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Polymorphic transitions of the alkali bromides and iodides at high pressures to 200°C
J. Phys.
Chem. Solids
Pergamon Press 1965. Vol. 26, pp. 1003-1011.
POLYMORPHIC BROMIDES
AND
TRANSITIONS IODIDES
Printed in Great Britain
OF THE ALKALI
AT HIGH
PRESSURES
TO 200°C* CARL
W. F. T. PISTORIUSt
Chemical Physics Group of the National Physical and National Chemical Research Laboratories, South African Council for Scientific and Industrial Research, Pretoria, South Africa (Received
18 September
1964)
Abstract-LiBr and LiI have no transitions to 40 kbar in the temperature range 20-150°C. The temperature dependence of the transitions from the NaCl to the CsCl type structure was determined to 200°C for KBr, RbBr, KI and RbI. Easily measurable slopes were found for the RbBr and RbI transition lines in spite of the fact that Bridgman reported these transitions to be independent of temperature. The transition pressures of KBr and KI are almost independent of temperature and are thus exceptionally well suited for calibration of high-pressure equipment at elevated temperatures. These transitions are sluggish near room temperature, but above 50°C the hysteresis drops sharply to about +30 bar. This is among the lowest hystereses encountered. Extrapolation of our high temperature data to room temperature probably yields data of higher precision on KBr and KI than those submitted by Kennedy and LaMori. NaBr and NaI appear to have very sluggish transitions near lo-14 kbars and 200°C. The evidence is not conclusive, however.
INTRODUCTION
POLYMORPHISMin the alkali halides at elevated pressures was discovered by SLATER~) in RbBr and RbI. Later BRIDGMAN(~>~) observed transitions also in KBr and KI, as well as in RbCl and KCl. JACOBS@) determined the structure of the highpressure form of RbI by means of X-ray diffraction, and found that the transition involved transformation from the NaCl type to the CsCltype structure. Much later JAMIESON@) and PIERMARINI and WEIR@) reported that the highpressure form of KI also crystallized in the CsCltype structure. WEIR and pIEEMAEINI(‘) recently found this to be true also for RbBr and KBr. BRIDGIVL~*) failed to find any polymorphism in the sodium halides. However, recently strong evidence was found for polymorphism in sodium *Publication No. 413 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California. t Now at Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California.
chloride(s~le) and sodium fluoride(llyls) and it is reasonable to expect the other sodium halides also to show polymorphism when subjected to elevated pressures. The calculation and comparison of lattice energies by means of the BORN-MAYER method(ls914) requires some knowledge of the thermal energy involved in the transition, and values for the transition pressures which are as accurate as possible, since the lattice energies are very sensitive to the lattice constants.(7) BRIDGIMAN’Sdata(ss*ls) on transition pressures and latent heats are inadequate, and in most cases even the sign of the latent heat is in doubt.@) The piston-rotation method(lsv17) in pistoncylinder devices allows a considerable improvement in the precision of measurement of rapid transitions such as those of the potassium and rubidium halides. It was consequently decided to undertake a study of the alkali halides with the specific aim of obtaining precise transition pressures at various temperatures.
1003
1004
CARL
W.
F.
EXPERIMENTAL
The various chemicals were dried for some hours at 400°C before use. Each salt was precompressed in a pill press at about 5 kbar to a solid slug 0.5 in. dia. and 0.5-l in. long, wrapped in thin lead foil, and inserted in the pressure vessel of a pistoncylinder device similar to that described by KENNEDY and LA MoRI.(‘s) Thewalls of the pressure vessel were coated with molykote to minimize friction. The sample could be heated to 200°C by wrapping a heavy-duty heating coil around the pressure plate. Temperature was measured by means of a thermocouple inserted in a well in the pressure plate. These readings had to be calibrated against a dummy run with a second thermocouple at the lower end of the sample position. LA MoRI@~) found that in this type of set-up there is a temperature gradient along the sample amounting to 10°C at 200°C. However, this should not influence the present results since pressure is read at the beginning of the transition when the transition is running just above the piston. Temperature measurements may be considered correct to l-2°C. The displacement of the piston was measured with a dial gauge which could be read to 0.0001 in. The pressure at which the rapidly running transitions of KBr, RbBr, KI and RbI occur could be measured to high accuracy by means of the pistonrotation method(rsJ7) where the piston-cylinder device is, in effect, used as a free piston gauge. Our experience is that the transition pressure is unaffected by the rate and amount of shear. This is in agreement with work done elsewhere.(rQ~sQ) The effect of any possible local temperature rise due to rotation of the piston was eliminated by waiting for two minutes after piston rotation before taking a reading. However, this effect appeared to be negligible. The pressure values have been corrected for the weight of the main ram, thermal expansion of the piston at higher temperatures and the distortion introduced in the piston by the high pressure.(Qi) The two latter corrections lie within the uncertainty of the method. In addition, the listed limits of error include the probable uncertainty in reading the Heise-Bourdon tube gauge which monitored the oil pressure in the main ram. This uncertainty amounts to approximately +25 bar in the total pressure. In order to detect sluggish transitions or to
T.
