Thecrystalstructures ofclinoenstatite andpigeol1ite …rruff.info/doclib/zk/vol114/ZK114_120.pdf · are.distinct from the augite-type pyroxenes, which have asimpler structure inthe

Zeitschrift fUr Kristallographie, Bd. 114, S. 120-147 (1960)

The crystal structures of clinoenstatite and pigeol1iteBy N onuo MORIMOTO

Geophysical Laboratory, Carnegie Institution ofvVashington,vVashington, D.C.and Mineralogical Institute, Tokyo University, Tokyo

and

DANIEL E. ApPLEllIAN and HOWARD T. EVANS, JH.U.S. Geological Survey, Washington, D.C. ;

With 6 figures

(Received December 12, 1959)

Auszug

Die Kristallstrukturen del' monoklinen Pyroxene Klinoenstatit MgSi03 undFerropigeonit (Ca,Mg,Fe)Si03 wurden auf Grund von \Veissenberg-Aufnahmenurn die a-, b- und c-Achse bestimmt und mittels zweidimensionaler Fourier-Analyse und del' Methode del' kleinsten Quadrate verfeinert. Die Atomabstiindewurden auf 0,05 A genau ermittelt, Die Abweichungen gegeniiber del' Diopsid-

struktur werden erliiutert und kristallchemisch begri.indet. Die Einfi.igllng dol'kleinen zweiwertigen Kationen in die fi.ir den Diopsid charakteristischen ein-fachen Si03-Ketten bedingt, daB die beiden Ketten del' Elementarzelle kristallo-graphisch verschieden werden, und damit den Ubergang von C2/c beim Diopsid

zu P21/c. Beim Ferropigeonit ist jedes del' Metalle Ca und Mg einer del' beidenLagen M1 und Mil zllgeordnet; Fe verteilt sich auf beide Lagen. Die groBeronMetallatome bevorzugen die MrLagen: Die Koordinationszahl von M1 ist irnDiopsid acht, im Pigeonit sieben und im Klinoenstatit sechs, wiihrencl cliejenigevon Mil in allen drei Strukturen sechs betriigt. Die Pigeonitstruktur verrnitteltzwischen den Strukturen von Diopsid und Klinoenstatit.

Abstract

The crystal structures of the two monoclinic pyroxenes clinoenstatite,MgSi03, and ferropigeonite, (Ca,Mg,Fe)Si03, have been determined from two-dimensional x-ray diffraction data, and refined by Fourier and least-squaresmethods. Bond lengths have been determined with a standard error of 0.05 A.Deviations in these structures from that of diopside have been elucidated andexplained in terms of crystal-chemical principles. The introduction of smallbivalent cations into the single-chain silicate structure characteristic of diopsideis shown to result in the production of two crystallographically non-equivalentchains in the unit cell, with a corresponding change in the space group from

C2/c to P21/c. In ferropigeonite complete order of Ca and Mg is found betweenthe two metal positions, M1 and MIl' while Fe occupies both sites. Analysis of the

coordination environments of the metal atoms in the clinoenstatite, pigeoniteand diopside structures indicate that the larger atoms, where present, occupy the

:onite

lngton, D.C.

MgSiOa undAufnahmenler Fourier-)mabstandeler Diopsid-lfLigung dertischen ein-lIe kristallo-Jim Diopsicl, der beiden~ie gr6f3eren

[l M1 ist irnleI cliejenige

[' vermittelt

tloenstatite,from two-

Jast-squares

r of 0.05 A.~idated and)n of small

: of diopsiclel-equivalentgroup from

nd betweenalysis of thee, pigeonite, occupy the

I The crystal structures of clinoenstatite and pigeonite

Mr positions preferentially; thus the coordination number of M1 is eight indiopside, seven in pigeonite and six in clinoenstatite, while the coordinationnumber ofMn is six in all three structures. The pigeonite structure appears to beintermediate between those of diopside and clinoenstatite.

IntroductionThe determination of accurate crystal structures of rock-forming

minerals of known chemical composition formed under various condi-tions has become an important field of investigation in mineralogy.From this viewpoint, many excellent crystallographic studies havebeen carried out on feldspars and amphiboles. A corresponding studyof pyroxene structures, however, has not yet been made, in spite ofrecent developments in the petrological and experimental study ofminerals of this group, and in spite of their relatively simple crystalstructures compared with those of feldspars and amphiboles. Thisstudy has been undertaken as a part of a program to obtain crystallo-chemical knowledge of pyroxenes in general.

Previous work on pyroxene structures

The natural pyroxenes fall into two classes: orthorhombic andmonoclinic. The orthorhombic pyroxenes are known only in the com-position range MgSi03-FeSi03, with less than 10 mol percent ofCaSi03 (KUNO, 1954; HESS, 1952). 'VARREN and MDDELL (1930) havemade an x-ray analysis of hypersthene of composition (Fe.30MK7o)Si03.ITO (1950) has re-examined this structure using a hypersthene of com-position (Fe.16MK84)Si03,and discussed the relationship between mono-clinic pyroxenes and orthorhombic pyroxenes. Protoenstatite, anotherorthorhombic form of MgSi03, which forms synthetically at hightemperatures, was described by THILO and ROGGE (1939), and FOSTER(1951), and its structure was analyzed by SlYIITH(1959). This paper isconfined to a structure study of the monoclinic group of pyroxenes(clinopyroxenes).

VVYCROFF,MERWIN and WASHINGTON (1925) have shown thatdiopside, CaMgSi206; synthetic acmite, N aFeS~06; jadeite, N aAISi206 ;hedenbergite, CaFeSi206; and various augites have similar structuresand belong to the clinopyroxenes. Among these pyroxenes, diopsidewas the first mineral to be analyzed by x-ray diffraction methods(\VARREN and BRAGG, 1928). WARREN and BISCOE (1931) have com-pared diopside, hedenbergite, augite, acmite, jadeite, clinoenstatite(MgSi03), and spodumene (LiAISi206), and concluded that all thesesubstances are members of the monoclinic pyroxene group with

121

..

122 N. MORTl\lOTO, D. E. ApPLEMAN and H. T. EVANS, JR.

diopside as type structure. They have also shO\yn that the structureof spodumene is slightly distorted as compared with diopside due to'the small size of the Li atoms. :MORIMOTO(1956), and BOWN and GAY(1957) have found that c1inoenstatite and pigeonite, (Mg,Fe )2Si206'belong to the space group P21/c, whichis' different from that of diopside,C21c.

Although accurate measurement of unit cell dimensions of pyroxeneswith various compositions has been made (HESS, 1952; KUNO and

II

augiteillllllllllllll""'"""""""",

Rl!gion of probabll! immiscibility II'1IIIIIIIllllltIIIIIIIIIlIIIIIJIIII!IIJiJIIII

Mg5iOjctinoenstatite

pigeonite oFe5iOj

ferrositite

Fig. 1. Composition diagram for the clinopyroxenes. Circles indicate compositionof specimens studied in this work

HESS, 1953), no refinement of their structures such as is possible withmodern techniques has been made and the minor structural variationsamong the different members of the series have not been investigated.

The relation between clinoenstatite, pigeonite and diopside

The most important pyroxenes found in nature occur in the ternarysystem MgSi03-FeSi03-CaSi03, shown in Fig. 1, with less than50 mol percent CaSi03, although some replacement by other cationssuch as AI, Ti, Fe+3, etc. usually takes place. The monoclinic pyroxenesin this field may be divided into two different types. One is near theCaMgSi206-CaFeSi206 join, with more than 25°/0 and less than 50° If}CaSi03 component, and is typified by augite, diopside and heden-bergite. The other lies near the MgSi03-FeSi03 join with less than

15°/0 CaSi03 component, typified by pigeonite and clinoenstatite.Some evidence of immiscibility between these two types has beenobserved in a region indicated by hatching in Fig. 1, in nature and in

I

I

tructure~ due tomd GAY

, 'e)2S~06',

liopside,

lrroxenesJ:NO and

)J

lE

If

ti

II,

)1 nposition

. <

. i<

n hIe ,,,ithlC . .

lnatIOns-;tigated.

r

iopsidenc. .

. ternary

mf 'ss thanr

', cations

cae,ToxenesIn

near the:0l-e Ian 50%

gr l heden-ncJ ess thanal~ nstatite.e,

b1as een,0<'e and in

r The crystal structures of clinoenstatite and pigeonite

.;

(

the laboratory (POLDERVAARTand HESS, 1951; ATLAS, 1952; SOHAIRERand BOYD, 1957). The monoclinic pyroxenes of the pigeonite type,namely~ clinoenstatite and pigeonite, have the space group P21/c andare. distinct from the augite-type pyroxenes, which have a simpler

structure in the space group 02/c.

