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The single-crystal investigation of the self-hosting σ-structure of β-tantalum (β-Ta) at 120 K (low-temperature, LT, structure) and at 293 K (RT-I before cooling and RT-II after cooling and rewarming; RT represents room temperature) shows that this structure is indeed a specific two-component composite where the components have the same (or an integer multiple) lattice constants but different space groups. The space groups of both host (H) and guest (G) components cause systematic absences, which result from their intersection. The highest symmetry of a σ-structure can be described as [H: P42/mnm; G: P4/mbm (cG = 0.5cH); composite: P42/mnm]. A complete analysis of possible symmetries is presented in the Appendix. In β-Ta, two components modify their symmetry during the thermal process 293 K (RT-I) ⇒ 120 K (LT) ⇒ 293 K (RT-II): [H: P\bar 421m; G: P\bar 421m; composite: P\bar 421m] ⇒ [H: P\bar 4, G: P4/mbm (cG = 0.5cH), composite: P\bar 4] ⇒ [H: P\bar 421m, G: P4/mbm (cG = 0.5cH), composite: P\bar 421m]. Thus, the phase transition is reversible with respect to H and irreversible with respect to G.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768103009005/sn0032sup1.cif
Contains datablocks global, I, II

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768103009005/sn0032Isup2.hkl
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768103009005/sn0032IIsup3.hkl
Contains datablock II

Computing details top

For both compounds, program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

(I) top
Crystal data top
Ta30Z = 1
Mr = 5428.4F(000) = 2190
Tetragonal, P421mDx = 16.316 (3) Mg m3
a = 10.201 (1) ÅMo Kα radiation, λ = 0.71073 Å
c = 5.3075 (5) ŵ = 147.75 mm1
V = 552.30 (9) Å3
Data collection top
Oxford Instruments CCD
diffractometer
Rint = 0.094
Absorption correction: for a sphere
(Jana2000; Petricek and Dusek, 2000)
θmax = 28.1°, θmin = 3.8°
Tmin = 0.028, Tmax = 0.050h = 1313
5271 measured reflectionsk = 1113
683 independent reflectionsl = 66
474 reflections with I > 3σ(I)
Refinement top
Refinement on FWeighting scheme based on measured s.u.'s w = 1/σ2(F)
R[F2 > 2σ(F2)] = 0.058(Δ/σ)max = 0.001
wR(F2) = 0.040Δρmax = 24.22 e Å3
S = 3.93Δρmin = 11.35 e Å3
474 reflectionsExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
24 parametersExtinction coefficient: 0.000648
