High Temperatures ^ High Pressures, 2000, volume 32, pages 461 ^ 466
15 ECTP Proceedings pages 445 ^ 450
DOI:10.1068/htwu48
Points of melting ^ crystallisation and polymorphic
transformations of sulfur in density ^ temperature
coordinates
Anatolii S Basin
Department of Thermodynamics, Institute of Thermophysics, Siberian Branch of the Russian
Academy of Sciences, Novosibirsk 630090, Russia; fax: +7 3832 343480; email: [email protected]
Boris G Nenashev
Department of Crystals, Institute of Mineralogy and Petrography, Siberian Branch of the Russian
Academy of Sciences, Novosibirsk 630090, Russia
Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany,
5 ^ 9 September 1999
Abstract. Experiments were carried out in situ and with automatic analogue signal registration
during the continuous heating or cooling processes of sulfur samples in the temperature range
20 ^ 350 8C with detailed investigation of the melting and crystallisation intervals. The transformation temperatures were measured, and the expansion coefficients, specific volumes, and density of
sulfur with different purity grades were calculated. The investigation was carried out with the application of a narrow gamma-radiation beam passing through the sample. Hysteresis of heating and cooling
processes as well as the dependence of temperature and volumetric characteristics of melting and
solidification on the purity of sulfur samples were discovered. The peculiarities of the processes in
connection with sulfur crystallisation and melting are discussed.
1 Introduction
Sulfur and its compounds are substances of very broad practical application and
importance. At the same time, pure sulfur is a very interesting substance with a number
of unique individual properties, especially strikingly exhibited in liquid and gas states.
Sulfur atoms have an exclusive ability to describe a set of molecular forms, from S2 to
S20 , including ring molecules, S6 , S8 , S12 , etc (Meyer 1965, 1976). A completely unique
property of the molecular forms of sulfur is the ability to polymerise spontaneously in
a liquid state (L-S) during transition through the l and m phases at temperature
tl=m 170 8C (Bellissent et al 1994; Alwarenga et al 1996). This self-polymerisation results
in a sharp increase of liquid sulfur viscosity, a change of colour, and other macroproperties of sulfur. The special properties of S atoms and polymolecularity are also exhibited
in the solid state of sulfur as an allotropy and a set of polymorphous transformations.
Perhaps, the report about nineteen `melting points' follows from this (Meyer 1965). However, this large number of melting points remains disputable (Vezzoli and Walsh 1977).
Only five crystallisation points of very pure sulfur in coordinates of density, r, and
temperature, t, and approximately ten singular points were observed in our experiments
between 20 and 270 8C. Some of them coincided with those observed earlier (Meyer
1965), but not all of them.
The main purposes of our experiments consist in deriving precise data of sulfur density
changes throughout the interval of melting ^ crystallisation temperatures. This area of
physical transformations of substances is interesting no less than the l-phase points, but
has not been investigated so far in detail.
2 Experimental
The experiments were carried out by thermodilatometric analysis of the specific volume, v,
as a function of temperature, t, and thermometric analysis of t as a function of time, t,
by the gamma-ray attenuation technique. We used the same gamma-ray dilatometer as
462
A S Basin, B G Nenashev
15 ECTP Proceedings page 446
for our iron research (Basin et al 1979), but with the improved measuring system (Basin
and Alekseev 1991). As a whole, this technique is similar to that used in other works
(Drotning 1981). Sulfur samples were prepared by a long vacuum distillation in glass
silica ampoules. The mass of each sample was about 75 g; the volume of the ampoules
was about 50 cm3. The path of the 137Cs gamma-radiation beam through the sample was
approximately 37 mm. Two thermocouples were placed inside the sample. Gamma-ray
intensity and thermocouple thermo-emf were measured by digital instruments and simultaneously registered with an x ^ y positional recorder. This double method for recording
measured magnitudes allowed us to observe melting and crystallisation effects in a continuous process of heating and cooling of the sample and reliably to fix process
features, which are not observed in experiments with a thermostatic sample.
