_{2}BeF

_{4}, has been analysed by the Rietveld method on neutron diffraction patterns collected at 1.5, 50, 100, 150, 200 and 300 K, with the aim of detecting low-temperature instabilities. Atomic parameters based on the isomorphic β-K

_{2}SO

_{4}crystal in the paraelectric phase were used as the starting model at room temperature; no evidence for any phase transition has been detected at lower temperature. The structure was determined in the orthorhombic space group

*Pnma*. All the atoms (except one F atom) occupy sites with

*m*symmetry. We have compared the structure with those of other compounds of the β-K

_{2}SO

_{4}family, at room temperature, in order to gain insight into their observed instabilities. The irregular coordination of the cations may indicate stereochemical activity of the Tl

^{I}lone pair but does not indicate a possible structural instability.

### Supporting information

Crystallographic Information File (CIF) https://doi.org/10.1107/S010827010503249X/fa1150sup1.cif | |

Rietveld powder data file (CIF format) https://doi.org/10.1107/S010827010503249X/fa1150_I_300Ksup2.rtv | |

Rietveld powder data file (CIF format) https://doi.org/10.1107/S010827010503249X/fa1150_I_200Ksup3.rtv | |

Rietveld powder data file (CIF format) https://doi.org/10.1107/S010827010503249X/fa1150_I_150Ksup4.rtv | |

Rietveld powder data file (CIF format) https://doi.org/10.1107/S010827010503249X/fa1150_I_100Ksup5.rtv | |

Rietveld powder data file (CIF format) https://doi.org/10.1107/S010827010503249X/fa1150_I_50Ksup6.rtv | |

Rietveld powder data file (CIF format) https://doi.org/10.1107/S010827010503249X/fa1150_I_1.5Ksup7.rtv |

Tl_{2}BeF_{4} was obtained *via* the reaction BeF_{2}(*s*) + H_{2}F_{2}(aq) + Tl_{2}CO_{3}(*s*) → Tl_{2}BeF_{4} + CO_{2} + H_{2}O. BeF_{2}, H_{2}F_{2} (48%) and Tl_{2}CO_{3} were analytical grade. After completion of the reaction at pH 7, the sample was slowly evaporated at room temperature. After a few days, a polycrystalline powder was obtained. The sample was not evaporated to dryness in order to avoid possible contamination. The polycrystalline powder was filtered and dried. Thermal analyses were carried out on a Perkin–Elmer differential scanning calorimeter Pyris I-DSC. The sample was measured in the temperature range 98–293 K, with a warming rate of 10 K min^{−1} and a total scale sensitivity of 0.1 mW. The sample mass was 27.76 mg. This analysis showed no thermal anomaly. The high-resolution neutron powder diffractometer 3 T2 at the Orphée reactor of Laboratoire Léon Brillouin (Saclay, France) was used for data collection with high direct space resolution (λ = 1.2251 Å, Q_{max} = 9.2 Å^{−1}). A helium cryostat was used in order to keep the sample at the correct temperature during the diffraction experiments. We present the data collected at 1.5, 50, 100, 150, 200 and 300 K.

Rietveld refinement of the six powder diffraction patterns was carried out with the program *FULLPROF* (Rodríguez-Carvajal, 2005) and the visualization of the results was performed using the program *WINPLOTR* (Roisnel & Rodríguez-Carvajal, 2005). The experimental profiles were all modelled using a pseudo-Voigt profile shape function, with five adjustable parameters (*U*, *V*, *W*, η and *X*); initial values were obtained from the instrumental resolution parameters. After preliminary refinements to establish the scale factor, zero point displacement, cell parameters and profile parameters, several cycles were performed to refine the atomic positions and isotropic displacement parameters. The starting values for the atomic positions were those of the β-K_{2}SO_{4} structure, in space group *Pnma*. Space group *Pn2*_{1}*a* was also examined, without any improvement. Owing to the poor values obtained for the agreement factors and the modulated residuals that remained after the refinements, it was necessary to apply a Fourier filtering treatment, in order to model the background and to improve the results. This can be justified because from the modulated residues it has been possible to calculate the radial distribution function of other fluoroberyllates, because of the coexistence of an amorphous phase with the crystalline material (da Silva *et al.*, 2005).

For all compounds, cell refinement: FULLPROF (Rodríguez-Carvajal, 2005); program(s) used to refine structure: FULLPROF; molecular graphics: Diamond (Brandenburg & Berndt, 1999); software used to prepare material for publication: FULLPROF.

Tl_{2}BeF_{4} | V = 476.39 (2) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | D_{x} = 6.884 Mg m^{−}^{3} |

Hall symbol: -P 2ac 2n | Neutron radiation, λ = 1.2251 Å |

a = 7.7238 (2) Å | T = 300 K |

b = 5.90226 (17) Å | white |

c = 10.4499 (3) Å | cylinder, 50 × 10 mm |

3T2 Line diffractometer | Data collection mode: transmission |

Radiation source: nuclear reactor | Scan method: step |

Ge 335 monochromator | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Specimen mounting: vanadium can |

Refinement on I_{net} | Excluded region(s): 0° to 10°; no reflection region with a complex background shape |

Least-squares matrix: full with fixed elements per cycle | Profile function: pseudo-Voigt |

