a-dimension. It is possible that some undetermined structural relationship exists between these phases which could include the 2:3 compound as a member of the series. If this is true, the cubic symmetry designated for the 2:3 compound would represent a pseudocell and the true symmetry may be hexagonal.

4. References

[1] Schneider, S. J., Waring, J. L., and Tressler, R. E., J. Res. Nat. Bur. Stand. (U.S.), 69A (Phys. and Chem.), No. 3, 245–254 (May-June 1965).

[2] McDaniel, C. L. and Schneider, S. J., J. Res. Nat. Bur. Stand. (U.S.), 71A (Phys. and Chem.), No. 2, 119-123 (Mar.-Apr. 1967).

[3] McDaniel, C. L. and Schneider, S. J., J. Res. Nat. Bur. Stand. (U.S.), 72A (Phys. and Chem.), No. 1, 27–37 (Jan.-Feb. 1968). [4] Barber, C. R., Metrologia 5 [2], 35–44 (1969).

[5] Swanson, H. E., Gilfrich, N. T., and Ugrinic, G. M., Nat. Bur. Stand. (U.S.), Circ. 539, 68 pages (1955).

[6] Schumacher, E. E., J. Am. Chem. Soc. 48, 396–405 (1926).

[7] Swanson, H. E., Fuyat, R. K., and Ugrinic, G. M., Nat. Bur. Stand. (U.S.), Circ. 539, 10 pages (1955).

[8] Swanson, H. E., Morris, M. C., and Evans, E. H., Nat. Bur. Stand. (U.S.), Monogr. 25, Sect. 4, 85 pages (1965).

[9] Muan, A., Am. J. Sci. 256, 171–207 (1958).

[10] Negas, T. and Roth, R. S., J. Res. Nat. Bur. Stand. (U.S.), 73A (Phys. and Chem.), No. 4, 431-442 (Nov.-Dec. 1969).

[11] Schafer, H. and Heitland, H. J., Z. Anorg. Allgem. Chem. 304, 249 (1960).

[12] Cordfunke, E. H. P. and Meyer, G., Rec. Trav. Chim. 81, 495– 504 (1962).

[13] Randall, J. J. and Katz, L., Acta Cryst. 12, 519–21 (1959). [14] Randall, J. J., Katz, L., and Ward, R., J. Am. Chem. Soc. 79, 266-7 (1957).

[15] Longo, J. M., Kafalas, J. A., and Arnott, R. J., J. Solid State Chem. 3, (1971).

[16] Ruddlesden, S. N. and Popper, P., Acta Cryst. 10, 538 (1957). [17] Ruddlesden, S. N. and Popper, P., Acta Cryst. 11, 54 (1958). [18] Longo, J. M. and Sleight, A. W., Inorg. Chem. 7, 108-111

(1968).

(Paper 75A3-662)

i hkl

hkl

with i<j between pairs F and F of observed equivalent reflections Fnkt 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, σnkl, of the structure factors, Fhkl, were estimated from σhk=Fhk/5.7 for Fnkl < 5.7; σhkl=1 for 5.7 < Fnkt < 30; andσnk=Fnk/30 for Fnkt 30 where Fm 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.

hkl

max

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 Å2 and an exponent of 1.00 for sin 0/λ. Our experience has been that the quasi-normalized structure factor statistics are normally much closer to the theoretical values and the exponent of sin 0/X is closer to 2.00 than was calculated here for barytocalcite.

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 (E21) coefficients and an Fo 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 P21 to Rw=0.65, R=0.057 and then anisotropically in P21 to R= 0.036, R= 0.028 using the x-ray 67 system of computing programs [10]. The least-squares refinements used the full matrix,

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

minimized Σw (Fol-Fel)2, and included those unobserved reflections for which Fnk 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 z of O(2), (iii) x of O(4) and x of O(5) and (iv) z of O(4) and z of O(5); 0.80 to 0.90 between (i) B11 of O(1) and B11 of O(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.

11

The isotropic extinction parameter, r, where F2-Func (1+ BrFane) and Func F2 = Fine (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 Rw=0.027, R= 0.022. The structure obtained had essentially the symmetry P21/m; subsequent anisotropic refinement in P2,/m gave Rw 0.036, R=0.028 without extinction refinement and Ru=0.028, R=0.025 in refinements in which refined to 0.000100(4) cm. All unconstrained parameters were varied. Finally, three cycles of refinement including corrections for anomalous dispersion and extinction gave Rw=0.028, R=0.023; r became 0.000100(5) cm. The largest change in the other parameters was an increase of ~0.1 Å2 in all B11 parameters of Ca. In the final cycle, the average shift/error was 0.02, and the standard deviation of an observation of unit weight, [Σw(Fo−Fc)2/(1652–56)]/2, was 0.43.

w

ii

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。 — Fc)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 P21/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 0.60 and were between the scale factor and the extinction parameter, and between the scale factor and B1, B22, and B33 of Ba.

Because Sr has been reported [13] in the alstonite phase of BaCa(CO3)2, a refinement of barytocalcite in which the cation positions were considered to be occupied by Sr2+ 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)O3 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, 2), O(1', 2), O(1", 2"), O(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.