The problem of the stability relationships between the monoclinicpigeonite-type pyroxenes, the orthorhombic pYroxenes (hypersthenes)and. proto enstatite has not yet been settled. When the FeSi03 com-ponent is less than about 30 mol percent, high-temperature x-ray andquenching experiments confirm the existence of three polymorphs,

enstatite, protoenstatite and clinoenstatite (FOSTER, 1951), although

only the enstatite form is known in nature. FOSTER and also ATLAS(1952) have assumed the following relations: protoenstatite-high-temperature form; enstatite-low-temperature form; and clinoen-statite-,--low-temperature, metastable form. Of the pyroxenes along

the MgSi03-FeSi03 join with more than 30 mol percent FeSi03 com-ponent,the monoclinic form, pigeonite, and the orthorhombic form,hypersthene, have been found in nature (POLDERVAART and HESS,1951). The mode of occurrence clearly shows that pigeonite is a high-temperature form and hypersthene is a low-temperature form (BOWENand SOHAIRER, 1935; POLDERVAART and HESS, 1951).

On the basis of the pyroxene relationships so far known, ourinterest has been concentrated on the following two crystallographicproblems: (1) the structural relations between diopside, pigeonite andc1inoenstatite; and (2) the structural relations between the three poly-morphs of MgSi03, i. e. enstatite, protoenstatite and clinoenstatite.Solution of the first problem 'will clarify the effect of different metalatoms on the silicate chain stru?ture and on the stability relationsofclinopyroxenes. This paper is only concerned with this problem.The structure analyses of clinoenstatite and ferropigeonite have beengiven in parts I and II respectively, and in part III 'we will discussthe relations among the structures of clinoenstatite, pigeonite anddiopside. The structure refinement of enstatite is no'v in progressand a study of the second problem will be published in the nearfuture.

The comparisons between our structure determinations of clinoen-statiteand pigeonite with the diopside structure are based on theclassic study made of diopside by VVARREN and BRAGG (1928). Theirtrial-and-error analysis was subsequently augmented by Fouriersynthesis studies, the first ever made in crystal structure analysis,

123

--

...

124 N. MORIMOTO,D. E. ApPLEMAN and H. T. EVANS, JR.

by BRAGG (1929). By modern standards, the Fourier series used arevery poorly resolved, and we believe that the structure coordinatesobtained earlier by WARREN and BRAGG (1928) are more reliable.These are the data we have used in this paper. Obviously, a redeter-mination of the diopside structure is urgently needed.

The present study is based only on two-dimensional data, con-sisting of three projections for each structure. The refinements havebeen carried by the method of least-squares analysis to close to thebest possible stage, but the standard errors of the interatomic distancesare still appreciable, about 0.05 A for metal-oxygen and 0.07 A foroxygen-oxygen distances. Such accuracy is sufficient for the mainpurpose of this work, namely, interpretation of changes of coordinationand adjustments in silicate-chain dimensions which accompanysubstitutions of metal ions for one another. We believe that the struc-ture of diopside as given by VVARREN and BRAGG (1928) is also suffi-ciently accurate for this degree of interpretation. Studies of relation-ships among ionic charge, bond length and bond number must await amore accurate structure refinement, which can only be carried out IIIthree dimensions.

I. Structure analysis of clinocnstatiteExperimental

The specimens of clinoenstatite used in these experiments wereobtained by Dr. J. F. SOHAIRERof the Geophysical Laboratory, byheating Bishopville enstatite at 14000 C for 24 hours. The chemicalcomposition in weight percentages of this enstatite is: Si02 59.97,MgO 39.33, and FeO 0.40, according to SMITH (1873). Clinoellstatitethus obtained always shows fine po!ysynthetic twinning on (100). Asit was impossible to get single crystals free from twinning, it wasnecessary to use twinned crystals to measure the intensities.

The cell constants were obtained from the powder patterns usingquartz and silicon as internal standards. The results are: a = 9.620

:f: 0.005 A, b = 8.825 :f: 0.005, c = 5.188 :f: 0.005, and f3 = 108020'

:f: 10'. These values are in good agreement with those of syntheticclinoenstatite (KUNO and HESS, 1953). There are four chemical units

of composition MgSiOa in the unit cell. The space group is P21!c (C~h)'Throughout this paper, an unconventional monoclinic setting is usedin which the positive senses of the ((, and c axes enclose an acuteangle f3, following the setting of axes in diopside by WARREN andBRAGG (1928).

J

r

used arelordinates

~reliable.1 redeter-

~~ata,con-

:mts have)se to the

distances.07 A for

the mainordination:companybhe struc-1lso suffi-

I relation- .,

3t await aI ed out In

II_mts were

'1tory, byI

chemicalr

O2 59.97,

I )enstatite

(100). Asg, it was

I

. rns usmg: (. = 9.620

: 108020'[

synthetic

: ical units: 21lc (C~h)'

19 is usedan acute

: mEN andI

The crystal structures of clinoenstatite and pigeonite 125

Both standard and integrating- W eissenberg photographs weretaken around the a, b, and c axes, using the multiple-film technique.The crystal used for the experiments was about 0.2 X 0.2 X 0.5 mm3 insize. CuKcx radiation was used for the hkO and hOl zones, and MoXcxradiation for the Okl zone. The relative intensities were estimatedvisually from the standard Weissenberg photographs and by thephotometer from the integrating- Weissenberg photographs. Thevalues obtained by both methods are in agreement within 5% for eachreflection. Their average was taken as the observed relative intensity.The twinning on (100) affects the intensities of the hOl and Okl reflec-tions. On these photographs, the intensities of those reflections whichare common to the two twinned lattices were corrected according tothe relative intensities of the respective lattices as a whole. Therelative intensities were corrected for Lorentz and polarization factorsgraphically. No correction was made for absorption, nor for extinction.After the r!3lative intensities were adjusted to the same scale using thecommon reflections, they were converted to absolute values on thebasis of the calculated structure factors of diopside, taking intoconsideration the difference of composition between diopside andclinoenstatite. These values were resealed through the course of thework as each new set of structure factors was calculated. For thecalculation of the structure factors, the scattering factor curves ofBRAGG and 'VEST (1928) were used in the earlier stages of refinementand the curves of BERGHUIS et al. (1955) were used in the later stages.

j

I

Structure analysis and refinement

The structure analysis of clinoenstatite was started from the knownstructure of diopside. Since reflections with h + k odd do not appearin diopside, we were not able to obtain the signs of these reflectionsfrom the diopside structure and the usual procedure of refinement didnot give the structure of clinoenstatite. The signs of these reflectionswere determined in the following way.

The difference of the structure factors between diopside andclinoenstatite is most noticeable with the hOl reflections. The firststep, therefore, was taken with the [010] projection, to find thedeviation of the atoms in the clinoenstatite from those of the diopsidestructure. Contour maps (BRAGG and LIPSON, 1936) of the strongestreflections: 702, 304, 704, 306, 102 and 304, which are not given bythe diopside structure, were made. The assumption of the sign of 102gave the possible area of the atomic displacement from the diopside


structure by using the contour map of 102. The other six contour ;niapsof the strong reflections listed above restricted the possible area of thedisplacement of atoms, giving the sign of each reflection. These sixh+k odd reflections .vere used for the first Fourier synthesis, togetherwith all h+k even reflections, the signs of which were determined from

the diopside structure given by WARREN and BRAGG. The resolutionof atoms in this projection "vas not sufficiently good to locate theoxygen atoms, but new positions of lYIgand Si atoms were determined.The coordinates of the oxygen atoms were estimated from geometricalconsideration of the structure on the basis of the newMg and Sipositions. These coordinates were used for calculation of hkO, hOl and

Okl structure factors to obtain signs, and Fourier syntheses were againcarried out for each projection. The atomic coordinates obtained fromthese electron density maps gave discrepancy factors

)Ii, .,-.

'!j

:.I

of about 30 percent.

