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Critical evaluation and thermodynamic modeling of the Pd–Sn system

The single crystalline material PdSn 4 , a homologue of the Dirac nodal arc semimetal PtSn 4 , is a promising candidate to search for new topological states with fascinating quantum physical properties. In the present work, the thermochemistry and phase diagram information of the Pd–Sn system published in the literature was collected and critically reviewed, two thermodynamic reassessments of the Pd–Sn system were carried out in the frame of the CALPHAD approach to optimize the Gibbs free energy of each phase presented in the system. The liquid phase was described using respectively the Bragg-Williams random mixing model and the associate solution model. All the reliable thermodynamic property and phase equilibria data can be generally described using the presently obtained thermodynamic descriptions of the Pd–Sn system. Issues related to the further improvement of the thermodynamic descriptions of the Pd–Sn system are discussed.

36 MATERIALS SCIENCE↗

Materials Data on SnPd by Materials Project

PdSn is Modderite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Pd is bonded in a 6-coordinate geometry to six equivalent Sn atoms. There are a spread of Pd–Sn bond distances ranging from 2.70–2.85 Å. Sn is bonded in a 6-coordinate geometry to six equivalent Pd atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sn3Pd by Materials Project

PdSn3 crystallizes in the orthorhombic Cmce space group. The structure is two-dimensional and consists of two PdSn3 sheets oriented in the (0, 1, 0) direction. Pd is bonded in a 9-coordinate geometry to eight Sn atoms. There are a spread of Pd–Sn bond distances ranging from 2.83–2.89 Å. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded in a 4-coordinate geometry to four equivalent Pd and one Sn atom. The Sn–Sn bond length is 3.00 Å. In the second Sn site, Sn is bonded in a 2-coordinate geometry to two equivalent Pd atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sn2Pd by Materials Project

PdSn2 crystallizes in the tetragonal I4_1/acd space group. The structure is three-dimensional. Pd is bonded in a 8-coordinate geometry to one Pd and eight Sn atoms. The Pd–Pd bond length is 2.90 Å. There are a spread of Pd–Sn bond distances ranging from 2.85–2.88 Å. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded in a 7-coordinate geometry to four equivalent Pd and one Sn atom. The Sn–Sn bond length is 2.96 Å. In the second Sn site, Sn is bonded to four equivalent Pd atoms to form a mixture of distorted edge and corner-sharing SnPd4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on SnPd2 by Materials Project

Pd2Sn is Cotunnite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Pd sites. In the first Pd site, Pd is bonded in a 4-coordinate geometry to six equivalent Pd and five equivalent Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.96–3.20 Å. There are a spread of Pd–Sn bond distances ranging from 2.71–3.04 Å. In the second Pd site, Pd is bonded in a 5-coordinate geometry to eight Pd and five equivalent Sn atoms. Both Pd–Pd bond lengths are 2.92 Å. There are a spread of Pd–Sn bond distances ranging from 2.75–3.00 Å. Sn is bonded in a 10-coordinate geometry to ten Pd atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sn4Pd by Materials Project

PdSn4 crystallizes in the orthorhombic Aea2 space group. The structure is two-dimensional and consists of two PdSn4 sheets oriented in the (0, 1, 0) direction. Pd is bonded in a 8-coordinate geometry to eight Sn atoms. There are a spread of Pd–Sn bond distances ranging from 2.82–2.85 Å. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded in a 2-coordinate geometry to two equivalent Pd atoms. In the second Sn site, Sn is bonded in a 2-coordinate geometry to two equivalent Pd atoms.

