Creator:John C. Jamieson
Date Created:
Place Created:Chicago, Illinois
Keywords:high-pressure polymorphism,x-ray diffraction
Context:article reprinted from The Journal of Geology
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Introductory Studies of High-Pressure Polymorphism to 24,000 Bars by X-Ray Diffraction with Some Comments on Calcite II
JOHN C. JAMIESON
Reprinted for private circulation from
THE JOURNAL OF GEOLOGY
Vol. 65, No. 3, May 1957
rsmrao ov u.s.a.
INTRODUCTORY STUDIES OF HIGH-PRESSURE POLYMORPHISM TO 24,000 BARS BY X-RAY DIFFRACTION WITH SOME COMMENTS ON CALCITE II1
john c. jamieson University of Chicago
ABSTRACT
A technique is described by which X-ray diffraction studies may be made of substances at pressures in the neighborhood of 24,000 bars. Potassium iodide transforms from the NaCl structure to the CsCl structure above 18,000 bars. Cadmium displayed no transitions at 16,000 bars. Aragonite and vaterite showed no transition to 24,000 bars. A thermodynamic argument shows calcite II and calcite III to be unstable with respect to aragonite. X-ray patterns of calcite II and thermodynamic evidence are consistent with the interpretation that calcite II is an anion-disordered form of normal calcite.
introduction
Although it is of fundamental geophysical importance, the experimental study of high-pressure polymorphism has lagged seriously. The geophysicist who is interested in the state of matter in the earth's interior is forced to rely on the known properties of phases as they can be obtained in the laboratory, either by quenching from a given pressure and temperature; by study at high temperatures and room pressure utilizing X-rays; or by simple detecting techniques, such as volume measurements, electrical or magnetic measurements which can be made at both elevated temperatures and pressures. The only available method for X-ray examination of materials at pressures greater than about 5,000 bars is a miniature pressure vessel relatively transparent to X-rays, through which pass the diffracted beams from a sample, which is pressed between two pistons. Lawson and Riley (1949) and Guen-gant and Vodar (1954) describe beryllium pressure vessels. These techniques have an
1 Manuscript received November 28,1956.
effective working range of 10,000 bars due to creep of the beryllium. However, at the cost of shortened bomb life, studies can be made to about 20,000 bars (Lawson, personal communication) at room temperature. For work at pressures in the neighborhood of 30,000 bars, Lawson and Tang (1950) describe a bomb made from two single-crystal diamonds clamped together. The following may be described as the next logical step in the series of single-stage unsupported pressure vessels which are transparent to X-rays.
experimental
The pressure vessel is a roughly three-carat single-crystal diamond (pi. 1, A). A highly polished straight hole, 0.015 inch in diameter and 0.172 inch in length, has been ground through the diamond with a flat at each end of the hole. (The grinding was exceedingly well done by the Indiana Wire Die Co., Fort Wayne, Ind.) The flats are perpendicular to the axis of the hole. The diamond is industrial grade, "mechanically flawless," chosen and oriented by the grinding concern. The
PLATE 1 A, The diamond bomb
B, X-ray patterns using the diamond bomb
a,	ki at 20,800 bars, CsCl type.	a tes e.i'-c,-Calcite at zero pressure.
b,	KI at zero pressure, after transition.	d, Calcite II at 22,000 bars.
334
Journal of Geology, Volume 65
Jamieson, Plate 1
B
The diamond bomb; X-Ray patterns
HIGH-PRESSURE POLYMORPHISM BY X-RAY DIFFRACTION	335
original crystal faces make up its roughly-spherical exterior. After delivery, microscopic examination showed no visible flaws, and the diamond went to virtual extinction under crossed nicols. X-ray examination showed only a thin strained layer next to the central hole. The hole was found to be drilled parallel to a cubic axis. The camera and miniature press (utilizing a calibrated spring) described by Lawson and Riley (1949) were employed. Ten-hour exposures with molybdenum radiation at 50 kv. and 18 ma. were taken with a 0.010 pinhole collimator and a ZrC>2 filter in front of the film. The pistons are air-hardened drill rod, 0.090 inch long. A limit of 30,000 bars was placed on the stress in the pistons so as to prolong their working life and protect the diamond from a suddenly snapped piston.
