Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270101006667/br1328sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270101006667/br1328Isup2.hkl |
Ce-doped SrMgF4 crystals were grown by the Bridgman method (ref?). The starting 4 N grade powders were mixed together in the ratio CeF3:SrF3:MgF2 = 0.005:0.995:1. This mixture was placed into a carbon crucible which was heated in a resistance furnace under an Ar gas atmosphere. A colourless single-crystal of about 18 mm in diameter and 30 mm in length was grown by displacing the crucible vertically at a speed of 0.07 mm h-1. The atomic ratio of Sr to Ce was determined by X-ray fluorescence spectrometry to be 0.9994:0.0006. Since the concentration of Ce was considered to be negligible, a stoichiometric composition, SrMgF4, was assumed for the structure analysis.
Since there are virtually no significant reflections at 2θ angles higher than 90°, all data in this region were eliminated. Equivalent reflections were merged using Xtal3.4 (Hall et al., 1995). Friedel pairs were considered as separate reflections for the merge. In all, 4369 independent Friedel pairs with I>3σ(I) and Rint = 0.0731 were used for the structure determination and the refinement procedure. The z coordinate of Sr4 was fixed at 1/2 to define the origin. The Flack parameter suggested a trace of the inversion twin component.
Data collection: RAPID AUTO (Rigaku, 1999); cell refinement: RAPID AUTO; data reduction: RAPID AUTO; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: CRYLSQ in Xtal3.4 (Hall et al., 1995); molecular graphics: ATOMS (Dowty, 1999); software used to prepare material for publication: BONDLA and CIFIO in Xtal3.4.
SrMgF4 | F(000) = 1032 |
Mr = 187.92 | Dx = 3.907 Mg m−3 |
Monoclinic, P1121 | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: P 21 | Cell parameters from 87446 reflections |
a = 7.8249 (8) Å | θ = −30–70° |
b = 7.4930 (7) Å | µ = 16.99 mm−1 |
c = 16.9248 (17) Å | T = 298 K |
β = 90° | Irregular shape, colourless |
V = 958.34 (17) Å3 | 0.30 × 0.20 × 0.15 mm |
Z = 12 |
Rigaku R-AXIS RAPID diffractometer | 4369 reflections with I > 3σ(I) |
ω scans | Rint = 0.073 |
Absorption correction: gaussian RAPID AUTO (Rigaku, 1999) | θmax = 45.3°, θmin = 2.4° |
Tmin = 0.020, Tmax = 0.257 | h = −13→15 |
58521 measured reflections | k = −14→11 |
7537 independent reflections | l = −33→33 |
Refinement on F | Weighting scheme based on measured s.u.'s |
Least-squares matrix: full | (Δ/σ)max < 0.001 |
R[F2 > 2σ(F2)] = 0.044 | Δρmax = 2.00 e Å−3 |
