1. science
2. physics
3. optics

American Mineralogist, Volume 72, pages 617-624, 1987
optics:Responseto (OH-) orientationand
Amblygonite-montebrasite
rapid estimationof F fram 2V
DlNrnr- J. GnorNnnr* F. DoNll,o
Br,oss
Department of Geological Sciences,Virginia Polytechnic Institute and State University, Blacksburg,Virginia 24061, U.S.A.
Assrnlcr
For I I crystalsof the amblygonite-montebrasiteseries,LiAIPO.(F,OH), ranging in composition from 4.0 to 91.8 mol0/oF (and only 2 containing significant Na), 2Zand principal
refractive indices were determined to 0.5oand 0.0005, respectively,by spindle-stagemethods. If the F content is <60 molo/oand therefore 2l/. < | l6o, as is true for the vast majority
of natural specimens,the F content can usually be estimated to within 2 molo/ofrom
evaluatingtFl: -66.3 + 1.08 x 2V, as well as from similar reglessionequationsinvolving the refractive indices a, B, and 7. Above 60 molo/oF, the optical properties are
less sensitively (and nonlinearly) related to F content. Estimates of F content are feasible
despite significant substitution of Na for Li. By contrast, this substitution may introduce
significant errors when estimating F content by methods involving lattice parameters.
Progressivesubstitution of (OH), a natural dipole involving a covalent bond, for the
relatively nonpolarizable F anion causesall three principal refractive indices to increase;
,y increasesmore than a or B becauseits corresponding principal vibration ditection Z
becomessubparallel to the O-H vector in the structure as (OH) content increases.
INrnorucrroNi
For the amblygonite-montebrasite solid-solution series, "(Li,NaCa)vI(Al,Fe,Mg)'uPOo(F,OH), the elements
in boldface representthe primary constituents. Thus, in
the common representativesof this series,less than 100/o
of the five-coordinatedLi sitescontain Na andlor Ca and
less than 0.lolo of the six-coordinated Al sites contain Fe
and/or Mg. Thus these specimensrepresent essentially
binary solid solutions betweenthe end members,amblygonite (amb), LiAIPO4F, and montebrasite (mtb), LiAlPO4(OH).Natural membersof the seriesrangefrom ambo
to ambrr, but specimensmore F-rich than ambu,are rare.
Members of the amblygonite-montebrasite series are
triclinic and biaxial. If negative in sign, they are called
amblygonites,and if positive, montebrasites.Phillips and
Griffen (1981) indicated that the optic sign changesfrom
(+) to (-) at amb-rr, but presentevidence,as will be
demonstrated, places the change closer to amb.o. The
structural similarity betweenamblygonite and titanite becomes apparent when a nearly monoclinic cell is chosen
as suggested
by Simonov and Belov (1958) and as employed recently by Hawthorne (pers. comm.) during refinements of amblygonite-montebrasitestructures.
The dependenceofthe physical properties ofthe series
on the dominant F-(OH) substitution has been studied
by many investigators. The usual goal has been to find
one or more physical properties to serve as reliable estimators of the F content. In such event, particularly if the
* Present
HerculesInc.,Bacchus
Works,Magna,Utah
address:
84044,U.S.A.
17$02.00
0003-004x/87/0506-06
physical property were quickly and preciselymeasurable,
monitoring the F contents in members of the amblygonite-montebrasite seriescould permit recognition of the
F-(OH) zoning in pegmatites, where these minerals exclusively occur.
Although initiated by Bragg (1924), studies relating a
crystal's optical properties to its composition and structure are infrequent in mineralogy, often due to the imprecision of available data. Thus, prior to the development of microprobe and spindle-stage techniques, a
chemical analysisof a l- or 2-g sample of a biaxial mineral-itself renderedsuspectbecauseof the possiblepresenceof impurities in the sample-was often coupled with
a refractive index a measured from one grain, B from
another, and 7 from still a third. Moreover, the precision
of their measurement,usually +0.002 or +0.003, was
insufficient and frequently overly optimistic. Now, however, from one and the same grain it is possible to measure all indices to +0.0005 by spindle stage,transfer the
goniometer head containing the grain to an X-ray camera
for such X-ray studies as desired, and, ultimately, determine this same grain's composition by microprobe analys1s.
