JOURNAL MINERALOGICAL SOCIETY OF AMENCA

28I

THE CRYSTAL STRUCTURE OF SOME METALLICSULFIDES*
of Michigan
LBwrs S. ReuslBr-t, (Jtci'aersi'ty
Assrnacr

Cinnabar has a simple rhombohedral structure'and hence doArgentite and acanthite are shown to have identical structures'
not represent distinct mineral species.
from the comVa-lues obtained for the atomic radii of selenium and tellurium
pounds PbSe and PbTe are Se 1.15 A, and Te 1'27 A'
INTRODUCTION

The determination of the structure of a crystal is importantin

Aside from certain groups where the isomorphism is very evident'
it is a matter of opinion as to what compositions can be considered
as analagous, or what forms are strikrngly similar' In thrs investigation it was decided to use the crystal structure as the final test of
isomorphism' This introduces nothing radically difierent into o-ur.on."ption of isomorphism. It is merely making use of a fundamental fact rather than a certain manifestation of that fact' The
crystal form is ordinari$r the outward expression of the inner
structure, but if for urry iearon it furnishes evidence which is not* From a dissertation submitted in partial fulfillment of the requirements for the1925'
degree of Doctor of Philosophy in the Universitv of Michigan, June'

282

THE AMERICAN MINERALOGIST

well defined, the isomorphism should be based upon the structure
itself.
This investigation covered the sulfides of a number of the metallic
elements,and also included the closely related selenidesand tellurides, as well as one arsenideand an antimonide. The term metallic
sulfide is used in a general sensethroughout the paper, and includes
these similar compounds.
The equipment used in this investigation was an X-ray Difrraction Apparatus built by the General Electric Company. It is aself-contained unit, consisting of a high tensidn transformer and awater cooled Coolidge tube, with a molybdenum target. The
radiation is rendered practically monochromatic by the use of azroz filter. The tube was ordinarily run at about 25 mil-amperes
and from 30 to 35 kilovolts, and the exposuresvaried from 15 to 40

TIIE GALENA GROUP
This group consists of a series of monosulfides, selenides,and
tellurides of lead, silver, and copper, of which the more importantmembers are as follows:
GalenaPbS
Clausthalite PbSe
AltaitePbTe
ArgentiteAgzS
I llessite
Ag2Te(Ag, Cu)zSe
Bucairite
Naumannite (Agz,Pb)Se

The reason for including the galena group in this investigation
was to determine whether or not the difierent members have thesame structures. According to the theory of spacegroups it shouldbe impossible for a compound like AgzS to have a structure similar
to that of PbS. If the structures are different, similarity of crystaform is merely a coincidence,and does not indicate a fundamentai
relationship. In that case the compounds should not be consideredisomorphous
GarBnaGalena has the NaCl type of structure,l although no data havebeen published. The results secured by means of powder photo-

AMENCAJOT]RNALMINERALOGICAL SOCIETY OF

283

of the plT,ttgraphs are shown in Table I, where the sp^acings
units' The
Angstromincausing the reflection. ur. git'"tt directly

usedwereas follbws:(1) a cleavae".itugTlTt
specim"ens
llll:lfrom Uoloraoo; \rirlrrkrro*n locality; (2) an argentilerous galena(4)material prepareda non-argentiferous galena f.om Kansas;(5)material preparedartificially by precipitation from solution;
There was no
artificially Uy itre direct union of the elements'(3)'
This was to(2)andmeasurabledifferencebetween specimens
classedas awasbe e*pected, for although the one from -Colorado
much overnotwasgood ,il't er ore, the actial percentageof silver
determinedcube.as0.1 per cent' The length oithe side of-the unit
100 (2) was 5'93 A'
from the averageof tie results from the planeface centered
The structure is made up of two interpenetrating
a simple faceofcubes, but the diffraction iattern is characteristic
power ofreflecting
centered cube arrange-".ri. Thi, is becausethe
that
atoms
Pb
the
the S atoms is relatively so much less than that ofthebydeterminedisthey are practically n"gligibl", and thepattern
theofintensities
Pb atoms alone. The ih"]o'"titut and the observed
II'
Table
in
reflectionsfrom the different planes are shown
Cr-ausrner-rrB
the measurelgn-ts
No specimenof natural PbSe was available' soshown in Table I'
were made on artificial material' The results are
Itwill.benoticedthattheinterplanardistancesarealittlegreaterof the larger Se atoms
than in the caseof galena,for the introduction
The length ofnaturally causesan enlargement of the structure'-thepattern was-qurte
cube sidl was found to be 6.14 A. ttte diffractionin the relative
similar to that of galena, except for some variation
corresponcling planes' due to theintensities of reflectionr'f,owith the S atoms'
greater reflecting power of the Se as comparedin Table II'
balculated and' observed intensities are given
Alutrp
was available
A specimenof the natural mineral from New Mexico
were
spacmgs
The
PbTe'
than
ratherS)
but iiproved to be Pb(Te,aslarge
not aslarger than for either galena or clausthalite' but
atoms'
larger Te*oita U" expected from the introd'uction of thewith themeasured'wasmaterial
prepared
Accord.inglyi artificiallyresults shown in Table I.
of the two preThe pattern obtained was different from thosearrangement rather
ceding -inerals. It indicated a simple cube