wR(F2) = 0.037 | Δρmin = −1.85 e Å−3 |
S = 3.20 | Extinction correction: Zachariasen (1968), Eq22 p292 "Cryst. Comp." Munksgaard 1970 |
4130 reflections | Extinction coefficient: 2351 (63) |
326 parameters | Absolute structure: Flack (1983) |
0 restraints | Absolute structure parameter: 0.097 (8) |
0 constraints |
SrMgF4 | V = 958.34 (17) Å3 |
Mr = 187.92 | Z = 12 |
Monoclinic, P1121 | Mo Kα radiation |
a = 7.8249 (8) Å | µ = 16.99 mm−1 |
b = 7.4930 (7) Å | T = 298 K |
c = 16.9248 (17) Å | 0.30 × 0.20 × 0.15 mm |
β = 90° |
Rigaku R-AXIS RAPID diffractometer | 7537 independent reflections |
Absorption correction: gaussian RAPID AUTO (Rigaku, 1999) | 4369 reflections with I > 3σ(I) |
Tmin = 0.020, Tmax = 0.257 | Rint = 0.073 |
58521 measured reflections |
R[F2 > 2σ(F2)] = 0.044 | 0 restraints |
wR(F2) = 0.037 | Δρmax = 2.00 e Å−3 |
S = 3.20 | Δρmin = −1.85 e Å−3 |
4130 reflections | Absolute structure: Flack (1983) |
326 parameters | Absolute structure parameter: 0.097 (8) |
Experimental. Intensity data were collected at 298 K using the imaging-plate diffractometer Rigaku R-axis Rapid with Mo Ka radiation monochromated by a graphite plate. The cylindrically shaped imaging plate covers the two-theta angular range between -60 and 140° with a crystal-film distance of 127.4 mm. The diffraction pattern was recorded on an imaging plate by oscillating the crystal around ω by 3° with a residence time of 240 sec/°. In all, 297 images were taken successively by varying ω with 6 sets of different χ and ϕ values. Overlaps of 0.2° in ω were taken into consideration at both ends of each scan. The crystal used for data collection was bounded by 10 faces with a volume of 0.00751 mm3. Crystal shape determination and the numerical absorption correction using the Gaussian method were also carried out using the Rapid Auto program package. Cell dimensions were refined together with other offset parameters of the diffractometer using all reflections with I>3σ(Io) measured in the 2θ range between -60 and 140°. |
x | y | z | Uiso*/Ueq | ||
Sr1 | 0.18015 (12) | 0.2084 (2) | 0.51587 (7) | 0.0138 (4) | |
Sr2 | 0.33110 (9) | 0.81636 (15) | 0.67731 (9) | 0.0124 (3) | |
Sr3 | 0.83449 (8) | 0.83076 (12) | 0.33420 (8) | 0.0089 (3) | |
Sr4 | 0.66509 (10) | 0.16189 (12) | 1/2 | 0.0090 (3) | |
Sr5 | 0.83511 (9) | 0.83651 (17) | 0.67013 (8) | 0.0128 (4) | |
Sr6 | 0.31952 (10) | 0.77828 (12) | 0.35089 (7) | 0.0113 (4) | |
Mg1 | 0.5423 (3) | 0.6592 (4) | 0.52297 (16) | 0.0075 (10) | |
Mg2 | 0.5403 (3) | 0.6683 (3) | 0.19079 (16) | 0.0076 (10) | |
