SOLID ELECTROLYTES, BATTERIES, AND METHODS

Abstract

Electrolytes, methods of preparing electrolytes, and batteries include electrolytes. Electrolytes may include a material of formula (I), Li.sub.3PS.sub.4-xO.sub.x, wherein x is 0<x≤1. The electrolytes may be glass-ceramic electrolytes. Batteries including electrolytes may be lithium-ion batteries.

Claims

1. An electrolyte comprising a material of formula (I):
Li.sub.3PS.sub.4-xO.sub.x  formula (I); wherein 0<x≤1.

2. The electroyte of claim 1, wherein 0<x<1.

3. The electrolyte of claim 1, wherein 0<x≤0.5.

4. The electrolyte of claim 1, wherein 0<x≤0.35.

5. The electrolyte of claim 1, wherein 0<x≤0.31.

6. The electrolyte of claim 1, wherein x is (i) 0.1, (ii) 0.25, (iii) 0.31, or (iv) 0.5.

7. The electrolyte of claim 1, wherein the electrolyte consists of the material of formula (I).

8. The electrolyte of claim 1, wherein the electrolye is in the form of a powder.

9. The electrolyte of claim 1, wherein the electrolye is in the form of a pellet, the pellet having a density of about 1.5 g/cm.sup.3 to about 2 g/cm.sup.3.

10. The electrolyte of claim 1, wherein x is greater than 0, and the electrolye has an activation energy that is less than an activation energy of β-Li.sub.3PS.sub.4.

11. The electrolyte of claim 10, wherein the activation energy is at least 5% less than the activation energy of β-Li.sub.3PS.sub.4.

12. The electrolyte of claim 1, wherein x is greater than 0, and the electrolyte has an ionic conductivity that is at least 5 times greater than an ionic conductivity of β-Li.sub.3PS.sub.4.

13. A lithium-ion battery comprising the electrolyte of claim 1.

14. A method for forming the electrolyte of claim 1, the method comprising: contacting Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 to form the electrolyte.

15. The method of claim 14, wherein the contacting of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 comprises (i) mixing Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5, (ii) homogenizing Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 under vacuum, or (iii) a combination thereof.

16. The method of claim 14, wherein the homogenizing of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 under vacuum comprises milling Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 with a milling media, wherein a weight ratio of the milling media to the total weight of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 is about 10:1 to about 20:1.

17. The method of claim 14, wherein the electrolye is a powder, and the method further comprises pressing the powder into a pellet.

18. The method of claim 17, wherein the pressing of the powder into the pellet comprises subjecting the powder to a pressure of at least 200 MPa, and a temperature of at least 200° C.

19. The method of claim 18, wherein the powder is subjected to the pressure and the temperature simultaneously.

20. An electrolyte comprising a material of formula (I):
Li.sub.3PS.sub.4-xO.sub.x  formula (I); wherein x is 0.1<x≤0.31.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIG. 1A depicts powder X-ray diffraction (PXRD) patterns of embodiments of Li.sub.3PS.sub.4-xO.sub.x and β-Li.sub.3PS.sub.4.

[0018] FIG. 1B depicts a plot of ΔH.sub.mix of embodiments of Li.sub.3PS.sub.4-xO.sub.x.

[0019] FIG. 2 depicts PXRD patterns of embodiments of Li.sub.3PS.sub.4-xO.sub.x.

[0020] FIG. 3A depicts .sup.6Li nuclear magnetic resonance (NMR) spectra for Li.sub.3PS.sub.4-xO.sub.x.

[0021] FIG. 3B depicts .sup.6Li quantitative analysis for embodiments of Li.sub.3PS.sub.4-xO.sub.x.

[0022] FIG. 4A depicts experimental .sup.6Li spectra and deconvolution of Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3PS.sub.3.69O.sub.0.31.

[0023] FIG. 4B depicts experimental .sup.31P spectra and deconvolution for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3PS.sub.3.69O.sub.0.31.

[0024] FIG. 4C depicts simulated .sup.6Li spectra for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, and Li.sub.3PS.sub.3.75O.sub.0.25.

[0025] FIG. 4D depicts simulated .sup.31P spectra for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, and Li.sub.3PS.sub.3.75O.sub.0.25.

[0026] FIG. 5 depicts a plot of .sup.7Li spin-lattice relaxation times, T.sub.1, for embodiments of Li.sub.3PS.sub.4-xO.sub.x, (x=0, 0.1, 0.25, and 0.31).

[0027] FIG. 6A depicts .sup.31P magic angle spinning (MAS) NMR spectra for x in embodiments of Li.sub.3PS.sub.4-xO.sub.x.

[0028] FIG. 6B depicts .sup.31P quantitative analysis for embodiments of Li.sub.3PS.sub.4-xO.sub.x, (x=0, 0.1, 0.25, and 0.31).

[0029] FIG. 7A depicts conductivity isotherms from −40° C. to 120° C. of Li.sub.3PS.sub.3.69O.sub.0.31.

[0030] FIG. 7B depicts an Arrhenius plot for x in Li.sub.3PS.sub.4-xO.sub.2 using the Arrhenius relation between σ.sub.DC and inverse temperature to calculate E.sub.a,DC.

[0031] FIG. 8A depicts a Nyquist plot of Li.sub.3PS.sub.4 at −40° C.

[0032] FIG. 8B depicts a Nyquist plot of Li.sub.3PS.sub.3.9O.sub.0.1 at −40° C.

[0033] FIG. 8C depicts a Nyquist plot of Li.sub.3PS.sub.3.75O.sub.0.25 at −40° C.

[0034] FIG. 8D depicts a Nyquist plot of Li.sub.3PS.sub.3.69O.sub.0.31 at −40° C.

[0035] FIG. 8E depicts a Nyquist plot of Li.sub.3PS.sub.3.5O.sub.0.5 at −40° C.

[0036] FIG. 8F depicts a Nyquist plot of Li.sub.3PS.sub.3O at −40° C.

[0037] FIG. 9A depicts conductivity isotherms (σ′) of embodiments of Li.sub.3PS.sub.4 acquired from −40° C. to 120° C.

[0038] FIG. 9B depicts conductivity isotherms (σ′) of embodiments of Li.sub.3PS.sub.3.9O.sub.0.1 acquired from −40° C. to 120° C.

[0039] FIG. 9C depicts conductivity isotherms (σ′) of embodiments of Li.sub.3PS.sub.3.75O.sub.0.25 acquired from −40° C. to 120° C.

[0040] FIG. 9D depicts conductivity isotherms (σ′) of embodiments of Li.sub.3PS.sub.3.69O.sub.0.31 acquired from −40° C. to 120° C.

[0041] FIG. 9E depicts conductivity isotherms (σ′) of embodiments of Li.sub.3PS.sub.3.5O.sub.0.5 acquired from −40° C. to 120° C.

[0042] FIG. 9F depicts conductivity isotherms (σ′) of embodiments of Li.sub.3PS.sub.3O.sub.1 acquired from −40° C. to 120° C.

[0043] FIG. 10A depicts Arrhenius plots for x in embodiments of Li.sub.3PS.sub.4-xO.sub.x.

[0044] FIG. 10B depicts the number of Li with varying Li—Li distance for embodiments of Li.sub.3PS.sub.4-xO.sub.x.

[0045] FIG. 11A depicts the frequency dependence of M″ (the imaginary part of the complex electric modulus) of Li.sub.3PS.sub.3.69O.sub.0.31.

[0046] FIG. 11B depicts the temperature dependence of τ.sub.M″.sup.−1 of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1).

[0047] FIG. 12 depicts the normalized crossover frequency, ω.sub.c, of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1).

[0048] FIG. 13 depicts fractions of Li exhibiting MSC>5 Å.sup.2 from the 600K ab initio molecular dynamics (AIMD) trajectory of 200 ps with respect to x in Li.sub.3PS.sub.4-xO.sub.x.

