Estimation of Thermodynamic Properties of Li

Abstract

Given the lack of thermodynamic data on Li_1+xM_1-xO₂ materials, LiAlO₂ was split in accordance with the principle of the group contribution method. Mathematical models for estimating the ∆G^θ_f,298, ∆H^θ_f,298, and C_p of LiAlO₂ were proposed on the basis of thermodynamic principles. The group contribution method was used to estimate the ∆G^θ_f,298, and ∆H^θ_f,298 of 56 solid inorganic compounds and the C_p,298 of 54 solid inorganic compounds to test the reliability and applicability of the model. The group contribution method was used to estimate the mathematical model of solid inorganic compounds. Results show that the experimental data selected by fitting group parameters are accurate and reliable, and the group division method is appropriate. Mathematical models for estimating the ∆G^θ_f,298, ∆H^θ_f,298, and C_p of three types of Li_1+xM_1-xO₂ materials were constructed on the basis of the satisfactory results. The ∆G^θ_f,298, ∆H^θ_f,298, and C_p,298 of the 63 common Li_1+xM_1-xO₂ materials were also estimated.

Keywords

lithium-rich cathode materials; the group contribution method; ∆G^θ_f,298; ∆H^θ_f,298; C_p,298

Science Press

The gradual depletion of traditional fossil energy has led to the emergence of various energy materials and energy conversion devices. Electromagnetic (EM) functional materials support the rapid expansion of modern automation engineering, electronic science and information technology. As representatives of low-dimensional electromagnetic functional materials, silicon carbide, zinc oxide, carbon materials, transition metals and their oxides, metal-organic framework materials, etc, due to their excellent electromagnetic functions, have been used in the fields of communication and imaging, electromagnetic wave absorption and shielding, etc, showing a broad application prospect^[1]. In addition, a lot of work is continuously devoted to the development and update of the collection and conversion of environmental capabilities, such as water wave energy, light energy, and heat energy^[2]. High-performance rechargeable lithium-ion batteries, as a representative of advanced energy storage technology, have made great efforts to develop cathode and anode materials. For example, Cao et al prepared layered NiCo₂O₄ nanofibers assembled with hollow nanoparticles through simple electrospinning technology and annealing process to improve the electrochemical performance of lithium-ion batteries^[3]. Cao et al^[4] designed a high-capacity electrode with a three-dimensional layered Co₃O₄ flower-like structure with mesogenic nanostructures.

Lithium-ion batteries have the characteristics of light weight, small size, low self-discharge rate, long cycle life, and wide operating temperature range while lack of memory effect. Since their inception, lithium-ion batteries have been developed rapidly and widely used in 3C digital consumer electronics products, pure electric vehicles (EVs), hybrid vehicles (HEVs), and plug-in HEVs^[5-7]. The challenges of lithium-ion batteries continue to grow with the increasing functional demands of consumer electronic products and the mounting of EVs. The lithium-ion battery cathode material LiCoO₂ and ternary material LiNi_xCo_yMn_zO₂ has a theoretical specific capacity of 272 mAh/g, but it is prone to irreversible phase change due to excessive delithiation in actual use. Generally, the maximum deintercalation of lithium accounts for 60%~80% of the total content. Thus, the actual specific capacity of the lithium-ion battery cathode material is less than 200 mAh/g, which is lower than the anode capacity of commercial carbon electrodes (350 mAh/g). In turn, the anode capacity of commercial carbon electrodes is considerably lower than that of silicon and tin anode electrodes. Given that the energy density of lithium-ion batteries depends mainly on the specific capacity of their cathode materials, researching and developing new lithium-ion battery cathode materials with increased specific capacity is necessary to meet the development requirements of EVs and HEVs in the future^[8,9].

Lithium-ion battery cathode materials currently on the market are mainly classified as (1) hexagonal layered LiCoO₂, LiNiO₂, and LiNi_xCo_yMn_zO₂ structures with R-3m spatial point groups; (2) spinel-structured LiMn₂O₄ with Fd-3m spatial point groups; and (3) compound LiFePO₄ with a polyanionic structure. The difference in the spatial structure determines the lithium ion adsorption behavior and electrochemical performance of the two-dimensional material, and from the micro level, the basic relationship between the electronic structure and its electrochemical properties is that the electrical conductivity of the material and the adsorption strength of the intermediate are the key factors determining the electrocatalytic kinetics^[10].