Tight relations among optics, composition, and structure can thus be establishedand have led to an increasing
numberof recentstudies(Selkreggand Bloss,1980;Armbruster and Bloss, 1982; Su et al., 1984; Mereiter and
Preisinger,1986;Lager, 1986;to cite only a few). Combined X-ray, spindle-stage,and microprobe studiesof the
membersof a solid-solution serieshave beenof particular
interest. With the substitution of one atomic speciesfor
617
618
GREINER AND BLOSS: AMBLYGONITE-MONTEBRASITE
TABLE1. Sampledescriptionsand pegmatitelocalities
Samplenos.
Descriptionand locality
Bluish water-clearcrystals from pegmatite
vugs with quartz and cleavelandite;
F
contentnot determined(Plumbago,Newry, Maine)
AF-43-2 117775- Grayish-whitecleavagefragment(Gunnison
Co., Colorado)
e A-22"
Brownishtranslucent,massive
4 A-98.Paleyellowtranslucentmass
5.
Pale pink core of a zoned crystal (see A-2),
slightlycontaminatedby secondarymontebrasite(-5%)
6. AF-46
1 0 5 9 1 4 ' Palebluishcleavagefragments(Karibib,
South Africa)
7. AF-55
62576- Colorlesscleavablemass (Hebron,Maine)
8 AF-65
142741 Translucentfragmentswith faint bluishtint
(Chursdorf,Saxony)
9. A-2+
Yellow outer rim of a zoned crystal (see
A-1)
1 0 A-C+
Yellowtranslucent,veinedby A-4.
1 1 AF-50
10432',
Pale brown transparent mass (Coolgardie,
Western Australia)
1. AF-47
Note: Modifiedfrom Cerndet al. (1973).All crystals removedfrom these
samplesand studiedopticallywere clear,containedtew inclusions,and
showed no evidenceof zoning. Crystals for AF-43,A-22, AF-50, and AF65 each containeda few lamellaeof a polysynthetictwin component The
crystal studied optically tor sample AF-43 is the same crystal for which
Hawthorne(pers.comm.)performeda structureanalysis.
. U S. NationalMuseumsamDlenumber
t BritishMuseumof NaturalHistorysamplenumber.
{ Samplenumberof specimensfrom the Tanco pegmatite,BernicLake,
Manitoba,Cern6et al. (1973).
another in a solid-solution series,the optical properties
often change, because the substitution may involve
changesin atomic number and electronic shell structure,
polarizability, ionic radius, valence, electronegativity,
charge transfer, disposition and distances of nearest
neighborsaround the site ofthe substituent, and/or even
the proportion ofone bond type relative to another.
The amblygonite-montebrasiteseries was thus of interest,becauseit involved the replacementof a relatively
nonpolarizable anion, F , by a natural dipole, (OH)-,
containing an appreciably covalent bond that tended to
be directionally oriented in the structure.
OPTICS
of these crystals showed Mg and Fe to be below detectable limits and Ca to be below 0.1 molo/0.Na was below
detectablelimits for all samplesexcept numbers 7 and 8,
in which it exceeded2 wto/o.Al and P were nearly constant. This suggestedthat the eight crystals contained no
significant substitutions other than F for (OH). Attempts
to determine F content by calculation from microprobe
analyseswere unsuccessful.An initial spindle-stagestudy
of several different crystals from each specimen yielded
2V values,as calculatedby nxcelrnn (Bloss,l98l), that
differed by two degreesat most except for one sample in
which they differed by four degrees.Thus, it seemedvalid
to assume that crystals from a given specimen differed
little in optical properties and composition from each
other. Accordingly, the F compositions (neutron activation) and (OH) compositions (gravimetric analysis) obtained by Cern6 et al. (Table 2, 1973) were acceptedas
valid for thesecrystals.For sample8, Moss et al. (1969)
determined F from its distillate using the zirconium-Eriochrome-cyaninemethod of Megregian(1954).No complementary (OH) analysishas been performed on sample 8.
In this paper the F content will be expressedas mole
percent F [F]-that is, as 100 times the atomic frequency
of F in the formula unit. [F] and [OH] (mole percent
hydroxyl) were calculatedby Cern6 et al. (1973) from the
weight percentagesthey obtained for F and HrO. The
values for [fl and [OH] were adjusted for the presenceof
minor Na, Ca, K, Mg, and Fe. Complete chemical analysis of sample 8 has not been performed. Accordingly,
for sample 8, [fl was calculatedfrom the equation
lFl : 7.7845 x wto/oF.