[0049] FIG. 14A depicts the real part of resistivity (ρ′) of Li.sub.3PS.sub.3.69O.sub.0.31 as a function of inverse temperature.

[0050] FIG. 14B depicts the temperature dependence of ρ′ of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1) when measured at 1 MHz.

[0051] FIG. 15 depicts VT-EIS summary for x in Li.sub.3PS.sub.4-xO.sub.x.

[0052] FIG. 16A depicts the radial pair distribution function of S—Li and O—Li bond pairs for varying concentrations of oxygen in Li.sub.3PS.sub.4-xO.sub.x.

[0053] FIG. 16B depicts the number of Li (n.sub.Li) surrounding S and O within a first coordination shell.

[0054] FIG. 17A depicts Li spatial density with respect to the Li—Li distance parameter for embodiments of electrolytes herein.

[0055] FIG. 17B depicts Arrhenius plots of Li.sub.3PS.sub.3O localized and dispersed.

DETAILED DESCRIPTION

[0056] Provided herein are electrolytes, batteries, and methods for making electrolytes, such as the electrolytes described herein.

Electrolytes and Batteries

[0057] In some embodiments, the electrolytes provided herein include a material of formula (I):

Li.sub.3PS.sub.4-xO.sub.x  formula (I);

wherein x is 0<x≤1.

[0058] In some embodiments, the electrolyes provided herein include a material of formula (I), wherein 0<x<1, 0<x<0.9, 0<x<0.8, 0<x<0.7, 0<x<0.6, 0<x<0.5, 0<x<0.4, 0<x<0.35, 0<x<0.31, 0<x<0.3, 0<x<0.25, 0<x<0.2, 0<x<0.15, or 0<x<0.1.

[0059] In some embodiments, the electrolyes provided herein include a material of formula (I), wherein 0<x≤1, 0<x≤0.9, 0<x≤0.8, 0<x≤0.7, 0<x≤0.6, 0<x≤0.5, 0<x≤0.4, 0<x≤0.35, 0<x≤0.31, 0<x≤0.3, 0<x≤0.25, 0<x≤0.2, 0<x≤0.15, or 0<x≤0.1.

[0060] In some embodiments, the electrolyes provided herein include a material of formula (I), wherein 0.1<x<1, 0.15<x<1, 0.2<x<1, 0.25<x<1, 0.3<x<1, 0.31<x<1.

[0061] In some embodiments, the electrolyes provided herein include a material of formula (I), wherein 0.1<x≤1, 0.15<x≤1, 0.2<x≤1, 0.25<x≤1, 0.3<x≤1, or 0.31<x≤1.

[0062] In some embodiments, the electrolyes provided herein include a material of formula (I), wherein 0.1<x<0.5, 0.15<x<0.5, 0.2<x<0.5, 0.25<x<0.5, 0.3<x<0.5, 0.31<x<0.5.

[0063] In some embodiments, the electrolyes provided herein include a material of formula (I), wherein 0.1<x≤0.5, 0.15<x≤0.5, 0.2<x≤0.5, 0.25<x≤0.5, 0.3<x≤0.5, 0.31<x≤0.5.

[0064] In some embodiments, the electrolytes provided herein include a material of formula (I), wherein x is 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8, 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, or 0.99.

[0065] In some embodiments, the electrolyte consists of a material of formula (I).

[0066] The electrolytes provided herein may be in any physical form. The electrolytes, for example, may be solid electrolytes. The solid electrolytes may be glass-ceramic electrolytes. As used herein, the phrase “glass-ceramic electrolyte” refers to an electrolyte having at least one type of functional crystalline phase and a residual glass. The solid electrolytes may be in the form of a powder. The solid electrolytes may be in the form of a pellet. The pellet may have any density that is suitable for a desired application, such as lithium-ion batteries. In some embodiments, the solid electrolytes, such as the solid electrolytes in the form of a pellet, have a density of about 1 g/cm.sup.3 to about 3 g/cm.sup.3, about 1.5 g/cm.sup.3 to about 2.5 g/cm.sup.3, or about 1.5 g/cm.sup.3 to about 2 g/cm.sup.3.

[0067] In some embodiments, x is greater than 0, and the electrolye has an activation energy that is less than an activation energy of β-Li.sub.3PS.sub.4. The activation energy, for example, may be at least 1%, at least 3%, at least 5%, at least 10%, at least 20%, or at least 25% less than an activation energy of β-Li.sub.3PS.sub.4.

[0068] In some embodiments, x is greater than 0, and the electrolyte has an ionic conductivity that is at least 3 times, at least 4 times, at least 5 times, at least 6 times, at least 7 times, or at least 10 times greater than an ionic conductivity of β-Li.sub.3PS.sub.4.

[0069] Also provided herein are batteries that include one or more electrolytes provided herein. In some embodiments, the battery is a lithium-ion battery. The batteries may include an anode, a cathode, and an electrolyte described herein. The electrolyte may be arranged between the anode and the cathode.

Methods

[0070] Also provided herein are methods of forming electrolytes. In some embodiments, the methods include contacting Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 to form an electrolyte. When the methods are used to produce electrolytes that include a composition of formula (I), the ratios of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 that are contacted may be selected to achieve a desired value for “x” of formula (I).

[0071] The Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 may be contacted using any known technique. In some embodiments, the contacting of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 includes (i) mixing Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5, (ii) homogenizing Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 under vacuum, or (iii) a combination thereof.

[0072] The homogenizing of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 under vacuum may include milling Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 with a milling media, wherein a weight ratio of the milling media to the total weight of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 is about 10:1 to about 20:1, about 12:1 to about 18:1, about 12:1 to about 16:1, about 13:1 to about 15:1, or about 14:1. As used herein, the term “milling” refers to crushing, grinding, or a combination thereof, and the phrase “milling media” refers object(s) used to crush and/or grind. Non-limiting examples of milling media that may be used in the methods herein include one or more three-dimensional objects, such as balls, cylinders, etc., which may be formed of metal, ceramic, glass, etc.

[0073] In some embodiments, the methods also include pressing an electrolyte, such as an electrolyte in powder form, into a pellet. The pressing of the elecrolyte, such as an electrolyte in powder form, into a pellet includes subjecting the electrolyte to a pressure of at least 100 MPa, at least 150 MPa, at least 200 MPa, at least 250 MPa, or at least 300 MPa, and a temperature of at least 100° C., at least 150° C., at least 200° C., at least 250° C., or at least 300° C. The electrolyte may be subjected to the pressure and the temperature simultaneously, sequentially, or a combination thereof.

EMBODIMENTS

[0074] The following listing provides non-limiting embodiments of the electrolytes, batteries, and methods provided herein:

Embodiment 1

[0075] An electrolyte comprising a material of formula (I):

Li.sub.3PS.sub.4-xO.sub.x  formula (I);

wherein x is 0<x≤1.

Embodiment 2

[0076] The electrolyte of Embodiment 1, wherein 0<x<1, 0<x<0.9, 0<x<0.8, 0<x<0.7, 0<x<0.6, 0<x<0.5, 0<x<0.4, 0<x<0.35, 0<x<0.31, 0<x<0.3, 0<x<0.25, 0<x<0.2, 0<x<0.15, or 0<x<0.1.

Embodiment 3

[0077] The electrolyte of Embodiment 1, wherein 0<x≤1, 0<x≤0.9, 0<x≤0.8, 0<x≤0.7, 0<x≤0.6, 0<x≤0.5, 0<x≤0.4, 0<x≤0.35, 0<x≤0.31, 0<x≤0.3, 0<x≤0.25, 0<x≤0.2, 0<x≤0.15, or 0<x≤0.1.

