American Mineralogist, Volume 82, pages 149-157, 1997
Hydrofluoric acid solution calorimetric investigationof the effectsof
anorthitecomponenton enthalpiesof K-Na mixing in feldspars
Guv L. Hovrs
Departmentof Geology and Environmental Geosciences,Lafayette College, Easton,Pennsylvania18042, U.S.A
AssrRAcr
Enthalpiesof solution have been measuredat 50 'C in 2O.l wtTohydrofluoric acid under
isoperibolic conditions for a nine-memberK-Na ion-exchangeseriesbasedon a disordered
oligoclasespecimencontaining23.1 mol%oanorthite(An) component.The seriesdisplays
positive enthalpiesof K-Na mixing, but magnitudes are substantiallyreduced relative to
An-free analogs.Volumes of K-Na mixing for the seriesare similarly reduced;the asymmetry of these with respect to composition is the opposite of that for alkali feldspars.
Lower magnitudesof the mixing properties are probably related to the shortenedcompositional range of this series, relative to normal alkali-feldspar series, and to a 23VoAn
structural background against which the energetic effects of K-for-Na substitution are
dampened.
InrnonucrroN
Most minerals are not simple binary solutions, yet
knowledge of the thermodynamic mixing properties of
minerals is confined primarily to binary systems.If thermodynamic data are to be used to predict phaseequilibria
in natural systems,it is essentialto know the effects of
third and fourth componentson thermodynamicmixing
behavior.For enthalpy,third-componenteffects on binary
mixing properties have been systematically investigated
on few systems(Hovis and Roux 1993).
The binary mixing properties of alkali feldspars have
been studiedextensively.Currently there are reliable data
for enthalpiesof K-Na mixing (Hovis 1988), volumes of
K-Na mixing (Waldbaum and Thompson 1968; Waldbaum and Robie 1971; Hovis 1986; Kroll et al. 1986;
Hovis and Navrotsky 1995),and entropiesof K-Na mixing (Hovis et al. 1991).From thesesamestudieswe also
know the effects of Al-Si distribution on enthalpiesand
volumes. Additionally, we have been able to estimatethe
effects of short-rangeorder (Hovis et al. l99l1' Haselton
et al. 1983; Hovis and Navrotsky 1995) on the thermodynamic behaviorof theseminerals.Lastly, we have studied the effects of temperatureon both enthalpies (Hovis
and Navrotsky 1995)and volumesof mixing (Hovis and
Graeme-Barber,199;7).Becauseof this solid foundation
of data, feldsparsare excellent for the study of the thermodynamic effects of additional chemical components.
Most naturally occurring feldspars are at least ternary
solutions, so it is a natural extension of work on alkali
(K, Na) feldsparsto quantify the effects of anorthitecomponent on thermodynamicmixing properties.As an initial
step in investigating the KAlSi.O, (Or)-NaAlSi3Os(Ab)CaAlrSirO, (An) ternary system, therefore, we synthesized a K-Na seriesof feldsparshaving moderateAn content and studied their volumes and enthalpiesof mixing.
0003-004x/97l0102-0149$05.00
SranrrNc MATERTAL
The starting material for the presentinvestigation was
oligoclase 80165, a colorless translucent specimen from
the Hawk Mica Mine, Bakersville, North Carolina. The
specimen was obtained from the United StatesNational
Museum (SmithsonianInstitution). Data provided by the
USNM gavea compositionof Abr,oOrrrAn23r
on thebasis of spectrochemicalanalysesmade by Dr. Tren Haselton at the United StatesGeological Survey. The same
specimen was also analyzed by Kracek and Neuvonen
(1952; techniquenot described),who gave a composition
of Abr,,OrrrAnr.r. We too measuredthe composition on
the basis of two partial atomic absorption spectrometric
analysesfor CaO, Na,O, and K,O performed at the Pennsylvania State University. The averageof these nearly
identical analysesmatched the Haselton result, so we
adoptedthat as the oligoclasecomposition.
From this oligoclase specimen we synthesizeda disordered nine-memberK-Na ion-exchangeseries.The primary purpose of this paper,then, is to report on the volumes and enthalpiesof K-Na mixing determinedfor this
series and to compare these results with similar data for
An-poor alkali feldspars(Hovis 1986, 1988).
Saiupr,B PREPARATToN
Because the state of Al-Si order is known to affect
thermodynamicmixing properties(Hovis 1986, 1988),reliable comparison of the mixing properties of an oligoclase-basedserieswith thoseof an An-free feldspar series
requires that the two series have similar Al-Si distributions. In the present case this was complicated because
the parent materials had different values of Al:Si and
could not possibly attain the same Al-Si distribution, and
becausethe parent materials had formed under different
geologic conditions and representeddifferent degreesof
149
150
HOVIS: ANORTHITE IN K.Na FELDSPARS
Tnele 1. Synthesishistoriesof disorderedoligoclasesamples
DISOBOEFEO
POTASSIUM
oltGocusE
Feldspar
No,
Synthesishistory
D , 8 0 1 6 5 ,1 1 3 1 , 2 1 . 6( 8 7 1 4 \ .