On account of the difficulty of finding accurate positions of oxygenatoms, because of overlapping of atoms in the electron-density maps,the structure factors corresponding to a hypothetical structure con-sisting only of Mg and Si atoms were calculated. Fourier syntheseswere then carried out using these values but subject to the same con-ditions of termination of series as are imposed in'the Fourier synthesesby the observed structure factors. The resulting electron-densitydistributions were subtracted point by point from the experimentallydetermined ones, thereby giving projections free from the effects ofMg and Si atoms. The new coordinates of oxygen atoms obtained fromthese partial difference electron-density maps were used for thecalculation of the structure factors together with the coordinates ofInetal atoIllS previously given. t3tarting IrVIn thm;t) lWW t;\,rulj\,urlj

factors, the usual (Fo - FJ synthesis was made twice, in which termsfor reflections with Fo = 0 were given half weight. In the process ofthese (Fo - FJ syntheses, different overall temperature factors were.used for different projections. Finally, the coordinates were refined bythe least-squares method with an individual isotropic temperaturefactor for each atom.

Table 1A shows the method used for refinement at each stage,and the progress of the refinement as indicated by the usual discrepancyfactor R. In calculating this factor, only those reflections with IFo I > 0have been used. The observed intensities of the hOl and Olelreflections

~-

~

l,

nit::rilaps

eaof

the~hese.sixtogetherled

from

~solutioncate.

thejrm

ined.

metrical

<:U

andSi

......""

~hOland

c<:Ub',

.""~re

agaIn~~H

~dfrom~t3<:U......"" .....t3.....co~<:U

.\;\C~.""

.....,Q

:oxygen--.c.....

ym

aps,~<:U

lrecon-

~<:U

~rntheses.N--.<:U

~me

con-<:U

~.rntheses.....Q

:.density

;;3~.....co

lentally<:U

...-:.....

Ifectsof

--.c

;ed

fromco

.....,.""t3

forthe

.....<:U

~(latesof

.,...,

tiructure<D

..........0

]hterm

s~~r)cess

of

:rsw

ere

Einedby

i'erature2l: l

stage,

,'epancy.rj'

I>0

u. .0

lections

rn+"~<D

§00

~.....,~-0

~f:q

.....,0-..::::

~~0~-

~~'"d

0...c:+"<D;g(!)

b.O

~+"W

.

The

crystalstructures

ofclinoenstatite

andpigeonite

o~o~------

00t-~o

H

L~M

00L~

C'-lC'l

C'l.......

o

H

AtomsClinoenstatite Pigeonite Diopside*

xI

yI

z xI

yI '"

xI V I

z

Mr 0.242 0.986 0.193 0.246 0.981 0.231 i 0.250 0.944 0.250i

MIl .247 .347 .220 .251 .344 .23G I .250 .333 .250Sir .457 .658 .294 .453 .661 .274

,.461 .661 .236,

SiIJ .053 .661 .264 .049 .662 .252 I (.039 .661 .2(4)iOr .362 .156 .320 .372 .168 .315

I

.372 .153 .361i

0/ .124 .159 .112 .127 .166 .161 (.128 .153 .139)On .377 .498 .298 .378 .506 .323 .392 .500 .319On' .137 .518 .103 .125 .508 .147 (.108 .500 .181)am .395 .775 .101 .395 .773 .070 .406 .731 0am

,.105 .813 .051 .108 .782 -.OOG (.094 .769

,0 )I

128 N. MORIMOTO, D. E. ApPLEMAN and H. T. EVANS, JR. I

are probably less accurate than those of the hkO reflections because ofthe existence of twinning on (100) in the crystals used. The pooreragreement between Fo and Fe for the hOl and Okl reflections may thusbe accounted for. The final (Fo - Fe) maps along the band c axes werecalculated and are shown in Fig. 2. The final atomic coordinates aregiven in Table 2. The values of Fo and Fe obtained for the structurewhich was finally adopted are given in Table 3A.

"

Accuracy of the structure determination

The least-squares analyses of the three zones of data (in whichthe non-diagonal terms of the normal equations are neglected) givethe following average standard errors of the position parameters in.Angstrom units: Mg 0.016, Si 0.013, and 0 0.037. Thus, cation-oxygen bond lengths have a maximum probable error of about 0.05 .A

and oxygen-oxygen distances about 0.07 .A.The individual isotropic temperature factors B are erratic in their

distribution, and are subject to large standard errors. Thus, in thetwo refined projections, as shown in Table 4, the temperature factorfor Mg ranges from zero to 0.45, with an average standard deviationof 0.25; for Si, B ranges from 0.11 to 0.84 with an average standarddeviation of 0.21; and for 0, B ranges from zero to 2.49 with anaverage standard deviation of 0.62. vVithout knowing the influence

Table 2. Final atomic parameters of clinoenstatite and pigeon'ite compared withthose of diopside (WARREN and BRAGG, 1928)

* The origin of the coordinates of diopside is displaced by (.25, .25, 0) fromthe origin given by WARREN and BRAGG (1928), to show the differences of coor-dinates among the three structures directly. The coordinates given in parenthesesare crystallographically equivalent with those immediately above.

.

, The crystal structures of clinoenstatite and pigeonitei

)ecause of Table 3.Final observed and calculated structure factors for clinoenstatite and pigeonite

he poorer A. Clinoeqatatite

may thus b k 1 Fe F. h k 1 Fe F F F h k 1 F F. e . e .axes were 2 o 0 - 70 58 9 5 0 30 38 0 9 1 12 10 6 21 19

ina tes are 3 o 0 - 8 6 10 5 0 7 8 o 10 1 50 %8 11 6 21 23

!I o 0 2~ 19 6 0 171 173 0111 - 8 1 7 - 21 19

structure 5 o 0 5 6 1 6 0 4 o 12 1 16 H 0 2 7 - 7

6 o 0 -12~ 117 2 6 0 _ 28 23 0 o 2 -201 207 0 3 7 - 2~

7 0 0 - 5 6 0 - 5 1 2 - ~0 ~7 - 68 0 0 82 89 6 0 50 ~8 2 2 - 51 53 0 5 7 - 17

9 o 0 6 6 5 6 0 - 2 3 2 - 8 11 0 6 7 - 910 o 0 - 75 90 6 6 0 - 55 ~9 ~2 31 33 0 7 7 - 12

1 0 - 22 15 7 6 0 - ~0 5 2 33 35 8 7 -H

(in which 2 0 2 8 6 0 35 ~1 6 2 -H8 150 0 o 8 31 31

0 10~ 101 6 0 6 0 7 2 - 5 0 1 8 9 16

~ted) gIve 0 - ~10 6 0 - 70 62 0 8 2 - 12 15 0 2 8 2

0 39 ~~70 10 11 0 9 2 5 0 3 8

meters In 0 1 7 0 6 o 10 2 3~ 38 0 ~8~0

51 58 3 7 0 2 o II 2 17 19 0 5 8 - 23 25

s, cation- 8 0 - 3 4 7 0 o 12 2 - ~9 ~5 0 6 8 23 25

,ut 0.05 A 0 - 19 17 5 7 0 53 ~8 0 1 3 - 19 20 0 7 8 1

10 0 - 0 6 7 0 2 0 2 3 6 0 8 8

11 0 15 H 7 7 0 27 22 0 3 3 - 22 21

0 2 0 - 3 10 8 7 0 - 8 0 ~3 - ~4 t2 1 o 0 1

lC in their 1 2 0 3 7 0 11 11 0 5 3 - 6 13 2 o 0 - 71 63

2 2 0 - 89 90 8 0 19 22 0 6 3 - 17 21 3 o 0 - 8 6

IS, In the 3 2 0 - 5 1 8 0 - 5 7 3 - 20 19 ~o0 28 21

factor4 2 0 ~8 ~O 2 8 0 - 29 25 0 8 3 - 23 20 5 o 0 5 6

Ire 5 2 0 9 3 8 0 9 3 5 6 o 0 -128 129

deviation 6 2 0 - 12 12 ~80 7 o 10 3 - 33 31 7 o 0 - 7

7 2 0 - 8 5 8 0 0113 - 9 8 o 0 89 98

standard 8 2 0 35 H 6 8.0 - 17 18 o 12 3""