Embodiment 4

[0078] The electrolyte of Embodiment 1, wherein 0.1<x<1, 0.15<x<1, 0.2<x<1, 0.25<x<1, 0.3<x<1, 0.31<x<1.

Embodiment 5

[0079] The electrolyte of Embodiment 1, wherein 0.1<x≤1, 0.15<x≤1, 0.2<x≤1,0.25<x≤1,0.3<x≤1, or 0.31<x≤1.

Embodiment 6

[0080] The electrolyte of Embodiment 1, wherein 0.1<x<0.5, 0.15<x<0.5, 0.2<x<0.5, 0.25<x<0.5, 0.3<x<0.5, 0.31<x<0.5.

Embodiment 7

[0081] The electrolyte of Embodiment 1, wherein 0.1<x≤0.5, 0.15<x≤0.5, 0.2<x≤0.5, 0.25<x≤0.5, 0.3<x≤0.5, 0.31<x≤0.5.

Embodiment 8

[0082] The electrolyte of Embodiment 1, wherein x is 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8, 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, or 0.99.

Embodiment 9

[0083] The electrolyte of any one of Embodiments 1 to 8, wherein the electrolyte consists of the material of formula (I).

Embodiment 10

[0084] The electrolyte of any one of Embodiments 1 to 9, wherein the electrolyte is a solid electrolyte.

Embodiment 11

[0085] The electrolyte of Embodiment 10, wherein the solid electrolyte is a glass-ceramic electrolyte.

Embodiment 12

[0086] The electrolyte of Embodiment 10 or 11, wherein the electrolye is in the form of a powder.

Embodiment 13

[0087] The electrolyte of any of Embodiments 1 to 12, wherein the electrolye is in the form of a pellet.

Embodiment 14

[0088] The electrolyte of Embodiment 13, wherein the pellet has a density of about 1 g/cm.sup.3 to about 3 g/cm.sup.3, about 1.5 g/cm.sup.3 to about 2.5 g/cm.sup.3, or about 1.5 g/cm.sup.3 to about 2 g/cm.sup.3.

Embodiment 15

[0089] The electrolyte of any of Embodiments 1 to 14, wherein x is greater than 0, and the electrolye has an activation energy that is less than an activation energy of β-Li.sub.3PS.sub.4.

Embodiment 16

[0090] The electrolyte of Embodiment 15, wherein the activation energy is at least 1%, at least 3%, at least 5%, at least 10%, at least 20%, or at least 25% less than an activation energy of β-Li.sub.3PS.sub.4.

Embodiment 17

[0091] The electrolyte of any of Embodiments 1 to 16, wherein x is greater than 0, and the electrolyte has an ionic conductivity that is at least 3 times, at least 4 times, at least 5 times, at least 6 times, at least 7 times, or at least 10 times greater than an ionic conductivity of β-Li.sub.3PS.sub.4.

Embodiment 18

[0092] A battery including an electrolyte of any of Embodiments 1 to 17.

Embodiment 19

[0093] The battery of Embodiment 18, wherein the battery is a lithium-ion battery.

Embodiment 20

[0094] A method forming an electrolyte, such as an electrolyte of any of Embodiments 1 to 17, wherein the method includes contacting Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 to form the electrolyte.

Embodiment 21

[0095] The method of Embodiment 20, wherein the contacting of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 comprises (i) mixing Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5, (ii) homogenizing Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 under vacuum, or (iii) a combination thereof.

Embodiment 22

[0096] The method of Embodiment 20 or 21, wherein the homogenizing of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 under vacuum comprises milling Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 with a milling media.

Embodiment 23

[0097] The method of Embodiment 22, wherein a weight ratio of the milling media to the total weight of Li.sub.2S, P.sub.2S.sub.5, and P.sub.2O.sub.5 is about 10:1 to about 20:1, about 12:1 to about 18:1, about 12:1 to about 16:1, about 13:1 to about 15:1, or about 14:1.

Embodiment 24

[0098] The method of any of Embodiments 20 to 23, wherein the method further comprises pressing the electrolyte into a pellet.

Embodiment 25

[0099] The method of Embodiment 24, wherein the pressing of the elecrolyte, such as an electrolyte in powder form, into a pellet includes subjecting the electrolyte to a pressure of at least 100 MPa, at least 150 MPa, at least 200 MPa, at least 250 MPa, or at least 300 MPa, and a temperature of at least 100° C., at least 150° C., at least 200° C., at least 250° C., or at least 300° C.

Embodiment 26

[0100] The method of Embodiment 25, wherein the electrolyte is subjected to the pressure and the temperature simultaneously, sequentially, or a combination thereof.

[0101] All referenced publications are incorporated herein by reference in their entirety. Furthermore, where a definition or use of a term in a reference, which is incorporated by reference herein, is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply.

[0102] While certain aspects of conventional technologies have been discussed to facilitate disclosure of various embodiments, applicants in no way disclaim these technical aspects, and it is contemplated that the present disclosure may encompass one or more of the conventional technical aspects discussed herein.

[0103] The present disclosure may address one or more of the problems and deficiencies of known methods and processes. However, it is contemplated that various embodiments may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the present disclosure should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.

[0104] In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was at the priority date, publicly available, known to the public, part of common general knowledge, or otherwise constitutes prior art under the applicable statutory provisions; or is known to be relevant to an attempt to solve any problem with which this specification is concerned.

[0105] In the descriptions provided herein, the terms “includes,” “is,” “containing,” “having,” and “comprises” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to.” When methods or apparatuses are claimed or described in terms of “comprising” various steps or components, the methods or apparatuses can also “consist essentially of” or “consist of” the various steps or components, unless stated otherwise.

[0106] The terms “a,” “an,” and “the” are intended to include plural alternatives, e.g., at least one. For instance, the disclosure of “an electrolyte,” “a pellet,” “a powder”, and the like, is meant to encompass one, or mixtures or combinations of more than one electrolyte, pellet, powder, and the like, unless otherwise specified.

[0107] Various numerical ranges may be disclosed herein. When Applicant discloses or claims a range of any type, Applicant's intent is to disclose or claim individually each possible number that such a range could reasonably encompass, including end points of the range as well as any sub-ranges and combinations of sub-ranges encompassed therein, unless otherwise specified. Moreover, all numerical end points of ranges disclosed herein are approximate. As a representative example, Applicant discloses, in some embodiments, that the pellet may have a density of about 1.5 g/cm.sup.3 to about 2 g/cm.sup.3. This range should be interpreted as encompassing about 1.5 g/cm.sup.3 to about 2 g/cm.sup.3, and further encompasses “about” each of 1.6 g/cm.sup.3, 1.7 g/cm.sup.3, 1.8 g/cm.sup.3, and 1.9 g/cm.sup.3, including any ranges and sub-ranges between any of these values.

[0108] As used herein, the term “about” means plus or minus 10% of the numerical value of the number with which it is being used.

EXAMPLES

[0109] The present invention is further illustrated by the following examples, which are not to be construed in any way as imposing limitations upon the scope thereof. On the contrary, it is to be clearly understood that resort may be had to various other aspects, embodiments, modifications, and equivalents thereof which, after reading the description herein, may suggest themselves to one of ordinary skill in the art without departing from the spirit of the present invention or the scope of the appended claims. Thus, other aspects of this invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein.

Example 1

Synthesis of Li.SUB.3.PS.SUB.4-x.O.SUB.x

[0110] This example provides a solid-state synthesis of Li.sub.3PS.sub.4-xO.sub.x, wherein x=0.31, which yielded a sevenfold increase in ionic conductivity and a lower activation energy compared to experimental β-Li.sub.3PS.sub.4. Detailed variable temperature electrochemical impedance spectroscopy (EIS) analysis was implemented to probe the short-range and long-range Li-ion motion and Arrhenius prefactor.