R_{p} = 0.036 | 35 parameters |

R_{wp} = 0.048 | 0 restraints |

R_{exp} = 0.076 | Weighting scheme based on measured s.u.'s |

R_{Bragg} = 0.075 | (Δ/σ)_{max} = 0.01 |

R(F) = 0.055 | Background function: Fourier filter |

χ^{2} = 0.395 | Preferred orientation correction: Not used |

2384 data points |

Tl_{2}BeF_{4} | V = 476.39 (2) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | Neutron radiation, λ = 1.2251 Å |

a = 7.7238 (2) Å | T = 300 K |

b = 5.90226 (17) Å | cylinder, 50 × 10 mm |

c = 10.4499 (3) Å |

3T2 Line diffractometer | Scan method: step |

Specimen mounting: vanadium can | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Data collection mode: transmission |

R_{p} = 0.036 | χ^{2} = 0.395 |

R_{wp} = 0.048 | 2384 data points |

R_{exp} = 0.076 | 35 parameters |

R_{Bragg} = 0.075 | 0 restraints |

R(F) = 0.055 |

^{2}) top

x | y | z | U_{iso}*/U_{eq} | ||

Tl1 | 0.1679 (6) | 0.25000 | 0.0901 (5) | 0.0299 (13)* | |

Tl2 | −0.0078 (6) | 0.25000 | 0.6943 (4) | 0.0282 (13)* | |

Be1 | 0.2343 (6) | 0.25000 | 0.4195 (5) | 0.0211 (12)* | |

F1 | 0.3021 (7) | 0.0370 (9) | 0.3517 (5) | 0.0401 (16)* | |

F2 | 0.0355 (10) | 0.25000 | 0.4167 (9) | 0.045 (2)* | |

F3 | 0.2997 (11) | 0.25000 | 0.5575 (8) | 0.041 (2)* |

Be1—F1 | 1.535 (6) | Tl1—F3^{ii} | 2.9812 (14) |

Be1—F2 | 1.536 (9) | Tl1—F3^{vii} | 2.9812 (14) |

Be1—F3 | 1.528 (10) | Tl2—F1^{viii} | 2.875 (7) |

Tl1—F1 | 3.182 (7) | Tl2—F1^{ix} | 2.846 (6) |

Tl1—F1^{i} | 3.152 (7) | Tl2—F1^{x} | 2.875 (7) |

Tl1—F1^{ii} | 3.022 (7) | Tl2—F1^{xi} | 2.846 (6) |

Tl1—F1^{iii} | 3.022 (7) | Tl2—F2 | 2.920 (10) |

Tl1—F1^{iv} | 3.182 (7) | Tl2—F2^{xii} | 3.178 (4) |

Tl1—F1^{v} | 3.152 (7) | Tl2—F2^{viii} | 3.178 (4) |

Tl1—F2 | 3.563 (11) | Tl2—F3 | 2.772 (10) |

Tl1—F2^{vi} | 2.840 (9) | Tl2—F3^{xiii} | 2.990 (9) |

Tl1—F3^{i} | 3.235 (10) | ||

F1—Be1—F1^{iv} | 110.0 (3) | F1—Be1—F3 | 108.8 (2) |

F1—Be1—F2 | 109.4 (2) | F2—Be1—F3 | 110.4 (5) |

Symmetry codes: (i) x−1/2, −y+1/2, −z+1/2; (ii) −x+1/2, −y, z−1/2; (iii) −x+1/2, y+1/2, z−1/2; (iv) x, −y+1/2, z; (v) x−1/2, y, −z+1/2; (vi) x+1/2, −y+1/2, −z+1/2; (vii) −x+1/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1; (ix) −x+1/2, −y, z+1/2; (x) −x, −y, −z+1; (xi) −x+1/2, y+1/2, z+1/2; (xii) −x, y−1/2, −z+1; (xiii) x−1/2, −y+1/2, −z+3/2. |

Tl_{2}BeF_{4} | V = 470.03 (2) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | D_{x} = 6.977 Mg m^{−}^{3} |

Hall symbol: -P 2ac 2n | Neutron radiation, λ = 1.2251 Å |

a = 7.69999 (15) Å | T = 200 K |

b = 5.86734 (11) Å | white |

c = 10.4039 (2) Å | cylinder, 50 × 10 mm |

3T2 Line diffractometer | Data collection mode: transmission |

Radiation source: nuclear reactor | Scan method: step |

Ge 335 monochromator | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Specimen mounting: vanadium can |

R_{p} = 0.042 | Profile function: pseudo-Voigt |

R_{wp} = 0.055 | 35 parameters |

R_{exp} = 0.076 | 0 restraints |

R_{Bragg} = 0.072 | Weighting scheme based on measured s.u.'s |

R(F) = 0.047 | (Δ/σ)_{max} = 0.01 |

χ^{2} = 0.526 | Background function: Fourier filter |

2384 data points | Preferred orientation correction: Not used |

Excluded region(s): 0° to 10°; no reflection region with a complex background shape |

Tl_{2}BeF_{4} | V = 470.03 (2) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | Neutron radiation, λ = 1.2251 Å |

a = 7.69999 (15) Å | T = 200 K |

b = 5.86734 (11) Å | cylinder, 50 × 10 mm |

c = 10.4039 (2) Å |

3T2 Line diffractometer | Scan method: step |

Specimen mounting: vanadium can | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Data collection mode: transmission |

