"This investigation was supported in part by research grant DE-02659-02 to the American Dental Association from the National Institute of Dental Research and is part of the dental research program conducted by the National Bureau of Standards, in cooperation with the Council on Dental Research of the American Dental Association; the United States Army Medical Research and Development Command; the Dental Sciences Division of the School of Aerospace Medicine, USAF; the National Institute of Dental Research; and the Veterans Administration.

"Research Associates of the American Dental Association at the National Bureau of Standards, Washington, D.C. 20234. Present address for Dr. E. C. Moreno, Forsyth Dental Center, Boston, Mass. 02100.

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

All the chemicals used in the present study were reagent grade. Stock solutions of sodium fluoride were prepared by weighing the salt which was dried at 100 °C for 24 h; the salt was dissolved with conductivity water in borosilicate volumetric flasks and immediately transferred to polyethylene bottles for storage. The systems used in the potentiometric measurements were made by taking 100 ml of sodium fluoride solutions of suitable concentrations and adding various aliquots of standard hydrochloric acid. In this way it was possible to obtain systems with a wide concentration range in both sodium fluoride and hydrochloric acid. The estimated standard error in the concentrations of sodium fluoride and hydrochloric acid was 1.3 percent of the amount present.

2.2. Potentiometric Measurements

The cell used in these measurements may be schematically represented by

418-535 OL - 71 - 5

hkl

hkl

hkl

with i<j between pairs F and F of observed equivalent reflections Fakt was 0.018 calculated over 1189 pairs. i and j are the sequence numbers in the list of equivalent reflections. Absorption corrections for a sphere with μ=85.6 cm-1 were applied. The maximum and minimum transmission factors were 0.347 and 0.317, respectively.

The 0-20 scans were carried out on an automated Picker diffractometer at 2°/min for 20: backgrounds were counted for 20 s each. Because the least significant digit in all counts was dropped by the Picker hardware, standard deviations, Ohki, of the structure factors. Fnki, were estimated from σhki Fnkt/5.7 for Fnkt < 5.7; σnki = 1 for 5.7 < Fnkt < 30; andσnki=Fnku 30 for Fnkt >30 where Fmax on this arbitrary scale is 113. The scattering factors used were those for the neutral atoms in reference 6 for the x-ray 67 refinements and those in references 7 and 8 for the extinction and anomalous dispersion refinements.

The quasi-normalized structure factor statistics on our barytocalcite data indicate that the structure is acentric, since <E>=0.885, < E2 >= 1.00 (fixed), <│E2 - 1¦ >= 0.709: the corresponding theoretical values are 0.886, 1.000, 0.736 for the acentric case and

0.798, 1.000. 0.968 for the centric case. E is the quasinormalized structure factor [9]. The fraction of E values greater than 1.0, 2.0 and 3.0. respectively, was found to be 0.405, 0.0027 and 0.0000: the corresponding theoretical values are 0.368, 0.0183. 0.0001 for the acentric case and 0.317, 0.0455, 0.0027 for the centric case. The statistical procedure suggested an average temperature factor, B, of about 2.5 A and an exponent of 1.00 for sin X. Our experience has been that the quasi-normalized structure factor statistics are normally much closer to the theoretical values and the exponent of sin A is closer to 2.00 than was calculated here for barvtocalcite.

Because of the presence of the strongly scattering Ba ions, this indication that the space-group is the acentric P2, was not considered to be reliable. The structure of barytocalcite was redetermined by us from a sharpened Patterson function calculated with (E-1) coefficients and an F., Fourier electron density synthesis phased from the positions of the Ba and Ca ions. The y coordinate of Ba was set equal to zero to define the origin along b. The structure was refined isotropically in space-group P2, to R, =0,65, R=0,057 and then anisotropically in P2, to R = 0.036, R = 0,028 using the x-ray 67 system of computing programs The least-squares refinements used the tuil matrix.

0:

minimized Zw (Fo-Fel). and included those unobserved reflections for which Fnkt calculated more than 2σ (Fnkt).

The highest peak in an electron density difference synthesis calculated after anisotropic refinement was equivalent to about 1/3 of an electron and was 0.49 A from Ba. When the space-group is assumed to be P21 the largest correlation coefficients are 0.90 to 0.95 between (i) x of O(1) and x of O(2), (ii) z of O(1) and: of O(2), (iii) x of O(4) and x of O(5) and (iv) z of O(4) and z of 0(5); 0.80 to 0.90 between (1) B11 of O(1) and B11 of (2), (ii) B13 of O(4) and B13 of O(5), and (iii) B23 of O(4) and B23 of O(5). There are 48 correlation coefficients greater than 0.50.