284

, THE AMERICAN MINERALOGIST

than a face centered cube. No reflections
were securedfrom theplanes lll,3ll,
and 331, whereasthey were all present for galena
and clausthalite,but this doesnot meanthat it porr..r., a aifr"..rrt
structure. The Te atom is so much greaterin its reflectirrg po*".
caln:t be ignored as was tire S atom in galenafBoth:;1",-i,tne -Hb and the Te atoms must be considered.
The effect of two
interpe,etrating face centered cube lattices,where both are nearly
e.quivalentin reflecting power, is practicallythe same as that of i
simple cube arrangement, with a .ubeedge only one half as longl
Such a^cubeshould give reflectionsfrom
ilun", 100, 110, 111, 100(2),2l0,and 2ll. To make thesecomparablewith the larger cube,
the order of reflection wourd have to be
murtipried by twol Thesep l a n e st h e n b e c o m e1 0 0 ( 2 ) , 1 t 0 ( 2 ) , I 1 1 ( 2 ) , 1 0 0(4); 2tO(2), and22r(2), and it will be seenin Table r that
ihese are the praneswhichgave reflectionsfor pbTe. The value forthe spacingfrom the plane100(2) gives 6.34 A for the length of theunit cube edse.
TableI. Varunsor fNrnnprnNenDrsrrrxcrsrN A
Umrrs
Galena PbS

Plane
t00aa
110
111
100(2)
210aa
2llaa
110(2)
100(3)
22laa
310aa
311
111(2)
320aa
321aa
100(4)
4lOaa
330aa
331

1.490

1.480

1.363

210(2)
211(2)

1.362

1s2s r.328
1.210 r.210 7 . 2 1 0

1

2

a
3.42
2.e8

a
3.40
2.ss

2.100
a

2.08s
a

PbSe

PbTe

34s
aaaa,a
aaaaa
3.40
3.42
2.95
2.98
aaaaa
aaaaa

3.40
2.95

3.55
s .o7

a
3. 19

2.085 2.100

2.085 2.r7

2.26

aaaaa
aaaaa
aaaaa

1. 7 9 5
1.720

1 . 78 2
1.708

1.782 1.790 1.780 1.840
a1.708 r.720 1.700 1.7fi
1.84s
aaaaa
aaaaa
1.485
1.485
aaaaa
aaaaa
1.362
1 .328

1.480

1.525

1.600

1.40
L360

a
1.430

1.240 1.310

Erplanation oJ therabre'- An possibleplanes
for a cubic structure with spacings
greaterthan that of 211(2)are listed. The
retter ,.a,,signifiesthat no reflection
was secured.

AMERICAJOURNAL MINERALOGICAL SOCIETY OF
Table II.
PIane
111
100(2)
110(2)
311
111(2)
100(4)331

2r0(2)
2rr(2)

Cercullrno

285

exp OssrRvpn lNrnNsrtrns or Rr'rr'ecrron

PbS
ab
8.7 |
10.0 |
9.2 1
5.4 2
3.7 4
2.0 6
3.0 5
6.3 3
5.0 3

PbSe
abab
3.4 4
10.0 1
8.9 1
2.2 5
3.7 3
2.1 5
t.2 6
6.0 2
4.8 3

PbTe
0.9 0
10.0 1
8.9 1
0.6 0
3.7 3
2.1 4
0.3 0
6.1 2
4.9 3

(column a) were calculated
Erplanation of the tabl'e.-The theoretical intensities
reduced to a scale of ten'values.wereandtheUy -"ur,, oi the intensity formula,2In
the case of the observed
10'
so that the most intense reflections have the value
quantitatively.
intensities
themeasureto*od"values (column b) no attemfi *u.
given the value ol 1' and the(orwaslines)
line
intense
most
the
film
each
On
o{
of decreasiru intensity tith the values
il;tderremaining lines werethethat"rr"";;;
be
seen
will
It
2, 3, 4, and so on, with 0'indicating complete absence'the calculated intensities'
orCer so obtained agrees closely withthe order offrom PbTe is of aThis table shows why the difiraction patternintensities for planes
difierent type than those of the other two' Theof the remainlng
111, 311, and 331 are very lbw compared'to thosedistinctly, thesevery
showedotheritheplanes. On a film *here
blackening of thethree would be entirely obscured by the generalplanes 100(2)'film. The pattern *outa consist' tien, of oniy the
before'tll(2),100(4), 2lo(2), and' 2tl(2)' As mentioned
itqrl,
these become theif . the order of these ,.hectiorr. is divided by two,of whose edge
planes characteristic of a simple cube, the length
has been reduced bY one half'
Aroutc Raorr or Se axo Te
replaced by
If in a compound selenium or tellurium is partly
naumineral
the
in
as
silver'sulfur, or if lead is partly replaced byanyHence'.
changed'be,.ru.r.rit., the size of tftl unit ceil willmaterial
on
made
be
must
measurementsas to the size of the atoms
is known' or on
in which the exact amount of the replacementcase is muchlatterThrs
material where there is no replacement'
the artifrom
entirelys"totedsimpler, and the data have L""n
PbTe'
and
ficially prepared pure PbS, PbSe,
given element'
There is no definite radius for the atom of aI"
implies that theitforjustified'
fact, the term "radius" is hardly