This equation correctly relates mole percent to weight
percent F for samples wherein only the F-(OH) substitution occurs. Such a condition is not strictly valid for
sample 8, sinceit contains significant (>2 wto/o)Na. Still,
any errors introduced by falsely assuminga lack of substitutions other than F for (OH) for these sampleswill be
very small. The equation
w t o /Fo : 0 . 1 2 9 4 6 x [ F ]
will convert these values to weight percent F for all amblygonites and montebrasitesin which substitutions exThe experimental
methodsusedhavebeendescribed
fully by cept (OH) for F can be consideredminimal. Table 2 sumGreiner(1986).In summary,opticalconstants
weredetermined marizes the content of [fl and [OH] in the specimens
for eachcrystal(Tablel) by spindle-stage
methods.Estimated from which the crystals studied were drawn.
precisions
are2V (+0.5), refractive
indices(+0.0005),andlocation of the principalvibration axesX Y, and Z (+0.5" or
VlnHrroNs oF oprIcAL pRopERTIESwITH
better).Transferofthe goniometer
headfrom theSupperspindle
MOLE PERCENT F
stageto an X-ray precession
camerapermitteddetermination
of
work
Previous
the angularattitudeofthe triclinic axes(Palache,1943)relative
to X. Y. and Z.
Researchon the optical properties of the amblygonitemontebrasite series is limited. Winchell and Winchell
CrrsN{rsrnv
(1951) plotted refractive index and the optic axial angle
The amblygonite-montebrasitecrystalsexamined were 2 Z versus (OH) content, using data from the literature,
from the same specimensstudied by Cern6 et al. (1973), but the data points were widely scattered.Dubois et al.
ranging from translucent to gem quality and relatively (1972) performed least-squaresregressionson 2 Zand rehomogeneous in composition throughout each single fractive-index data measuredfor samplesin the ambo to
specimen (P. Cernj', pers. comm.). Microprobe analyses ambrorange.Thedata show considerablescatterabout the
ExpnnrnrnNTAr- METHoDS
GREINER AND BLOSS: AMBLYGONITE-MONTEBRASITE
Taele 2. F and OH contents
lFl
Sample (mol%)
I
e
4
o
7
9
10
'11
toHl tFl + toHl
(mol%)
(mol%)
4.0'
10.8
144
26 5
42.7
55.3
79 2
91I
27.9
34 8
96 5
85.3
834
70.2
54.8
47.0
25.0
96.1
97.8
96.7
97.5
102 3
104.2
J4 3
3J.J
65.9
53.6
93.8
88.4
108.0
tFl.
HrO+*
(wt%)
HrO *
(wt%)
0.30
1.40
1.88
3.44
5 56
7 .24
10.17
11.80
3 65
4.51
7.07
5.98
5.25
5.11
4.43
3.39
2.92
1.53
0.10
0.07
0.06
0.05
0.10
0.05
0.09
4.09
3.30
3.29
0.04
0.08
0.23
(wt%)
- Calculatedvalue;
see Cerndet al. (1973).
trends, and theseregressionsindicated, for the most part,
lower 2V and refractive-index values than those predicted by Winchell and Winchell's graphs over the same
compositional range. Cern6 et al. (1973) measured the
index 7' for crystalslying on the { 100} cleavageand found
that it exceededthose that Winchell and Winchell had
reported for .y. This underscored the need for a more
accurateset ofoptical data for the series.The application
of spindle-stagetechniques to the chemically well-characteized specimensassembledby Cern6 et al. (Table l)
thus seemedin order.
Optic orientation
Burri (1956) introducedthe use ofEuler anglesto express quantitatively the optic orientation of the optical
indicatrix's principal vibration axes(X, Y, and Z) relative
to the crystallographic axes of a triclinic crystal. In essence,he related the intrinsically orthogonal set of axes
(X, Y, and Q Io a second orthogonal set obtained by
choosing(l) a reciprocal crystallographicaxis; (2) one of
the two direct crystallographic axes perpendicular to it;
and (3) a third axis that is perpendicular to both (l) and
(2). The cleavageplanes for the amblygonite-montebrasite seriesmade it expedient to select from the crystallographic axes chosen by Palache et al. (1943) the orthogonalset (l) a*; (2) c; and (3) B, whereB symbolizes
a direction perpendicular to both a* and c. Euler angles
for Na light (Table 3) were calculated (Greiner, 1986)
such that if the correspondingrotations were performed,
6t9
OPTICS
X would coincide with B, I with a*, and Z with c (Fig.
l).