Mg3 | 0.4568 (3) | 0.3296 (3) | 0.35532 (16) | 0.0071 (10) | |
Mg4 | 0.0379 (3) | 0.6634 (4) | 0.52280 (15) | 0.0076 (10) | |
Mg5 | 0.0432 (3) | 0.6633 (3) | 0.19041 (16) | 0.0072 (9) | |
Mg6 | 0.9579 (3) | 0.3290 (3) | 0.35714 (16) | 0.0071 (10) | |
F1 | 0.5964 (5) | 0.8285 (6) | 0.4314 (3) | 0.0124 (18) | |
F2 | 0.5008 (6) | 0.4286 (5) | 0.4660 (3) | 0.0133 (17) | |
F3 | 0.5905 (6) | 0.8897 (5) | 0.5874 (3) | 0.0129 (19) | |
F4 | 0.4749 (6) | 0.5519 (5) | 0.6293 (3) | 0.019 (2) | |
F5 | 0.5656 (6) | 0.8222 (6) | 0.0958 (3) | 0.015 (2) | |
F6 | 0.5779 (6) | 0.8994 (5) | 0.2561 (3) | 0.013 (2) | |
F7 | 0.5463 (5) | 0.5698 (5) | 0.3029 (2) | 0.0135 (18) | |
F8 | 0.4114 (6) | 0.2036 (6) | 0.2564 (3) | 0.016 (2) | |
F9 | 0.3749 (5) | 0.0934 (5) | 0.4186 (3) | 0.0127 (18) | |
F10 | 0.7898 (5) | 0.6663 (7) | 0.5418 (3) | 0.016 (2) | |
F11 | 0.2826 (5) | 0.6224 (6) | 0.2042 (3) | 0.018 (2) | |
F12 | 0.2190 (5) | 0.3753 (6) | 0.3670 (3) | 0.018 (2) | |
F13 | 0.0584 (5) | 0.7965 (6) | 0.4248 (3) | 0.0143 (19) | |
F14 | 0.9613 (6) | 0.4252 (5) | 0.4700 (3) | 0.0156 (19) | |
F15 | 0.1094 (5) | 0.9048 (5) | 0.5835 (3) | 0.0118 (19) | |
F16 | 0.9534 (5) | 0.4351 (5) | 0.1329 (3) | 0.0162 (18) | |
F17 | 0.0965 (5) | 0.8283 (5) | 0.0972 (3) | 0.0109 (18) | |
F18 | 0.1196 (6) | 0.8921 (5) | 0.2565 (3) | 0.0129 (18) | |
F19 | 0.9808 (5) | 0.5533 (5) | 0.2970 (3) | 0.0144 (18) | |
F20 | 0.9274 (6) | 0.1631 (6) | 0.2637 (3) | 0.012 (2) | |
F21 | 0.9246 (5) | 0.0993 (5) | 0.4220 (3) | 0.0089 (17) | |
F22 | 0.2901 (6) | 0.6563 (7) | 0.5101 (3) | 0.021 (2) | |
F23 | 0.8038 (5) | 0.7162 (6) | 0.1893 (3) | 0.015 (2) | |
F24 | 0.6963 (5) | 0.2872 (6) | 0.3586 (3) | 0.016 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Sr1 | 0.0076 (4) | 0.0213 (5) | 0.0131 (4) | 0.0051 (3) | 0.0012 (2) | 0.0061 (2) |
Sr2 | 0.0067 (3) | 0.0165 (3) | 0.0145 (3) | 0.0039 (2) | −0.0007 (3) | −0.0068 (3) |
Sr3 | 0.0065 (3) | 0.0119 (3) | 0.0087 (3) | 0.0028 (2) | −0.0004 (2) | −0.0024 (3) |
Sr4 | 0.0079 (3) | 0.0110 (3) | 0.0086 (3) | 0.0030 (2) | 0.0014 (3) | 0.0020 (3) |
Sr5 | 0.0078 (3) | 0.0236 (6) | 0.0084 (4) | 0.0066 (3) | −0.0008 (2) | −0.0056 (3) |
Sr6 | 0.0082 (4) | 0.0157 (4) | 0.0106 (4) | 0.0043 (3) | −0.0012 (2) | −0.0027 (3) |
Mg1 | 0.0071 (12) | 0.0085 (11) | 0.0071 (10) | 0.0022 (9) | −0.0004 (8) | −0.0000 (8) |
Mg2 | 0.0076 (10) | 0.0072 (10) | 0.0081 (12) | 0.0024 (8) | 0.0000 (8) | −0.0010 (9) |
Mg3 | 0.0067 (11) | 0.0072 (10) | 0.0072 (11) | 0.0011 (8) | −0.0003 (9) | −0.0005 (9) |