286

THE AMERICAN MINERALOGIST

atom is spherical. The act ral meaning of
the term can be explained
as follows' As atoms occur in a structire,
there is a certain distance
between the centers of two adjacent atoms.
If the two are alike,half of this distance is referred io as theirradius. rf they are unrike,a certain fraction of this distance is assigned
to one of the atoms
as a measureof its radius, and the remaining
distance as the radiusor tne other atom.
If we assume that the S atom in thesulfides has a constanr
radius, then it is a simplb matter to calculate
the radii of se and re.
rn the mineral pyrite, FeS2, the two
S atoms are so ptu."Jltut
they are much nearer to each other thanto any of the Fe atoms.
This distance of nearest approach is 2.08
A, ,o ti" ;;il;
"iT'*
pb
the
diJancefromaatom to a S is 2.96
A.
1.t11 .In-galena,
rr r.U4 A ot this distance is assigned
to the S atom, then the pb
atom must have a radius of t.92 A. Using
this value in turn in thetwo compounds pbse and pbre gives
1.15 A and r.27 L as theradii of Se and Te, respectivelv.
It might be consideredthat s"incepyrite
and galena have different
types of str!:ctures, the S atoms would
not necessarily have thesame radius in the two compounds. fnthat casethe value of 1.04 A
wo'ld not hold for S in galena, and the values
oUtui".Ji*d;;Te would-be wrong, although theywould still represent the corrlct
relative sizesin comparison to S.
AncnNrtru
The similarity of the crystal formsof argentife and galena isapparently good evidence for considering
them isomorpholus. The
cube, octahedron, and dodecahedro'ar". commonly observed on
both minerals. However, argentite crystals
are frequently distorted.
Distortion usually refers to an unequal
development of facesbelong_
ing to the same form, without ani change
in the angular positionof the faces. fn the case of argentite, "theinterfacial angles are
sometimes distorted. For example,
the specimen referred to as
number 2 occurred in well formed
crystals, which at first glance
appeared to be octahedrons. Measurementof the angles ,fi;;;however, that instead of the theoreticalvalue of d;;;;y70", they were actually about 63.. fn",ig.rifi.urr.. of this will be
discussedlater.
of AgzS were used, as follows: (1) a crystal
fromraxony'whrch appeared to be a cube in combination"^li:n:.1:ens
witha trigonal

JOURNAL MINERALOGICALSOCIETY OF AilIEMCA

287

trisoctahedron; (2) the steep octahedral crystal already mentioned,from Mexico; (3) and (4) massive specimensfrom an unknown
locality; (5) material artificially prepared by precipitation fromsolutionl and (6) material artificially prepared by the direct unionof the elements. AII six samplesgave identical diffraction patternsof an unexpectedtype.
It is well known that the interplanar spacingsin a cubic crystal
have a very simple relationship. If ao be the length of the side of
the unit cube, or in other words, if ao:droo, then the spacing for&o

any other plane hkl for anyorder n is equal toV(nh)'?*(nk)'*(nI)'This means that no matter what the absolute size of a cubic struc-in theratiotIJI,h,#:ffnetc'
arealways
ture,thespacings
It is accordingly possible to calculate the spacings for all possible
planes in terms of ao. In Table I, for instance, all planes with&olrom
spacrngs
ro $ *.r. listed. Not all of these gave reflec-

tT

,rro

tions, however; but since there are no other possible planes withspacingswithin the above limits, there can be no other reflections
than those which correspond to these planes. Atty additionalreflection would correspond to a plane with impossible spacings.'
If the spacingscalculated from an extenderl,rri", $, 3l\/I \/z

are plotted on a logarithm scale, then the difierences due to thedifferent values of a6 disappear. Whatever the absolute value of ao,
the relative spacings would be the same, and all cubic structures
would be comparable. Such a plotting of the logarithms of thespacings might be referred to as a generalized cubic diffraction
pattern. No matter how complex a cubic structure might be, it
could not have lines in its diffraction pattern which did not correspond to this general pattern if they were plotted on a logarithm
scale.
It was stated that the diffraction pattern from argentite was ofan unexpected type. The spacingsas determined from its patternwere plotted on the logarithm scale and there was no agreementwith the generalizedpatte{n. Not only do the lines occur in different
positions, but their spacingsare much closer together.

288

THE AMERICAN MINERALOGISTThere are two possible explanations for this. As the interplanar
spacings become smaller the lines of the pattern are much closer
together. These lines correspond to planes of either high orders
or of complex indices, and are usually securedfrom complex structures. The first explanation, then, would be that argentite has acomplex cubic structure, and that its lines would match the generalized pattern in the region where the lines are very close together.
Such a matching rs difficult to detect because the error involved
becomes as great as the distances between adjacent lines. This
explanation, however, is not in accord with the available crystal
structure data. Simple compoundsappear to have simple structures,and there would seem to be no justrfication for assuming a simple. compound like AgzS to have a complex structure. The second
explanation is more reasonable:namely, that argentite is not cubic.
Structures other than cubic are apt to have the lines in their patterns
crowded close together. This rs illustrated by comparing the cubic
and orthorhombic systems. In the cubic, where the three axes are
all equal, the planes 001, 010, and 100 are identical, as are also 110,011, and 101; or 123, I32, 213, 231, 312, and 321; etc.,while in theorthorhombic these would all be difierent, and would have different
spacings. This fact makes the patterns of such crystals usually very
complex, and the solution of their structures is difficult.
Doubt as to the true cubic character of angentite is suggestedby
the distorted angles observed on some crystals. Furthermore,
AgzS occurs also as the mineral acanthite, classed by Danas as
orthorhombic, but possibly merely distorted argentite. Several
specimens of acanthite were available and all gave diffraction
patterns identical to those from argentite, indicating that there isno differencein structure between the two minerals. The apparently
authentic cubic forms on argentite can be accounted for by assuming that AgzS has a high temperature cubic modification, which isunstable at lower temperatures. A crystal formed as cubic would
retain its genera,l outward form on cooling, but would undergomolecular readjustment, becoming a pseudomorph of acanthiteafter the high temperature form. This is somewhat similar to thecaseof the mineral leucite, which is cubic above 500"C. Below thistemperature there occurs a readjustment, involving the formationof a complex twinned structure, composedof orthorhombic individuals. The outward form is still apparently cubic, with only veryslight changesin the interfacial angles.