22 9 o 0 6 6

9 2 0 6 7 8 0 - 2 0 o ~112 115 10 o 0 - 85 99I with an 10 2 0 - 13 H 8 8 0 23 26 0 1 ~28 28 11 o 0 - 8

influence11 2 0 6 9 0 0 2 ~- 9 o 2 -202 197

3 0 - 5 9 9 0 21 10 0 3 ~- 9 9 o 2 - 26 2~

3 0 3 6 9 0 ~0 ~~-16 18 2 o 2 12 ~2

~3 3 0 - 35 38 3 90 0 0 5 ~- 26 22 o 2 8 12

pared with ~30 - 1 ~90 6 0 6 ~69 61 o 2 -125 120

5 3 0 19 20 9 0 19 17 0 7 ~2 5 o 2 - 22 32

6 3 0 9 0 6 8 ~6 o 2 123 118

7 3 0 15 20 o 10 0 -33 27 9 ~7 o 2 52 63

lde* 8 3 0 5 1 10 0 ~o 10 ~_26 27 8 o 2 - 61 75

9 3 0 13 15 2 10 0_ 12 11 o 11 ~- 23 20 o 2 - 10 12

Z 10 3 0 1 3 10 0 0 o 12"

20 21 10 o 2 86 109

11 3 0 - 15 15 ~10 0 - 23 20 1 5 28 25 11 o 2 11

0.250 ~0 31 32 o 11 0 0 2 5 10 11 12 o 2 - 2

1 ~0 - 2 1 11 0 ~5 ~~35 23 20 0 o ~111 111

.250 2 ~0 -47 ~~211 0 8 0 ~5 15 12 1 o ~25 17

.236 3 ~0 - 2 3 11 0 _ ~8 60 0 5 5 2~ 23 2 o ~24 20

~~0 - 31 36 0 6 5 19 17 3 o ~- 59 71.264) 5 ~0 12 13 0 2 0 - 1 8 0 7 5 12 12 ~o4 121 134

.361 6 ~0 - 20 26 0 ~0 33 3~ 0 85 19 5 o ~22 17

.139)7 0 - 6 0 6 0 17~ 176 0 9 5 11 6 o ~-110 87

~0 ~5 }6 0 8 0 25 2~ o 10 5 26 22 7 o ~_ ~6 ~2

.319 9 ~0 3 o 10 0 - 29 28 0 o 6 - 50 52 8 o ~19 12

.181)10 ~0 27 22 o 12 0 5~ ~8 0 1 6 -H 9 9 o ~2~ 12

1 5 0 97 93 0 1 1 17 11 0 2 6 1 10 o ~- 50 57

0 2 5 0 - 0 0 2 1 - 33 ~5 0 3 6 1 11 o ~-27 2~

0 3 5 0 - 75 65 0 3 1_ 20 18 0 ~6 12 12 o ~26

~5 0 - 3 0 ~1 66 6~ 0 5 6 28 27 0 06 - ~7 42

5 5 0 -H 2~ 0 5 1 27 21 0 6 6 - J~ 31 1 06 - 18 17~5,0) from 6 5 0 3 0 6 1 27 30 0 7 6 0 2 o 6 17 17

es of coor- 7 5 0 -108 112 7 1_ 14 0 8 6 3 3 o 6 44 J7

8 5 0 2 8 1 2 0 9 6 ~~o6 - 85 6z

arentheses

Z. Kristallogr. Bu. 114, 1!~ 9

130

h k 1

5 0 66 0 6

7 0 68 0 6

I 0 2

"2 0 2

h k

2 0 0

:I 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

10 0 0

1 1 0

2 1 0

:I 1 0

4 1

5 1

6 1 0

7 1 0

8 1 0

1

10 1

11 1

o 2 0

2 0

2 2 0

:I 2 0

4 2 0

5 2 0

6 2 0

7 2 0

2 0

2 0ci;~ I

~ ~,

,II

b 1~'t""~

10 2 0

11 2

1

2

3 0

3 0

3 0

3

5 36 3

7 3 0

3 0

3 010 3

11 3

o 4

1 4 0

2 4

3 44 4 0

5 4 06 ~ 0

7 ~ 08 4 0

~

_ ~o

JJ

~5

- 8

47

115

_ 6

-H- 23_ 2

- 75

- 19~611

- 59_ 8

~

9-

- 3~7

- 5H

- 2

- 13- 12

H

- 223

- 61

10

18

138

N. MORIMOTO, D.E. ApPLEMAN and H. T. EVANS, JR.

r cr o

h k 1

17 J 0 2

4" 0 2

'5 2b 2

"7 0

"8

Table 3. (Continued)

- 22

-105

- 756

- 16

- 30

2~55

_ 8

- 61

- 9- 39

13

- 739

1816

150

15

- 1

- 1521

- 15

- 38

- 151915

- 51H26

r ch k 1

10

10_

- 12

- 78

5267

- 33

- 21

-H160

19_ ~o

56

19

- 33

Fc r o h

'5b 0

"7 0 ~

h

30 11 3o 12 3

13 31_ 3

o 15 316 3o ~

~

-3 ~

- -o 5-o 6_o 7-

8 ~

o 9-o 10

_

11_

o 12 It

- 17

- ~-10

- 9- 12

- 133

- 1637~3

-H

- 6

- 35- 36

39

- 21

- 23

13I_

I

19

- 3~

33

- 1

33_ 0

25

50

125

r c Fo

2_

42

h k 1

12

26

10 ~ 0

1 5 0

5 0

3 5 0_ 5 0

5 5 06 5 0

7 5 0

8 5 0

9 5 010 5 0

6 0

6

6 0

3 64 6

5 6 06 6 0

7 6 08 6

9 610 6 0

7

73 74 7

5 76 7

7 7 08 7

78 0

r o

17 '9 0 2111 10 02

I

70 "2

12 J

39 4"

B. Pigeooi te

Fc

62

42

85

r c Fo

28

3525

60

42

~6

30

23

32

35

10

20 3 5~ 5

5 55

5

5

9 510 5

11

12 5

6

6

6

3 6o ~ 6

5 66 6

7 6

o 8 6

9 610 6

11 6

12 6

1 7o 0- ,3 74 7

5 76 7

7 7

25

~

711

16

20

- 17

- 1

11

- 920

7

-H- 10

- 382

- 26

26

728

69

19

47

5116

9

90

38

~o

20

15

11

27

55

12

17

15

5

10

17

16

18

8 0

3 8 0

4 8 0

5 0

6 0

7

8 0

1 9 0

2 9 0

9 0

9 0

5 9 0

6 9 0

10 0

10 0

10 0

10 0

10 0

11 0

11 0

20

912

12

35

27

21

27

23 11

57

o 2 0

50 0 4 0

5 0 6 0

3~ 0 8 0

o 10 0

80 0 12 0

o H 0

20 0 16 0

1~ 0 1 1

150 0 1

16 1

1

25

~

33

11

17

11

7

H

1~

- 27

16 5

23 6

15 0 7

35 0 8

17

20 0 10

12 0 11

56 0 12

17 13

23 H

~5 15 1

16 1

3"1521 0

12 3 :2

H

17 0

16 0

27

12

o 8

15 0 9 2

17 0 10 2o 11 2

12 2

17

6

o

17

o

2

511

152

- 3~

8

- 18

o_ 16

26

15 13o H 2

o 15 2

o 16

16 0 1 3

16 2 3

3 3

35 0 ~ 3o 5 3

16 6 3

7 3

17 0 8 3

19 0 9 310 3

12

156

18

36

62

21

- 56

- 39

~7

30

27

- 2

- 38

- 1

36

18

17

2

15

-12_

17

115

8

11

19

37

~8

86

~

17

- 10

-133953

- 9-o

- 18

3933_"26

- 173

26

- 3323

- 25

- ~3

- 26o

- 21

- 1

- 8- 22

3633~5

720

29

23

H

~2

25

21

r c r o

1762

Fc Fo

10

17

2

H

37

46

10

28

12

~o

~1

10

}

I

I

1700

20

31

36

23

10

19 :lO

- 2L ,""

19

3

13 2326

1027

11

6

11

10

11

15

21

12

23_ 6

-16

8

11

15

10

o

16

7

9

1~

.. l The crystal structures of clinoenstatite and pigeonite

Table 3. (Oontinued)

, 1 F F 0 h k 1 F Fo h k 1 P Po h k 1 Pc P h k 1 Pc Pc c c 0 .)