H , 8 7 1 4 + 8 8 1 7 ,8 4 5 , 1 8 3 ( 8 8 1 8 ) .
H, 8714 + 8817, 845, 18.3 (8819); H, 881I,
884, 5.25 (8844);H, 8844, 931, 5.04
(8848).
H, 8714 + 8817, 845, 18 3 (8820);H, 8820,
884, 5.25 (8845);H, 8845, 931, 5.04
(8849);H, 8849, 935, 4 45 (8903).
( 8 8 3 5 )H
; , 8835,
H,8714 + 8817,75O,18.1
793,24.0 (8840);H, 8840,842,5.46
(88s1);H, 8851, 860, 10.0 (8854);H, 8854,
9 0 1 ,s . 7 1( 8 9 1 1 ) .
; , 8836,
H , 8 7 1 4 + 8 8 1 7 , 7 5 0 , 1 81 ( 8 8 3 6 ) H
; , 8841,842,5.46
7 9 3 , 2 4 . 0( 8 8 4 1 ) H
; ,88s5,
( 8 8 5 2 )H
; , 8 8 5 2 , 8 6 0 ,1 0 . 1( 8 8 5 5 ) H
860, 4 45 (8904).
H , 8 7 1 4 + 8 8 1 7 ,7 5 0 , 1 8 1 ( 8 8 3 7 ) .
H, 8714 + 8817,75O,18 1 (8838).
l , 8 7 1 4 , 1 . 0 , 8 0 80, . 9 6( 8 8 1 6 )l;, 8 8 1 6 ,1 0 ,
8 0 5 , 0 . 9 0( 8 8 1 7 ) .
8714
8 8 18
8848
0.035
o 127
0.217
8903
0.308
8 9 11
0 399
8904
0 491
Frcunr 1. Plot of theb vs. c unit-celldimensions
for membersof the ion-exchange
series.
8837
8838
8 8 17
0 581
o 672
0.769
Al-Si disorder. It seemedreasonablethat the most valid
comparisonof K-Na mixing propertieswould be provided
by a disorderedoligoclase series,the propertiesof which
could be compared with those of disordered alkali feldspars,namelythe sanidine-analbite
seriesof Hovis (1986,
1988).
Parent oligoclase 80165 was disorderedthrough annealingat 1l3l (*l)'C in a DeltechModel DT-31 furnace for 518.5 h, resulting in specimen8714. Although
we were not successfulin producing a perfect monoclinic
Al-Si distribution, the resulting feldspar did achieve a
high degreeof disorder,as discussedin detail in the next
section. Furthermore,the b unit-cell dimension of specimen 8714 significantly increasedrelative to that of the
80165 parent material, and the c dimension decreasedas
a result of disordering (Fig. l), in exactly the same way
that the unit-cell dimensions of alkali feldspars change
with disorder(Stewartand Ribbe 1969).
From the disordered parent material a corresponding
"pure potassiumoligoclase" (i.e.,Na-free)was produced
by double ion exchangein molten KCl. That is, oligoclase
8714 was first K exchangedin molten KCI at 808 1*4;
"C for 23.0 h in a Lindberg Model 51844 box furnace;
the exchange was performed in platinumware using a
large excessof salt over feldspar.The feldspar was separatedby dissolution of the quenchedsalt in distilled water, then dried and reexchangedin fresh KCI for an additional 21.7 h at 805 1-t41'C, againwith a large excess
of salt over feldspar.
Feldspars of intermediate composition were made by
combining powders of the parent material (8714) and the
correspondingpotassium oligoclase (8817) in desired
proportions. These mixtures were placed in cylindrical
platinum crucibles, compressed,and annealedfor various
durations at elevated temperatures.Powders were normally removed from the furnace every 24 h, remixed in
acetoneto randomizegrains of various compositions,and
then repacked and reloaded for further annealing. This
same procedure has been successfulin homogenizing K
and Na in alkali feldspars (Hovis 1986), as reflected in
Note: | : molten chloride ion-exchange experiment, H : dry
homogenizationexperiment,and D : disorderingexperiment.For ionexchangeexperiments,the numberafterthe "1" identifiesthe plagioclase
sample used as the startingmaterial,followedby the compositionof the
salt (givenby the mole fractionof KCI in the salt),the temperature("C),
and the durationof the run (d). The bracketednumberat the end is that
experiments,
and disordering
of the resultingfeldspar.For homogenization
the "H" or "D" is followed by the identificationnumber of the starting
plagioclasesample,the temperature("C),the durationof the run (d), and
the identityof the resultingseries member.
c (A)
ORDEFED PMEM
OLIG@LASE
I
I
DISORDERED
qtG@nsE
t2.a
't2.9
13 . 0
bl)
the current study by the sharp 201 X-ray peaks of the
resulting specimens. Synthesis conditions for various
specimensare given in Table 1. Compositionsreported in
Table 2 reflect carefully weighed proportions of the two
end-members.