For the six crystalsfor which the optic orientation had
beendetermined relative to the crystallographicaxeschosen by Palache et al. (1943), optic orientation changed
systematicallyas [Fl varied from 4 to 92 (Fig. l). Note
that with increasing[fl, the two optic axes(OA, and OA,)
move away from Z and approachX so that the optic sign
changesfrom (+) to (-). For [F] :79 and 92, however,
note that OA, and OA, no longer move directly toward
X but turn slightly away. Thus, 2V* ceasesto decrease
(and 2V, to increase)as rapidly with increasedF when
[F] exceeds-60. With increasedF, one optic axis (OA,)
changesrelatively little in position, whereasOA, changes
markedly. The situation is reminiscent of another triclinic solid-solution series,the plagioclases(Reinhard, l93l),
in which one optic axis changesmarkedly in position as
Ca content changes,whereas the other does not (Bloss,
l 978).
Refractive indices and 2V
Principal refractive indices (a, B, and 7) and values of
2V, calcl.:Jated
by excer-rnn for Na light (Table 3) were
determinedfor specimensI to 11. Exceptfor samplesI
and 8, an F analysis and an independent (OH) analysis
had been reported for each (Cern6 et al., 1973).These F
and (OH) analyseswere consistent for specimens2 to 7
in that [F] + [OH] = 100. For specimens9, 10, and ll,
however, the sum deviated by more that 5o/ofrom l000/0.
Accordingly, the data for specimens9, 10, and ll were
omitted from the calculationswhen regressionswere performed. The following models relating optical parameters
to [fl (: mole percentF), and indeed all subsequentones,
were derived by a combined use of the srepwrse and
(Cp option) proceduresof the SASInstitute (Ray,
RSeUARE
l 982).
R2
a: 1.617
55(78)- 5.3r(27)x 10 alFl
+ l l4(33)x l0-'o[r]4
0;996 (1)
p : r . 6 2 57 0 ( l l ) - 3 . 0 7 ( l l )x l 0 o l F l
+ 3.98(29)x l0 6[F]'z
+ 3.60(22)x l0-8[F]3
0.999 (2)
TneLe3. Refractiveindices,2V, and EuleranglesO, O, and V as observedfor Na light
Sample
IF]
1
4.0'
10.8
14.4
26 5
42.7
55.3
79.2
91.8
27.9
34.8
54.5
2
4
o
7
I
I
10
11
dT
1.61476
1. 6 1 08 8
1.61043
1.60536
1.59530
1.58856
1.57923
1 . 5 7 72 3
1.60052
1 59532
1 59123
PI
1 62440
1 . 6 2 19 0
1.62067
1.61533
1. 6 0 81 6
1.60263
1. 5 9 4 1 7
1.59180
1.61283
1. 6 0 84 0
1. 6 0 53 6
tt
1.64589
1.64026
163800
1 62963
1 . 6 1 78 4
1.60913
1 . 5 9 74 9
1.59560
1.62488
1. 6 1 75 3
1.61273
2V.f
66.27
82.4
71.63
72.82
85.15 86.3
100.76 92.0
112.57 100.5
125.98 43.0
129.47 55.5
92.87
99.31
106.98
f c, B, and 7 shouldbe roundedto the 4th and zvzto the 1st decimalplace.
" Calculatedvalue,see Cern6et al. (1973).
-26.0
77.8
-23.9
-20.8
- 14.3
14.7
18.2
76.4
77.8
8 1. 0
18.0
30.0
GREINER AND BLOSS: AMBLYGONITE-MONTEBRASITE
620
OPTICS
.=
bt"
,P
bp
oAz
B
Or
45
oxa
F
o4
9?
