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Redetermination of the crystal structure of R5Si4 (R = Pr, Nd) from single-crystal X-ray diffraction data

aDepartment of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan, bDepartment of Chemistry, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan, and cThe Institute for Solid State Physics, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
*Correspondence e-mail: watanuki-ryuta-sm@ynu.ac.jp

Edited by P. Roussel, ENSCL, France (Received 20 January 2020; accepted 28 February 2020; online 10 March 2020)

The crystal structures of praseodymium silicide (5/4), Pr5Si4, and neodymium silicide (5/4), Nd5Si4, were redetermined using high-quality single-crystal X-ray diffraction data. The previous structure reports of Pr5Si4 were only based on powder X-ray diffraction data [Smith et al. (1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]). Acta Cryst. 22 940–943; Yang et al. (2002b[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002b). J. Alloys Compd. 339, 189-194.]). J. Alloys Compd. 339, 189–194; Yang et al., (2003[Yang, H. F., Rao, G. H., Liu, G. Y., Ouyang, Z. W., Liu, W. F., Feng, X. M., Chu, W. G. & Liang, J. K. (2003). J. Alloys Compd. 263, 146-153.]). J. Alloys Compd. 263, 146–153]. On the other hand, the structure of Nd5Si4 has been determined from powder data [neutron; Cadogan et al., (2002[Cadogan, J. M., Ryan, D. H., Altounian, Z., Wang, H. B. & Swainson, I. P. (2002). J. Phys. Condens. Matter, 14, 7191-7200.]). J. Phys. Condens. Matter, 14, 7191–7200] and X-ray [Smith et al. (1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]). Acta Cryst. 22 940–943; Yang et al. (2002b[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002b). J. Alloys Compd. 339, 189-194.]). J. Alloys Compd. 339, 189–194; Yang et al., (2003[Yang, H. F., Rao, G. H., Liu, G. Y., Ouyang, Z. W., Liu, W. F., Feng, X. M., Chu, W. G. & Liang, J. K. (2003). J. Alloys Compd. 263, 146-153.]). J. Alloys Compd. 263, 146–153] and single-crystal data with isotropic atomic displacement parameters [Roger et al., (2006[Roger, J., Babizhetskyy, V., Jardin, R., Halet, J. F. & Guérin, R. (2006). J. Alloys Compd. 415, 73-84.]). J. Alloys Compd. 415, 73–84]. In addition, the anisotropic atomic displacement parameters for all atomic sites have been determined for the first time. These compounds are confirmed to have the tetra­gonal Zr5Si4-type structure (space group: P41212), as reported previously (Smith et al., 1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]). The structure is built up by distorted body-centered cubes consisting of Pr(Nd) atoms, which are linked to each other by edge-sharing to form a three-dimensional framework. This framework delimits zigzag channels in which the silicon dimers are situated.

1. Chemical context

In natural science, there are some essential concepts concerned with symmetry, among which chiral symmetry is one of the fundamentals in all fields of physics, especially magnetism in solid-state materials. A chiral magnet in solids is of great inter­est in both science and technology. These magnets have been studied for novel phenomena such as chiral magnetic soliton lattices and use in future spintronic devices such as magnetic memories and logic gates. The critical point is that the crystal-structure chirality affects the arrangement of magnetic moments in these materials. The symmetry of crystals plays an important role in the spatial arrangement of the magnetic moments. For example, the inter­metallic compound YbNi3Al9 has a trigonal ErNi3Al9-type structure in space group R32, a member of the Sohncke group (Gladyshevskii et al., 1993[Gladyshevskii, R. E., Cenzual, K., Flack, H. D. & Parthé, E. (1993). Acta Cryst. B49, 468-474.]). This compound exhibits a characteristic helical magnetic structure, reflecting the symmetry of the crystal (Aoki et al., 2018[Aoki, R., Togawa, Y. & Ohara, S. (2018). Phys. Rev. B, 97, 214414.]). To study magnetism for chiral symmetry, we focused on the inter­metallic compound R5Si4 (R = Pr and Nd), which has a tetra­gonal Zr5Si4-type crystal structure in the chiral space group P41212 (Smith et al., 1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]).

Roger et al. (2006[Roger, J., Babizhetskyy, V., Jardin, R., Halet, J. F. & Guérin, R. (2006). J. Alloys Compd. 415, 73-84.]) isolated a small single crystal of Nd5Si4 by crushing the solidified sample and collected single-crystal X-ray data. Very recently, Sato et al. (2018[Sato, Y. J., Shimizu, Y., Nakamura, A., Homma, Y., Li, D., Maurya, A., Honda, F. & Aoki, D. (2018). J. Phys. Soc. Jpn, 87, 074701.]) reported the single-crystal growth and magnetic properties of Ce5Si4, which has the same crystal structure as Pr5Si4 and Nd5Si4. At present, there has only been a report of large-size single-crystal growth for R = Ce, and there are no reports of a large single crystal having been grown successfully for R = Pr or Nd. In particular, for Pr5Si4, the crystal-structure analysis is based only on powder XRD data (Yang et al., 2002a[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002a). J. Alloys Compd. 334, 131-134.],b[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002b). J. Alloys Compd. 339, 189-194.],c[Yang, H. F., Rao, G. H., Liu, G. Y., Ouyang, Z. W., Liu, W. F., Feng, X. M., Chu, W. G. & Liang, J. K. (2002c). J. Alloys Compd. 346, 190-196.], 2003[Yang, H. F., Rao, G. H., Liu, G. Y., Ouyang, Z. W., Liu, W. F., Feng, X. M., Chu, W. G. & Liang, J. K. (2003). J. Alloys Compd. 263, 146-153.]; Cadogan et al., 2002[Cadogan, J. M., Ryan, D. H., Altounian, Z., Wang, H. B. & Swainson, I. P. (2002). J. Phys. Condens. Matter, 14, 7191-7200.]; Smith et al., 1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]). It is still unknown, however, whether there is a relationship between chiral symmetry and electronic properties, including magnetic ones. In this paper, we report the details of crystallographic studies of single-crystal X-ray analysis of high-quality single-crystalline Pr5Si4 and Nd5Si4, which are expected to be candidate materials for chiral magnets.

2. Structural commentary

The crystal structures of Pr5Si4 and Nd5Si4 refined in this study are essentially the same as those determined previously, belonging to chiral space group P41212 (No. 92) for R = La, Ce, and Nd (Yang et al., 2002a[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002a). J. Alloys Compd. 334, 131-134.]; Sato et al., 2018[Sato, Y. J., Shimizu, Y., Nakamura, A., Homma, Y., Li, D., Maurya, A., Honda, F. & Aoki, D. (2018). J. Phys. Soc. Jpn, 87, 074701.]). The asymmetric unit of these compounds consists of three Pr (Nd) and two Si atoms. The Pr1(Nd1) atom occupies the Wyckoff 4a site, and the Pr2 (Nd2), Pr3 (Nd3), Si1 and Si2 are located on the general position 8b sites. The principal units in the crystal structures of Pr5Si4 and Nd5Si4 are illustrated in Fig. 1[link], and selected bond lengths are given in Tables 1[link] and 2[link]. The Pr1(Nd1) coordination environment in these compounds can be described as a distorted cube with four Pr2 (Nd2) and four Pr3 (Nd3) [Pr1—Pr2 and Pr1—Pr3 bond lengths ranging from 3.4914 (4) to 3.6423 (3) Å, Pr2—Pr3 bond lengths in the range 3.9156 (3) to 4.0074 (2) Å, Nd1—Nd2 and Nd1—Nd3 bond lengths of 3.4725 (5)–3.6265 (3) Å and Nd2—Nd3 bond lengths of 3.9094 (4)–3.9752 (2) Å]. In addition, the Pr1(Nd1)—Si bonds protruding through the distorted rectangular faces formed by two Pr2 (Nd2) and two Pr3 (Nd3) atoms have Pr1—Si bond lengths ranging from 3.0985 (13) to 3.1780 (13) Å and Nd1—Si bond lengths from 3.0744 (15) to 3.1661 (16) Å. The distorted cubes are connected through common two Pr2—Pr3 (Nd2—Nd3) edges, and Si1 (Si2) atoms form dimers with Si2 (Si1) atoms in the adjacent unit (Fig. 2[link]). The Si1—Si2 bond length in Pr5Si4 is 2.4738 (16) Å, and that of Nd5Si4 is 2.482 (2) Å. The extended structure is shown in polyhedral representation in Fig. 3[link]. The structure is built up by distorted body-centered cubes consisting of Pr (Nd) atoms, which are linked to each other by edge-sharing to form a three-dimensional framework. This framework delimits zigzag channels oriented along the [100] and [010] directions, in which the Si–Si dimers are situated.