The experimental curves (figures 1 ^ 3) show separate fragments of a rather extensive
complex of measurements. The experiments were conducted on five sulfur samples of
high purity (99.999% for two samples and 99.9999% for three samples) chemicals with
an amount of bitumens less than 1610ÿ3 and 3610ÿ5 wt%, respectively. Such a purity
was reached as the outcome of long vacuum degassing of the sulfur at 120 ^ 150 8C and
sublimation at 300 ^ 370 8C. The pressure inside the hermetic ampoules was no more
than the saturation vapour pressure of liquid sulfur (5 225 mm Hg).
0.57
A
v=cm3 gÿ1
0.54
R
0.53
0.54
0.53
Ue
0.51
0.51
R
0.50
50
100
100
t=8C
150
t=8C
200
150
*
0.56
S4.2h
B
S4.2h
H
Figure 1. Experimental plot of gamma-radiation
intensity versus thermo-emf, which has been
transformed to a plot of specific volume, v, versus temperature, t. The present plot shows
the result of the S4.1 sample test. The S4.1cl
curve represents the process of liquid sulfur cooling
(A ! P ! L ! U), solidification, U ! R ! C, and
cooling of solid sulfur at t 5 tc .
50
C
Cid
C
M
U
0.52
0.52
50
100
t=8C
150
Figure 2. Experimental plot for test S4.2. The
right curve shows the heating process (h) and
melting, H ! B ! M. The left curve shows the
liquid cooling process and solidification,
L ! U ! Ue ! R ! C.
200
A
S1.2cl
0.55
v=cm3 gÿ1
L
0.55
U
P
S4.2cl
0.56
L
0.55
v=cm3 gÿ1
P
S4.1cl
0.56
U
0.54
0.53
R1
S1.1cl
U
R2
0.52
R2
C
C
0.51
0
50
t=8C
+
100
150
Figure 3. Experimental plot for tests S1.1 and
S1.2: processes of liquid cooling and solidification,
U ! R1 ! R2 ! C.
Melting ^ crystallisation and polymorphic transformations of sulfur
463
15 ECTP Proceedings page 447
3 Results and discussion
Figure 1 shows a typical experimental curve of sulfur-sample cooling, which begins in a
liquid state for t ˆ tA , continues through the p ! l transition (polymerisation point P)
and the interval of solidification, L ! U ! R ! C, finishing in a solid state at t 40 8C.
The cooling rate of a sample for t 4 tL was set at approximately 2 8C minÿ1 , but in the
area R ! C it was spontaneously reduced to 4 1:3 8C minÿ1 as the outcome of sequential
selection of heat. The process U ! R is the speed process of self-heating of sulfur because
of initial spontaneous crystallisation. Spontaneous sulfur crystallisation finishes at tR ,
which corresponds to a site on the thermogram t(t). Therefore, temperature tR should be
considered as a usual `point' of solidification. However, tR of sulfur is badly reproduced,
as is seen in table 1. Besides, the closing stage of sulfur crystallisation, R ! C, considerably differs from an expected ideal, R ! Cid at tR ˆ const, and is stretched across the
interval DtRC 30 8C. It should be noted that the presence of the C point was fixed
for the first time, the temperature, tC , was 83 8C, and this value did not appear among
the singular points of sulfur before (Meyer 1965, 1976).
Table 1. Measured temperatures of crystallisation of sulfur.
Number of samples
and test
tA =8C
tP =8C
tU1 =8C
tR1 =8C
tU2 =8C
tR2 =8C
S1.1
S1.2
S3.1
S3.2
S3.3
S4.1
S4.2
S5.1
277
270
262
263
245
244
267
353
152
155
161
165
148
162
161
157
77.6
76.9
97.6
86.6
81.0
98.1
82.1
102.4 a
92.1
94.1
89.9
98.0
93.9
105.5
96.2
87.0
91.9
94.5
96.1
87.2
87.3
a Recalescence
tD =8C
89.9
92.7
tC =8C
78.9
85.3
82.7
83.0
79.8
83.4
83.2
86.2
is not fixed in the given test.
