temperatures 40 deg below Ty. Negative drift, or energy absorption, for the annealed glass started to show up just about at its Tg. These drifts indicate the directions in which the glasses tend to move themselves toward the equilibrium configurations of the supercooled liquid. The minimum in the drift at temperatures above the T, of a annealed glass shows that the heat capacity measurement was carried out at a faster rate than the relaxation rates governing configurational changes below and at 7. At higher temperatures the relaxation time decreases to the order of the experimental time scale. The maximum in the drift at temperatures below the Ty of a quenched glass is produced because the experimental time is long in comparison to the relaxation time for many of the configurational changes in the quenched glass. The minimum and the maximum in the drift plot correspond roughly to the inflection points in the heat capacity curves. Above 205 Kan equilibrium liquid is produced within the normal experimental time irrespective of the previous history. The difference in the heat capacities between the liquid and the glass at 200 K is 30.5±0.5 J/K/mol.

3.2. Crystallization

Crystallization of the sample may be detected by warming drifts in the temperature range from 235 to 270 K. If the sample has been cooled to temperatures below T since its last melting, the maximum rate of energy release from the sample is about 1 mW/mol at 250 K. If the sample has not been cooled below 240 K since its last melting, the rate of energy release is much smaller, presumably due to fewer nuclei being formed. It takes about 4 hr to measure heat capacities through the crystallization region. The total energy released by the sample in this time is in the order of 10 J/mol. This energy corresponds to a degree of crystallinity of about 0.25 percent, based on a heat of fusion of 4360 J/mol obtained from the melting points of a polymer-diluent system [15].

3.3. Liquid

Except for the results of a few determinations where crystallization and fusion occurred, the heat capacity of the liquid above 205 K can be fitted by least squares to a cubic expression in T with a standard deviation of 0.035 percent. In the crystallization range of 235 to 270 K, the rate of spontaneous energy release passes through a maximum as a function of temperature. At the maximum the half-time for the crystallization is in excess of 25 hr [4]. The rate of crystallization appears to be constant at fixed temperature. The observed calorimetric drift includes both the heat release from crystallization as well as the heat leak in the calorimetric system. By extrapolating the combined drifts to the midpoint of a heating period, the heat capacity of the sample is determined with minimal effect from the crystallization process. The heat capacity so deter mined in the crystallization range shows a deviation on the order of 0.1 to 0.2 percent, from values interpolated from higher and lower temperatures. This is probably due to the nonlinear change in the combined drift during the heating period and to the uncertainties in determining the linear region for relatively large drifts. The small amount of crystals, produced during the heat capacity measurements in the crystallization range, can be observed to melt around 270 K. The melting process sometimes introduces a somewhat longer time constant than normal for the system to reach a steady state. However, it does not introduce an additional contribution to the quasi-adiabatic temperature drift beyond that due to the heat leak of the calorimetric system. Hence the energy required to melt the crystal cannot be eliminated from the determination of the apparent heat capacity by extrapolation of drifts. The deviation at 270 K, about 0.5 percent higher than the base, is probably due to the inclusion of the heat for melting.

A comparison of literature values [1, 3] with the result from this research as the base line is shown in

-.004

-.008

140

1. Introduction

As part of a program of studies [1, 2]1 to obtain precise structural parameters on calcium carbonates, calcium carbonate hydrates, calcium phosphates, and related compounds, we have reinvestigated the crystal structure of Ca2Na(CO3)3, which exists in nature as the mineral shortite. The structural features in these compounds are important in the consideration of possible epitaxial, syntaxial, and substitutional solid solution relationships in the major inorganic phases found in vivo.

Shortite was first found [3] in a matrix of montmorillonite clay which also contains pyrite (FeS2), calcite (CaCO3), and a carbonate of magnesium in crystals which were too small to be identified. Massive deposits of the commercially important mineral trona (Na2CO3 · NaHCO3 H2O) are also found in the vicinity. A crystal structure for shortite has been reported by Wickman [4], who suggested atomic positions on the basis of refractive indices, spatial considerations, and the intensities of the Okl reflections. We found this structure to contain one incorrect feature. The corrected structure of shortite is reported here.

2. Data Collection and Structure Refinement

The crystal used in the data collection is an approximate sphere, radius 0.112(4) mm, ground from a shortite

*Department of Chemistry, University of Maryland Baltimore County, Baltimore, Md. **Director, American Dental Association Research Program. National Bureau of Standards, Washington, D.C. 20234.

Figures in brackets indicate the literature references at the end of this paper.

fragment from mineral sample 105807, National Museum of Natural History, Smithsonian Institution, Washington, D.C. (sample supplied by J. S. White, Jr.). The sphere was mounted on the goniometer head in our usual way [2].

formula (ideal): Ca2 Na2(CO3)3
cell: orthorhombic

a = 4.947(1) Å

b = 11.032(2) Ă c = 7.108(1) Å volume = 387.9 Å3

space-group Amm2;

cell contents 2[Ca2Na2(CO3)3]

reciprocal lattice extinctions: k+1=2n+1 for hkl:

calculated density 2.620 g cm-3;

observed density 2.629 g cm-3 [3].

