar- senide.In this case,the presenceof the monarsenideindicated when the arsenic content of the sample was lessthan the minimum arsenic content of the diarsenide. Although pure Co and Fe diarsenidescould be synthesized readily at 800o C., some diffi.culty was experiencedin forming homogeneousram- melsbergite.Niccolite (NiAs) formed first and then reacted with arsenic to make rammelsbergite. This resulted in grains with niccolite cores armored by rammelsbergitecrystals. Similar inhomogeneity in synthetic Ni arsenideshad beennoted previouslyby Beutell (1916),Holmes (1947), and Heyding and Calvert (1960).In the presentstudy, a singleregrinding and reheating produced a homogeneousrammelsbergite, except for one very large sample which required additional grinding. In samples with arsenic in excess,a second regrinding and reheating caused no further increasein arsenic content of the rammelsbergite. Range of arseniccontent. The range in arsenic content for loellingite at 800' C. is at Ieast FeAsr.sso+o.oozto FeAsz.o00l0.00r. Three "tube-in-tube" runs with iron in the inner tube produced loellingite with the composi- tion FeAsr.ee610.00ralter 12 days, FeAs2.00rt0.00rafter 19 days, and FeAsr.ggs+o.oorafter 27 days,respectively. The last of thesewas reground and heated for another 12 days with no further changein weight. Runs of FeAsl.ees+6.662and FeAsr.seo+o.oozproduced homogeneousloellingite, but runs of FeAsr.gzo+o.oozand lower in arsenicproduced loellingite and an iron monarsenidephase. The limits on aII of these compositions are based on the precision with which the samplescould be weighed. Examination of polished sectionsof samplesunder the polarizing microscopewould prob- ably have detected one part in 10,000of a secondcrystalline phase. Heyding and Calvert (1960) sublimed excessarsenic from an alloy- arsenic mixture in the Fe-As system at 400o C. The final composition corresponded to FeAs1.e3.Assuming that their final product was com- pletely homogeneous,this indicates that at lower temperatures a greater deviation from stoichiometric proportions is possiblethan at 800' C. Rammelsbergite was found to be stoichiometric within the limits of errors of the investigation. "Tube-in-tube" runs with nickel in the inner tube contained niccolite armored by rammelsbergite crystals after 19 274 EUGENE H. ROSEBOOM
days at 800o C. Regrinding and six more days of heating at 800oC. gave compositionsof NiAs1.ee8i0.00r,NiAs1.eee16.60r, and NiAsr.oor+o.oor.A third grinding and seven more days of heating at 800o C. gave NiAsl.eee+s.s01, NiAs1.ee31s.661,and NiAsr.ee6l0.00r,respectively, for the same three runs. Polished sections indicated that these runs were homogeneous.A large run containing almost a gram of Ni after two regrindings and reheatings had combined with more than 2 grams of arsenic to give a composition of NiAs1.eee31s.se65.A simple sealedtube containing material of the composi- tion NiAs2.s60r0.002resulted in only rammelsbergite after two regrindings. A run of NiAsr.ggoro.o62and runs lower in arseniccontent, after two re- grindings and reheatings, still contained rammelsbergite and niccolite Thus rammelsbergiteis very near NiAs2 in composition. As explained above, simple sealed tubes were used for determining both maximum and minimum arsenic content of Co diarsenide. Runs of CoAs1.ee6+e.6orand CoAsr.e80r0.002compositions produced a singlehomo- geneousphase. A run of CoAs2.66616.eozproduced a diarsenide plus a trace of skutterudite while runs of CoAsr.seo+o.oozand lower arseniccontenr pro- duced a diarsenidephase plus a cobalt monarsenidephase. No changein d-values with the variation in arsenic content of loelling- ite could be detected. Four specimensof loellingite, one made with excess crystalline arsenic present, two with compositions of FeAsr.eeand FeAs1.es,and one sample with both loellingite and a trace of an iron rnonarsenidephase present, were measuredas describedin the section on r-ray measurements.The (120),(101), (210), and the (111)d-values were measured. If any systematic variation in d-value with arsenic content exists,it is too small to be detected when superimposedupon the random errors in measurement. Heyding and Calvert (1960) were also unable to detect any variation in d-values with arseniccontent in loellingites.
Co:Ni:Fe Rarros oF SyNTHErrcDTARSENTDES Synthesi.s.Homogeheous Co-Fe and Fe-Ni diarsenide solid solutions were made from the elementsor from mixtures of the end-memberphases at 800oC. in runs ranging from 60 hours to 36 days. The Co-Ni diarsenide phasesrequired one or two regrindings and reheatings before homogene- ous phaseswere produced. Care was taken to keep the mechanicalloss of material as small as possible.Because the sampleswere fine-grained mix- tures of phases which were similar in their physical properties, any material that was lost would probably be of about the same composition as the bulk of the sample. Becauseof the difficulty mentioned above in making rammelsbergite, runs of CoAsz mixed with NiAs2 produced homogeneoussolid solutions more readily than the corresponding mix- tures of pure elemental phases and were used throughout the Co-Ni CO-NI-FE DIARSENIDES 275 diarsenide series.Even in these runs, cobalt-rich skutterudite and nicco- lite formed metastably along with the stable Co-Ni diarsenide solid solu- tion. With regrinding and reheating the skutterudite and niccolite first diminished and then disappeared.The diarsenide peaks did not change in position as the amounts of skutterudite and niccolite diminished. Thus the composition of the diarsenide should be about the same, whether or not a small amount of skutterudite and niccolite remained undetected. Rangein Co: Ni Fe ratios. At 800oC there is extensivesubstitution of Co, Ni, and Fe among the diarsenides. Complete solid solution series exist between CoAszand NiAsr and between CoAszand FeAsz.The series between NiAss and FeAszis interrupted by a solvus, which probably ex- tends into ternary compositionsas shown in Fig. 2. CoAs.
222 2t9 223 220 224 ?21 260 NiAs. FeAs.