[0111] In addition, the Jonscher-type power law exponent was computed to confirm the enhanced dimensionality of Li-ion motion in Li.sub.3PS.sub.4-xO.sub.x compared to the experimental β-Li.sub.3PS.sub.4. Li.sub.3PS.sub.4-xO.sub.x were investigated using PXRD to confirm the β-Li.sub.3PS.sub.4 phase at room temperature in addition to .sup.6Li and .sup.31P MAS NMR to elucidate the change in local structure. Computational studies using AIMD simulations were also carried out to understand the cause of the enhanced conductivity and decreased activation energy. These results, as explained below, showed that optimal amounts of oxygen substitution with respect to electrochemical performance could yield 3D Li-ion transport pathways and an intrinsic concentration gradient of Li, giving widened Li channels.

[0112] In this example, Li.sub.3PS.sub.369O.sub.0.31 was synthesized, and the Li.sub.3PS.sub.369O.sub.0.31 had an ionic conductivity of 1.38 mS/cm at 25° C., which was 7 times greater than that of pristine β-Li.sub.3PS.sub.4.

[0113] Detailed analysis of variable-temperature EIS and solid-state NMR showed that the enhanced Li-ion conduction could likely be ascribed to a transition from 2D to 3D Li-ion motion upon oxygen substitution, due to the formation of a (PS.sub.3xO.sub.x).sup.3− unit.

[0114] Further oxygen substitution likely caused the evolution of lithium phosphate impurities, which probably contributed to a decline in ionic conductivity. Computational studies to understand the origin of this enhancement supported the enhancement in dimensionality of Li-ion motion also, likely due to a wider Li channel attributed to the intrinsic Li concentration gradient up to a critical oxygen concentration.

[0115] All chemicals were used as received. Stoichiometric amounts of Li.sub.2S (Alfa Aesar, 99.9%), P.sub.2S.sub.5 (Sigma-Aldrich, 99.9%), and P.sub.2O.sub.5 (Alfa Aesar, 99.99%) were gently mixed using Agar mortar and pestle for 10 m and then homogenized for 10 h under vacuum using a SPEX 8000M high energy mixer. The ratio of the milling media (two zirconia balls; ∅.sub.OD=10 mm) to the total weight of precursors was roughly 14:1. The mixed powders were pressed into a 6-mm diameter pellet (Across International) under a pressure of ˜400 MPa and then heated at 230° C. for 2 h (ramping rate of 1° C./minute) followed by natural cooling. The approximate pellet density used was 1.8 g/cm.sup.3. Sample handling and heat treatment were all performed under Ar (H.sub.2O<1 ppm and O.sub.2<1 ppm) in glovebox.

[0116] Materials Characterization. Impedance measurements on Li.sub.3PS.sub.4-xO.sub.x were carried out using a Gamry Ref 600′ and home-built PEEK cylindrical cell with indium foil as blocking electrodes. Variable-temperature Nyquist spectra were collected from −40° C. to 120° C. (increment of 10° C. per measurement, except 25° C.) within a scanning frequency range from 5 MHz to 1 Hz under a biased potential of 100 mV.

[0117] All the measurements were performed in a Cincinnati Sub-Zero Temperature Chamber under dry air atmosphere to prevent H.sub.2O contamination. PXRD measurements were conducted with a PANalytical X′Pert Pro-MPD Powder Diffractometer with Cu-K.sub.α radiation. KAPTON® film was employed to reduce reactions of Li.sub.3PS.sub.4-xO.sub.x with moist air. MAS NMR measurements on Li.sub.3PS.sub.4-xO.sub.x were performed on a Bruker Avance III 500 MHz NMR spectrometer with a spinning rate of 25 kHz at room temperature. .sup.31P (Larmor frequency=202.404 MHz) NMR spectra were acquired using a Hahn Echo pulse sequence with a pulse length of 4.200 μs and a recycle delay of 200 s. A single pulse with a pulse length of 4.750 μs was employed to obtain .sup.6Li (Larmor frequency=73.58 MHz) NMR spectra using a recycle delay of 200 s). .sup.7Li spin-lattice relaxation time was performed using an inversion recovery pulse sequence. .sup.6Li and .sup.31P chemical shift were referenced to solid LiCl (−1.1 ppm) and to 85% H.sub.3PO.sub.4 (0 ppm), respectively.

Example 2

Calculations

[0118] The structure of β-Li.sub.3PS.sub.4 was taken from Materials Project (ID: mp-985583). Vienna ab initio simulation package (VASP) was used for density functional theory (DFT) energy calculations with the projector-augmented-wave method (see, e.g., P. E. Blöchl, Physical Review B 1994, 50, 17953-17979; G. Kresse, J. Furthmüller, Physical Review B 1996, 54, 11169-11186) in Perdew-Burke-Ernzerhof generalized-gradient approximation (PBE-GGA) (J. P. Perdew, K. Burke, M. Ernzerhof, Physical Review Letters 1996, 77, 3865-3868). An energy cutoff of 520 eV and a k-point density of around 800 per number of atoms in the unit cell were used for all computations. The software suite pymatgen was employed to order the 25 structures of O-substituted Li.sub.3PS.sub.4 at different substitution levels with the lowest energy determined by electrostatic interaction (S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, G. Ceder, Computational Materials Science 2013, 68, 314-319). The energy above hull for each structure was calculated based on the database of Materials Project after DFT energy was obtained from the geometry optimization on VASP. All the other parameters involved were the same as default settings in pymatgen. The isotropic chemical shifts were calculated by magnetic shieldings using perturbation theory (linear response) (C. J. Pickard, F. Mauri, Phys. Rev. B 2001, 63, 245101; and J. R. Yates, C. J. Pickard, F. Mauri, Phys. Rev. B 2007, 76, 024401). The calibration factors of .sup.6/7Li (+90.5 ppm) and .sup.31P (+254 ppm) were estimated from the difference between experimental and calculated isoshift of pristine β-Li.sub.3PS.sub.4. All the configurations that were selected for NMR calculations had the lowest total energy among all the DFT-optimized structures of the same O doping level. An energy cutoff of 600 eV was applied to the system to meet the high-accuracy criterion for such calculations. For better visualization, Lorenzen line-broadening was conducted with broadening factors listed in the following table:

TABLE-US-00001 Summary of simulated Lorenzen line-broadening factors of different peaks in Li.sub.3PS.sub.4-xO.sub.x (x = 0, 0.125, 0.25). Modified Sample Li½ Li3 Li □-PS.sub.4.sup.3− PS.sub.3O.sup.3− Li.sub.3PS.sub.4 0.9 0.5 0.95 1 N/A Li.sub.3PS.sub.3.875O.sub.0.125 0.9 0.5 0.95 2 4.2 Li.sub.3PS.sub.3.75O.sub.0.25 0.9 0.5 0.95 10.5 8

[0119] Line-broadening was more significant for calculated results since they were determined at 0 K and no ion exchange was simulated. At room temperature, rapid Li.sup.+ ion exchange reduced line width of NMR peaks.

[0120] FIG. 1A shows the PXRD patterns of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1) at room temperature. No obvious phase other than β-Li.sub.3PS.sub.4 was identified up to x=0.31 in Li.sub.3PS.sub.4-xO.sub.x, suggesting the average structures of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31) were similar. A successful replacement of S with O, as depicted at FIG. 2, manifested the shift in diffraction peaks to higher angles (2θ) upon incorporation of oxygen into the β-Li.sub.3PS.sub.4, indicating a contraction of the crystal lattice.

[0121] FIG. 2 depicts PXRD patterns of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1). A gradual shift of diffraction peaks to higher angles (2θ) upon oxygen substitution was observed, which confirmed successful incorporation of O into β-Li.sub.3PS.sub.4 structure. Dash lines are guide-to-eye.