PISTORIUS
search for possible new transitions, however, it is necessary to increase pressure in steps of about 200 bar and to plot the points obtained after the system has reached an apparent state of equilibrium. It was found that no further change in pressure or piston displacement occurred after 2-3 min. A transition is recognized by inspecting the plot of piston displacement against pressure. The results were approximately corrected for friction by taking the mean of the transition pressures with increasing and with decreasing pressure. RESULTS
Lithium bromide and lithium iodide No transitions were observed in these substances to 40 kbar at 20°C or 150°C. Sodium bromide* Hopkin and Williams G.P.R. sodium bromide was used. The main impurity was 0.5% NaCl. The curves of piston displacement against pressure indicated a very sluggish, but reversible, transition near 11.5 rf:2.5 kbar at 175°C and 200°C. At lower temperatures the transition could not be observed, probably due to increased sluggishness. The kinetics of the transition appeared to be very similar to the kinetics of the corresponding transition in the alkali fluorides.(ls) It is possible that this transition is the expected one from the NaCl-type structure to the CsCltype structure found in the other alkali halides. It is doubtful whether the transition will run to a sufficient extent at room temperature to make X-ray identification of the high-pressure phase possible. Probably a high-pressure X-ray technique at temperatures well above 200°C will be required. Potassium bromide BRIDGMANt3) first encountered the KBr transition at 18.92 kbar, 25°C. However, his final values@) for the transition pressure were 18.07 kbar at 25”C, and 19.02 kbar at -78°C. These data indicated a transition line in the P-T plane with a negative slope. KENNEDY and LA MoRI~‘) obtained a transition pressure of recently 17.880 +0.060 kbar at 25°C using the piston rotation technique. * A preliminary report of the work on sodium bromide and sodium iodide has appeared elsewhere.(22)
POLYMORPHIC
TRANSITIONS
OF ALKALI
BROMIDES
AND IODIDES
AT HIGH
PRESSURES
1005
Table 1. Transition pressures of KBr
Temperature 16.2’C 54*s”c 76-S’% 92*5’C 118’C 139.sac 161-S’% 179v
Corrected pressure on upstroke 17.888 17.506 17.464 17.483 17.501 17.499 17.507 17.516
Corrected pressure on downstroke
kB kB kB kB kB kB kB kB
BDH Analar grade KBr was used. The major impurities present were 0*20/oKCl, O*1o/oNaBr and O*OSo/o KI. At 16.2’C the transition was sluggish, and it was assumed that lengthy slow piston rotation would be necessary to improve the value obtained. At higher temperatures, just as in the case of KCl,(s) this sluggishness disappeared entirely, and excellent transition pressures could be obtained after only a few rotations of the piston. The values found are listed in Table 1. The slope of the transition line is
dP = 05.5 + O-7 bar/deg dT and is almost certainly positive, since the error is probably overestimated. Our best extrapolated value for the transition pressure at 25°C is Pzs = 17.425 + 0.070 kbar. This value differs markedly from KJINNEDY and LA MORI’S values(l7) (mean 17.782 + O-190 kbar, best 17880 + 0.060 kbar). However, Kennedy and La Mori’s best value is not convincing. They made eight separate determinations of the transition pressures of the potassium halides at room temperature. In seven of the eight cases the uncertainty of the determination was near & 250 bar, while in one of the three determinations for KBr an uncertainty of only +80 bar was found. Furthermore, the upstroke pressures for their first and third KBr measurements were almost the same, while the downstroke pressures differed by 428 bar. We would suggest that Kennedy and La Mori’s third KBr value is in error, and should
17.328 17.406 17.424 17443 17.461 17.459 17.467 17.496
kB kB kB kB kB kB kB kB
Mean pressure 17*61+0*30 kB 17.456 +O-075 kB 17444~0+45 kB 17.463 f 0.045 kB 17*481&0*045 kB 17.479 +0*045 kB 17.487 f O-045 kB 17.506~0.035 kB
be discarded. Their mean value then becomes 17.723 kO.245 kbar at 25”C, which is in fair agreement with the present room temperature point of 17*61+0*28 kbar at 16.2”C. Within experimental limits all observed points, including the BRIDGMANvalues@) with very large friction, can be fitted by a straight line, which is shown in Fig. 1. Using the X-ray value(T) for the change of volume at the transition, viz. -AV/I’f,, = 19*3%, and the known compression of the low-pressure phase,@) the latent heat at 25°C can now be calculated by means of the Clapeyron-Clausius expression. It is found that AH25 = (1.4 & 1.7) X lo9 erg/mole = 33 + 42 Cal/mole.
Rubidium bromide The transition in RbBr was originally discovered by SLATER.~) BRIDGMANfirst(s) found a transition pressure of 4.82 kbar, and later@) a pressure of 4.51 kbar, independent of temperature between -78°C and 100°C. Rubidium bromide with a purity of 99.9% was supplied by Light and Co. The transition was somewhat sluggish at all temperatures, and the transition pressures obtained were not as good as for KBr. However, the hysteresis between upstroke and downstroke pressures after piston rotation is not temperature dependent, and the slope of the transition line should be reliable. The transition pressures obtained by piston rotation, after the usual corrections, are given in Table 2.
1006
CARL
A least-squares
W.
F.
T.
fit of the observed points gives
PISTORIUS
There is no explanation for Bridgman’s repeated failure to observe the temperature dependence of the transition, which would be 0.4 kbar over his range.
P = 4140( f 200)+2*19( + 0*8)t where P is the transition pressure in bars at PC. The transition line is shown in Fig. 2. The average deviation of the points from a straight line fit is 11 bar, and the uncertainty given above for the possible error in the slope is generous. The same considerations held in the case of RbCl,@) where it was found that the line extrapolated to a point only 30 bars from the triple point on the melting curve,(s4) some 650°C beyond the observed range. Using the X-ray value(T) for the change of volume at the transition, one finds for the latent heat at 25°C:
Sodium iodide
Hopkin and Williams NaI was used. No transition was found at temperatures ranging up to 14O”C, but at 164°C a transition was picked up at 10.2 f 2.5 kbar. The sodium iodide transition was less sluggish at elevated temperatures than the corresponding transition in NaBr, and was easily reversible. The transition pressure at 194°C was 12.0 & 2 kbar. The transition was also observed at 171.5”C (11*0+2*5 kbar), 175°C (11.6+2.5 kbar) and 190°C (14.0 _ f 3 kbar). The slope of the transition line appears to be positive.
AHss = 4.3 + 1.6 x 109 erg/mole = 103 * 38 Cal/mole.
17.7-
fs? .6.g ‘7
, C.s Cl -Type
9 2
, 175!?S z EI 174-
T
--
No
E
173 I 0
I 20
I 40
-
Cl-Type
1 60
t 60
T 1
Id
T
I 100
I 120
I 140
I 160
I I60
TEMPERATURE *C FIG.
1. Transition
line of KBr to 2OO’C.
Table 2. Transition pressures of RbBr
remperature 18°C 39-5x 62.S’C 86°C 106.5’C 128% 151°C 174v 178.5”C
Corrected pressure on upstroke 4.365 4.465 4.525 4.565 4.585 4.630 4.670 4.750 4.730
kB kB kB kB kB kB kB kB kB
Corrected pressure on downstroke 3.985 4.025 4.085 4.105 4.185 4.210 4.270 4.350 4.370
kB kB kB kB kB kB kB kB kB
Mean pressure 4.175 + 0.190 4.245 + 0.220 4.305 kO.220 4.335 50.230 4.385 kO.200 4.420+0.210 4.470 f 0.200 4.550 & 0.200 4.550? O-180
kB kB kB kB kB kB kB kB kB
POLYMORPHIC
TRANSITIONS I
OF ALKALI I
I
BROMIDES I
I
AND I
IODIDES I
AT HIGH
I
PRESSURES
1007
I
4.8 Cs Cl-Type
No Cl-Type 3.6 0
1
I
I
I
1
I
I
I
I
20
40
60
60
100
120
140
160
I80
200
TEMPERATURE-oC
FIG. 2. Transition line of RbBr to 200°C.
