American Mineralogist, Volume 66, pages 932_937, IggI
Synthetic Fe/Zn staurolitesand the ionic radius of IvZn2*
DeNe T. GnrrpeN
Departmentof Geology
Brigham Young University
Provo, Utah 84602
Abstract
Ztnc and iron end-memberstaurolites,as well as three FelZn stauroliteswith intermediate
compositions,have been synthesizedin a tetrahedral press at approximately 30 kbar and
750"C. All are dimensionally orthorhombic, but are assumedto be monoclinic by analogy
withnaturalstaurolites.
Indicesofrefractionofzincstauroliteatea: l.6g3,B:1.694,r:
1.700.Lattice parametersfor the Fe/Zn seriesvary linearly with composition,in generalconsonancewith previousmodelsof staurolitecrystalchemistry.Disorder of Zn and Fe2* is tentatively suggestedb-ymolar volume data. The efective ionic radius of tetrahedrally-coorditated Zn2* is 0.574 (+0.01A) based on unit cell volumes of synthetic staurolitesand on
previouslypublished data for Zn2* tetrahedraloxvanions.
Introduction
Although all natural staurolites reported to date
contain more iron than other metals,minor amounts
of Ti, Mn, Cr, and V are nearly always present(see
Smith, 1968;Griffen and Ribbe, 1973);these have
comparativelylittle effecton the crystal chemistry of
the mineral. Relatively large concentrationsof Mg
and Zn are common,and Skerl and Bannister(1934)
have reported a cobaltoan variety. Zinc-rich staurolites have been reported in regionally metamorphosedpelites at moderatelyhigh grade(e.g.,Guidotti, 1970),and at unusually high grade (Ashworth,
1975);in medium grademetabasitesof igneousorigin
(Gibson, 1978);in high pressure,medium-gradethermally metamorphosed"graywacke" (Hollister, 1969);
and in pegmatitesand hydrothermal veins (Tarnovskii, 1973;von Knorring et al., !979).
The staurolite crystal structure contains layers of
approximate kyanite composition and atomic arrangementthat alternatealong D with .,monolayers"
of approximatecompositionFerAt.,Or(OH), (Smith,
1968;Griffen and Ribbe, 1973).The kyanite layers
contain the tetrahedral Si and octahedral Al(lA),
Al(1B), and Al(2) sites',which are all nearlv fullv ocrTo avoid confusion between chemical
symbols and Smith's
site names,the latter are printed in boldfacc type. Sitc occupancies
referred to are based on Smith's (1968) structure refinement.
00p.3-,00/.)[./
8r/09 1H932$02.00
cupied. The monolayers contain the tetrahedral Fe
site (occupancy0.92), octahedralAl(3A) and Al(3B)
sites (occupancies0.42 and 0.28, respectively),and
octahedralU(l) and U(2) sites(occupancies0.08 and
0.04,respectively).Along the c direction they possess
chains of edge-sharingAl(3A,8) octahedrawith attached Fe tetrahedra.Along a the chains are separated laterally by nearly vacant U(1,2) sites. An
"idealized" average chemical formula, necessarily
imprecise becauseof the many partially occupied
cation sites in staurolite, is MoAl,r3(Si,Al)tO48Ho,
where M : Fe, Mg, Zn (Griffen, Gosney,and Phillips, in preparation).
The apparent preference of zinc for tetrahedral
sites in silicates has often been noted (e.g., Evans,
1966;Burns, 1970).The Fe site in staurolire (Smith,
1968)is the only tetrahedral site in common metamorphic minerals that is of appropriatesizefor zinc.
The data of Guidotti (1970) and Ashworth (1975)
suggestthat the partitioning of zinc into staurolite
stabilizesit (relative to zinc-free staurolite)to higher
temperatures.The P-T stability of staurolite as a
function of zinc contenthas not yet beeninvestigated
quantitatively.
Among natural specimenszinc content is reported
to range from zero to -7 weight percentZnO, but is
commonly between0.1 and 2.0 weight percentZnO.
This correspondsto approximately0.02 to 0.5 atoms
of zinc on the basisof 4 metal atoms in the general-
GRIFFEN: SYNTHETIC Fe/Zn STAUROLITES
ized staurolitechemicalfonnula. A major purposeof
the presentstudy was to investigatethe rangeof solubility of zinc in stauroliteby attemptingto synthesize
zinc-rich specimens.