" - 17 17 0 87 15 7 o 0 - 21 21 1 o" "

11 7 o 6 28 27)"

-.. 62 0 97 1 17 8 o 0 "7 "8 2 o"

28 18 '1 o 2 83 75)

"10 o 10 7 _ 0 o 0 6 22 o

"- 80 90 2" o 2 67 75

0 o 8 - 9 10 o 0 - 56 5" o"

57 73 3 o 2 - 35 290 1 8 25 22 11 o 0 - 7 5 o

"29 110 i; o 2 - 63 51

0 2 8 -11 0 o 2 -121 113 6 o"

- 12 30 '5 o 2 - 19 190 3 8 6 1 o 2 - 27 22 7 o

" - 57 52 b o 2 22 220

"8 - 10 2 o 2 - 63 65 o

"_

1" 13 "7 o 2 - 18 190 5 8 - 36 28 o 2 - 13 12 o

" - 10 11 '8 o 2 10 50 6 8 - 8 o 2 - 66 73 10 o

"-13 20 '9 o 2 13 1",1 F F0 0 7 8 15 5 o 2 - 21 12 12 o

"- 9 10 o 2 70 63c

6 o 2 66 61 0 o 6 _ 18 15 '1 o"

10 110I 3 - 9 1 o 0 7 o 2 99 70 o 6 - 25 21 2" o

" - 5 17! 3 - 12 10 2 o 0 - 6 8 o 2 - 18 27 o 6 _ 26 11 3 o

" 8" 57..~3 -13 17 3 o 0 - 13 10 9 o 2 1 7 3 o 6 51 5"

i; o"

33 35,

3 3"

o 0 _ 26 27 10 o 2 37 H"

o 6" 2" '5 o

" - 19 1"i 3 5 o 0 - 0 5 11 o 2 3 6 5 o 6 6 b o

" - 26 2"; 3 - 16 H 6 o 0 - 73 77 0 o"

32 37 6 o 6 2 11 "7 o"

- 0)"

37 37!

""3 "6

!"

-H 10on the data of absorption and twinning in the crystal, it is felt that~" - 6

," - 35 26 great significance be attached to this distribution of tem-

i" - 36 "0 no can. " 39 "1 perature factors. The same observation may be made about the final.." 12 10

!"

- 5 residual maps of Fig. 2, which do not show any interpretable features,)" - 0

especially in regard to anisotropic thermal motions.I" - 21 17

" - 23 0'>,

"19 20

i" - 3 Table 4. Isotropic temperature factors obtained by the least-squares method,

" "33 31~5 - 1

AtomsClinoenstatite Pigeonite

;5 33 36

I I0.)

BhkO £B BOkl £E BhkO CE BOkl CE, 5 -; 5 25 210, 5 Mr 0.43 0.26 0.07 0.26 1.32 0.17 0.64 0.09. 5 25 23

MIl .45 .26 .00 .20 1.09 .22 .62 .11i 5I 5 10 Sir .41 .23 .25 .17 .49 .34 .75 .17, 5 Sin .84 .27 .11 .17 .73 .37 .80 .16

19 ::!o, 5 Or .96 .62 .26 .47 .81 .71 1.53 .60, 6 - 2L 16

Or' 1.24 .66 .47 .50 .00 .56 1.19 .556 - 25 -,

, 6 19 I. On 2.49 .80 .73 .57 .86 .93 .91 .47.6 - 3 °n/ .86 .60 .47 .60 1.44 1.03 .73 .48

6 13 23,6 27 26 Om .65 .68 .75 .65 .00 .59 1.02 .51. 6 -11 10 Onr' .00 .47 .80 .77 .00 .62 .94 .58. 6 - 6, 6 6 10 R 0.11 0.12 0.11 0.07, 6 - 11 11

6 12 15

6 23 21

6 - 6 11II. Structure analysis of pigeonite7 - 16 15

7 8Experimental. 7 10

7 0The crystals used for the structure analysis are taken from ferro-7 - 16 I.

7 7 pigeonite speCImens kindly donated by Professor H. KUNO. He7 - 9

collected them from andesite-dacite dikes near the Asio Mine, Japan,

9*

,I..

il..'1'

;

,i

,~

It.i;

!;

.,132 N. MORIMOTO,D. E. ApPLEMAN and H. T. EVANS, JR.

and described the chemical composition as follows (personal communi-cation, 1959):

Mole ratiosWeight per cent

Si02 48.36Al20g 0.41Fe20g 1.36FeO 32.86Ti02 0.39MnO 0.84MgO 11.34CaO 4.58Na20 trK20 trH20(+) 0.15H20 (-) trP2050.04

100.33

Crystals of about 0.3 X 0.3 X 0.5 mm3 were used for the standard

and integrating-\Veissenberg photographs as in the case of clinoen-statite, and CuJ(C(, FeJ(C( and MoJ(C( radiations were used. There was

no twinning in these crystals. The cell constants were determinedby the powder method using silicon as a standard substance. They are:

a = 9.731 :::!: 0.005 A, b = 8.953 :::!: 0.005, c = 5.256 :::!: 0.005 andfJ = 108033' :::!: 10'. The space group is P21!c (C~h)' the same as thatof clinoenstatite. There are eight formula units of Cao.l01Ylgo.34Feo.56Si03in the unit cell. Intensities were obtained in the same way as forclinoenstatite. The intensities were corrected for Lorentz and polariza-tion factors and scaled by comparison with calculated structurefactors in the usual way. The structure refinement was carried outin almost the same way as for clinoenstatite.

SiAlFe+3Fe+2TiMnMgCa

1.933

}0.0180.0411.0970.0110.0280.6750.195

2.01

1.99

CaSiOg : MgSiOg :FeSiOg (includingMn~iOg)

= 10 : 34 : 56*

Refinement

The atomic coordinates obtained for clinoenstatite by the use ofcontour maps of strong hOl reflections were used for the first structure-factor calculation of pigeonite. Completely disordered distribution ofmetal atoms Mg, Fe and Ca over the available positions was assumedin this calculation. Using the signs of the calculated structure factors,

* This table represents a revision of an earlier analysis by KUNO (personalcommunication), in which these ratios were determined to be 12: 26: 62. Allof our structure factor calculations for ferropigeonite are based on these earlierratios. vVe have not repeated the calculations using the improved ratios, becausethe difference is not great enough to affect the structure determination.

communl-

standard)f clinoen-

There waseterminedThey are:1.005 and

lle as that

FeO.56 Si 03'ay as for1polariza-structure

nried out

jhe use of

structure-ibution of

3 assumedre factors,

o (personal26 : 62. Allhese earlieros, becauseJon.

The crystal structures of clinoenstatite and pigeonite

the electron-density maps projected along [100], [010] and [001] werecalculated. It was obvious from the difference in peak heights on thesemaps that some ordered distribution of metal atoms is present in thestructure.

..

c2

.,,--...../" '

0)

... o2

..

\'

I\ / /\ ", ,,"

'-"

b2

b)I

o1

3~I

7I

2

Fig. 2. Final (Fo-Fc) syntheses for clinoenstatite projected (a) along the a axisand (b) along the c axis. Contour intervals: for (a) 1 electronjA2; for(b)O.5

electronjA2. The zero contours are omitted, negative contours dashed.

133


There are two crystallographic ally different positions for metalatoms in the structure ofpigeonite as in diopside. One, called theMr position, is considered to be suitable for larger metal atoms, suchas Ca in diopside, and the other, called the lVIIIposition, is associated

1L2

xMil, ,/' , '

I \ ,, \ \ \\ , J \',"'- \...~

", --,I

,

\ I

'"

/'--"',\I I,--,,/

a)

..a2

.

;. (

,4 "

~\'.I

,_

.~,

.,,'

oO/[J'

b) o 1I

2I

3~

Fig. 3. Final (Fo-Fc) syntheses for pigeonite projected (a) along the a axis and(b) along the c axis. Contour intervals, 1 electron! A2; zero contour omitted,.

negative contours dashed

-

for metal}aIled. the)ms, suchLssociated

':Laxis andr omittedy


with smaller atoms such as Mg in diopside. Four likely arrangementsfor the: metal atoms in pigeonite of composition CaO.l0lYIgO.34Feo.56Si03were considered as follows:

ICase

I

I

(1)(2)(3)(4)

Ca20FesoCa20F e50lVIg3oCalolVIg34Fe56Ca2oMg6sF e12

lVIg6sFe32lVIg3sFe62

CaloMg34Fe56FelOO

Assumption

Complete order of Ca and l\IgComplete order of Ca onlyComplete disorder of Ca, Mg and FeComplete order of Ca, Mg and Fe

Ratio ofelectrondensity(lVIliMn)

1.501.001.000.59

The electron-density ratio obtained from the peak heights at theMr and MIl positions is found to be 1.40, which is closest to case (1).The ordered distribution of metal atoms reduced the discrepancyfactor of the hOl reflections from 0.45 to 0.35. The electron-densitymaps showing only oxygen atoms were constructed by subtractionof the calculated contributions of metal and Si atoms from the ob-served structure factors. The further refinement process has beencarried out in the same way as in clinoenstatite, and is shown inTable 1. In that table, only the reflections with IFo I > 0 were con-sidered in calculation of the discrepancy factors.