36 MATERIALS SCIENCE↗

Materials Data on SnPd3 by Materials Project

Pd3Sn is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Pd is bonded to eight equivalent Pd and four equivalent Sn atoms to form PdSn4Pd8 cuboctahedra that share corners with twelve equivalent PdSn4Pd8 cuboctahedra, edges with eight equivalent SnPd12 cuboctahedra, edges with sixteen equivalent PdSn4Pd8 cuboctahedra, faces with four equivalent SnPd12 cuboctahedra, and faces with fourteen equivalent PdSn4Pd8 cuboctahedra. All Pd–Pd bond lengths are 2.86 Å. All Pd–Sn bond lengths are 2.86 Å. Sn is bonded to twelve equivalent Pd atoms to form SnPd12 cuboctahedra that share corners with twelve equivalent SnPd12 cuboctahedra, edges with twenty-four equivalent PdSn4Pd8 cuboctahedra, faces with six equivalent SnPd12 cuboctahedra, and faces with twelve equivalent PdSn4Pd8 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Sn9Pd13 by Materials Project

Pd13Sn9 crystallizes in the trigonal P3_121 space group. The structure is three-dimensional. there are eight inequivalent Pd sites. In the first Pd site, Pd is bonded in a 12-coordinate geometry to six Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.86–3.05 Å. There are a spread of Pd–Sn bond distances ranging from 2.79–2.90 Å. In the second Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.88–3.06 Å. There are a spread of Pd–Sn bond distances ranging from 2.71–2.94 Å. In the third Pd site, Pd is bonded in a 12-coordinate geometry to six Pd and six Sn atoms. There are two shorter (2.86 Å) and two longer (3.01 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.78–2.93 Å. In the fourth Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. There are a spread of Pd–Pd bond distances ranging from 2.91–2.99 Å. There are a spread of Pd–Sn bond distances ranging from 2.82–2.99 Å. In the fifth Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. There are one shorter (2.89 Å) and one longer (3.06 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.69–2.93 Å. In the sixth Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. Both Pd–Pd bond lengths are 2.98 Å. There are a spread of Pd–Sn bond distances ranging from 2.82–3.00 Å. In the seventh Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. There are one shorter (2.89 Å) and one longer (3.03 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.69–2.90 Å. In the eighth Pd site, Pd is bonded in a 4-coordinate geometry to six Pd and seven Sn atoms. There are a spread of Pd–Sn bond distances ranging from 2.80–3.33 Å. There are five inequivalent Sn sites. In the first Sn site, Sn is bonded in a 7-coordinate geometry to eight Pd atoms. In the second Sn site, Sn is bonded in a 9-coordinate geometry to nine Pd atoms. In the third Sn site, Sn is bonded in a distorted body-centered cubic geometry to eight Pd atoms. In the fourth Sn site, Sn is bonded in a 9-coordinate geometry to nine Pd atoms. In the fifth Sn site, Sn is bonded in a 10-coordinate geometry to ten Pd atoms.