Experimentalmethodsand results
Syntheses
Synthesisexperimentswere carried out in a tetrahedral press (Hall, 1958) at 30 (t2) kbar and
750(+40)'C. Uncertainties in pressureand temperature were estimated from the data of Eatough
(1968).Starting materialswere zincite (ZnO), wiistite
(FeO), boehmite (AIO(OH) and quartz (SiO,), in
the mole proportions4(ZnO + FeO):18AIO(OH):7.5
SiOr, with water added as a catalyst.All crystalline
compoundsusedweresyntheticand of reagentgrade.
The amount of hydroxyl in the boehmiteis in excess
of that needed for the formation of staurolite, but
runs madewith insufficientHrO resultedin staurolite
* gahnite t corundum + kyanite t quartz. The ratio
4:18:'7.5was chosen instead of 4:18:8 because
Richardson (1966) noted that the ratio 4:9:8
(FeO:AlrO.:SiOr)yielded staurolite + quartz,
whereas quartz was not produced in 4:9:7.5 mixtures.2
Run times were mostly I to 2 hours, although runs
of up to 60 hours duration were made with no apparent differencesin run products. Synthesizedphases
were identified by X-ray diffraction using both a
Gandolfi camera and a General Electric XRD-5
powder diffractometer.Only staurolitewas identified
in the products of runs that startedwith excessHrO.
Both Zn and Fe end memberswere synthesized,as
well as ZrrrFerr, ZnroFero,and ZnrrFe, intermediate
members (subscriptsindicate mole percent of end
members).Table I summarizessynthesisdata.
Table l. Summary of staurolitesyntheses
.
Run
durati-on (hrs)r
Run
product s "'
Starting
Materials*
P(kb)
4 t 0 ' . 1 8i 7 \
30
750
3:l tI8 t7\
30
750
Zn/Fe- staurol
212:18171
30
7S0
Zn/F e- st aurol it e
1 1 3 . 1 8t 7 \
30
750
Zn/F e- st aurol ite
O| 4 : 1 8 i 7 \
30
750
Fe- staurol ite
*
ZrP:F&:AfO(OH):SiO2
#
P!zkb,rx4o"c
runs
+
Sevetaf
**
Rure
in
with
insufficient
kgilite,
which
and
#
were
ontq
r('a)"
+
naale
H20
(excess)
for
each
stauro-lite
H20
also
Zn- staurol ite
1-60
it e
comtosition
was
variousfg
produced
ale
produced
tabu-ldted'
@rundufr,
Runs
gahnite,
quattz.
gation, parallel extinction, and large 2V. Indices of
refraction, measuredin Nao light by standard immersiontechniques,are d = 1.683,B : 1.694,and't
: 1.700(all + 0.005).Thesepropertiesare consistent
with the optical properties of natural staurolites
(Juurinen, 1956; Grifen and Ribbe, 1973),the refractive indices being smaller becausethe atomic refractivity of zinc is lessthan that of iron (Batsanov,
1961).Optical constantsof Fe and Fe/Zn staurolites
were not measuredbecauseof small crystal size.
Latticeparameters
Refined unit cell dimensionswere obtained from
X-ray powder patterns run on a General Electric
XRD-5 X-ray diffractometer,using Ni-filtered CuKa
Microscopy
Run products were examined by both petrographic
microscope and scanning electron microscope. Crystals up to -20 pm long and of bladed habit were observed,with the zinc end member providing the largest and most well-formed examples (Fig. l). Znc
staurolite is biaxial negative, showing positive elon-
2 The deficiency of Si (that ig less than 8 atoms per unit cell) is
very consistent in published staurolite analyses,even though the
Si sitcs (8 per unit cell) are essentially fully occupied (Smith,
1968). It is lkely that bond strength sums at the Si site preclude
full occupancy by Sia*, and require the substitution ofsome Al3*
(Griffen and Ribbe, 1973).
Fig. l. SEM photomicrograph of synthetic zinc staurolite
crystals. Lcngth of scale bar r€presents l0 microns. Angles
measured on this and other SEM photos suggest that the large
crystal facesare (010), modifed by (ll0), (201), and (201), with
crystals elongated on c.
934
GRIFFEN: SYNTHETIC Fe/Zn STAUROLITES
radiation and a goniometerscanrateof 2o2|/minute.