Lithium-rich cathode materials (Li_1+xM_1-xO₂, 0<x<1, M=Ni, Co, Mn···) have an α-NaFeO₂ structure and belong to the hexagonal crystal system and the R-3m space group. Li occupies the 3a position, the transition metal M occupies the 3b position, and O occupies the 6c position. The transition metal layer Li, transition metal M, and the structure of the transition metal layer are similar to those of LiCoO₂^[11-13]. The lithium-rich Li_1+xM_1-xO₂ cathode material is a solid solution that is composed of different proportions of LiMO₂ and Li₂MnO₃ materials, namely xLi₂MnO₃·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···), if the cation ordering problem is ignored. LiMO₂ has an α-NaFeO₂ layered structure and belongs to the R-3m space group. Transition metal ions occupy octahedral positions to form the MO₆ layer in LiMO₂; by contrast, and the structure in the Li layer is tetrahedral^[14,15]. Li₂MnO₃ belongs to the monoclinal crystal system and the C2/m spatial group and is a layered rock salt structure. Li⁺ and Mn⁴⁺ in Li₂MnO₃ are arranged alternately at the molar ratio of 1:2 to form a transition metal layer [Li_1/3Mn_2/3]. The superlattice structure is ascribed to the mixing effect of Li⁺ and Mn⁴⁺ present between transition metal layers and is reflected as a sawtooth peak in the 2θ range of 20°~28° in XRD patterns. The lithium-rich cathode material is also considered as a transition metal moiety that replaces Li⁺ and Mn⁴⁺ in the Li[Li Mn ]O transition metal layer, which is expressed as Li[M_1-xLi_x/3Mn_2x/3]O₂^[16,17]. The valence states of the transition metals are Ni²⁺, Co³⁺ and Mn⁴⁺, and the three elements have different effects on material electrochemical properties. Mn⁴⁺ can improve material structural stability, thermal stability, and safety while reducing the costs. Nevertheless, it lacks electrochemical activity during charging. Excessive Mn⁴⁺ content will reduce the specific capacity of materials and subsequently facilitate spinel phase production and destroy the layered material structure. Although Ni²⁺ is helpful for improving charging and discharging capacity, excessive Ni²⁺ will cause a miscible effect in combination with Li⁺. This miscible effect will result in poor cycling performance and multiplier performance. Co³⁺ can effectively inhibit cationic mixing and improve electronic conductivity and cycle performance of the material. However, increasing Co³⁺ ratio will reduce capacity^[18-21]. Fig.1 shows the schematic of the layered Li₂MnO₃ and LiMO₂ structures, where M is a transition metal, such as Ni, Co, or Mn.

Fig.1 Structural schematic diagram of layered Li₂MnO₃ (a) and

LiMO₂ (b) (M is Ni, Co, or Mn)

The initial discharge specific capacity of the lithium-rich material in the high voltage state can exceed 300 mAh/g, which is much higher than that of currently commercially available cathode materials. However, layered lithium-rich materials cannot meet application requirements because they exhibit several problems, such as large initial irreversible capacity loss, voltage attenuation during cycling, low tap density, and poor rate performance^[22,23]. These deficiencies can be improved through element doping and surface coating. Layered lithium-rich materials are now considered as ideal cathode materials for next-generation lithium-ion batteries with the development of the synthesis and modification technology of lithium-rich materials, because of their high specific capacity, excellent cycling ability and novel electrochemical charging and discharging mechanism^[24-26].

Current research on lithium-rich Li_1+xM_1-xO₂ materials is mainly focused on their structure and electrochemical properties and little attention is paid on their thermodynamic properties. The development of novel lithium-rich Li_1+xM_1-xO₂ materials with high energy density and capacity is dependent on the internal relationship among their structures, thermodynamic properties, and electrochemical properties. It is specifically manifested with changing the crystal phase of the material by adjusting the different charge distribution and electronic structure of various atomic configurations. The phase change process in the chemical reaction involved in this process requires reliable thermodynamic data to guide. It also provides a theoretical reference for estimating actual battery energy density and theoretical capacity. Other issues include the further improvement of the charging and discharging performances of lithium-ion batteries, the development of new electrode materials and battery systems, and the optimization of battery structure. The limited understanding of the thermodynamic properties of Li_1+xM_1-xO₂ restricts the development and utilization of new lithium-rich materials. The study of the thermodynamic properties of Li_1+xM_1-xO₂ are crucial for guiding theoretical calculations toward the improvement and usage of lithium-rich new materials in the long run.

