A. WJECKOWSKI: Ultramarine
Study by EPR
125
phys. stat. sol. 42, 125 (1970)
Subject classification: 19; 5; 22.8
Radiospectroscopy Laboratory, Institute ol Physics, Polish Academy ol Sciences, Poznan
Ultramarine Study by EPR
By
A. WIECKOWSKI
Dedicated
to Prof. Dr. Dr. h.c. P. GORLICH,on the occasion of his 65th birthday
By EPR, ion-radicals .S-, .S2, and 'S3"are found to arise in the process of synthesizing
ultramarine.
Typical, blue ultramarine
contains 'S3"ions. At room temperature,
the line
width is found to be determined to a large extent by spin-lattice interaction, whereas at
liquid nitrogen temperature (77 OK) almost exclusively by spin-spin interaction.
The EPR
line shape was analyzed by linear anamorphosis ofthe resonance curve. The second moment
was used for computing the density of polysulfide ions 'S3"according to Van Vleck's formula. The results indicate that the 'S3" radicals form a face centred cubic lattice in an
elementary celI with lattice constant d' = 2 d = 18.12 A, where d is the lattice constant
of the elementary celI determined by the X-ray method.
Mittels EPR wurde gefunden, daB die Ionen-Radikale
'S-, 'S2 und 'S3"bei der Synthese
von Ultramarin
auftreten.
Typisches blaues Ultramarin enthiilt .S3"-Ionen. Bei Zimmer.
temperatur wird die Linienbreite zum gro Ben Teil durch Spin-Gitter-Wechselwirkung
be.
stimmt, wiihrend sie bei der Temperatur des fliissigen Stickstoffs (77 OK) fast ausschlieBlich
durch Spin-Spin- \Vechselwirkung verursacht wird. Die EPR-Linienform
wurde durch eine
lineare Anamorphose der Resonanzkurve
analysiert. Das zweite Moment wurde nach der
Van Vleckschen Formel zur Berechnung der Dichte der Polysulfidionen
'S3"benutzt. Die
Ergebnisse zeigen, daB die 'S3"Radikale ein kubisch fliichenzentriertes
Gitter in einer
Elementarzelle
mit der Gitterkonstante
d' = 2 d = 18,12 A bilden, wobei d die Gitterkonstante der ElementarzeIle ist, die durch Rontgenmethoden
bestimmt wurde.
1. Introduction
Ultramarine is a sodium aluminosilicate containing sodium polysulfides. Like
lazurite (lapis lazuli), ultramarine presents the crystal structure of minerais
of the sodalite group, which belong to the space group of symmetry Tc1(P43n).
The elementary cen corresponds to the formula NasA16Si6024S4'The lattice
constant is d = 9.06 A.
Gardner and Fraenkel [1] in 1955 observed paramagnetic resonance absorption in ultramarine, and found the paramagnetism to be due to a sulfur free
radical (SFR) present aIso in molten sulfur as wen as in solutions of sulfur in
fuming sulfuric acid.
In 1959, Matsunaga [2] found that the tint, splitting factor IJand line-width
of ultramarine depend strongly on the cation replacing the sodium ions Na+.
This suggests that sulfur enters a complex with the cation and presumably is
electro- nega tive.
In 1961, Folin [3] proposed to apply ultramarine in EPR studies as a standard
of the num ber of spins, and to use a mixture of ultramarine, and DPPH as
indicator of magnetic field strength.
In 1967, B6ttcher et al. [4] observed the EPR line-width of ultramarine to
increase with growing temperature, suggesting a dependence of the line-width
on the spin-lattice
relaxation
time Tl'
126
A. WIECKOWSKI
It was not until1968 that Morton [5] established the nature of the paramagnetic centre present in uItramarine, and by comparing the spectroscopic splitting factors g for the relevant ions 'S-, 'S2, and 'S'3 in the lattices of alkali
halogenides, found that ultramarine contains paramagnetic ion radicals 'Ss
beside diamagnetic ions S~-.