The internal standard was CaF2 annealedat g00oc
(ao: 5.4630A).Peakswere indexedwith referenceto
the calculated powder pattern of Borg and Smith
(1969),and lattice parameterswere refined with the
least-squares
program of Evanset al. (1963).By analogy with natural staurolites,the synthetic staurolites
were assumedto be monoclinic with B : 90o, and
with the hkl and ftOlpeaksthereforepresentas unresolved doublets.Each hkl (or ftOl)peak was thus assigned two indices-ftkl andh*t 1or h1l and EODto
avoid biasing the B angle.Refined lattice parameters
for the five staurolitessynthesizedin this study, as
well as for staurolitessynthesizedpreviously by others and usedin this study, are reported in Table 2.
Linear correlation coefficientsare (respectively)0.98,
0.99,and 0.94for a, b, and c versuscomposition,and
all are statistically highly signifcant. This is in contrast to similar plots for twenty natural staurolites
(Griffen and Ribbe, 1973),wherein the correlation
betweencell edgeand iron content was highly signif:
icant for only the b dimension, while that for c was
moderately signifiesll for that for a was not significant. Assuming the metal atoms to be restricted essentially to the FerAL.?Or(OH),monolayer,theseauthors rationalized that an increase in Fe (the largest
of the substituent metal atoms) would expand the
thickness of the monolayer independent of the kyanite layer; hence the strong correlation of D with Fe
content. Parallel to c, an increasein Fe content
would tend to lengthen the octahedral/tetrahedral
Discussion
chainsin the monolayer,but this expansionwould be
limited by the requirement that the monolayer ..fit"
Lattice parameters
the presumablynon-expandirg kyanite layer. Along
As seenin Figure 2, the lattice parametersof syn- a, the presenceof nearly empty U sites between
thetic Fe/Zn staurolites x1s lingsl or nearly linear chains would make a slighl sellapse of those octafunctions of composition. The least-squareslines hedra easier than expansionof the monolayer. For
were calculatedusing both the data of this study and the synthetic Fe/Zn staurolitesthe variation in D is
the synthetic iron staurotte of Richardson (1966). four to five times that in a or c, suggestingthat the
Table 2. Lattice parameters of synthetic staurolites
Nunber
of peaks
C o m p oist i o n
"
Zn
100
?
([)
b(.()
"(,()
F(
J
v(A )
Reference
This study
+
7.861(r)'
1 6 .s 3 s( 1 )
s.646(1)
e0.00(r)
7 3 3 s. ( 1 )
Zn
Fe
75 25
72
7 .866(2)
1 6 .s s s ( 3 )
s.648(1)
e 0 . 0 0( 2 )
73s.s(2)
Zn
Fe
50 50
71
7 . 8 7 1( 1 )
r 6 . s 8 0( 3 )
s.6s4(1)
s0.00(r)
7 3 7. 9 ( r )
Zn
Fe
25 75
65
7.878(2)
r 6 . 6 0 6( 4 )
s . 6 6 2( r )
s o .0 0( 2 )
7 4 0 . 7( 2 )
62
7.882(1)
1 6 .6 3 9( 3 )
s.6se(1)
s 0 . 0 0( 2 )
742.2(2)
7.887(10)
r 6 . 6 3 9( 8 )
s . 6 6 s( 3 )
74s.4(r0)
Fe
100
nr
Fe
100
I
Fe
M-e2
98
nr
7.891(2)
1 6. 6 3 7( 2 )
s.667(1)
J+5.tlz)
Fe
Mg
90 l0
nr
7 . 8 8 r( 7 )
1 6 . 6 2(16 )
s . 6 6 2( 6 )
74r.6(r4)
Fe
Mp.