TOLTRNAL MTNERALOGICAL SOCIETY OF AMERICA

In regard to argentite, the uninterpreted diffraction pattern isinsufficient to prove it to be orthorhombic. However, it is identicalwith acanthite, and both are entirely different from galena. The
two probably have structures similar to orthorhombic chalcocite,
CuzS. It should also be emphasizedthat even a hrgh temperature
cubrc form could not be structurally isomorphous with galena'becausetwo Ag atoms could not be equivalent to one Pb atom.
HrssrrB
A specimen of hessite from Transylvania was available forinvestigation. This gave a diffraction pattern very similar toargentite, indicating that this mineral, also, is not isomorphouswith galena. This furnishes additional proof that Agr is not equivalent to Pb in a crystal structure.
Eucarnrrp
There is no mineral corresponding to the composition AgzSe,soeucairite was used. The Ag and Cu selenidesshould be able to form
mixed crystals, and jt would be expected that (Ag, Cu)zSe woulc
have the same structure as AgzSe. The specimenavailable was not
pure. The eucairite was intimately mixed with an unknown mineral,and both were embedded in calcite. The latter was removed bytreatment with dilute acid, while the former was partially removed
by hand sorting under a magnifying glass. The diffraction patternsecured may not be due entirely to eucairite, but none of the,'lines
agreed wrth the generalizedcubic pattern. The introduction of the
Cu atoms would change the crystallographic constants so that thepattern could not be expected to resemblethat of argentite. While
there is no direct proof of isomorphism with argentite, it is clearly
establishedthat eucairite is not isomorphous with galena.
Neuuarrttr
It was thought that the study of a compound such as this mightthrow some light on the relation of galena and argentite. If they
are isomorphous,they ought to be able to form mixed crystals, with
the Ag and the Pb in varying proportions. If they are not isomorphous, mixed crystals should not occur.
No specimenof naumannite lvas available, but the corresponding
sulfide was prepared artificrally. Two alloys of Pb and Ag were'
made, one with about 13 per cent and the other about 20 per cent290

TH E AMERICAN MINERALOGISTof Ag. These were finely divided, mixed with sulfur, and heated.
The heat of the reaction drives off the excesssulfur not needed for
combination.
The diffraction pattern from these two PbAg sulfidesproved tobe that of pure PbS, whrch was rather unexpected. ft was expectedthat the pattern would either be that of a mixture of the two
sulfides, or else correspond to a PbS structure with a different
sized unrt cell, becauseof the presenceof the Ag atoms. Since theunit cell js of the samb size,it must mean that there are no Ag atoms
replacing Pb atoms in the structure.
There is a marked difference in the readiness with which leadand silver combine with sulfur. MolBcular quantities of lead andsulfur unite rapidly wrth evolution of heat, while to form AgzS it isnecessaryto use excesssulfur and prolonged heating. It may bethat the lead in the alloy combined with the sulfur, while thesilver did not. fn that casethe silver would be mechanically held in
the PbS structure. It would not be present as crystallized silver, andhence would not give the silver difiraction pattern.
This again supports the conclusionthat PbS and AgzS are not isomorphous. The X-ray evidencein each casehas indicated this fact.
This does not establish the general conclusion that two monovalentatoms can never replacea single bivalent atom in a given structure,but it does prove it in this case,and further study of similar cases
will probably show the same results.
THE PYRITE GROUP
This group consists of the following minerals:
PyriteHauerite
Sperrylite
Ullmannite
Gersdorffite
Cobaltite
Smaltite
Chloanthite

FeSz
MnSr
PtAs:
NiSbS
NiAsS
CoAsS
CoAsz
NiAsz

These minerals occur in good crystals, the pyritohedron, cube,
and octahedron being commonly observed. Their compositions are
entirely analagous, and the series has long been considered as awell establishedcase of isomorphism. It is only recently that anyquestion has been raised as to the validity of this isomorphism.

JOURNAL MINERALOGICAL SOCIETYOF AMERICA

291

Cobaltite occurs in perfectly formed crystals, and has been foundby both the Braggsa and Mechlingb to have the pyrite structure,
but Schneiderhiihn6reports that it is not cubic at all His examination of polished sections of the crystals by reflected polarized lightrevealed a structure made up of intimately twinned orthorhombic
individuals. This, again, would seem to suggesta condition similar
to the mineral leucite, which was referred to under the discussionof argentite as having high and low temperature modifications. rf
this be the true explanation, it would mean that the high temperature form was isomorphous with pyrite, rather than the ordinary
or low temperature form. But, this does not explain the results
securedby the Braggs and Mechling. It was thought that further investigation might settle this question'
PvnttBThe structure of pyrite has been worked out very thoroughlyT'8'
Four moleculesof FeSz are associatedwith each unit cell' The Featoms lie at the corners and face centersof the unit cube, the lengthof whose edgeis 5.38 A. This unit cube can be thought of as drvided
into eight smaller cubes by passing planes through the center-from
top to bottom, from side to side, and from front to rear' The alternate corners of one of these cubeswill be occupiedby the Fe atoms,
and any diagonal through the center will always run from a corner
occupiedby an Fe atom to a vacant one. A sulfur atom is situatedin each cube and lies on the diagonal toward the vacant corner, at a
distance from it of approximately one fifth of the length of thereflection.
HlunnrrB
This mineral was not included in this investigation. Its structure
has been determinede and there is no question concerning its isomorphism with pyrite.
SpnnnvurB
The difiraction pattern from sperrylite is essentially the same asthat from pyrite. There are differencesin the relative intensities,

292

THE AMEKICANMINERALOGIST

due to the differencein reflecting power of the Fe and S atoms, ascompared with the Pt and As. The theoretical and observed irr.
tensities for the important planes are shown in Table III.
For
calculating the theoretical values it was assumedthat the pt and As
atoms were both larger than the Fe and S in the same general pro_portion. Thus the As atoms should occupy the same relative
positions on the diagonals of the small cubes as do the S atoms inpyrite. The observedintensities and those calculated on this basis
agree fairly well, indicating that this assumption is approximately
correct. The size of the unit cube of sperrylite was found to bes.e4A.