Saprpr,B CHARACTERTzATION
Unit-cell dimensions were determined from data collected on an automatedScintag DMS 2000 X-ray powder
diffraction system.We usedNational Bureau of Standards
640a Si, with a statedunit-cell dimensionof 5.430825A,
as an internal standardin all spectra.Burnham's (1962)
LCLSQ program was utilized to calculate unit-cell dimensionsfrom the feldspar data.The resulting parameters
are given in Table 2. A plot of the b vs. c unit-cell dimensionsof the resulting feldspars(Fig. 1) shows a trend
similar to those seenin analagousdiagramsfor the alkali
feldspars(Kroll and Ribbe 1983; Hovis 1986).The plot
also reflects the changein stateof order from the original
parent oligoclase (80165) to its disorderedequivalent
(8714\.
We also plotted the quantity (1 - cos 0) (see Thompson and Hovis 1978) as a function of composition in Figure 2. This function, where cos d : sin "y sin o*, is zero
for a dimensionally monoclinic feldspar. Figure 2 illustrates that (1 - cos $) values for the three most potassic
members of the series come close to, but do not quite
reach, zero (note also the non-90' values for ct and ^yin
Table 2). The lack of perfect monoclinic symmetry is also
indicated by the failure of certain "split" X-ray peaks
151
HOVIS: ANORTHITE IN K-Na FELDSPARS
TreLe 2. Unit-celloarameters
Feldspar No.
80165
8714
8818
8848
8903
8911
8904
8837
8838
8817
p/p'
d/d
0 035
8 . 16 8 2 ( 13 )
0.136751(20)
0 035 8.1649(12)
o 136724(21',)
0 . 1 2 7 8 2067(13)
0 135978(23)
0 . 2 1 7 8.2433(25)
0.135296(45)
0 308 8.2784(24)
0.134627(35)
0 399 I 3278(42)
0 133710(60)
0 491 8.3574(1
9)
0 133171(30)
0 581 8 4105(27)
0 132237(36\
0 672 8 4340(221
0 131823(30)
0 7 6 9 I 4578(21)
0 131457(31)
12 8431(14)
0 078042(9)
12 8814{12)
0.077813(7)
12 9021(17)
0 077655(11)
129296(27)
o 077447(17)
129487(23\
0.077294(14].
12 9734(24)
o 077111(14\
129927(20)
0.076979(1
2)
13 0034(23)
0.076905(1
4)
13.0097(24)
0.076867(1
4)
13.0186(21)
0.076814(12)
Unit-cell
volume
(4")
7 1354(9)
93.794(1
4)
0 1 5 6 8 6 7 ( 1 6 ) 86 23e(13)
7 1113(7)
9s 377(11)
0 . 15 7 2 5 1( 13 ) 86.096(1
0)
7 1209(9)
9s.086(15)
0 1 5 6 9 4 1 ( 1 8 ) 86.472\15)
7 1285(13)
e2.585(23)
0.156612(22) 87.030(221
7 1371(15)
92.090(24)
0.156260(35) 87 628(21)
7.1453(16)
91.429(27].
0 155887(26) 88 397(26)
7 1543(14)
90 951(22)
0 155588(21) 88 961(20)
7 1583(15)
90.452(231
o 155372(23) 89 562(20)
7 1 6 1 0 ( 1 4 ) s0 321(25)
0.1s5259(27) 89 692(22)
7 1653(13)
90 245(24)
0 1 5 5 1 7 0 ( 3 8 ) 89 775(21)
116.449(10) 89 043(13)
63.556(10) 8 9 1 8 1 ( 1 2 )
1 1 6 3 2 1 ( 9 ) 90 275(11)
6 3 6 1 2 ( 9 ) 88.020(10)
1 1 6 2 9 7 ( 1 3 )9 0 1 7 1 ( 1 4 )
63 652(13) 88 282(141
116.242(171 so 179(22)
63 720(18) 88.s25(21)
116 . 17 7 ( 19 ) 90 088(24)
63 801(1e) 88.874(21)
116 087(26) 90 024(22)
63 904(26) 89 273(20)
1 1 6 0 3 5 ( 1 7 )89 961(21)
7) 8 9 . 5 7 9 (81)
63.962(1
1 1 5 9 5 4 ( 2 1 )89 866(25)
64.046(21
) 8s 929(22)
11 5 . 9 15 ( 19 ) 89.899(24)
e) 8 9 . 9 5 6 ( 2 1 )
64.086(1
11 5 . 9 19 ( 2 2 ) 8e.so2(22)
9)
64 081(22]. 89.990(1
Molar
volume
(J/bar)
Molar
volume
(cm.)