R_{p} = 0.042 | χ^{2} = 0.526 |

R_{wp} = 0.055 | 2384 data points |

R_{exp} = 0.076 | 35 parameters |

R_{Bragg} = 0.072 | 0 restraints |

R(F) = 0.047 |

^{2}) top

x | y | z | U_{iso}*/U_{eq} | ||

Tl1 | 0.1667 (4) | 0.25000 | 0.0908 (4) | 0.0216 (10)* | |

Tl2 | −0.0083 (4) | 0.25000 | 0.6944 (3) | 0.0160 (9)* | |

Be1 | 0.2352 (4) | 0.25000 | 0.4199 (4) | 0.0132 (9)* | |

F1 | 0.3044 (5) | 0.0359 (7) | 0.3526 (4) | 0.0278 (11)* | |

F2 | 0.0353 (7) | 0.25000 | 0.4154 (7) | 0.0301 (14)* | |

F3 | 0.3013 (8) | 0.25000 | 0.5597 (6) | 0.0277 (16)* |

Be1—F1 | 1.534 (5) | Tl1—F3^{ii} | 2.9617 (10) |

Be1—F2 | 1.540 (6) | Tl1—F3^{vii} | 2.9617 (10) |

Be1—F3 | 1.541 (7) | Tl2—F1^{viii} | 2.873 (5) |

Tl1—F1 | 3.181 (6) | Tl2—F1^{ix} | 2.826 (5) |

Tl1—F1^{i} | 3.116 (5) | Tl2—F1^{x} | 2.873 (5) |

Tl1—F1^{ii} | 3.001 (5) | Tl2—F1^{xi} | 2.826 (5) |

Tl1—F1^{iii} | 3.001 (5) | Tl2—F2 | 2.922 (8) |

Tl1—F1^{iv} | 3.181 (6) | Tl2—F2^{xii} | 3.155 (3) |

Tl1—F1^{v} | 3.116 (5) | Tl2—F2^{viii} | 3.155 (3) |

Tl1—F2 | 3.525 (8) | Tl2—F3 | 2.765 (7) |

Tl1—F2^{vi} | 2.839 (6) | Tl2—F3^{xiii} | 2.949 (7) |

Tl1—F3^{i} | 3.220 (7) | ||

F1—Be1—F1^{iv} | 110.0 (2) | F1—Be1—F3 | 108.43 (15) |

F1—Be1—F2 | 109.47 (14) | F2—Be1—F3 | 111.0 (4) |

Symmetry codes: (i) x−1/2, −y+1/2, −z+1/2; (ii) −x+1/2, −y, z−1/2; (iii) −x+1/2, y+1/2, z−1/2; (iv) x, −y+1/2, z; (v) x−1/2, y, −z+1/2; (vi) x+1/2, −y+1/2, −z+1/2; (vii) −x+1/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1; (ix) −x+1/2, −y, z+1/2; (x) −x, −y, −z+1; (xi) −x+1/2, y+1/2, z+1/2; (xii) −x, y−1/2, −z+1; (xiii) x−1/2, −y+1/2, −z+3/2. |

Tl_{2}BeF_{4} | V = 466.82 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | D_{x} = 7.025 Mg m^{−}^{3} |

Hall symbol: -P 2ac 2n | Neutron radiation, λ = 1.2251 Å |

a = 7.69020 (13) Å | T = 150 K |

b = 5.84889 (9) Å | white |

c = 10.37848 (17) Å | cylinder, 50 × 10 mm |

3T2 Line diffractometer | Data collection mode: transmission |

Radiation source: nuclear reactor | Scan method: step |

Ge 335 monochromator | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Specimen mounting: vanadium can |

R_{p} = 0.047 | Profile function: pseudo-Voigt |

R_{wp} = 0.063 | 35 parameters |

R_{exp} = 0.076 | 0 restraints |

R_{Bragg} = 0.075 | Weighting scheme based on measured s.u.'s |

R(F) = 0.047 | (Δ/σ)_{max} = 0.01 |

χ^{2} = 0.682 | Background function: Fourier filter |

2384 data points | Preferred orientation correction: Not used |

Excluded region(s): 0° to 10°; no reflection region with a complex background shape |

Tl_{2}BeF_{4} | V = 466.82 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | Neutron radiation, λ = 1.2251 Å |

a = 7.69020 (13) Å | T = 150 K |

b = 5.84889 (9) Å | cylinder, 50 × 10 mm |

c = 10.37848 (17) Å |

3T2 Line diffractometer | Scan method: step |

Specimen mounting: vanadium can | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Data collection mode: transmission |