Ulrlraxwtrp
ullmannite is of interest because crystals have been observed
which have lower symmetry than that of pyrite. The ordinary
form is the cube, sometimes with pyritohedral striations. Miersio
reports the occurrenceof tetrahedral forms on crystals from carinthia. The combination of tetrahedral and pyritohedral symmetry
means that the crystals should be referred to the lowest sy-metry
class of the cubic system. The explanation has been given that thislower symmetry is due to the substitution of an Sb atom for oneof the two S atoms. In pyrite the sul_furatoms are svmmetricallyplaced with respect to three planes at right angles to each other.
Since the sb atom is not equivalent to the S in size, its substitution
in alternate positions occupied by S would destroy this symmetry.
No statement of an actual proof for this kind of a structure is on
record, nor are there any data concerning the size of the unit cell.
The diffraction pattern is fairly similar to that of pyrite, andindicates that the structure is the same. The Sb atoms must occuDv
alternate positions with the S, for no other arrangement would bl
possible according to the theory of spacegroups.
Nickel has practically the same reflecting power as iron, but thepresence of the antimony should make an appreciable difierencein the relative intensities of reflection from pyrite and uilmanite.
This is shown in Table III, where the observed intensities are
given. fn pyrite the planes 3Il, 2ll, and 210 have the intensities
1, 5, and 4 respectively, whereas in ullmannite these same planes
are rated as 1.5, 2, and l.
By assuming that the Sb atoms occupy the same relative positionon the diagonalsof the small cubesas do the S atoms in pyrite, theJOURNAL MINERALOGICAL SOCIETY OF AMERICA

calculated values do not agree closely with the observedintensities.
For example, the reflection from the plane 111 was plainly visible,
although not very intense, but according to the calculated value it
should have been too weak to appear at all' Apparently, the positions have been sfightly changed with reference to pyrite. The
whole structure is, of course, on a larger scale becauseof the introduction of the larger Sb atoms. It is evident from a study of a three
dimensional model of the structure that the Sb atoms would lie alittlecloser, and the S atoms a little farther Irom the vacant cornersof the small cubes than do the S atoms in pyrite. By making sucha change arbitrariiy, the calculated results given in Table III weresecured,and it will be seenthat the agreementis fair.
The reflection obtained from the 100(2) plane gave a value of 5.91
A for the length of the side of the unit cube.
GBnsoonrrlrp
The first specimen examined was from Austria and gave a diffraction pattern identical to those which were obtained fromsmaltite, indicating that it was NiAsz rather than NiAsS. A second
specimen,from Germany, proved to be gersdorfiite. Its difiraction
pattern is quite analagous to that of ullmann te, as would be expected. The side of the unit cube was found to be 5.68 A' It should
be pointed out that such dimensions as these refer only to thespecimenexamined. The size of the unit cell may vary greatly because of the extensive replacements which occur in the sulfide
minerals. Gersdorffite, for example, may contain from 2 to 6 percent of iron, small amounts of cobalt, and sometimesantimony. To
obtain exact measurements of the unit cell, artificially preparedpure material would have to be used.
CosArrrtn
The conflicting evrdencein regard to cobaltite has already beenstated. The diffraction pattern securedin this investigation was.a
cubic one, and gave a value for the side of the unit cell of 5.58 A.
This confirms the results obtained by the Braggs and by Mechling.
As far as is known, none of the crystals used for X-ray analysis
were examined by reflected light. It would be easy to conclude,
therefore, that these are all cubic, while those examined by Schneiderhdhn are orthorhombic.
This scarcely seems possible, for
Schneiderhiihnfound that without exception all crystals examined294

THE AMERICAN MI N ERALOGIST

were orthorhombic. On the other hand, crystals from widelydifferent localities were used for X-ray analysis, and all were uniformly cubic. It would seem necessaryto conclude that either the
X-ray data are correct, and the observations of Schneiderhiihn
wrong, or that his observations are correct, and the X-ray data
wrong.
The method of examining polished sections of crystals by reflected polarized light is a sound one, and there seems to be no
ground for doubting the results. On the other hand, judging fromthe large amount of consistent X-ray data obtained from alltypes of compounds, it would seem unwarranted to conclude thatapparently authentic data can be securedwhich are not in accord
with the structure producing them. If both results are correct,
there must be some manner of reconciling them. Two possibilities
suggest themselves. The first is concerned with the relative sensibility of the X-ray methods, and the second with the surface
efiects which may be produced by grinding and polishing mineral
sections.
The first possibility can be explained as follows: chalcopyrite,
CuFeS2,crystallizes in the tetragonal system. Its axial ratio is 1:
0.985, which is very nearly 1:1. Its diffraction pattern is, to allappearances, a cubic one, showing that X-rays, in the powder
method at least, cannot distinguish between a cubic crystal and atetragonal crystal with a value for the c axis so near to unity. ft
might be that the cobaltite structure is orthorhombic, but sonearly cubic that the X-ray data appear to be cubic.
fndirect evidence bn this point can be obtained from pyrite
and marcasite, the cubic and orthorhombic forms of FeS2, respectively. Their diffraction patterns, although similar in somerespects, show distinct difierences, and that of marcasite could
not be interpreted as belonging to a crystal isomorphous with
pyrite. There is no orthorhombic mineral with the exact com.
position CoAsS. Ifowever, glaucodot is orthorhombic and.
difiers from cobaltite in composition only in the presenceof someiron, its composition being (Co,Fe)AsS. It gives an entirely
different pattern than does cobaltite. It is logical to conclude,
therefore, that there is sufficient difference between cubic andorthorhombic coAsS to distinguish their diffraction patterns, andthat cobaltite, if really twinned orthorhombic, ought not to givea cubic pattern.