100.69(2) 10067(2)
6 6 8 6 6 ( 11 )
668.83(10) 10071(2) 10070(2)
6 7 4 . 6 7 ( 1 3 ) 1 0 15 9 ( 2 ) 1 0 1 5 8 ( 2 )
680.54(21) 102.48(3) 10.246(3)
686.00(20) 103.30(3) 10.32e(3)
693.07(29) 104 36(4)
10.4s5(4)
6 9 79 0 ( 1 8 ) 1 0 5 . 0 9 ( 3 ) 1 0 . 5 0 8 ( s )
7038e(22)
105.99(3) 10.598(3)
70671(201 106.42(3) 10 640(s)
70e.60(1s) 106.85(3) 10 684(3)
A/ote.Uncertainties
in the final decimalolacesare shown in brackets
(e.g., l3l-131 and 132-132)to close fully for the same
three feldspar samples.
The degreeof disorder of our samplescan be estimated
using the method of Kroll (1983; see also Viswanathan
1971).From equationV in his Table 1, after correcrion
of "y for No. content, we calculated the difference in the
mole fractionsof Al in the Tlo and Tlm tetrahedralsites
for sample 8'714to be 0.05 (the value would be zero for
a topochemicallymonoclinic Al-Si distribution).A similar calculation for the original orderedparent oligoclase,
also after correction for No. content, gave a difference of
0.59. Clearly,the annealingof parentfeldspar80165was
successfulin producing a highly disordered product in
om
(1 - cos Q)
8714,even thoughthe sampledid not attaina monoclinic
Al-Si distribution. Al-Si reorderingis known not to occur
in alkali feldsparsfor the relatively low temperaturesand
short durations of our K exchange and homogenization
experiments(e.g., Waldbaumand Robie 1971), so it is
reasonableto assume that all members of the ion-exchange serieshave the same Al-Si distribution.
N.. contents for individual members of this seriescan
be estimatedfrom either the c unit-cell dimension or the
201 X-ray diffraction maximum, both of which vary substantially with K./Na.Coefficientsfor determinativeequations are reported in Table 3.
It is important to recognizethat the K-Na ion-exchange
series synthesizedin this investigation is limited in its
compositional variation relative to a normal alkali-feldspar series.Becausethe K-exchangeexperimentsdid not
remove An component from the feldspar samples, all
membersof the presentserieshave a constantAn content
of 23.1 molVo.Even the most K-rich sample(with zero
Na), therefore,contains only 76.9 molVoOr, not 1007oas
would be the case for an alkali-feldspar end-member.
Thus, one would not expect the differences in unit-cell
dimensions, nor indeed in other properties, between Na
and K ends of the series to be as sreat as those for an
alkali-feldspar series.
for No,
TeeLe3. Determinative
equations
0l
(Or0 Ab-/69 An23.1)
02
0.3
0.4
ffo,
o7
(Or7o9 Abo An23.i)
Frcunn 2. Plot of (l - cos g), definedin the text, vs composition (N". : mole fraction KAlSirO8) for membersof the ionexchangeseries The three most potassicmembersdisplay nonzero values for feldspars that are nearly, but not exactly,
monoclinic
a
201
201
18.434
32.850
21 192
38.889
x1
For No.
2 2624
3.9748
o 96267
- 1 7905
<0.58
>0.58
<0 58
>0.58
Note: Equationshave the form No. : xo + \Q, where Q is eitherthe
fits are
value for a ot 2O1 Correlationcoefficientsfor all least-souares
0.997 or higher
152
HOVIS: ANORTHITE IN K-Na FELDSPARS
Cnr,onrnnrRrc
pRocEDUREs
Each feldspar sample was dissolvedin 910.I g (approximately one liter) of 20.1 wtTo hydrofluoric acid at
50'C underisoperibolicconditionsusing an internalsample container (Waldbaum and Robie 1970). Either one or
two dissolutionswere performed in a single acid solution.
Multiple experimentsin the samesolution violate the rule
of strict stoichiometry (Hovis 1974),bnt no effect on the
data was observedwithin the precision of our experiments. This is probably due to the high dilution of dissolved ions in the acid solution, as most experimentsused
only 0.25 g of sample,and none utilized more than 0.31 g.
In connection with sample synthesis,specimenswere
ground to pass through a 325-mesh sieve and then elutriated in deionizedwater to remove the finest grain sizes.
These grain sizes are well above those that would affect
calorimetric data (Nitkiewicz et al. 1983; Roux and Hovis, 1996).