Table 1
Selected bond lengths (Å) for Pr5Si4

Pr1—Pr2i 3.4914 (4) Pr1—Si1ix 3.1756 (13)
Pr1—Pr2ii 3.5319 (4) Pr1—Si2ii 3.1780 (13)
Pr1—Pr2iii 3.5319 (4) Pr1—Si2iii 3.1780 (13)
Pr1—Pr2iv 3.4914 (4) Pr2—Pr2i 3.9561 (6)
Pr1—Pr3v 3.6423 (3) Pr2—Pr3vii 3.9414 (4)
Pr1—Pr3vi 3.6423 (3) Pr2—Pr3x 3.9717 (3)
Pr1—Si1vii 3.1756 (13) Pr2—Pr3xi 3.9156 (3)
Pr1—Si1viii 3.0985 (13) Pr3—Pr3ii 4.0074 (2)
Pr1—Si1 3.0985 (13) Si1—Si2 2.4738 (16)
Symmetry codes: (i) −y + 1, −x + 1, −z + [{1\over 2}]; (ii) −y + [{3\over 2}], x + [{1\over 2}], z + [{1\over 4}]; (iii) x + [{1\over 2}], −y + [{3\over 2}], −z + [{3\over 4}]; (iv) −x + 1, −y + 1, z + [{1\over 2}]; (v) −y + 2, −x + 1, −z + [{1\over 2}]; (vi) −x + 1, −y + 2, z + [{1\over 2}]; (vii) −y + [{3\over 2}], x − [{1\over 2}], z + [{1\over 4}]; (viii) y, x, −z + 1; (ix) x − [{1\over 2}], −y + [{3\over 2}], −z + [{3\over 4}].

Table 2
Selected bond lengths (Å) for Nd5Si4

Nd1—Nd2i 3.4725 (5) Nd1—Si1ix 3.1528 (16)
Nd1—Nd2ii 3.5021 (5) Nd1—Si2ii 3.1661 (16)
Nd1—Nd2iii 3.5021 (5) Nd1—Si2iii 3.1661 (16)
Nd1—Nd2iv 3.4725 (5) Nd2—Nd2i 3.9202 (7)
Nd1—Nd3v 3.6265 (3) Nd2—Nd3x 3.9094 (4)
Nd1—Nd3vi 3.6265 (3) Nd2—Nd3xi 3.9378 (4)
Nd1—Si1vii 3.1528 (16) Nd2—Nd3vii 3.9061 (4)
Nd1—Si1viii 3.0744 (15) Nd3—Nd3xii 3.9752 (2)
Nd1—Si1 3.0744 (15) Si1—Si2 2.482 (2)
Symmetry codes: (i) −y + 1, −x + 1, −z + [{1\over 2}]; (ii) −y + [{3\over 2}], x + [{1\over 2}], z + [{1\over 4}]; (iii) x + [{1\over 2}], −y + [{3\over 2}], −z + [{3\over 4}]; (iv) −x + 1, −y + 1, z + [{1\over 2}]; (v) −y + 2, −x + 1, −z + [{1\over 2}]; (vi) −x + 1, −y + 2, z + [{1\over 2}]; (vii) −y + [{3\over 2}], x − [{1\over 2}], z + [{1\over 4}]; (viii) y, x, −z + 1; (ix) x − [{1\over 2}], −y + [{3\over 2}], −z + [{3\over 4}].
[Figure 1]
Figure 1
Principal units in the structure of (a) Pr5Si4 and (b) Nd5Si4, illustrated using VESTA (Momma & Izumi, 2011[Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272-1276.]). Displacement ellipsoids are drawn at the 90% probability level. Symmetry codes: (i) −y + 1, −x + 1, −z + [{1\over 2}]; (ii) −y + [{3\over 2}], x + [{1\over 2}], z + [{1\over 4}]; (iii) x + [{1\over 2}], −y + [{3\over 2}], −z + [{3\over 4}]; (iv) −x + 1, −y + 1, z + [{1\over 2}]; (v) −y + 2, −x + 1, −z + [{1\over 2}]; (vi) −x + 1, −y + 2, z + [{1\over 2}]; (vii) −y + [{3\over 2}], x − [{1\over 2}], z + [{1\over 4}]; (viii) y, x, −z + 1; (ix) x − [{1\over 2}], −y + [{3\over 2}], −z + [{3\over 4}].
[Figure 2]
Figure 2
Parts of the crystal structure showing five distorted body-centered cubes sharing Pr2—Pr3 edges (polyhedral drawing). Si1 and Si2 atoms form dimers with atoms Si2 and Si1, respectively, of the adjacent unit.
[Figure 3]
Figure 3
Polyhedral representation of the crystal structure of Pr5Si4 showing the Si–Si dimers situated in zigzag channels running along the [100] and [010] directions.

3. Synthesis and crystallization

We have succeeded in growing single-crystalline samples of Pr5Si4 for the first time. For Nd5Si4, Roger et al. (2006[Roger, J., Babizhetskyy, V., Jardin, R., Halet, J. F. & Guérin, R. (2006). J. Alloys Compd. 415, 73-84.]) obtained a very small single crystal, but we have succeeded in growing a large single crystal. These compounds are incongruently melting compounds (Shukla et al., 2009[Shukla, A., Kang, Y. B. & Pelton, A. D. (2009). Int. J. Mater. Res. 100, 208-217.]), so we synthesized source materials with the non-stoichiometric molar ratio of Pr (Nd):Si of 58:42 in a mono-arc furnace. Each melted button of source materials was turned over and remelted three times to ensure homogeneity. Single crystals of Pr5Si4 and Nd5Si4 were grown by the Czochralski pulling method in a tetra arc furnace in an argon atmosphere on a water-cooled copper hearth. A tungsten rod was used as a pulling axis with no seed crystal, and after optimizing the initial conditions of the growth, the crystal was pulled at a constant rate of 12 mm hour−1. The sizes of the grown ingots were about 30 mm in length and 5 mm in diameter. The grown single-crystal samples were characterized by powder X-ray diffraction using a Rigaku MiniFlexII diffractometer with Cu Kα radiation. The powder X-ray diffraction peaks can be well indexed based on the tetra­gonal Zr5Si4-type structure. In addition, it has been confirmed that the whole grown crystal is a single grain crystal by means of the back-reflection Laue method.