TOURNAL MINERAINGICALSOCIETY OF AMENCA

295

photograph through a section of a twinned crystal might be afiected,
tut in the powder method there would be no efiect unless thetwinning were sub-microscopic, in which case it could not be
detecteJ by optical methods.
The secondpossiblemethod of reconciling the conflicting evidence
is based on the assumption that cobaltite is metastable at ordinary

on these sectionsare not made by transmitted light' A change in a
few atomic layers would be sufficient to be detected by opticalmethods, while no efiect at all would be observed on the X-ray

theseems to be no way in which evid.encecould be secured as tosurface structure by X-ray methods, for it would be impossible
to obtain these surface layers, only a few atoms deep, separate
from the remaining unchanged material.
is
It is not possible to prove at present if this second possibility
The
found'
becorrect, or whether stili another explanation mightwhole question of the dimorphous sulfide minerals is one deserving
further studv.

296

THE AMERICAN,SMAITITE

MINERAIOGI ST

AND CHLoANTHITE

These two minerals have the compositions CoAsr and NiAsz;
respectively. The exact compositions represent the end membersof a seriesof mixed crystals and rarely occur. The names smaltite
and chloanthite are given to the various members of the series;
depending upon which element predominates. There is so little'
difference between the Ni and co atoms in size or in reflecting
power that the diffraction patterns of the pure compounds shouldbe very similar, and no difference at ail. shourd be observed whenboth Co and Ni are present in considerableamounts.
This was found to be true. Samples prepared from specimensfrom Germany, which qualitative tests showed to contain both coand Ni, gave indistinguishable patterns.
Specimens labelled"gersdorffite" and "skutterudite" also gave patterns of the same
type, proving that they were actually either smaltite or chloan_
thite. In all, then, difiraction patterns were obtained from four
samples.
Thesepatterns are of a very pu,zzringnature.Except for two rines,
thgy agreeperfectly with a cubic arrangement. carcurations basedon the density, the weight of a molecule, and the assumption thatthe unit cell contains four molecules,as doespyrite, give the length
for the side of the unit cube of 5.96 A, which checks closely w-ith
the value determined from the pattern.
However, the intensities of the reflections actually observed do
not agree with those calculated for the pyrite structure. The
reflection from plhne 210 is strongest, while the calculated varue isfourth, and that from 100(2) is absent,whilb for the pyrite structure
it is quite strong, being rated second. These two variations do notpresent any specral difficulties, for the former can be accounted

corners are consideredas the origin, the co_ordinatesof an S atom
would be uuu, where u equals .338a0.(asis the length of the edgeofthe unit cube). It is evident from a study of a three dimensionalmodel that if larger As atoms be substituted for the smaller
S.
while Ni or Co are practicaliy the same as Fe, the value of a would
have to be less. fn other words, the As atoms would
not be soJOURNAL MINERALOGICAL SOCIETYOF AMENCA

297

relatively close to the vacant corners. By assuming u to have avalue of about .350 instead of .388, the reflection from plane 100(2)disappears.
other reflections have intensities that cannot thus be reconciled,however. The reflection from plane 211 is missing. If a were aboutreflection is the most intense, and lno value of u can be assumed
which will greatly reduce it'
The difiraction pattern presents two dificulties, then. Two lines
do not fit in with a cubic pattern' and some of those that do fit do
not have the intensities expected from the pyrite type of structilre'of either smaltite of chloanthite. The fraction might be due to aslight error in the density determination, but neither ten nor
el&en moleculescould be arranged in a cube with cubic symmetry'mechanically mixed with the substance, then each would give apattern, the one superposedon the other. If it were present in only

298

THE AMERICAN MINERALOGISTfor the extra lines in the smaltite pattern. rf they correspondedto
the chief lines of the skutterudite pattern, the whole question would
be solved.
rt has been impossiblb to securea single crystal of skutterudite.
Extremely small crystals were picked out from a specimenlabelled
skutterudite, but they gave the CoAs2pattern, indicating that they
were smaltite. Material consisting of an intimate mixture of
skutterudite and smaltite was treated with sulfuric acid and KCloB,
according to the method of parsons,ls and a difiraction patternsecuredfrom the residue, supposed to be CoAsa. If this residue isskutterudite, it is quite certain that Beutell was right, and that it
is not cubic, for the pattern was very complex. Moreover, there
were no lines in positrons which would account for the irregularlines from smaltite and chloanthite. . . . If this really is the sku-tterudite pattern, it is eliminated as a possible causeof the extra lines.
Attempts to prepare NiAsz and CoAsz artificially have failed
sofar. rf this can be done, it wilr be possible to determine
if the unusual pattern was due to material other than the twodiarsenides.
until this is done, it is not likely that an exact determinationof
their structures can be made, and their isomorphismwith pyrite
cannot be proved from the structural standpoint.
Teeu III. OssnnvEDeNDCercurernoIxrawsrrmsor.RnlrEcrrom
Plane
111
100(2)
210
211

PyriteSperrylite
Observ. Observ. Calc.

Ullmannite

Observ.

Calc.

1.5

325

5x550x12
22970s227
436671590
543102320

rr0(2)

328704rrs

311

1

1

1434

Erplanation of tobte.-This tabre gives theobserved values of the i'tensities
of reflection from the most important planesof pyrite; and the observed andcaluclated values for the corresponding planesof sierryrite and utmannite.
For
the observed values, 1 represents the mostintense line. For the carcurated values.
the.intensities are proportional to the number
gir"".
ih;;;;;;;r;;;;;
units, and.cannot be used in compari.rlg
th. ,u*" planes from different
iiltlly
mrnerals' rhe relative difierences in the intensities
for planes 37r,277, and 210
for pyrite and ullmannite is very apparent.
The retter ,.x,, indicates that the rine
was so obscured by the general brackening
on the film that its comparative intensity
could not be determined.