-20
80
nr
7.8e0(7)
1 6 .6 16 ( 6 )
s . 6 6 0( 2 )
742.o(8)
Fe
M-e3 0
70
nr
7.887(6)
l 6 . s 9 7( s )
s . 6 6 s( 2 )
M
" 'or o o
47
*
Mole
t
e.s.d's,
F
nt
r6.ss2(2)
7.887(1)
s.63s(r)
Z end menbers
= not
**
$ teprted
tt
Orthorhonbic
given
in
pnratheses,
'"etet
to
Last
teIElted
as
"9Oo within
sgmettg
exgrerimental
assumed
error',
deciml
place
Richardson (1966)
740.2(7)
90
+.t-
73s.6(2)
Schreyer and
Seifert (r969)
GRIFFEN: SYNTHETIC Fe/Zn STAUROLITES
7.90
7.88
c
r6.62
.9
U'
c r6.60
o
E
o 1658
sized staurolites as a function of composition. The relation is either linear or very close to it, implying the
possibility of thermodynamic ideality, with Zn and
Fe'* disorderedwith respectto eachother. In view of
the preference of Zn for tetrahedrally-coordinated
sitesand the absenceofsuch a preferencein the case
of iron, someordering might be expected.The apparent linearity of Figure 3 may therefore be a fortuitous result of conplex site substitutions among Fe,
Zn, and Al, with someAl in the Fe site, as in natural
specimens.
Efective ionic radius of "Zn2'
Shnnnonand Prewitt (1969)and Shannon(1976)
have proposed 0.60A as the radius of tetrahedrally
coordinatedZn2'in oxides,basedon crystal structure
t654
determinations of inorganic compounds containing
tuZn'*. Using similar data treated in a different way,
5.67
Griffen and Ribbe (1979,Fig. 8) suggested0.57A as
5,65
more likely. The present data on zinc staurolite and
data available for synthetic Fe, FelMg, and Mg
o204060
r00 staurolites (this study: Richardson 1966; Schreyer
80
Fe - Slourolite
Zn - Slourolife
and Seifert, 1969) raise the possibility of an indeMole %
pendent determinationof the tvzn2+radius.
Fig. 2. Variation of lattic€ parameters with mmposition for
Figure 4 is a plot of the cube of the mean effective
synthetic FelZn staurolites. Symbols: rectangles, this study;
ionic radius of the metal atom (Shannon, 1976) vervcrtical bars, Richardson(1966).Symbolsare 2 esds in height.
srs unit cell volume. (The radii used for Fe'* and
Mg2* were those for tetrahedral coordination; this is
a possible source of error and is discussedbelow.)
samegeneralmodel applies.The much better corre- The least-squa1s5
linsar fit was determinedusing the
lations may be a reflection of the controlled composi- sevensynthetic Fe, FelMg and Mg staurolites,and
tional variation for the synthetic crystals.In natural was extrapolatedto the observedunit cell volume of
staurolitesa predominantsubstitutionof Al e (Fe + syntheticzinc stauroliteto give r' : 0.17A'. This corMg + Zn) occurs concurrently with (and nearly independent of) metal-metal substitutions(Griffen, Gosney, and PhilliFs, in preparation),tending to obscure
the effectsofthe latter and to scatterthe data. In the o
(1966)I
Richordson
synthetic Fe/Zn staurolitesthe unit cell Al content E
This
SludyI
E
was constrainedat l8 by choiceof starting materials,
"r\
and the effects of the metal € metal substitution E
c) 4 4 6
alone are evidgnt.It is also possiblethat someFelAl
o
substitution occurs in the kyanite layer of the syn- E
thetic staurolites,resultingin expansionof both kinds of
444
of layers.
Although substitution of Zn for Fe2* clearly con- o
trols the physical and optical properties of the syn- o
thetic staurolites reported herein, the substitution
does not necessarilyoccur at the Fe site alone. Smith
roo
80
o2040
(1968) inferred partial Fe/N disorder from MdssFe- Slourolife
Zn - Slourolile
bauer spectroscopy and crystal chemical deduction
Mole%
for a natural specimen from St. Gotthard, SwitzerFig. 3. Molar volume rs. composition for synthetic Fe/Zn
land. Figure 3 shows molar volu'ne of the synthe- staurolitcs. Symbols are 2 esds in height.
o
O
r6.56
GRIFFEN: SYNTHEI:IC Fe/Zn STAUROLITES
936
the degreeof metal/aluminum order for the various
staurolites plotted, the less error would arise from
this source.
For reasonscited above the f vs. V plot must be
consideredlessreliable than the crystal structure refinementsused by Griffen and Ribbe (1979).Nevertheless,it tends to confirm the'uZn2* radius of those
authors.The value of 0.57A(+0.014) for r('"2n2*) is
therefore recommended for use with Shannon's
(1976) radii, which are based on an assumedvrO2radius of 1.40A.The effectiveionic radii proposedby
Whittaker and Muntus (1970) are basedon r(v'O2-)
: 1324, and are a more suitable set for radius ratio
radius consistentwith that
considerations.The tvznL2+
set is 0.65A.