R_{p} = 0.047 | χ^{2} = 0.682 |

R_{wp} = 0.063 | 2384 data points |

R_{exp} = 0.076 | 35 parameters |

R_{Bragg} = 0.075 | 0 restraints |

R(F) = 0.047 |

^{2}) top

x | y | z | U_{iso}*/U_{eq} | ||

Tl1 | 0.1664 (4) | 0.25000 | 0.0909 (3) | 0.0170 (8)* | |

Tl2 | −0.0098 (4) | 0.25000 | 0.6941 (3) | 0.0119 (7)* | |

Be1 | 0.2361 (4) | 0.25000 | 0.4200 (3) | 0.0117 (7)* | |

F1 | 0.3062 (5) | 0.0356 (6) | 0.3527 (4) | 0.0218 (9)* | |

F2 | 0.0355 (6) | 0.25000 | 0.4158 (5) | 0.0237 (11)* | |

F3 | 0.3022 (6) | 0.25000 | 0.5606 (5) | 0.0181 (12)* |

Be1—F1 | 1.533 (4) | Tl1—F3^{ii} | 2.9512 (8) |

Be1—F2 | 1.543 (6) | Tl1—F3^{vii} | 2.9512 (8) |

Be1—F3 | 1.545 (6) | Tl2—F1^{viii} | 2.867 (5) |

Tl1—F1 | 3.180 (5) | Tl2—F1^{ix} | 2.820 (5) |

Tl1—F1^{i} | 3.096 (5) | Tl2—F1^{x} | 2.867 (5) |

Tl1—F1^{ii} | 2.991 (5) | Tl2—F1^{xi} | 2.820 (5) |

Tl1—F1^{iii} | 2.991 (5) | Tl2—F2 | 2.909 (6) |

Tl1—F1^{iv} | 3.180 (5) | Tl2—F2^{xii} | 3.145 (2) |

Tl1—F1^{v} | 3.096 (5) | Tl2—F2^{viii} | 3.145 (2) |

Tl1—F2 | 3.519 (6) | Tl2—F3 | 2.771 (6) |

Tl1—F2^{vi} | 2.839 (6) | Tl2—F3^{xiii} | 2.928 (6) |

Tl1—F3^{i} | 3.212 (6) | ||

F1—Be1—F1^{iv} | 109.74 (19) | F1—Be1—F3 | 108.33 (15) |

F1—Be1—F2 | 109.79 (14) | F2—Be1—F3 | 110.8 (3) |

Symmetry codes: (i) x−1/2, −y+1/2, −z+1/2; (ii) −x+1/2, −y, z−1/2; (iii) −x+1/2, y+1/2, z−1/2; (iv) x, −y+1/2, z; (v) x−1/2, y, −z+1/2; (vi) x+1/2, −y+1/2, −z+1/2; (vii) −x+1/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1; (ix) −x+1/2, −y, z+1/2; (x) −x, −y, −z+1; (xi) −x+1/2, y+1/2, z+1/2; (xii) −x, y−1/2, −z+1; (xiii) x−1/2, −y+1/2, −z+3/2. |

Tl_{2}BeF_{4} | V = 463.75 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | D_{x} = 7.072 Mg m^{−}^{3} |

Hall symbol: -P 2ac 2n | Neutron radiation, λ = 1.2251 Å |

a = 7.68265 (11) Å | T = 100 K |

b = 5.83059 (8) Å | white |

c = 10.35278 (15) Å | cylinder, 50 × 10 mm |

3T2 Line diffractometer | Data collection mode: transmission |

Radiation source: nuclear reactor | Scan method: step |

Ge 335 monochromator | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Specimen mounting: vanadium can |

R_{p} = 0.048 | Profile function: pseudo-Voigt |

R_{wp} = 0.062 | 35 parameters |

R_{exp} = 0.076 | 0 restraints |

R_{Bragg} = 0.063 | Weighting scheme based on measured s.u.'s |

R(F) = 0.037 | (Δ/σ)_{max} = 0.01 |

χ^{2} = 0.666 | Background function: Fourier filter |

2384 data points | Preferred orientation correction: Not used |

Excluded region(s): 0° to 10°; no reflection region with a complex background shape |

Tl_{2}BeF_{4} | V = 463.75 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | Neutron radiation, λ = 1.2251 Å |

a = 7.68265 (11) Å | T = 100 K |

b = 5.83059 (8) Å | cylinder, 50 × 10 mm |

c = 10.35278 (15) Å |

3T2 Line diffractometer | Scan method: step |

Specimen mounting: vanadium can | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Data collection mode: transmission |