36 MATERIALS SCIENCE↗

Materials Data on Sn13Pd20 by Materials Project

Pd20Sn13 crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are twenty-two inequivalent Pd sites. In the first Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. There are a spread of Pd–Pd bond distances ranging from 2.87–3.02 Å. There are a spread of Pd–Sn bond distances ranging from 2.81–2.99 Å. In the second Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. There are a spread of Pd–Pd bond distances ranging from 2.89–3.00 Å. There are a spread of Pd–Sn bond distances ranging from 2.81–2.95 Å. In the third Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. There are a spread of Pd–Pd bond distances ranging from 2.84–2.99 Å. There are a spread of Pd–Sn bond distances ranging from 2.80–2.96 Å. In the fourth Pd site, Pd is bonded in a 11-coordinate geometry to five Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.83–3.03 Å. There are a spread of Pd–Sn bond distances ranging from 2.69–2.96 Å. In the fifth Pd site, Pd is bonded in a 5-coordinate geometry to six Pd and five Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.83–3.02 Å. There are a spread of Pd–Sn bond distances ranging from 2.68–2.97 Å. In the sixth Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.86–3.08 Å. There are a spread of Pd–Sn bond distances ranging from 2.71–2.98 Å. In the seventh Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.89–3.04 Å. There are a spread of Pd–Sn bond distances ranging from 2.69–2.95 Å. In the eighth Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.88–3.02 Å. There are a spread of Pd–Sn bond distances ranging from 2.70–2.98 Å. In the ninth Pd site, Pd is bonded in a 5-coordinate geometry to six Pd and five Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.82–3.03 Å. There are a spread of Pd–Sn bond distances ranging from 2.67–2.90 Å. In the tenth Pd site, Pd is bonded in a 3-coordinate geometry to seven Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.85–3.04 Å. There are a spread of Pd–Sn bond distances ranging from 2.78–3.29 Å. In the eleventh Pd site, Pd is bonded in a 4-coordinate geometry to six Pd and seven Sn atoms. There are one shorter (2.89 Å) and one longer (3.03 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.78–3.37 Å. In the twelfth Pd site, Pd is bonded in a 4-coordinate geometry to six Pd and seven Sn atoms. There are one shorter (2.87 Å) and one longer (2.97 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.82–3.38 Å. In the thirteenth Pd site, Pd is bonded in a 12-coordinate geometry to six Pd and six Sn atoms. There are two shorter (2.88 Å) and two longer (3.00 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.77–2.92 Å. In the fourteenth Pd site, Pd is bonded in a 12-coordinate geometry to six Pd and six Sn atoms. There are a spread of Pd–Pd bond distances ranging from 2.83–3.02 Å. There are a spread of Pd–Sn bond distances ranging from 2.78–2.96 Å. In the fifteenth Pd site, Pd is bonded in a 5-coordinate geometry to six Pd and five Sn atoms. There are one shorter (2.86 Å) and one longer (2.98 Å) Pd–Pd bond lengths. There are a spread of Pd–Sn bond distances ranging from 2.68–2.85 Å. In the sixteenth Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. The Pd–Pd bond length is 2.98 Å. There are a spread of Pd–Sn bond distances ranging from 2.71–2.93 Å. In the seventeenth Pd site, Pd is bonded in a 6-coordinate geometry to five Pd and six Sn atoms. The Pd–Pd bond length is 2.97 Å. There are a spread of Pd–Sn bond distances ranging from 2.69–2.94 Å. In the eighteenth Pd site, Pd is bonded in a 12-coordinate geometry to six Pd and six Sn atoms. There are a spread of Pd–Sn bond distances ranging from 2.77–2.88 Å. In the nineteenth Pd site, Pd is bonded in a 12-coordinate geometry to six Pd and six Sn atoms. There are a spread of Pd–Sn bond distances ranging from 2.78–2.92 Å. In the twentieth Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. There are a spread of Pd–Sn bond distances ranging from 2.83–2.96 Å. In the twenty-first Pd site, Pd is bonded to six Pd and six Sn atoms to form a mixture of distorted face and corner-sharing PdSn6Pd6 cuboctahedra. There are a spread of Pd–Sn bond distances ranging from 2.80–2.99 Å. In the twenty-second Pd site, Pd is bonded in a 12-coordinate geometry to eight Pd and six Sn atoms. There are a spread of Pd–Sn bond distances ranging from 3.19–3.25 Å. There are thirteen inequivalent Sn sites. In the first Sn site, Sn is bonded in a 8-coordinate geometry to nine Pd atoms. In the second Sn site, Sn is bonded in a 9-coordinate geometry to nine Pd atoms. In the third Sn site, Sn is bonded in a 10-coordinate geometry to ten Pd atoms. In the fourth Sn site, Sn is bonded in a 8-coordinate geometry to nine Pd atoms. In the fifth Sn site, Sn is bonded in a 10-coordinate geometry to ten Pd atoms. In the sixth Sn site, Sn is bonded in a 9-coordinate geometry to nine Pd atoms. In the seventh Sn site, Sn is bonded in a 10-coordinate geometry to ten Pd atoms. In the eighth Sn site, Sn is bonded in a 10-coordinate geometry to ten Pd atoms. In the ninth Sn site, Sn is bonded in a 10-coordinate geometry to ten Pd atoms. In the tenth Sn site, Sn is bonded in a 7-coordinate geometry to nine Pd atoms. In the eleventh Sn site, Sn is bonded in a 7-coordinate geometry to eight Pd atoms. In the twelfth Sn site, Sn is bonded in a 7-coordinate geometry to eight Pd atoms. In the thirteenth Sn site, Sn is bonded in a distorted body-centered cubic geometry to eight Pd atoms.

36 MATERIALS SCIENCE↗