An accurate determination of the crystal structure of triclinic potassium dichromate, K, Cr, 0,

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1 An accurate determination of the crystal structure of triclinic potassium dichromate, K, Cr, 0, J. K. BRANDON' AND I. D. BROWN Departlnellt of Plzysics, McMaster University, Hamilton, Olrtnrio Received October 12, 1967 The crystal structure of triclinic potassium dichromate has been determined by single crystal X-ray diffraction. The cell constants are a = , b = 7.376, c = A, ci = 90.75", P = 96-21", y = 97.96" with four K2CrZ07 units per cell. Refinement of 2600 reflections in both the spacegroups P1 and Pi leads to the same structure. This is in agreement with the results of anomalous dispersion measurements, confirming that Piis the correct space group. The final agreement index, R, is The two crystallographically independent dichromate ions are similar, deviating only slightly from CZv symmetry. The Cr-0 (terminal) distance is 1.63 A, the Cr-0 (bridging) distance is 1.79 A and all angles at the chro- mium atoms are tetrahedral except for one of the O(bridging)-Cr-O(termina1) angles in each ion which is 106". The angles at the bridging oxygen atoms are 124' and 128". The geometry of the anion is compared with that found in a number of similar groups. Canadian Journal of Chemistry, 46, 933 (1968) Introduction In 1833 Mitscherlich (I) reported that a phase transition occurs at about 250 "C in potassium dichromate, K,Cr,O,. Since that time there has been a succession of papers dealing with the polymorphism and crystallography of potassium dichromate but only recently has the crystal structure of its room temperature phase been reported by Kuz'min, Ilyukhin, and Belov (2). We have independently determined the crystal structure of this phase, and since our results are somewhat more accurate and give a better picture of the detail of the structure, we present them here. One of the points frequently discussed in earlier papers is whether the correct space group of the room temperature form of potassium dichromate is P1 or Pi. Klement and Schwab (3) have reviewed the work up to More recently, papers have been published by Rao (4), Podisko (5), and Parvov and Shubnikov (6). We give below our reasons for favoring the space group Pi which was also used by Kuz'min et al. (2). Experimental Crystals of triclinic potassium dichromate were grown by slowly evaporating a saturated solution of technical grade K,Cr,O, in distilled water at room temperature. The characteristic habit of the clear-orange crystals is shown in 'Present address: Crystallographic Laboratory, Cavendish Laboratory, Free School Lane, Cambridge, England. " \ \ (I 0 T) (1 00) FIG. 1. Habit of triclinic K2Cr207 crystals. TABLE I Clystal data for triclinic K2Cr207 Formula weight System Space group Cell constants a b C ci P Y Unit cell volume Density Measured Calculated Number of formula units ~ eunit r cell 4 ~-;ay absorption coefficient WOK,) Triclinic Pi A3 2.66k0.05 gm cn~-~ gm 42.4 cm-i

2 934 CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, 1968 TABLE I1 Coordinates and temperature factors (X lo5) of the atoms in triclinic K2Cr,0,. The coordinates in parentheses are those reported by Kuz'min et a/. (2) transformed to the same unit cell. The standard errors are those indicated by the least squares refinement Coordinates Temperature factor components ( x lo5) Atom x Y z I322 p33 I312 p23 K 1.I5845.I (. 159) (. 160) (.916) K I (-. 136) (. 198) (. 656) K (. 639),60346 (.604) (.668) K (. 348) (.749) (. 768) Crl Fig. 1. The choice of axes in Fig. 1 corresponds precession photographs taken with Zr-filtered to those of the actual crystal used in this Mo-radiation. These films were calibrated with analysis. Our cell convention has been chosen to rutile (a = and c = A (10)). The allow easy comparison with related structures crystal data are given in Table I. such as (NH,),Cr,O, (7), K2S207 (8), and The crystal selected for intensity measure- P-Ca2P207 (9). ments approximated a cylinder (the cylinder Accurate cell parameters were measured from axis was [OlO]) with a mean diameter of 0.25 mm