4. Database survey

A survey of the Inorganic Crystal Structure Database (ICSD; Belsky et al., 2002[Belsky, A., Hellenbrandt, M., Karen, V. L. & Luksch, P. (2002). Acta Cryst. B58, 364-369.]) for Pr5Si4 yielded three hits. In all three, it is reported that Pr5Si4 has a Zr5Si4-type structure (Smith et al., 1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]; ICSD 649362; Yang et al., 2002b[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002b). J. Alloys Compd. 339, 189-194.]; ICSD 95099; Yang et al., 2003[Yang, H. F., Rao, G. H., Liu, G. Y., Ouyang, Z. W., Liu, W. F., Feng, X. M., Chu, W. G. & Liang, J. K. (2003). J. Alloys Compd. 263, 146-153.]; ICSD 98352). On the other hand, for Nd5Si4, previous reports have shown that Nd5Si4 has two types of crystal structure, a Sm5Ge4 type (Raman, 1968[Raman, A. (1968). Trans. Indian Inst. Met. 21, 5-8.]; ICSD 645983; Roger et al., 2006[Roger, J., Babizhetskyy, V., Jardin, R., Halet, J. F. & Guérin, R. (2006). J. Alloys Compd. 415, 73-84.]; ICSD 154658 and 154659) and a Zr5Si4-type structure (Smith et al., 1967[Smith, G. S., Tharp, A. G. & Johnson, W. (1967). Acta Cryst. 22, 940-943.]; ICSD 645939; Mokra et al., 1978[Mokra, I. R., Bodak, O. I. & Gladyshevskii, E. I. (1978). Dopovidi Akademiï Nauk Ukrains'koï RSR, Seriya A Fiziko-Mat. Tekh. Nauk, 1043-1045.]; ICSD 645946; Eremenko et al., 1984[Eremenko, V. N., Meleshevich, K. A., Buyanov, Y. I. & Obushenko, I. M. (1984). Dokl. Akad. Nauk Ukr. SSR, Ser. A, 11, 80.]; ICSD 600990; Yang et al., 2002a[Yang, H. F., Rao, G. H., Chu, W. G., Liu, G. Y., Ouyang, Z. W. & Liang, J. K. (2002a). J. Alloys Compd. 334, 131-134.]; ICSD 94987; Yang et al., 2002c[Yang, H. F., Rao, G. H., Liu, G. Y., Ouyang, Z. W., Liu, W. F., Feng, X. M., Chu, W. G. & Liang, J. K. (2002c). J. Alloys Compd. 346, 190-196.]; ICSD 190404; Cadogan et al., 2002[Cadogan, J. M., Ryan, D. H., Altounian, Z., Wang, H. B. & Swainson, I. P. (2002). J. Phys. Condens. Matter, 14, 7191-7200.]; ICSD 190404). Roger et al. (2006[Roger, J., Babizhetskyy, V., Jardin, R., Halet, J. F. & Guérin, R. (2006). J. Alloys Compd. 415, 73-84.]) reported that Sm5Ge4-type Nd5Si4 could be obtained only with the addition of a tiny amount of boron of less than three at.% in the initial mixture, and that when synthesized with Nd and Si alone, Zr5Si4-type Nd5Si4 was obtained.

5. Refinement

Crystal data, data collection, and structure refinement details are summarized in Table 3[link]. The highest and deepest remaining difference electron density features are located at 0.90 Å from Pr2 and 1.08 Å from Pr3 for Pr5Si4, and 0.74 Å from Nd1 and 1.38 Å from Nd2 for Nd5Si4. The absolute structures of the samples were well-defined in space group P41212 (No. 92), although the bulk samples possibly also contain the other enanti­omer; space group P43212 (No. 96).

Table 3
Experimental details

  Pr5Si4 Nd5Si4
Crystal data
Mr 816.91 833.56
Crystal system, space group Tetragonal, P41212 Tetragonal, P41212
Temperature (K) 223 223
a, c (Å) 7.9001 (2), 14.9568 (6) 7.8644 (2), 14.8085 (5)
V3) 933.48 (6) 915.89 (6)
Z 4 4
Radiation type Mo Kα Mo Kα
μ (mm−1) 26.03 28.27
Crystal size (mm) 0.13 × 0.08 × 0.03 0.12 × 0.09 × 0.07
 
Data collection
Diffractometer XtaLAB AFC12 (RINC): Kappa dual offset/far XtaLAB AFC12 (RINC): Kappa dual offset/far
Absorption correction Analytical [CrysAlis PRO (Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Oxford Diffraction, Yarnton, England.]) based on Clark & Reid (1995[Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897.])] Analytical [CrysAlis PRO (Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Oxford Diffraction, Yarnton, England.]) based on Clark & Reid (1995[Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897.])]
Tmin, Tmax 0.588, 0.830 0.561, 0.702
No. of measured, independent and observed [I > 2σ(I)] reflections 5553, 1260, 1225 6054, 1238, 1203
Rint 0.025 0.032
(sin θ/λ)max−1) 0.710 0.708
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.013, 0.026, 1.10 0.015, 0.028, 1.09
No. of reflections 1260 1238
No. of parameters 43 43
Δρmax, Δρmin (e Å−3) 0.69, −0.85 1.10, −0.71
Absolute structure Flack x determined using 431 quotients [(I+)−(I)]/[(I+)+(I)] (Parsons et al., 2013[Parsons, S., Flack, H. D. & Wagner, T. (2013). Acta Cryst. B69, 249-259.]) Flack x determined using 422 quotients [(I+)−(I)]/[(I+)+(I)] (Parsons et al., 2013[Parsons, S., Flack, H. D. & Wagner, T. (2013). Acta Cryst. B69, 249-259.])
Absolute structure parameter −0.04 (2) −0.01 (3)
Computer programs: CrysAlis PRO (Rigaku OD, 2019[Rigaku OD (2019). CrysAlis PRO. Oxford Diffraction, Yarnton, England.]), SHELXT (Sheldrick, 2015a[Sheldrick, G. M. (2015a). Acta Cryst. A71, 3-8.]), SHELXL (Sheldrick, 2015b[Sheldrick, G. M. (2015b). Acta Cryst. C71, 3-8.]), OLEX2 (Dolomanov et al., 2009[Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. (2009). J. Appl. Cryst. 42, 339-341.]) and publCIF (Westrip, 2010[Westrip, S. P. (2010). J. Appl. Cryst. 43, 920-925.]).

Supporting information


Computing details top

For both structures, data collection: CrysAlis PRO (Rigaku OD, 2019); cell refinement: CrysAlis PRO (Rigaku OD, 2019); data reduction: CrysAlis PRO (Rigaku OD, 2019); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: publCIF (Westrip, 2010).