There are three major difficulties with the technique—absorption and scatter by the diamond, absorption by the sample, and lack of a true hydrostatic pressure within the sample. The first puts two limits on the technique. Molybdenum or harder radiation must be used so that the weak coherent scatter from the sample may penetrate through the diamond, while the diamond scatter provides Laue spots and an over-all background. This latter factor prohibits the use of long exposure times to bring out faint lines.
Since the radius of the sample is fixed, it is necessary to dilute absorbing substances to obtain satisfactory diffraction patterns. "Optimum" sample thicknesses were calculated using the rule 2/n (Buerger, 1942), where ju is the linear absorption coefficient cm-1. The result was divided into the diameter of the hole, to approximate the required dilution. Zinc stearate was used for dilution because of its low absorption and scattering power. It also serves as a lubricant, at least in the lower pressure range (Guengant and Vodar, 1954). No diffraction lines from the amount of zinc stearate used were observed except in the Cd study, which was performed at relatively high dilution.
To allow for absorption and geometrical errors, the camera was calibrated separately for each substance, using a room-pressure
pattern. A North American Phillips 114.59-mm. camera with Straumanis-type mount, using filtered iron radiation, was used to obtain the lattice constants for the desired substance from high-angle reflections. The positions for molybdenum radiation were then calculated, and the observed 6 values were plotted against the calculated 6 values, giving a calibration curve of effective camera radius against 6 with an error of 0.2 per cent. The mean effective camera diameter is 96.3 mm. Films were measured to 0.1 mm. The combination of errors leads to 0.5 per cent in 6 for higher-angle lines. The error from
Kilobars P,
Fig. 1.—Calibration curve, using KI. Pi is internal pressure; P, is stress on piston.
sample absorption due to density increase with pressure was neglected, as was that for the difference in film shrinkage between the standard pattern and the unknown.
To correct for friction between the sample, pistons, and the diamond, the internal pressure was measured by using the change in lattice spacings of KI, which was chosen for its large volume change; for its NaCl-type structure, which facilitates measuring the lattice parameters; and for its polymorphic transition near the top of the present range. Bridgman's (1940) data were used for the volume decrements. The results (fig. 1) are presented only for increasing pressure, for reasons discussed below, and are terminated at 27,000-bar gauge pressure by the appear-
336
JOHN C. JAMIESON
ance of the high-pressure form of KI. It is thought safe to extrapolate the curve to 30,000 bars, the present upper limit of work. It is interesting to compare these measurements with a rough derivation of Bridg-man's (1937) on the effect of friction between a solid and the walls of the pressure vessel in which it is contained. Bridgman assumes that the pressure is constant perpendicular to the walls and, in the absence of transitions, he obtains
P=P0e-^x/r	(1)
for a piston advancing onto a sample in a blind hole; P is the quasi-hydrostatic pressure, x the distance from the piston face, r the chamber radius, n the coefficient of friction, and Pa the stress at the piston face. If we further assume that the pressure is symmetrical about the mid-point of the sample in the present case where two pistons are used, the same formula applies; however, x is now permitted to take values only up to Z/2, where L is the sample length; yu is unknown for mixtures of KI and zinc stearate against diamond; however, Bridgman (1937) states that 0.1 is not an uncommon value in the realm of plastic flow, so we shall adopt that value. For KI at Pa = 30,000 bars, L = 0.015 inch, and r = 0.0075 inch. This gives a pressure at the center of the sample of 24,600 bars as compared with 24,400 bars from the calibration curve in figure 1. The agreement is due partly to a mutual displacement of error, since Pa is actually reduced by a slight extrusion of material between the piston and the diamond, while the X-ray line spacings are biased by the pressure gradient toward a higher pressure than actually exists in the sample center, since the diffraction pattern is generated by the entire sample.
If a transition occurs, equation (1) no longer holds, and presumably the interior adjusts itself to a uniform pressure until the pressure is further increased. In the absence of a transition, when the pressure is decreased after an initial excursion to the maximum, the central pressure may remain constant, thus actually surpassing the piston pressure until the effect of friction can be
overcome by the developing pressure gradient.