R_{p} = 0.048 | χ^{2} = 0.666 |

R_{wp} = 0.062 | 2384 data points |

R_{exp} = 0.076 | 35 parameters |

R_{Bragg} = 0.063 | 0 restraints |

R(F) = 0.037 |

^{2}) top

x | y | z | U_{iso}*/U_{eq} | ||

Tl1 | 0.1667 (3) | 0.25000 | 0.0901 (3) | 0.0113 (6)* | |

Tl2 | −0.0108 (3) | 0.25000 | 0.6930 (3) | 0.0079 (6)* | |

Be1 | 0.2364 (3) | 0.25000 | 0.4198 (3) | 0.0082 (6)* | |

F1 | 0.3085 (4) | 0.0336 (5) | 0.3523 (3) | 0.0160 (7)* | |

F2 | 0.0352 (5) | 0.25000 | 0.4139 (5) | 0.0180 (9)* | |

F3 | 0.3016 (5) | 0.25000 | 0.5612 (4) | 0.0126 (9)* |

Be1—F1 | 1.545 (3) | Tl1—F3^{ii} | 2.9407 (6) |

Be1—F2 | 1.547 (4) | Tl1—F3^{vii} | 2.9407 (6) |

Be1—F3 | 1.547 (5) | Tl2—F1^{viii} | 2.861 (4) |

Tl1—F1 | 3.185 (4) | Tl2—F1^{ix} | 2.805 (4) |

Tl1—F1^{i} | 3.086 (4) | Tl2—F1^{x} | 2.861 (4) |

Tl1—F1^{ii} | 2.972 (4) | Tl2—F1^{xi} | 2.805 (4) |

Tl1—F1^{iii} | 2.972 (4) | Tl2—F2 | 2.911 (6) |

Tl1—F1^{iv} | 3.185 (4) | Tl2—F2^{xii} | 3.124 (2) |

Tl1—F1^{v} | 3.086 (4) | Tl2—F2^{viii} | 3.124 (2) |

Tl1—F2 | 3.501 (6) | Tl2—F3 | 2.761 (5) |

Tl1—F2^{vi} | 2.831 (4) | Tl2—F3^{xiii} | 2.925 (5) |

Tl1—F3^{i} | 3.213 (5) | ||

F1—Be1—F1^{iv} | 109.50 (15) | F1—Be1—F3 | 108.17 (11) |

F1—Be1—F2 | 109.90 (11) | F2—Be1—F3 | 111.2 (3) |

Symmetry codes: (i) x−1/2, −y+1/2, −z+1/2; (ii) −x+1/2, −y, z−1/2; (iii) −x+1/2, y+1/2, z−1/2; (iv) x, −y+1/2, z; (v) x−1/2, y, −z+1/2; (vi) x+1/2, −y+1/2, −z+1/2; (vii) −x+1/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1; (ix) −x+1/2, −y, z+1/2; (x) −x, −y, −z+1; (xi) −x+1/2, y+1/2, z+1/2; (xii) −x, y−1/2, −z+1; (xiii) x−1/2, −y+1/2, −z+3/2. |

Tl_{2}BeF_{4} | V = 460.96 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | D_{x} = 7.115 Mg m^{−}^{3} |

Hall symbol: -P 2ac 2n | Neutron radiation, λ = 1.2251 Å |

a = 7.67874 (9) Å | T = 50 K |

b = 5.81248 (7) Å | white |

c = 10.32788 (12) Å | cylinder, 50 × 10 mm |

3T2 Line diffractometer | Data collection mode: transmission |

Radiation source: nuclear reactor | Scan method: step |

Ge 335 monochromator | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Specimen mounting: vanadium can |

R_{p} = 0.053 | Profile function: pseudo-Voigt |

R_{wp} = 0.068 | 35 parameters |

R_{exp} = 0.076 | 0 restraints |

R_{Bragg} = 0.061 | Weighting scheme based on measured s.u.'s |

R(F) = 0.033 | (Δ/σ)_{max} = 0.01 |

χ^{2} = 0.807 | Background function: Fourier filter |

2384 data points | Preferred orientation correction: Not used |

Excluded region(s): 0° to 10°; no reflection region with a complex background shape |

Tl_{2}BeF_{4} | V = 460.96 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | Neutron radiation, λ = 1.2251 Å |

a = 7.67874 (9) Å | T = 50 K |

b = 5.81248 (7) Å | cylinder, 50 × 10 mm |

c = 10.32788 (12) Å |

3T2 Line diffractometer | Scan method: step |

Specimen mounting: vanadium can | 2θ_{min} = 6.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Data collection mode: transmission |