Pentapraseodymium tetrasiliside (A) top
Crystal data top
Pr5Si4Dx = 5.813 Mg m3
Mr = 816.91Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P41212Cell parameters from 4009 reflections
Hall symbol: P 4abw 2nwθ = 3.8–30.3°
a = 7.9001 (2) ŵ = 26.03 mm1
c = 14.9568 (6) ÅT = 223 K
V = 933.48 (6) Å3Plate, metallic gray
Z = 40.13 × 0.08 × 0.03 mm
F(000) = 1404
Data collection top
XtaLAB AFC12 (RINC): Kappa dual offset/far
diffractometer
1260 independent reflections
Radiation source: micro-focus sealed X-ray tube1225 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.025
Detector resolution: 5.8140 pixels mm-1θmax = 30.3°, θmin = 3.7°
ω scansh = 1111
Absorption correction: analytical
[CrysAlisPro (Rigaku OD, 2019) based on Clark & Reid (1995)]
k = 1010
Tmin = 0.588, Tmax = 0.830l = 1917
5553 measured reflections
Refinement top
Refinement on F2 w = 1/[σ2(Fo2) + (0.0078P)2 + 0.0556P]
where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full(Δ/σ)max = 0.001
R[F2 > 2σ(F2)] = 0.013Δρmax = 0.69 e Å3
wR(F2) = 0.026Δρmin = 0.85 e Å3
S = 1.10Extinction correction: SHELXL (Sheldrick, 2015b), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1260 reflectionsExtinction coefficient: 0.00247 (9)
43 parametersAbsolute structure: Flack x determined using 431 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons et al., 2013)
0 restraintsAbsolute structure parameter: 0.04 (2)
Primary atom site location: dual
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Pr10.81086 (3)0.81086 (3)0.5000000.00721 (8)
Pr20.51578 (3)0.37028 (3)0.12478 (2)0.00578 (7)
Pr30.51088 (3)0.87144 (3)0.04758 (2)0.00676 (7)
Si10.92537 (16)0.71000 (16)0.30916 (8)0.0069 (2)
Si20.69967 (16)0.66478 (16)0.19702 (8)0.0078 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pr10.00720 (10)0.00720 (10)0.00723 (16)0.00017 (11)0.00069 (9)0.00069 (9)
Pr20.00587 (11)0.00618 (12)0.00529 (12)0.00033 (9)0.00050 (9)0.00083 (8)
Pr30.00630 (12)0.00650 (12)0.00748 (12)0.00045 (7)0.00114 (9)0.00172 (9)
Si10.0074 (5)0.0078 (6)0.0056 (6)0.0011 (4)0.0004 (4)0.0001 (5)
Si20.0066 (5)0.0074 (6)0.0094 (6)0.0018 (4)0.0012 (5)0.0007 (5)
Geometric parameters (Å, º) top
Pr1—Pr2i3.4914 (4)Pr2—Pr3xi3.9156 (3)
Pr1—Pr2ii3.5319 (4)Pr2—Si1xi3.0641 (13)
Pr1—Pr2iii3.5319 (4)Pr2—Si1i3.1005 (14)
Pr1—Pr2iv3.4914 (4)Pr2—Si1xii3.0668 (14)
Pr1—Pr3v3.6423 (3)Pr2—Si22.9480 (13)
Pr1—Pr3vi3.6423 (3)Pr2—Si2xi2.9737 (13)
Pr1—Si1vii3.1756 (13)Pr2—Si2i3.0730 (13)
Pr1—Si1viii3.0985 (13)Pr3—Pr3ii4.0074 (2)
Pr1—Si13.0985 (13)Pr3—Si1xiii3.1554 (13)
Pr1—Si1ix3.1756 (13)Pr3—Si1xii3.3434 (12)
Pr1—Si2ii3.1780 (13)Pr3—Si1xiv3.1957 (12)
Pr1—Si2iii3.1780 (13)Pr3—Si2xiii3.2566 (12)
Pr2—Pr2i3.9561 (6)Pr3—Si2xii3.1708 (12)
Pr2—Pr3vii3.9414 (4)Pr3—Si23.1442 (12)
Pr2—Pr3x3.9717 (3)Si1—Si22.4738 (16)
Pr2i—Pr1—Pr2iv71.331 (11)Si2xi—Pr2—Si2i124.47 (4)
Pr2iii—Pr1—Pr2ii68.120 (11)Pr1xvi—Pr3—Pr1xii97.461 (6)
Pr2iv—Pr1—Pr2ii176.841 (6)Pr1xvi—Pr3—Pr2x99.525 (8)
Pr2i—Pr1—Pr2iii176.841 (6)Pr1xii—Pr3—Pr2xvii158.527 (9)
Pr2i—Pr1—Pr2ii110.343 (4)Pr1xvi—Pr3—Pr2xiii136.554 (9)
Pr2iv—Pr1—Pr2iii110.343 (4)Pr1xii—Pr3—Pr2x97.821 (7)
Pr2iv—Pr1—Pr3v109.131 (9)Pr1xii—Pr3—Pr2xiii99.441 (7)
Pr2iii—Pr1—Pr3vi74.025 (6)Pr1xvi—Pr3—Pr2xvii102.639 (8)
Pr2i—Pr1—Pr3v70.258 (6)Pr1xvi—Pr3—Pr3ii98.905 (6)
Pr2ii—Pr1—Pr3v74.025 (6)Pr1xii—Pr3—Pr3ii56.190 (4)
Pr2ii—Pr1—Pr3vi106.588 (8)Pr2xiii—Pr3—Pr2xvii60.464 (9)
Pr2i—Pr1—Pr3vi109.131 (9)Pr2xvii—Pr3—Pr2x86.316 (6)
Pr2iv—Pr1—Pr3vi70.258 (6)Pr2xiii—Pr3—Pr2x117.252 (7)
Pr2iii—Pr1—Pr3v106.588 (8)Pr2x—Pr3—Pr3ii149.882 (8)
Pr3vi—Pr1—Pr3v179.290 (14)Pr2xvii—Pr3—Pr3ii112.494 (8)
Si1—Pr1—Pr2iii122.55 (3)Pr2xiii—Pr3—Pr3ii60.158 (7)
Si1viii—Pr1—Pr2i127.07 (3)Si1xii—Pr3—Pr1xvi89.84 (2)
Si1—Pr1—Pr2ii54.63 (3)Si1xiv—Pr3—Pr1xii54.18 (2)
Si1ix—Pr1—Pr2iii128.63 (2)Si1xiii—Pr3—Pr1xvi55.14 (2)
Si1ix—Pr1—Pr2iv54.47 (2)Si1xii—Pr3—Pr1xii51.84 (2)
Si1—Pr1—Pr2i55.75 (3)Si1xiii—Pr3—Pr1xii144.17 (3)
Si1vii—Pr1—Pr2iv54.52 (2)Si1xiv—Pr3—Pr1xvi53.40 (2)
Si1viii—Pr1—Pr2iii54.63 (3)Si1xiii—Pr3—Pr2xiii89.98 (2)
Si1ix—Pr1—Pr2i54.52 (2)Si1xiv—Pr3—Pr2xiii108.89 (3)
Si1vii—Pr1—Pr2iii124.06 (2)Si1xii—Pr3—Pr2xvii134.80 (2)
Si1vii—Pr1—Pr2i54.47 (2)Si1xiv—Pr3—Pr2x129.63 (3)
Si1—Pr1—Pr2iv127.07 (3)Si1xii—Pr3—Pr2xiii131.45 (2)
Si1viii—Pr1—Pr2ii122.55 (3)Si1xiii—Pr3—Pr2xvii50.33 (3)