In Fig. 3, the final (Fo - Fc) maps along the band c axes are shown.The final coordinates are given in Table 2. Table 3 B shows the valuesof Fo and Fc obtained from the structure 'which was finally adopted*.

Accuracy of the structure determination

The least-squares estimates of the standard errors of the atomiccoordinates are comparable to the results obtained for c1inoenstatite.Again, little significance can be attributed to the indiyidual tem-perature factors calculated. The residual maps shown in Fig.3 alsoshow no special features. These maps, together with the low dis-crepancy factors obtained in the parameter refinements confirm thecorrectness of the assumption that was made regarding the distributionof metal atoms over the sites Mr and MIl'

III. Discussion of the structuresThe structures of clinoenstatite and pigeonite are projected along

[010] in Fig.4 and compared with that of diopside. In Fig. 5, theprojections along [001] for the three structures are given on the

* See footnote, p. 132.

"136 N. MORIMOTO, D. E. ApPLEMAK and H. T. EVANS, JR.

(a) Clino-enstatite

(b) Pigeonite

(c) Diopside

Fig. 4. Orystal structures of clinoenstatite, pigeonite and diopside projectedalong the b axis. Numbers represent heights of atoms above the plane of the a

and c axes in hundredths of the b length.

,- -

% 01' A'XOII' 'XA

. . SilJOnglf1 b.......------ ---.....

4 tIII

a~xt.OIJ' 01' 4

I>: I

] II

E ~"* ~. 01\0 0

r Ml M1 MIl MII.~.

Q xAOI A>(Xi::.

/0111'a 1 SiII .

Eo Diopside

1rA Pigeonife

35 0][x Clino -enstatite J/s. /IJIxi::.

xi::. A 01 om'

jh

"jst:ibl

~are


assurnption that they have exactly the same unit cell. It is clear fromthese figures that the difference in the atomic coordinates is greatestalong the c axis, except for the M1 atoms. The interatomic distancesand interbond angles in these structures calculated from the finalparameters are given in Table 5. The results show in detail the con-figuration of the single silicate chain, in clinoenstatite and pigeonite,which is the characteristic feature of the pYroxene group. Further, the

Fig. 5. Comparison of atomic positions in clinoenstatite, pigeonite and diopsidebased on a common unit cell projected along the c axis

o (26GeE

coordin'ation environments of the metal atoms are defined, and theeffect of these atoms 011the crystal chemistry of the pyroxene struc-tures in general is clarified. \IVe will discuss in detail the structuresfound for clinoenstatite and pigeonite and compare them with that ofdiopside.

Metal atoms

The ~:rI positions in diopside are occupied by Ca atoms and coor-dinated by eight oxygen atoms, and the 1\ln positions by 1\1g atomshaving a coordination of six oxygen atoms. Mr positions are regarded

os, :1.IOn r (

1e projected

ane of the a

Table 5. Interatomic distances and interbond angles of clinoenstatite,pigeonite and diopside

A. Interatomic distances in Angstrom units

AtomsI

Clinoenstatite Pigeonite Diopside

Si-O (::!:: 0.05 A)

SiI-OI 1.65 1.62 1.56

SiI-On 1.61 1.55 1.59

SiI-Om 1.67 1.69 1.60

SiI-Om 1.63 1.59 1.65Av. SiI-O 1.64 1.61 1.60

Sin-Or' 1.62 1.63 1.56

Sin-On' 1.58 1.58 1.59

Sin-Om,

1.70 1.68 1.65

Sin-Om' 1.74 1.63 1.60Av. Sin-O 1.66 1.63 1.60

M-O (::!:: 0.04 A)

MI-OI 2.12 2.20 2.36

MI-Or' 2.02 2.12 2.36

MI-On 2.06 2.12 2.36

MI-On' 2.05 2.13 2.36I

MI-OIII 2.33 2.35 2.55 IM 1-0 III (3.73) (3.48) 2.74

IMI-OIII' 2.29 2.76 2.74

MI-OIII' (3.26) 2.84 2.55

IAv. MI-O 2.15 2.36 2.50

I

Mu-Ol 2.17 2.09 2.16 (M n-O I 2.02 2.15 2.06

MIl-Or' 2.21 2.11 2.16

MIl-Or' 2.00 2.18 2.06

MII-Ou 1.96 2.05 2.12

MII-Ou' 2.04 2.06 2.12Av. MII-O 2.07 2.11 2.12

0-0 (+ 0.07 A)in Sil tetrahedron

01-011 2.80 2.72 2.61

01 -011I 2.75 2.57 2.66

01 -011I 2.74 2.69 2.55

all -011I 2.63 2.71 2.63

Ou -011I 2.59 2.40 2.59

Om-Om 2.63 2.66 2.64

A v. 0-0 2.69 2.63 2.61


,.

AtomsI

Clinoenstatite Pigeonite Diopside


.statite, Table 5A (Continued)

1.561.591.601.651.601.561.591.651.601.60

0-0 (:t 0.07 A)in Sin tetrahedron0/ -On'0/ -am'Or' -am'On' -am'On' -am'am' -Onr'Av. 0-0

2.772.612.71

2.732.702.642.602.592.692.66

2.612.552.662.632.592.642.61

Diopside

2.702.652.822.71

B. Interbond angles

2.362.362.362.362.552.742.742.552.50

O-Si-O (:t 20)r

Or -Sir -OnOr -Sir -amOr -Sir -amOn -Sir -amOn -Sir -amOm-Sir -amAv. O-Sir-O

116.80114.00110.90106.4 0

107.00105.70110.10

118.70

106.4 0

109.1099.70

113.70108.30109.30

111.70111.70107.60106.20110.90108.80109.50

2.162.062.162.062.122.122.12

Or' -Sin-On'Or' -Sin-Om'

0/ -Sin-Om'On' -Sin-Om'On' -Sirr-0m'Om'-Sin-Om'Av.O-Sin-O

120.10103.10109.50108.80107.00110.10109.80

116.90112.00105.80107.40

106.0°108.60

109.5°

111.70107.60111.70110.90106.20108.80109.50

Si-O-Si (:t2°)Sir -am -SirSin-Om'-Sin

136.80125.10

139.1 °135.30

140.80140.80

['

2.612.662.552.632.592.642.61

as occupied by the univalent cations or by larger bivalent cations, and

MIl by the smaller bivalent cations.Table 6 gives the distribution of metal atoms between the Mr and

lVIIlpositions, the coordination numbers of the metal atoms, and theaverage atomic distances from the metal atoms to the neighboringoxygen atoms. These data are consistent with the assumption that metalatoms Ca, Fe and Mg are in almost completely ordered distributionbetween the Mr and MIl positions, with the larger atoms (Ca) occupyingthe Mr position by preference. If enough larger atoms are not available,smaller atoms (Fe, Mg) occupy this position and the coordination

c

hc

Coordi - Average Displacement

Atoms nation M-O of atoms*number distance a

I

bI

c

Clinoenstatite Mr Mg 6 2.15 A 0.08 0.38 0.30

MIl Mg 6 2.07 .03 .13 .16

Pigeonite Mr CaO.20FeO.S0

I

7 2.36 .04 .33 .10

MIl MgO.6SFeo.32 6 2.11 .01 .10 .07

Diopside Mr Ca 8 2.50(vV ARREN and MIl Mg 6 2.12BRAGG, 1928)

* Deviations from the diopside metal positions, given in Angstrom units inthe a, b, and c directions.


II

I

\

iI

Table 6. The nature of the metal atoms in clinoenstatite, pigeonite and diopside

tends to decrease from eight to six. The coordinations of the MI andIVlnpositions are shown in Fig.4 with dotted lines for MIl and dashed-and-dotted lines for lVII.In comparison w'ith other oxygen atoms the0nr and Onr' atoms are always slightly farther frOlll the Mr positions,making the coordination of 1\1:rirregular. The Mn position is evidentlyoccupied by the smaller divalent atoms (Mg or Fe) and has nearlyregular octahedral coordination in all three structures.