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ta10.500.2470.0050 (15)
Ta20.7611 (3)0.0674 (3)0.24630.005
Ta30.0343 (3)0.1286 (3)0.24150.0041 (9)
Ta40.1043 (3)0.6043 (3)0.2450.0046 (10)
Ta50.81862 (16)0.31863 (16)00.0058 (5)
Ta60.81862 (16)0.31863 (16)0.50.0058 (5)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ta10.0069 (19)0.0069 (19)0.001 (4)0.001 (2)00
Ta20.0055880.0071590.0022180.0002160.000340.003739
Ta30.0078 (14)0.0037 (15)0.0007 (17)0.0015 (10)0.000 (5)0.001 (5)
Ta40.0066 (14)0.0066 (14)0.001 (2)0.0002 (17)0.001 (6)0.001 (6)
Ta50.0076 (6)0.0076 (6)0.0022 (11)0.0022 (14)00
Ta60.0076 (6)0.0076 (6)0.0022 (11)0.0022 (14)00
Bond lengths (Å) top
Ta1—Ta1i5.3075Ta2—Ta4viii5.646 (5)
Ta1—Ta1ii5.3075Ta2—Ta52.936 (3)
Ta1—Ta2i5.9813 (15)Ta2—Ta5ii4.786 (2)
Ta1—Ta22.751 (3)Ta2—Ta5iii4.841 (3)
Ta1—Ta2ii5.9747 (15)Ta2—Ta5xxxviii5.950 (4)
Ta1—Ta2iii5.680 (3)Ta2—Ta5xl5.967 (4)
Ta1—Ta2iv5.713 (3)Ta2—Ta5xiii2.969 (3)
Ta1—Ta2v5.680 (3)Ta2—Ta5xiv4.807 (2)
Ta1—Ta2vi5.713 (3)Ta2—Ta6i4.754 (2)
Ta1—Ta2vii5.9813 (15)Ta2—Ta62.953 (3)
Ta1—Ta2viii2.751 (3)Ta2—Ta6iv4.851 (3)
Ta1—Ta2ix5.9747 (15)Ta2—Ta6xxxix5.959 (4)
Ta1—Ta2x5.9813 (15)Ta2—Ta6xl5.975 (4)
Ta1—Ta2xi2.751 (3)Ta2—Ta6xiii4.774 (2)
Ta1—Ta2xii5.9747 (15)Ta2—Ta6xiv2.986 (3)
Ta1—Ta2xiii5.680 (3)Ta3—Ta3i5.3075
Ta1—Ta2xiv5.713 (3)Ta3—Ta3ii5.3075
Ta1—Ta2xv5.680 (3)Ta3—Ta3xxi3.203 (3)
Ta1—Ta2xvi5.713 (3)Ta3—Ta3xxii3.349 (3)
Ta1—Ta2xvii5.9813 (15)Ta3—Ta3xliv5.962 (2)
Ta1—Ta2xviii2.751 (3)Ta3—Ta3xxv2.716 (5)
Ta1—Ta2xix5.9747 (15)Ta3—Ta3xlv5.962 (2)
Ta1—Ta34.929 (3)Ta3—Ta3xi4.863 (5)
Ta1—Ta3xx5.606 (3)Ta3—Ta3xlvi3.203 (3)
Ta1—Ta3xxi4.604 (3)Ta3—Ta3xlvii3.349 (3)
Ta1—Ta3xxii4.674 (3)Ta3—Ta3xlviii5.852 (5)
Ta1—Ta3xxiii4.604 (3)Ta3—Ta4xlix5.992 (2)
Ta1—Ta3xxiv4.674 (3)Ta3—Ta4xxxii2.816 (5)
Ta1—Ta3xxv5.606 (3)Ta3—Ta4xxxiii5.090 (4)
Ta1—Ta3viii4.929 (3)Ta3—Ta4xxxiv5.164 (4)
Ta1—Ta3xxvi5.606 (3)Ta3—Ta4l5.096 (4)
Ta1—Ta3xi4.929 (3)Ta3—Ta4li5.170 (4)
Ta1—Ta3xxvii4.604 (3)Ta3—Ta4lii5.532 (5)
Ta1—Ta3xxviii4.674 (3)Ta3—Ta4xxv5.054 (5)
Ta1—Ta3xxix4.604 (3)Ta3—Ta5liii3.200 (3)
Ta1—Ta3xxx4.674 (3)Ta3—Ta5liv4.980 (2)
Ta1—Ta3xviii4.929 (3)Ta3—Ta5iii3.216 (3)
Ta1—Ta3xxxi5.606 (3)Ta3—Ta5iv4.991 (2)
Ta1—Ta4xxxii5.708 (3)Ta3—Ta5viii4.971 (4)
Ta1—Ta4xxxiii3.0141 (16)Ta3—Ta5lv5.974 (4)
Ta1—Ta4xxxiv3.0875 (16)Ta3—Ta5lvi4.960 (4)
Ta1—Ta4xxxv3.0141 (16)Ta3—Ta6lvii4.908 (2)
Ta1—Ta4xxxvi3.0875 (16)Ta3—Ta6liii3.237 (3)
Ta1—Ta4xxxvii5.708 (3)Ta3—Ta6iii4.918 (2)