Frc. 2. Compositionsinvestigated in the system CoAs2-NiAsa-FeAsz.Circles indicate compositionof samples.Numbers correspondto samplenumbers used in the text and in Table 2. The dashedline indicatesthe possibleextent of tlie solvusat 800" C. The solws is known to +l.o/son the NiAxrFeAsr sidebut its shapeis only guessedat from the fact that d-valuesof two diarsenidesappear in sampte139. The d-valuesof all other samplesin- dicateda continuoussolid solutionoutside of the solws' 276 EUGENE H. RoSEBooM
The evidencefor the existenceof the solidsoiution series consists of the fact that the dimensionsof the interplanar spacings(and consequently the cell edges)are smooth and apparently continuous functions of com- position.In Fig. 3, the d-valuesof the (120),(101), (210), and (lll) r-ray diffraction peaks are plotted as a function of compositionfor the three binary series.The solid solution seriesbetween CoAsz and NiAs2and be- tween CoAs2and FeAs2are completeas shown by the continuouschange in d-valueswith composition.In the seriesbetween NiAsz and FeAs2,the d-values change continuously from 100 per cent FeAszto 31 per cent FeAsr. Beyond this point, the d-values remain unchangedbut the in- tensitiesof the diffraction peaksdecrease toward NiAsz.In addition, the peaks of a different phase appear and increasein intensity toward NiAs2 but have a constantd-value. If the curvesof d-valuesversus composition are extrapolatedfrom 31 per cent FeAs2to 100per cent NiAszas shownin Fig. 3, the d-valuesof the secondphase would intersect them at about 7.5per cent FeAs2. The break in the NiAsz-FeAsrseries at 800' C. was found to be smaller at 850oC. and wider at 750' C. Samplesfrom the two-phaseregion were reheatedat 750" C. and 850' C. for 18 days and 7 days,respectively. The
Frc. 3. The efiect of composition on the (101), (111), (120), and (210) d-spacingsof the Fe-Co, Co-Ni, and Ni-Fe diarsenides.Near CoAszthe (111) Iine splits into (111) and (I1l) and the (101) Iine splits into (101) and (T01) as the symmetry changes from orthorhombic to monoclinic. Between NiAsz and FeAs: there is a two-phase region where rammelsbergite coexists with Ni-rich loellingite. All samples were heated at 800" c. and quenched. com- positions are in moi per cent. CO-NI-FEDIARSENIDES 277 rl-valuesin the 750' C. samplecorrespond to two phases,one at 6.5 per cent FeAszand the other at 33 per cent FeAsz.The d-valuesin the 850' C. samples corresponded to a phase with the composition 8.5 per cent FeAsr and 26 per cent FeAsz. The fact that the extent of solid solution increased with rising tem- perature on both sides of the break in the seriessuggests to the writer a solvus rather than a transition loop. By projection, the crest of the solvus shouldlie near 900o+ 25oC. and 15* 5 mol per cent FeAs2,the solid solu- tion beingcomplete above this temperature. From the extensivesolid solutionin the binary systems,one would ex- pect that at 800o C. there is also extensive solid solution among diar- senidescontaining all three metals,cobalt, iron, and nickel.The composi- tions shown in Fig. 2 wereinvestigated. Homogeneous diarsenides were obtained from runs with the following ratios of Co:Ni:Fe: Run 238, 1:1:1; Run 192,3:3:14; Run 193,3:9:28; Run 194,9:3:28. The last three were synthesizedin the presenceof solid arsenic. In addition' pre- Iiminary r-ray examination of seven other ternary compositions shown in Fig. 2 indicated a single diarsenide and a small amount of unreacted skutterudite. These ternary diarsenidesalso indicated a smooth change in d values with composition. Had these runs been reground and re- heated,they would probably have also producedhomogeneous diarsen- ides. Becauseof the solvusin the NiAsz-FeAszseries, one would not ex- pect every ternary composition to produce a homogeneousdiarsenide. One run (No. 139) with a ratio of 1:4:l producedtwo diarsenidesnot very different in d-values from those on the solvus in the seriesNiAsz- FeAsr.Thus the solvusextends at least beyond that compositiontoward the CoAsz-NiAszsideline.
X-nay Cnvsrar-r-ocRAPHY Structuresand spacegroups. Ail the Co, Ni, Fe diarsenides,with the ex- ception of pararammelsbergite,probably possessthe marcasitestructure (C18 type) or someslight distortion of it. Buerger(1932) determined that loellingite had a marcasite structure with space group Pnnm (in the orientation used here). Peacock(1941) confirmed this spacegroup and Peacockand Dadson (1940) found the same spacegroup for rammels- bergite. Kaiman (1946) confirmed this spacegroup for rammelsbergite and reportedthat it, like loellingite,had a marcasitestructure. Becausecomplete solid solution seriesextend from NiAsz to CoAszand from FeAsz to CoAs2, CoAsz is almost certain to be isostructural with rammelsbergite and loellingite and thus have a marcasite structure also. In the caseof CoAszhowever, the marcasitestructure is apparently dis- torted enough to change the orthorhombic symmetry to monoclinic. 278 EUGENE H. ROSEBOOM
Quesnel and Heydin1 0962) report a space group of Phfc for CoAsz (which would transform to P21fn ior the unit cell used in the present paper). Peacock (1944) studied Weissenbergphotographs of a natural saf- florite intermediatein the CoAs2-FeAsrseries and found the spacegroup tobe P2/m. He reported that it had monoclinicsymmetry but with a B angle of 90o.The structure was probabiy analogousto that of loellingite and the lower symmetry was due to iron and cobalt not occupingequiv- alent sites.Berry and Thompson (1962,p. 129) noted that Peacockde- tected interplanar spacingswhich should be absent with space group Pnnm and thesespacings produce lines too weak to be observedby means of x-raypowder methods. X-ray measuremenls.For measurementson the diarsenides,four of the strongestr-ray diffraction peakswere used: the (120), (101), (210), and (111) peaks. These four were chosenbecause they could be accurately measuredfor ali compositionsin the solid-solutionseries. All four peaks werebetween 30o and 41" 20 ior Cu radiation. The dimensionsof the unit cells were calculatedfrom the (120), (101), and (210) peaks. Different internal standardshad to be used for difierent compositionsto prevent diarsenidepeaks from overlapping the peaks of the internal standards. The CoAsz-FeAszseries and the iron-rich half of the FeAsz-NiAs2series were run on the diffractometer at ] degreeper minute, with quartz as an internal standard.The CoAsz-NiAs2series and the nickel-richremainder of the FeAsr-NiAszseries were run at $ degreeper minute, using either siliconor sodium chlorideas an internal standard, the choicedepending on the spacingsin the individual cases.The cell edgesused for the internal standardswere those given by Parrish (1953)and are as foilows: silicon (5.