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The calorimetric and dielectric properties of Pb5Al3F19 in the five phases stable under ambient pressure are correlated with structure for fuller characterization of each phase. The first-order transition between ferroelectric phase V and antiferroelectric phase IV at TV,IV = 260 (5) K exhibits a thermal hysteresis of 135 (5) K on heating, with a maximum atomic displacement Δ(xyz)max = 1.21 (6) Å; the transition from phase IV to ferroelastic phase III at 315 (5) K is also first order but with a thermal hysteresis of 10 (5) K and Δ(xyz)max = 0.92 (7)  Å; that from phase III to paraelastic phase II at 360 (5) K is second order without hysteresis and has Δ(xyz)max = 0.69 (4) Å; and the transition from phase II to paraelectric phase I at 670 (5) K is second or higher order, with Δ(xyz)max = 0.7 (4) Å. The measured entropy change ΔS at TV,IV agrees well with ΔS as derived from the increased configurational energy by Stirling's approximation. For all other phase transitions, 0.5 ≥ ΔS > 0 J mol−1 K−1 is consistent with an entropy change caused primarily by the changes in the vibrational energy. The structure of phase III is determined both by group theoretical/normal mode analysis and by consideration of the structures of phases II, IV and V reported previously; refinement is by simultaneous Rietveld analysis of the X-ray and neutron diffraction powder profiles. The structure of prototypic phase I is predicted on the basis of the atomic arrangement in phases II, III, IV and V. The introduction of 3d electrons into the Pb5Al3F19 lattice disturbs the structural equilibrium, the addition of 0.04% Cr3+ causing significant changes in atomic positions and increasing TIV,III by ∼15 K. Substitution of Al3+ by 20% or more Cr3+ eliminates the potential minima that otherwise stabilize phases IV, III and II.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768103011509/br0115sup1.cif
Contains datablocks Pb5Al3F19/2003/Abrahams_et_al/structure, I

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103011509/br01151Xsup2.rtv
Contains datablock 1X

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103011509/br01152Xsup3.rtv
Contains datablock 2X

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108768103011509/br01153Nsup4.rtv
Contains datablock 3N

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S0108768103011509/br0115sup5.pdf
Tables 1S-13S, Figs. 1S-4S

Computing details top

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
[Figure 9]
[Figure 10]
[Figure 11]
[Figure 12]
[Figure 13]
[Figure 14]
pentalead trialuminum nonadecafluoride top
Crystal data top
Pb5Al3F19V = 1473.39 (4) Å3
Mr = 1477.94Z = 4
Triclinic, I1F(000) = 2480
Hall symbol: -I 1Dx = 6.663 (1) Mg m3
Dm = 6.66 (5) Mg m3
Dm measured by phase IV, by immersion in bromobenzene
a = 14.2624 (2) Å? radiation, λ = ? Å
b = 14.2808 (2) ÅT = 320 K
c = 7.2340 (1) ÅParticle morphology: plate like
α = 90.001 (10)°colourless
β = 90.509 (1)°?, ? × ? × ? mm
γ = 90.001 (10)°
Data collection top
Refinement top
Refinement on Inet146 parameters
Least-squares matrix: full with fixed elements per cycle0 restraints
Rp = 0.0780 constraints
Rwp = 0.112Weighting scheme based on measured s.u.'s
Rexp = 0.049(Δ/σ)max = 0.05
χ2 = 5.290Background function: Polynomial of order 5 for each dataset.
? data pointsPreferred orientation correction: none
Profile function: pseudo-Voigt
Crystal data top
Pb5Al3F19β = 90.509 (1)°
Mr = 1477.94γ = 90.001 (10)°
Triclinic, I1V = 1473.39 (4) Å3
a = 14.2624 (2) ÅZ = 4
b = 14.2808 (2) Å? radiation, λ = ? Å
c = 7.2340 (1) ÅT = 320 K
α = 90.001 (10)°?, ? × ? × ? mm
Data collection top
Refinement top
Rp = 0.078? data points
Rwp = 0.112146 parameters
Rexp = 0.0490 restraints
χ2 = 5.290
Special details top

Experimental. Pb5 Al3 F19 melts incongruently at 825 (5) K, the thermal limit of crystalline stability.

Geometry. atomic displacements at the phase transition from phase III to phase II are < or = 0.33 Å by Pb, < or = 0.37 Å by Al and < or = 0.69 Å by F; at the phase transition to phase IV, the atomic displacements are < or = 0.53 Å by Pb, < or 0.49 Å by Al and < or = 0.92 Å by F.