lzg
26
43
55
79
92
OH^Z
2t.6
17.3
t5.5
t7.9
40.9
45.8
Fig. l. Stereographicdepiction of the variation in orientation of the two optic axes (OA, and OAr) and the three principal
vibration axes(X, Y, and Z\ relative to c and a* as mole percent F varies in the amblygonite-montebrasiteseries.The dots represent
data for the six crystals whose optic orientations were determined empirically; the numbers adjacent to the dots representmole
percent F for these crystals.The subscript p indicates crystal axes chosenby Palacheet al. (1943); the subscript m and the small
squaresdesignatethe almost monoclinic axes employed by Hawhorne (pers. comm.). The triangle representsthe O-H bond
direction as determined by Hawthorne. The inset representsthe anglebetween Z and the O-H vector for the six crystalswhose [Fl
values are listed. The Palacheaxesa* and c were chosenbecausethey are defined by the perfect {100} cleavageand the good {l 10}
cleavage.Thus, a* is normal to the perfect cleavageand c representsthe trace ofthe good cleavageon this perfect cleavage.
7:
zvz:
1 . 6 4 8 8 4 ( 3 1- ) 7 . 5 0 ( 1 1x) l 0 - ' [ F ]
+ 2 . 1 7 ( 1 6 )x l O - ' o [ l 4
0.999 (3)
60.86(95)+ 0.96(3)[fl
0.998 (4)
+ 2.73(40)x l0-'[F]o
Thesemodels and the data from which they were derived,
along with the data for specimens9, 10, and I l, are plotted in Figure 2. The dashedcurve (22.') represents2Zz
as calculated from the refractive-index curyes below it.
Note that it closely conforms to the solid curve (22'*)
representinga regression(Eq. a) on the 2V. vahrcs calculated by rxcerrnn.
Although the nonlinear refractive-index and 2V' curves
in Figure 2 appearto suitably relate sample I through 8
to F content, similar relations could not be established
with F content taken as the dependentvariable. It appears
from Figure 2, however, that 2V and the principle refractive indices for the amblygonite-montebrasiteseriesmay
actually vary linearly between 0 and 60 [F]. Indeed, of
regressionstested on only the optical data for specimens
I to 6. linear models, with F content as the dependent
variable, most aptly fit the data and are given below:
R2
a : r . 6 t 7 2 7 ( 7 r ) - 5 . 1 0 ( 2 3 )x l 0 - o l F i
P : 1 . 6 2 6 s 1 ( 2 0 ) 4 . 2 9 ( 6 )x l O + [ F ]
1: r.64834(22) 7.rr(7) x 10-o[fl
2 V z : 6 r . 3 0 ( 8 1 )+ 0 . 9 2 ( 3 ) [ F l
0.996
0.999
0.999
0.998
(s)
(6)
(7)
(8)
If these models were also plotted in Figure 2, their lines
would closely follow along the nonlinear models until [fl
exceeded-60 (Fig. 3). Above [F] : 60, the linear models
begin to deviate markedly from the nonlinear curves of
Figure 2 and do not adequatelyfit the 2V and refractiveindex data.
Upon examination of Figure 3, one might suspectthat
GREINERAND BLOSS:AMBLYGONITE-MONTEBRASITE
OPTICS
621
| 50'
|20'
?YZ
?YZ
90"
6o"
r.55
OU
r65
. ",o
F (mol%)
Fig. 2. Nonlinearmodelsfor 2V, and refractiveindicesvs.
[Fl (mole percentF). Solid refractive-indexcurvesobtain from
regression
Equations1,2, and3. The solidcurvedenoted2ll"*
(Eq. 4) of Excelrsn-derived,2V.values
represents
a regression
vs. [fl; the dashedcurve(denoted2Z^,)represents
2V, as calculatedfrom the refractive-index
curvesbelow.For samples9,
10, and I 1, whoseF contentswereuncertain,horizontallines
extendfrom analyzed
[Fl to 100minusthe analyzed[OH] value
(l - OH)]. The verticalticksindicatethe valuesof
[symbolized
molepercentF for thesesamplesif [fl plus [OH] is normalized
to 100molo/0.
the F contents of samples 7 and/or 8 may actually be
lower and that the linear models of refractive index are
valid acrossthe entire series.If this were true, the "yand
B refractive-index curveswould intersectand result in the
existenceof a pseudo-uniaxial amblygonite at the composition having 7: B. Examination of Figure l, however,
clearly shows that the migration curves of the two optic
axesdo not convergeso as to eventually coincide with a
principal direction, X in this case,as would be required
of a biaxial mineral approaching uniaxiality.