$A62 A), sodium chloride (5.63937A), quartz (a:4.981 fi c:5.4064 A). Two measurementswere made on eachline, one with the goniometer driving toward high 20 angles and one with the goniometer driving toward low 20 angles.The probableprecision of measurementis discussedin the sectiontitled "Cell edgesand volumesof solidsolutions." Cell ed.gesoJ CoAs2, NiAsz and FeAsz. X-ray data for the diarsenides show good agreementfor the Co, Ni and Fe end-members.Table 1 sum- marizesthe cell-dimensiondata for diarsenidesin the literature for com- parison with the resultsof the presentwork. The earliestwork is that of de Jong (1926), who claimed that the patterns of loellingite,rammels- bergite and safforite were identical. He gave a single set of lattice con- stantswhich failed to agreewith thoseof subsequentworkers on the three minerals.The causeof this discrepancyis unknown. Peacock and Nlichener (1939) presented*-ray data for what they believed to be rammelsbergite.Later, however, Peacock and Dadson CO-NI-FE DIARSENIDES 279
'Iasr,a 1. Cnr,r,DrurNsroNs (rN A; ol Reuurrsnrncrrn, Lorr,rrNcrrn, Selrlonrru, eNn Coeart DtAnsnurno
Reference c Material
Rammelsbergite-NiAs: deJong (1926) 487 5 81 6.36 Natural Peacockand Dadson (1940) 479 5.79 3.54 Natural Yund (1961) 4 757 5.793 3 544 Synthetic Heyding and Catvert (1960) 476 579 354 Synthetic Swanson ?, al. (1960) 4.759 5 797 3 539 Synthetic Present work 4 75510.003 5.801+0 004 3 542+0 003 Synthetic Loellingite-FeAs2 deJong (1926) 487 581 6 36 Natural Buerger (1932) 5.26 5.93 2 85 Natural Peacock(1941) 529 5 ,98 2 87 Natural Heyding and Calvert (1960) 5 300 5.982 2.882 Synthetic Swanson rl ol. (1960) 5 .300 5 983 2 882 Synthetic Berry and Thompson (1962) s .3023 s.9818 2.8802 Natural Present work s 301t0.004 5.97910 005 2.882tO OO2 Synthetic Cobalt Diarsenide-CoAsr Rosenqvist(1943) 508 5.89 3. 10 Synthetic Heyding and Calvert (1960) 5 005r s.87 3.11r Synthetic Swaonsonet al,. (1960) 5 047 5 872 3 127 (P:90o51') Synthetic Quesneland Heyding (1962) 4 894t s.885 3 1672(P:90432') Synthetic Present work 5.051t0 002 5.87310 002 3.12710 001 Synthetic (B:90o27')
AII measurements prior to 1946 were changed from kX units into Angstrom units. Orientations are not always those of original papers but follow the recommendations of Buerger (1937). Measurements by Swanson (1960) el al' were made on materials synthesized by Roseboom.The t values for NiAsz and FeAs: are standard deviations as describedin the text. The t values for CoAsr are standard errors oI tbe means for four samples. t These values are one-half the values given by Heyding and calvert (1960) in their original paper. z The original valuesof Quesneland Heyding (1962)arc a:5.805, b:5.885, c:5.853, E:114.11,. Their cell can be transformedto that usedbv the miter by meansof the matrix (101/0101101).
(1940) compared these data with authenticated rammelsbergitefrom r islebenand Schneeberg,Germany, and concludedthat the material de- scribed in 1939was actually an NiAsz polymorph which they named para- rammelsbergite.The measurementsof Yund (1961), Heyding and Cal- vert (1960),and Swansonet al. (1960)on synthetic NiAsz are all within two standarddeviations of the value obtainedby the writer. Buerger (1932) analyzed the structure of loellingite, and gave the cell edgeslisted in Table 1 for natural loellingitefrom Franklin, New Jersey. Peacock(1941) gave d-values and cell dimensionsfor a natural loeilingite also from Franklin, New Jersey.Berry and Thompson (1962) gave cell edgeson Franklin loellingiteredetermined by R. J. Traill. Theseplus the measurementsof Heyding and Calvert (1960)and Swansonet al. (1960) on synthetic material are all within two standarddeviations of the value obtainedby the writer. Co diarsenideis apparently monoclinic.T. R. Rosenqvist(1953) in re- porting the data of A. n{. Rosenqvist (1943) gave only the cell edges which are listed in Table 1. Heyding and Calvert (1960)indexed CoAsr 280 EUG]JNEH. ROSEBOOM on the basisof an orthorhombiccell with the a and c edges(c and Din the orientationin the original paper) approximatelytwice thoseof the mono- clinic cell. By using the larger orthorhombic cell, they obtained addi- tional hkl's to account for the lines which could not be explained by a smaller orthorhombic cell. However, even this larger cell only provided onehkl for the very strong line at 2.41h. This line, which they reported as broad, is actually two distinct lines as shown in Fig. 3' Swansonel o/. (1960), starting with monoclinic cell dimensionsgiven by the writer (Roseboom,1958) indexed a sampleof the writer's synthetic CoAszand obtained the values given in Table 1. Quesneland Heyding (1962) in- dexed CoAs: by direct comparison of the five or six strongest lines with RhPz and RhSb2.This produceda monocliniccell which is related by a simple transformationmatrix (lU/010/1O1) to the cell of Swansonet al. (1960)and the writer. Swansonet at. (196O)indexing accountsfor all of the observedlines exceptsix very weak ones.Quesnel and Heyding ob- servedtwo of these six lines, their (102) and (213)_lines.These ind_ices transform by meansof the above matrix to (3/2O 1/2) and (5/2I I/2) which suggeststhat perhapsthe o and c axesgiven in Table 1 should be doubled. I{owever, the smaller cell of Swansonand the writer will be used in this paper to facilitate comparisonswith the orthorhombic diarsenides.This cellis similar to the cellsof the orthorhombicdiarsenides but is slightly distorted (B:go' 27')' rJntortunately, no crystals of CoAsz suitable for single crystal studies were synthesizedduring the present study. The presentstudy indicatesthat aithough the Co-rich diarsenidesare probably monoclinic,they form a completesolid solution with the ortho- rhombic Ni and Fe diarsenidesat 800" C. The evidencefor