Mg4 | 0.0066 (12) | 0.0090 (12) | 0.0068 (10) | 0.0012 (9) | 0.0007 (8) | 0.0007 (8) |
Mg5 | 0.0057 (10) | 0.0078 (10) | 0.0076 (11) | 0.0011 (7) | 0.0008 (8) | −0.0003 (9) |
Mg6 | 0.0059 (11) | 0.0074 (10) | 0.0077 (11) | 0.0010 (8) | 0.0000 (8) | −0.0001 (9) |
F1 | 0.0093 (19) | 0.015 (2) | 0.011 (2) | 0.0000 (15) | 0.0013 (14) | −0.0010 (15) |
F2 | 0.020 (2) | 0.0087 (17) | 0.011 (2) | 0.0031 (14) | −0.0013 (15) | −0.0042 (14) |
F3 | 0.016 (2) | 0.0077 (19) | 0.013 (2) | −0.0004 (15) | −0.0023 (15) | −0.0020 (15) |
F4 | 0.032 (3) | 0.0123 (19) | 0.015 (2) | 0.0100 (17) | 0.0080 (18) | 0.0035 (15) |
F5 | 0.016 (2) | 0.018 (2) | 0.011 (2) | 0.0044 (17) | 0.0020 (16) | 0.0026 (16) |
F6 | 0.019 (2) | 0.008 (2) | 0.012 (2) | 0.0052 (16) | 0.0005 (16) | 0.0012 (14) |
F7 | 0.019 (2) | 0.0092 (18) | 0.011 (2) | 0.0010 (15) | −0.0012 (15) | 0.0033 (13) |
F8 | 0.016 (2) | 0.020 (2) | 0.012 (2) | 0.0055 (17) | −0.0036 (15) | −0.0042 (16) |
F9 | 0.017 (2) | 0.009 (2) | 0.010 (2) | −0.0013 (15) | −0.0031 (16) | −0.0007 (14) |
F10 | 0.011 (2) | 0.019 (2) | 0.020 (2) | 0.0064 (16) | −0.0028 (16) | −0.0064 (18) |
F11 | 0.0064 (18) | 0.029 (2) | 0.020 (2) | 0.0071 (15) | 0.0008 (15) | −0.0019 (18) |
F12 | 0.010 (2) | 0.026 (2) | 0.020 (2) | 0.0065 (16) | 0.0002 (17) | 0.0013 (18) |
F13 | 0.015 (2) | 0.018 (2) | 0.013 (2) | 0.0096 (16) | 0.0003 (15) | 0.0084 (15) |
F14 | 0.022 (2) | 0.0092 (18) | 0.013 (2) | −0.0004 (15) | 0.0003 (16) | −0.0062 (15) |
F15 | 0.015 (2) | 0.005 (2) | 0.015 (2) | 0.0015 (15) | −0.0032 (15) | 0.0006 (14) |
F16 | 0.021 (2) | 0.0103 (18) | 0.015 (2) | −0.0019 (15) | 0.0046 (16) | −0.0078 (15) |
F17 | 0.0103 (19) | 0.013 (2) | 0.011 (2) | 0.0059 (15) | 0.0006 (15) | 0.0039 (15) |
F18 | 0.014 (2) | 0.010 (2) | 0.013 (2) | −0.0003 (15) | −0.0007 (15) | −0.0005 (14) |
F19 | 0.021 (2) | 0.0085 (17) | 0.014 (2) | 0.0036 (14) | 0.0046 (16) | 0.0066 (14) |
F20 | 0.016 (2) | 0.011 (2) | 0.012 (2) | 0.0068 (16) | 0.0013 (15) | −0.0034 (15) |
F21 | 0.0107 (18) | 0.0052 (19) | 0.0113 (19) | 0.0032 (14) | 0.0015 (14) | 0.0003 (13) |
F22 | 0.0076 (19) | 0.031 (3) | 0.025 (3) | 0.0084 (17) | 0.0013 (16) | −0.001 (2) |
F23 | 0.0097 (17) | 0.017 (2) | 0.018 (2) | 0.0065 (14) | −0.0002 (16) | −0.0007 (18) |
F24 | 0.0050 (17) | 0.022 (2) | 0.023 (2) | 0.0051 (14) | 0.0013 (16) | 0.0067 (19) |
Sr1—F5 | 2.465 (5) | Sr5—F11 | 3.370 (5) |
Sr1—F15 | 2.477 (4) | Sr6—F13 | 2.430 (5) |
Sr1—F21 | 2.518 (4) | Sr6—F1 | 2.504 (4) |
Sr1—F17 | 2.519 (4) | Sr6—F18 | 2.534 (5) |
Sr1—F9 | 2.541 (5) | Sr6—F6 | 2.557 (4) |
Sr1—F2 | 2.753 (4) | Sr6—F9 | 2.559 (4) |