PnnorcuoN
oF MoLE pERcENT F
Previouswork
Moss et al. (1969), using uncalibratedpowder films and
diffractometer tracings, determined the relationship of F
content to cell parameters and to 2d,r,(CuKa,) for the
amblygonite-montebrasiteseries.Cern6 et al. (1973) used
diffractometer tracings of amblygonite and montebrasite
powder, intermixed with quartz, as an internal standard,
to accomplish this. Even though the unit-cell parameters
showed only small variations in responseto F content,
the F contents proved predictable to +4 molo/ofrom values of 2d,r,(CuI(a,).Cern6 et al. also plotted, relative to
F content, the peak differences(2000,- 20,or),where 200u,
representedthe l2l, I 10, 021, 0l l, and 120
successively
40
60
roo
80
F (mol%)
Fig. 3. Linear models(dashed)comparedto the nonlinear
modelsfor 2V.and refractiveindicesvs. [Fl. The linearmodels
represent
Equations5-8.
peaks.Again, estimatesof F content to +4 molo/oresulted. Although the method is faster than the 2d,r, method,
these peaks may overlap within several compositional
ranges. Kallio (1978) utilized four uncalibrated reflections between46 and 54 20 (CuKar) to estimate F contents to +5.5 molo/0.
Fransolet and Tarte (1977) studied infrared spectraof
this seriesand establishedlinear relationships betweenF
content and the frequenciesof both the stretching (vo")
and bending (Do")vibrations of the (OH) molecule. Thus,
zo" arrd 6o, servedto estimate F content to +4 mol9oand
+3 molo/0,respectively.Cern6 et al. (1973) examined the
applicability of specificgravity and of differential thermal
analysis as determinative techniques. Neither proved
useful because,as they stated,"specific gravity is too sensitive to the presenceof impurities, and diferential thermal behavior is too strongly dependent on the experimental setup."
This study
Regressions,performed on the data for specimensI to
6 using [F] as the dependentvariable, yielded the following models, which are only valid for [Fl < 60 molo/oand
t h u s f o r a > 1 . 5 8 7 ,p > 1 . 6 0 1 ,7 > 1 . 6 0 6 ,a n d 2 V , <
ll6.:
- r946(87)a
IFI : 3148(139)
2327(3s)p
3785(56)
tFl:
2317(22)
1405(14)1
tFl:
tn:
R2
0.992 (9)
0.999 (10)
0.9e9 (l l)
-66.3(2.6)+ 1.08(3)x 2V, 0.997 (r2)
Of these models, Equation 12 seemsthe most practical
622
GREINER AND BLOSS: AMBLYGONITE-MONTEBRASITE
TeeLe4. Observedand estimatedF contentsin molTofor samples with [Fl < 60
F predicted from
F observed from
Sample [F]1oo_ro"I [FJo,"
'1"
e
o
9
10
11
H?
AA
3.5
14.7
16.6
29.8
452
530
34 1
46.4
46.5
40
10.8
14.4
26.5
42.7
553
279
348
c+.c
170
450
1 00
tFl"
tFl,
tFl,
IFl",
5.1
12.6
5.0
1 08
3.5
11.4
14.5
55
11. 3
12.6
z6-J
ZJ.V
42.9
s5.1
32.9
43.3
500
342
42.8
55.6
34.3
41.3
49.6
230
( E q . 9 ) ( E q . 1 0 ) ( E q . 1 1 ) (Eq.12)
1Q E
tJ.o
23.4
43.0
260
42.7
co. I
cc.o
32.8
42.9
50.9
31.9
59.1
31.8
42.1
49.2
36.1
4-O
cz.+
t4.c
*
is trom direct [OH] measurement,and [F]orRis calculated
[F],oo-rort
from 100 [OH] for this sample.
. ' H a a p a l a( 1 9 6 6 ) .
t Mookherieeet al. (1979).
$ Gallagher(1967)
because(l) 2Vz can be quickly measuredto a fraction of
a degree by using a simple detent spindle stage (Bloss,
1981) to collect extinction data for Na light and then
processingthe data with ExceLBn; and (2) accordingly,
if 2V? < - I 16o,F shouldbe predictableto within 2 molo/0.
Thus, unless [fl exceeds60 mol0/0,which is rare, Equation 12 probably representsthe most rapid method yet
known for precisely calculating the F content of a montebrasite or amblygonite from a physical property.