RESULTS
Three substances were investigated: KI, Cd, and CaC03. Since the main purpose was to ascertain whether the diamond bomb could be used in a routine manner, the initial substances were chosen to obtain general data on high-pressure polymorphism while testing the diamond, without becoming involved in extensive sample preparations.
potassium iodide
Rbl, RbBr, and RbCl are known to have polymorphic transitions near 5,000 bars (Slater, 1924; Bridgman, 1928). Bridgman (1935, 1940) found the apparently equivalent series of transitions in KI, KBr, and KC1 in the neighborhood of 20,000 bars. The room-pressure structures of both series of halides are NaCl type. Jacobs (1938) found the high-pressure modification of Rbl to be CsCl type and offered a theoretical argument that the other five halide transitions were of this nature. To check the upper pressure series, KI was studied.
"Baker's analyzed" KI was recrystallized once from distilled water, annealed at 450° C. for | hour, and ground in an agate mortar. A powder pattern using the 114.59-mm. camera and iron radiation gave ao = 6.064 ± 0.001 A. This compares favorably with the value a0 = 6.0655 for especially pure KI obtained by Swanson and Tatge (1953).
Ten-hour exposures were taken at 22,000 and 24,400 bars, in addition to room-pres-sure pictures before and after. Transformation was partial at 22,000 bars and almost complete at 24,400. The high-pressure modification was easily indexed as cubic, CsCl type, with a0 = 4.13 + 0.02 A. The highest 6 value visible corresponded to 321, with all lower 6 values appearing. Two additional lines were identified as belonging to a minor amount of untransformed KI. The calculated AF/To leads to an internal pressure of 20,800 bars after transformation.
The KI sample had been ground thoroughly but was left unsieved, so that at least
HIGH-PRESSURE POLYMORPHISM BY X-RAY DIFFRACTION	33
qualitative information could be gained about the manner of transformation of individual particles. The initial pattern and the patterns taken at pressures up to the transition consisted of uniform diffraction lines with occasional spots from the larger oriented grains. As can be seen in plate 1, B, the high-pressure form gives a uniform pattern without spots, showing that the larger grains are broken up and do not transform in a relatively large single-crystal fashion. The "after" pattern (pi. 1, B) also has uniformly constituted diffraction lines; closer inspection, however, shows a remarkably uniform distribution of megascopic, equidimensional "Bragg spots" making up each line, with a diffuse background. This would seem to indicate that the reverse transformation took place with definite grain growth to a limiting size but not up to the initial grain size. It must be pointed out that the sample is not rotated in the present work. Rotation was tried but proved impracticable, owing to the larger size of the diamond, which made grossly smeared-out Laue spots on rotation, thus obscuring the sample lines.
cadmium
Cd is already hexagonal close packed at room pressure. Bridgman's (1925) reported transitions (two under 7,000 bars) raised the question of the possible transformation of a hexagonal close-packed metal under pressure. Jacobs (1938a) had found no change in Cd to 4,500 bars. He tried several sources of Cd and concluded that the (lower) transition does not involve a change in crystal structure.
In the present work, one sample of Cd powder (spectrographic analysis showed ~0.01 per cent Pb; ~0.01 per cent Cu; ~0.001 per cent Ag) diluted with three parts zinc stearate was used. The powder was coarse (to pass 100 mesh), so as to obtain additional information as before. Ten-hour exposures were taken at 0, 4,000, 10,000, and 16,000 bars and again at 0. No change in the pattern appeared other than readjustment and cold-working of the larger grains. The same sample was subjected to 16,000 bars three times, then photographed
again at room pressure. No change in the pattern was observed.
At this point Bridgman's (1925) data were reinspected. He reports no evidence of a discontinuity in electrical resistance, compressibility, or thermal e.m.f. when pressure studies are made of polycrystalline aggregates. The transitions are found only in linear compressibility and electrical resistance measurements on Cd single crystals. The discontinuities in length were both increases and decreases. They disappeared after several pressure cycles, presumably because the single crystal broke up into domains. Since there is no total volume change, Bridgman states that the structure must be transforming by a contraction in one direction coupled with an expansion in the other.