this was found in the solid solution seriesbetween FeAsz and CoAsuand betweenNiAsz and coAsz.In both series,the (101)and the (111)peaks were observed to split into two peaksof equalintensity near the cobalt end of the seriesas shown in Fig. 3 and Table 2. In x-ray powder photographsof cobalt saffiorite,the (101) and the (111) line each appearedas a single broad and somewhatdifiuse line. However, with the *-ray diffractometer,split peaksof about equal intensity were clearly observed.One can interpret this splitting of lines as a degenerationof the orthorhombic cell to a monocliniccell. Such a symmetry changewould causeall peakswith the indices (h)l) anc)(hkl) to split into (h}t) and,(k}l), (hht) and (ilkl), rc' spectively.Thus the_(101)peak of the orthorhombic phaseswould split into the (101) and (101) peaks,and the (111) peak would split into the (111) and lttt;. fne sizeof the observedsplit would correspondto a 0 angle of abort 9Ao27'for CoAsz.The accuracy of this frgurefor the B angle is uncertain due to the overlapping of the split peaks on the difiractom- CO-NI-FE DIARSENIDES 281
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The last figure in eachequation is the standarderror of the estimate.The standarderror of the estimateis: CO-NI.FEDIARSENIDES 283 Standarderror of estimate: -"!- l/ N-n Where R is the difference between calculated and measured cell volume, 1/ is the number of samples,and z is the number of constantsin the equation. Thus (lil-z) equalsnumber of degreesof freedom. The linear relationshipapparently holds for ternary compositionsalso. A least squaresplane was fitted to the samplesused in calculatingequa- tions (2), (3) and (4) abovewith the following result: (5) V:0.01s1X+O.06+2v +9r.s3 + 0.r2 Equation (5) was then usedthe calculatecell volumesfor samplesNo. 238, 194, 192, and 193 in Table 2. The measuredcell volumes less the calculatedcell volumes were -0.02, +0.15, -0.22, and *0.95 At, re- spectively,for the four samples.The largedifference for sampleNo. 193is probably due to the overlapping(210) and (111)peaks. Statistical lreatment.An examination of the precisionof the r-ray meas- urementson the diarsenidesshould answer two related questions.How much reliancecan be placedon the data?Is there a linear relationshipbe- tween cell volume and composition?If the hypothesis of a linear relation- 575 525 - 500 i47s 475 o< 3so 350 325 300 980 940 920 592.O I 900 90_o FeAsz FeAsz Frc.4. The efiect of composition on the cell edges and cell volumes of Fe-Co, Co-Ni and Ni-Fe diarsenides. CeII edges were calculated from the data illustrated by Fig. 1 and given in Table 2. Compositions are in mol per cent. 2U EAGENE H, ROSEBOOM ship is correct.the amount of scatter in the cell volumesabout the least squaresplane should be approximately equal to the scatter in the cell volumes of a large number of samples with the same composition. Thus the standarderror of the estimateof equation 5 should be about equal to the averagestandard deviation obtained when a number of different sam- ples of diarsenides with the same composition are measured by the method described;that is, one completeoscillation of the diffractometer over the (120),(101) and (210)peaks. Unfortunately, statistically rigorous conclusionscannot be drawn from the data becauseof the small number of repeatedmeasurements and the many sourcesof error. However, the writer feelsthat an attempt to esti- mate the error is better than noneat all. Somesources of error are certain to be relatively small when compared with others and will be neglectedin the following analysis. With repeated measurements,each of the three internal standards would probable give slightly different average cell edgesfor the same diarsenide but these systematic errors are relatively small. If the errorsin weighingout the materialsaltered the composition by as much as 0.05 per cent, the errors in cell edge that could result would ra-ngefrom about 0.0005 A in the NiAsz-FeAszseries to about 0.00002A. Thus, weighingerrors might make a small, though noticeable contribution, to the scatter in the measurementsof the o and c edgesin some composition ranges. However, for simpiification, all errors are assumedto be in the r-ray measurements.The relative intensity of the peaksvaried to someextent with compositionas can be seenfrom Table 2. Similarly,the backgroundradiation was lowest with NiAszand highest with CoAsz.However, in all casesthe peakswere strong and easyto measure. Standard deviationsfor the o-ray data were estimatedin three ways. Each of these estimatesadmittedly has some undesirablefeature. The usual method of calculating a standard deviation was used for four sam- ples of CoAs2and four samples of loellingite (but with difierent arsenic contents). These standard deviations do not invoive factors such as weighingerrors which would causeadditional scatterin samplesof solid solutions. Also, four samples are too few for a reliable estimate. The secondmethod provides an averagestandard deviation basedon all 32 samplesof diarsenides.This averagestandard deviation can then be ap- plied to individual samplesif we assumethat the standarddeviation does not vary greatly with composition.The averagestandard deviation for the cell volumescan be comparedwith the standarderror of the estimate of equation(5) to seeif the cellvolumes change linearly with composition. Finally, a maximum value for the average standard deviation for each cell edge and d-value can be derived from the standard error of the esti- mate of equation (5). CO-NI-FEDIARSENIDES 285 A standard deviation for the cell volume of CoAszwas obtained from measurementsof four difierent samples,each sample having been given a single complete oscillation on the diffractometer. Standard deviations for the four oscillations across each peak were used to calculate standard deviations for the cell edgesand the cell volume by the usual methods for combining independent random errors according to the law of propaga- tion of errors (for example,Scarsborough, 1955, Beers, 1953). The results are shown in a of Table 3. Four different samplesof loellingite were handled in a similar way (see d of Table 3). The four samplesof loellingitediffered in arseniccontent, ranging from FeAs2.6eto