Mostafa et al^[27,28] proposed that the thermodynamic properties of solid inorganic compounds are the sum of the thermodynamic group contributions of their constituent cations, anions, and ligands (such as water of crystallization). The ∆H^θ_f,298 values of 938 solid inorganic compounds and the ΔG^θ_f,298 values of 687 solid inorganic compounds were subjected to multiple linear regression analysis (84% of the data are published by the International Union of Pure and Applied Chemistry). The group contribution values of 136 cations, 23 anions, and 5 ligand molecules were obtained, and the relative errors of each group contribution value were estimated by the standard deviation of the parameters. The C_p,298 values of 664 solid inorganic compounds were also subjected to multiple linear regression analysis. The group contribution values of 129 cations, 17 anions, and 2 ligands were acquired. The group contribution method has a wide range of applications and high reliability and accuracy. Thus, the mathematical models for estimating the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of three kinds of lithium-rich Li_1+xM_1-xO₂ materials were constructed for the first time by the group contribution method. Moreover, the ΔH^θ_f,298, ΔG^θ_f,298 and C_p,298 of 63 common lithium-rich Li_1+xM_1-xO₂ materials were estimated.

1 Estimation Method

1.1 Mathematical model for estimating the thermody-namic data of matter using the group contribution method

The success of the group contribution method in estimating material property data is associated with the physical basis of the mathematical model related to group parameters and properties, the accuracy and reliability of the experimental data selected for fitting group parameters, and the appropriateness of the group partitioning method. LiAlO₂ was split in accordance with the principle of the said method to determine the reliability and application range of the group contribution method for estimating the ∆H^θ_f,298, ∆G^θ_f,298 and C_p,298 of solid inorganic compounds. Moreover, the mathematical models for estimating the ∆H^θ_f,298, ∆G^θ_f,298 and C_p of LiAlO₂ were proposed in accordance with thermodynamic principles.

Table 1 shows the group contribution values of Li⁺, Ni²⁺, Ni³⁺, Co²⁺, Co³⁺, Mn³⁺, Mn⁴⁺, and O^2- to the ∆H^θ_f,298 and ∆G^θ_f,298 of the solid inorganic compounds. The ∆H^θ_f,298 and ∆G^θ_f,298 of LiAlO₂ were estimated by the group contribution method, as follows. (1) The molecular formula of the solid inorganic compound was written. (2) The molecular formula was deconstructed into the structural groups of cations, anions, or ligands. The contribution value of each molecular structure group was multiplied by the distribution number of the group in the molecular formula. Then, the contribution value of each group was calculated. (3) The mathematical model for estimating the thermodynamic properties of the substance was established. Table 2 presents the estimation process and results.

Table 1 Solid inorganic compound groups of cationic, anionic and ligand molecule groups, their contributions (Δ_H,j, Δ_G,j), number of occurrences in the regression, and standard deviations (S_Δj) associated with them for standard heats and free energies of formation^[27]

	Group	No. of occurrence for ΔH,j	ΔH,j/kJ·mol-1	SΔj for ΔH,j	No. of occurrence for ΔG,j	ΔG,j/kJ·mol-1	SΔj for ΔG,j
Cation	Al3+	129	-553.115	12.713	118	-420.023	23.951
	B3+	50	-392.895	13.015	49	-273.681	24.327
	Be2+	23	-402.267	13.713	15	-297.827	19.827
	Ca2+	131	-520.898	14.734	124	-432.414	16.222
	Co2+	23	-76.275	30.537	3	4.128	35.818
	Co3+	1	-37.950	-	1	94.826	-
	Cr3+	15	-290.075	27.492	15	-168.532	25.868
	Fe2+	40	-126.475	13.177	22	-43.568	19.883
	Fe3+	30	-122.815	14.811	22	-8.638	25.237
	Hf4+	1	-769.852	-	1	-606.500	-
	Li+	42	-292.950	8.187	29	-250.254	11.449
	Mg2+	116	-461.804	9.478	72	-372.414	16.624
	Mn2+	16	-250.029	14.052	13	-167.203	19.858
	Mn3+	1	-167.921	-	1	-100.187	-
	Mn4+	1	-85.813	-	1	66.580	-
	Mo6+	38	-234.996	25.436	82	-17.811	47.790
	NH4+	8	-164.486	16.381	5	-53.199	20.031
	Ni2+	20	-91.381	14.364	14	0.357	20.625
	Ni3+	2	-20.042	31.141	1	149.483	-
	P5+	4	-481.148	29.622	4	-285.069	44.693
	Si4+	174	-575.556	16.706	159	-411.036	32.072
	Ti4+	15	-571.358	22.030	17	-408.836	34.023
	V5+	32	-369.937	22.053	33	-162.620	40.397
	W6+	40	-367.612	26.321	40	-131.422	48.219
	Zn2+	33	-191.646	11.753	32	-91.944	17.855
Anion	CO32-	26	-616.496	14.214	28	-635.990	19.167
	F-	291	-310.918	4.638	168	-326.667	8.264
	NO3-	97	-175.710	6.206	40	-126.405	10.288
	O2-	1946	-173.650	8.264	1725	-229.836	15.876
	PO43-	22	-1197.521	16.826	20	-1206.614	26.773
	SO42-	121	-814.755	9.861	91	-795.046	16.975
Ligand molecule	H2O	718	-298.933	1.133	394	-244.317	1.470