It is possible to reconcile the X-ray work with that of Bridgman in three ways. Jacobs' (1938a) and the writer's samples of Cd may have been insufficiently pure to transform. Or the structure changes may be too slight to detect with the available X-ray techniques. A third alternative is that Bridgman was detecting some effect other than polymorphism. Cd is known to deform readily by twinning (an extensive recent study of Cd twinning has been given by Thompson and Millard, 1952). Deformation twinning, inaugurated by shear around crystal imperfections, is sufficient to explain Bridgman's (1925) results. The hydrostatic pressure provides uniform boundary conditions at the crystal surface, so that the twinning is partially reversible; but a number of pressure cycles will cause the Cd crystal to be so thoroughly twinned as no longer to report a "transition."
the metastability of calcite ii and calcite iii
The phase diagram of CaCC>3 is shown in figure 2. Before describing the present work, it is necessary to discuss the status of the two phases, calcite II and calcite III, discovered by Bridgman (1939). The equilibrium curve between calcite and aragonite may now be regarded as established (Jamieson, 1953; MacDonald, 1955). For a transition to proceed with increasing pressure at constant
33
JOHN C. JAMIESON
temperature, the high-pressure phase must be of greater density. Using Bridgman's (1939) values for AF/F0 and initial density for CaCC>3, we obtain a density of 2.94 for calcite III at 20,000 kg/cm2 and 25° C. This compares with an X-ray density of 2.93 (Swanson et al., 1954) for aragonite at room pressure. Madelung and Fuchs's (1921) determination of the compressibility of aragonite extends to only a few hundred bars. Its extrapolation to 20,000 bars leads to a density of 3.04 for aragonite. Even a gross error in this extrapolation does not affect the con-
calcite II and calcite III only from calcite as initial material. Both transitions were reversible, and calcite (I) was the end-product after return to atmospheric conditions.
We note the following: calcite I at 15,000 bars, in the absence of a transition to aragonite, is itself metastable. The transitions I —> II and II —> III are thermodynamically possible, since AF is negative for each with increasing pressure (0.00135 and 0.00956 cm3/gm, respectively [Bridgman, 1939]). The reverse transitions are also thermodynamically possible. The calcite-aragonite
Fig. 2.—Phase diagram of CaCC>3. (Heavy lines denote experimentally determined transition curves, either stable or metastable.)
elusion that, at the pressures of transition of calcite I —»calcite II and calcite II —> calcite III, aragonite is more dense than either calcite II or calcite III and hence aragonite is the stable modification at 20,000 bars and room temperatures. The lack of compressibility data as a function of temperature for aragonite precludes extending this calculation for temperatures other than room temperature; however, Kozu and Kani's (1934) thermal expansion data for aragonite lead to a room-pressure density of aragonite of 2.90 at 200° C. Therefore, it seems probable that aragonite is also stable with respect to calcite II and calcite III at that temperature and 20,000 bars. Bridgman (1939) obtained
transition is reconstructive (Kozu and Kani, 1934; Buerger, 1951). At room temperature there is insufficient. thermal agitation for calcite to convert to aragonite within the aragonite field, and apparently neither of the two calcite polymorphs presents a drastic enough structural change for aragonite to form. The conclusion that the calcite I<-> II <-> III transitions are structurally minor was also reached earlier by Bridgman (1939).
Using Bridgman's (1939) data, we can obtain further information by using
-if <2>
HIGH-PRESSURE POLYMORPHISM BY X-RAY DIFFRACTION
33
for the equilibrium curves and
-AG(1,D
f (3)
= J AV CP, T) dP^PAV ,
where S, V, H, and G are the molal entropy, volume, enthalpy, and Gibbs's free energy of the phases; AS is the entropy difference, etc., as tabulated in table 1 for 25° C.; and AG(1, T) is the room-pressure free energy difference at T = 25° C. The values for cal-cite-aragonite are taken from an earlier study (Jamieson, 1953) and are deemed much more accurate than those of the calcite polymorphs. However, this loss of accuracy should not affect the over-all picture, which will be discussed after the presentation of the experimental results which follows.
x-ray evidence on calcium carbonate
A precipitated aragonite containing a faint trace of calcite was exposed to 24,400 bars and photographed. No change in pattern took place. A precipitated vaterite containing about 10 per cent calcite (estimated from powder patterns) was cycled 0, 16,000, 0, 22,000, 24,400, and several lower pressures, taking 10-hour exposures at each pressure. No change was noted in the patterns; however, these were of comparatively poor quality, because of the fineness of the vaterite and the presence of calcite, so that minor changes would not be noted. The hope that the calcite would nucleate a transition in vaterite proved unfounded, though the calcite did make possible a qualitative study of the relative compressibility of vaterite with respect to calcite. Vaterite proved the less compressible, judging from relative line shift; therefore, we see immediately that neither of the two known calcite polymorphs can be identified with vaterite, since its initial density is somewhat less than calcite (cf. Dana).