Potassium iodide At room temperature BRIDGMAN(~~) obtained values for the transition pressure of KI ranging from 17.18 to 18.19 kbar. At -78°C the range was from 18.16 to 19.00 kbar, thus indicating a negative slope of the transition line. Recently KENNEDY and LA MORIW obtained a value of 17.485 aO.240 kbar at 25”C, using the piston rotation technique. Merck Reagent grade KI was used. The major impurities were O*Ol% KC1 and KBr, and 0.03% NaI. Below 40°C the reaction was sluggish and the value obtained by KENNEDY and LA MoRW) could not be improved, although the present point at 15°C is virtually identical with their determination at 25°C. At higher temperatures, as in the cases of KCl(s) and KBr, the sluggishness of the transition disappeared entirely, and excellent transition pressures could be obtained after only a few rotations of the piston. The values found are listed in Table 3. The transition line is shown in Fig. 3, and it is obvious that the slope is negative, and steeper than for either KC1 or KBr. The slope of the transition line is dP dT=
- 1.88 10.56 bar/deg
and the extrapolated
transition
pressure at 25°C is
Ps5 = 17.343 of:0.045 kbar. Using the X-ray value(7) for the volume at the transition, viz. - AV/Vf,, the latent heat at 25°C is found to be
change of = 22*2%,
AHss = - 6.6 + 2-O x 10s erg/mole = 158 + 47 Cal/mole. Rubidium iodide The transition in RbI was first found by SLATER.(~)BRIDGMAN(2p1g) found a transition pressure of 3.97 kbar. This value was independent of temperature from -78°C to 1OO’C. Rubidium iodide with a purity of 99.9% was obtained from Light and Co. The transition was less sluggish than for RbCl@) and RbBr. The hysteresis between upstroke and downstroke pressures after piston rotation is not temperature dependent. The transition pressures, after the usual corrections, are given in Table 4. The transition line, with a positive slope, is shown in Fig. 4. The slope of the transition line is dP = 1.94 of:0.40 bar/deg dT
1008
CARL
1%‘. F.
T.
PISTORIUS
T
17.7
LAMORI
--KENNEDY
17.6
Cs CI - TYPE
17.2 No CI- TYPE
17.1 170l-l-
o
--z-
1
10
60
80
100
TE~~RATURE FIG. 3. Transition
I20
t 140
160
180
- oC
Iine of KI to 180°C.
Table 3. Trmsition pressures of KI
Temperature 15°C 34*s”c 50*S°C 74°C 89*S°C 109°C 145.sot
Corrected pressure on upstroke
Corrected pressure on downstroke
19-14 kB 17.62 kB 17.303 kB 17.261 kB 17,219 kB 17.205 kB 17.119 kB
and the transition pressure at 25°C is I’25
=
3.590 + O-160kbar.
All observed points lay in a straight line with an average deviation of 10 bar. Using the X-ray value(T) for the change of volume at the transition, viz. -AY[Vfce = 13.9%, the latent heat at 25°C is found to be AH25 = 4-S & 1*0X log erg/mole = 115 + 20 caljmoie.
15.82 kB 16.82 kB 17.243 kB 17,241 kB 17-219 kB 17.177 kB 17.099 kB
Mean pressure 17*48_tl*68 kB 17.22kO.42 kB 17.273 rt O-055 kB 17.251 +O-035 kB 17.219 +O-025 kB 17.191 ltO.039 kB 17.109+0*035 kB
DISCUSSION In the cases of NaF, KF, RbF and CsF(rs) the transition is quite sluggish and difficult to observe unless special care is taken. Usually only an estimated 5-lOo/o of the sample undergoes the transition-at least within 5 kbar of the transition pressure, and on the time scales used in these experiments-and presumably the transition keeps on running, albeit very slowly, as pressure is increased still further. Very often the transition could hardly be observed at all at temperatures
POLYMORPHIC
TRANSITIONS
OF ALKALI
BROMIDES
AND
IODIDES
AT HIGH
PRESSURES
1009
Table 4. Transition pressures of RbI
Temperature
ls”c 35*s”c 68°C 88=‘C 109.sot 128*5’C 156’C 203’C
[ 4.0
-
3.9
-
3.8
-
3.6
-
3.5
-
I
I
Corrected upstroke pressure
Corrected downstroke pressure
3.711 kB 3 -772 kB 3-832 kB 3.893 kB 3.873 kB 3.913 kB 3 a994 kB 4.014 kB
3.427 kB 3 -448 kB 3 -508 kB 3 -529 kB 3.589 kB 3.691 kB 3 *752 kB 3.812 kB
I
I
I
I
I 100
I 120
Mean pressure 3.57 +0*14 3*61+0*16 3.67 kO.16 3-71 kO.18 3.73 kO.14 3+X0+0*11 3.87 kO.12 3.91 +O.lO
I
I
I 140
I 160
I
kB kB kB kB kB kB kB kB
I
CsCl-Type
No Cl-Type
* 3.4
0
I 20
I 40
1 60
I 80
I
I
I80
200
TEMPERATURE-‘C
FIG. 4. Transition line of RbI to 2OO’C. below 100°C. All the sodium halides also fall into this group, with NaI at 200°C being the least sluggish. At room temperature, however, NaF is the least sluggish. There are, however, some puzzling aspects in connection with the transitions found in NaF, NaCl, NaBr and NaI. Although EVDOKIMOVAand VERESHCHAGIN(~~)discovered the NaCl-type to CsCl-type transition in NaCl by means of highpressure X-ray techniques, JAMIESON@~)could not observe any transition at room temperature near 20 kbar. LA MoRI,(~@using techniques similar to
those used in this paper, twice obtained transitionlike phenomena near 150°C at essentially the same pressure as found by the present author@) but could not reproduce them every time. JAMIESON(~~) also failed to detect any transition in NaF. It must be concluded that, although there is strong evidence in favor of the reality of the sodium halide transitions, their existence cannot as yet be considered to have been proved conclusively. In the cases of KCl, KBr and KI the transition is sluggish at and near room temperature. The minimum obtainable hysteresis appears to be
1010
CARL
W.
F.
