fHE AMEi.rcAw nrxei.a,lociSt,
vor, so,NoveMsni. DECEMBEA,ieii
THE DEPENDENCE OF THE WAVELENGTH OF AIKa RADIATION FROM ALUMINO-SIICATES
ON THE AI-O DISTANCE
Rouer,r WanolB AND G. W. BnrNlrru, Materials ReseorchLaboratory
and.DepartmentoJ Geochemistryand.Mineralogy, The PennsylaoniaStote
(-In'iaersity, U niaersity P ar k, P ennsylz'ania 16802
ABsrR.{cr
AlKa emission wavelengths from a range of substances are compared with that from
aluminum metal. The wavelength shift, A),, and the angular shift A,(24)using a pentaerythritol analyzing crystal, are shown to be related primarily to the average Ai-O distances
rather than to coordination number as previously emphasized. The importance of this
result in relation to the estimation of AI in 4- and 6-fold coordination is discussed.
INrnonucrroN
Over the past few years, many studies have been made of the wavelengths of characteristic X-radiation excited from certain cations in
oxide materials in relation to their coordination number. The method has
been applied particularly to the coordination of Al3+ ions in aluminosilicatesby comparing the emitted wavelength with that from a particuIar substance, usually metallic aluminum. Since the wavelength change
AX is small, the results are often expressedby A(20):20(Ll metal)
-20(Ll, sample), where 20 is the diffraction angle for the measuring
crystal.
The initial studies were concernedwith showing that the A(2d) values
fall mainly into two groups corresponding to the coordination numbers 4
and 6. When more than one coordination state occurs, then A(2d) is related to the weighted average of the two coordinations (White, McKinstry, and Bates, 1959; Brindley and McKinstry, 196l;Day,1963). Subsequently measurements of A(20) have been used to estimate the proportions of AlIv and AIVr in mixed systems, such as gels and glasses,on
the basis of a linear vdriation of A(20) between chosen end members.
Some of the end members so chosen are kaolinite and AIPOa (DeKimpe
et a1,.,t96t1 Gastuche et al., 1963), gibbsite and AIPOa (Leonard et al.,
1967), a\lzOr and sanidine (White and Gibbs, 1969), and kaolinite and
feldspar (Steinberg, 1970). The hazards of using this technique for estimating Alrv/Alvr ratios are discussedlater.
The variations of A(2d) or A\ within a given coordination group have
been attributed generally to variations of interatomic distances (Laputina and Narbutt, 1967; Shuvaev et al., 1967; White and Gibbs, 1967;
1969).When the presentwork was completed,a paper by Lziuger(1971)
appeared in which the variations are discussedon the basis of the electronegativity of the cations in the secondcoordination shell.
2t23
2r24
RONALD WARDLE AND G. W. BRINDLEV
In all these studies, A(20) or Atr is consideredto be primarily a function
of coordination number.
It now appears,as will be shown in the present note, that A(20) can be
correlated with interatomic distances without reference to coordination
number so that the primary variable seemsto be the interatomic distance,
a result which appears to be consistent with an approximate theoretical
treatment by Shuvaev (1964).
ExpnruwNrarThe A(24) of the AlKa peak for several minerals was measured with respect to that for
Al metal powder mixed with silica flour to give approximately the same Al concentration
in the standard as in the samples (15-30 wt. percent). The samples were prepared as the
front face of a methyl cellulose compact as often used for X-ray fluorescence analysis
(Ingamells and Suhr, 1963). The spectra were recorded on a Siemens SRSI X-ray spectrometer with a chromium target at 40-45 kV and 12-16 mA The anal1'zing crystal was
pentaerythritol (2d:8.75 A) and a gas-flow counter was used. A vacuum of 0.1-0.2 torr
was maintained to reduce absorption of the emitted AlKa radiation. The scanning speed
was either 0.125o or 0.250' (20)/min. and the chart speed was chosen such that 1o (2d)
was equivalent to 8 cm. chart paper. Under these conditions the peak width at half maximum intensity was about 0.8" (20) and, the peak position at half maximum intensity could
be measured to * 0.0030 (2d). Readings of the Al metal standard and of the minerals studied
were alternated so that any drift in the recording process could be taken into account.
Resurrs ANDDrscussroN
The presentresults,Table 1 and Figure 1, show that a singlecurve can
be drawn through almost all the data, certainly within the limits of
experimental error, when A(2d) is representedas a function of the mean
Al-O distance. For this purpose, accurately determined distances are
necessaryand the sourcesof the data used are indicated in the footnote
to the table. To verify that this result is not peculiar to the present measurements, the A\- values given by Lduger have been converted to
A(20) values and plotted with triangles in Figure 1. That the two curves
are not coincident is not surprising in view of the small shifts to be measured. The significant result is that Lduger's data show the same trend
as the present results, with most of the A(28) values falling on a single
curve.
In both sets of data, the aAlrOr results fall below the mean curves and
this may well be due to the next nearest neighbor effect as explained by
Liiuger since the AI-AI distance is 2.65 A (Newnham and DeHaan, 1962).
The A(2d) value for anhydrous AIPO4 lies on the mean curve for the
present results but is very greatly displacedfrom the mean curve through
Lduger's data. SinceAlPOr. 2H2Ogivesa considerablyIargerA(20) value,
within the range of 6-fold coordinations (see Table 1), a possible explanation is that the AIPOI used by Liiuger may have been partly hydrated.