[0122] The broadening in diffraction peaks with low intensity indicated that Li.sub.3PS.sub.4-xO.sub.x was glass-ceramic. When x was higher than 0.31 in Li.sub.3PS.sub.4-xO.sub.x, a further reduction of crystallinity lead to an almost featureless powder pattern, which made the phase identification challenging. The change in long-range order from glass-ceramic to nearly glass in Li.sub.3PS.sub.4-xO.sub.x could be explained by the enthalpy of mixing, ΔH.sub.mix calculations. As shown in FIG. 1B, the ΔH.sub.mix in both Li.sub.3PS.sub.3.5O.sub.0.5 and Li.sub.3PS.sub.3O.sub.1 was larger than in Li.sub.3PS.sub.3.875O.sub.0.125 and Li.sub.3PS.sub.3.75O.sub.0.25. In general, the larger the ΔH.sub.mix, the more a composition was assumed to be unstable; hence, decomposing to thermodynamically more stable phases. Therefore, FIG. 1B depicts the stability of β-Li.sub.3PS.sub.4-xO.sub.x as reflected by ΔH.sub.mix. Each square marker indicates a distinct structural configuration. The terminal compounds, Li.sub.3PS.sub.4 and Li.sub.3PO.sub.4, were thermodynamically the most stable phases.

[0123] To understand the structural evolution of local environment due to oxygen substitution in Li.sub.3PS.sub.4-xO.sub.x, .sup.6Li and .sup.31P solid-state NMR was employed. As shown at FIG. 3A, .sup.6Li MAS (25 kHz) NMR spectra revealed a significant upfield shift (smaller ppm) upon oxygen substitution, indicating the Li.sup.+ local environment became more ionic. FIG. 3A depicts .sup.6Li NMR spectra for Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1).

[0124] Since there was a large loss of crystallinity for higher oxygenated samples, deconvolution was only performed on Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3P.sub.3.69O.sub.0.31 as shown at FIG. 3A, with the corresponding quantitative analysis shown in FIG. 3B. FIG. 3B depicts .sup.6Li quantitative analysis for Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31).

[0125] For Li.sub.3PS.sub.4, there were three peaks assigned, one was the combined Li1/Li2 site which corresponded to the 8d and 4b Wyckoff sites respectively and were assigned together due to their close distance and fast exchange (H. Stöffler, T. Zinkevich, M. Yavuz, A. Senyshyn, J. Kulisch, P. Hartmann, T. Adermann, S. Randau, F. H. Richter, J. Janek, et al., J. Phys. Chem. C 2018, 122, 15954-15965). The other was the Li3 site, which corresponded to the 4c Wyckoff site.

[0126] The last peak was at 1.5 ppm and was assigned to an unknown impurity, comprising 4% integral total. With increasing oxygen substitution, the impurity decreased to a negligible amount. In addition, the .sup.6Li integral % of the combined Li ½ assignment increased with a maximum for Li.sub.3P.sub.3.69O.sub.0.31. A decrease in the .sup.6Li integral % of the Li3 site occurred and the emergence of a new Li site (modified Li site) could be seen. This modified Li site was expected to promote long-range 3D Li-ion conduction and composed of Li in an off-centered tetrahedral site due to its bond with O. Isotropic .sup.6Li chemical shifts were simulated using perturbation theory for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, and Li.sub.3PS.sub.3.75O.sub.0.25 from DFT optimized structures of the same composition (FIG. 4C). The results showed good agreement with the experimental data and further supported successful oxygenation.

[0127] FIG. 4A depicts experimental .sup.6Li spectra and deconvolution of Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3PS.sub.3.69O.sub.0.31. FIG. 4B depicts experimental .sup.31P spectra and deconvolution for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3PS.sub.3.69O.sub.0.31. FIG. 4C depicts simulated .sup.6Li spectra for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, and Li.sub.3PS.sub.3.75O.sub.0.25. FIG. 4D depicts simulated .sup.31P spectra for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, and Li.sub.3PS.sub.3.75O.sub.0.25.

[0128] To study the change in Li-ion mobility upon oxygen substitution, .sup.7Li spin-lattice relaxation time, T.sub.1, for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3P.sub.3.69O.sub.0.31 was performed as depicted at FIG. 5. T.sub.1 was the time required for a spin to restore its longitudinal magnetization back to equilibrium state. For Li.sub.3PS.sub.4, a T.sub.1 of 2.1 ms was measured, in comparison to 0.9 ms for Li.sub.3P.sub.3.69O.sub.0.31. Showing that the T.sub.1 was more than halved upon oxygen substitution, which was indicative of increased Li-ion mobility upon oxygen substitution, which was also reflected in the EIS data.

[0129] The local environment of the anionic sublattice in Li.sub.3PS.sub.4-xO.sub.x was investigated with .sup.31P NMR and the results are shown at FIG. 6A. FIG. 6A depicts .sup.31P MAS NMR spectra for x in Li.sub.3PS.sub.4-xO.sub.x. Assigned deconvoluted peaks for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.9O.sub.0.1, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3P.sub.3.69O.sub.0.31 are shown in FIG. 4B with the corresponding quantitative results shown at FIG. 6B. FIG. 6B depicts .sup.31P quantitative analysis for Li.sub.3PS.sub.4-xO.sub.x, (x=0, 0.1, 0.25, and 0.31. The most intense resonance at 86.3 ppm was assigned to the crystalline (PS.sub.4).sup.3 unit, in which the peak intensity decreased and gradually evolved into a featureless lineshape as the amount of oxygen substitution increased (FIG. 6A). This correlated well with the observed trend from the PXRD patterns (FIG. 1A) such that the incorporation of O into β-Li.sub.3PS.sub.4 created more disordered environments, i.e., loss of crystallinity, as manifested by the wide distribution of .sup.31P resonance at 86.3 ppm.

[0130] The .sup.31P resonances at 88 ppm and at 93 ppm were assigned to the (γ-PS.sub.4).sup.3− unit and the (P.sub.2S.sub.7).sup.4− unit, respectively. Li.sub.3P.sub.3.69O.sub.0.31 showed a minimum .sup.31P integral % of the (γ-PS.sub.4).sup.3 unit and a maximum for that of the (P.sub.2S.sub.7).sup.4 unit. In addition, an unknown sulfide impurity peak became apparent at 91 ppm, beginning when x=0.5. Since the unknown appeared small by intensity and likely did not contribute much to the changes in conductivity, it was not further studied. Upon greater oxygen introduction, lithium phosphate impurity peaked at 75 ppm, 70 ppm, 37 ppm, 9 ppm, and −3 ppm were increasingly formed, which were assigned to (POS.sub.2).sup.− (PS.sub.2O.sub.2).sup.3−, (PSO.sub.3).sup.3−, (PO.sub.4).sup.3− and (P.sub.2O.sub.7).sup.4−, respectively, as seen in FIG. 6A. The impurity lithium phosphates, particularly Li.sub.3PO.sub.4, were considered to have low ionic conductivity and likely contributed to the decrease in ionic conductivity when x>0.31. These results were also supported by the enthalpy of mixing calculations from FIG. 1B, as they suggested the metastability of x=0.5 and 1 and the thermodynamically favorable formation of stable decomposition products such as the low conducting phosphates. Furthermore, a growing peak at 85 ppm upon oxygen substitution was assigned to a combined environment of glassy-(PS.sub.4).sup.3− and (PS.sub.3O).sup.3− units, as their individual shifts were very close to each other, making accurate deconvolution challenging. DFT NMR calculations for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, and Li.sub.3PS.sub.3.75O.sub.0.25 confirmed the generation of a new peak for the (PS.sub.3O).sup.3− unit and was also in close agreement with the experimental spectra (F).