T.
t-250 bar at 25°C. However, above 50°C it drops sharply to typically + (10-40) bar. This is among the lowest hystereses so far encountered, rivalling the Bi I/II transition.(ls,17) The present results are in sharp contrast to BRIDGMAN’S findings. He mentions an “effective region of indifference of 78008900 kg/ems” for KBr and KI. It is obvious that the major portion of this “region of indifference” is merely friction. In the present study it was often possible to bracket the transition at room temperature within _+2 kbar or usually better without even using piston rotation. This point is emphasized because some workers(7,ss) are apparently under the impression that the 7800-8900 kg/cm2 mentioned by BRIDGMAN(23) represents the region of indifference after frictional corrections have been made. This is certainly not the case. KENNEDY and LA MORI’S values for the transition pressures of KCl, KBr and KI(t7) at 25”C, as well as the present values near room temperature, are 250-500 bar too high, judging from the extrapolation of the more accurate points at higher temperatures. The extrapolation does pass through the quoted hysteresis interval in all cases (except KBr,G7) which is discussed above), but usually through the lowest part of it. It is possible that all these potassium halides have nonlinear transition lines with the deviation from linearity near SO”C, but this is unlikely. BRIDGMANc2’) found that the hysteresis of a polymorphic transition is seldom exactly symmetrical, even under completely hydrostatic conditions, and it is suggested that this is the most probable explanation of this effect. In the cases of RbCl, RbBr and RbI it was found that the hysteresis was approximately temperatureindependent. This implies that, although the individual points on the transition curves are uncertain to f (140-220) bar, the slope of the transition line will be reliable. Easily measurable slopes were found for the rubidium halides in spite of the fact that BRIDGMAN(2s23)reported these transitions to be independent of temperature. The transitions in KCl@) and KBr have extremely low temperature dependences. This, together with the sharpness of the transitions above 60°C and the large volume changes involved, make these transitions exceptionally well suited for the pressure calibration of high-pressure equipment
PISTORIUS
at elevated temperatures. The KC1 transition line, for instance, falls from 19*22+0*08 kbar at 25°C to only 18.95 rf:0.10 kbar at 1042+ S°C.(s,s4) The KBr and KI transitions are even more rapid than the KC1 transition. However, their usefulness as calibration points over a large temperature range suffers somewhat from the fact that the transition pressures have been determined accurately only from 20”-2OO”C, and that no values are available for the intersections on the melting curve. KCl, KBr or KI can probably be used to replace bismuth as the first stage support medium in double stage piston-cylinder devices such as the one described by JAYARAMANet al.@) They may be especially useful for work at high temperatures when the support medium itself becomes hot, since their transition pressures are much less sensitive to changes in temperature than the bismuth I/II transition, while the volume changes are large.* Furthermore, once the support medium is at a temperature above 60°C the transitions in KCl, KBr and KI run almost as rapidly, and with as small a hysteresis, as the bismuth I/II transition. Under these conditions the 14-17% friction and hysteresis found by BoYD(2g) while using KBr as a first stage support medium can probably be reduced to a very much smaller amount. Acknowledgements-It is a pleasure to acknowledge discussions with Dr. G. GAFNER and Dr. F. H. HERBSTEIN of this laboratory, PHILIP N. LAMORI of Northwestern University and Professor JOHN C. JAMIESON of the University of Chicago. The author is indebted to Professor-GEORGE C. -KENNEDY, Dr. ELIZIER RAPOPORT and LEWIS H. COHEN, Institute of Geophysics and Planetary Physics, U.C.L.A., for having critically read the manuscript.
REFERENCES 1. SLATER J. C., Proc. Amer. Acad. Arts Sci. 61, 144 (1926). 2. BRIDGMANP. W., Z. Krist. 67, 363 (1928). 3. BRIDCMANP. W., Phys. Rev. 48, 893 (1935). 4. JACOBSR. B., Phys. Rev. 54, 468 (1938). 5. JAMIESONJ. C., J. Geol. 65, 334 (1957). 6. PIERMARINIG. J. and WEIR C. E., J. Res. Nat. Bur. Stand. 66A, 325 (1962). 7. WEIR C. E. and PIERMARINIG. J., J. Res. Nat. BUT. Stand. 68A, 105 (1964). 8. BRIDGMANP. W., Proc. Amer. Acad. Arts Sci. 72, 45 (1937). * This proposal is due to Dr. E. Rapoport of the Institute of Geophysics and Planetary Physics, U.C.L.A.
POLYMORPHIC
TRANSITIONS
OF ALKALI
BROMIDES
9. PISTORIUS C. W. F. T., J. Phys. Chem. Solids 25, 1477 (1964). L. F., Fiz. 10. EWOKIMOVA V. V. and VEFLE~HCHAGIN Tverd. Tela 4, 1965 (1962) [Translated in Sov. Phys. Solid-State 4, 1438 (1962-3)]. 11. PISTORIUSC. W. F. T., Nature 201, 1321 (1964). 12 PISTORIUSC. W. F. T. and SNYMAN H. C., Z. phys. Chem. (Frankfurt), 43, 1 (1964). 13. BORN M. and MAYER J. E., Z. Phys. 75, 1 (1932). 14. TOSI M. P. and FUMI F. G., J. Phys. Chem. Solids 23, 359 (1962). 15. BRIDGMAN P. W., Proc. Amer. Acad. Arts Sci. 76, 1 (1945). 16. KENNEDY G. C. and LA MORI P. N. in: B~NDU F. P., HIBBARD W. R. and STRONG H. M., Progress in Very High Pressure Research, p. 304. Wiley, New York (1961). 17. KENNEDY G. C. and LA MORI P. N., J. Geophys. Res. 67, 851 (1962). 18. LA MORX P. N., personal communication. 19. DACHILLE F. and ROY R., in: DEBOER J. H.,
AND IODIDES Reactivity (1961).
AT HIGH
of Solids,
PRESSURES
p. 502. Elsevier,
1011
New York
20. DACHILLE F. and ROY R., J. Geol. 72, 243 (1964). 21. JOHNSON D. P. and N~HALL D. H., Trans. Amer. Sot. Mech. Engrs. 75, 301 (1953). 22. PISTORIUSC. W. F. T., Nature 204,467 (1964). 23. BRIDGMAN P. W., Proc. Am. Acad. Arts Sci. 74, 21 (1940). 24. CLARK S. P., J. Chem. Phys. 31, 1526 (1959). 25. JAMIESONJ. C., personal communication. 26. WEIR C. E., in: LA MORI P. N., in: GIARDINI A. A. and LLOYD E. C., High-pressure Measurement, p. 336. Butterworths, Washington (1962). 27. BRIDGMAN P. W., Proc. Amer. Acad. Arts Sci. 51, 581 (1916). 28. JAYARAMAN A., KLEMENT W., NEWTON R. C. and KENNEDY G. C., J. Phys. Chem Solids 24, 7. (1963). 29. BOYD F. R., in: WENTORF R. H., Modern Very High Pressure Techniques, p. 15 1. Butterworths, Washington (1962).