R_{p} = 0.053 | χ^{2} = 0.807 |

R_{wp} = 0.068 | 2384 data points |

R_{exp} = 0.076 | 35 parameters |

R_{Bragg} = 0.061 | 0 restraints |

R(F) = 0.033 |

^{2}) top

x | y | z | U_{iso}*/U_{eq} | ||

Tl1 | 0.1668 (3) | 0.25000 | 0.0895 (2) | 0.0056 (5)* | |

Tl2 | −0.0112 (3) | 0.25000 | 0.6924 (2) | 0.0023 (5)* | |

Be1 | 0.2375 (3) | 0.25000 | 0.4202 (3) | 0.0047 (5)* | |

F1 | 0.3114 (3) | 0.0321 (4) | 0.3532 (3) | 0.0098 (6)* | |

F2 | 0.0366 (4) | 0.25000 | 0.4118 (4) | 0.0082 (7)* | |

F3 | 0.3016 (5) | 0.25000 | 0.5621 (3) | 0.0074 (7)* |

Be1—F1 | 1.551 (3) | Tl1—F3^{ii} | 2.9300 (5) |

Be1—F2 | 1.545 (4) | Tl1—F3^{vii} | 2.9300 (5) |

Be1—F3 | 1.546 (4) | Tl2—F1^{viii} | 2.868 (3) |

Tl1—F1 | 3.202 (3) | Tl2—F1^{ix} | 2.793 (3) |

Tl1—F1^{i} | 3.066 (3) | Tl2—F1^{x} | 2.868 (3) |

Tl1—F1^{ii} | 2.945 (3) | Tl2—F1^{xi} | 2.793 (3) |

Tl1—F1^{iii} | 2.945 (3) | Tl2—F2 | 2.921 (5) |

Tl1—F1^{iv} | 3.202 (3) | Tl2—F2^{xii} | 3.1052 (16) |

Tl1—F1^{v} | 3.066 (3) | Tl2—F2^{viii} | 3.1052 (16) |

Tl1—F2 | 3.476 (5) | Tl2—F3 | 2.753 (4) |

Tl1—F2^{vi} | 2.840 (4) | Tl2—F3^{xiii} | 2.915 (4) |

Tl1—F3^{i} | 3.212 (4) | ||

F1—Be1—F1^{iv} | 109.51 (12) | F1—Be1—F3 | 107.85 (11) |

F1—Be1—F2 | 109.89 (9) | F2—Be1—F3 | 111.8 (3) |

Symmetry codes: (i) x−1/2, −y+1/2, −z+1/2; (ii) −x+1/2, −y, z−1/2; (iii) −x+1/2, y+1/2, z−1/2; (iv) x, −y+1/2, z; (v) x−1/2, y, −z+1/2; (vi) x+1/2, −y+1/2, −z+1/2; (vii) −x+1/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1; (ix) −x+1/2, −y, z+1/2; (x) −x, −y, −z+1; (xi) −x+1/2, y+1/2, z+1/2; (xii) −x, y−1/2, −z+1; (xiii) x−1/2, −y+1/2, −z+3/2. |

Tl_{2}BeF_{4} | V = 459.53 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | D_{x} = 7.137 Mg m^{−}^{3} |

Hall symbol: -P 2ac 2n | Neutron radiation, λ = 1.2251 Å |

a = 7.67735 (10) Å | T = 2 K |

b = 5.80377 (8) Å | white |

c = 10.31316 (13) Å | cylinder, 50 × 10 mm |

3T2 Line diffractometer | Data collection mode: transmission |

Radiation source: nuclear reactor | Scan method: step |

Ge 335 monochromator | 2θ_{min} = 7.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Specimen mounting: vanadium can |

R_{p} = 0.067 | Profile function: pseudo-Voigt |

R_{wp} = 0.085 | 35 parameters |

R_{exp} = 0.093 | 0 restraints |

R_{Bragg} = 0.069 | Weighting scheme based on measured s.u.'s |

R(F) = 0.036 | (Δ/σ)_{max} = 0.01 |

χ^{2} = 0.834 | Background function: Fourier filter |

2364 data points | Preferred orientation correction: Not used |

Excluded region(s): 0° to 10°; no reflection region with a complex background shape |

Tl_{2}BeF_{4} | V = 459.53 (1) Å^{3} |

M = 493.77_{r} | Z = 4 |

Orthorhombic, Pnma | Neutron radiation, λ = 1.2251 Å |

a = 7.67735 (10) Å | T = 2 K |

b = 5.80377 (8) Å | cylinder, 50 × 10 mm |

c = 10.31316 (13) Å |

3T2 Line diffractometer | Scan method: step |

Specimen mounting: vanadium can | 2θ_{min} = 7.30°, 2θ_{max} = 125.45°, 2θ_{step} = 0.05° |

Data collection mode: transmission |

R_{p} = 0.067 | χ^{2} = 0.834 |

R_{wp} = 0.085 | 2364 data points |

R_{exp} = 0.093 | 35 parameters |

R_{Bragg} = 0.069 | 0 restraints |

R(F) = 0.036 |

^{2}) top

x | y | z | U_{iso}*/U_{eq} | ||

Tl1 | 0.1668 (3) | 0.25000 | 0.0906 (2) | 0.0000 (4)* | |

Tl2 | −0.0115 (3) | 0.25000 | 0.6930 (2) | 0.0018 (4)* | |

Be1 | 0.2385 (3) | 0.25000 | 0.4196 (3) | 0.0045 (5)* | |

F1 | 0.3140 (4) | 0.0284 (5) | 0.3536 (3) | 0.0080 (6)* | |

F2 | 0.0361 (4) | 0.25000 | 0.4123 (4) | 0.0061 (7)* | |

F3 | 0.2974 (5) | 0.25000 | 0.5636 (3) | 0.0042 (7)* |

Be1—F1 | 1.566 (3) | Tl1—F3^{ii} | 2.9281 (5) |

Be1—F2 | 1.556 (4) | Tl1—F3^{vii} | 2.9281 (5) |

Be1—F3 | 1.552 (4) | Tl2—F1^{viii} | 2.870 (4) |

Tl1—F1 | 3.208 (4) | Tl2—F1^{ix} | 2.766 (4) |

Tl1—F1^{i} | 3.053 (4) | Tl2—F1^{x} | 2.870 (4) |

Tl1—F1^{ii} | 2.934 (3) | Tl2—F1^{xi} | 2.766 (4) |

Tl1—F1^{iii} | 2.934 (3) | Tl2—F2 | 2.918 (5) |

Tl1—F1^{iv} | 3.208 (4) | Tl2—F2^{xii} | 3.1042 (16) |

Tl1—F1^{v} | 3.053 (4) | Tl2—F2^{viii} | 3.1042 (16) |

Tl1—F2 | 3.466 (5) | Tl2—F3 | 2.721 (4) |

Tl1—F2^{vi} | 2.835 (4) | Tl2—F3^{xiii} | 2.908 (4) |

Tl1—F3^{i} | 3.251 (4) | ||

F1—Be1—F1^{iv} | 110.39 (15) | F1—Be1—F3 | 107.93 (11) |

F1—Be1—F2 | 110.40 (11) | F2—Be1—F3 | 109.7 (3) |

Symmetry codes: (i) x−1/2, −y+1/2, −z+1/2; (ii) −x+1/2, −y, z−1/2; (iii) −x+1/2, y+1/2, z−1/2; (iv) x, −y+1/2, z; (v) x−1/2, y, −z+1/2; (vi) x+1/2, −y+1/2, −z+1/2; (vii) −x+1/2, −y+1, z−1/2; (viii) −x, y+1/2, −z+1; (ix) −x+1/2, −y, z+1/2; (x) −x, −y, −z+1; (xi) −x+1/2, y+1/2, z+1/2; (xii) −x, y−1/2, −z+1; (xiii) x−1/2, −y+1/2, −z+3/2. |