between FeAsl es and FeAsr.sz.However, as mentioned in the section on arseniccontent, the d-values of thesefour did not differ significantly. A standard deviation calculated from these four specimensshould be either equal to or larger than any standard deviation for stoichiometricloellingite, depending on whether or not the four sam- ples really have the samecell edges. Two methods of estimating an averagestandard deviation for all 32 sampleswere employed and both gavevery similar results.Both methods TnerE,3.Esuuarro SrlNoant DnvreuoNs(S.D.) ron e Srwcro Oscrrlerror ol rrm DrrlnacroMETER (An oscillation consists of the average of two measurements, one with the goniometer driving toward larger values of 20 and. one toward smaller values) S.D. for d-values S.D. for cell edses " b'u' lor (x10-3A) (x10-s A) volume (x1o-3 A3 (2ro) (120) (101) FeAs: a. S.D. of 4 samples 0.43 0.86 0.65 1.3 2.6 1.0 55 b. Using average S.D. 0.59 0,58 0.57 1.6 t.9 0.9 48 c. Using standard error of estimate 1.48 1.45 t.43 4.0 4.8 2.3 t20 CoAsz d. S.D. of 4 samples 1.2 0.9 |.l 3.3 3.0 2.0 97 e. Using average S.D. .53 .55 .62 1.6 1.9 1.1 51 f. Using standard error of estimate 1.24 r.29 1.46 3.8 4.5 2.6 t20 NiAsz g. Using average S.D. .49 .53 .72 1.4 1.9 1.5 h. Using standard error of estimate 1.02 1.10 |.49 2.9 3.9 3.1 120 286 EUGENEH. ROSEBOOM are describedby Wilson (1952,p.244-245).In the first method the rela- tionship between range and standard deviation in a normal population is used.For a pair of measurementsthe standarddeviation shouldbe equal to 0.886times the range.Although the rangeof individual pairsof meas- urementsvaries widely, an averagevalue for the rangecan be calculated from the 32 samples.The secondmethod makesuse of a formula which for pairs of measurementsreduces to: 7 /zDz-; tv whereD is the differencebetween the two measurementsin eachpair and n is the number of pairs. Inasmuch as this standard deviation appliesto singlemeasurements, it must be multiplied by l/ t/2 to obtain the stand- ard deviationfor a completeoscillation (two measurements). The averagestandard deviationsin degrees20 for the (210), (120) and (101) peaks were then convertedinto Angstroms for FeAs2,CoAsr and NiAs2,and standarddeviations for the cell edgesand volumeswere calcu- lated accordingto the law of propagationof error. The resultsare shown in b, e and g of Table 3. The above estimatesof the averagestandard deviation are probably too low. Oscillation of a single slide producesa smallerscatter in the measurementsthan duplicate measurementsof two difierentslides of the samesample. In 15 pairs of measurementson a syn- thetic digenite (CueS6),the writer found that remaking the slide after eachmeasurement increased the standarddeviation by about 50 per cent over that obtainedfrom repeatedoscillations of the sameslide. Probably somesimilar factor should be applied to the valuesin lines b, e and g of Table 3. In view of this and the additional sourcesof scatter previously men- tioned, the difierencesbetween the estimatedstandard deviationsof the volume (a, b, d, e, g, of Table 3) and the standarderror of the estimatefor the leastsquares plane are of doubtful significance.If the cell volumesdo not vary linearly with composition,measurements of greater precision than those of the present study will be necessaryto detect the discrep- ancy. Maximum values for the standard deviation of the cell edgesand d- values can be approximatedby assumingthat the standard error of the estimatefor the cell volumesoI 0.12A3 equalsthe averagestandard devi- ation; that is, all of the scatteris random error. The standard deviations of the (120), (101) and (210) peaks (and consequentlvthe cell edges) shouldbe in the sameratios as in b, e and g of Table 3. Consequently,the standard deviations in the cell edgesand peaks that would produce a standard deviation in the volume of fl.12 A (th. standard error of the CO.NI-FDDIARSENIDES 287 estimate) can be easily determined. These values are given in c, f and h of Table 3. In Table 1, the standarddeviations for the cell edgesgiven for FeAszand NiAsz correspondto c and h of Table 3, respectively'Those for CoAs2correspond to one-half of the valuesin d or f of Table 3 because these cell edges are the average values from four samples of the same composition. Retationship to loellingite and marcasitestruclules. Buerger (1937) and Rosenqvist (1953)have recognizedtwo distinct divisions of compounds with the marcasitestructure, a marcasitegroup and a loellingitegroup' The marcasite group all have cfb ratios of 0.60 to 0.63. Whereas the Ioellingitegroup all have ratios between0.47 and 0.53, rammelsbergite belongsto the marcasitegroup with a ratio of 0.61.Cobalt saffioritehas a ratio of 0.53 and belongsto the loellingite group if its small departure from orthorhombic symmetry is ignored. The ratios intermediate be- tween the two groupsfall in the region of the solvusin the Ni-Fe series and in the middle of the Co-Ni series.The solvusprobably intersectsthe middle of the Co-Ni seriesat lower temperatures.Thus it appearsthat the phaseswith ratios intermediatebetween the loellingiteand marcasite groups require higher temperaturesto be stable than those within the groups. Narunar, Drensnwrpos Composition range. Some chemical analyses of natural diarsenides of Co, Ni, and Fe have indicatedthe presenceof small amountsof S, Sb' Bi, Cu, Ag and Pb. Such "impurities" could be due to either the presenceof small amounts of other mineralsin the diarsenideor atoms of theseele- mentsproxying for other atoms in the structure.At present,only the sub- stitution of S for As has been demonstrated.The remaining elements listed above rarely aggregatemore than one or two weight per cent. The extent of substitution of Co, Ni, and Fe among the natural diar- senidescan be seenfrom Fig. 5 which containsthe analysescollected by Holmes (1947),those made by Jouravsky (1959),and those summarized by Godovikov (1960).one group of analyseslie near the NiAsz corner. These representthe rammelsbergitesand pararammelsbergites.The re- maining analysesare distributed near the CoAsr-FeAszside and represent saffiorites and loellingites. No saffiorites containing more than about 80 per cent CoAszhave beenreported. AII but one of the