Solid-state electrolyte, method of preparing solid-state electrolyte and lithium battery including solid-state electrolyte

A lithium battery comprising:

• a cathode;
• an anode;
• and a solid-state electrolyte layer disposed between the cathode and the anode,
• wherein at least one of the cathode, the anode, or the solid-state electrolyte layer comprises a solid-state electrolyte,
• the solid-state electrolyte is a garnet-type solid-state electrolyte including a compound represented by Formula 1,
• wherein the garnet-type solid-state electrolyte includes a crystalline phase including a cubic phase, and a 7Li nuclear magnetic resonance spectroscopy spectrum of the solid-state electrolyte includes a first peak appears in a range of about −2 parts per million to about 8 parts per million, and a full width at half maximum of the peak is about 0.3 parts per million to about 4.0 parts per million under stated acquisition parameters:
• Formula 1
• (LixM1x1)(LayM2y1)(ZrzAa)O12+δ
• wherein in Formula 1,
• M1 is a monovalent cation, a divalent cation, a trivalent cation, or a combination thereof,
• M2 is a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, or a combination thereof,
• A is two or more elements independently selected from a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, or a pentavalent cation,
• 6≤x≤8, 0≤x1≤2, 0<y≤4, 0≤y1≤4, 0<z≤3, 0<a≤3, and
• δ is a value determined to satisfy charge neutrality, wherein −1≤δ≤1.

A method of preparing a solid-state electrolyte, the method comprising:

• providing a solid-state electrolyte precursor having an amorphous phase;
• and
• heat-treating the solid-state electrolyte precursor at a temperature of 700° C. or lower,
• wherein the solid-state electrolyte comprises a compound represented by Formula 1, includes a cubic crystalline phase, and a 7Li nuclear magnetic resonance spectroscopy spectrum of the solid-state electrolyte includes a peak in a range of about −2 parts per million to about 8 parts per million, and a full width at half maximum of the peak is about 0.3 parts per million to about 4.0 parts per million under stated acquisition parameters:
• Formula 1
• (LixM1x1)(LayM2y1)(ZrzAa)O12+δ
• wherein in Formula 1, M1 is a monovalent cation, a divalent cation, a trivalent cation, or a combination thereof,
• M2 is a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, or a combination thereof,
• A is two or more elements independently selected from a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, or a pentavalent cation,
• 6≤x≤8, 0≤x1≤2, 0<y≤4, 0≤y1≤4, 0<z≤3, and 0<a≤3, and
• δ is a value determined to satisfy charge neutrality, wherein −1≤δ≤1.