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<p>Fast-ion conductors are critical to
the development of solid-state batteries. The effects of mechanochemical
synthesis that lead to increased ionic conductivity in an archetypical
sodium-ion conductor Na<sub>3</sub>PS<sub>4</sub> are not fully understood. We
present here a comprehensive analysis based on diffraction (Bragg, pair
distribution function), spectroscopy (impedance, Raman, NMR, INS) and <i>ab-initio</i> simulations aimed at
elucidating the synthesis-property relationships in Na<sub>3</sub>PS<sub>4</sub>.
We consolidate previously reported interpretations about the local structure of
ball-milled samples, underlining the sodium disorder and showing that a local tetragonal
framework more accurately describes the structure than the originally proposed
cubic one. Through variable-pressure impedance spectroscopy measurements, we
report for the first time the activation volume for Na<sup>+</sup> migration in
Na<sub>3</sub>PS<sub>4</sub>, which is ~30% higher for the ball-milled samples.
Moreover, we show that the effect of ball-milling on increasing the ionic
conductivity of Na<sub>3</sub>PS<sub>4</sub> to ~10<sup>-4</sup> S/cm can be
reproduced by applying external pressure on a sample from conventional high
temperature ceramic synthesis. We conclude that the key effects of
mechanochemical synthesis on the properties of solid electrolytes can be
analyzed and understood in terms of pressure, strain and activation volume.</p>
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