[0131] To relate the structure of Li.sub.3PS.sub.4-xO.sub.x to the electrochemical performance, EIS was performed. The conductivity isotherms of Li.sub.3PS.sub.3.69O.sub.0.31 are shown at FIG. 7A. FIG. 7A depicts conductivity isotherms from −40° C. to 120° C., using Li.sub.3PS.sub.3.69O.sub.0.31 as an example. The filled symbol represents the isotherm measured at 25° C. The fitted line is extrapolated to y-axis for identification of σ.sub.DC. From low (−40° C.) to high (120° C.) temperature, only one frequency-independent direct current (DC) plateau was observed. This suggested that the macroscopic Li-ion conduction involved bulk process. Examining the Nyquist plots for x in Li.sub.3PS.sub.4-xO.sub.x at −40° C. (FIG. 8A-FIG. 8F) further supported this point as only one semicircle was detected, representing the bulk ionic conductivity. Towards higher temperatures, the DC plateau fell off the detection limit with the emergence of inductance causing the reverse reading of σ′. In addition, electrode polarization was shown at the lower frequency. FIG. 8A-FIG. 8F depict Nyquist plots of Li.sub.3PS.sub.4-xO.sub.x at −40° C. Simulation of each plot was performed with an equivalent circuit shown in FIG. 3A, in which R and CPE stand for resistor and constant phase element respectively; el stands for blocking electrodes processes.

[0132] For the conductivity isotherms of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1; FIG. 9A-FIG. 9F), the dependence of the real part (σ′) of the complex ionic conductivity on angular frequency (ω=2πf; f=scanning frequency), can be approximated with the Jonscher-type power law, σ′=σ.sub.DC+Aω.sup.n, where σ.sub.DC is the DC conductivity, A is the alternating current coefficient, and n is the power law exponent.

[0133] FIG. 9A-FIG. 9F depict conductivity isotherms (σ′) of Li.sub.3PS.sub.4-xO.sub.x acquired from −40° C. to 120° C. (increment of 10° C.; except 25° C.). ω (Hz)=2×π×f, f=scanning frequency (5 MHz to 1 Hz). DC ionic conductivity (σ.sub.DC) is approximated with the Jonscher-type power law (σ′=σ.sub.DC+Aω.sup.n). A representative fitting curve at −20° C. is shown in each panel to demonstrate the change in σ.sub.DC (cf. FIG. 5). Green filled symbols are designated to signals obtained at 25° C.

[0134] The obtained σ.sub.DC of Li.sub.3PS.sub.3.69O.sub.0.31 reached a maximum of 1.38 mS/cm, giving greater than a sevenfold enhancement in ionic conductivity compared to the experimental Li.sub.3PS.sub.4, which had a σ.sub.DC of 0.19 mS/cm. Substituting O for S with x>0.31 in Li.sub.3PS.sub.4-xO.sub.x lead to a reduction of ionic conductivity (see table below). The energy barrier of a.sub.Dc could be quantified with E.sub.a,DC using the Arrhenius law, σ.sub.DCT=σ.sub.0 exp(−E.sub.a,DC/(k.sub.BT)), where T is temperature in kelvin, σ.sub.0 is the Arrhenius pre-factor, and k.sub.B is the Boltzmann constant. As illustrated at FIG. 7B, a minimum E.sub.a,DC of 0.34 eV was reached for Li.sub.3PS.sub.3.69O.sub.0.31, indicating that the optimal amount of oxygen substitution lowered the energy barrier for macroscopic Li-ion conduction (see table below). FIG. 7B depicts an Arrhenium plot for x in Li.sub.3PS.sub.4-xO.sub.2 using the Arrhenius relation between σ.sub.DC and inverse temperature to calculate E.sub.a,DC.

[0135] To better understand the EIS results, AIMD simulations were carried out at 600-1300 K for Li.sub.3PS.sub.4-xO.sub.x: x=0.0, 0.125, 0.25, and 1.0. With O.sup.2− doping, Li.sup.+ conductivity increased substantially. Optimal Oxygen concentration (x=0.25) lead to the highest conductivity and least Li-migration barrier (E.sub.a). Gradual oxygenation and resulting faster diffusion behavior till x=0.25 were associated with widening of Li-diffusion channel. At higher oxygen concentration, say x=1, channel width dropped and so did the conductivity.

[0136] Although computational prediction of optimal value of x to maximize the Li-conductivity had close agreement with the experiment, it was noted that AIMD results depicted the diffusion behavior at high temperature (>600K), shown at FIG. 10A. FIG. 10A depicts Arrhenius plots for x in Li.sub.3PS.sub.4-xO.sub.x. Indeed, a quantitative agreement between high temperature experimental behavior and AIMD derived Ea values were observed and discussed in the later section. Furthermore, the extrapolated room temperature conductivity was overestimated and Ea was underestimated. Nevertheless, optimal oxygenation lead to a decrease in the activation barrier, which was associated with redistribution of Li, as shown in the Li—Li correlation function (FIG. 10B). FIG. 10B depicts the number of Li with varying Li—Li distance, obtained from the AIMD-averaged Li-density at 600 K for 200 ps. Such Li-redistribution upon oxygenation lead to 2D to 3D transformation of the Li-conducting channels, according to lithium probability density results collected for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3PS.sub.3O from ab initio molecular dynamics simulation (see table below).

[0137] Li probability density was plotted for three compositions of x in Li.sub.3PS.sub.4-xO.sub.x, and the results showed that when near the optimal amount of oxygen substitution with respect to ionic conductivity, a change from quasi-2D to 3D Li-diffusion paths was observed. Also, at the upper limits of oxygen substitution, Li.sub.3PS.sub.3O, localized Li-hopping occurred with interrupted long-range diffusion. This coincided well with the experimental power law exponent measurements as discussed above.

[0138] This explained the enhanced three-dimensional diffusion at x=0.25. However, loss of interconnection among the Li-domains lead to lowering in the long-range ionic conductivity for higher x, Li.sub.3PS.sub.3O, despite the higher dimensionality.

TABLE-US-00002 Calculated activation energy, conductivtiy, and Li channel width for Li.sub.3PS.sub.4, Li.sub.3PS.sub.3.875O.sub.0.125, Li.sub.3PS.sub.3.75O.sub.0.25, and Li.sub.3PS.sub.3O from ab initio molecular dynamics simulations x E.sub.a, eV σ, mS/cm l, Å 0 (β) 0.33 ± 0.02 0.60-1.16 1.82 0.125 0.31 ± 0.02 1.32-2.51 1.83 0.25 0.28 ± 0.01 4.76-6.76 1.84 1 0.31 ± 0,02 1.05-1.81 1.71

[0139] The power law exponent, n, is an empirical indicator to describe the effective dimensionality for conducting solids. 3D conduction was typically correlated with n≥0.7. Through analyzing the conductivity isotherm (−20° C.) for Li.sub.3PS.sub.4-xO.sub.x (0.sub.x (FIG. 9A-FIG. 9F and the following table), a positive correlation between the exponent n and the amount of O.sup.2− was observed.