The splitting factor for ultramarine amounts to g = 2.029, and thus differs
from those of other, typical free radicals, pointing to a considerable contribution from spin-orbit coupling within the sulfur atom. According to McClure
[6], the spin-orbit coupling constant A.for sulfur is A. = -382 cm-l.
This paper is aimed at determining the distribution of ion radicals 'S'3in the
crystallattice of ultramarine.
2. The Sulfur Radicals Present in Ultramarine
In our earlier work, we identified by EPR the various SFR's which arise
by temperature-processing of ultramarine [7]. This led to the identification of
three types of SFR denoted as A, B, and D, respectively, and presenting characteristicaliy weli-defined g-factors and line-widths. With regard to Morton's
results [5], the foliowing attributions can be postulated:
type A is the ion radiacl 'S;,
type B is the ion radical 'Ss,
type D is the ion radical 'S-.
The line of type B SFR is the line specific for ultramarine.
In order to determine how the EPR line-width depends on the concentration
of spins, we proceeded to a synthesis of ultramarine in the laboratory [8]. In
the concentration range of 1018to 1019spin s per gram, the line-width was found
to grow with the concentration, and the resonance line was of Gaussian shape,
pointing to spin-spin interaction between the free radical centres. On the
other hand, from 1019to 1020spinsJg, the line-width decreased with concentration, and the line changed to Lorentzian shape. This decrease in line-width
is due to the occurrence of exchange interaction, which is strongly dependent
on the distance between the centres as a result of overlapping of the orbitals
of unpaired electrons of neighbouring ion radicals 'S'3.
3. The Distribution ol S~- lons and 'S3 lon Radicals in Ultramarine
We proceeded to an investigation of the interaction between paramagnetic
centres in ultramarine, with the aim of determining the distribution of 'Ss ion
radicals in the crystallattice from an analysis of resonance line-width and shape,
using a sample of powdered blue "Standard Export" uItramarine from the
Ultramarine Works at Kalisz, Poland. This sample presented the foliowing
characteristics :
a) a high sulfur content (14.8% S),
b) a high concentration of paramagnetic centres (2 X 1020spinsJg),
c) a narrow EPR line (10 G).
Since there were 5.9 X 1020elementary cells per gram, the number of paramagnetic centres per elementary cell amounted to 0.34 :f: 0.05 spins per celi.
However, it should be kept in mind that ultramarine is by no means chemically
homogeneous; beside ultramarine proper (radical ultramarine), it contains in
admixture various other chemical compounds presenting basically the structure
of alumino-silicates and resembling the mineraIs of the sodalite group.
127
Ultramarine Study by EPR
The results of B6ttcher et al. [4] point to a marked temperature dependence
of the line-width in ultramarine. One has thus to expect a strong spin-lattice
interaction reducing the relaxation time Tl and giving rise to an increase in
EPR line-width. According to van Vleck's theory [9], the EPR spectrum can
serve for determining the distribution of paramagnetic centres in the lattice,
provided the line-width depends on spin-spin interaction alone, Le., if it is
defined solely by the relaxation time T2. Hence, the relaxation time Tl has
to be large as compared with T2. Consequently, the EPR spectrum of ultramarine measured at room temperature cannot serve for studying spin-spin
interactions between paramagnetic ions 'Ss because such a spectrum is additionally broadened by interaction with the lattice. According to Kronig [10],
for spin S = 1/2, and not excessively low temperatures, the energy of the unpaired electron is transferred to the vibrations of the lattice in a two-phonon
process, and the relaxation time Tl is inversely proportional to the square of
the resonance magnetic field strength and the seventh power of the absolute
temperature
H-2 T-7.
Tl ("oo.J
Hence the line-width plotted against the product H2 T7 should be a straight
line, since the relaxation time T2 changes but insignificantly with temperature.