Si1viii—Pr1—Pr2iv55.75 (3)Si1xii—Pr3—Pr2x48.60 (2)
Si1ix—Pr1—Pr2ii124.06 (2)Si1xiii—Pr3—Pr2x108.41 (2)
Si1vii—Pr1—Pr2ii128.63 (2)Si1xiv—Pr3—Pr2xvii136.01 (3)
Si1—Pr1—Pr3vi124.12 (2)Si1xiii—Pr3—Pr3ii101.66 (2)
Si1viii—Pr1—Pr3v124.12 (2)Si1xii—Pr3—Pr3ii108.02 (2)
Si1vii—Pr1—Pr3v54.62 (2)Si1xiv—Pr3—Pr3ii50.43 (2)
Si1viii—Pr1—Pr3vi55.90 (2)Si1xiv—Pr3—Si1xii85.949 (17)
Si1ix—Pr1—Pr3v124.76 (3)Si1xiii—Pr3—Si1xii137.237 (18)
Si1ix—Pr1—Pr3vi54.62 (2)Si1xiii—Pr3—Si1xiv90.036 (12)
Si1vii—Pr1—Pr3vi124.76 (3)Si1xiv—Pr3—Si2xiii90.54 (3)
Si1—Pr1—Pr3v55.90 (2)Si1xiii—Pr3—Si2xiii45.35 (3)
Si1—Pr1—Si1vii91.45 (4)Si1xiii—Pr3—Si2xii92.74 (3)
Si1viii—Pr1—Si1ix91.45 (4)Si2xii—Pr3—Pr1xii87.19 (2)
Si1—Pr1—Si1ix90.57 (2)Si2—Pr3—Pr1xii54.53 (2)
Si1viii—Pr1—Si1vii90.57 (2)Si2—Pr3—Pr1xvi145.87 (2)
Si1—Pr1—Si1viii177.18 (5)Si2xiii—Pr3—Pr1xii123.76 (2)
Si1ix—Pr1—Si1vii88.74 (5)Si2xiii—Pr3—Pr1xvi90.26 (2)
Si1vii—Pr1—Si2ii178.20 (3)Si2xii—Pr3—Pr1xvi55.08 (2)
Si1ix—Pr1—Si2ii92.22 (3)Si2xiii—Pr3—Pr2xvii49.43 (2)
Si1vii—Pr1—Si2iii92.22 (3)Si2xiii—Pr3—Pr2xiii47.45 (2)
Si1—Pr1—Si2ii90.07 (3)Si2xiii—Pr3—Pr2x135.71 (2)
Si1ix—Pr1—Si2iii178.20 (3)Si2xii—Pr3—Pr2xiii164.53 (2)
Si1—Pr1—Si2iii87.88 (3)Si2—Pr3—Pr2xiii48.31 (2)
Si1viii—Pr1—Si2iii90.07 (3)Si2—Pr3—Pr2xvii103.99 (2)
Si1viii—Pr1—Si2ii87.88 (3)Si2xii—Pr3—Pr2xvii110.50 (2)
Si2iii—Pr1—Pr2ii54.20 (2)Si2—Pr3—Pr2x103.11 (2)
Si2iii—Pr1—Pr2iv127.29 (2)Si2xii—Pr3—Pr2x47.59 (2)
Si2ii—Pr1—Pr2ii51.80 (2)Si2xiii—Pr3—Pr3ii67.57 (2)
Si2iii—Pr1—Pr2i125.04 (2)Si2—Pr3—Pr3ii50.90 (2)
Si2ii—Pr1—Pr2iv125.04 (2)Si2xii—Pr3—Pr3ii133.74 (2)
Si2ii—Pr1—Pr2iii54.20 (2)Si2xii—Pr3—Si1xiv86.34 (3)
Si2iii—Pr1—Pr2iii51.80 (2)Si2—Pr3—Si1xii86.35 (3)
Si2ii—Pr1—Pr2i127.29 (2)Si2xiii—Pr3—Si1xii175.55 (3)
Si2iii—Pr1—Pr3vi125.73 (2)Si2xii—Pr3—Si1xii44.54 (3)
Si2ii—Pr1—Pr3vi54.90 (2)Si2—Pr3—Si1xiv92.48 (3)
Si2ii—Pr1—Pr3v125.73 (2)Si2—Pr3—Si1xiii136.40 (3)
Si2iii—Pr1—Pr3v54.90 (2)Si2—Pr3—Si2xiii91.079 (17)
Si2iii—Pr1—Si2ii86.85 (5)Si2xii—Pr3—Si2xiii138.014 (18)
Pr1xv—Pr2—Pr1xii103.710 (6)Si2—Pr3—Si2xii130.86 (2)
Pr1xii—Pr2—Pr2i55.940 (5)Pr1—Si1—Pr1xvii123.37 (4)
Pr1xv—Pr2—Pr2i140.135 (10)Pr1—Si1—Pr2i68.56 (3)
Pr1xv—Pr2—Pr3vii102.847 (8)Pr1—Si1—Pr3ii70.13 (2)
Pr1xv—Pr2—Pr3x106.888 (8)Pr1xvii—Si1—Pr3ii134.03 (4)
Pr1xii—Pr2—Pr3xi106.191 (8)Pr1xvii—Si1—Pr3v71.14 (3)
Pr1xii—Pr2—Pr3vii105.646 (8)Pr1—Si1—Pr3v70.70 (3)
Pr1xii—Pr2—Pr3x117.969 (7)Pr1—Si1—Pr3xi136.94 (4)
Pr1xv—Pr2—Pr3xi149.920 (8)Pr2xiii—Si1—Pr1xvii68.02 (3)
Pr2i—Pr2—Pr3x112.953 (9)Pr2ii—Si1—Pr169.90 (3)
Pr3vii—Pr2—Pr2i59.445 (6)Pr2xiii—Si1—Pr1139.92 (4)
Pr3xi—Pr2—Pr2i60.092 (6)Pr2ii—Si1—Pr1xvii67.99 (3)
Pr3xi—Pr2—Pr3x61.068 (5)Pr2i—Si1—Pr1xvii141.38 (4)
Pr3xi—Pr2—Pr3vii65.880 (8)Pr2xiii—Si1—Pr2i129.66 (4)
Pr3vii—Pr2—Pr3x117.851 (7)Pr2ii—Si1—Pr2i138.39 (4)
Si1xi—Pr2—Pr1xv57.51 (2)Pr2xiii—Si1—Pr2ii83.22 (3)
Si1i—Pr2—Pr1xii96.00 (2)Pr2xiii—Si1—Pr3xi82.63 (3)
Si1xii—Pr2—Pr1xii55.47 (2)Pr2xiii—Si1—Pr3ii76.47 (3)
Si1xii—Pr2—Pr1xv57.49 (2)Pr2ii—Si1—Pr3xi138.21 (4)
Si1i—Pr2—Pr1xv55.69 (2)Pr2ii—Si1—Pr3v87.20 (3)
Si1xi—Pr2—Pr1xii147.18 (3)Pr2ii—Si1—Pr3ii79.97 (3)
Si1xii—Pr2—Pr2i111.25 (2)Pr2i—Si1—Pr3xi78.10 (3)
Si1xi—Pr2—Pr2i155.46 (3)Pr2i—Si1—Pr3ii84.10 (3)
Si1i—Pr2—Pr2i90.03 (3)Pr2i—Si1—Pr3v81.41 (3)
Si1xi—Pr2—Pr3vii104.88 (3)Pr2xiii—Si1—Pr3v138.72 (4)
Si1xi—Pr2—Pr3x54.93 (2)Pr3xi—Si1—Pr1xvii70.24 (3)
Si1i—Pr2—Pr3x145.54 (2)Pr3xi—Si1—Pr3v78.24 (3)
Si1i—Pr2—Pr3vii51.57 (2)Pr3xi—Si1—Pr3ii133.50 (4)
Si1xi—Pr2—Pr3xi97.03 (3)Pr3v—Si1—Pr3ii140.82 (4)
Si1xii—Pr2—Pr3x101.67 (2)Si2—Si1—Pr1116.82 (5)
Si1xii—Pr2—Pr3xi147.77 (2)Si2—Si1—Pr1xvii119.66 (5)
Si1i—Pr2—Pr3xi117.17 (2)Si2—Si1—Pr2xiii63.92 (4)
Si1xii—Pr2—Pr3vii140.10 (2)Si2—Si1—Pr2ii135.25 (5)
Si1xii—Pr2—Si1i92.601 (18)Si2—Si1—Pr2i65.79 (4)
Si1xi—Pr2—Si1i93.56 (3)Si2—Si1—Pr3v137.54 (6)
Si1xi—Pr2—Si1xii92.85 (4)Si2—Si1—Pr3ii64.03 (4)
Si1xi—Pr2—Si2i140.79 (3)Si2—Si1—Pr3xi69.49 (4)
Si1xii—Pr2—Si2i90.38 (3)Pr1xii—Si2—Pr3xi135.69 (4)
Si2i—Pr2—Pr1xv92.68 (2)Pr2—Si2—Pr1xii70.30 (3)
Si2—Pr2—Pr1xii57.90 (2)Pr2xiii—Si2—Pr1xii141.97 (4)
Si2xi—Pr2—Pr1xii158.04 (2)Pr2i—Si2—Pr1xii68.78 (3)
Si2i—Pr2—Pr1xii57.02 (2)Pr2—Si2—Pr2xiii132.15 (4)
Si2—Pr2—Pr1xv152.08 (2)Pr2—Si2—Pr2i82.12 (3)
Si2xi—Pr2—Pr1xv98.16 (2)Pr2xiii—Si2—Pr2i134.64 (4)
Si2xi—Pr2—Pr2i107.11 (2)Pr2xiii—Si2—Pr3ii80.47 (3)
Si2—Pr2—Pr2i50.30 (2)Pr2xiii—Si2—Pr3xi82.34 (3)