It is well to point out that the present technique will yield, at best, only rough compressibilities, due partially to lack of precise knowledge of the pressure but more directly to the error in measuring the spac-ings ( + 0.5 per cent). For a cubic substance,
the volume can be calculated to +1.5 per cent from each line, but the use of several lines reduces this error considerably. For materials of lower symmetry, high-order reflections directly measuring the unit cell may be too faint to record, while the many unresolved doublets with molybdenum radiation reduce the number of well-measured 6 values to the point that a statistical solution is meaningless. The spacing error rules out the use of simultaneous equations. For example, an error of, say, +1 per cent in the axial values of an orthorhombic structure leads to a volume error of +3 per cent, which is the same order of magnitude as the
TABLE 1
PERTINENT THERMODYNAMIC PARAMETERS,
Including the Entropy and Enthalpy Increments at 25° C. and the Pressures of Transition
	AS	Aff	AG(1, T)
	(Cal/	(Cal/	(Cal/
Transition	Mole ° C.)	Mole)	Mole)
I-»II.........	+0.032	+ 10	+ 46
II—»III.......	-1.28	-381	+438
I—>aragonite. .	. -1.24	-370	+273
total volume change at 20,000 bars of many materials. Hence the absolute compressibility is indeterminate. The use of a larger camera combined with multiple exposures would improve the situation. Unfortunately, radiation softer than molybdenum is not feasible with the diamond bomb.
The initial calcite material was Johnson-Mathey's Specpure CaCOs. Several runs to 24,400 bars were made with different loads and different degrees of dilution with zinc stearate. The most satisfactory patterns were obtained from undiluted samples.
The structure of calcite is rhombohedral with a0 — 4.989 A and Co = 17.062 A (S wan-son and Fuyat, 1953), using the hexagonal pseudo-cell. The only feature of the structure demanding a Co axis of this length is the two possible orientations of the triangular carbonate ion (Mauguin, 1923; Lander, 1949). If the carbonate ions were disordered or if they were ordered unidirectionally, Co would be halved. Mauguin (1923) pointed out that 11.3 was the strongest line proving
3
JOHN C. JAMIESON
carbonate ion orientation. Lander (1949) noted the absence of 11.3 in X-ray spectrometer patterns of SrC03 and BaC03 above their transition points. Both are aragonite type at lower temperatures. SrC03 transforms at 912° C. and BaC03 transforms at 803°. Lander (1949) argues that the high-temperature forms of each are essentially of an anion-disordered calcite type. He did not accept the absence of 11.3 and similar reflections as evidence of disorder because of the relatively high scattering power of Ba and Sr and the high temperatures at which he worked. In the case of calcite at room temperature and high pressure, it would seem somewhat safer to rely on the absence of 11.3 as evidence of anion disorder.
The calcite form of CaC03 shows a marked diminution in the intensities of high-angle lines and a decrease in the relative intensity of 11.3 with respect to the rest of the pattern as pressure is increased. The process reverses with decreasing pressure. By visual estimate, the phenomena start at 15,000 bars and proceed gradually to 20,000 bars. The next pattern taken at 22,000 bars (pi. 1, B) shows a complete loss of lines farther out than 11.6, the virtual extinction of 11.3, and a noticeable broadening and general weakening of the remaining lines. The pressure gradient in the sample prohibits determining the exact point of transition, but the major effect takes place between 20,000 and 22,000 bars. The high-line loss and genera] broadening suggest either that a high state of strain exists in the sample or that grain size has been much reduced. Neither of these possibilities explains the behavior of 11.3, which implies either that a state of orientation disorder exists in the anion array or that a different ordering has been induced so as to halve the Co axis. (The hexagonal nomenclature has been retained, under the assumption that the crystallographic change is minor.) The loss of lines and broadening
evidence from thermodynamic parameters
A glance at table 1 shows that the AH for II —■> III is comparable with that for
I	—* aragonite. The latter is a reconstructive transformation; yet the former involves a structural change between two metastable phases so slight that the stable aragonite form does not appear. If the change from
II	—> III is so minor and does not involve major bond realignment, then intuitively one would expect a smaller AH. One way to explain the large AH is to assume a configu-rational contribution to the entropy difference of R In 2 corresponding to a two-posi-tion anion disorder in calcite II with respect to an ordered array in calcite III. This does not conflict with the calcite I-calcite II transition line, since with respect to the ordered calcite I, calcite II (at a constant pressure) is the high-temperature form of higher entropy. The disorder picture does demand either a gradual disordering in calcite I before the transition or a cancellation of the major part of the configurational portion of the entropy by the vibrational portion, in order to explain the low AS and AH for I —»II. The X-ray evidence does not conflict with either a gradual disorder or a sharp transition moving gradually across the pressure gradient.