Experimental details

(I_300K) | (I_200K) | (I_150K) | (I_100K) | |

Crystal data | ||||

Chemical formula | Tl_{2}BeF_{4} | Tl_{2}BeF_{4} | Tl_{2}BeF_{4} | Tl_{2}BeF_{4} |

M_{r} | 493.77 | 493.77 | 493.77 | 493.77 |

Crystal system, space group | Orthorhombic, Pnma | Orthorhombic, Pnma | Orthorhombic, Pnma | Orthorhombic, Pnma |

Temperature (K) | 300 | 200 | 150 | 100 |

a, b, c (Å) | 7.7238 (2), 5.90226 (17), 10.4499 (3) | 7.69999 (15), 5.86734 (11), 10.4039 (2) | 7.69020 (13), 5.84889 (9), 10.37848 (17) | 7.68265 (11), 5.83059 (8), 10.35278 (15) |

V (Å^{3}) | 476.39 (2) | 470.03 (2) | 466.82 (1) | 463.75 (1) |

Z | 4 | 4 | 4 | 4 |

Radiation type | Neutron, λ = 1.2251 Å | Neutron, λ = 1.2251 Å | Neutron, λ = 1.2251 Å | Neutron, λ = 1.2251 Å |

µ (mm^{−}^{1}) | ? | ? | ? | ? |

Specimen shape, size (mm) | Cylinder, 50 × 10 | Cylinder, 50 × 10 | Cylinder, 50 × 10 | Cylinder, 50 × 10 |

Data collection | ||||

Diffractometer | 3T2 Line diffractometer | 3T2 Line diffractometer | 3T2 Line diffractometer | 3T2 Line diffractometer |

Specimen mounting | Vanadium can | Vanadium can | Vanadium can | Vanadium can |

Data collection mode | Transmission | Transmission | Transmission | Transmission |

Scan method | Step | Step | Step | Step |

2θ values (°) | 2θ_{min} = 6.30 2θ_{max} = 125.45 2θ_{step} = 0.05 | 2θ_{min} = 6.30 2θ_{max} = 125.45 2θ_{step} = 0.05 | 2θ_{min} = 6.30 2θ_{max} = 125.45 2θ_{step} = 0.05 | 2θ_{min} = 6.30 2θ_{max} = 125.45 2θ_{step} = 0.05 |

Refinement | ||||

R factors and goodness of fit | R_{p} = 0.036, R_{wp} = 0.048, R_{exp} = 0.076, R_{Bragg} = 0.075, R(F) = 0.055, χ^{2} = 0.395 | R_{p} = 0.042, R_{wp} = 0.055, R_{exp} = 0.076, R_{Bragg} = 0.072, R(F) = 0.047, χ^{2} = 0.526 | R_{p} = 0.047, R_{wp} = 0.063, R_{exp} = 0.076, R_{Bragg} = 0.075, R(F) = 0.047, χ^{2} = 0.682 | R_{p} = 0.048, R_{wp} = 0.062, R_{exp} = 0.076, R_{Bragg} = 0.063, R(F) = 0.037, χ^{2} = 0.666 |

No. of data points | 2384 | 2384 | 2384 | 2384 |

No. of parameters | 35 | 35 | 35 | 35 |

(I_50K) | (I_1.5K) | |

Crystal data | ||

Chemical formula | Tl_{2}BeF_{4} | Tl_{2}BeF_{4} |

M_{r} | 493.77 | 493.77 |

Crystal system, space group | Orthorhombic, Pnma | Orthorhombic, Pnma |

Temperature (K) | 50 | 2 |

a, b, c (Å) | 7.67874 (9), 5.81248 (7), 10.32788 (12) | 7.67735 (10), 5.80377 (8), 10.31316 (13) |

V (Å^{3}) | 460.96 (1) | 459.53 (1) |

Z | 4 | 4 |

Radiation type | Neutron, λ = 1.2251 Å | Neutron, λ = 1.2251 Å |

µ (mm^{−}^{1}) | ? | ? |

Specimen shape, size (mm) | Cylinder, 50 × 10 | Cylinder, 50 × 10 |

Data collection | ||

Diffractometer | 3T2 Line diffractometer | 3T2 Line diffractometer |

Specimen mounting | Vanadium can | Vanadium can |

Data collection mode | Transmission | Transmission |

Scan method | Step | Step |

2θ values (°) | 2θ_{min} = 6.30 2θ_{max} = 125.45 2θ_{step} = 0.05 | 2θ_{min} = 7.30 2θ_{max} = 125.45 2θ_{step} = 0.05 |

Refinement | ||

R factors and goodness of fit | R_{p} = 0.053, R_{wp} = 0.068, R_{exp} = 0.076, R_{Bragg} = 0.061, R(F) = 0.033, χ^{2} = 0.807 | R_{p} = 0.067, R_{wp} = 0.085, R_{exp} = 0.093, R_{Bragg} = 0.069, R(F) = 0.036, χ^{2} = 0.834 |

No. of data points | 2384 | 2364 |

No. of parameters | 35 | 35 |

Computer programs: FULLPROF (Rodríguez-Carvajal, 2005), FULLPROF, Diamond (Brandenburg & Berndt, 1999).