It is interesting to compare the distribution of metal atoms inclinopyroxenes obtained here with the similar situation that existsin the amphiboles. Most amphiboles are represented by the generalformula X2-aYsZs022 (OH,Fh, where X is Na, K. or Ca; Y is Mg,Fe+2, Fe+3 etc; and Z is Si or AI. The general formula of pyroxenesmay be written as XYZ206 in the same way. In some amphiboles eitherMg or Fe atoms accompany Ca atoms in the X positions in the struc-tures, as in the structure of clinopyroxenes. The results of WHI'l"l'AKER(1949) 'on crocidolite and of ZU8Sl\IAN(1955) on actinolite suggest thatthe Mg atoms enter the X positions, which correspond to the Mrpositions in clinopyroxene structure, in preference to iron, in contrastto the case of clinopyroxenes. According to a recent study by GnosE(1960) the structure refinement of the amphiboles grunerite andcummingtonite gives a metal atom distribution similar to that ofpigeonite, with the Fe atoms rather than Mg occupying preferentiallythe X positions not filled by Ca. As far as the ionic radii are concerned,Fe+2 atoms would be expected to occupy the large space of the X or

Mr positions.

-I


r:Lnd diopsideBoth Mr and MIl sites are on the two-fold axes in the diopside

structure. In clinoenstatite and pigeonite these sites are in generalpositions, since the two-fold axes are absent in these structures. Metalatoms at the Mr and MIl positions in diopside are exactly superposedin the projection on (010), but in pigeonite and clinoenstatite they showsome separation in this projection. The deviations of the coordinatesof the Mr and MIl positions in clinoenstatite and pigeonite from thoseof diopside are also given in Table 6 in Angstrom units. The deviationof both Mr and MIl positions is greater in clinoenstatite than inpigeonite. Also, the deviation of the Mr position is greater than thatof MIl in both clinoenstatite and pigeonite. The displacement of themetal atoms is easily understood as the result of two effects whichtend to compensate each other: first, the tendency of the metal atomsto assume regular octahedral coordination; and second, the relativerigidity of the silicate chain.

lacementLtoms*

b c

0.38 0.30.13 .16

.33 .10

.10 .07

rom units in

jhe Mr and

ld dashed-atoms the

[ positions,

s evidentlyhas nearly

Single silicate chains

Although the structures of clinoenstatite and pigeonite are builtup from the single silicate chains found in diopside, a number ofdifferences in the details of the chain structure are revealed by thisanalysis.

The silicate chains in the three clinopyroxenes are projectedperpendicular to (100) in Fig. 6, where the Si atoms are taken to liein the plane of the paper, and the heights of oxygen atoms are represent-ed in Angstrom units. There is only one kind of chain in diopside(Fig. 6E) because all chains must be crystallographic ally equivalent.There are, on the other hand, two crystallographically different kindsof chains in clinoenstatite and pigeonite. Fig. 6A and B are chainsof clinoenstatite and C and D are those of pigeonite. A fact of interestis the constant distance of 3.05 ::f::0.02 A bet\veen neighboring Siatoms belonging to the same chain in all three structures, regardlessof the kind of metal atoms present. The difference in the shapes of thechains results from a slight rotations of Si04 tetrahedra around theaxis passing through the Si and Or atoms, without changing therelative position of Si atoms. The rotations of Si04 tetrahedra belongingto two crystallographic ally different chains in the same structure haveopposite senses.

The main effect of the metal atoms on the single silicate chainscan be observed in the change of relative position of silicate chainsalong the c axis together with the change of relative position of atoms

l atoms injhat existshe general

Y is Mg,pyroxenesloles either

;11(' struc-

fHI'l'TAKER

19gest thatto the MrIn contrastby GROSE:1erite andto that ofJerentiallyconcerned,f the X or

1:-;..

.~,';..~~~,..":~'1?~'~JJ8I.Zi;~~~;~;~~~"'.~[i;:~~"7ff.;~~~~""'J.L,~_.

~::'-~,;;.::~~. '~~~~'~-:_ . -":~~'.:.;1R'.~::~2~~''''''~:~.,'':;' '.J"~__ -~T:.~._ ~

Clino-enstotite

(A) (8)

om,o.57

o;48c:rrr\

n: 077

~~or', 162

01(0.77 om;048

oo

(C)

om,054

:::.; ...:: ~

Pigeonite

(0)

orr;072

-0

Diopside

(E)

o ill,0.52

Fig. 6. Silicate chains in the structures of clinoenstatite, pigeonite and diopside projected on the (100) plane. Numbers

represent distances in Angstrom units above and below (negative) a plane passed through the silicon atoms.

The crystal structures of clinoenstatite and pigeonite143

,s, Jlt.

in the chain itself, to give appropriate coordination of oxygen atomsto the metal atoms as shown in Fig. 4. The changes both of the shapeand of the relative position of the chains are greater in clinoenstatitethan in pigeonite when compared with diopside.

)

Onr'-

Conformity to PAULING'S rule of valency sums

It is interesting to examine to what extent PAULING'S rule is obeyed

in the structure of clinoenstatite and pigeonite, in connection withthe interatomic distances. The valency sums were calculated for eachoxygen atom in the usual ,yay for clinoenstatite and pigeonite as given

in Table 7. PAULING'Srule is apparently not satisfied completely. Thedeviation from the expected valency sums may be reduced to some

)Table 7. The valency s'ums of oxygen atoms in clinoenstat'ite, pigeonite and diopside

Diopside

Oxygenatorns

.

Clinoenstatite

UJ;..;o

,.Q

'""........~(1)

Z

Sir1\lr

MJI

Sill

1\1r

MIl

Sill

Sin

Mr

Pigeonite

12°121

2;\Ig

SirMrMn

113121

2Ca,

Sin1\1rMn

SinSin

SiCa p1

112

Si

Cn

Mg

SiSi

144 N. MORIMOTO, D. E. ApPLE::\IAN and H. T. EVANS, JR.

extent by taking account of the lengthening of the atomic distancesbetween Sin and Onr' atoms, and between Onr, Onr' and Mr atoms,reducing the bond number of these links. While some differences arefound in the various Si-O distances as shown in Table 5, they arehardly greater than the estimated standard errors, and we do not feelthat we can interpret these distances in this ,yay at present. The samesituation would be expected in the diopside structure, though noaccurate structure determination is yet available to enable us to testthe point in that case, either.

Distri bu tion of cations in pigeonite

The chemical composition of natural pigeonite shows that Caatoms are present usually to the extent of about 9 atomic percent andat most 15 percent of all metal atoms in the structure. The maximumamounts of Fe and Mg atoms in the natural pigeonite are each limitedto less than 70% of all metal atoms in the structure. As Ca and Mgatoms have a tendency to occupy respectively the Mr and Mn positionspreferentially, the distribution of metal atoms in pigeonite can bedefined as follows: lVIr = (Ca20 Feso-x Mgx) ; Mrr =-= (Mg1OO_yFe1/), where

always either x = 0 or y = 0, and x and y can have maximum valuesof 40 and 60 respectively. If the value of x is over 40, the pyroxeneapproaches the clinoenstatite-type and apparently is metastable. Ifthe value of y becomes more than 60, the pyroxene is not stable at anytemperature and changes to olivine and silica.

The results of the structure analyses indicate that the structureof pigeonite is intermediate between those of clinoenstatite anddiopside, giving seven-fold coordination to the Mr position insteadof eight as in diopside, or six as in clinoenstatite. Ca, Fe and Mg atomsare evidently distributed randomly in the 1\1rposition. It is possible,however, to give the results of the analysis of pigeonite another inter-pretation, namely, that the seven-fold coordination of the Mr positionis the average effect of local eight coordination around Ca atoms andsix coordination around Fe or Mg atoms. The same interpretation canbe applied to the deviations of the Mr and Mrr positions in pigeonitefrom those in diopside; that the deviations are the average of thedeviation of the Mg atoms and the normal positions of Ca atoms. Atthe present stage, it is not possible to decide which interpretation isbetter, especially because of poor resolution of the electron densityin the (010) projection.

,

1

0, JR.

tomic distances

a8Mr atoms,. differences arelble 5, they arel we do not feel'sent. The sameIre, though notable us to test

.hows that Catic percent andThe maximum

'e each limitedAs Ca and ~lgi Mrr positionseonite can be,j_yFey), where

x8m valuest"~'~)yroxene

netastable. If, stable at any

the structuremstatite andsition insteadmd Mg atoms[t is possible,

mother inter-e Mr position.~aatoms and

pretation can-) in pigeonite

'erage of theJa atoms. At~rpretation is~tron density

8


BOWN and GAY (1957) have reported that the h+k odd reflectionsof some pigeonites were observed to be diffuse. VVe have not consideredthe diffuseness of reflections in estimating the intensity, althoughsome h+k odd reflections are slightly diffuse in our photographs.This diffuseness of reflections in pigeonite could be explained on thebasis of the local adjustments of coordination about the metal atomsas suggested in the last section, or by incipient exsolution into Carich regions and Fe, Mg rich regions.