Ta1—Ta54.7799 (15)Ta3—Ta6iv3.253 (3)
Ta1—Ta5iii2.9267 (14)Ta3—Ta6viii4.995 (4)
Ta1—Ta5iv4.7768 (9)Ta3—Ta6lv5.994 (4)
Ta1—Ta5viii4.7799 (15)Ta3—Ta6lviii4.984 (4)
Ta1—Ta5xiii2.9267 (14)Ta4—Ta4i5.3075
Ta1—Ta5xiv4.7768 (9)Ta4—Ta4ii5.3075
Ta1—Ta64.7887 (15)Ta4—Ta4lii3.010 (5)
Ta1—Ta6iii4.7504 (9)Ta4—Ta5lix3.287 (3)
Ta1—Ta6iv2.9409 (14)Ta4—Ta5lx5.017 (2)
Ta1—Ta6viii4.7887 (15)Ta4—Ta5xxi3.354 (3)
Ta1—Ta6xiii4.7504 (9)Ta4—Ta5xxii5.061 (2)
Ta1—Ta6xiv2.9409 (14)Ta4—Ta5viii3.287 (3)
Ta2—Ta2i5.3075Ta4—Ta5ix5.017 (2)
Ta2—Ta2ii5.3075Ta4—Ta6lxi4.975 (2)
Ta2—Ta2xxxviii4.434 (4)Ta4—Ta6lix3.308 (3)
Ta2—Ta2xxxix4.481 (4)Ta4—Ta6xxi5.019 (2)
Ta2—Ta2viii5.502 (5)Ta4—Ta6xxii3.375 (3)
Ta2—Ta2xl5.065 (5)Ta4—Ta6vii4.975 (2)
Ta2—Ta2xi4.740 (5)Ta4—Ta6viii3.308 (3)
Ta2—Ta2xiii4.434 (4)Ta5—Ta5i5.3075
Ta2—Ta2xiv4.481 (4)Ta5—Ta5ii5.3075
Ta2—Ta2xv5.736 (4)Ta5—Ta5iii5.289 (2)
Ta2—Ta2xvi5.772 (4)Ta5—Ta5xxxviii5.289 (2)
Ta2—Ta2xli5.736 (4)Ta5—Ta5lxii5.233 (2)
Ta2—Ta2xlii5.772 (4)Ta5—Ta5xiii5.289 (2)
Ta2—Ta2xvii5.998 (2)Ta5—Ta5xxvii5.289 (2)
Ta2—Ta2xviii2.794 (5)Ta5—Ta6i2.6537
Ta2—Ta2xix5.998 (2)Ta5—Ta62.6537
Ta2—Ta3xx2.856 (5)Ta5—Ta6iii5.918 (2)
Ta2—Ta3xxxiii4.673 (4)Ta5—Ta6iv5.918 (2)
Ta2—Ta3xxxiv4.746 (4)Ta5—Ta6xxxviii5.918 (2)
Ta2—Ta3xxiii4.655 (4)Ta5—Ta6xxxix5.918 (2)
Ta2—Ta3xxiv4.728 (4)Ta5—Ta6lxiii5.868 (2)
Ta2—Ta3viii2.891 (5)Ta5—Ta6lxii5.868 (2)
Ta2—Ta3xi5.684 (5)Ta5—Ta6xiii5.918 (2)
Ta2—Ta3xxvii2.8433 (19)Ta5—Ta6xiv5.918 (2)
Ta2—Ta3xxviii2.9612 (19)Ta5—Ta6xxvii5.918 (2)
Ta2—Ta3xxix5.985 (4)Ta5—Ta6xxviii5.918 (2)
Ta2—Ta3xviii5.604 (5)Ta6—Ta6i5.3075
Ta2—Ta3xxxi4.951 (5)Ta6—Ta6ii5.3075
Ta2—Ta4xliii4.845 (5)Ta6—Ta6iv5.289 (2)
Ta2—Ta4xxxiii4.875 (4)Ta6—Ta6xxxix5.289 (2)
Ta2—Ta4xxxiv4.925 (4)Ta6—Ta6lxii5.233 (2)
Ta2—Ta4xxxv3.082 (2)Ta6—Ta6xiv5.289 (2)
Ta2—Ta4xxxvi3.160 (2)Ta6—Ta6xxviii5.289 (2)
Ta2—Ta4xxxvii4.920 (5)
Symmetry codes: (i) x, y, z1; (ii) x, y, z+1; (iii) y, x+1, z; (iv) y, x+1, z+1; (v) x1/2, y+1/2, z; (vi) x1/2, y+1/2, z+1; (vii) x+1, y, z1; (viii) x+1, y, z; (ix) x+1, y, z+1; (x) y+1/2, x+1/2, z1; (xi) y+1/2, x+1/2, z; (xii) y+1/2, x+1/2, z+1; (xiii) y+1, x1, z; (xiv) y+1, x1, z+1; (xv) x+3/2, y1/2, z; (xvi) x+3/2, y1/2, z+1; (xvii) y+1/2, x1/2, z1; (xviii) y+1/2, x1/2, z; (xix) y+1/2, x1/2, z+1; (xx) x+1, y, z; (xxi) y, x, z; (xxii) y, x, z+1; (xxiii) x+1/2, y+1/2, z; (xxiv) x+1/2, y+1/2, z+1; (xxv) x, y, z; (xxvi) y+1/2, x1/2, z; (xxvii) y+1, x, z; (xxviii) y+1, x, z+1