Similar nonideality of a solidification curve was observed for all investigated sulfur
examples (figures 2, 3). However, the solidification curves were not reproduced even in
sequential experiments with the same sample (figure 2).
Figure 2 shows the features and compares the solidification curve and the melting
curve belonging to the same sulfur sample, S4. A significant difference between process
U ! R and the process observed in figure 1 is shown here. However, the main result is
that the melting process H ! B ! M happens in a different temperature interval. The
end of the melting point (point M in figure 2) in all experiments was closer to point P
than to point L. The measured temperature, tR , was not below 130 8C, and reached
150 8C (that is close to a triple point, L=b=vapour, of sulfur) in one of the experiments.
The position of marked melting start points (H) was close to the reference data of melting points a-S and g-S (Emsley 1991).
Figure 3 shows the most impressive crystallisation features of a certain sulfur sample.
Such features were observed in three experiments out of the eight. A feature of the
crystallisation process here is the presence of two points, R1 and R2, and two
temperatures, tR1 and tR2 , which correspond to point R in figures 1 and 2. Point R1 in
experiment S1.1 in figure 3 is poorly distinguishable in view of overwriting on sites
L ! U and U ! R1, but the thermogram, t(t), of this experiment reliably recorded
the start of undercooling of the melt (L ! U) and its recalescence (U ! R1).
Obviously, the second self-heating of a crystallised sample finishing at point R2
happened in an interval of two-phase conditions. The process of second self-heating was
also observed for the first time, and the reasons for it are not vague. Some other features
464
A S Basin, B G Nenashev
15 ECTP Proceedings page 448
of the melting ^ crystallisation processes of sulfur were also observed. Many of them are
given in our detailed initial paper (Basin et al 1996), but their analysis requires additional
experiments.
Only the following is clear. Most of the features of melting ^ crystallisation processes
of high purity sulfur are a consequence of polymorphism: the existence of independently
identified a, b, g, and other crystalline states of sulfur and their slow transformations in
an interval of 83 ^ 150 8C. In particular, the processes R ! C in figures 1 ^ 3 are stipulated by a parallel course of liquid l-S crystallisation under crystalline state b-S8 and
transformation of b-S8 into a-S8 , which begins for ta=b  95:4 8C (Meyer 1965, 1976;
Tackray 1970) and finishes at tC  83 8C. The processes of undercooling, L ! U, recalescence, U ! R, and b ! a transformations can also be influenced by nucleation centres
g-S and crystalline phase g-S.
On the whole, the results indicate a strong dependence of the melting and crystallisation characteristics of sulfur on the purity of certain samples. Moreover, the observable
melting processes can be stimulated by a degree of completion of b ! a transformation
in a certain sulfur sample, stored for a long time at a room temperature of 20 ^ 25 8C.
However, all this has a relatively small effect on the integrated characteristics of a
specific volume (figures 1 ^ 3) and density of sulfur (figure 4).
r=g cmÿ3
a=l
g=l b=l
a=b
2.04
3
2.00
4
5
1.96
1
2
10
H
C
6
1.92
7
1.88
11
9 R
1.84
l=p
8
1.80
8
0
20
40
60
80 100 120 140
t=8C
MP
160
Figure 4. Density ^ temperature plot of sulfur
within intervals of melting ^ solidification and
in their vicinity. Solid lines illustrate experimental results; dashed lines demonstrate
results of extrapolation and generalisation: 1,
a-S monocrystal; 2, a-S polycrystal; 3, a-S
slow heating with a ! b continuous transformation; 4, amorphous S; 5, b-S monocrystal; 6, b-S polycrystal; 7, amorphisation of
undercooled l-S; 8, liquid S (l-S); 9, experimental crystallisation curve in test S3.1; 10,
experimental cooling curve of solid sample
S3.1; 11, generalised melting curve with respect
to most of the tests on S4.2; a=b, g=l, a=l, b=l
are temperature positions of sulfur basic transformations. Vertical lines show boundaries of
experimental errors.