Si2i—Pr2—Pr2i47.57 (2)Pr2—Si2—Pr3ii140.09 (4)
Si2i—Pr2—Pr3vii53.61 (2)Pr2i—Si2—Pr3ii87.54 (3)
Si2xi—Pr2—Pr3x51.94 (2)Pr2—Si2—Pr3xi78.08 (3)
Si2xi—Pr2—Pr3xi52.15 (2)Pr2i—Si2—Pr3xi76.97 (3)
Si2xi—Pr2—Pr3vii70.89 (2)Pr2xiii—Si2—Pr379.53 (3)
Si2i—Pr2—Pr3xi100.75 (2)Pr2—Si2—Pr385.15 (3)
Si2—Pr2—Pr3xi54.47 (2)Pr2i—Si2—Pr3140.56 (4)
Si2i—Pr2—Pr3x160.33 (3)Pr3—Si2—Pr1xii71.78 (3)
Si2—Pr2—Pr3x70.64 (3)Pr3ii—Si2—Pr1xii70.02 (3)
Si2—Pr2—Pr3vii102.52 (2)Pr3—Si2—Pr3xi136.07 (4)
Si2—Pr2—Si1xii95.16 (3)Pr3—Si2—Pr3ii78.78 (3)
Si2—Pr2—Si1i139.57 (4)Pr3ii—Si2—Pr3xi136.58 (4)
Si2i—Pr2—Si1i47.24 (3)Si1—Si2—Pr1xii121.26 (5)
Si2xi—Pr2—Si1xii140.11 (3)Si1—Si2—Pr2i66.96 (4)
Si2xi—Pr2—Si1i97.97 (3)Si1—Si2—Pr2xiii67.74 (4)
Si2xi—Pr2—Si1xi48.35 (3)Si1—Si2—Pr2135.86 (5)
Si2—Pr2—Si1xi125.48 (3)Si1—Si2—Pr3ii71.43 (4)
Si2—Pr2—Si2xi100.995 (18)Si1—Si2—Pr3138.49 (5)
Si2—Pr2—Si2i93.03 (4)Si1—Si2—Pr3xi65.16 (4)
Symmetry codes: (i) y+1, x+1, z+1/2; (ii) y+3/2, x+1/2, z+1/4; (iii) x+1/2, y+3/2, z+3/4; (iv) x+1, y+1, z+1/2; (v) y+2, x+1, z+1/2; (vi) x+1, y+2, z+1/2; (vii) y+3/2, x1/2, z+1/4; (viii) y, x, z+1; (ix) x1/2, y+3/2, z+3/4; (x) y, x, z; (xi) x+3/2, y1/2, z+1/4; (xii) y1/2, x+3/2, z1/4; (xiii) x+3/2, y+1/2, z+1/4; (xiv) y+1, x+2, z+1/2; (xv) x+1, y+1, z1/2; (xvi) x+1, y+2, z1/2; (xvii) y+1/2, x+3/2, z1/4.
Pentaneodymium tetrasiliside (B) top
Crystal data top
Nd5Si4Dx = 6.045 Mg m3
Mr = 833.56Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P41212Cell parameters from 3985 reflections
Hall symbol: P 4abw 2nwθ = 3.8–30.4°
a = 7.8644 (2) ŵ = 28.27 mm1
c = 14.8085 (5) ÅT = 223 K
V = 915.89 (6) Å3Plate, metallic gray
Z = 40.12 × 0.09 × 0.07 mm
F(000) = 1424
Data collection top
XtaLAB AFC12 (RINC): Kappa dual offset/far
diffractometer
1238 independent reflections
Radiation source: micro-focus sealed X-ray tube1203 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.032
Detector resolution: 5.8140 pixels mm-1θmax = 30.2°, θmin = 3.7°
ω scansh = 1110
Absorption correction: analytical
[CrysAlisPro (Rigaku OD, 2019) based on Clark & Reid (1995)]
k = 1010
Tmin = 0.561, Tmax = 0.702l = 2019
6054 measured reflections
Refinement top
Refinement on F2 w = 1/[σ2(Fo2) + 0.4858P]
where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full(Δ/σ)max = 0.001
R[F2 > 2σ(F2)] = 0.015Δρmax = 1.10 e Å3
wR(F2) = 0.028Δρmin = 0.71 e Å3
S = 1.09Extinction correction: SHELXL (Sheldrick, 2015b), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1238 reflectionsExtinction coefficient: 0.00090 (6)
43 parametersAbsolute structure: Flack x determined using 422 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons et al., 2013)
0 restraintsAbsolute structure parameter: 0.01 (3)
Primary atom site location: dual
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Nd10.81184 (4)0.81184 (4)0.5000000.00637 (9)
Nd20.51490 (3)0.36933 (4)0.12498 (2)0.00518 (7)
Nd30.51034 (4)0.87021 (4)0.04676 (2)0.00649 (7)
Si10.9274 (2)0.7098 (2)0.30921 (10)0.0060 (3)
Si20.7003 (2)0.6636 (2)0.19543 (10)0.0078 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.00630 (11)0.00630 (11)0.00652 (17)0.00026 (13)0.00064 (11)0.00064 (11)
Nd20.00538 (14)0.00534 (14)0.00483 (12)0.00002 (12)0.00035 (11)0.00097 (10)
Nd30.00617 (15)0.00631 (14)0.00700 (13)0.00027 (9)0.00098 (11)0.00152 (11)
Si10.0060 (7)0.0066 (7)0.0054 (6)0.0007 (5)0.0001 (5)0.0001 (6)
Si20.0069 (7)0.0073 (7)0.0093 (6)0.0016 (5)0.0015 (6)0.0017 (6)
Geometric parameters (Å, º) top
Nd1—Nd2i3.4725 (5)Nd2—Nd3vii3.9061 (4)
Nd1—Nd2ii3.5021 (5)Nd2—Si1x3.0366 (16)
Nd1—Nd2iii3.5021 (5)Nd2—Si1i3.0848 (17)
Nd1—Nd2iv3.4725 (5)Nd2—Si1xii3.0436 (17)
Nd1—Nd3v3.6265 (3)Nd2—Si22.9272 (17)
Nd1—Nd3vi3.6265 (3)Nd2—Si2x2.9533 (17)
Nd1—Si1vii3.1528 (16)Nd2—Si2i3.0565 (15)
Nd1—Si1viii3.0744 (15)Nd3—Nd3xii3.9752 (2)
Nd1—Si13.0744 (15)Nd3—Si1xiii3.1359 (15)
Nd1—Si1ix3.1528 (16)Nd3—Si1xii3.3315 (14)
Nd1—Si2ii3.1661 (16)Nd3—Si1xiv3.1748 (15)
Nd1—Si2iii3.1661 (16)Nd3—Si2xiii3.2425 (15)
Nd2—Nd2i3.9202 (7)Nd3—Si2xii3.1619 (16)
Nd2—Nd3x3.9094 (4)Nd3—Si23.1177 (14)
Nd2—Nd3xi3.9378 (4)Si1—Si22.482 (2)
Nd2i—Nd1—Nd2iv71.144 (14)Si2x—Nd2—Si2i123.86 (5)
Nd2iii—Nd1—Nd2ii68.070 (13)Nd1xvi—Nd3—Nd1xii97.355 (7)
Nd2iv—Nd1—Nd2ii177.032 (7)Nd1xvi—Nd3—Nd2xi99.740 (9)
Nd2i—Nd1—Nd2iii177.032 (7)Nd1xii—Nd3—Nd2xiii99.322 (9)