3 BRANDON AND BROWN: CRYSTAL STRUCTURE OF TRICLINIC POTASSIUM DICHROMATE 935 TABLE I11 Observed (F,) and calculated (F,) hko and Okl structure amplitudes in units of 1/10 electron per unit cell with the estimated relative standard errors (o) of the former. The symbols following F, have the following meaning: -, unobserved reflection; *, unreliable F, measurement which was given zero weight during refinement; X, reflection believed to show extinction effects H K L and a length of 0.46 mm. An integrating precession camera with Zr-filtered Mo-radiation was used to photograph layers with h = 0, 1, and 2, and I = 0, 1, 2, and 3. The intensities were measured using a recording photomicrodensitometer, and a standard error was estimated for each reflection for use in weighting the data during the least squares refinement. Unobserved intensities were assigned the local minimum observable value. The intensity data consisted of 2604 measured reflections of which 324 were unobserved. During the final stages of refinement 25 low angle reflections suspected of showing extinction effects were given zero weight. The intensity data and their estilnated standard errors were then corrected for Lorentz and polarization effects. Absorption corrections were not considered necessarv. The structure was solved using Patterson function and electron density projections down [OOl] and [loo]. A trial three dimensional structure was formulated in space group P1 with

4 CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, I968 TABLE IV Interatomic distances (in A) and angles (in degrees) in triclinic potassiunl dichromate. Figures in parentheses denote standard errors in the last digits quoted as indicated by the least squares refinement. The true standard errors are probably 5 or 10 times as large. Symmetry transfornlations from the atom coordinates given in Table I1 are designated as follows: n = [loo], b = [OlO], c = [OOl], d = [OTj], e = [loll, f = [TTO], 2 = [IOO], b = [OTO]. The prime denotes inversion in the center of symmetry at either (0, 112, 112) or (112, 112, 1/21 Dichromate ions Thermally Thermally Distances Uncorrected corrected Distances Uncorrected corrected Mean corrected Cr-0 (bridge) = Crl (3) Cr (4) (3) (4) ioi4j i3j Cr (3) Cr (4) (3) (3) (3) (3) Mean corrected Cr-0 (terminal) = OBI B Angles Angles 022 io8.5(ij (1) Cr (1) 041-CrG (1) Cr (1) 042-Cr6043 K-0 distances OBlc * OB B3h 3.90

5 BRANDON AND BROWN: CRYSTAL STRUCTURE OF TRICLINIC POTASSIUM DICHROMATE 937 TABLE IV (Concluded) 0-0 distances less than 3.20 A between dichromate ions *~hese distances are greater than 4 A. FIG. 2. The structure of triclinic K2Cr2O7 projected down [OOl]. FIG. 3. Side and end views of the two independent Cr2072- ions in triclinic K2Cr207.