saffioritescontain less than 8 mol per cent NiAsr, while a few loellingites apparently run as high as 30 per cent NiAs2,if one assumesthat the analyzedmaterial was homogeneous.The distribution of the analysesdoes not indicate a break between saffiorite and loellineite. It was for this reason that Holmes' 288 EUGENE H. ROSEBOOM placement of the boundary at the 70 per cent FeAs2line was necessarily arbitrary. The natural separationof the diarsenidesinto rammelsbergiteson the one hand and the loellingite-saffioriteseries on the other is probably due to the expansionat lower temperatureof the solvuswhich was observed at 800o C. in the synthetic diarsenides.Assuming that the three deter- minationsof the loellingiteside of the solvusat 750o,800o and g50owere near equilibrium, one could reasonableexpect the loellingite field along the NiAsrFeAsz side to extendfrom FeAszto about $ to $ of the way to NiAszat room temperature.The inversionof rammelsbergiteto pararam- melsbergitemight further reducethe loellingitefield becausethe solubil- Co+Nl+FB -\. \a + vo \ I !7 I 50' '/o I \ I I 435 t4a Ni re Co+Ni+Fc Co+ Ni+ Fe Frc. 5. Co'Ni'Fe atomic ratios of analysed natural diarsenides.Black circleswith num- ,,P" bers are after Godovikov (1960). Black circle labeled is from Peacock (1944). Open circles are from Holmes' (1947) compilation. Crosses are Jouravsky,s (lg5g) analyses. Short dashes show approximate extent of sclrrus observed at 800o C. Long dashes suggest the extent of the solvus at a much lower temperature as a possible explanation for the con- centration of analyses near the Ni corner and near the Co-Fe side. 29O EUGENDII. ROSEBOOM saffiorite or loellingite.Eilsworth (1916)made a similar observationon ore from the Kerr Lake Nline, ontario. His etched specimenshowed three minerals and the chemicalanaryses (after subtra.ling urr.no-pyrite) in- dicated a diarsenidecomposition near 2r per cent coAs2, 7i per cent FeAszfor the remainingtwo minerals.No nickel waspresent. Todd's analyses and observationson his specimens5 and 11 indicate a possible secondbreak in the seriesnear 60 per cent coAszand 40 per cent FeAs2. Both specimensconsist predominantly of saflorite and loellingite according to Todd. Thompson (1930)re_examined specimen 5 and stated that he "was able to confirm his (Todd's) impressionthat the cobalt min- eral was orthorhombic and that the other predominant mineral was loellingite." After subtractingthe chemicalcompositions of the other ob- served minerals,one is left with a total compositionnear 61 per cent coAs2, 39 per cent FeAs2for the saffiorite and loellingite. This ca., be e*- plained by the presenceof one minerarricher in cobariand anotherpoorer in cobalt than the total given. x-ray d'ata on naturar sffiorite and. roeilingila. Sampres of anaryzed saffiorite and loellingitefor which the cell edgeshave beendetermined are rare. Eight suchsamples have beendescribed by Godovikov (1960) and one by Peacock(1944). The measuredcell edgesand someatomic ratios for thesesamples are given in table 4 rn Fig. 6, the cell edgesof the minerarsand the synthetic phaseshave been plotted as a function of 100.co/(cofF"). ihe ceil edgesof the mineralsare shown as crossesand the cell edgesof the synthelic phare, are open circlesconnected by a solid line. The solid circlesare the cell edges of numbers 3095 and 3119 as determined by Godovikov. These specrmens appear to have been incorrectly indexed and the revised cell edges derived from Godovikov's d-values are shown as crossesfor the samecomposition. The a and b cell - edgesof the natural diarsenides,with the exceptionof Peacock's specimen,are smarlerthan the cell edgesof synthetic pirasesof equivalent Co/(Cof Fe) ratios. Similarly, the c edges oi tt" natural diarsenides,with the sameexception, are iarger than those of the equiv- alent synthetic phases.rn addition to the major constituents,the ele- ments, Ni, S, Sb, Bi, Cu and Au are reportedin someof the analyses.We will attempt to evaluate the reiative effect of the first four of theseele- ments on the cell edges.Cu is presentin only one analysis (3119).Au is present in three (486, 519, 520), but the maximum amount is onlv 0.2 weight per cent. r The effectof nickel on the cell edgesof saffioriteand loelringitecan be determined from'the data of Fig. 4 and rable 2. rf one plots-thesecell edges on a eoAsz-NiAs2-FeAs2mol per cent triangle o.r" .un draw linesof CO NI-F]J DIARSENIDES 6.OO b 5.90 5.20 o{ O.s @ o, 'octr u.J q) () 3.ro.= c f c 3.OO ..-"!o"^ + 02.866 2.90 20 40 60 80 CoAs2 FeAs2 Mol Percenf No. 519,21.3/s;No. 50,25.66Vo; No. 520,25.6616; No. "P," 44'816;No' 3095,64O3/s; Nc.3119,75.n!o. 292 EUGENE H. ROSEBOOM equalcell edgethat within the limits of accuracyare straight lines.These iines are essentially parailel but are more closely spaced as one moves away from the FeAszcorner. As a consequence,the efiect of a given per_ centage of NiAsz on a cell edge is not constant but depends on the Co/(Cof Fe) ratio. This can be seenin Fig. 6 where the dashedlines in- dicate the cell edgesof loellingite and saffiorites,with eight per cent of the Co and Fe atoms replaced by atoms of Ni. On the CoAsz-NiAsz-FeAsz triangle, the slope of the lines of equal a dimension is such that the change in cell edgedue to an increasein nickel content of one per cent is equiv- alent to an increasein the cobalt content of 1.6per cent. For the b and.c dimensions,the changeof one per cent in nickel content is equivalentto changesof 1.5and 2.0 per cent cobalt respectively.Thus one can make a correction for each cell edge by multiplying the molecular amount of NiAs2 by the appropriate factor and adding it to the value of l00Co/ (Co*Niff'e) determined from the chemical analysis. The resulting value of "equivalent CoAsz"is the content of CoAs2which, in a Ni-free co-Fe diarsenide, would result in the same cell edge as that of the Ni- ,,equivalent bearing diarsenide. Thus values of cobalt,,, determined separatelyfor eachof the three cell edges,can be appliedto the curvesof Fig. 4 or 6. The effect on the cell edges of sulfur substituting for arsenic can be handledin a similar way. Neumann et al. (1955)observed that surfur con- tent affected the d-values of loellingite. clark (1960) determined the effectof