Sr1—F14 | 2.761 (5) | Sr6—F11 | 2.727 (5) |
Sr1—F12 | 2.794 (5) | Sr6—F7 | 2.773 (4) |
Sr1—F23 | 2.986 (5) | Sr6—F22 | 2.836 (5) |
Sr1—F22 | 3.243 (6) | Sr6—F19 | 2.895 (4) |
Sr1—F13 | 3.359 (4) | Sr6—F12 | 2.929 (4) |
Sr2—F8 | 2.456 (5) | Mg1—F2 | 1.931 (5) |
Sr2—F6 | 2.456 (4) | Mg1—F10 | 1.950 (5) |
Sr2—F3 | 2.481 (5) | Mg1—F1 | 1.978 (5) |
Sr2—F20 | 2.533 (5) | Mg1—F22 | 1.980 (5) |
Sr2—F15 | 2.563 (5) | Mg1—F4 | 1.985 (5) |
Sr2—F16 | 2.625 (4) | Mg1—F3 | 1.994 (5) |
Sr2—F4 | 2.648 (5) | Mg2—F4 | 1.929 (5) |
Sr2—F5 | 2.959 (4) | Mg2—F5 | 1.959 (5) |
Sr2—F22 | 3.057 (5) | Mg2—F11 | 1.969 (4) |
Sr2—F24 | 3.158 (5) | Mg2—F23 | 1.999 (4) |
Sr3—F13 | 2.392 (5) | Mg2—F6 | 2.010 (5) |
Sr3—F21 | 2.453 (4) | Mg2—F7 | 2.041 (5) |
Sr3—F1 | 2.482 (5) | Mg3—F8 | 1.910 (5) |
Sr3—F18 | 2.527 (4) | Mg3—F7 | 1.966 (4) |
Sr3—F6 | 2.565 (5) | Mg3—F24 | 1.981 (5) |
Sr3—F23 | 2.589 (5) | Mg3—F12 | 1.987 (5) |
Sr3—F7 | 2.627 (3) | Mg3—F2 | 2.011 (5) |
Sr3—F20 | 2.685 (4) | Mg3—F9 | 2.025 (5) |
Sr3—F19 | 2.695 (4) | Mg4—F13 | 1.921 (5) |
Sr4—F5 | 2.451 (5) | Mg4—F14 | 1.946 (5) |
Sr4—F3 | 2.464 (4) | Mg4—F10 | 1.973 (5) |
Sr4—F17 | 2.474 (4) | Mg4—F22 | 1.999 (6) |
Sr4—F24 | 2.559 (5) | Mg4—F16 | 2.012 (5) |
Sr4—F21 | 2.565 (4) | Mg4—F15 | 2.028 (5) |
Sr4—F9 | 2.590 (4) | Mg5—F16 | 1.934 (4) |
Sr4—F14 | 2.674 (4) | Mg5—F17 | 1.981 (5) |
Sr4—F1 | 2.680 (4) | Mg5—F11 | 1.989 (5) |
Sr4—F2 | 2.704 (5) | Mg5—F19 | 1.990 (5) |
Sr5—F8 | 2.375 (5) | Mg5—F18 | 2.004 (5) |
Sr5—F20 | 2.441 (5) | Mg5—F23 | 2.013 (5) |
Sr5—F18 | 2.454 (4) | Mg6—F19 | 1.934 (5) |
Sr5—F3 | 2.486 (5) | Mg6—F20 | 1.987 (5) |
Sr5—F10 | 2.497 (5) | Mg6—F12 | 1.989 (4) |
Sr5—F15 | 2.540 (4) | Mg6—F24 | 1.989 (5) |
Sr5—F17 | 2.724 (4) | Mg6—F21 | 2.000 (5) |
Sr5—F16 | 3.004 (5) | Mg6—F14 | 2.040 (5) |
Sr5—F4 | 3.139 (4) | ||
F2—Mg1—F10 | 92.4 (2) | F13—Mg4—F14 | 92.5 (2) |
F2—Mg1—F1 | 98.1 (2) | F13—Mg4—F10 | 94.8 (2) |
F2—Mg1—F22 | 90.0 (2) | F13—Mg4—F22 | 88.4 (2) |
F2—Mg1—F4 | 97.2 (2) | F13—Mg4—F16 | 169.8 (2) |
F2—Mg1—F3 | 176.5 (3) | F13—Mg4—F15 | 90.4 (2) |
F10—Mg1—F1 | 93.7 (2) | F14—Mg4—F10 | 90.9 (2) |
F10—Mg1—F22 | 176.8 (3) | F14—Mg4—F22 | 89.9 (2) |
F10—Mg1—F4 | 91.2 (2) | F14—Mg4—F16 | 96.9 (2) |
F10—Mg1—F3 | 85.6 (2) | F14—Mg4—F15 | 176.6 (2) |
F1—Mg1—F22 | 88.2 (2) | F10—Mg4—F22 | 176.7 (3) |
F1—Mg1—F4 | 163.7 (3) | F10—Mg4—F16 | 88.9 (2) |
F1—Mg1—F3 | 85.0 (2) | F10—Mg4—F15 | 87.2 (2) |
F22—Mg1—F4 | 86.3 (2) | F22—Mg4—F16 | 87.8 (2) |
F22—Mg1—F3 | 91.9 (2) | F22—Mg4—F15 | 91.9 (2) |
F4—Mg1—F3 | 80.0 (2) | F16—Mg4—F15 | 80.23 (18) |