JOURNAL MINERALOGICAL SOCIETV OF AMERICA

299

CINNABAR GROUP
The two minerals cinnabar (HgS) and covellite (CuS) have been
considered as forming an isomorphous group' Their compositions
are analagous,and both crystallize in the hexagonalsystem' Grothl6
and Dana 17refer cinnabar to the trigonal trapezohedralclass,withan axial ratio of 1:1.1453.They assignto covellitea ratio of I:1.t466,
but expressdoubt as to the class of symmetry to which it belongs'
In view of this uncertainty, it was thought that X-ray data might
be able to determine whether covellite had the same structure as
cinnabar or not. If it did, its symmetry would be clearly established.
ClNNasanhas an axial ratio ol l:2.29, whicli gives c a value just twice thatwhich has been assignedto the crystals. In Table IV the spacings
for the various planes which recorded reflections on the-film arecompared with the calculated values for a rhombohedron of thedimensionsgiven above.
The customary calculations, involving the density of cinnabar,the volume of the unit cell, and the weight of one molecule of HgS,

rhombohedron, and a S atom in the center. Each corner Hg atom
would be shared in com'mon by eight adjacent rhombohedrons' sothat only one eighth of each atom would belong 1e an individual
rhombohedron; but there are eight corners, so there would be a
total of eight pighths belonging to each unit cell. The S atom at
the center, would, of course,furnish one atom for every cell'
At first sight the steep rhombohedral character of the unit cell
seemsto represent a less simple structure than that of the similar
compounds PbS (galena), which is face centeredcubic' As a matterof fact, its structure is very much like that of galena' There is no300

THE AMERICAN MINERALOGI ST

specialsignificanceto this similarity, except that it shows that there
is no great differencein structure involved in this change to lower
symmetry, and the type of bond between the atoms must be quite
similar.
The rhombohedron of cinnabar could be thought of as a greatly
distorted cube, but this would involve a change in the axiar ratio(regarding the cube as a specialrhombohedron with an angl'bof 90")
from 1 :1.22to l:2.29. (Figure Ia). This would mean thatlhere wasa considerable difference rn the interatomic forces of the twocompounds.
A more simple relationship between galena and cinnabag can befound. The points of a face centered cube can be connected so as
to form a rhombohedron. (Figure Ib). This has an axial ratro of
l:2.45. A slight compressionalong the c axis would change this toa rhombohedron with the ratio found for cinnabar: namely, l:2.29.
The relative changeinvolved is shown in Figure lc.

It
D

FIGURE 1
In this change the face-centered-cubepositions of the pb atoms
in the galena structure become the rhombohedron-corner positionsof the Hg in cinnabar. ilhe S atom at the center of the galena cube
would still be at the center of the rhombohedron. It is not easy tovisualize the change from the old positions of the s at the middleof the cube edgesin galena to the new position in the rhombohedron.
Ifowever, they would fall into their proper plgces at the centers ofadjacent rhombohedrons, and every position of the galena cube
would have its equivalent position in the cinnabar structure. Thereis, therefore, a very close relation between the two structures. The
two minerals cannot be considered isomorphous, becausethey are
essentially different in their crystallographic properties, and yet aslight deformation will derive either structure from the other.

IOURNAL MINERALOGICALSOCIETVOF AMERICA

301

have d casein which a very slight deviation from the rhombohedral
isarrangement is not detected by the X-ray analysis, and yet
sufficient to make a marked differencein the optical properties.
Covn'r-urp
Becauseof the doubt as to the proper symmetry class to whichcovellite should be assigned,it was thought that a determination
lower
of its structure would show whether or not the symmetry wasthan that of cinnabar. The difiraction pattern was difierent thanIn
was obtained,for crnnabar' This in itself is of no significance'asspacings'
if
their
be
comparedthe cubic system all crystals canInlogarithmically'plottedrecorded on the difiraction patterns, are
all the other systems crystals are not thus comparable unless they
have the same axial ratios, for a very slight changein the ratio mayofmake a marked difierence in the position' or even in the number'lines in the pattern. .Covellite has an axial ratio similar to cinnabar'The
but there could very well be some difierence in the pattern'rhombohedral
simpleapattern secured,however, did not agreewith
arrangement of any axial ratio whatsoever'theAttempts were made to secureLaue photographs to establish
structure'
the
to
as
information
give
additional
symmetry and to
were
Covellite has perfect basal cleavage, and the photographs
plane'
cleavagethetotaken rvith the X-ray beam perpendicularfrom
Instead of the usual pattern of spots, only streaks radiating
deformathe center were secured. These are usually attributed towere benttion of the crystal, so it may be that the rather soft plates
no better
however,manipulation,
carefulEven
withby handling.
results were securedin repeated attempts.
The actual structure of coveilite cannot be deduced from theisavailable evidence, but it does seem clearly established that it
not isomorphouswith cinnabar, and probably doeshave a difierent
symmetry.

302

THE AI,TERICAN MINERALOGIST
Tanrn IV. Onsrnvnu aNn Cer,curerro
Plar-e
1011
0001
0112
1120
1014
0221
1123
10I1(2)0001(2)
tjI2(2)
2131
rzSz\

