I
A
J. Phys. Chern. Solids
Pergamon Press 1968. Vol. 29, pp. 877-880.
Printed in Great Britain.
THE PHASE DIAGRAM OF RUBIDIUM NITRATE IN
THE RANGE 200-330°C AND 0-1500 atm
B. CLEAVER and J. F. WILLIAMS·
Department of Chemistry, The University, Southampton, Hampshire, England
(Received 19 October 1967; in revised/orm 11 January 1968)
Abstract- The phase diagram of RbN03 has been determined between 200° and 330°C at pressures
up to 1500 atm. There are three stable solid phases in this region, coexisting at a triple point at 294'5° ±
1° and 780 ± 20 atm. There is a second triple point, between two of the solids and the melt, at 304°± 1°
and 900 ± 20 atm. The diagram is shown to be consistent with the heats of transition between the
phases, and with densities calculated from unit cell dimensions.
The freezing curve of RbN0 3 saturated with argon was also measured, to 500 atm. The solubility
of argon in the melt was found to be 2 X 10- 7 moles m1- 1 atm- I •
A similarity is noted between the liquidus curves of RbN0 3 and KN0 3 , leading to the suggestion
that RbN0 31 may be isostructural with KN0 3 V.
INTRODUCTION
EXPERIMENTAL
AT AMOSPHERIC pressure, RbN0 3 has four
stable crystalline modifications between room
temperature and the melting point[ 1-4]:
The measurements were made in two pressure vessels, which have been described elsewhere [10, 11]. The vessels were externally
III 21.2°
trigonal
cubic
II
hexagonal
283'So
~
I 312'SO melt
~
cubic
The phase diagram was investigated by heated, and the temperature gradient across
Bridgman[S, 6], and by Rapoport [7], to SOkb the sample was less than O·so. Pressures were
and 700°C. Owens [8] measured the freezing measured to ±lO atm by Bourdon gauges
curve of III from 2·3 to 7·2 kb. No measure- which had been calibrated against a deadments have been reported in the region 0-2 kb weight tester. Temperatures were measured
and 200-3S0°. The aim of the present work to ±o·so by platinum resistance thermometers,
was to make good this deficiency. using positioned next to the samples inside the presapparatus designed to give accurate results sure vessels. The thermometers were checked
in this restricted range. All the above workers by comparison with standard mercury-in-glass
used 'piston-cylinder' apparatus. With this thermometers, and at the freezing points oftin
technique, friction at the piston pressure seal and lead. Corrections were made for the effect
causes some uncertainty in the measurement of pressure on the resistivity of platinum [10].
of the pressure applied to the salt [9]. In our
The I-II and II-III equilibrium lines were
work, this source of error was excluded by established by recording the change in electriusing argon as the pressure transmitting cal conductance of pellets of RbN0 3 • 13 mm
medium. The phase changes were detected diameter and 2-3 mm thick, pressed from
by noting the abrupt changes in electrical powdered salt (Johnson, Matthey and Co.,
conductivity of the salt when a transition 99·9 per cent, recrystallised once from distiIJed
water). The circular faces of the pellets were
occurred.
painted with a colloidal gold preparation (Leitgold
60, DEGUSSA, Frankfurt am Main) to
· Present address: English Clays Lovering Pochin and
Co. Ltd. , St. Austell, Cornwall, England.
give good electrical contact. The pellets were
877
878
B. CLEAVER and 1. F . WILLIAMS
held between platinum electrodes, which were
kept in firm contact with the gold-coated surfaces by a spring loaded mounting. Conductances were measured with a Wayne-Kerr
bridge (B221). Some points were obtained by
varying the temperature isobarically (maximum rate 0'2 deg/min), others by varying the
pressure isothermally (at 5 atm/min). Points
on the diagram refer to the completion of the
resistance charge after the phase line had been
crossed.
The freezing curve of the pure salt was
measured using the cell shown in Fig. I(A).
Platinum wires enter the cell at each end and
extend to within 5 mm of each other at the
middle of the capillary. The resistance measured across the two wires changed by several
orders of magnitude when the salt froze or
melted. The long capillary was necessary to
hinder the diffusion of dissolved argon into the
measuring region, so preventing it from lowering the freezing point of the salt [1 1].
Fig. 2. The phase diagram of RbN0 3 in the range 200330°C and 0-1500 atm (full line). The broken line is the
freezing curve of argon-saturated RbN 0 3 ,
0 - melt, .6. - phase 1,0 - phase II , 'V - phase III.
Ordinate: temperature ("C)
Abscissa: pressure (atm).
II and III, at 294·5±1° and 780±20atm,
the other between I, III and melt at 304 ± 1
and 900 ± 20 atm. Some curvature is present
in the freezing curve of I; the slope at zero
pressure is -{)·005 deg/atm, changing to -{)'012
deg/atm at the triple point. The other lines are
straight, within experimental error, and the
slopes are:
0
[2CM
A
B
Fig. 1. Conductivity ceUs used in the phase diagram
determination: (A) freezing curve of pure RbN0 3 , (B)
freezing curve of argon-saturated RbN03 •
RESULTS
The phase diagram is shown in Fig. 2.
There are two triple points; one between I,
I-II:
II-III:
III-melt:
I-III
+0.014 5 deg/atm
+0·097 deg/atm
+0·034 deg/atm
+0·078 deg/atm.