Table 2 Estimation of the ΔH^θ_f,298, and ΔG^θ_f,298 of LiAlO₂(kJ·mol^-1)

Group	∆Hθf,298	∆Gθf,298
Li+	-292.50	-250.254
Al3+	-553.115	-420.023
2O2-	2×(-173.650)	2×(-229.836)
Total	-1193.37	-1129.95

The mathematical models for estimating the ∆H^θ_f,298 and ΔG^θ_f,298 of LiAlO₂ by the group contribution method are as follows:

∆Hθf,298(LiAlO2)=∆Hθf,298(Li+)+∆Hθf,298(Al3+)+2∆Hθf,298(O2-)

(1)

∆Gθf,298(LiAlO2)=∆Gθf,298(Li+)+∆Gθf,298(Al3+)+2∆Gθf,298(O2-)

(2)

in which 1, 1, and 2 are the distribution numbers of Li⁺, Al³⁺, and O^2- in the LiAlO₂ molecular formula, respectively.

Table 2 shows that the estimated values of the ∆H^θ_f,298, and ΔG^θ_f,298 of LiAlO₂ are ‒1193.37 and ‒1129.95 kJ·mol^-1, respectively. Compared with the values given in the literature (‒1188.70 and ‒1126.30 kJ·mol^-1), it reveals that the corres-ponding relative errors of the estimated values are 0.39% and 0.32%^[29].

Table 3 shows the group contribution values of Li⁺, Ni²⁺, Ni³⁺, Co²⁺, Co³⁺, Mn³⁺, Mn⁴⁺, and O^2- to the C_p of the solid inorganic compound. The group contribution method was used to estimate the C_p of LiAlO₂, as follows. (1) The molecular formula of the solid inorganic compound was written. (2) The formula was broken into the cationic and anionic structural groups given in Table 1, and the contribution value of each group was multiplied by the distribution number of the group in the molecular formula to calculate the contribution value of each group. (3) The contribution values of ∑_jn_jΔ_a,j, ∑_jn_jΔ_b,j, ∑_jn_jΔ_c,j and ∑_jn_jΔ_d,j were determined by tallying the contribution values of each group. (4) The mathematical model for estimating the thermodynamic properties of the material was developed. Table 4 presents the estimation process and results.

Table 3 Solid inorganic salt groups of cationic, anionic groups and their contribution (Δ_a,j, Δ_b,j, Δ_c,j, Δ_d,j) and number of occurrences in the regression^[28]

	Group	No. of occurrence	Δa,j	Δb,j	Δc,j	Δd,j
Cation	Al3+	81	10.306	4.518	-0.623	-3.701
	B3+	59	-13.188	16.765	0.273	-0.219
	Be2+	16	-5.164	22.314	-0.002	6.544
	Ca2+	64	20.470	-6.225	-0.026	-3.219
	Co2+	17	26.552	-19.272	0.327	5.245
	Co3+	1	34.158	-42.075	-0.149	-4.614
	Cr3+	22	21.086	-16.392	0.067	5.298
	Fe2+	15	20.486	-5.415	0.055	5.393
	Fe3+	26	16.618	3.328	0.082	5.002
	Hf4+	9	20.580	-22.025	-0.050	2.633
	Li+	47	15.639	4.124	-0.007	7.973
	Mg2+	32	14.639	-0.637	-0.074	-0.609
	Mn2+	15	21.419	-15.908	0.265	5.652
	Mn3+	4	8.913	3.070	0.454	5.448
	Mn4+	1	-3.593	22.048	0.643	5.244
	Mo6+	11	-7.473	-7.423	1.279	13.430
	Ni2+	14	22.497	-6.671	-0.022	6.234
	Ni3+	1	3.549	-7.964	0.413	7.913
	P5+	12	-39.486	50.248	1.686	2.325
	Si4+	79	-2.308	4.382	-0.041	-3.301
	Ti4+	34	10.043	-7.562	0.299	11.414
	V5+	20	-1.279	-5.243	0.697	13.608
	W6+	20	-23.788	35.451	1.836	9.893
	Zn2+	18	12.599	-0.744	0.377	4.203
	Zr4+	13	17.188	-23.478	-0.063	7.098
Anion	CO32-	15	47.278	86.757	-0.887	-5.133
	F-	247	22.041	15.652	-0.244	1.538
	NO3-	120	49.766	83.928	-0.478	-7.040
	O2-	1155	28.152	12.043	-0.747	-4.023
	PO43-	6	95.827	56.863	-2.462	-7.691
	SO42-	49	85.866	52.357	-1.925	-0.047