6 CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, 1968

7 BRANDON AND BROWN: CRYSTAL STRUCT 'URE OF TRICLINIC POTASSIUM DICHROMATE independent atoms per unit cell. This trial structure possessed approximate centers of symmetry but further refinement was performed without imposing any such constraints. A fill1 matrix least squares calculation was used to refine the atomic coordinates and isotropic temperature factors of all atoms together with separate scale constants for each of the seven layers of data. Weights for each reflection were set equal to one over the standard error in the observed structure factor (F,), except for those unobserved reflections for which the calculated structure factor (F,) was less than the smallest observable F,. In these cases the weight was set equal to zero. The best weighted agreement index, obtained an agreement index of R = CCw2(lFo( - ( F~~)~~CW~IF~~~~~'~, obtained in the space group P1 with individual isotropic temperature factors was Since this structure still possessed an approximate center of symmetry a refinement was also performed in the space group Pi with individual isotropic temperature factors giving an agreement index of Hamilton's statistical tests (11) applied to these agreement indices indicated a less than 0.5 % probability of Pi being the correct space group. However, the P1 model was unsatisfactory in that it did not differ in any chemically meaningful way from the Pi model, and, consequently, an attempt was made to look for anomalous dispersion effects. Structure factor calculations with the PI model indicated that --- there were several pairs of reflections hkl and kkl whose intensities should be markedly different when photographed with Cu-radiation if the space group really were non-centrosymmetric. A Weissenberg h01 photograph taken with CuK, radiation failed to show these differences thus indicating that the P1 model was wrong. Fmther examination of the two models showed that during the refinement of the P1 model, the extra degrees of freedom were being used to compensate for anisotropic temperature effects. When the Pi model was refined with anisotropic temperature factors the agreement index dropped to It was not possible to refine the P1 model with anisotropic temperature factors because of the large correlations between the positional and temperature variables and so it was not possible to use statistical tests to compare the two models at this stage. However, the absence of an observable anomalous dispersion effect, the low value of the agreement index, and the satisfactory molecular geometry of the Pi model all indicate that any deviations from the PT symmetry must be very small. The atomic coordinates and anisotropic temperature factors are given in Table I1 for the best anisotropic Pi model. For comparison, the coordinates of Kuz'min et al. (2) are also given. These have been converted to our cell convention by the transformation x = (112) - y'; y = (112) - 2'; z = 1 - x', where x', y', and z' are the coordinates given in their paper. With these coordinates they Table I11 gives some of the observed structure amplitudes (F,) and their estimated standard errors (o) together with the structure factors (F,) calculated from our parameters in Table 11. The complete set of refined structure factor data is given in ref. 12. The atomic scattering factors used were those for K', Cr3+, and 0- given in International Tables (1 3). Discussion The present determination of the structure of K2Cr207 agrees with that of Kuz'min et al. (2) but, because of its greater accuracy, it reveals more clearly the configuration of the Cr2072- ion. This ion consists of two nearly tetrahedral CrO, groups joined through a shared oxygen atom. The ion is almost in the eclipsed configuration and is close to having the symmetry C,,. The anisotropic temperature factors of the chromium and oxygen atoms indicate that the Cr20,2- ion undergoes a librational motion with a root mean square amplitude of about 6" around an axis passing through the two chromium atoms. Interatomic distances and angles calculated for K2Cr207 from our data are given in Table IV. The bond distances within the Cr2072- ion are given both before and after corrections have been made for thermal motioil (14). Figure 2 shows the structure projected down [OOl]. Figure 3 shows side and end views of the two crystallographically distinct CI-,O,~ - ions. When viewed along the Cr-Cr directions, the ions show twists of about 5" and 10" away from an exactly eclipsed configuration, reducing the