Fig. l shows the slope width !:::..H1s
of the EPR line of ultramarine versus the
product of the squared magnetic field strength and the seventh power of the
temperature. The experimental points are for X, K, and Q and for liquid
nitrogen temperature (77 OK),room temperature, as well as higher temperature.
The trend of the graph permits the conclusion that the EPR spectrum obtained
in the X-band at 77 oK (the point furthest to the left) has a line-width which,
practically, depends solelyon spin-spin interaction (!:::..Hls
= 6 G). The width
and shape of the EPR line are due to dipole-dipole interaction between 'S3
centres as well as to exchange interactions.
The EPR line of ultramarine was subjected to an analysis by the method of
linear anamorphosis of the resonance curve (Fig. 2). The line, in its central
portion, was found to present Lorentzian shape, whereas at the wings it was
Gaussian. This indicates that the width of the outer parts is due to spin-spin
t 40
~
30
+
8
~
7
~6
5
o
o
10 20 30 40 50 60
-05
112J7(10-18(/01<7)_
Fig. 1. Graph showing trend of the slope width, f!,.H,8, for
ultramarine versus the product of the squared resonance
magnetic field strength and the seventh power of the temperature, H' T' (the point furthest to the left is for the
X-band and 77 OK)
Fig. 2. Linear anamorphosis of the resonance curve of
ultramarine in the X-band and at 77 oK. Abscissa: 1 unit
z' = 21.4 G'; O O left part of the line (z < O),+ X right
part of the line (z > O)
750
x2-
128
A. WIECKOWSKI
interaction and that the centre is narrowed as a result of exchange. Resorting
to the theory of Anderson and Weiss [11] as well as Kubo and Tomita [12],
the following parameters of the resonance curve were determined:
a) second-slope width I::..H-l.equal to halfwidth AHr/2
10.5:1::
0.7 G;
(central Lorentz-shaped
part) [13]:
52 :I:: 18G;
b) exchange field He:
21 :I:: 3 G;
c) first-slope width AHfs (Gaussian wings):
435 :I:: 120 G2.
d) second moment #2:
The above parameters
are related
as follows:
I::..H~s= l/n
(I::..Hfs)2,
V 2
He
with the condition I::..H~s I::..Hfs
He
Hres.
According to van Vleck [9], the second moment
the formula
<
#2
<
<
of the EPR
line is given by
_3
= 4 g2(328 (8 + l) Ek rit (3 cos2 Ou - 1)2.
Since here uItramarine was studied in erystal powder form, the factor (3 cos2 Olk- 1)2 has to be averaged, yielding
#2 = 35 g2(328 (8
+ l) Ek
rit .
The crystallattice of ultramarine being regular (lattice constant d
the sum E rit takes the form
k
=
9.06 A),
E rit = O n2 d-6 .
k
0:'
A
e=
n3
with O a numerical constant specific for the lattice, e the num ber of sites per
elementary cell of lattice constant d, A the number of sites per elementary cell
of lattice constant d' = n d, n an integer.
The polysulfide ions S§- and "8"sare disposed as in the regular body-centred
lattice (see, e.g., Remy [14]). It is asked which of the polysulfide ions are paramagnetic ions. In order to answer this question, the following assumptions
were made:
L Paramagnetic centres .Ss are distributed in ultramarine in accordance
with one of the following three simplest possible dispositions of sites for a cubic
lattice, namely:
a) simple lattice: P,
b) body-centred lattice: I,
c) face-centred lattice: F.
2. The lattice constant d' of the elementary cell assumed with regard to the
disposition of paramagnetic ions in ultramarine is an integer multiple of the
lattice constant d = 9.06 A:
d' = nd.
The experimental and theoretical values of parameters characterizing the
density of distribution of sites in the crystallattice of uItramarine are compiled
in Table l, whence the best agreement is seen to resuIt if the paramagnetic
129
Ultramarine Study by EPR
Table
Experimental
and theoretical values of parameters characterizing the density of disposition
of sites in the crystallattice
of ultramarine
(The symbols are given in the text)
C
Types
of cubic Symlattice
boI
I
(theor.)