General principles and proceduresof acid-solutioncalorimetry have been discussedby Robie and Hemingway
(1912). Solution calorimetric measurementsduring the
present investigation were made on an automateddataacquisition system previously describedby Hovis and
Roux (1993), except that a more sensitivedigital voltmeter (Hewlett Packard Model 34584), one able to read
voltages to two additional significant figures, was used
instead of the HP Model 34564 for voltage measurements.Calorimetric sampleswere weighed on a new Mettler AT-201 electronicbalance,which improved weighing
accuracy.Both of these changesare reflected in the improved precision of the calorimetric data, relative to precision that was alreadyvery high (e.g.,Hovis and Roux
1993). Experiments conducted in our present reaction
vessel produced slightly higher absolute values for enthalpies of solution than those in the model used for earlier work on feldspars(Hovis 1988)becauseof a slightly
different superheatingcorrection for the latter (see discussionby Hovis and Roux 1993).On the basis of calibration experiments using Fisher 4-581 reagent-grade
aluminum hydroxide, enthalpies of solution for present
experimentswere multiplied by a factor of 0.9980. This
has only a small effect on the calorimetric data and in no
way affects conclusions.
M,q.rHnNrnrICAL TREATMENToF DATA
a (A)
0.1
0.3
flo,
Frcuns 3. Plot of thea unit-celldimensionvs.composition.
Note that the seriescanbe analvzedas consistinsof two linear
segments.
slope in both cases occurring near the composition of
feldspar 8837 (N* = 0.581). We show below that enthalpies of mixing display a double maximum, and that
the minimum between thesecould indeed be related to a
phasechangenear the potassicend of the series.Because
we cannot demonstratethat there is a phasechangealong
the series, we treat the series as continuous, but note in
various places the consequencesof treating the series as
two separateentities.
Vor-ulrns oF K-NA MIXING
Molar and unit-cell volumes for all feldspar samples
are included in Thble 2. When treated as a continuous
series,the best least-squaresfit to the data is third order
(Fig.4A):
V [J/(bar.mol)]: 10.044+ 0.774 No,
(1)
+ 0 . 9 1 8N a . - l . l 0 N &
-t-0.008
J/ftar.mol) and a correwith a standarderror of
lation coefflcient of 0.999. This equation,of course,is
valid only for compositionsup to the pure-K end-member
at No. : 0.769. These molar volumes can be converted
to other units (cubic centimetersper mole) or to unit-cell
volumes (cubic angstroms)through multiplication of all
coefficients on the right side of Equation 1 by 9.9998 or
66.418,respectively.
Correspondingmolar volumes of mixing (Fig. 5) are
expressedas
V". [J/(bar.mol)]: -0.058 No.
The correct mathematicaltreatmentof both volumetric
and calorimetric data is important. From the failure of (l
- cos S) valuesto reach zero (Fig. 2), it is evidentthat
this series does not undergo a true phase transition as a
function of composition; therefore, it can be treated as a
single continuous series. Nevertheless,the series does
mimic such a phasetransition,as valuesof (l - cos 0)
changesteeply,and in fact linearly, near the sodic end of
the series and then level off to near-zerovalues for the
+ 0.918Na.- 1.10Na.
Q)
three most potassicmembers.Furthermore,two segments
of the serieshave different trends on plots of both a (Fig. again valid for No. values up to 0.769. The asymmetry of
3) and volume (Fig. 48) vs. composition,with a break in the volumes of mixine is the reverse of that in alkali
HOVIS: ANORTHITE IN K-Na FELDSPARS
eE
E
o
10.6
?
o
E
:t
u.l
uJ
=
f
10.5
=
f
J
o
J
0.04
o
10.4
LINE OF
IDEAL MIXING
IE
5
o
153
J
o
=
10.3
o
(t
=
lr.l
o
x
uI
0.00
.
0.1
LINE OF IDEAL MIXING
0.1
0.4
o.2
0.3
04
flo,
[o,
Frcunn5. Volumesof mixingderivedfrom thevolumeanalysisof Figure4.A The curvecorresponds
to Equation2.
=o
10.7
o
lt
?
10.6
UJ
10.5
=
clinic and near-monoclinic regions each behave linearly
with composition(Fig. 4B); for suchan analysisvolumes
of mixing are nonexistent.Equations for these lines are
V U/(bar'mol)l: 10.035+ 0.971No,
f
J
o
for the seven most sodic compositions, with a standard
enor of fit of *0.006 J/6ar'mol) and a correlation coefficient of 0.999, and
10.4
tr
J
o
=
(3)
r0.3
(4)
V U/(bar.mol)l: 10.332+ 0.457 No.
for the three most potassiccompositions,with a standard
error of +0.0003 J/(bar.mol) and a correlation coefficient
of 1.000.Note that the volume of feldspar8837 was used
in both fits.