sulfur and cobalton the (101),(111), (120), and (210)d-values of synthetic loellingite.using cobalt content as one axis and sulfur content as the other, clark contouredthe d-valuesfor the four spacingsabove. He found that the contours were straight lines. rf one converts clark's data from d-valuesinto cell edges,one finds that contoursdrawn on the a (or b or c) edgesare also nearly straight lines. These contours are not parallel,however, but tend to converge.rf the contoursfor eachcell edge are extendedbeyond the limits of the diagram,one can locatean approxi- mate focal point. Hence one can closelyapproximate any contour by a straight line passingthrough the focalpoint. Therefore,given a particular co and S content,one can draw a line through it and the focal point along which the cell edgeis approximatelyconstant. rf one takes the composi- tion at which this line intersectsthe co axis and usesit as an "equivalent CoAs2"value, one can then determinethe value of the cell edgefrom Fig. 3 or Fig. 5. Thus the value of the "equivalent CoAs2',(C") correctedfor S can be expressedas follows: az-bx (6) C": CO-NI-FEDIARSENIDES 293 The letters a and b are the coordinatesof the focal point in terms of Co and S contents respectively,whereas x and z representthe ratios 100 Col(Co*Ni*Fe) and 100S/(As*S) respectiveiy. One can correctfor both Ni and S by replacingx of the equation(6) by expressionsfor the "equivalent CoAsz"content for Ni bearingdiarsenides. For eachcell edge,these expressions are simply: (7) CNi : mY where Y is equal to 100 Ni/(Co*Ni*Fe) and m is 1.6, 1.5, and 2.0 f'or the a, b and c edgesrespectively. Thus equating x of equation (6) with CNrof (7) and replacinga and b with the appropriateconstants, one ob- tains the following equations: (8) a edge: ?t <* r <1., J- )11. J-.\t^t!-Jt-e-4 C": 32.5* z (9) 6 edge: l4x I 2ly -f l48z Co: 14lz (10) c edge: 65x*130y-|2002 CC: In theseequations, x is the mol ratio, 100Co/(Co*Ni*Fe), y is the mol ratio, 100Ni/(Cof Ni*Fe), and z is the mol ratio, 100 S/(As*S). The valuesof "equivalent CoAs2"(C,, Caand C") which one obtains are then usedon the appropriatecurves of figure4 or Fig. 6. One may visualizethese corrections geometrically by consideringa tri- angular prism resting on its base as shown in Fig. 7. Co, Ni and Fe diarsenideslie at the cornersof the triangular baseand CoAsS,NiAsS and FeAsSat the cornersof the top. Within this prism, one may visualize familiesof surfaces,each composed of all compositionsthat have the same value for the a (or b or c) edge.The intersectionof sucha surfaceand the CoAsz-FeAsz-CoAsS-FeAsSside of the prism is a straight line as shown from Clark's data. Similarly the intersectionof the surfaceand the base is a straight line as can be shownfrom the data in Table 2. Thesetwo lines intersectat somepoint alongthe CoAsz-FeAs2edge. Thus it seemsreason- able, lacking any information to the contrary, to assumethat the surface approximatesa plane near the CoAsz-FeAszedge and is defined by the two intersectingstraight lines.This is the only assumptioninvolved in equa- tions (8), (9) and (10). Given the compositioncoordinates of any point on any plane of constant cell edge,one can determineby meansof these equationswhere that planeintersects the CoAsz-FeAszedge of the prism. With this information (i.e., the "equivalent CoAs2") one can obtain a 294 EUGI'NE H. ROSEBOOM numerical value for the cell edge from the data on the series,CoAs2- FeAsz. In Table 4, the cell dimensionslabeled "calc." were calculated by means of equations (8), (9) and (10) from the chemical analyses.The differencesbetween the measuredvalues and the calculatedvalues are still relatively largein many cases.Furthermore, there is no obviousrela- tion between the differencesand the Co, Ni or S content. Similariy, if one contours thesedifferences against any pair of these three elements, one finds no clear relation. It remained to be seenwhether Bi or Sb substituting for As would ex- plain the differences.One can crudely estimate the effect of Sb on the dif- NiAsS CoAsS ( CoAs. T----:_l_r+- 7___--____-__===>A Frc. 7. Illustration of method used to calculate cell edges for saffiorites and loellingites containing some Ni and S in solid solution. The shaded planes represent typical surfaces of constant cell edge within the solid figure. The intersections of the planes with the coAsa NiAs5FeAs2 base are parallel straight lines. The intersections with the coAsz-FeAsz- FeAsS-CoAsS side are straight lines that converge at point A as basecl on calculations ol cell edges from the data of clark (1960). If the surfaces are planes, they should all converge along a line A-A', parallel to the lines on the base. rf one knows the composition of the diarsenide, he can calculate by means of equations (s), (9) and (10) (he intersection of the plane containing that composition with the CoAg-FeAsz edge. The value of this intersec_ tion, called here "equivalent coAs2," is applied to the solid curves of Fig. 6 to obtain the cell edge. CO-NI.FE DIARSENIDES 295 T,lslr 4. Cnr,r,Encrs lln Snrc:rno Arourc Rerros on'Arnr,ysnn Nnruna.r, Sell'lonttrs exo Lont,r,tNcrtlns SpecimenNo. 486 3095 3119 100Co 282 4.35 122 20 90 20 95 22 93 448 61.50 72 66 Co*NilFe 100Ni ? 2.35 1.92 10 65 ? 3.96 3 .64 Co*Ni*Fe 100 s 8.8.1 3.15 654 7.75 2.94 2 0r 4.44 671 As*S 100sb ? o 42 0.84 As*S*Sb*Bi 100Bi 0 002 0.34 019 041 ? 007 007 As*S*Sb*Bi 100(As+s) 1.85 201 208 1.78 1.88 1.96 1.84 2.O7 Co*Ni*Fe Cell edges(in A) d meas, 5.238 5 285 5 271 5.214 5.24r .5.183 5.25 5. 131 5 097 10 004 10.004 t0 007 +0.013 10 008 +0 007 a calc. 5.228 5.274 5 233 5.196 5.247 5 229 5.242 5 113 -5.O22 Ditr. + 010 +.011 +.038 + 018 - 006 - 046 +.008 + 018 +.075 Dmeas. 