TABLE-US-00003 Summary of EIS analysis on Li.sub.3PS.sub.4−xO.sub.x (x = 0, 0.1, 0.25, 0.31, 0.5, and 1). σ.sub.DC @ E.sub.a, DC 25° C. Ln σ.sub.0 E.sub.a, M′′ E.sub.ρ′, LT E.sub.ρ′, HT Sample (eV) (mS/cm) (S/cm*K) n (eV) (eV) (eV) Li.sub.3PS.sub.4 0.39 0.19 12.50 0.62 0.34 0.20 0.34 Li.sub.3PS.sub.3.9O.sub.0.1 0.38 0.51 12.69 0.65 0.35 0.19 0.33 Li.sub.3PS.sub.3.75O.sub.0.25 0.35 1.20 12.45 0.85 0.35 0.17 0.30 Li.sub.3PS.sub.3.69O.sub.0.31 0.34 1.38 12.09 0.87 0.34 0.18 0.28 Li.sub.3PS.sub.3.5O.sub.0.5 0.37 0.76 12.66 0.88 0.38 0.19 0.31 Li.sub.3PS.sub.3O.sub.1 0.39 0.20 12.55 0.95 0.39 0.23 0.33 E.sub.a, $ denotes activation energies obtained via EIS analysis under various conditions, in which $ = DC (direct current), M′′ (imaginary part of the complex electric modulus), and ρ′ (real part of resistivity), σ.sub.0 is Arrhenius pre-exponential factor. n is the Jonscher-type power law exponent. LT and HT denote low-temperature and high temperature, respectively.

[0140] This suggested a change in dimensionality of Li-ion conduction from 2D (Li.sub.3PS.sub.4; n=0.62) to 3D (Li.sub.3PS.sub.3.69O.sub.0.31; n=0.87). The improved dimensionality of conducting space was attributed to greater correlated ion motion.

[0141] This explained the lowering in ionic conductivity for Li.sub.3PS.sub.3.5O.sub.0.5 and Li.sub.3PS.sub.3O despite higher n. In fact, the exponent n represented the ratio of the backward hopping rate of ion motion to the site relaxation rate. Therefore, assuming the site relaxation rate was nearly the same, the stronger correlation among Li.sup.+—Li.sup.+ and the Li.sup.+—O.sup.2− pairs may have caused a rise in the backward hopping rate, that is, an unsuccessful hopping for Li.sup.+ to jump through the potential minima.

[0142] The physical picture of this behavior was localized ion hopping without any macroscopic Li-ion conduction. Also examined was whether the observed response of ion dynamics to frequency was coupled with grain boundary, i.e., low frequency response. Thus, the EIS data was analyzed with imaginary component of the complex electric modulus, M″. Take Li.sub.3PS.sub.3.69O.sub.0.31 as an example (FIG. 11A), M″ was computed from Z′ (the real part of the complex impedance) via ω⋅A⋅ϵ.sub.0⋅Z′/l, in which A, ϵ.sub.0, and l refer to the contact area between the indium electrode and Li.sub.3PS.sub.4-xO.sub.x, the permittivity of free space, and the thickness of the Li.sub.3PS.sub.4-xO.sub.x pellet, respectively. FIG. 11A depicts the frequency dependence of M″ (the imaginary part of the complex electric modulus) of Li.sub.3PS.sub.3.69O.sub.0.31. ω (Hz)=2×π×f, f=scanning frequency from 5 MHz to 1 Hz. Only representative M″-isotherms are shown at FIG. 11A for the sake of clarity. Discontinuity of data points at high frequency were attributed to contact between the indium blocking electrodes and solid electrolyte.

[0143] The single peak confirmed that bulk process was likely exclusively responsible for the observed Li-ion conduction; otherwise, another shoulder associated with the grain boundary should have emerged at the lower scanning frequency. The broad and slightly asymmetric lineshape indicated that the bulk process involved a distribution of macroscopic diffusion in different pathways. The ω.sub.max was identified on each isotherm to calculate the electrical relaxation rate, τ.sub.M″.sup.−1 (⋅.sub.max/2π=f.sub.max=τ.sub.M″.sup.−1). As the temperature increased, the ω.sub.max shifts to higher frequency; therefore, faster relaxation. Then, the activation energy E.sub.a,M″ (FIG. 11B) was compared with E.sub.a,DC. FIG. 11B depicts the temperature dependence of τ.sub.M″.sup.−1 of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1. A fair agreement between E.sub.a,M″ and E.sub.a,DC suggested that the carrier concentration, i.e., Li.sup.+, throughout Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1) was almost the same.

[0144] The pre-factor could be understood according to the following equation:

[00001]$\begin{array}{cc}{\sigma }_0=z\frac{{N\left(q\right)}^2}{k_b}{e}^{\frac{\Delta s_m}{k_B}}{a}^2{v}_0& \left(4\right)\end{array}$

[0145] Where z was the geometric factor, k.sub.B was the Boltzmann constant, N was the number of charge carriers, q was the charge of the ions, ΔS.sub.m was the migration entropy, a was the jump distance between sites, and v.sub.0 was the jump frequency. The number of charge carriers was not expected to largely contribute to the change in σ.sub.0, because the amount of Li per formula remained constant for all the compositions. To determine the contribution of the jump frequency to the pre-factor, the crossover frequency, ω.sub.c, was calculated according to:

[00002]$\begin{array}{cc}{\omega }_c={\left(\frac{{\sigma }_{\mathrm{DC}}}{{\sigma }_0}\right)}^{\frac{1}{n}}& \left(5\right)\end{array}$

[0146] The crossover frequency, where the transition from the σ.sub.DC plateau to the high-frequency dispersive region occurred, was used as an rough approximation for v.sub.0. The results given in FIG. 12 showed a change in ω.sub.c within an order of magnitude and the trend opposite to the one observed for the σ.sub.0, giving a maximum jump frequency for Li.sub.3PS.sub.3.69O.sub.0.31. FIG. 12 depicts the normalized crossover frequency, ω.sub.c, of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1). coy is extracted from Equation 4 shown in main text. Dash line is a guide-to-eye.

TABLE-US-00004 Crossover frequency and normalized values for x in Li.sub.3PS.sub.4-xO.sub.x (x = 0, 0.1, 0.25, 0.31, 0.5, and 1). Normalized Sample ω.sub.c (Hz) ω.sub.c Li.sub.3PS.sub.4 2.08 × 10.sup.7 0.32 Li.sub.3PS.sub.3.9O.sub.0.1 2.33 × 10.sup.7 0.36 Li.sub.3PS.sub.3.75O.sub.0.25 5.53 × 10.sup.7 0.86 Li.sub.3PS.sub.3.69O.sub.0.31 6.44 × 10.sup.7 1.00 Li.sub.3PS.sub.3.5O.sub.0.5 1.69 × 10.sup.7 0.26 Li.sub.3PS.sub.3O.sub.1 7.11 × 10.sup.6 0.11

[0147] From this, the change in jump frequency was not expected to contribute largely to the change in σ.sub.0 either, otherwise the trend would have followed that of the Arrhenius prefactor. Moreover, the migration entropy (ΔS.sub.m), as illustrated in the Meyer-Neldel rule, was increased because more activated sites became available for Li.sup.+ to visit (FIG. 13). FIG. 13 depicts fractions of Li exhibiting MSC>5 Å.sup.2 from the 600K AIMD trajectory of 200 ps with respect to x in Li.sub.3PS.sub.4-xO.sub.x. However, it should be noted that for macroscopic Li-ion conduction to occur other factors such as dimensionality, successful ion hopping, were considered. Considering the pattern of crossover frequency (ω.sub.c) (FIG. 12) and entropy of migration (ΔS.sub.m), and their minimal role in affecting σ.sub.0, other factors including correlation factors likely had a large impact on determining the Arrhenius prefactor.

[0148] To study ion dynamics on a different time-scale, the real part of resistivity (ρ′=M″/ω) as a function of temperature was examined. As seen at FIG. 14A, faster ion dynamics lead to the shift of the ρ′ -peak toward the low-T side. FIG. 14A depicts the real part of resistivity (ρ′) of Li.sub.3PS.sub.3.69O.sub.0.31 as a function of inverse temperature. Three representative peaks are shown with respect to the scanning frequency at 5, 1 and 0.1 MHz, respectively. Each ρ′-peak presented high-temperature (HT) and low-temperature (LT) flank, which characterized the activation energy for long-range (E.sub.a,ρ+(HT)) and short-range (E.sub.a,ρ′(LT)) ion motion, respectively.