C,l.r onrunrRrc RESULTS
Calorimetric data arc given in Table 4 and presented
[o,
in Figure 6. The precisionof the datais high; differences
Frcuna4. (A) Analysisof molarvolumeas a singlecontin- between the maximum and minimum heats of solution
uousseries.Theleast-squares
curvethroughthedatacorresponds (i.e., the spread in values) at individual compositions
to Equation1. (B) Plot of molarvolumevs. composition
Note ranges from just 0.057oto 0.24Voof the enthalpiesof
that the seriescan be dividedinto two linear segments.
Operi solution and averages0.74Vofor the nine seriesmembers.
symbolsarefor nearlymonoclinicmembers.
This level of precision is excellent considering the small
sample weights per experiment. Small samplesnot only
are prone to higher weighing errors, on a percentagebafeldspars,with a larger departurefrom ideality at potassic sis, but they generatesmaller temperaturechangesduring
compositions.The reasonfor this is not clear, but it is dissolution, producing greater uncertaintiesin the AZ reaccountedfor by the same effect that changesthe trend lated to dissolution, and thereby greater uncertaintiesin
in V-N". relations near the potassicend of the series.
the heats of solution. That this double effect was overThe maximum magnitudesfor V.. are only about one- come atteststo improvementsin our calorimetric system
half those of disorderedalkali feldspars (Hovis and Na- noted earlier, namely the addition of a more sensitive
vrotsky 1995). Indeed, one might expect lower magni- voltmeter and a better balancefor weighing samples.
tudes for a series that has a "shortened" compositional
span, in this case only 77Vothat of a normal alkali-feld- Enthalpy of disorder
spar serles.
The averagedifference in the enthalpiesof solution of
If treated as two separateseries, volumes for the tri- specimen80165 and its disorderedequivalent(8714) is
0.t
0.3
0.4
0.7
154
HOVIS: ANORTHITE IN K-NA FELDSPARS
TneLe4. Calorimetric
data
Sample Expt
80165
80165
80165
80165
8714
8714
87't4
8714
8818
8818
8818
8848
8848
8848
8903
8903
8903
8911
8911
8911
8904
8904
8904
659
662
685
686
641
643
671
676
646
672
682
644
673
678
648
674
683
645
666
684
649
670
679
ooJ/
o/c
8837
8838
8838
8838
8817
8817
8817
680
650
669
681
642
667
677
Composition
(No,)
Sample
weight
(g)
f change
during
dissolution
fc)
0.035
0.035
0 035
0.035
0.035
0 035
0 035
0 035
o 127
o 127
o 127
o217
o 217
o217
0 308
0 308
0 308
0 399
0.399
0 399
0.491
0 491
0 491
0.581
0.581
o 672
0 672
o 672
0 769
0.769
0 769
0.25591
o 27662
0 25592
0.25388
0 30584
0 26528
0 25603
o 25261
0.25507
0.24921
0.25329
0.27000
0.25298
0.24993
0 25489
0.25082
0.25093
0.25448
0.25079
0.24919
0.25441
0.25098
0.24694
0.25175
0.24835
0.25596
0.252'14
0.25081
0.30804
0.25104
o 25177
0.164499
0.177293
0.164245
0.163528
0.199373
0 173199
0.16741
o.'164711
0 . 16 5 3 1I
0 161683
0 164334
0 173355
0.162771
0 160457
0.162555
0.159892
0.160083
0.160730
0.158454
0 157556
0 159689
o 157266
0 155101
0 156875
0 154539
0 157994
0.155509
0 155090
0 188000
0 153143
0 153893
Calorimeter Calorimeter
heat
Mean
heat
solutionf
capacityI
capacityll
(Jfc)
(Jfc)
fC)
3877 31
3875 97
3874.84
3870.66
3875.81
3875.35
3870.28
3874.43
3879.40
3874.09
JO/J.CC
3876.39
3870.45
3875.60
3875.93
3874.68
3871.20
3877.44
3874.80
3874.80
3876.73
3874.93
3871.20
3870 91
3874.51
3876 85
3874.47
3870 41
3876 64
3875 10
3871.79
3874 64
3872 92
3874.64
3871 92
3876.52
3874.55
3870 12
3874 30
3877 90
3873.17
3872.92
3875 93
3870.79
3873 51
J6/J.Od
3873 21
3871 20
3876 39
3874.30
3874.43
3875.22
JO/J
IJ
3870.79
3870.70
3874.55
3875.10
3872.00
3870.66
3874.22
3872.79
3871.87
50.011
50 007
50 020
50.025
50.036
50 006
49 994
50.014
50.007
49.988
50.023
50.010
49.992
50.005
50.006
50.007
50.019
50.004
50.043
50.021
50.007
49.992
50.006
50.009
50.012
50.002
49.996
50.013
50.026
49.993
50.006
Negative
enthalpyof
Gram formula solutionI
weight(g/mol) (kJ/mol)
Negative
enthalpyof
solutionll
(kJ/mol)
664 160
661 997
662.704
664 398
673289
674.247
674394
673222