; (xxix) x+1/2, y1/2, z; (xxx) x+1/2, y1/2, z+1; (xxxi) y+1/2, x+1/2, z; (xxxii) x, y+1, z; (xxxiii) y+1, x, z; (xxxiv) y+1, x, z+1; (xxxv) x+1/2, y1/2, z; (xxxvi) x+1/2, y1/2, z+1; (xxxvii) x+1, y1, z; (xxxviii) y+1, x+1, z; (xxxix) y+1, x+1, z+1; (xl) x+2, y, z; (xli) x+3/2, y+1/2, z; (xlii) x+3/2, y+1/2, z+1; (xliii) x+1, y+1, z; (xliv) x, y, z1; (xlv) x, y, z+1; (xlvi) y, x, z; (xlvii) y, x, z+1; (xlviii) y1/2, x+1/2, z; (xlix) x, y+1, z1; (l) x1/2, y1/2, z; (li) x1/2, y1/2, z+1; (lii) x, y1, z; (liii) x1, y, z; (liv) x1, y, z+1; (lv) x+1, y+1, z; (lvi) y, x1, z; (lvii) x1, y, z1; (lviii) y, x1, z+1; (lix) x1, y1, z; (lx) x1, y1, z+1; (lxi) x1, y1, z1; (lxii) x+2, y+1, z; (lxiii) x+2, y+1, z1.
(II) Metal top
Crystal data top
30.0TaDx = 16.417 (1) Mg m3
Mr = 5428.4Synchrotron radiation, λ = 0.70013 Å
Tetragonal, P4Cell parameters from 8379 reflections
a = 10.1815 (5) Åθ = 3.8–30.5°
c = 5.2950 (1) ŵ = 148.66 mm1
V = 548.90 (4) Å3T = 120 K
Z = 1Isometric irregular, silver
F(000) = 21900.02 × 0.02 × 0.02 × 0.02 (radius) mm
Data collection top
MAR345
diffractometer
1708 independent reflections
Radiation source: bending magnet 1 at ESRF1530 reflections with I > 3σ(I)
Si(111) double crystal monochromator with bent second crystal for sagital focusingRint = 0.082
Detector resolution: 6.667 pixels mm-1θmax = 30.5°, θmin = 3.8°
φ–scansh = 1414
Absorption correction: for a spherek = 1414
Tmin = 0.024, Tmax = 0.049l = 77
8379 measured reflections
Refinement top
Refinement on FWeighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
R[F2 > 2σ(F2)] = 0.036(Δ/σ)max = 0.001
wR(F2) = 0.050Δρmax = 11.04 e Å3
S = 1.74Δρmin = 9.89 e Å3
1530 reflectionsExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
72 parametersExtinction coefficient: 0.0009 (3)
Special details top

Experimental. The wavelength was calibrated with a standard Si powder pattern. All reflections were involved in a global scaling procedure to correct for beam decay (the measurements were performed on a synchrotron) and inhomogeneities (in beam, sample mount absorption etc.). No assumptions were made about the sample symmetry were made in the scaling procedure, i.e. only repeated measurements were considered equivalent and Friedel's law was not assumed valid.

Cell parameters were determined in a refinement of cell parameters, setting angles and mosaicity after scaling (Otwinowski & Minor, 1997).