In addition, Boeke (1912) reported a reversible change in the heat content of calcite (also reported by Eitel, 1922), without optical change at 1,248° K. Lander (1949) interpreted this as an anion disorder analogous to that of the high-temperature forms of BaC03, SrC03, and several nitrates. In figure 2 it can be seen that the calcite II —> calcite III line extrapolates roughly to this figure.
If this extrapolation is accepted, then the calcite-aragonite equilibrium line must terminate in a triple point in the rough neigh-prohibit the determination of cell size, borhood offeopL and 10,000 bars, with a Bridgman's (1939) data on volume changes disordered calcite as the third phase. This demonstrate this also. Since the X-ray evi- triple point, if correct, implies that the dence is inconclusive, we must look else- upper portion of MacDonald's (1955) study where.	on calcite-aragonite was performed under
HIGH-PRESSURE POLYMORPHISM BY X-RAY DIFFRACTION	3
metastable conditions, because of the impossibility of quenching a readily reversible transition.
To study this potential triple point, we turn to Boeke's (1912) data. He reports temperature versus time for the heating and cooling of his CaC03 samples. Three of his curves are sufficiently linear (the other, Carrara marble is not) above and below the transition to give an effective temperature lag, due to the transition, of 10°-15° C. Using his sample mass (8 gm.) and Kelley's (1934) extrapolated cp data for calcite, assumed constant over the interval, we obtain a total heat change of 27.2-40.8 cal/8 gm, or 340-510 cal/mole. This corresponds to an entropy change of 0.27-0.41 cal/mole ° C. This falls in line with the entropy value in table 1, when it is remembered that the latter is an entropy decrement at transition, while the former covers a temperature interval and hence involves some contributions from the disordering prior to transition.
Although reported by both Boeke (1912) and Eitel (1922), the existence of a-calcite (the terminology for the high-temperature calcite) has been questioned by Smyth and Adams (1923) on the basis of absence of twinning in a single crystal of Iceland spar put repeatedly through the transition (Boeke had reported extensive twinning), the lack of a break in slope for the equilibrium curve CaO + C02 «-> CaC03 obtained by them, and the lack of a heat effect on a differential thermocouple arrangement. The validity of the latter two points are in question owing to their disagreement with the CaO + CO2 *-*■ CaC03 equilibrium curve obtained recently by quenching (Harker and Tuttle, 1955). Further experimental work is necessary on this point, taking into account the comparatively small heat change involved or the exceedingly small volume change and the probable gradual nature of the transition. As to the first point, until further studies have been made on the effect of impurities, initial materials, and cooling rates on the presence or absence of twinning in calcite which has been heated above 970° C. under sufficient CO2 pressure, it
would be unwise to draw any conclusions from the opposed data.
We now consider in detail the three-phase equilibrium between calcite (I), aragonite (A), and a-calcite (II). From the first equality in equation (2) and
A5i_»a + ASa-»ii + ASn-»i =0 (4)
at the triple point, we obtain
dP~\	dP~\
AFi-^a+j^ A Fa—hi dTi i_,a	dT J A-m
(5)
+	A Fn-»i = 0
dl Jim
or
dPl _ dPl A Fa—>1 rfrJa-m dTJa-h A Fa-hi
(6)
_dP~\ A F11—>1. dTi n_>i A Fa—>11'
since Fi ^ Fn, the first term predominates, and thus
. (7)
(£TJa-»ii dT Ja-h
This implies that the normally expected break in slope at a triple point is very small in this case. MacDonald's (1956) data indicate this as well, since they can be fitted by a straight line. However, the upper portion of his data must now be taken to be an equilibrium between aragonite and an anion-dis-ordered calcite rather than normal calcite.
The slope of the curves for the transition aragonite structure to anion-disordered calcite structure is of the same sign in CaC03, SrCOs, BaC03, and KN03. As Lander (1949) shows for BaC03 and SrC03, the effect of pressure is to raise the transition temperature in each case. In the case of KN03, the effect is the same (Bridgman, 1916).