Chem. Solids
Pergamon Press 1965. Vol. 26, pp. 1003-1011.
POLYMORPHIC BROMIDES
AND
TRANSITIONS IODIDES
Printed in Great Britain
OF THE ALKALI
AT HIGH
PRESSURES
TO 200°C* CARL
W. F. T. PISTORIUSt
Chemical Physics Group of the National Physical and National Chemical Research Laboratories, South African Council for Scientific and Industrial Research, Pretoria, South Africa (Received
18 September
1964)
Abstract-LiBr and LiI have no transitions to 40 kbar in the temperature range 20-150°C. The temperature dependence of the transitions from the NaCl to the CsCl type structure was determined to 200°C for KBr, RbBr, KI and RbI. Easily measurable slopes were found for the RbBr and RbI transition lines in spite of the fact that Bridgman reported these transitions to be independent of temperature. The transition pressures of KBr and KI are almost independent of temperature and are thus exceptionally well suited for calibration of high-pressure equipment at elevated temperatures. These transitions are sluggish near room temperature, but above 50°C the hysteresis drops sharply to about +30 bar. This is among the lowest hystereses encountered. Extrapolation of our high temperature data to room temperature probably yields data of higher precision on KBr and KI than those submitted by Kennedy and LaMori. NaBr and NaI appear to have very sluggish transitions near lo-14 kbars and 200°C. The evidence is not conclusive, however.
INTRODUCTION
POLYMORPHISMin the alkali halides at elevated pressures was discovered by SLATER~) in RbBr and RbI. Later BRIDGMAN(~>~) observed transitions also in KBr and KI, as well as in RbCl and KCl. JACOBS@) determined the structure of the highpressure form of RbI by means of X-ray diffraction, and found that the transition involved transformation from the NaCl type to the CsCltype structure. Much later JAMIESON@) and PIERMARINI and WEIR@) reported that the highpressure form of KI also crystallized in the CsCltype structure. WEIR and pIEEMAEINI(‘) recently found this to be true also for RbBr and KBr. BRIDGIVL~*) failed to find any polymorphism in the sodium halides. However, recently strong evidence was found for polymorphism in sodium *Publication No. 413 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California. t Now at Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California.
chloride(s~le) and sodium fluoride(llyls) and it is reasonable to expect the other sodium halides also to show polymorphism when subjected to elevated pressures. The calculation and comparison of lattice energies by means of the BORN-MAYER method(ls914) requires some knowledge of the thermal energy involved in the transition, and values for the transition pressures which are as accurate as possible, since the lattice energies are very sensitive to the lattice constants.(7) BRIDGIMAN’Sdata(ss*ls) on transition pressures and latent heats are inadequate, and in most cases even the sign of the latent heat is in doubt.@) The piston-rotation method(lsv17) in pistoncylinder devices allows a considerable improvement in the precision of measurement of rapid transitions such as those of the potassium and rubidium halides. It was consequently decided to undertake a study of the alkali halides with the specific aim of obtaining precise transition pressures at various temperatures.
1003
1004
CARL
W.
F.
EXPERIMENTAL
The various chemicals were dried for some hours at 400°C before use. Each salt was precompressed in a pill press at about 5 kbar to a solid slug 0.5 in. dia. and 0.5-l in. long, wrapped in thin lead foil, and inserted in the pressure vessel of a pistoncylinder device similar to that described by KENNEDY and LA MoRI.(‘s) Thewalls of the pressure vessel were coated with molykote to minimize friction. The sample could be heated to 200°C by wrapping a heavy-duty heating coil around the pressure plate. Temperature was measured by means of a thermocouple inserted in a well in the pressure plate. These readings had to be calibrated against a dummy run with a second thermocouple at the lower end of the sample position. LA MoRI@~) found that in this type of set-up there is a temperature gradient along the sample amounting to 10°C at 200°C. However, this should not influence the present results since pressure is read at the beginning of the transition when the transition is running just above the piston. Temperature measurements may be considered correct to l-2°C. The displacement of the piston was measured with a dial gauge which could be read to 0.0001 in. The pressure at which the rapidly running transitions of KBr, RbBr, KI and RbI occur could be measured to high accuracy by means of the pistonrotation method(rsJ7) where the piston-cylinder device is, in effect, used as a free piston gauge. Our experience is that the transition pressure is unaffected by the rate and amount of shear. This is in agreement with work done elsewhere.(rQ~sQ) The effect of any possible local temperature rise due to rotation of the piston was eliminated by waiting for two minutes after piston rotation before taking a reading. However, this effect appeared to be negligible. The pressure values have been corrected for the weight of the main ram, thermal expansion of the piston at higher temperatures and the distortion introduced in the piston by the high pressure.(Qi) The two latter corrections lie within the uncertainty of the method. In addition, the listed limits of error include the probable uncertainty in reading the Heise-Bourdon tube gauge which monitored the oil pressure in the main ram. This uncertainty amounts to approximately +25 bar in the total pressure. In order to detect sluggish transitions or to
T.