[0149] This feature resembled the NMR T.sub.1 relaxation rate, which permitted the ion dynamics on different length scale, i.e., short-range vs. long-range, to be probed. To characterize ion dynamics on both scales with activation energy, ρ′-peaks (1 MHz) of all Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1) were collectively compared. As displayed at FIG. 14B, T.sub.max,ρ′ characterizes the temperature at which the maximum quantity of ρ′ appears. The faster the ion motion is, the lower the T.sub.max,ρ′ was detected. FIG. 14B depicts the temperature dependence of ρ′ of Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1) when measured at 1 MHz. Accordingly, Li.sub.3PS.sub.3.69O.sub.0.31 shows the lowest T.sub.max,ρ′. Following the Arrhenius law, the high temperature activation energy (E.sub.a,ρ′HT) and low temperature activation energy (E.sub.a,ρ′LT) could be determined in Li.sub.3PS.sub.4-xO.sub.x (FIG. 14B). Solid lines represent the Arrhenius fit for the high-T and low-T regime of ρ′-peaks. The least energy barrier of long-range conduction (E.sub.a,ρ′HT) for Li-ion conduction was identified with Li.sub.3PS.sub.3.69O.sub.0.31. The trend of both the E.sub.a,ρ′HT and E.sub.a,ρ′LT was in line with that of σ.sub.0, implying that the Arrhenius pre-factor played the key role in dictating the activation energy. Moreover, the E.sub.a,ρ′HT values were quite close to the simulated long-range diffusion energy barrier predicted via AIMD, giving further evidence to the reliability of both techniques to probe on a large length scale.

[0150] The overall evolution of Li-ion conduction in Li.sub.3PS.sub.4-xO.sub.x (x=0, 0.1, 0.25, 0.31, 0.5, and 1) is summarized at FIG. 15 and several features can be drawn. FIG. 15 depicts VT-EIS summary for x in Li.sub.3PS.sub.4-xO.sub.x; the dash lines are guide-to-eye.

[0151] 1) The change in the characteristic temperature, T.sub.max,ρ′, shared a similar pattern with the E.sub.a,DC but related to σ.sub.DC with an opposite fashion. All these physical parameters showed that Li.sub.3PS.sub.3.69O.sub.0.1 possessed the highest Li-ion conduction, which was in accordance with the Meyer-Neldel rule 2) Both the pre-factors (v.sub.ρ′0 and ρ.sub.0) experienced a similar dependence on temperature, in which the smallest value of the pre-factors was found as in the case of the activation energies (E.sub.a,DC and E.sub.a,ρ′). Consequently, the balanced factors in Li.sub.3PS.sub.3.69O.sub.0.31 lead to the optimal performance as revealed by EIS. 3) short-range and long-range experimentally determined energy barriers aligned well with that from simulations and showed that a low long-range energy barrier appeared to be important for obtaining high overall conductivity.

[0152] Also analyzed was the Li-A (A=O, S) bonding characteristics in order to investigate the origin of the tunable Li-diffusion path after oxygenation. FIG. 16A depicts radial pair distribution functions of S—Li and O—Li bond pairs for varying concentration of oxygen in Li.sub.3PS.sub.4-xO.sub.x. Specifically, FIG. 16A depicts the radial pair distribution function of S—Li and O—Li bond pairs for varying concentrations of oxygen in Li.sub.3PS.sub.4-xO.sub.x.

[0153] How the Li-ion number density surrounding S and O within the 1.sup.st coordination sphere evolved are shown in at FIG. 16B. FIG. 16B depicts the number of Li (n.sub.Li) surrounding S and O within the first coordination shell; the results were derived from 600 K AIMD trajectory. There were three noteworthy findings: firstly, within the first coordination shell Li-ion concentration was higher in the vicinity of ‘S’ compared to ‘O’, leading to inhomogeneous Li-distribution throughout the framework. Despite the smaller sized O incorporation there was no significant volume shrinkage up to x=0.25. As a result, Li-density remained dispersed up to x=0.25, leading to the wide Li-diffusion channel and fast Li-conduction in the oxygenated framework. Li-density in the first coordination shell surrounding O/S was enhanced for x=1.0, pointing towards the localized Li due to overall decrease in free volume. Thus, further increase in the oxygen content lead to the narrow diffusion channel and slow Li-conduction.

[0154] To isolate the effect of relative position of O-content for the chemical stoichiometry, x=1, two structural configurations of Li.sub.3PS.sub.3O: (i) Dispersed: PS.sub.3O units (ii) Localized: both PS.sub.4 and PS.sub.2O.sub.2 units were examined. Specifically, Li-distribution in Li.sub.3PS.sub.3O with two different O-distribution patterns: localized and dispersed O-atoms containing PS.sub.2O.sub.2 and PS.sub.3O moiety, respectively, at a particular oxygen concentration, x=1. The Li chemical environment (FIG. 17A and the following table) for these two different structural analogues of the same composition Li.sub.3PS.sub.3O were significantly different. FIG. 17A depicts Li spatial density with respect to the Li—Li distance parameter. The results were obtained from 600 K AIMD trajectory for 200 ps.

TABLE-US-00005 Calculated NMR shift for Li.sub.48P.sub.16S.sub.48O.sub.16 (localized) and Li.sub.12P.sub.4S.sub.12O.sub.4 (dispersed). The experimental NMR results support that the dispersed structure was synthesized. Relative Composition Ion Span Skew Chemical Shift Li.sub.48P.sub.16S.sub.48O.sub.16; x = 1 Li 6.91 −0.45 −0.34 Li 7.85 −0.05 −0.08 Li 6.77 −0.25 1.48 Li 7.85 −0.05 −0.08 P 80.47 0.44 75.12 Li.sub.12P.sub.4S.sub.12O.sub.4; x = 1 Li 5.99 −0.06 0.32 Li 7.39 0.18 1.79 Li 7.69 0.56 0.83 Li 3.33 −0.04 1.01 P 48.09 0.8 43.47 P 116.64 0.66 86.27

[0155] Dispersed O-arrangement exhibited more downfield Li-chemical shift compared to the localized O-arrangement, associated with a much lower Li-migration barrier for the former, 0.31±0.02 meV versus 0.46±0.03 meV (FIG. 17B). This computational experiment highlighted the importance of the spatial arrangement of O-content to directly correlate with the degrees of Li-distribution, hence enhanced lithium conductivity. The spatial effect became more prominent at higher O-content, e.g., x=1. Thus, not only the composition, but also the O-distribution appears to have regulated the Li chemical environment and induced significant changes to flatten energy landscape to promote fast Li-diffusivity. The (PS.sub.3O).sup.3− unit was expected for successful incorporation of oxygen into the β-Li.sub.3PS.sub.4 structure and was apparently important for the conductivity enhancement. With respect to ionic conductivity, the optimal amount of (PS.sub.3O).sup.3−, i.e., oxygen substitution, should be achieved without the generation of low conducting phosphate impurities containing (PS.sub.yO.sub.4-y).sup.3− (y>1).

[0156] Thus, varying oxygen concentration tuned the Li-ion redistribution surrounding S and O, leading to maximum or increased widening of the Li-diffusion channel at a critical composition of Li.sub.3PS.sub.3.75O.sub.0.25. Criticality arose because for sufficiently low oxygen concentration (0≤x≤0.25 in Li.sub.3PS.sub.4-xO.sub.x) oxygenated thiophosphates motifs were well dispersed, which in combination with inhomogeneous Li-distribution surrounding S and O resulted in a gradual increase in the free volume. However, further increase in the O-content resulted in close proximity of the O-domains and overall shrinkage of the lattice (hence channel width) due to shorter Li-O bonds which attributed to sluggish Li-diffusion.