S y n l h e l i cS t o u r o l i t e s '
I
742
;-
s
f e Z v g ( R i c h o r d s o1n9, 6 6 )
I n i l g( S c n r e y eIr S e i f e r t , 1 9 6 9 )
O re tttis sruoy)
A Z n ( T h i sS t u d y )
E too
s
(D
ro
(-) z'""
=
Conclusion
o 16
0 t8
0?o
o22
024
r 3 (43)
Fig. 4. Unit cell volume of synthetic FelMg staurolite as a
function of the cubeof the meaneffectiveionic radius of the metal
atom (Shannon, 1976).The value of f for tvZn2* is determined
by extrapolating the least-squaresline to the observedunit cell
volume of zinc staurolite(Table l). Symbolsare 2 esdsin hcight.
responds to a radius of 0.56A fottuZn2'.
The average
value of r obtainedfrom unit cell volumesof all four
zinc-bearingstaurolitesis also 0.564.
Three possiblesourcesoferror in the radius determination are apparent. (l) The accuracy of the
radius for Zn'* estimatedin this way is limited by the
accuracyof the radii usedfor Mg'z*and Fe2*.Griffen
and Ribbe (1979,Figure 8) confrrm Shannon's(1976)
radius for ''Fe'*. but Griffen and Ribbe did not include 'vMg2* in their study. The paucity of crystal
structure data involving '"Mg'* makes its radius
somewhat less certain than that of rvFe2*.(2) The
precision of Richardson's(1966) cell volumes is not
sufficientto determinewhetherthe f vs. Zplot is linear or curvilinear. The unit cell volumesof zinc and
nagnesium staurolites are close enough, however,
that no reasonablenonlinearity would changethe estimate of the'uZn2*radiusby more than -0.01A. (3)
If there is any disorder betweenthe metal atoms and
aluminum, then someof the metalsare in octahedral
coordination and use of the tetrahedral radii is not
strictly correct.Nevertheless,the differencesbetween
the four- and six-coordinatedradii of Fe2*,Mg'*, and
Zn'* ate nearly the same,so that the method is approximately valid in any case.The more nearly alike
The synthesisof both Zn staurolite and Fe/Zn
staurolite at approximately 30 kbar and 750oC suggeststhat there are no apparentcrystal chemicallimitations to the amount of zinc incorporatedin staurolite. Availability of zinc in various geologic
environmentsor possiblethermodynamiclimitations
to the stability of Zn-containhg staurolitesmay govern the concentrationsof zinc observed in natural
specimens.All unit cell dimensionsfor the Fe/Zn series vary linearly with composition,but the large variation in D (comparedto that of a and c) indicates
that the decreasein thicknessof the metal-containing
(020) monolayer,as Zn is substitutedfor Fe, is much
more important than contraction parallel to the
monolayer. The explanation given by Griffen and
Ribbe (19'13)for lattice parametervariationsin natural staurolitesthus applieswith little modification to
thesesyntheticanalogs.The known preferenceof Zn
for tetrahedral coordination suggeststhat the apparent linearity of the molar volume vs. composition
plot (Fig. 3) may be a fortuitious result due to partial
metal/aluminum disorder combined with partial
iron/zinc order.
An effectiveionic radius of 0.57A fat'uZn2* is proposedfor use with the radii of Shannon(1976).This
correspondsto a radius of 0.65A for use with the
radii of Whittaker and Muntus (1970).
Acknowledgments
I thank J.F. Cannon (BYU Chemistry Department)for assistancein using the tetrahedralpress,and M.G. Best,C. V. Guidotti,
and W.R. Phillips for helpful reviewsof the manuscript.Financial
supportfor this researchwasprovided by a SummerResearchFellowship from the College of Physical and Matlematical Sciences,
Brigham Young Univcrsity. The manuscript was typcd by Mrs.
Sue Farrow, and frgureswere drafted by Mr. Brad Jobnson.
GRIFFEN: SYNTHETIC Fe/Zn STAUROLITES
References
937
considerations: Equipment for use at 100,000atmospheresand
3000'C. Reviewsof Scientific Instrumentation,29, 267-27 5.