673745
673.524
673.448
670 545
670.930
670.356
669566
669.084
668 992
666 967
666 762
667 243
666.130
664 863
665.796
663 988
663.691
662.256
6 6 1. 3 1 0
662.348
658.461
657.896
658.649
663.704
661 474
662.633
664.578673411
674 105
674 331'
673.160
673.490
673 348
673302
670 465
670 992669 992
6 6 95 1 9
668 817
668 950666.783
666 637
667.135
6 6 58 6 7
664.557
665725"
663 955"
663 662
661 955
660.888
662 356"
658 047
657 511
658 662-
266.4811
266.4811
266.4811
266.4811
266.4811
266.4811
266.4811
266 4811
267 9618
267 9618
267 96't8
269.4184
269 4184
269.4184
270 8749
270 8749
270.8749
272 3427
272 3427
272 3427
273 8251
273 8251
273 8251
275.2719
275.27't9
276 7446
276 7446
276 7446
278 3075
278.3075
278 3075
. Usingacid of precedingexperiment
10.6 + 1.7 kJ/mol. This value is less than that of 12.0 +
2.0 kJ/mol (Hovis 1988,Eq. 7) fcrr the transitionof perfectly ordered low albite to fully disorderedanalbite. Although thesevalues are within the combineduncertainties
of each other, the difference between them is probably
real. Unlike analbite,sample 8714 does not have a true
monoclinicAl-Si distribution,nor doesthe degreeof disorder associatedwith the 10.6 kJ/mol changein enthalpy
representthe difference between a perfectly ordered and
a fully disorderedstate(seediscussionof site populations =
0
under Sample Characterization).Furthermore,one would
E
expect a lower enthalpy of disorder in oligoclase than in J
albite becauseits higher Al:Si should combine with Al
o
q
avoidance to quantitatively limit the degree of disorder
I
that is possible relative to that in albite.
t
Enthalpies of K-Na mixing
Perusalof the calorimetric data (Fig. 6) suggestsa linear relationship between heat of solution and composition; in fact, such a flt produces a good correlation coefficient of 0.919. Howevet we believe that there are
several valid reasonsfor considering higher order fits to
the data. First, a linear fit fails to intersect data at four
compositions, including the end-members,and data for
the latter both lie below such a line, possiblyimplying a
concavedownward relationship and positive enthalpiesof
mixing. Second, volumes for this series clearly display
0.1
0.3
o.7
No,
Frcurn 6. Negative enthalpiesof solution vs. composition.
Data are given in Table 4. The fourth-order curve corresponds
to Equation 5.
HOVIS: ANORTHITE IN K-Na FELDSPARS
E
2.0
=
l.s
tive heatsof mixing. However, data near the sodic end of
the series,especiallyat N". : 0.127, aremissedbadly by
the resulting curve. That factor and the very high precision of data for the three calorimetric experimentsat the
latter composition (note the data in Table 4) convinced
us to considerhigher order expressions.It is not until a
fourth-order equation is used that data near the sodic end
of the series are well represented.We accept this as the
best representationof the data but recognizethat alternate
interpretationsare nearly as reasonable.The resulting relationship, statedhere as the negative of the enthalpiesof
solution(-H,.,) so that the mixing coefficientsreflectthe
positive enthalpiesof mixing shown in Figure 6, is
I
E
!\.
x
o
E
155
I
r.o
LINE OF IDEAL MIXING
-H..' (kJ/mol) = 613.63 + 12.24 No, - 173.64 NL,
(5)
+ 342.30Nt - 222.62 N6,
valid for No, values from zero to 0.169, with a correlation
coefficientof 0.991 and a standarderror of *0.50 kJ/mol.
No,
The enthalpies of K-Na mixing (F1.-) derived from
Equation
5 are expressedas
Frcuns7. Enthalpies
of K-Namixingresultingfromanalysis
of thecalorimetricdatagivenin Figure6 Thecurvecorresponds
I1". (kJ/mol) : 32.34 Ne - 173.64 N')o,
to Equation6.
+ 342.30 N'* - 222.62 N3, (6)
-1.0
0.3
0.4
0.5
0.6
0.7
positive excessquantities associatedwith K-Na substitution. Third, positive volumes and enthalpies are clearly
associatedwith K-Na mixing in alkali-feldspar systems
(Hovis 1988).For thesereasons,we believe it is likely
that the oligoclase-basedseriesof this investigation does
indeed possess positive (obviously small) excess
enthalpies.