2o2sJ

Spacrxcs ron CrnNlren

Observedspacings

Calculated
spacings

3.364

3.36A

J.l/

2. 8 7
2. 0 8
1.98
r.764
|.73
1.680
1.580
1.440
1.340

2.86s
2.074
1.980
1.764
1. 7 3 5
1.680
1.585
1.432
1.341

r.312

1. 3 0 5

SUMMARY
GnraNa cRoup-claustharite and altaite have structures similar
to galena, but with larger unit cells, while the other members of thegroup do not have the galena structure, and hence are not isomorphous with galena. They are probably orthorhombic. The
existence of argentite and acanthite as two separate minerals isdefinitely disproven. The cubic form of argentite is explained as a
pseudomorph after a high temperature form of AgzS.
Pvurn cnour-sperrylite
has the same structure as pyrite, as_
does also ullmannite. The lower symmetry of the crystais ofthelatter is accounted for by the substitution of large, Sb atoms
forhalf of the S atoms. Gersdorffite is very similar to ullmannite
andhas the same symmetry, although no ciystals have been observed
which showed this. The X-ray data indiiate that cobartite rikewise
has the pyrite structure, with the same symmetry as ullmannite.
A
possible explanation is given to account for the opticar
data whichapparently contradict the X-ray evidence concerning the crystal
form of cobaltite. Smaltite and chloanthite should be isomorphouswith pynte, but the X-ray d.ata aredecidedly unsatisfactory, urrd
rroexplanation could be found for the diffraciron patterns, altbough
it may be that the crystals were not homogeneous.
CrNNasen cnoup-A simple rhombohedral structure is deduced
for cinnabar from the X-ray data. The unit rhombohedron
has anaxial ratio twice that usually given to the crystals, andcontains
one molecule of HgS. Although the structure of covellite
was not

TOT]RNAL MINERALOGICALSOCIETY OF AMERICA

303

determined, the evidence showed that it is unlike that of cinnabar.
and that they are not isomorphous.
CONCLUSIONS
fsomorphism is essentially a means of classification, and its
validity depends upon the extent to which it is based on fundamental rather than superficial facts. The ordinary conception of
isomorphism antedates any knowledge of actual crystal structure.
In an attempt to get at more fundamental relationships than were
evident from the crystal form, there were introduced such ideas asequivalent parametersls and topical axes for molecular distanceratioslelbut still more fundamental than theseis the structure itself,of which all these others are merely expressions. Since there is now
a means of determining the structures, it is possible to base isomorphism directly upon them.
Ordinarily the crystal form can be regarded as fundamental,
but apparently there are caseswhere this cannot be done. The
crystals of argentite are either pseudo-cubic,or, if the structure be
assumed to be complex cubic and not orthorhombic, their resemblance to the crystals of galena is merely a coincidence. This likewise applies to hessite, eucairite, and naumannite. fn the pyrite
group, the lower symmetry of ullmannite is not due to any fundamental difierencein structure. It still has the pyrite structure, andshould be consideredisomorphouswith it.
If structure is to be the criterion of isomorphism, we should nolbnger have isomorphous groups in which the members have a
different number of atoms. An exception to this might have to bemade to cover the substitution of a group such as NHa for a single
rnonovalent atom. The indications are that this group functions as
a crystallographic entity as well as a chemical entity2o and canoccupy a position in a structure analagous to that occupied by asingle atom; but in no way could two Ag atoms in AgrS occupy a
position correspondingto one Pb atom in PbS, without violating theprinciples of spacegroup theory.
Not only can the structure be used instead of the crystal form
in determining isomorphism, but it also has a direct bearing on
the analogy in chemical compositions. Apparently similar compounds may have the samenumber of atoms with the samevalences,and yet have different structures, as HgS and CuS. This means thatvalence alone is not sufficient to determine the analogy in composi-

304

THE AMERICAN MINERALOGISTtion. Hg and Cu do not occur in the same famrly of the periodic
table, and the atoms themselves are not of analagous types, so
there is no reason to expect the two compounds to have similar
structures. On the other hand there are cases of isomorphousgroups wrth elements from different families. It would seem best,then, to make the criterion of analogy the similarity of interatomic
forces, which, in turn, means similarity of crystal structures.
In the majority of cases the old definition of isomorphism will
suffice,but the analogyin chemicalcomposition must be understood
as applying only to such compoundsas have analagousstructures,aswell as similar chemical natures. Moreover, it must be rememberedthat while the crystal form ordinarily is an accurate expressionof
the structure, it may be at variance with it. In such cases thecriterion to be used must be the more fundamental of the two, thecrystal structure.
RnrrnrNcrs
I W. H. andW. L. Bragg:X-nnvsam CnvsrerSrnucruno(lst ed.)p. 173(19f5).
' R. W. G.Wyckoff:TrrnSrnucrunnor Cnvsrar,s 107(1924).
,p.
,

3 E. S. Dana: Svsrru or MrNERAloclr, (6th ed.) p. 55, (1914).
a W. H. and W. L. Bragg : X-r.rvs exo Cnvsrar, SrRUcruRE (4th ed.) p. laa
G924).
6 Mechling: Aband..Math. Phys. Ahad.. Wiss. Leipzig,3T-51 (1921).
6 Schneiderhdhn: ANllrruxc
zuR MrKRosKoprscHEN BtsrrlrlruNc voN ERZEN rN
AUIIAILENDEN Licrr.
Berlin (1922).
Abstr. Econ. Geol.,18,6M (1923).
7 W. H. and W. L. Bnecc: X-nlvs ewo Cnvsrlr, Srnucrunr,(re24).

(4th ed.) p. ll5-l2l

8 Ewald: Ann. d..Physik,44,1183,(1914).
eEwald : Ann. d..Physih, 44, 1183,(1914).
10H. A. Miers: MrxnnAr,ocy,p. 332 (1902).
u Alling: Jour. Geol.,29,194-294(1921).
12Volkhardt Z. Krist.14, 407 (1888).
t3Baumhauer.
Z.Kri.st.12,15 (1886).
raBeutell: Centr.Mi,n. Geol.,2O6-221(1916).
15Parsons:Contributionsto CanadianMineralogy,p.9,
Q92a).
16Groth. Tabellarischeiibersicht der Mineralien p. 28, (1898).
17E. S. Dana: Svsrnn or Mrxnur.ocy. (6th ed.)p. 66 (1914).
18Barlow and Pope: Chem.Soc.Trans.,89,1675(1906).
leMuthmann:Z. Krist,22,497 (1894);Tutton:Chem.Soc.Trans.,65,628(1894).
20R. W. G. Wyckoff: TnB SrnucrunBol Cnvsrer,s,p.320,L924.