Nd2i—Nd1—Nd2ii110.453 (5)Nd1xvi—Nd3—Nd2xvii102.777 (9)
Nd2iv—Nd1—Nd2iii110.453 (5)Nd1xii—Nd3—Nd2xi97.621 (8)
Nd2iv—Nd1—Nd3v70.374 (8)Nd1xii—Nd3—Nd2xvii158.298 (11)
Nd2iii—Nd1—Nd3vi106.665 (10)Nd1xvi—Nd3—Nd2xiii136.478 (12)
Nd2i—Nd1—Nd3v108.985 (11)Nd1xvi—Nd3—Nd3xii57.694 (6)
Nd2ii—Nd1—Nd3v106.665 (10)Nd1xii—Nd3—Nd3xii137.385 (10)
Nd2ii—Nd1—Nd3vi73.978 (8)Nd2xvii—Nd3—Nd2xiii60.212 (10)
Nd2i—Nd1—Nd3vi70.374 (8)Nd2xiii—Nd3—Nd2xi117.333 (8)
Nd2iv—Nd1—Nd3vi108.985 (11)Nd2xvii—Nd3—Nd2xi86.968 (8)
Nd2iii—Nd1—Nd3v73.978 (8)Nd2xi—Nd3—Nd3xii59.212 (7)
Nd3vi—Nd1—Nd3v179.256 (17)Nd2xiii—Nd3—Nd3xii122.770 (9)
Si1—Nd1—Nd2iii122.55 (4)Nd2xvii—Nd3—Nd3xii62.562 (7)
Si1viii—Nd1—Nd2i126.97 (4)Si1xii—Nd3—Nd1xvi89.95 (3)
Si1—Nd1—Nd2ii54.67 (3)Si1xiv—Nd3—Nd1xii54.16 (3)
Si1ix—Nd1—Nd2iii128.53 (3)Si1xiii—Nd3—Nd1xvi55.00 (3)
Si1ix—Nd1—Nd2iv54.30 (3)Si1xii—Nd3—Nd1xii51.72 (3)
Si1—Nd1—Nd2i55.82 (3)Si1xiii—Nd3—Nd1xii143.78 (3)
Si1vii—Nd1—Nd2iv54.44 (3)Si1xiv—Nd3—Nd1xvi53.25 (3)
Si1viii—Nd1—Nd2iii54.67 (3)Si1xiii—Nd3—Nd2xvii50.52 (3)
Si1ix—Nd1—Nd2i54.44 (3)Si1xiv—Nd3—Nd2xvii135.69 (3)
Si1vii—Nd1—Nd2iii124.35 (3)Si1xii—Nd3—Nd2xiii131.30 (3)
Si1vii—Nd1—Nd2i54.30 (3)Si1xiv—Nd3—Nd2xi129.50 (3)
Si1—Nd1—Nd2iv126.97 (4)Si1xii—Nd3—Nd2xvii135.35 (3)
Si1viii—Nd1—Nd2ii122.55 (4)Si1xiii—Nd3—Nd2xiii90.04 (3)
Si1viii—Nd1—Nd2iv55.82 (3)Si1xii—Nd3—Nd2xi48.50 (3)
Si1ix—Nd1—Nd2ii124.35 (3)Si1xiii—Nd3—Nd2xi108.97 (3)
Si1vii—Nd1—Nd2ii128.53 (3)Si1xiv—Nd3—Nd2xiii108.81 (3)
Si1—Nd1—Nd3vi55.83 (3)Si1xiii—Nd3—Nd3xii51.39 (3)
Si1viii—Nd1—Nd3v55.83 (3)Si1xii—Nd3—Nd3xii91.19 (3)
Si1vii—Nd1—Nd3v124.78 (3)Si1xiv—Nd3—Nd3xii110.85 (3)
Si1viii—Nd1—Nd3vi124.19 (3)Si1xiv—Nd3—Si1xii85.88 (2)
Si1ix—Nd1—Nd3v54.57 (3)Si1xiii—Nd3—Si1xii137.46 (2)
Si1ix—Nd1—Nd3vi124.78 (3)Si1xiii—Nd3—Si1xiv89.678 (15)
Si1vii—Nd1—Nd3vi54.57 (3)Si1xiv—Nd3—Si2xiii90.11 (4)
Si1—Nd1—Nd3v124.19 (3)Si1xiii—Nd3—Si2xiii45.76 (4)
Si1—Nd1—Si1vii91.21 (4)Si1xiii—Nd3—Si2xii92.67 (4)
Si1viii—Nd1—Si1ix91.21 (4)Si2xii—Nd3—Nd1xii87.36 (3)
Si1—Nd1—Si1ix90.79 (3)Si2—Nd3—Nd1xii54.76 (3)
Si1viii—Nd1—Si1vii90.79 (3)Si2—Nd3—Nd1xvi146.00 (3)
Si1—Nd1—Si1viii177.21 (7)Si2xiii—Nd3—Nd1xii123.04 (3)
Si1ix—Nd1—Si1vii88.51 (6)Si2xiii—Nd3—Nd1xvi90.38 (3)
Si1vii—Nd1—Si2ii178.58 (4)Si2xii—Nd3—Nd1xvi55.09 (3)
Si1ix—Nd1—Si2ii92.27 (4)Si2xiii—Nd3—Nd2xiii47.19 (3)
Si1vii—Nd1—Si2iii92.27 (4)Si2xiii—Nd3—Nd2xvii49.57 (3)
Si1—Nd1—Si2ii89.96 (4)Si2xiii—Nd3—Nd2xi136.52 (3)
Si1ix—Nd1—Si2iii178.58 (4)Si2xii—Nd3—Nd2xvii110.79 (3)
Si1—Nd1—Si2iii88.01 (4)Si2—Nd3—Nd2xvii103.54 (3)
Si1viii—Nd1—Si2iii89.96 (4)Si2—Nd3—Nd2xiii48.09 (3)
Si1viii—Nd1—Si2ii88.01 (4)Si2xii—Nd3—Nd2xiii164.61 (3)
Si2iii—Nd1—Nd2ii54.28 (3)Si2—Nd3—Nd2xi102.77 (3)
Si2iii—Nd1—Nd2iv127.09 (3)Si2xii—Nd3—Nd2xi47.63 (3)
Si2ii—Nd1—Nd2ii51.78 (3)Si2xiii—Nd3—Nd3xii93.42 (3)
Si2iii—Nd1—Nd2i125.25 (3)Si2—Nd3—Nd3xii156.02 (3)
Si2ii—Nd1—Nd2iv125.25 (3)Si2xii—Nd3—Nd3xii50.23 (3)
Si2ii—Nd1—Nd2iii54.28 (3)Si2xii—Nd3—Si1xiv86.36 (4)
Si2iii—Nd1—Nd2iii51.78 (3)Si2—Nd3—Si1xii86.26 (4)
Si2ii—Nd1—Nd2i127.09 (3)Si2xiii—Nd3—Si1xii174.74 (4)
Si2iii—Nd1—Nd3vi54.98 (3)Si2xii—Nd3—Si1xii44.85 (4)
Si2ii—Nd1—Nd3vi125.68 (3)Si2—Nd3—Si1xiv92.77 (4)
Si2ii—Nd1—Nd3v54.98 (3)Si2—Nd3—Si1xiii136.26 (4)
Si2iii—Nd1—Nd3v125.68 (3)Si2—Nd3—Si2xiii90.54 (2)
Si2iii—Nd1—Si2ii86.97 (6)Si2xii—Nd3—Si2xiii138.34 (2)
Nd1xv—Nd2—Nd1xii103.774 (8)Si2—Nd3—Si2xii131.07 (3)
Nd1xii—Nd2—Nd2i55.965 (6)Nd1—Si1—Nd1xvii123.58 (5)
Nd1xv—Nd2—Nd2i140.405 (13)Nd1—Si1—Nd2i68.64 (3)
Nd1xv—Nd2—Nd3x149.935 (9)Nd1—Si1—Nd3ii70.00 (3)
Nd1xv—Nd2—Nd3xi107.244 (10)Nd1xvii—Si1—Nd3ii134.15 (5)
Nd1xii—Nd2—Nd3vii106.182 (10)Nd1xvii—Si1—Nd3vi71.13 (3)
Nd1xii—Nd2—Nd3x106.111 (9)Nd1—Si1—Nd3vi70.93 (3)
Nd1xii—Nd2—Nd3xi117.604 (9)Nd1—Si1—Nd3x136.75 (6)
Nd1xv—Nd2—Nd3vii102.810 (9)Nd2xiii—Si1—Nd1xvii68.23 (3)
Nd2i—Nd2—Nd3xi112.321 (11)Nd2ii—Si1—Nd169.84 (3)
Nd3x—Nd2—Nd2i59.853 (7)Nd2xiii—Si1—Nd1139.62 (5)
Nd3vii—Nd2—Nd2i59.937 (8)Nd2ii—Si1—Nd1xvii68.14 (4)
Nd3vii—Nd2—Nd3xi117.388 (8)Nd2i—Si1—Nd1xvii141.48 (5)
Nd3vii—Nd2—Nd3x65.627 (10)Nd2xiii—Si1—Nd2i129.31 (5)
Nd3x—Nd2—Nd3xi60.872 (7)Nd2ii—Si1—Nd2i138.41 (5)
Si1x—Nd2—Nd1xv57.47 (3)Nd2xiii—Si1—Nd2ii83.28 (4)
Si1i—Nd2—Nd1xii96.51 (3)Nd2xiii—Si1—Nd3x83.05 (4)
Si1xii—Nd2—Nd1xii55.49 (3)Nd2xiii—Si1—Nd3ii76.24 (3)
Si1xii—Nd2—Nd1xv57.42 (3)Nd2ii—Si1—Nd3x138.55 (5)