The procedure given in reference [2] was followed in the collection and processing of data with the following exceptions. The 0-20 scans were carried out at 20/min. Each background was counted for 20 s. 1659 reflections were collected from the hkl and hkl octants and were merged into a unique set of 711, of which 684 are "observed" and 27 are "unobserved." The R factor between observed equivalent reflections was 0.01. No absorption corrections were made because the maximum error in an intensity due to absorption is 0.8 percent. For Ca2 Na2(CO3)3, μ(Mo)= 15.7 cm ̄1. The Picker hardware dropped the least significant

* Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the

purpose.

413-992 O-71-3

digit during the data collection so that the standard deviations from counting statistics, and consequently our assessment of whether a given reflection is observed or unobserved, is only marginally correct. This affects very few reflections in the present case because the sample scattered strongly and nearly all reflections were unequivocally "observed" (modified hardware was used in later investigations). σ(F) was defined as F/10 for F< 10; 1 for 10< F < 43; and F/43 for F > 43, where Fmax was 211; weights in the least-squares refinements were 1/o2. Wickman's structure [4] for Ca2 Na2(CO3)3 would not refine to a residual, Rw, below 0.3. Examination of the Patterson function and an Fo electron density Fourier synthesis phased from structure factor calculations using the positions of the Ca and Na ions suggested new positions for the C(1) and O(1) atoms. This structure was refined isotropically to Rw=0.056, R=0.050, and anisotropically to R 0.030, R= 0.023 and then to Rw=0.025, R=0.020 with refinement on the isotropic extinction parameter, r, in addition to the previously varied parameters. The least-squares program RFINE written by Finger [5] was used. Only observed reflections were used in these refinements. The scattering factors for the neutral atoms were taken from Cromer and Mann [6]. No corrections for anomalous dispersion were made. The final value of r is 0.00017(1) cm where F2 = Fine (1+ Br Func 2) 1/2 and Func is the structure factor uncorrected for extinction. The notation is that of Zachariasen [7]; here r may be related to the average domain size if the crystal is of type II where the extinction is assumed to be governed by spherical domains. The z coordinate of Ca was set equal to zero to define the origin along c. In the final cycle, the average shift/error was 0.01 and the standard deviation of an observation of unit weight,

w

unc

was 0.45.

[ZW (Fo-Fe)/(711-50)]/2,

The highest peaks in an electron density difference synthesis calculated at R= 0.03 corresponded to about 0.1 of an electron. The largest correlation coefficients are 0.42-0.44 between the scale factor and the B11, B22, and B33 temperature factors of Ca and 0.64 be

tween the extinction parameter and the scale factor. All other correlation coefficients are less than 0.28.

The atomic parameters are given in table 1. All atoms but O(2) lie in special positions; the Wyckoff symbol and symmetry of these positions are given in table 1. The observed and calculated structure factors, uncorrected for extinction, are given in table 2.

3. Description of the Structure

The structure of Ca2 Na2(CO3)3 is shown in figures 1 and 2. There are CaNaCO3 layers at x=0.5 and Na(CO3)2 layers at x=0. The CO3 group containing C(2), O(3), O(4), and O(4') lies on the mirror at x=0.5 and is a member simultaneously of three cation-anion chains in which cations are coordinated to edges and opposite apexes of the CO3 group. One CaCO3 chain runs parallel to [011], one runs parallel to [011], and one NaCO3 chain runs parallel to [001]. Similar cationanion chains are present in the barytocalcite phase of BaCa(CO3)2 [8]. The bonding of the apex of the CO group in the NaCO3 chain to Na is weak, however. The CO3 group containing C(1), O(1), O(2), and O(2′), which is on the mirror at x=0 and has its plane parallel to (011) or (011), forms NaCO3 chains like those cation-anion chains at x=0.5. The two oxygens O(2) and O(2'), which lie above and below the mirror, provide bonding with cations in neighboring Ca2Na(CO3) layers. Each Na at x=0 is common to two chains. The CO3 groups have seemingly oriented themselves to maximize edge coordination to Ca; each CO3 group is bonded edgewise to two Ca ions and one Na ion. Preferential edge coordination of CO3 to Ca is in accord with Ca exerting the largest electrostatic attraction on the CO3 group and is consistent with the Ca coordinations in CaCO3. 6H2O [1], CaNa2(CO3)2 · 5H2O [9], and CaNa2(CO3)2 · 2H2O [9].

There is a void in the structure centered at about 0, 0.5, 0.8 (figs. 1 and 2). If the ionic radius of the oxygen in the CO3 groups is assumed to be 1.4 Å, this void is about 2.2-2.5 Å in diameter. Because it has both cations and anions in its surface, it is unlikely that it would be occupied, except perhaps by an inert gas

atom.