As the order of fit to the calorimetric data is increased,
conrelationcoefflcients improve. A second-orderfit produces a concave downward relationship and small posi3.0
2.5
E
E
3
2'o
l.s
x
o
r
1.0
-1.0
0.1
0.6
o.7
No,
Frcunr E. Enthalpiesof K-Na mixing resulting from analysis
of the calorimetric data as two separateseries,with an intermediate end-memberat N". : 0.578.
The fourth-order fit to the calorimetric data produces a
curve (Fig. 7) having a double maximum for the enthalpies of mixing, one that is symmetric about the compositionalcenterof the ion-exchangeseries.This is a mathematical consequenceof such a fit and in this case has
no physical basis that relatesto the minerals themselves.
We had no desire, however, to utilize a fifth-order fit for
a mineral series with only nine members; furthermore,
the latter produced a mixing curve quite similar to that
in Figure 7.
If the oligoclaseion-exchangeseriesis treatedas two
separateentities, the results in detail are different. Using
calorimetric data for sample 8837 for both parts of the
compositional range, we fitted the enthalpiesof solution
for the seven most sodic members of the series as a
fourth-order polynomial, and for the three most potassic
membersof the seriesas a second-orderpolynomial. Such
a treatment produced the enthalpies of K-Na mixing
shown in Figure 8, with a compositionally intermediate
end-member (determined by the intersection of the two
heat-of-solutioncurves) locatedat a N". value of 0.578.
In this case maximum enthalpiesof mixing are reduced
for the potassic part of the series but are maximized at
about the same magnitude and the samecomposition for
the sodic part of the series, relative to those shown in
Figure 7.
INrpnpnnrlTloN oF RESULTS
Regardlessof the model or order of fit used to represent the new data reported here, it is clear that the presence of An component in feldspars substantiallyreduces
excess properties associatedwith K-Na mixing. Maximum volumes of mixing are reduced by one-half. Maximum enthalpiesof mixing reach values of 5 kJ/mol for
disorderedAn-free feldspars(Hovis 1988;Hovis and Na-
156
HOVIS: ANORTHITE IN K-Na FELDSPARS
AcrNowr-nocMENTs
I thank Pete Dunn of the USNM for donation of the oligoclasestarting
material for this project, and Dexter Perkins III, Dave Snoyenbos,and
anotherreviewer for helpful commentson the manuscript.This work was
supportedby the Earth SciencesDivision of the National ScienceFoundation through grant EAR-9303814, and also by LafayetteCollegethrough
endowedfunds for the John H Markle Professorship
=
o
tr
3
r
RnpnnBr.rcns CITED
o
6
0.0
0.1
o.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
t.o
No,
Frcunn 9. Calorimetricdatafrom Hovis (1988)for disorderedalkalifeldspars.
ThisdiagramillustratesthatheatsofK-Na
mixing are substantially
reducedif dataat the sodicend of the
series,up to N". : 0.23,areeliminated.
vrotsky 1995) but are reducedto 2 kJ/mol for oligoclase.
The physical reason for these effects is uncertain. The
presenceof Ca in 23Voof the alkali sitesperhapsprovides
an averageoccupancyfor the alkali site againstwhich the
strain effects of K-for-Na substitution are substantially
dampened; there are simply fewer alkali positions in
which a large K* ion is situated near a smaller Na* or
Ca*2ion.
In alkali-feldspar serieswith near-zeroAn, it is instructive to note the shapesof the heat-of-solutioncurves (see
Hovis 1988,Fig. 2). Enthalpiesof solution behavemore
linearly at the potassicends of most series,which would
seem to imply that the substitution of Na into a pure
potassiumfeldspar is close to ideal. The enthalpic effects
of K substitutioninto pure sodium feldspars,however,are
somewhat different. As the feldspar becomes more potassic, the energy associatedwith K-for-Na substitution
decreases,causingthe heatsof solution to becomecurved
with composition. If we eliminate the most sodic 23Voof
the data for such a series,mixing effects are significantly
diminished (Fig. 9). In the present study it appearsthat
CaAl mimics the effect of NaSi at the sodic end of an
alkali-feldspar series. Thus, one could imagine that the
most curved part of the heat-of-solutioncurve, from 0 to
23Vo An, was inaccessibleduring the present study.
The reason for the double maximum in the heat-ofmixing curve for this series, if it is real, is unclear. We
can only surmise that it is related to the near attainment
of monoclinic symmetry in the compositionalregion near
N* = 0.5-0.6. There may be anotherphasetransitionthat
would account for this behavior, perhaps related to the
distribution of K-Na-Ca, but detailed analysis of X-ray
powder diffraction data did not reveal such a transition.
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MeNuscnrrr nrcerveu JaNueny 22, 1996
MaNuScnrrr AccEprEDSEr"rgMeen79, 1996