COMPARISON WITH PREVIOUS WORK
The III-melt line reported by Owens [8] is
displaced from ours by some 700 atm to higher
pressures. Since our pressures are accurate to
±10 atm we feel that the discrepancy is attri-
PHASE DIAGRAM OF RUBIDIUM NITRATE
butable to an error in pressure measurement
arising from frictional effects in Owens' apparatus. This error invalidates some of the
arguments used by Owens in deducing the
form of the diagram below 2 kb. He also overestimated the slope ofthe I-II line.
CHECK OF THE INTERNAL CONSISTENCY OF
THE DIAGRAM
The heats of the transformations between
IV, III, II, I and melt at atmospheric pressure
have been determined calorimetrically [12],
and are (in cals/mole):
IV
930
III
770
II 230
I
1110 melt.
The heat and volume changes for each
transition are related by the ClapeyronClausius equation:
AV= /lH dT
T dP"
~
,
Five such equations can be written for equilibria between I, II, III and melt (i.e. on~ for
each line on the diagram). Also, the sum of the
volume changes and of the heat changes must
be zero around each triple point. There are
therefore nine independent equations relating
the five sets of /lV, /lH and dT/dP values.
Since three of the heat changes are known,
and we have determined experimentally five
dT/dP values, a check of internal consistency
is possible. We have carried out the check by
calculating /lV and dT/dP for the I-III change
in two ways:
(i) from /lV, l l i and dT/dP for the I-II and
II-Ill lines, which gives /lVI-III = 5·8 mI/
mole and (dT/dP)I-ill = 0·078 deg/atm.
(ii) from /lV, /lH and dT/dP for the I-melt
and III-melt lines, which gives /lVI-ill =
6·3 mI/mole and (dT/dP)I-ill = 0·087 deg/
atm.
The value of (dT/dP)I-II1 estimated directly
from the diagram is 0·078 deg/mole. This is
satisfactory agreement, and indicates that the
diagram is internally consistent.
CALCULATION OF THE DENSITIES OF THE
SOLID PHASES
Taking a literature value for the density of
the melt at 312'5°, we have used the ClapeyronClausius equation to calculate the densities
of the solid phases. The results are compared
with densities calculated from unit cell dimensions, and with a directly measured density at
room temperature. The coefficients of cubic
expansion of I and II were assumed to be
3 X 10-4 deg- 1• Expansion coefficients of III
and IV were calculated from data given in
International Critical Tables [13]. Table I
shows the results, which are in satisfactory
agreement.
For Phase II, Brown and McLaren [1] considered that a tetragonal unit cell for which
deale = 2·92 gave better fit to the powder diffraction data than the hexagonal cell originally
proposed by Finbak et al.[4]. They also
mention three other cells which were consistent with the diffraction data but with less
good fit than the other two, deale for these
TabLe I. Densities from the phase diagram andfrom unit ceLL dimensions
Density
TeIIlperature
Phase
eC)
melt
I
II
III
IV
312·5
290
250
180
20
this work
(2'52)
2·51
2·56
2·95
3·10
879
from the literature
2'52, by direct measurement [I 4]
2'50, from cubic unit ceU[1]
2'58, from hexagonal ceU[4]
2 '96, from cubic ceU [I, 15]
3 ·11 , from trigonal ceU [1]
3'11-3·13, by direct
measurement [16]
880
B. CLEAVER and J. F. WILLIAMS
being 2·93, 2·73 and 2·87. Our work is consistent only with the cell proposed by Finbak.
Our value for AVI -melt at atmospheric pressure is --0·4 ml/mole, in moderate agreement
with a value of --0·13 ml/mole reported by
Sckinke and Sauerwald [17].
THE SOLUBILITY OF ARGON IN FUSED RbNOa
The freezing point of argon-saturated
RbN0 3 was measured with the cell shown
in Fig. I(B), at pressures up to 500 atm. The
melt was exposed to pressurised gas for twelve
hours before cooling. Exposure for longer
times did not cause the freezing temperature
to be depressed further, so it was assumed
that saturation had been reached. The freezing curve obtained is shown as a broken line
in Fig. 2. Using Raoult's law with a heat of
fusion of 1110 cal/mole, we derive a Henry's
Law constant of 2·0 X 10-7 moles ml- 1 atm- I •
This is somewhat smaller than the solubilities
of inert gases in sodium nitrate reported by
Copeland and his co-work6rs [18-20] .
GENERAL DISCUSSION OF THE PHASE DIAGRAM
OF RbNOa
The phase diagrams of all the univalent
nitrates are known to the liquidus and about
40 kb [5-8, 21-25]. Attention has been drawn
to the similarities between some of the diagrams ; in particular, the region above 15 kb is
very similar for KN0 3 , RbN0 3 , CsN03 and
TIN0 3 [23, 25] and it has been suggested that
the corresponding phases are isostructural.
Our work permits an extension of this comparison. The liquidus of KN0 3 shows a triple
point at 13 kb and 3600 between phases VI, V
and melt[23]. The melting curve of VI
has dT/dP = +0·022 deg/atm (cf. +0·034 for
RbN0 3 I1I) but that of V is practically parallel
to the pressure axis. This triple point corresponds to the I, III, melt triple point of RbN 0 3,
There is an obvious similarity between
KN0 3 V and RbN0 3 I, which may therefore
be isostructural. Also RbN0 3I and RbN0 3 11
have densities differing by only 0·01, and the
II-I transformation occurs without fragmentation of the crystal [1]. RbN 0 3 11 and I
may therefore themselves be closely related
structurally.
Acknowledgernents- We thank the Central Electricity
Generating Board for a Fellowship (B.C.) and a Studentship (J .F.W.) and for an equipment grant.
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