F4—Mg2—F5 | 92.0 (2) | F16—Mg5—F17 | 96.9 (2) |
F4—Mg2—F11 | 94.6 (2) | F16—Mg5—F11 | 93.6 (2) |
F4—Mg2—F23 | 88.8 (2) | F16—Mg5—F19 | 95.52 (19) |
F4—Mg2—F6 | 175.2 (2) | F16—Mg5—F18 | 175.2 (2) |
F4—Mg2—F7 | 101.2 (2) | F16—Mg5—F23 | 91.5 (2) |
F5—Mg2—F11 | 98.0 (2) | F17—Mg5—F11 | 97.8 (2) |
F5—Mg2—F23 | 86.7 (2) | F17—Mg5—F19 | 165.8 (2) |
F5—Mg2—F6 | 88.5 (2) | F17—Mg5—F18 | 86.7 (2) |
F5—Mg2—F7 | 165.5 (2) | F17—Mg5—F23 | 85.7 (2) |
F11—Mg2—F23 | 174.1 (2) | F11—Mg5—F19 | 88.3 (2) |
F11—Mg2—F6 | 90.1 (2) | F11—Mg5—F18 | 89.0 (2) |
F11—Mg2—F7 | 87.1 (2) | F11—Mg5—F23 | 173.4 (2) |
F23—Mg2—F6 | 86.5 (2) | F19—Mg5—F18 | 80.5 (2) |
F23—Mg2—F7 | 87.5 (2) | F19—Mg5—F23 | 87.1 (2) |
F6—Mg2—F7 | 77.79 (19) | F18—Mg5—F23 | 85.6 (2) |
F8—Mg3—F7 | 91.9 (2) | F19—Mg6—F20 | 95.4 (2) |
F8—Mg3—F24 | 90.4 (2) | F19—Mg6—F12 | 91.9 (2) |
F8—Mg3—F12 | 96.3 (2) | F19—Mg6—F24 | 90.1 (2) |
F8—Mg3—F2 | 172.3 (2) | F19—Mg6—F21 | 177.3 (2) |
F8—Mg3—F9 | 93.2 (2) | F19—Mg6—F14 | 101.3 (2) |
F7—Mg3—F24 | 91.8 (2) | F20—Mg6—F12 | 97.3 (2) |
F7—Mg3—F12 | 90.8 (2) | F20—Mg6—F24 | 87.7 (2) |
F7—Mg3—F2 | 95.53 (18) | F20—Mg6—F21 | 86.0 (2) |
F7—Mg3—F9 | 174.7 (2) | F20—Mg6—F14 | 162.7 (2) |
F24—Mg3—F12 | 172.6 (3) | F12—Mg6—F24 | 174.4 (3) |
F24—Mg3—F2 | 87.4 (2) | F12—Mg6—F21 | 90.2 (2) |
F24—Mg3—F9 | 86.7 (2) | F12—Mg6—F14 | 86.6 (2) |
F12—Mg3—F2 | 85.5 (2) | F24—Mg6—F21 | 87.6 (2) |
F12—Mg3—F9 | 90.0 (2) | F24—Mg6—F14 | 87.8 (2) |
F2—Mg3—F9 | 79.31 (19) | F21—Mg6—F14 | 77.11 (19) |
Experimental details
Crystal data | |
Chemical formula | SrMgF4 |
Mr | 187.92 |
Crystal system, space group | Monoclinic, P1121 |
Temperature (K) | 298 |
a, b, c (Å) | 7.8249 (8), 7.4930 (7), 16.9248 (17) |
γ (°) | 105.041 (11) |
V (Å3) | 958.34 (17) |
Z | 12 |
Radiation type | Mo Kα |
µ (mm−1) | 16.99 |
Crystal size (mm) | 0.30 × 0.20 × 0.15 |
Data collection | |
Diffractometer | Rigaku R-AXIS RAPID diffractometer |
Absorption correction | Gaussian RAPID AUTO (Rigaku, 1999) |
Tmin, Tmax | 0.020, 0.257 |
No. of measured, independent and observed [I > 3σ(I)] reflections | 58521, 7537, 4369 |
Rint | 0.073 |
(sin θ/λ)max (Å−1) | 1.000 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.044, 0.037, 3.20 |
No. of reflections | 4130 |
No. of parameters | 326 |
Δρmax, Δρmin (e Å−3) | 2.00, −1.85 |
Absolute structure | Flack (1983) |
Absolute structure parameter | 0.097 (8) |
Computer programs: RAPID AUTO (Rigaku, 1999), RAPID AUTO, SHELXS97 (Sheldrick, 1997), CRYLSQ in Xtal3.4 (Hall et al., 1995), ATOMS (Dowty, 1999), BONDLA and CIFIO in Xtal3.4.