Si1i—Nd2—Nd1xv55.54 (3)Nd2ii—Si1—Nd3vi87.22 (4)
Si1x—Nd2—Nd1xii147.02 (3)Nd2ii—Si1—Nd3ii80.06 (4)
Si1xii—Nd2—Nd2i111.31 (3)Nd2i—Si1—Nd3x77.79 (4)
Si1x—Nd2—Nd2i155.46 (3)Nd2i—Si1—Nd3ii83.83 (4)
Si1i—Nd2—Nd2i90.59 (3)Nd2i—Si1—Nd3vi81.65 (4)
Si1x—Nd2—Nd3x97.14 (3)Nd2xiii—Si1—Nd3vi138.92 (5)
Si1x—Nd2—Nd3xi55.26 (3)Nd3x—Si1—Nd1xvii70.43 (3)
Si1i—Nd2—Nd3xi145.44 (3)Nd3x—Si1—Nd3vi78.09 (3)
Si1i—Nd2—Nd3x117.05 (3)Nd3x—Si1—Nd3ii133.33 (5)
Si1x—Nd2—Nd3vii104.58 (3)Nd3vi—Si1—Nd3ii140.92 (5)
Si1xii—Nd2—Nd3xi101.82 (3)Si2—Si1—Nd1116.71 (6)
Si1xii—Nd2—Nd3vii140.39 (3)Si2—Si1—Nd1xvii119.56 (6)
Si1i—Nd2—Nd3vii51.69 (3)Si2—Si1—Nd2xiii63.78 (5)
Si1xii—Nd2—Nd3x147.88 (3)Si2—Si1—Nd2ii135.29 (6)
Si1xii—Nd2—Si1i92.69 (2)Si2—Si1—Nd2i65.57 (5)
Si1x—Nd2—Si1i93.26 (4)Si2—Si1—Nd3vi137.48 (7)
Si1x—Nd2—Si1xii92.72 (5)Si2—Si1—Nd3ii63.95 (4)
Si1x—Nd2—Si2i140.91 (4)Si2—Si1—Nd3x69.39 (5)
Si1xii—Nd2—Si2i90.60 (4)Nd1xii—Si2—Nd3x135.36 (6)
Si2i—Nd2—Nd1xv92.89 (3)Nd2—Si2—Nd1xii70.04 (4)
Si2—Nd2—Nd1xii58.18 (3)Nd2xiii—Si2—Nd1xii142.04 (5)
Si2x—Nd2—Nd1xii157.63 (3)Nd2i—Si2—Nd1xii68.47 (3)
Si2i—Nd2—Nd1xii57.24 (3)Nd2—Si2—Nd2xiii133.24 (5)
Si2—Nd2—Nd1xv151.99 (3)Nd2—Si2—Nd2i81.83 (4)
Si2x—Nd2—Nd1xv98.52 (3)Nd2xiii—Si2—Nd2i134.00 (5)
Si2x—Nd2—Nd2i106.53 (3)Nd2xiii—Si2—Nd3ii80.09 (4)
Si2—Nd2—Nd2i50.51 (3)Nd2xiii—Si2—Nd3x82.54 (4)
Si2i—Nd2—Nd2i47.66 (3)Nd2—Si2—Nd3ii139.78 (6)
Si2i—Nd2—Nd3x100.42 (3)Nd2i—Si2—Nd3ii87.23 (4)
Si2x—Nd2—Nd3xi52.28 (3)Nd2—Si2—Nd3x78.46 (4)
Si2x—Nd2—Nd3vii70.03 (3)Nd2i—Si2—Nd3x76.59 (3)
Si2x—Nd2—Nd3x51.78 (3)Nd2xiii—Si2—Nd380.12 (4)
Si2i—Nd2—Nd3vii53.85 (3)Nd2—Si2—Nd385.51 (4)
Si2—Nd2—Nd3vii102.94 (3)Nd2i—Si2—Nd3140.17 (6)
Si2i—Nd2—Nd3xi159.76 (3)Nd3—Si2—Nd1xii71.70 (3)
Si2—Nd2—Nd3xi69.76 (3)Nd3ii—Si2—Nd1xii69.93 (3)
Si2—Nd2—Nd3x54.35 (3)Nd3—Si2—Nd3x137.09 (5)
Si2—Nd2—Si1xii95.25 (4)Nd3—Si2—Nd3ii78.55 (4)
Si2—Nd2—Si1i140.41 (4)Nd3ii—Si2—Nd3x136.04 (5)
Si2i—Nd2—Si1i47.67 (4)Si1—Si2—Nd1xii120.80 (6)
Si2x—Nd2—Si1xii140.61 (4)Si1—Si2—Nd2i66.76 (5)
Si2x—Nd2—Si1i97.55 (4)Si1—Si2—Nd2xiii67.28 (5)
Si2x—Nd2—Si1x48.93 (4)Si1—Si2—Nd2135.73 (6)
Si2—Nd2—Si1x124.91 (4)Si1—Si2—Nd3ii71.20 (5)
Si2—Nd2—Si2x100.44 (2)Si1—Si2—Nd3138.40 (7)
Si2—Nd2—Si2i93.45 (5)Si1—Si2—Nd3x64.85 (5)
Symmetry codes: (i) y+1, x+1, z+1/2; (ii) y+3/2, x+1/2, z+1/4; (iii) x+1/2, y+3/2, z+3/4; (iv) x+1, y+1, z+1/2; (v) x+1, y+2, z+1/2; (vi) y+2, x+1, z+1/2; (vii) y+3/2, x1/2, z+1/4; (viii) y, x, z+1; (ix) x1/2, y+3/2, z+3/4; (x) x+3/2, y1/2, z+1/4; (xi) y, x, z; (xii) y1/2, x+3/2, z1/4; (xiii) x+3/2, y+1/2, z+1/4; (xiv) y+1, x+2, z+1/2; (xv) x+1, y+1, z1/2; (xvi) x+1, y+2, z1/2; (xvii) y+1/2, x+3/2, z1/4.
Selected bond lengths (Å) for Pr5Si4 top
Pr1—Pr2i3.4914 (4)Pr1—Si1ix3.1756 (13)
Pr1—Pr2ii3.5319 (4)Pr1—Si2ii3.1780 (13)
Pr1—Pr2iii3.5319 (4)Pr1—Si2iii3.1780 (13)
Pr1—Pr2iv3.4914 (4)Pr2—Pr2i3.9561 (6)
Pr1—Pr3v3.6423 (3)Pr2—Pr3vii3.9414 (4)
Pr1—Pr3vi3.6423 (3)Pr2—Pr3x3.9717 (3)
Pr1—Si1vii3.1756 (13)Pr2—Pr3xi3.9156 (3)
Pr1—Si1viii3.0985 (13)Pr3—Pr3ii4.0074 (2)
Pr1—Si13.0985 (13)Si1—Si22.4738 (16)
Symmetry codes: (i) -y+1, -x+1, -z+1/2; (ii) -y+3/2, x+1/2, z+1/4; (iii) x+1/2, -y+3/2, -z+3/4; (iv) -x+1, -y+1, z+1/2; (v) -y+2, -x+1, -z+1/2; (vi) -x+1, -y+2, z+1/2; (vii) -y+3/2, x-1/2, z+1/4; (viii) y, x, -z+1; (ix) x-1/2, -y+3/2, -z+3/4.
Selected bond lengths (Å) for Nd5Si4 top
Nd1—Nd2i3.4725 (5)Nd1—Si1ix3.1528 (16)
Nd1—Nd2ii3.5021 (5)Nd1—Si2ii3.1661 (16)
Nd1—Nd2iii3.5021 (5)Nd1—Si2iii3.1661 (16)
Nd1—Nd2iv3.4725 (5)Nd2—Nd2i3.9202 (7)
Nd1—Nd3v3.6265 (3)Nd2—Nd3x3.9094 (4)
Nd1—Nd3vi3.6265 (3)Nd2—Nd3xi3.9378 (4)
Nd1—Si1vii3.1528 (16)Nd2—Nd3vii3.9061 (4)
Nd1—Si1viii3.0744 (15)Nd3—Nd3xii3.9752 (2)
Nd1—Si13.0744 (15)Si1—Si22.482 (2)
Symmetry codes: (i) -y+1, -x+1, -z+1/2; (ii) -y+3/2, x+1/2, z+1/4; (iii) x+1/2, -y+3/2, -z+3/4; (iv) -x+1, -y+1, z+1/2; (v) -y+2, -x+1, -z+1/2; (vi) -x+1, -y+2, z+1/2; (vii) -y+3/2, x-1/2, z+1/4; (viii) y, x, -z+1; (ix) x-1/2, -y+3/2, -z+3/4.
 

Acknowledgements

The authors gratefully thank the Instrumental Analysis Center of Yokohama National University for providing access to the single-crystal X-ray diffractometer.

Funding information

Funding for this research was provided by: JSPS Grant-in-Aid for Scientific Research (KAKENHI) (grant No. 18K049922 and 18K03536).

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