Table 4 compares the observed F contents-namely,
those determined directly by chemical analysis [F]o," or
by hydroxyl diference, 100 - [OH] or [F]r00-roHr-with
the F contents determined by inserting the measuredoptical parametersof samples I to 6 and 9 to 1l into Equations 9 to 12. Clearly, 2V, and all three refractive indices
are successfulestimators of F contents between 0 and 60
mol0/0.However, if the chemically determined F contents
taken from the literature for specimens I to 6 were systematically high or low, the same will be true of the valuesdeterminedfrom Equation 12.
For specimens9, 10, and 11, wherein a discrepancy
existedbetween [flo,* and [Fl,oo-rorr,the value predicted
from 2V. almost coincided with [F],oo-,or1for specimen
9 and fell between[F]o,* and [F],ooro.rfor specimensl0
and ll. Note also that the optical properties of sample
10 closelyconform to those of sample5.
A searchof the literature disclosedthree specimens(A,
B, and C in Table 4) for which F contents and partial
optical analyseswere available (Haapala, 1966; Mookerjeeet al., 1979;,Gallagher,1967).However, significant
discrepanciesexist betweentheir reported F contentsand
thosepredicted by inserting their reported optical parametersinto Equation 9, 10, I l, or 12. Thesediscrepancies
may have resultedfrom incorrect chemical and/or optical
data, or there may actually have been differencesin F
contentbetweenthe samplesexaminedoptically and those
chemically analyzed.
OPTICS
Cern6et al. (1973)carefullyselectedhomogeneousmaterial for each of the samples used in their study and,
subsequently,in severalother studies,including this one.
Such attentive preparation of samplesmay have been absent in previous optical work, and thus, as statedby Cern6 et al., "the diferences between the analyzed and the
optically studied materials in many earlier studiesare the
most probable explanation for the poor correlation of optics with fluorine content in Winchell and Winchell's
(1951) graph." Concerningdifferencesin F content between samplesanalyzedchemically and samplessubjected to measurement of physical properties, Cern6 et al.
(1973) stated,"grains and crystalsof amblygonite-montebrasiteminerals frequently show primary compositional zoning and/or secondaryreplacementby members of
the same serieswith different fluorine contents."
Discrepanciesbetween optically and chemically determined F contentsmay also be due to the presenceof fluid
inclusions and daughter minerals that contain F in concentrations greater or less than that of the host mineral.
F contained within fluid inclusions and daughter minerals would be incorporated into the F analysisof a sample by a technique such as neutron activation. By contrast, F estimatesbased on optical properties refer only
to that contained in the host mineral, assumingthat the
equations used for estimation were derived, as they indeed were, from a suite of sampleswith few inclusions.
Cern6et al. (1973)reportedtheir specimenAF-1, which
contained abundant inclusions, to contain 62.7 molo/oF
by neutron activation (: [F]",.) but 73.0 molo/oby hydroxyl difference(: [F],oo ro"r).The angle 2V, measured
for a crystal of AF-I, estimated [F] by use of Equation
12, at 57.0. The sample is very cloudy; thus, refractive
indicescould only be roughly estimated.Estimationsfrom
them placed [F] at 55 to 60. Finally, the optic orientation
of AF- I is nearly identical to that of sample 6 (n :
55.3).Thus, it appearsthat the host amblygonitefor AF-1
contains 55 to 60 molo/oF and that possibly F is present
in a higher concentration in the fluid inclusions and
daughter minerals. Microscopic examination of the fluid
inclusions in AF-l revealed the presence of a cubic
daughter mineral, possibly villiaumite (NaFt R. J. Bodnar, pers. comm.). Thus, for samplesof amblygonite and
montebrasitethat contain a significant amount of included material, 2V, measurement is clearly superior to
chemical analysisin evaluating the F content of the host
mineral.
Influence of Na content on F prediction
Most natural amblygonites and montebrasitescontain
minor Na via substitution for up to l0 molo/oLi (Dubois
el aI., 1972); thus, an evaluation of the influence of Na
content on the accuracyof Equations 9-12 seemsin order. The substitution of Na for Li in this seriesresults in
minor changesin density and involves ions that have
very similar polarizabilities (Pirenne and Kartheuser,
1964) and electronegativities(Pauling, 1960). This suggeststhat Na content should have very little effect on the
GREINER AND BLOSS: AMBLYGONITE.MONTEBRASITE
OPTICS
623
relationships between optical properties and F content structure and causesthe correspondingrefractive index'y
establishedin this study. Indeed, the refractive indices to increaseat a faster rate than a or B.