I
p
8.40
I
I
7.26
F
7.23
C fi
(exper.)
I
Simple lattice
Body-centered
lattice
Face-centered
lattice
1
I
,
l
r
1.5 :f: 0.4
A
(theor.)
1
e (n =
I
e (n = 2)
1)
(theor.)
I
(theor.)
e
I
(exper.)
1
'0.125
10.43:f:0.06
2
2
0.25
0.46 :f: 0.06
4
4
0.5
0.46 :f: 0.06
I
In the last column, the discrepancies in density values eexper.are due to disci'epancies in the
constant Ctheor..
centres 'Sa are assumed to be disposed in ultramarine according to a face-centred
cubic lattice with elementary cell of linear dimensions twice larger than the
lattice constant d = 9.06 A.
4. COllclusiolls
The essential conclusion to be drawn from the present analysis of the EPR
line shape obtained in the X-band at 77 oK resides in the statement that the
elementary magnetic cell of ultramarine has a period twice larger than the identity period of the elementary cell determined by the X-ray method. Since
according to Morton [5] the paramagnetism of ultramarine is due to the ion
radical 'S3, this conclusion entails a revision of the present viewpoint regarding
the elementary chemical cell. A chemical formula of the general shape
Na6H
A16-n Si6+n 024(S2h.5-m
('S3)0.5 Vm
is assumed for the elementary cell of lattice constant d = 9.06 A, with m the
number of vacancies v in place of ions S~-, n that of Al3+ ions replaced by
Si4+ ions, x = 3.5 - 2 m - n; the values n, m, and x can lie in the intervals
O < n < 1.5 ,
OS m < l ,
1.5 < x < 3.5 .
The primary advantage of this chemical formula resides in the fact that it
preserves constant the aluminosilicate structure present in various ultramarines
but leaves the door open for the experimentally established differences in their
chemical compositions.
S~- and 'S'3are permanent ions in the aluminosilicate system of ultramarine,
whereas, e.g., ions 'S2 and Si- do not normally occur. This may be due essentially to steric causes. In ultramarine and lazurite, the four-atom ({our-centre)
system
Na+ (S-S)2- Xa+
(diamagnetic)
as well as the four-atom system
Na+(S-'S-S)(paramagnetic)
can be presumed to be privileged.
Fig. 3 shows schematically the newelementary cell of ultramarine as established by the method of electron paramagnetic resonance. With the aim
of obtaining a clear picture, all Na+, AI3+, Si4+, and 02- ions are omitted,
leaving only the ions 'Sa and, in one eighth of the cell, the ions S~-.
9 physlca 42/1
130
A. WIECKOWSKI:Ultramarine Study by EPR
Fig. 3. Disposition of diamagnetic S;- ions and paramagnetic 'S;;
ions in the elementary cell of ultramarine with doubled la ttice eonstant d' = 2 d = 18.12 A (the S; - ions are plotted in 1/8 of the cell
only)
It should still be stressed that ultramarine is chemicalIy inhomogeneous.
The number of paramagnetic 'S3 centres per celI computed from the second
moment of the EPR line is e = 0.5, whereas the integral line intensity leads
to a value of e = 0.34. This shows that the substance investigated here consisted of 70 per cent of ultramarine proper and of about 30 per cent of foreign
diamagnetic compounds.
Acknowledgements
The authol' wishes to thank Prof. Dr. A. Piekara, Head of the Group of
Nonlinear Optics and Physical Chemistry ofWarsaw University, for his valuable
remarks, and is highly indebted to Doc. Dr. J. Stankowski, Director of the
Radiospectroscopy Laboratory of the Institute of Physics, Polish Academy
of Sciences, at Poznan for his discussions and interest throughout the present
investigation.
References
[l]
[2]
[3]
[4]
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{14] H. REMY, Lehrbuch der Anorganischen
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Geest & Portig, Leipzig 1960 (p. 612).
(Received August 20, 1970)