5 971 5.967 5 964 5 938 5 959 5 972 5 97 5 919 5 88s t0 008 10 005 +0 008 +0.009 10.008 j0.006 D calc. 5 942 5 967 5.946 5 927 5.9.55 5.950 .s.957 5 893 -5 .872 DifI. + o29 -.000 +.018 +.011 +.004 +.022 +.013 + 026 + 017 6 meas. 2 900 2 909 2 916 2 949 2.956 2.986 2.93 3.036 3 094 t0.004 t0 002 :10.004 +0 003 +0 006 t0 003 c calc. 2.931 2 898 2.933 2 978 2 934 2.968 2 953 3 080 -3 137 Ditr. - 031 + 011 -.017 - 029 +.022 + 018 - O23 - 04+ -.043 All cell edges except those of have been converted from kX units to Angstroms. Specimens Nos, 143, "P" r'P" 486,49, 52O,519 and 50 are from Mikheyev (1952) as reported in Godowikov (1900). is from Peacock (1944). Nos. 3095 and 3119 are from Godovikov (1960). The cell e{ses of 3095 and 3119 are not those of the original paper but have been calculateC after reindering Godovikov's d-values. For specimens 1-lJ and 49, the above ratios were calculated from the atomic ratios (Co*Ni)/Fe, (As*S)/(Co*NifFe), and S/As, which were the only chemical data available. Only the ratio, Co,lFe/As, was gir.en for specimen "P." ferent cell edgesby assumingthat the cell edgesare a linear function of compositionbetween CoAsz and CoSbz,and betweenFeAsz and FeSbzas these phasesall have the marcasitestructure. From this one finds that Sb increasesall three cell edges.For a saffioritenear the middle of the CoAsz-FeAszseries, substituting one-per cent of the As by Sb would in- creaseeach cell edgeby about 0.005A. In Table 4,two analyses,3095 and 3119,report about 0.4 and 0.8 mol per cent Sb respectively.However, the differencesbetween calculated and observeda ar'd b cell edgesare several times the magnitude one would expect from the amount of Sb present. Furthermore, the c edgesare much smaller than the calculated values. EUGENE II. ROSEBOOM As there are no phasesin the systemsCo-Bi, Ni-Bi, or Fe-Ri in which the Co:Bi, Ni: Bi, or Fe:Bi ratio is l:2, onecannot evaluate the efiectof Bi substitution for arsenicin the way used for Sb. However, the efiect should be similar to that of antimony in increasingall three cell dimen- sions, but perhaps somewhat greater in magnitude. The maximum amounts of bismuth substituting for arsenicreported in the analysesfor Table 4 are 0.41 (no. 50) and 0.34 (no. 520) mol per cent. However, the measuredvalues for the a edgeof no. 50 and the c edgeof no. 520 are 0.46 and 0.29 Asmaller than the calculatedvalues while all of the other measurededges of thesetwo sampiesare larger than the calculatedvalues. As the relatively large differencesbetween calculatedand measured valuescannot be appreciablydiminished by correctingfor Sb or Bi con- tent, one must concludethat either the r-ray ot chemicaldata on the natural saffioritesand loellingitesis at fault or that the relation between cell edgesand compositionexpressed in equations (6), (7) and (8), al- though adequate lor either Ni or S substitution, is too simple for the combinationsof the two substitutions.Thus additional work should be done on synthetic diarsenidescontaining both nickel and sulfur. An error in Godovikov's (1960)indexing of specimens3095 and 3119 was suspectedwhen it was observedthat the b and c edgesof thesespeci- mens(shown by black circleson Fig. 6) werewell over on the oppositeside of the curvesof cell edgesfor pure CoAs2-FeAszsolid solutions,as com- pared with the other specimens.Thus none of the substitutionsdiscussed above could accountfor thesecell edges.In discussingthe changesin d- valueswith Co contentin the loellingite-saffioriteseries, Godovikov noted that in certain casespairs of lines in the Fe-rich specimensapparently convergedin 3095and 3119,with a concurrentchange in,i,ndices.In addi- tion he stated that someconverging pairs separatedagain with a change in indices.The writer decidedto consideran alternative possibilitythat the converginglines did not changetheir indicesbut crossedas in Fig.3. A plol of d-valuesversus composition was conslructed using the indexing of Swansonet al. (1960)for CoAs2,CoFeAsa, and FeAszplus two addi- tional sets of d-values calculated from the cell edgesin Fig. 2. This diagramrevealed that a largenumber of lines rvhichare clearlyseparated in the Fe-richdiarsenides cross each other in the vicinity of the composi- tions of 3095and 3119.Thus a number of Godovikov'slines actually rep- resenttwo closelyspaced iines. However, among the lines of smaller d- value, the 221, 321, 312, and 341 were unambiguous.From theselines, the celledges given in Table 4 werecalculatec. One might supposethat if equations(6), (7) and (8) can be shownto be valid when both S and Ni are present,then one couid determinethe com- position of saffioritesand loellingitesby measuringthe cell edges,deter- CO-NT.FEDIARSENIDES 297 mining Co, Ca and C" from Fig. 2 or Fig. 4, and solving the three simul- taneous equations in three unknowns. Unfortunately, unique solutions cannot be found for x, y and z when Co, C6and C" take on certain values which are describedby equation (11): (11) C' - 1.859C6 + 0.1001C": - 62'76 When equation (11) is satisfied,the three equations' (6)' (7) and (8) are not independent and an infinite number of solutions exist. For ex- ample' this occurswhen C": 70, C6:7 6, and C": 85' Unfortunately' as this situation describedby equation (11) is approached,very large errors in the Co. Ni. and S content result from small errors in measurementof the cell edges.For this reason,the method is unsatisfactoryfor deter- mination of composition over the whole composition range of saffiorite and loellingite,the errorsbeing especiallylarge in the co and Ni content. On the other hand, if one of the three composition variables, cobalt, nickel, or sulfur content is determined by some other method, equations (6), (7) and (8) could be used to determine the other two composition variables. AcrNowr-BocMENTS This work was begun as part of a Ph.D. Thesisat Harvard University and continuedat the GeophysicalLaboratory of the CarnegieInstitution of Washingtonand at the U. S. GeologicalSurvey. The author wishesto thank ProfessorsJames B. Thompson, Jr., Clifiord Frondel, and H' E' McKinstry of Harvard University and Gunnar Kullerud of the Geo- physical Laboratory for much advice and criticism. Brian J. Skinner and Philip Bethke of the U. S. GeologicalSurvey kindly criticizedthe manu- script. D. C. Alverson of the U. S. GeologicalSurvey translated some Russian publications. D. E. Appleman aided the writer in making least squarescomputations. RnrrnrNcrs Bnnns,Y. (1953)Introducti.on Lothe theory oJ error. Addison-wesley Publishing co. Bnnnv, L. G. eNo R. M. TrrourscN, (1962) X.ifay powder data for ore minerals. Geol'. Soc.Am. Mem.85. Bnurrrr, A. (1916) Synthese der Nickelarsenide. central,b. Mineral. Geol. 1916,49-56- Krist.32,165-187. BurRcrr., M. J. 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