Mg1—F2 | 1.931 (5) | Mg4—F13 | 1.921 (5) |
Mg1—F10 | 1.950 (5) | Mg4—F14 | 1.946 (5) |
Mg1—F1 | 1.978 (5) | Mg4—F10 | 1.973 (5) |
Mg1—F22 | 1.980 (5) | Mg4—F22 | 1.999 (6) |
Mg1—F4 | 1.985 (5) | Mg4—F16 | 2.012 (5) |
Mg1—F3 | 1.994 (5) | Mg4—F15 | 2.028 (5) |
Mg2—F4 | 1.929 (5) | Mg5—F16 | 1.934 (4) |
Mg2—F5 | 1.959 (5) | Mg5—F17 | 1.981 (5) |
Mg2—F11 | 1.969 (4) | Mg5—F11 | 1.989 (5) |
Mg2—F23 | 1.999 (4) | Mg5—F19 | 1.990 (5) |
Mg2—F6 | 2.010 (5) | Mg5—F18 | 2.004 (5) |
Mg2—F7 | 2.041 (5) | Mg5—F23 | 2.013 (5) |
Mg3—F8 | 1.910 (5) | Mg6—F19 | 1.934 (5) |
Mg3—F7 | 1.966 (4) | Mg6—F20 | 1.987 (5) |
Mg3—F24 | 1.981 (5) | Mg6—F12 | 1.989 (4) |
Mg3—F12 | 1.987 (5) | Mg6—F24 | 1.989 (5) |
Mg3—F2 | 2.011 (5) | Mg6—F21 | 2.000 (5) |
Mg3—F9 | 2.025 (5) | Mg6—F14 | 2.040 (5) |
Crystals of the (Sr,Ba)MgF4 solid solution have attracted attention as host materials for optical applications (Banks et al., 1980; Yamaga et al., 2000). The room-temperature structure of the end member, SrMgF4, was reported to have orthorhombic symmetry in the space group Cmcm, with a = 3.917 (2), b = 14.451 (8) and c = 5.637 (3) Å, determined by powder diffraction (Banks et al., 1982). In the present study, however, it was found that the Ce-doped SrMgF4 crystal has a monoclinic superstructure with doubled a and tripled c lengths with respect to the Cmcm unit cell.
The structure of SrMgF4 projected along c, a and b* is shown in Figs. 1, 2 and 3, respectively. The first setting, with the c axis unique, was used to match the 21 axis with those in the Cmcm and Cmc21 modifications. The structure is essentially regarded as the end member (n = 2) of the homologous series AnBnX3n+2 with perovskite-type slabs (Ishizawa et al., 1975), where A is an alkaline, alkaline earth or rare earth element, B is a metal element with octahedral coordination and X is oxygen or a halogen. The perovskite-type slab is composed of corner-sharing MgF6 octahedra and Sr atoms, and is extended infinitely along a and c. Neighbouring slabs are shifted by a/4, corresponding to half the height of an octahedron, as shown in Fig. 1. The rotation of MgF6 octahedra projected along a, as shown in Fig. 2, closely resembles those reported for the Cmc21 modifications of BaZnF4 (von Schnering & Bleckmann, 1968), BaMgF4 (Gingl, 1997) and Ba1 - xSrxMgF4 with x = 0.27 and 0.55 (Kubel et al., 1997).