The isotropic extinction parameter. r. where F2=Func(1+ BrFane) and Fune is the structure factor uncorrected for extinction, was then refined together with the structural and scale parameters using the least-squares program RFINE written by L. W. Finger of the Carnegie Institution of Washington; these refinements included only the observed reflections. The resulting R values were R=0.027, R=0.022. The structure obtained had essentially the symmetry P21/m: subsequent anisotropic refinement in P21/m gave R=0.036, R=0.028 without extinction refinement and R=0.028, R=0.025 in refinements in which r refined to 0.000100(4) cm. All unconstrained parameters were varied. Finally, three cycles of refinement including corrections for anomalous dispersion and extinction gave Ru=0.028, R=0.023; r became 0.000100(5) cm. The largest change in the other parameters was an increase of ~0.1 A in all B1, parameters of Ca. In the final cycle, the average shift error was 0.02, and the standard deviation of an observation of unit weight. [Sw(F-F)2/ (1652 — 56 )]12, was 0.43.

The final R values for the centric and acentric cases are near the limit of the experimental data. The weighting scheme is arbitrary, though reasonable. Further, there are large correlation coefficients in the acentric refinement. From the first two considerations, the authors feel that the ratio test [11] on Σw(F-F)2, the numerator of the R term, is not really applicable in this border-line case, even though it appears from this test that refinement in the acentric P2, is to be preferred at a confidence level greater than 99.5 percent. Because refinement in the centric space-group P21/m gives essentially the same result as refinement in P2, but has more restraints which remove the high correlation coefficients, the space-group of barytocalcite is assumed here to be P2 m. This is consistent with the symmetry of 2'm in the observed crystalline forms of the mineral 12]. With refinement in P21/m, the largest correlation coefficients were removed, and only Six were greater than 0.50. The four largest were about 0.50 and were between the scale factor and the extinction parameter, and between the scale factor and B, B., and B. 3 of Ba.

Because Sr has been reported [13] in the alstonite phase of BaCa(CO519, a refinement of barytocalcite in which the cation positions were considered to be occupied by Sr- in solid solution was carried out using Finger's least-squares program. The occupan

cies, 1.003(13) and 1.004(4), for Ba and Ca respectively, suggest that there is no solid solution of Sr ions in this sample of barytocalcite.

The atomic parameters from the final extinction refinement in space-group P21/m are given in table 1. The observed structure factors are given in table 2.

3. Description of the Structure

The structure of barytocalcite (fig. 1) consists of Ba... CO3 chains and Ca... CO3 chains, both parallel to [001], in which the cations are coordinated to an edge of one neighboring CO3 group in the chain, and to an apex of the other CO3 group. The C(2)03 group is in the CaCO3 chain with its plane parallel to (100). The C(1)O3 group is in the BaCO3 chain, with its plane nearly parallel to (101), and is pushed out of the line of the chain because of the large ionic radius of the Ba ion. The chains lie in layers parallel to (210), a perfect cleavage in BaCa(CO3)2. The structure may also be considered to consist of layers of CO3 groups coordinated to layers of cations, and is related in this way to the calcite [14] phase of CaCO3, with (201) of barytocalcite corresponding to (001) of calcite.

3.1. The Barium lon Environment

The Ba ion is coordinated (fig. 1, table 3) to 11 oxygen atoms with Ba . . . O distances less than 3.2 Å, i.e.,

in the normal range. These oxygens consist of 5 edges of CO3 groups, O(2, 21), O(11, 211), O(1", 2111), 0(3, 4), O(3', 4') and one apex, O(1). The Ba ion is more extensively coordinated than it is in the witherite phase of BaCO3, where it has a coordination of 9 oxygens. The structure of witherite resembles that of the aragonite phase of CaCO3.

3.2. The Calcium lon Environment

The Ca ion is coordinated (fig. 1, table 4) to seven oxygen atoms, including one edge, O(4, 4), of a CO group, with Ca . . . O distances in the normal range. The five apex oxygen atoms lie in a square pyramid. The center of the coordinated edge of the CO, group is near the remaining octahedral position. The coordination of Ca in barytocalcite is thus intermediate between the octahedral coordination of six CO3 apexes with no shared edges in the calcite phase of CaCO3 and the nine-fold coordination of three shared CO3 edges and three apexes in the aragonite phase of CaCO3.

TABLE 4. Ca environment in barytocalcite,
BaCa(CO3)2

3.3. The Carbonate Groups and Their Environments

There are two crystallographically different CO3 groups in the structure. One (table 5, fig. 2) is in the Ba... CO3 chains and the other (table 5, fig. 2) is in the Ca . . . CO3 chains. The former, the C(1) CO3 group, coordinates with all edges to Ba ions, and coordinates one apex, O(1), to another Ba ion. The two remaining apexes O(2, 21) are coordinated to Ca ions.

The C(2) CO3 group coordinates the edge containing the O(4, 41) atoms to Ca" and the remaining two edges,

2.8.5

The atomic labels refer to atoms in figure 2.

O(3, 4) and O(3, 41), to ions Ba and BaTM, respectively. The average values of the C-O bond distance in the C(1) and C(2) CO; groups, 1.283 Å and 1.283 Å, respectively, compare well with the C–O bond lengths ob

2.95

0(2), Ca11

2.305(2)

O(2), Ball

2.847(2)

0(2), Ba"

2.904(2)

O(3), Ca1

2.364(3)