At high temperatures, it is possible that the amount of Ca atomsin clinopyroxenes is between 15 and 30 mol percent of all metal atoms,covering the gap between augite and pigeonite (Ku:~w, 1955). Thisclinopyroxene, however, exsolves to augite and pigeonite on coolingby the diffusion of metal atoms. Thus the Mr positions in the pigeonitecontain Ca atoms to the extent of less than 30% and those of theaugite contain more than 50% Ca atoms (MORIMOTOand ITO, 1959).

I

I

The structural relationship of clinopyroxenes

Although the crystal structure of clinopyroxenes is principallybuilt up of single silicate chains, we have seen that a slight change inthese chains takes place depending on the kinds of metal atoms inthe structures. The changes in clinopyroxene structures can con-veniently be classified into the following three cases, taking thediopside structure as standard: (1) displacement of the silicate chains;(2) distortion of the silicate chains, and (3) displacement of the metal

atoms.The clinopyroxenes of the compositions along the diopside-

hedenbergite join are examples of case (1). Although the clinopyroxeneson this join have practically a constant translation along the c axis,which is the direction of the silicate chains, the distance between thesilicate chains changes to allow appropriate s~ace for metal atoms ofvarious sizes. This results in a slight change of the cell constants otherthan the c translation (KUNO and HESS, 1953).

When displacement of the silicate chains is not enough to givespace for metal atoms, a distortion of silicate chains takes place as inspodumene. Various augites also show the effect of case (2). Theclinopyroxenes of the above two cases have one kind of silicate chainand have all metal atoms on the two-fold axes, corresponding to thespace group C2/c. These are the augite-type pyroxenes.

Change of the position or distortion of the silicate chain is inadequateto compensate for the introduction of small bivalent cations such as

Z. Kristallogr. Ed. 114, 1/2 10

r

146 N. MORIMOTO, D. E. ApPLEMAN and H. T. EVANS, JR.

Fe or Mg atoms into the MI positions. The Fe or Mg atoms becomedisplaced from the special position characteristic of the diopsidestructure, producing two kinds of silicate chains. Thus the space groupbecomes P21/c. The clinopyroxenes with compositions adjacent to theenstatite-ferrosilite join are examples of case (3) corresponding to thissituation. These, the pigeonite-type pyroxenes, are no longer stablein nature and exist in a metastable state, or transform to ortho-pyroxenes, which are stable at low temperature, exsolving Ca atomsfrom the structures to form augite-type pyroxenes.

Acknowledgements

The authors are indebted to Prof. H. KUNO and Dr. H. S. YODER,JR., for their donation of specimens used in this study and for helpfuldiscussions on pyroxenes in general. They are indebted to Dr. J. F.SCHAIRER, Dr. F. BOYD and Dr. J. V. SMITH who gave various COlll-ments on the general problems of pyroxenes.

This study was initiated by one of the authors (N. NI.) when hewas at the Mineralogical Institute, Tokyo University, Japan. He isindebted to the Carnegie Institution of Washington for a PostdoctoralFellowship, which made it possible to complete this work.

ReferencesL. ATLAS (1952), The polymorphism of 1\IgSi03 and solid-state equilibria in the

system MgSi03-CaMgSi206. Jour. Geol. 60, 125-147.J. BERGHUIS, 1. 1\1. HAANAPPEL, M. POTTERS, B. O. LOOPSTRA, C. H. MAC-

GILLAVRY and A. L. VEENENDAAL (1955), Now calculations of atomicscattering factors. Acta Crystallogr. S, 478-483.

N. L. BOWEN and J. F. SCHAIRER (1935), The system MgO-FoO-Si02. Am.Jour. Sci. [5] 29,151-217.

M. G. BOWN and P. GAY (1957), Observations on pigeonite. Acta Crystallogr.10, 440-441.

W. L. BRAGG (1929), The determination of crystal structures by means ofFourier series. Proc. Roy. Soc. [London] 123A, 537-559.

W. L. BRAGG and H. LIPSON (1936), The employment of contoured graphs ofstructure factor in crystal structure analysis. Z. Kristallogr. 95, 323-337.

W. L. BRAGG and J. .WEST (1928), A technique for the x-ray examination ofcrystal structures with many parameters. Z. Kristallogr. 69, 118-148.

W. R. FOSTER (1951), High-temperature x-ray diffraction study of the poly-morphism of MgSi03. Jour. Am. Ceramic. Soc. 34, 255-259.

S. GHOSE (1960), Crystal structure of cummingtonite and Mg-Fe ordering inferromagnesian amphiboles. Bull. Geol. Soc. Am. 70.

H. H. HESS (1952), Orthopyroxenes of the Bushveld type, ion substitutionsand changes in the unit cell dimensions. Am. Jour. Sci., Bowen Volume,173-187.

itF .

~.

-;, JI~.

;. s becOllle)f e diopside

the space groupadjacent to the;ponding to thiso longer stableforlll to ortho-tving Ca atollls

'. H. S. YODER,and for helpfuled to Dr. J. F.e various COlll-

L M.) when heJapan. He is

a Postdoctoral

'k..equilibria in the

RA, C. H. l\IAC-ions of atomic

PeO-SiOz. Am.

,eta Crystallogr.

's by means of

)Ured graphs of

~r. 95, 323-337.examination of

I, 118-148.dy of the poly-I.

-Fe ordering in

In substitutions

Bowen Volume,.


T.l'ro (1950), X-ray studies of polymorphism. Maruzen, Tokyo.

II. KUNO (1954), Study of orthopyroxenes from volcanic rocks. Am. Min. 39,30-46.

II. KUNO (1955), Ion substitution in the diopside-ferropigeonite series ofclinopyroxenes. Am. Min. 40, 70-93.

II. KUNO and H. H. HESS (1953), Unit cell dimensions of clinoenstatite andpigeonite in relation to other common clinopyroxenes. Am. Jour. Sci. 251,741-752.

:N. :MORIMOTO (1956), The existence of monoclinic pyroxenes with the spacegroup Q,,-P21/c. Proc. Jap. Acad. 32, 750-752.

:N. MORIMOTO and T. ITO (1958), Pseudo-twin of augite and pigeonite. Bull.Geol. Soc. Am. 69, 1616 (abstract).

A. POLDERVAART and H. H. HESS (1951), Pyroxenes in the crystallization ofbasaltic magma. Jour. Geol. 59, 472-489.

J. F. SCHAIRER and F. R. BOYD JR. (1957), Annual Report of the Director ofthe Geophysical Laboratory, pp. 223-225.

J. L. SMITH (1873), Victoria meteorite iron. Am. Jour. Sci. [3] 5, 107-110.J. V. SMITH (1959), The crystal structure of proto enstatite, MgSi03. Acta

Crystallogr. 12, 515-519.

E. THILO and G. ROGGE (1939), Chemische Untersuchungen von Silikaten VIII.Uber die thermische Umwandlung des Anthophyllits Mg7Sis022(OHhBer. Deutsch. Chern. Ges. 72, 341-362.

B. E. 'WARREN and J. BISCOE (1931), The crystal structure of the monoclinicpyroxenes. Z. Kristallogr. SO, 391-401.

B. E. 'WARREN and VV. L. BRAGG (1928), The structure ofdiopside CaMg(Si03)2'Z. Kristallogr. 69, 168-193.

B. E. VVARREN and D. 1. MODELL (1930), The structure of enstatite MgSi03.Z. Kristallogr. 75, 1-14.

E. J. VV. VVHITTAKER (1949), The structure of Bolivian crocidolite. ActaCrystallogr. 2, 312-317.

R. VV. G. 'WYCKOFF, H. E. MERWI~ and H. S. WASHINGTO~ (1925), X-raydiffraction measurements upon the pyroxenes. Am. Jour. Sci. [5] 10,382-397.

J. ZUSSMAN (1955), The crystal structure of an actinolite. Acta Crystallogr. S,301-308.

10*

-.

Documents

Thecrystalstructures ofclinoenstatite andpigeol1ite …rruff.info/doclib/zk/vol114/ZK114_120.pdf · are.distinct from the augite-type pyroxenes, which have asimpler structure inthe