8 940 CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, 1968 ideal symmetry from C,, to C,. In addition, one, but only one, of the angles subtended at the chromium atoms in each ion (OBI-Crl-011 and 0B3-Cr3-03 1) is signifi cantly different from 109.5" thus reducing the symmetry further from C, to C,. The Cr-0-Cr bridging angles in the two ions are significantly different with values of 124.0" and 127.6". In both dichromate ions the two bridging Cr-0 distances are equal within experimental error (mean 1.79 $ A) as are the terminal Cr-0 distances (mean 1.63 $ A). It is of interest to compare the geometry of the Cr2072- ions with those found for similar groups in ionic crystals or in the gas phase. There is, unfortunately, no other determination of the structure of the dichromate ion of comparable accuracy, although three dichromate structures have been reported (2, 7, 15). Accurate structures have been reported for the pyrophosphate ions in P-Ca2P,07 (9) and Na4P207.10H,O (16). Like K2Cr207, P-Ca2P207 has two nonequivalent anions in the unit cell. The structure of potassium pyrosulfate, in which the S2072- ion has a crystallographic C, symmetry, has also been determined by X-ray diffraction (8) while the structure of C1,0, has been determined in the gas phase by electron diffraction (17). In every case, it is found that the immediate environment of both X atoms in the X207 group has the symmetry C,, so that two of the four X-0 bonds are equivalent within the limits of experimental accuracy. Table V gives, for the various X207 groups, interatomic distances and angles averaged over all the corresponding values within the crystal. From this table it can be seen that the groups FIG. 4. Idealized view of an X,07 group showing the atom names used in Table V. are all close to being eclipsed and have X-OB -X angles of about 120 to 130". These angles vary from group to group even within the same crystal and appear to be sensitive to the crystalline environment. The large deviation from the eclipsed configuration in Na4P,07. 1OH,O can be attributed to the hydrogen bonds present. As would be expected, the distance from the central atom (X) to the bridging oxygen atom is always longer than the distances from the central atom to the terminal oxygen atoms. Also, the angles subtended at X by the terminal oxygen atoms (01-X-02, 02-X-02, see Fig. 4 for an explanation of nomenclature) are larger than the angles subtended by the bridging oxygen atoms (OB-X-O1,OB-X-02) in all groups except Cr,072-. The reason for this can be understood if one realizes that the sum of the van der Waals radii for two oxygen atoms is 2.80A. In the smaller ions the oxygen atoms bonded to the same central atom are separated by distances much less than the sum of the van der Waals radii and are under considerable pressure. An additional pressure arises from the coulombic repulsions between the ionic charges which reside on these atoms. Both pressures can be relieved by increasing the angles between the bonds to the terminal oxygen atoms until all the 0-0 distances are about the same. Examination of the 0-0 distances in Table V shows that this occurs for all the groups except Cr In this case, the 0-0 distances are long enough that no distortion is necessary. Another common feature in these groups is the small size of the angle OB-X-01 compared with OB-X-02. This has been attributed to mutual repulsions between atoms in opposite halves of the X,07 group (17). Like the previous effect, this repulsion is largest when the group is smallest. In an ion the size of Cr,072- this effect should be absent. In fact, in each of the two crystallographically independent Cr,072 - ions in K2Cr,07 one, but only one, of the OB- X-01 angles is smaller than the tetrahedral angle. Since any intraionic repulsions should affect both halves of the ion equally, this distortion must be due to the influence of neighboring ions in K,Cr,07. Both CS,O,~ions are in similar environments. Further work on some of the other phases of the alkali metal dichromates is in progress in this laboratory.

9 BRANDON AND BROWN: CRYSTAL STRUCTURE OF TRICLINIC POTASSIUM DICHROMATE 94 1 Acknowledgments We wish to acknowledge the support of a research operating grant from the National Research Council of Canada and one of us (J. K. Brandon) wishes to thank the National Research Council of Canada for a Scholarship. 1. E. MITSCHERLICH. Ann. Physik, 28, 116 (1833). 2. E. A. KUZ'MIN, V. V. ILYUKHIN, and N. V. BELOV. Dokl. Akad. Nauk SSSR, 173, 1078 (1967). 3. U. KLEMENT and G. SCHWAB. Z. Krist. 114, 170 (1960). 4. G. S.RAO. J. Indian Inst. Sci. Sect. A, 41,47 (1959). 5. V. S. PODISKO. Tr. Inst. Kristallogr. Akad. Nauk SSSR, 9, 327 (1954). 6. V. F. PARVOV and A. V. SHUBNIKOV. Kristallografiva (1964). (Translation in Soviet Phvs.-Crvst. 7. A. BYSTROM and K. WILHELMI. Acta Chem. Scand. 5, 1003 (1951). 8. H. LYNTON and M. R. TRUTER. J. Chem. Soc (1960). \ -~-, 9. N. C. WEBB. Acta Cryst. 21, 942 (1966). 10. M. E. STRAUMANIS, T. EJIMA, and W. J. JAMES. Acta Cryst. 14, 493 (1961). 11. W. C. HAMILTON. Acta Cryst. 18, 502 (1965). 12. J. K. BRANDON. Ph.D. Thesis, McMaster University, Hamilton, Ont Table INTERNATIONAL TABLES FOR X-RAY CRYSTALLOGRAPHY. Vol Kynoch Press, Birmingham Tables 3.3.1A, 3.3.2B. 14. W. R. BUSING and H. A. LEVY. Acta Cryst. 17, 142 (1964). 15. L. A. ZHUKOVA and Z. G. PINSKER. Kristallografiya, 9, 44 (1964). (Translation in Soviet Phys.-Cryst. 9,

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