4 Generalised data
In table 1 the experimental data on crystallisation temperatures and other transformations
of sulfur are represented. Table 1 also includes the data on an upper bound of temperature of liquid sulfur in the given experiment (tA ). The data of tD in table 1 correspond
to features of the experimental curve, characteristic for the start of formation of porosity
in the hardening sulfur sample.
Figure 4 shows our calculated scheme of ranges for the majority of observed states and
processes for heating and cooling of sulfur, and singular points as well. Table 2 is similar
to figure 4, but some differences for the data of densities for single and polycrystalline
conditions are obvious as well as for liquid and amorphous sulfur. While compiling
table 2 and figure 4 we also used the data from reviews by Meyer (1965, 1976), some
modern papers (Kennedy and Wheeler 1983; Winter et al 1990), and others.
In table 3 our experimental data on integrated magnitudes of volume modification
for melting are represented. These data update numerical figures and the character of
the processes, which were studied only by Kopp (1855), To«pler (1894), and Tamman (1903).
Melting ^ crystallisation and polymorphic transformations of sulfur
465
15 ECTP Proceedings page 449
Table 2. Sulfur density, r=g cmÿ3, in reference and singular points, recommended data.
State
g-S
a-S
a-S
a-S
b-S
b-S
l-S,
sc
pc
sc
pc
l-S
20 8C
2.19
2.070
2.066
2.020
1.958
1.950
Temperatures of singular points=8C
83
95.4
105.8
112.8
2.029
2.008
1.984
1.937
1.914
1.837
2.021
1.997
1.972
1.932
1.908
1.827
2.014
1.987
1.961
1.931
1.901
1.817
2.010
1.982
1.927
1.898
1.812
119.0
152
159
1.924
1.893
1.807
1.780
1.773
sc, monocrystalline solid state; pc, polycrystalline solid state; a, amorphous solid state; l, liquid
state.
Table 3. The volume and density change of sulfur at melting (L and C refer to points L and C
in figures 1 ^ 3).
Process
of melting
tm =8C
DVm VL ÿ VC
cm3 gÿ1
ÿdrm … rL ÿ rC †=rC
%
this
work
a!l
b!l
g!l
112.8
119.0
106.8
0.0534 ± 0.0544
0.0321 ± 0.0236
0:0765
8.6 ± 9.8
4.5 ± 6.1
14
Kopp
(1855)
To«pler
(1894)
5.0
5.5
Tamman
(1903)
7:5?
7:5?
Table 3 shows that data on the volume change, DVm , and density change, drm , at
melting, known earlier, corresponded to the b ! l transition. The scattering of our data
for DVm can be explained by the indeterminacy in a=b phase transformation of samples
before the start of the next experiment with sulfur melting. This can be observed in other
experiments, if the time of endurance in a solid state was not long. Quite a stable
structure is the structure of liquid l-S only. The density of l-S can be represented by the
following linear dependence:
r…l-S†=g cmÿ3 ˆ 1:827 ÿ 8:5610ÿ4 ‰…t=8C ÿ 95:4†Š,
80 5 t=8C 5 159 ,
with an error less than 0.6%. All other data, r(t), in table 2 have an error higher than
that magnitude (except values for 20 8C ). However, to exclude distortion of the transformation pattern in figure 4, they are shown with an identical number of significant
figures.
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466
A S Basin, B G Nenashev
15 ECTP Proceedings page 450
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ß 2000 a Pion publication printed in Great Britain