WAVDLENGTH OF X-RADIATION
i,
(AI
= 2O
A(ZEI
TABI,E 1.
llo
.rr
Substance
I.DTAL)
2125
FROM ALUMINO-SILICATES
- 2€
(ST'BSTANCE)I MEAN AI-O
C@RDTNATToN NUMBERS FoR MTNEn.lIs
sruDrED
conposition
( rdeal )
At-O
A(ze)"
DISTANCES'
Distdce
r.94u
6
1.
Plrophyllite
Ar2si4010( oH)
2.
Kaolinite
Ar2si2o5 (oH)4
3.
phosAlein@
phate hydrate
ArPO4.2H2O
4.
Dickite
Ar^si-o_ (oH),
o.720
1.eol
6
5.
Kyeite
Ar2sio5
o . 11 6
1.972e
6
6.
Gibbsite
A 1( o H ) ,
o.472
1.9of
6
7.
Cotudu
*t"o,
o . 11 1
7.9779
6
8.
Andalusite
Ar2sio'
o.110
r.ggoh
5,6
9.
siIliEilite
Ar2sio;
o.104
t_ttt'
10.
Pyrophyllite
dehydroxylate
Alzti4ort
o.091
11.
Metakaolin
At2si207
o.o81
-
12.
Microcline
1r.
Albite*
14.
Analcine
15.
(hd)
( Id)
lfardte
bzwagin
cDrits
dllemna
esumhd
fl.tega*
exdination
ad
Brindtey
suggeEts
( 197-)
(1950)
t.g38"
4
KArsi30B
o.o81
t
NaAISirOg
o.o77
7.746k
Na.A'lSi206.HZO
o.o76
sall
6
z )
proportion
of
high
L.70-
dd
\too."y
De llaan
and Buerger
rBurhhffi
iB.o*
4
present.
albite
\iuu.
4
4
9Nemhm
(t963t)
zr.tJ
I
o.o75
( 1961)
(1955)
t.tfo
o.72lr
hBr*h-
(t96o)
and Kashaev
2
ArPO4
phosA1uinw
phate dhydrous
*X-ray
o.1ta
Coordination
N*u..
I
( 1962)
(1961)
(196ra)
*d
"t
Bailey
at.
( 1964)
(1969)
(1956)
Ld.uger'svalue for spinel, MgAI2Oa,is plotted with Al-O:1.927 A, a
value derived from the data of Bacon (1952) on the assumption that all
AI is in the octahedral cation sites, but if the spinel is partly inverse with
some Al in tetrahedral cation sites, then a smaller mean A1-O distance is
required; this would move the spinel point nearer the mean curve.
The result that A(20) appears to be a function of the Al-O distance is
generalll. consistent with a theoretical discussion given by Shuvaev
(1964) who points out that in compounds of elements in Period 2 iI all
the valence shell electronsare bonding, that is, no lone pairs of electrons,
the shift of the Kar,z lines relative to their position in the metal or pure
element must be approximately proportional to the change in electron
)06
R)NALDwenbLa ANb G. w. BntNoLzY
o
0.1
7.0
5r
2.5
=o
0.10
o
(D
c\
X
o{
a
0.08
18.0
0.
13.5
1.70
rJs
1.80
1.85
1.90
1.95
o
MeanAl-0 distance,A
Frc. 1. A(20)o:2do(Al metal)-20o(Al,
substance), and Atr plotted against Al-O distances, A, Upper curve and circles, present data, lower curve and triangles, from data of
Liiuger (1971). The numbers correspond to the numbers in Table 1. In addition in Lliuger's
data sp:spi1sl, Al-O:1.927 (Bacon, 1952), and ma:margarite, Al-O:1.841 (Takduchi,
1e66).
density of the valence electrons. This electron density can be calculated
over the whole volume of the ion which in turn introduces the ionic
radius and hence the interatomic distance.
It is proper to sound a note of caution regarding the use of. A(20)
WAVELENGTHOF X.RADIATION FROM ALUMINO-SILICAT]JS
2127
values to estimale the proportions of AI ions in 6-fold and 4-fold coordination in mixed systems by interpolating on a straight line joining
particular end members, often called "standards." This procedure is
reasonableonly if the Al-O distancesin the calibrating substancesand in
the particular system studied are closely similar. An example of the kind
of error which could arise in unfavorable circumstanceswould be to use
pyrophyllite and AIPO+ as calibrating substances to estimate the Al
coordinations in gibbsite; the data in Table 1 wouid lead to the conclusion that gibbsitehas 33 percentof the Al ions in 4-fold coordination.
The question whether the AI-O distances in feldspars vary with the
degreeof order may possibly be resolved by measurementsof A(20) if the
experimental accuracy can be improved. The possibilities of this approach are under consideration.
CoNcr,usroNs
It is concluded that A(20) for AlKa emissionfrom oxide systems measured with respect to emission from Al metal is related primarily to the
mean Al-O distance and only indirectly to coordination number. The result is generally consistent with the theoretical discussion of Shuvaev
(1964). Care is neededin using A(28) values to estimate the proportions
of Al ions in 4-fold and 6-fold coordination in mixed systems.
AcKNoWT,EDGMENT
This work forms part of a program supported by a National Science Foundation Grant
GA1698. We thank Drs. G. V. Gibbs, R. E. Newhnam, and E. W. White for useful comments.
RBlrrcNcts
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Manuscript receivd, March 23, 1971; accepted'Jor publication, May 18, 1971.
Note added in proof: A paper by A.J.Ldonard, P. N. Semaille, and J, J.l-ripiat, Proc.
Bri.t. Cer. Soc. (1969) 103-116, inadvertently overlooked in the review, discusses the AIka
shift for amorphous silico-aluminas in relation to the average Al-O distances determined
by radial X-ray analysis.