Although the six octahedra Mg1F6—Mg6F6 are crystallographically independent, they have approximately the same shape. The octahedral rotation occurs in a complicated manner, as shown in Fig. 3. The rotation can be split into three orthogonal components about the a, b* and c axes. All octahedra are rotated by 15–20° about a. Mg1F6 and Mg4F6 are rotated approximately 8° about b*, while the rotation for the other MgF6 octahedra is negligible about b*. Conversely, the rotation about c is negligible for Mg1F6 and Mg4F6, and approximately 8° for the other MgF6 octahedra. The complexity of the octahedral rotation results in the formation of a relatively large unit cell with tripled c and doubled a lengths.
Although there are no constraints among the positional parameters of the six independent Sr atoms, they align almost on a plane perpendicular to a, as shown in Figs. 1 and 3. The Mg1F6 and Mg4F6, Mg2F6 and Mg5F6, and Mg3F6 and Mg6F6 octahedra, respectively, are related by a pseudo-mirror plane formed by the Sr atoms. Since the neighbouring slabs are shifted by half the height of an MgF6 octahedron, these mirrors are local symmetries effective only within every other slab. Such local mirrors in perovskite-type slabs also exist in the monoclinic modifications of La2Ti2O7 (Gasperin, 1975) and Ca2Nb2O7 (Ishizawa et al., 1980), which are the n = 4 members of the AnBnX3n+2 series. The phase transition in BaMgF4 at 1082 K (Bingyi & Banks, 1982) could be the origin of such local mirror symmetries, as is the case for La2Ti2O7 (Ishizawa et al., 1982).
It is appropriate to assume that the prototype structure of BaMgF4 has orthorhombic Cmcm symmetry with unit cell vectors a0 = a/2, b0 = a/2 + 2 b and c0 = c/3. However, the Cmcm structure of SrMgF4 determined at room temperature by powder diffraction (Banks et al., 1982) contains some geometrical problems. In particular, the Mg atoms are shifted, somewhat unusually, from the centre of each coordination octahedron, resulting in a range of Mg—F bond distances, i.e. 1.71 Å × 2, 1.92 Å × 2 and 2.04 Å × 2. The 1.71 Å distances are rather short for MgF6 octahedra, as the effective ionic radius is 1.3 Å for F- and 0.72 Å for Mg2+ (Shannon, 1976). No such problem was observed in this study; all Mg—F distances in the six independent MgF6 octahedra fall within the range 1.91–2.04 Å.
As shown in Fig. 3, the Sr atoms are shifted onto the pseudo-mirror planes to fit in the space formed by the six MgF6 octahedra in a slab and one MgF6 in the neighbouring slab. The Ce dopant supposedly replaces Sr, as the ionic radius of Ce is much closer to Sr than Mg. Therefore, the modulation of the coordination geometry around various Sr sites becomes important for understanding the optical properties of Ce-doped SrMgF4. If we count F atoms with Sr—F distances less than the shortest Sr—Mg distance, there are eight F atoms around Sr1 in the range 2.46–2.80 Å, and three more in the range 2.98–3.36 Å. There is a gap of 0.18 Å between these two groups of bond distances. The coordination number of Sr1 may thus be expressed as 7 + 3 (not 8?). In a similar way, there are seven F (2.45–2.65 Å) plus three F (2.95–3.16 Å) around Sr2, nine F (2.39–2.70 Å) around Sr3, nine F (2.45–2.71 Å) around Sr4, seven F (2.37–2.73 Å) plus three F (3.00–3.38 Å) around Sr5 and ten F (2.43–2.93 Å) around Sr6. Regarding the coordination of Sr3, Sr4 and Sr6, there is no distinct gap in bond distances as seen for Sr1, Sr2 and Sr5.