Refinement. Simultaneous refinement of dataset 1, dataset 2 and dataset 3

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Pb10.2603 (2)0.4174 (2)0.5038 (6)0.030 (1)*
Pb20.4124 (5)0.2633 (5)0.4920 (3)0.027 (2)*
Pb30.2222 (3)0.0623 (3)0.4967 (7)0.034 (2)*
Pb40.0610 (3)0.2110 (3)0.5001 (5)0.025 (5)*
Pb50.0023 (5)0.4772 (2)0.2557 (14)0.052 (1)*
Al10.1519 (14)0.3193 (13)0.010 (3)0.007 (1)*
Al20.6925 (13)0.1735 (13)0.021 (3)0.007 (1)*
Al30.0044 (17)0.0128 (13)0.245 (3)0.007 (1)*
F10.2878 (13)0.1155 (13)0.681 (3)0.027 (1)*
F20.6116 (16)0.2637 (17)0.339 (3)0.027 (1)*
F30.2606 (14)0.6116 (14)0.349 (3)0.012 (1)*
F40.2519 (14)0.3867 (15)0.333 (2)0.012 (1)*
F50.5735 (13)0.2107 (13)0.149 (2)0.012 (1)*
F60.4092 (12)0.2165 (15)0.305 (3)0.027 (1)*
F70.1895 (13)0.4066 (14)0.175 (3)0.027 (1)*
F80.0912 (11)0.2937 (13)0.687 (3)0.012 (1)*
F90.0391 (13)0.3871 (14)0.045 (2)0.027 (1)*
F100.6078 (11)0.0683 (10)0.007 (3)0.012 (1)*
F110.2524 (15)0.2458 (13)0.055 (2)0.027 (1)*
F120.7357 (10)0.2641 (11)0.015 (3)0.012 (1)*
F130.000000.000000.500000.039 (2)*
F140.000000.000000.000000.039 (2)*
F150.1171 (14)0.0421 (14)0.254 (3)0.025 (1)*
F160.1273 (14)0.0583 (14)0.270 (3)0.025 (1)*
F170.0565 (15)0.1069 (16)0.711 (3)0.025 (1)*
F180.0588 (14)0.1055 (15)0.740 (3)0.025 (1)*
F190.1284 (15)0.5927 (14)0.037 (2)0.024 (1)*
F200.5811 (13)0.1257 (13)0.005 (3)0.024 (1)*
Geometric parameters (Å, º) top
Al1—F1i1.78 (3)Al2—F8i2.12 (4)
Al1—F2ii1.71 (4)Al2—F101.94 (3)
Al1—F6i1.80 (3)Al2—F121.43 (3)
Al1—F71.90 (3)Al3—F131.85 (3)
Al1—F91.87 (4)Al3—F141.78 (3)
Al1—F111.83 (4)Al3—F151.66 (4)
Al2—F3iii1.81 (4)Al3—F162.14 (4)
Al2—F4i1.60 (4)Al3—F17iv1.89 (4)
Al2—F52.01 (4)Al3—F18iv1.61 (4)
F1i—Al1—F2ii95 (1)F4i—Al2—F12106 (1)
F1i—Al1—F6i164 (3)F5—Al2—F8i72 (1)
F1i—Al1—F791 (1)F5—Al2—F1074 (1)
F1i—Al1—F994 (1)F5—Al2—F1298 (2)
F1i—Al1—F1195 (1)F8i—Al2—F1071 (1)
F2ii—Al1—F6i99 (1)F8i—Al2—F1294 (1)
F2ii—Al1—F7175 (4)F10—Al2—F12165 (2)
F2ii—Al1—F988 (1)F13—Al3—F14168 (2)
F2ii—Al1—F1191 (2)F13—Al3—F1592 (1)
F6i—Al1—F775 (1)F13—Al3—F1681 (1)
F6i—Al1—F980 (1)F13—Al3—F17iv76 (1)
F6i—Al1—F1191 (1)F13—Al3—F18iv89 (1)
F7—Al1—F990 (1)F14—Al3—F1595 (1)
F7—Al1—F1189 (1)F14—Al3—F1691 (1)
F9—Al1—F11171 (2)F14—Al3—F17iv95 (1)
F3iii—Al2—F4i85 (1)F14—Al3—F18iv98 (1)
F3iii—Al2—F5155 (2)F15—Al3—F16165 (2)
F3iii—Al2—F8i89 (1)F15—Al3—F17iv81 (1)
F3iii—Al2—F1084 (1)F15—Al3—F18iv110 (1)
F3iii—Al2—F12101 (1)F16—Al3—F17iv84 (1)
F4i—Al2—F5106 (2)F16—Al3—F18iv84 (1)
F4i—Al2—F8i165 (9)F17iv—Al3—F18iv163 (2)
F4i—Al2—F1089 (1)
Symmetry codes: (i) x+1/2, y+1/2, z+1/2; (ii) x1/2, y+1/2, z1/2; (iii) x+1/2, y1/2, z1/2; (iv) x, y, z+1.

Experimental details

Crystal data
Chemical formulaPb5Al3F19
Mr1477.94
Crystal system, space groupTriclinic, I1
Temperature (K)320
a, b, c (Å)14.2624 (2), 14.2808 (2), 7.2340 (1)
α, β, γ (°)90.001 (10), 90.509 (1), 90.001 (10)
V3)1473.39 (4)
Z4
Radiation type?, λ = ? Å
Specimen shape, size (mm)?, ? × ? × ?
Data collection
Diffractometer?
Specimen mounting?
Data collection mode?
Scan method?
2θ values (°)2θmin = ? 2θmax = ? 2θstep = ?
Refinement
R factors and goodness of fitRp = 0.078, Rwp = 0.112, Rexp = 0.049, χ2 = 5.290
No. of data points?
No. of parameters146

 

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