PISTORIUS
search for possible new transitions, however, it is necessary to increase pressure in steps of about 200 bar and to plot the points obtained after the system has reached an apparent state of equilibrium. It was found that no further change in pressure or piston displacement occurred after 2-3 min. A transition is recognized by inspecting the plot of piston displacement against pressure. The results were approximately corrected for friction by taking the mean of the transition pressures with increasing and with decreasing pressure. RESULTS
Lithium bromide and lithium iodide No transitions were observed in these substances to 40 kbar at 20°C or 150°C. Sodium bromide* Hopkin and Williams G.P.R. sodium bromide was used. The main impurity was 0.5% NaCl. The curves of piston displacement against pressure indicated a very sluggish, but reversible, transition near 11.5 rf:2.5 kbar at 175°C and 200°C. At lower temperatures the transition could not be observed, probably due to increased sluggishness. The kinetics of the transition appeared to be very similar to the kinetics of the corresponding transition in the alkali fluorides.(ls) It is possible that this transition is the expected one from the NaCl-type structure to the CsCltype structure found in the other alkali halides. It is doubtful whether the transition will run to a sufficient extent at room temperature to make X-ray identification of the high-pressure phase possible. Probably a high-pressure X-ray technique at temperatures well above 200°C will be required. Potassium bromide BRIDGMANt3) first encountered the KBr transition at 18.92 kbar, 25°C. However, his final values@) for the transition pressure were 18.07 kbar at 25”C, and 19.02 kbar at -78°C. These data indicated a transition line in the P-T plane with a negative slope. KENNEDY and LA MoRI~‘) obtained a transition pressure of recently 17.880 +0.060 kbar at 25°C using the piston rotation technique. * A preliminary report of the work on sodium bromide and sodium iodide has appeared elsewhere.(22)
POLYMORPHIC
TRANSITIONS
OF ALKALI
BROMIDES
AND IODIDES
AT HIGH
PRESSURES
1005
Table 1. Transition pressures of KBr
Temperature 16.2’C 54*s”c 76-S’% 92*5’C 118’C 139.sac 161-S’% 179v
Corrected pressure on upstroke 17.888 17.506 17.464 17.483 17.501 17.499 17.507 17.516
Corrected pressure on downstroke
kB kB kB kB kB kB kB kB
BDH Analar grade KBr was used. The major impurities present were 0*20/oKCl, O*1o/oNaBr and O*OSo/o KI. At 16.2’C the transition was sluggish, and it was assumed that lengthy slow piston rotation would be necessary to improve the value obtained. At higher temperatures, just as in the case of KCl,(s) this sluggishness disappeared entirely, and excellent transition pressures could be obtained after only a few rotations of the piston. The values found are listed in Table 1. The slope of the transition line is
dP = 05.5 + O-7 bar/deg dT and is almost certainly positive, since the error is probably overestimated. Our best extrapolated value for the transition pressure at 25°C is Pzs = 17.425 + 0.070 kbar. This value differs markedly from KJINNEDY and LA MORI’S values(l7) (mean 17.782 + O-190 kbar, best 17880 + 0.060 kbar). However, Kennedy and La Mori’s best value is not convincing. They made eight separate determinations of the transition pressures of the potassium halides at room temperature. In seven of the eight cases the uncertainty of the determination was near & 250 bar, while in one of the three determinations for KBr an uncertainty of only +80 bar was found. Furthermore, the upstroke pressures for their first and third KBr measurements were almost the same, while the downstroke pressures differed by 428 bar. We would suggest that Kennedy and La Mori’s third KBr value is in error, and should
17.328 17.406 17.424 17443 17.461 17.459 17.467 17.496
kB kB kB kB kB kB kB kB
Mean pressure 17*61+0*30 kB 17.456 +O-075 kB 17444~0+45 kB 17.463 f 0.045 kB 17*481&0*045 kB 17.479 +0*045 kB 17.487 f O-045 kB 17.506~0.035 kB
be discarded. Their mean value then becomes 17.723 kO.245 kbar at 25”C, which is in fair agreement with the present room temperature point of 17*61+0*28 kbar at 16.2”C. Within experimental limits all observed points, including the BRIDGMANvalues@) with very large friction, can be fitted by a straight line, which is shown in Fig. 1. Using the X-ray value(T) for the change of volume at the transition, viz. -AV/I’f,, = 19*3%, and the known compression of the low-pressure phase,@) the latent heat at 25°C can now be calculated by means of the Clapeyron-Clausius expression. It is found that AH25 = (1.4 & 1.7) X lo9 erg/mole = 33 + 42 Cal/mole.
Rubidium bromide The transition in RbBr was originally discovered by SLATER.~) BRIDGMANfirst(s) found a transition pressure of 4.82 kbar, and later@) a pressure of 4.51 kbar, independent of temperature between -78°C and 100°C. Rubidium bromide with a purity of 99.9% was supplied by Light and Co. The transition was somewhat sluggish at all temperatures, and the transition pressures obtained were not as good as for KBr. However, the hysteresis between upstroke and downstroke pressures after piston rotation is not temperature dependent, and the slope of the transition line should be reliable. The transition pressures obtained by piston rotation, after the usual corrections, are given in Table 2.
1006
CARL
A least-squares
W.
F.
T.
fit of the observed points gives
PISTORIUS
There is no explanation for Bridgman’s repeated failure to observe the temperature dependence of the transition, which would be 0.4 kbar over his range.
P = 4140( f 200)+2*19( + 0*8)t where P is the transition pressure in bars at PC. The transition line is shown in Fig. 2. The average deviation of the points from a straight line fit is 11 bar, and the uncertainty given above for the possible error in the slope is generous. The same considerations held in the case of RbCl,@) where it was found that the line extrapolated to a point only 30 bars from the triple point on the melting curve,(s4) some 650°C beyond the observed range. Using the X-ray value(T) for the change of volume at the transition, one finds for the latent heat at 25°C:
Sodium iodide
Hopkin and Williams NaI was used. No transition was found at temperatures ranging up to 14O”C, but at 164°C a transition was picked up at 10.2 f 2.5 kbar. The sodium iodide transition was less sluggish at elevated temperatures than the corresponding transition in NaBr, and was easily reversible. The transition pressure at 194°C was 12.0 & 2 kbar. The transition was also observed at 171.5”C (11*0+2*5 kbar), 175°C (11.6+2.5 kbar) and 190°C (14.0 _ f 3 kbar). The slope of the transition line appears to be positive.
AHss = 4.3 + 1.6 x 109 erg/mole = 103 * 38 Cal/mole.
17.7-
fs? .6.g ‘7
, C.s Cl -Type
9 2
, 175!?S z EI 174-
T
--
No
E
173 I 0
I 20
I 40
-
Cl-Type
1 60
t 60
T 1
Id
T
I 100
I 120
I 140
I 160
I I60
TEMPERATURE *C FIG.
1. Transition
line of KBr to 2OO’C.
Table 2. Transition pressures of RbBr
remperature 18°C 39-5x 62.S’C 86°C 106.5’C 128% 151°C 174v 178.5”C
Corrected pressure on upstroke 4.365 4.465 4.525 4.565 4.585 4.630 4.670 4.750 4.730
kB kB kB kB kB kB kB kB kB
Corrected pressure on downstroke 3.985 4.025 4.085 4.105 4.185 4.210 4.270 4.350 4.370
kB kB kB kB kB kB kB kB kB
Mean pressure 4.175 + 0.190 4.245 + 0.220 4.305 kO.220 4.335 50.230 4.385 kO.200 4.420+0.210 4.470 f 0.200 4.550 & 0.200 4.550? O-180
kB kB kB kB kB kB kB kB kB
POLYMORPHIC
TRANSITIONS I
OF ALKALI I
I
BROMIDES I
I
AND I
IODIDES I
AT HIGH
I
PRESSURES
1007
I
4.8 Cs Cl-Type
No Cl-Type 3.6 0
1
I
I
I
1
I
I
I
I
20
40
60
60
100
120
140
160
I80
200
TEMPERATURE-oC
FIG. 2. Transition line of RbBr to 200°C.