1.594,1.603,and 1.615reportedby Nriagu and Moore
AcxNowr,nlcMENTS
(1984), for a sample containing -56.0 molo/oNa and
-46.5 molo/oF, agreewell with the values 1.594, 1.607,
We thank Petr Cernj'and Iva Cern6(University of Manitoba) for kindly
providing analyzedsamples and for their prompt replies to numerous
and I .6 I 5 predicted by Equations 5, 6, and 7, when [fl :
46.5 was inserted. Thus, unless Na content only affects questions.We are grateful to Frank Hawthome (University of Manitoba)
for supplying structural data, which proved invaluable. We thank Paul
the B refractive index, which seemsvery unlikely, the Na Ribbe, who read the manuscript and made suggestionsthat contributed
content of most natural sampleswill not affect F predic- greatlyto its improvement. Shu-ChunSu'sand Mickey Gunter's help with
the statisticalaspectsofthis study is greatly appreciated,as is the drafting
tions basedon Equations9-12.
The differencein ionic radius between Na and Li is at of figuresby Melody Wayne and Tom Wilson.
teast 0.26 A lshannon and Prewitt, 1969) if Li is sixRnrnnrNcrs
coordinated. This is rather large when considering the
1.30-A radius of three-coordinatedF (Shannon and Armbruster, Thomas, and Bloss, F.D (1982) Orientation and effectsof
channel HrO and CO, in cordierite. American Mineralogist, 67,284Prewitt) and the I .34-A radius of three-coordinated(OH)
291
(Ribbe and Gibbs, l97l). Thus, predictionsof F content Bloss,F.D. (1978) The spindle stage:A turning point for optical crystalbasedupon subtle variations in lattice parameterswill be
lography.AmericanMineralogist,63, 433-447.
(l 98 l) The spindle stage:Principlesand practice CambridgeUnisignificantlyin error if the measuredsamplecontainseven versity Press,Cambridge and New York, 340 p.
minor Na. Measurementsof cell volume by Dubois et al.
Bragg,W. L- (1924) The refractive indices of calciteand aragonite.Royal
(1972)support this conclusion.
Proceedings,
A, 105,370-386.
Rnr,l.rroN oF oprICAL pRopERTTES
TO STRUCTURE
AND
POLARIZATION
Cern6 et al. (1973) and Hawthorne (pers.comm.) have
shown that as (OH) content increasesin the amblygonitemontebrasite series, the cell volume increases slightly,
whereasthe density decreasesslightly. Both structural effects are ordinarily associatedwith a decreasein refractive indices. In this series,however, their effect appears
to be overwhelmed by the increasein refractive indices
resulting from substitution ofthe highly polarizableanion
(OH)- for the relatively nonpolarizable F .
Influence of the polarizability of (OH) on optics
For hydroxyl-rich members of the amblygonite-montebrasite series, the principal vibration direction Z lies
reasonablycloseto the O-H bond direction (triangle, Fig.
l) locatedby Hawthorne (pers.comm.). Increasesin (OH)
content thus cause"y to increaseat a greater rate than a
or B. Conversely,the decreasein (OH) from left to right
in Figure 2 causes7 to decreasefaster than a or B. This
causesthe birefringence@ to decreasewith increas")
ing F content and also contributes
to the changein optic
sign from (+) for montebrasitesto (-) for amblygonites.
Positional changesin the two optic axes and X, Y, and Z
appearedmuch more abrupt as [fl increasedfrom 55 to
79 (Fig. l) than when it increasedfrom 79 to 92.
CoNcr,usroNs
l. For montebrasite-amblygonite crystals for which
[F] < 60 mol0/0,their F content can be estimated to -2
molo/ofrom their measuredvalues for 2V, a, B, or 7. Results seemedrelatively unaffectedby Na content.
2. Substitution of (OH)- for F in the amblygonitemontebrasite structure causesthe principal vibration direction Z to align subparallel to the O-H vector in the
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MrNuscnrst
MaNuscnrrr
REcETvEDSeprsr4ger 19, 1986
AccEprED J.rxunnv 30, 1987