Anion disordering in the calcite structure is also known in NaN03. Thermal expansion measurements by Kracek et al. (1932) show the transition to be of the second order and terminating ca. 275° C., and Siegel (1949) proposed that the nitrate ions were co-or-
3
JOHN C. JAMIESON
dinated aragonite-fashion with the sodium. The volume increases, and hence the transition temperature would initially be raised by pressure. The (P, T) continuation is unknown. In the absence of any general theory connecting the phase diagrams of different solid systems, it is difficult to state whether this is a count against the same anion-dis-ordered structure for calcite II.
Because of a lack of volume data in the vicinity of the triple point, it is not possible to evaluate equation (7) numerically. Hence the aragonite transition curve has been left colinear with its metastable extension in figure 2 as reported by MacDonald (1956). Rigorously speaking, this can be true only if calcite I goes to calcite II by way of a second-order transition. If further study should prove this to be the case, the various manipulations involving equation (2) to obtain AS, etc., must be regarded as being taken over a temperature interval rather than at a phase line, but the arguments still hold.
conclusions
The single-crystal diamond bomb may be used as a valuable tool in the study of high-pressure polymorphism. The temperature range 80°-600° K. is also available, and apparatus has been designed and partially constructed to work at high pressure with X-ray diffraction in this range.
Two out of three polymorphic transitions so far studied behaved unexpectedly. Cadmium refused to transform, thereby giving
rise to a twinning hypothesis to explain earlier results. This twinning mechanism may be active in the case of other "polymorphic transitions" found only by linear measurements. The study of CaCC>3 showed that pressure polymorphism can and does occur in a reversible fashion between metastable forms, and it illustrates the danger of extrapolating high-pressure transition lines, determined at comparatively low temperatures, into the realm of geological or geophysical conditions. The actually stable phase may be completely unknown at present. However, a transition line may be the metastable prolongation past a triple point. The calcite I —> calcite II is apparently of this type, and probably calcite II —> calcite III is also. CaC03 also illustrates the possibility that order-disorder phenomena may occur as a function of pressure, with the transition order —> disorder with increasing pressure. This is most likely to occur in substances containing one or more complex ions where orientation order-disorder can occur.
Acknowledgments.—The writer wishes to thank Professor A. W. Lawson for his continued interest and the use of his laboratory. Especial thanks must go to Dr. R. G. Johnson, who was instrumental in inaugurating the chain of circumstances leading to the information that a diamond could be satisfactorily drilled in this fashion. Mr. Otis Ferrier, owner of the Indiana Wire Die Company, was very cordial and helpful with regard to an unusual drilling job.
REFERENCES CITED
Boeke, H. E., 1912, Die Schmelzerscheinungen und die umkehrbare Umwandlung des Calcium-carbonats: Neues Jahrbuch f. Mineralogie u. Geologie, v. 1, p. 91-212.
Bridgman, P. W., 1925, Certain physical properties of single crystals of tungsten, antimony, bismuth, tellurium, cadmium, zinc, and tin: Am. Acad. Arts and Sci. Proc., v. 60, p. 305-383.
-1928, The pressure transition of the rubidium
halides: Zeitschr. f. Kristallographie, v. 67, p. 363-376.
- 1935, Polymorphism, principally of the elements, up to 50,000 kg/cm2: Phys. Rev., v. 48, p. 893-906.
-- 1937, Polymorphic transitions of thirty-five
substances to 50,000 kg/cm2: Am. Acad. Arts and Sci. Proc., v. 72, p. 45-135.
--- 1939, The high pressure behavior of miscellaneous minerals: Am. Jour. Sci., v. 237, p. 7-18.
—--- 1940, The compression of 46 substances to
50,000 kg/cm2: Am. Acad. Arts and Sci. Proc., v. 74, p. 21-51.
Buerger, M. J., 1942, X-ray crystallography: New York, John Wiley & Sons, Inc.
-—- 1951, in Smoluchowski, R., ei al., Phase
transformations in solids, p. 205: New York, John Wiley & Sons, Inc.
Eitel, W., 1922, Uber das System CaC03-NaAlSi04
HIGH-PRESSURE POLYMORPHISM BY X-RAY DIFFRACTION	33
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