On the representation of integers by binary cubic forms of positive discriminant

1983 ◽  
Vol 73 (1) ◽  
pp. 117-138 ◽  
Author(s):  
J. -H. Evertse
Keyword(s):  
Representation Of Integers ◽  
Cubic Forms ◽  
Positive Discriminant

scholarly journals Hydride-based antiperovskites with soft anionic sublattices as fast alkali ionic conductors

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shenghan Gao ◽  
Thibault Broux ◽  
Susumu Fujii ◽  
Cédric Tassel ◽  
Kentaro Yamamoto ◽  
...  
Keyword(s):  
Experimental Studies ◽  
Ionic Conductivities ◽  
Cubic Phase ◽  
Ionic Conductors ◽  
Large Size ◽  
Migration Barriers ◽  
Soft Phonon Mode ◽  
Aliovalent Substitution ◽  
Cubic Forms ◽  
The Ideal

AbstractMost solid-state materials are composed of p-block anions, only in recent years the introduction of hydride anions (1s2) in oxides (e.g., SrVO2H, BaTi(O,H)3) has allowed the discovery of various interesting properties. Here we exploit the large polarizability of hydride anions (H–) together with chalcogenide (Ch2–) anions to construct a family of antiperovskites with soft anionic sublattices. The M3HCh antiperovskites (M = Li, Na) adopt the ideal cubic structure except orthorhombic Na3HS, despite the large variation in sizes of M and Ch. This unconventional robustness of cubic phase mainly originates from the large size-flexibility of the H– anion. Theoretical and experimental studies reveal low migration barriers for Li+/Na+ transport and high ionic conductivity, possibly promoted by a soft phonon mode associated with the rotational motion of HM6 octahedra in their cubic forms. Aliovalent substitution to create vacancies has further enhanced ionic conductivities of this series of antiperovskites, resulting in Na2.9H(Se0.9I0.1) achieving a high conductivity of ~1 × 10–4 S/cm (100 °C).

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