Ashwonh, J. R. (1975)Stauroliteat anomalouslyhigh grade.Con- Hollister, L. S. (1969)Contact metamorphismin the Kwoiek area
tributions to Mineralogy and Petrology,53,'"t -291.
of British Columbia: An end membcr of metamorphicprooess.
Batsanov.S. S. (1959) Strukturnaya Refraktorn. rya. University
GeologicalSocietyof American Bulletin, 80,2465-2494.
Press,Moscow (trans. Sutton, P. P. (1961) Refractometryand Juurinen, A. (1956)Compositionand propertiesof staurolite.AnChemical Structure.ConsultantsBureau, New York).
nales AcademiaeScientiarumFennicae,SeriesA, III Gcology,
Borg, I. Y. and Smith, D. K. (1969)Calculatedx-ray powder pat47, r-53.
tems for silicate minerals. Geological Society of Amcrican Richardson, S. W. (1966) Staurolitc. Carnegie Institurion of
Memoir 122.
WashingtonYear Book, 65,248-252.
Burns, R. G. (1970)Mineralogical Applications of Crystal Field Schreyer,W. and Seifert, F. (1969) Higb pressurephasesin thc
Theory. University Press,Cambridge,England.
system MgO-AI2O3-SiO2-H2O.American Journal of Science,
Eatough,N. L. (1968)High pressure,high temperaturesyntheses
267-1|,407-443.
of rare earth diantimonidesand Th3Patype polymorphsof rare Shannon,R. D. (1976)Revisedeffectiveionic radii and systematic
earth sesquisulfidcs.Ph.D. dissertation,Brigham Young Unistudies of interatomic distancesin halides and chalcogenides.
versity, Provo, Utah.
Acta Crystallographica,A32, 75l-7 67.
Evans,H. T., Jr., Appleman, D. 8., and Handwerker,D. S. (1963) Shannon,R. D. and Prewitt, C. T. (1969)Effectiveionic radii in
The least squaresrefinem€ntof crystal unit cells with powder
oxidesand fluorides.Acta Crystallographica,825, 925-946.
diffraction data by an automatic computer indexing m€thod. Skerl, A. C. and Bannister,F. A. (1934)Lusakite,a cobalt-bearing
(abstr.) American Crystallographic Association Annual Meetsilicate from northem Rhodesia. Mineralogical Magazine, 23,
ing, Cambridge,Mass.,Program,42-43.
598-606.
Evans, R. C. (1966)An Introduction to Crystal Chemistry. Uni- Smith, J. V. (1968) The crystal structure of staurolitc. American
versity Press,Cambridge, England.
Mineralogist, 53, I 139-1155.
Gibson, G. M. (1978)Staurolitein amphibolite and hornblendite Tarnovskii, G. (1973)Zinc-containing staurolitefrom pcgmatites
sheetsfrom the Upper Seaforth River, central Fiordland, New
and hydrothermal formations of eastern Sib€ria. Voprosy MinZealara'd.Mineralogical Magazine, 42, 153-154.
eralogii i Geokhimii, MestorozhdeniiVostocbnor Sibiri, 1973,
Griffen, D. T. and Ribbe, P. H. (1973) The crystal chemistry of
70-76 (not secn: abstracted from Chemical Abstracts 82,
staurolite.American Journal of Science,273-A, 479495.
173s8
l).
Griffen, D. T. and Ribb€, P. H. (1979)Distortions in the tetrahe- von Knorring, O., Sahama,Th. G., and Siivola, J. (1979)Zincian
dral oxyanions of crystallinc substances.Neues Jahrbuch fur
staurolite from Uganda. Mineralogical Magazine,43,4/16.
Mineralogie Abhandlungen, 137, 5+73.
Whittaker, E.J.W. and Muntus, R. (1970)Ionic radii for usein geGuidotti, C. V. (1970)The mineralogyand petrologyof the transiochemistry.Geochimicaet CosmochimicaActa, 34,945-956.
tion from the lower to upper sillimanite zone in the Oquossoc
area, Maine. Joumal of Petrology,11,277-336.
Manuscript received,February 10,I98I;
Hall, H. T. (1958) Some high-pressure,high-lsmperaturedesign
acceptedforpublication,April 29, 1981.
© Copyright 2026 Paperzz