Potassium iodide At room temperature BRIDGMAN(~~) obtained values for the transition pressure of KI ranging from 17.18 to 18.19 kbar. At -78°C the range was from 18.16 to 19.00 kbar, thus indicating a negative slope of the transition line. Recently KENNEDY and LA MORIW obtained a value of 17.485 aO.240 kbar at 25”C, using the piston rotation technique. Merck Reagent grade KI was used. The major impurities were O*Ol% KC1 and KBr, and 0.03% NaI. Below 40°C the reaction was sluggish and the value obtained by KENNEDY and LA MoRW) could not be improved, although the present point at 15°C is virtually identical with their determination at 25°C. At higher temperatures, as in the cases of KCl(s) and KBr, the sluggishness of the transition disappeared entirely, and excellent transition pressures could be obtained after only a few rotations of the piston. The values found are listed in Table 3. The transition line is shown in Fig. 3, and it is obvious that the slope is negative, and steeper than for either KC1 or KBr. The slope of the transition line is dP dT=
- 1.88 10.56 bar/deg
and the extrapolated
transition
pressure at 25°C is
Ps5 = 17.343 of:0.045 kbar. Using the X-ray value(7) for the volume at the transition, viz. - AV/Vf,, the latent heat at 25°C is found to be
change of = 22*2%,
AHss = - 6.6 + 2-O x 10s erg/mole = 158 + 47 Cal/mole. Rubidium iodide The transition in RbI was first found by SLATER.(~)BRIDGMAN(2p1g) found a transition pressure of 3.97 kbar. This value was independent of temperature from -78°C to 1OO’C. Rubidium iodide with a purity of 99.9% was obtained from Light and Co. The transition was less sluggish than for RbCl@) and RbBr. The hysteresis between upstroke and downstroke pressures after piston rotation is not temperature dependent. The transition pressures, after the usual corrections, are given in Table 4. The transition line, with a positive slope, is shown in Fig. 4. The slope of the transition line is dP = 1.94 of:0.40 bar/deg dT
1008
CARL
1%‘. F.
T.
PISTORIUS
T
17.7
LAMORI
--KENNEDY
17.6
Cs CI - TYPE
17.2 No CI- TYPE
17.1 170l-l-
o
--z-
1
10
60
80
100
TE~~RATURE FIG. 3. Transition
I20
t 140
160
180
- oC
Iine of KI to 180°C.
Table 3. Trmsition pressures of KI
Temperature 15°C 34*s”c 50*S°C 74°C 89*S°C 109°C 145.sot
Corrected pressure on upstroke
Corrected pressure on downstroke
19-14 kB 17.62 kB 17.303 kB 17.261 kB 17,219 kB 17.205 kB 17.119 kB
and the transition pressure at 25°C is I’25
=
3.590 + O-160kbar.
All observed points lay in a straight line with an average deviation of 10 bar. Using the X-ray value(T) for the change of volume at the transition, viz. -AY[Vfce = 13.9%, the latent heat at 25°C is found to be AH25 = 4-S & 1*0X log erg/mole = 115 + 20 caljmoie.
15.82 kB 16.82 kB 17.243 kB 17,241 kB 17-219 kB 17.177 kB 17.099 kB
Mean pressure 17*48_tl*68 kB 17.22kO.42 kB 17.273 rt O-055 kB 17.251 +O-035 kB 17.219 +O-025 kB 17.191 ltO.039 kB 17.109+0*035 kB
DISCUSSION In the cases of NaF, KF, RbF and CsF(rs) the transition is quite sluggish and difficult to observe unless special care is taken. Usually only an estimated 5-lOo/o of the sample undergoes the transition-at least within 5 kbar of the transition pressure, and on the time scales used in these experiments-and presumably the transition keeps on running, albeit very slowly, as pressure is increased still further. Very often the transition could hardly be observed at all at temperatures
POLYMORPHIC
TRANSITIONS
OF ALKALI
BROMIDES
AND
IODIDES
AT HIGH
PRESSURES
1009
Table 4. Transition pressures of RbI
Temperature
ls”c 35*s”c 68°C 88=‘C 109.sot 128*5’C 156’C 203’C
[ 4.0
-
3.9
-
3.8
-
3.6
-
3.5
-
I
I
Corrected upstroke pressure
Corrected downstroke pressure
3.711 kB 3 -772 kB 3-832 kB 3.893 kB 3.873 kB 3.913 kB 3 a994 kB 4.014 kB
3.427 kB 3 -448 kB 3 -508 kB 3 -529 kB 3.589 kB 3.691 kB 3 *752 kB 3.812 kB
I
I
I
I
I 100
I 120
Mean pressure 3.57 +0*14 3*61+0*16 3.67 kO.16 3-71 kO.18 3.73 kO.14 3+X0+0*11 3.87 kO.12 3.91 +O.lO
I
I
I 140
I 160
I
kB kB kB kB kB kB kB kB
I
CsCl-Type
No Cl-Type
* 3.4
0
I 20
I 40
1 60
I 80
I
I
I80
200
TEMPERATURE-‘C
FIG. 4. Transition line of RbI to 2OO’C. below 100°C. All the sodium halides also fall into this group, with NaI at 200°C being the least sluggish. At room temperature, however, NaF is the least sluggish. There are, however, some puzzling aspects in connection with the transitions found in NaF, NaCl, NaBr and NaI. Although EVDOKIMOVAand VERESHCHAGIN(~~)discovered the NaCl-type to CsCl-type transition in NaCl by means of highpressure X-ray techniques, JAMIESON@~)could not observe any transition at room temperature near 20 kbar. LA MoRI,(~@using techniques similar to
those used in this paper, twice obtained transitionlike phenomena near 150°C at essentially the same pressure as found by the present author@) but could not reproduce them every time. JAMIESON(~~) also failed to detect any transition in NaF. It must be concluded that, although there is strong evidence in favor of the reality of the sodium halide transitions, their existence cannot as yet be considered to have been proved conclusively. In the cases of KCl, KBr and KI the transition is sluggish at and near room temperature. The minimum obtainable hysteresis appears to be
1010
CARL
W.
F.