_{2}BeF

_{4}at each temperature top

This dataitem was not found in the cif. |

Temperature (K) | Be—F | Tl—F | F—Be—F |

300 | 1.534 (8) | 3.040 (8) | 109.47 (27) |

200 | 1.537 (6) | 3.022 (6) | 109.47 (20) |

150 | 1.539 (5) | 3.014 (5) | 109.47 (18) |

100 | 1.546 (4) | 3.004 (4) | 109.47 (14) |

50 | 1.548 (4) | 2.997 (5) | 109.46 (13) |

1.5 | 1.560 (4) | 2.996 (5) | 109.46 (14) |

This dataitem was not found in the cif. |

We are interested in the large family of ferroelectric compounds having the general formula

A_{2}BX_{4}, with the β-K_{2}SO_{4}structure in the paraelectric phase (space groupPnma,Z= 4). The most widely studied compounds are K_{2}SeO_{4}, (NH_{4})_{2}SO_{4}and (NH_{4})_{2}BeF_{4}; they exhibit interesting properties, related to a low-temperature phase transition, which are strikingly different. For instance, the polar axis of (NH_{4})_{2}BeF_{4}is thebaxis, while that of (NH_{4})_{2}SO_{4}(Hoshinoet al., 1958) and K_{2}SeO_{4}is thecaxis (Yamadaet al., 1984). (NH_{4})_{2}SO_{4}has the ferroelectric phase transition atT_{c}= 223.5 K (Schlemper & Hamilton, 1966), while an incommensurate phase is observed in (NH_{4})_{2}BeF_{4}betweenT_{i}= 182.9 K andT_{c}= 177.2 K (Srivastavaet al., 1999), and in K_{2}SeO_{4}betweenT_{i}= 192.5 K andT_{c}= 93 K (Aiki & Hukuda, 1969). A review by Fabry & Pérez-Mato (1994) reported that the instability of a large number ofA_{2}BX_{4}compounds is related to the behaviour of the 11-coordinate cation, rather than to the nine-coordinate cation, and especially to the bond strength of the shorter cation–anion contact parallel to the pseudo-hexagonalaaxis. A detailed and comparative study of this type of compound is necessary. Alkali metal fluoroberyllates have been exceptional cases ofA_{2}BX_{4}-type compounds in the past, but we have recently studied them by neutron powder diffraction with refinement inPnmaat room temperature and 1.5 K (da Silvaet al., 2005). Moreover, thallium oxysalts, such as Tl_{2}SO_{4}, Tl_{2}CrO_{4}and Tl_{2}SeO_{4}, have also been studied; the last of these undergoes a phase transition at 72 K (Frieseet al., 2004). The different behaviour of thallium compounds with respect to other β-K_{2}SO_{4}compounds is a result of the stereoactivity of the 6s^{2}lone pair in the Tl^{I}cation (Fabry & Breczewsky, 1993).The aim of the present work is to compare the structure of Tl

_{2}BeF_{4}with the rest of this class of compounds to assess the role of the cations in the structural instability. The correct crystal structure of Tl_{2}BeF_{4}has not been reported previously [only the cell parameters, by Arendet al.(1980)] and a structural phase transition has never been observed. We have measured the neutron powder diffraction patterns of Tl_{2}BeF_{4}at room temperature and lower temperatures down to 1.5 K and we have refined the crystal structure using the Rietveld method in space groupPnmafor all temperatures. The fitted diffraction profile at room temperature is shown in Fig. 1 and the variation of the unit cell volume with temperature is shown in Fig. 2. From DSC analysis and from Fig. 2, no thermal anomaly is observed. The structure of Tl_{2}BeF_{4}consists of isolated BeF_{4}^{2+}tetrahedra, with Tl^{+}ions distributed between them. The cations are placed in two different cavities — one of them, within a slightly distorted bipyramidal hole, remains 11-coordinate, while the other cation, within the distorted octahedral hole, is surrounded by nine F atoms. As in other fluoroberyllates (da Silvaet al., 2005) and in thallium selenate (Frieseet al., 2004), the average Be—F bond length of the fluoroberyllate anion increases at low temperature. At variance with other compounds showing structural instability (González-Silgoet al., 1997; Solanset al., 1998), (1) we do not observe any significant rotation of the tetrahedra around thebaxis, so that the environment of the cations is not changed with temperature, and (2) the bond valence sum (Brown, 1992) at both the Tl1 and the Tl2 sites is close to 1 v.u. (valence units) for the entire temperature range. Otherwise, the five F atoms nearest to Tl1 are at distances less than 3.1 Å and lie on the same side of this cation (see Fig. 3a), thus indicating the stereoactivity of the Tl1 lone pair, as in other thallium compounds (Fabry & Breczewsky, 1993); this situation is maintained at lower temperatures. With respect to the Tl2 environment, the stereoactivity of the lone pair is less clear, although a tendency is observed at lower temperature; at 1.5 K, the three F atoms nearest this cation are at distances that are 0.1 Å shorter than the other Tl2—F contacts and lie approximately on the same side of Tl (Fig. 3b).