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ta10.500.2548 (5)0.0054 (3)
Ta2a0.75963 (10)0.06646 (7)0.2493 (4)0.0055 (3)
Ta2b0.43251 (8)0.26252 (9)0.2521 (5)0.0056 (3)
Ta3a0.03408 (9)0.12735 (10)0.2519 (5)0.0054 (3)
Ta3b0.37007 (9)0.53527 (9)0.2488 (5)0.0057 (3)
Ta40.10620 (9)0.60509 (9)0.2513 (4)0.0056 (3)
Ta50.81809 (3)0.31809 (3)00.00567 (15)
Ta60.81809 (3)0.31810.50.00567 (15)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ta10.0035 (7)0.0071 (7)0.0056 (3)0.0009 (2)00
Ta2a0.0066 (5)0.0057 (6)0.0040 (6)0.0048 (3)0.0013 (9)0.0010 (9)
Ta2b0.0054 (5)0.0039 (5)0.0075 (6)0.0040 (3)0.0012 (9)0.0006 (8)
Ta3a0.0064 (4)0.0062 (5)0.0036 (5)0.0008 (3)0.0010 (8)0.0010 (9)
Ta3b0.0035 (5)0.0052 (4)0.0083 (7)0.0006 (3)0.0036 (8)0.0006 (9)
Ta40.0068 (5)0.0041 (5)0.0059 (3)0.00047 (16)0.0002 (10)0.0009 (10)
Ta50.0056 (3)0.0062 (3)0.0052 (3)0.00029 (9)00
Ta60.0056 (3)0.0062 (3)0.0052 (3)0.00029 (9)00
Bond lengths (Å) top
Ta1—Ta2a2.7289 (10)Ta2b—Ta6i2.9245 (13)
Ta1—Ta2ai2.7289 (10)Ta2b—Ta6ix2.9739 (13)
Ta1—Ta2b2.7598 (9)Ta3a—Ta3axiv3.274 (3)
Ta1—Ta2bi2.7598 (9)Ta3a—Ta3axv3.242 (3)
Ta1—Ta4ii3.081 (3)Ta3a—Ta3axvi2.6844 (14)
Ta1—Ta4iii3.026 (3)Ta3a—Ta3aiv3.274 (3)
Ta1—Ta4iv3.081 (3)Ta3a—Ta3av3.242 (3)
Ta1—Ta4v3.026 (3)Ta3a—Ta4xvii2.8214 (14)
Ta1—Ta5vi2.9462 (12)Ta3a—Ta5xviii3.2227 (13)
Ta1—Ta5vii2.9462 (12)Ta3a—Ta5vi3.2325 (13)
Ta1—Ta6viii2.9235 (11)Ta3a—Ta6xviii3.2146 (13)
Ta1—Ta6ix2.9235 (11)Ta3a—Ta6viii3.2244 (13)
Ta2a—Ta2bi2.7950 (12)Ta3b—Ta3bii3.271 (3)
Ta2a—Ta3ax2.8622 (14)Ta3b—Ta3biii3.291 (3)
Ta2a—Ta3ai2.8819 (13)Ta3b—Ta3bxiii2.7414 (13)
Ta2a—Ta3axi2.911 (3)Ta3b—Ta3bxix3.271 (3)
Ta2a—Ta3axii2.900 (3)Ta3b—Ta3bxx3.291 (3)
Ta2a—Ta4iv3.109 (3)Ta3b—Ta42.7791 (13)
Ta2a—Ta4v3.103 (3)Ta3b—Ta5xiv3.2106 (14)
Ta2a—Ta52.9430 (12)Ta3b—Ta5i3.2087 (14)
Ta2a—Ta5vii2.9604 (12)Ta3b—Ta6xv3.2157 (14)
Ta2a—Ta62.9461 (12)Ta3b—Ta6i3.2138 (14)
Ta2a—Ta6ix2.9635 (12)Ta4—Ta4xxi3.0424 (13)
Ta2b—Ta3b2.8489 (13)Ta4—Ta5xxii3.3146 (12)
Ta2b—Ta3bii2.888 (3)Ta4—Ta5xiv3.3358 (12)
Ta2b—Ta3biii2.879 (3)Ta4—Ta5i3.3019 (12)
Ta2b—Ta3bxiii2.8773 (13)Ta4—Ta6xxii3.3092 (12)
Ta2b—Ta4ii3.128 (3)Ta4—Ta6xv3.3304 (12)
Ta2b—Ta4iii3.097 (3)Ta4—Ta6i3.2965 (12)
Ta2b—Ta5i2.9347 (13)Ta5—Ta6xxiii2.6475
Ta2b—Ta5vii2.9839 (13)Ta5—Ta62.6475
Symmetry codes: (i) x+1, y, z; (ii) y+1, x, z; (iii) y+1, x, z+1; (iv) y, x, z; (v) y, x, z+1; (vi) y, x+1, z; (vii) y+1, x1, z; (viii) y, x+1, z+1; (ix) y+1, x1, z+1; (x) x+1, y, z; (xi) y+1, x, z; (xii) y+1, x, z+1; (xiii) x+1, y1, z; (xiv) y, x, z; (xv) y, x, z+1; (xvi) x, y, z; (xvii) x, y+1, z; (xviii) x1, y, z; (xix) y, x1, z; (xx) y, x1, z+1; (xxi) x, y1, z; (xxii) x1, y1, z; (xxiii) x, y, z1.
 

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