T.
t-250 bar at 25°C. However, above 50°C it drops sharply to typically + (10-40) bar. This is among the lowest hystereses so far encountered, rivalling the Bi I/II transition.(ls,17) The present results are in sharp contrast to BRIDGMAN’S findings. He mentions an “effective region of indifference of 78008900 kg/ems” for KBr and KI. It is obvious that the major portion of this “region of indifference” is merely friction. In the present study it was often possible to bracket the transition at room temperature within _+2 kbar or usually better without even using piston rotation. This point is emphasized because some workers(7,ss) are apparently under the impression that the 7800-8900 kg/cm2 mentioned by BRIDGMAN(23) represents the region of indifference after frictional corrections have been made. This is certainly not the case. KENNEDY and LA MORI’S values for the transition pressures of KCl, KBr and KI(t7) at 25”C, as well as the present values near room temperature, are 250-500 bar too high, judging from the extrapolation of the more accurate points at higher temperatures. The extrapolation does pass through the quoted hysteresis interval in all cases (except KBr,G7) which is discussed above), but usually through the lowest part of it. It is possible that all these potassium halides have nonlinear transition lines with the deviation from linearity near SO”C, but this is unlikely. BRIDGMANc2’) found that the hysteresis of a polymorphic transition is seldom exactly symmetrical, even under completely hydrostatic conditions, and it is suggested that this is the most probable explanation of this effect. In the cases of RbCl, RbBr and RbI it was found that the hysteresis was approximately temperatureindependent. This implies that, although the individual points on the transition curves are uncertain to f (140-220) bar, the slope of the transition line will be reliable. Easily measurable slopes were found for the rubidium halides in spite of the fact that BRIDGMAN(2s23)reported these transitions to be independent of temperature. The transitions in KCl@) and KBr have extremely low temperature dependences. This, together with the sharpness of the transitions above 60°C and the large volume changes involved, make these transitions exceptionally well suited for the pressure calibration of high-pressure equipment
PISTORIUS
at elevated temperatures. The KC1 transition line, for instance, falls from 19*22+0*08 kbar at 25°C to only 18.95 rf:0.10 kbar at 1042+ S°C.(s,s4) The KBr and KI transitions are even more rapid than the KC1 transition. However, their usefulness as calibration points over a large temperature range suffers somewhat from the fact that the transition pressures have been determined accurately only from 20”-2OO”C, and that no values are available for the intersections on the melting curve. KCl, KBr or KI can probably be used to replace bismuth as the first stage support medium in double stage piston-cylinder devices such as the one described by JAYARAMANet al.@) They may be especially useful for work at high temperatures when the support medium itself becomes hot, since their transition pressures are much less sensitive to changes in temperature than the bismuth I/II transition, while the volume changes are large.* Furthermore, once the support medium is at a temperature above 60°C the transitions in KCl, KBr and KI run almost as rapidly, and with as small a hysteresis, as the bismuth I/II transition. Under these conditions the 14-17% friction and hysteresis found by BoYD(2g) while using KBr as a first stage support medium can probably be reduced to a very much smaller amount. Acknowledgements-It is a pleasure to acknowledge discussions with Dr. G. GAFNER and Dr. F. H. HERBSTEIN of this laboratory, PHILIP N. LAMORI of Northwestern University and Professor JOHN C. JAMIESON of the University of Chicago. The author is indebted to Professor-GEORGE C. -KENNEDY, Dr. ELIZIER RAPOPORT and LEWIS H. COHEN, Institute of Geophysics and Planetary Physics, U.C.L.A., for having critically read the manuscript.
REFERENCES 1. SLATER J. C., Proc. Amer. Acad. Arts Sci. 61, 144 (1926). 2. BRIDGMANP. W., Z. Krist. 67, 363 (1928). 3. BRIDCMANP. W., Phys. Rev. 48, 893 (1935). 4. JACOBSR. B., Phys. Rev. 54, 468 (1938). 5. JAMIESONJ. C., J. Geol. 65, 334 (1957). 6. PIERMARINIG. J. and WEIR C. E., J. Res. Nat. Bur. Stand. 66A, 325 (1962). 7. WEIR C. E. and PIERMARINIG. J., J. Res. Nat. BUT. Stand. 68A, 105 (1964). 8. BRIDGMANP. W., Proc. Amer. Acad. Arts Sci. 72, 45 (1937). * This proposal is due to Dr. E. Rapoport of the Institute of Geophysics and Planetary Physics, U.C.L.A.
POLYMORPHIC
TRANSITIONS
OF ALKALI
BROMIDES
9. PISTORIUS C. W. F. T., J. Phys. Chem. Solids 25, 1477 (1964). L. F., Fiz. 10. EWOKIMOVA V. V. and VEFLE~HCHAGIN Tverd. Tela 4, 1965 (1962) [Translated in Sov. Phys. Solid-State 4, 1438 (1962-3)]. 11. PISTORIUSC. W. F. T., Nature 201, 1321 (1964). 12 PISTORIUSC. W. F. T. and SNYMAN H. C., Z. phys. Chem. (Frankfurt), 43, 1 (1964). 13. BORN M. and MAYER J. E., Z. Phys. 75, 1 (1932). 14. TOSI M. P. and FUMI F. G., J. Phys. Chem. Solids 23, 359 (1962). 15. BRIDGMAN P. W., Proc. Amer. Acad. Arts Sci. 76, 1 (1945). 16. KENNEDY G. C. and LA MORI P. N. in: B~NDU F. P., HIBBARD W. R. and STRONG H. M., Progress in Very High Pressure Research, p. 304. Wiley, New York (1961). 17. KENNEDY G. C. and LA MORI P. N., J. Geophys. Res. 67, 851 (1962). 18. LA MORX P. N., personal communication. 19. DACHILLE F. and ROY R., in: DEBOER J. H.,
AND IODIDES Reactivity (1961).
AT HIGH
of Solids,
PRESSURES
p. 502. Elsevier,
1011
New York
20. DACHILLE F. and ROY R., J. Geol. 72, 243 (1964). 21. JOHNSON D. P. and N~HALL D. H., Trans. Amer. Sot. Mech. Engrs. 75, 301 (1953). 22. PISTORIUSC. W. F. T., Nature 204,467 (1964). 23. BRIDGMAN P. W., Proc. Am. Acad. Arts Sci. 74, 21 (1940). 24. CLARK S. P., J. Chem. Phys. 31, 1526 (1959). 25. JAMIESONJ. C., personal communication. 26. WEIR C. E., in: LA MORI P. N., in: GIARDINI A. A. and LLOYD E. C., High-pressure Measurement, p. 336. Butterworths, Washington (1962). 27. BRIDGMAN P. W., Proc. Amer. Acad. Arts Sci. 51, 581 (1916). 28. JAYARAMAN A., KLEMENT W., NEWTON R. C. and KENNEDY G. C., J. Phys. Chem Solids 24, 7. (1963). 29. BOYD F. R., in: WENTORF R. H., Modern Very High Pressure Techniques, p. 15 1. Butterworths, Washington (1962).