Table 4 Estimation of C_p,298 for LiAlO₂

Group	Δa,j	Δb,j	Δc,j	Δd,j
Li+	15.639	4.124	-0.007	7.973
Al3+	10.306	4.518	-0.623	-3.701
2O2-	2×28.152	2×12.043	2×(-0.747)	2×(-4.023)
∑jnjΔi,j	82.249	32.728	-2.124	-3.774
Cp,298=∑jnjΔa,j+(∑jnjΔb,j×10-3)T+(∑jnjΔc,j×106)/T2+(∑jnjΔd,j×10-6)T2 =82.249+(32.728×10-3×298+(-2.124×106)/2982 +(-3.774×10-6×2982)=67.75 J·mol-1·K-1

C_p(LiAlO₂)=∑_jn_jΔ_a,j+(∑_jn_jΔ_b,j×10^-3)T+(∑_jn_jΔ_c,j×10⁶)/T²

+(∑_jn_jΔ_d,j×10^-6)T²

∑_jn_jΔ_a,j=Δ_a,j(Li⁺)+Δ_a,j(Al³⁺)+2Δ_a,j(O^2-)

∑_jn_jΔ_b,j=Δ_b,j(Li⁺)+Δ_b,j(Al³⁺)+2Δ_b,j(O^2-)

∑_jn_jΔ_c,j=Δ_c,j(Li⁺)+Δ_c,j(Al³⁺)+2Δ_c,j(O^2-)

∑jnjΔd,j=Δd,j(Li+)+Δd,j(Al3+)+2Δd,j(O2-)

(3)

in which 1, 1, and 2 are the distribution numbers of Li⁺, Al³⁺, and O^2- in the LiAlO₂ molecular formula, respectively.

The C_p,298 of LiAlO₂ was calculated in accordance with the required temperature (with T=298 K as the reference data). The estimated value of C_p,298 is 67.75 J·mol^-1·K^-1. Compared with the value of 67.78 J·mol^-1·K^-1 given in the literature, the relative error of the estimated value is 0.04%.

Kopp's rule states that the constant pressure heat capacity C^θ_p of a compound is approximately equal to the sum of the molar heat capacity of the atoms that constitute the elements of the compound, as shown in Eq.(4). Table 5 lists the contribution values of elements, such as Ca, Al, Li, Ni, Co, Mn, and O^[30].

Cθp=∑jnjCθp,j

(4)

The C_p,298 of LiAlO₂ was estimated by Kopp's rule through the following steps. (1) The molecular structure formula of the solid inorganic compound was written. (2) The molecular structure formula was broken down in accordance with the types of elements, and the contribution values of the elements were ascertained from Table 5. The contribution value of the element was multiplied by the distribution number of the component in the molecular structure equation, and the contribution value of each element was calculated. (3) The estimated and reported values of C_p,298 are 68.16 and 67.78 J·mol^-1·K^-1, respectively. Thus, the relative error of the estimated value is 0.56%. Table 6 presents the estimation process and results.

Table 5 Contribution of elements to solid inorganic compound C_p,298

Element	New Kopps Solids	Element	New Kopps Solids	Element	New Kopps Solids	Element	New Kopps Solids	Element	New Kopps Solids
H	7.56	F	20.92	K	28.78	Ni	25.46	Ba	32.37
Li	23.25	Na	26.19	Ca	28.25	Cu	26.92	W	30.87
Be	12.47	Mg	22.69	Ti	27.24	Br	25.36	Hg	27.87
B	10.10	Al	18.07	V	29.36	Sr	28.41	Pb	31.60
C	10.89	Si	17.00	Mn	28.06	Zr	26.82	P	22.61
N	18.74	S	12.36	Fe	29.08	Mo	29.44	Cr	31.42
O	13.42	Cl	24.69	Co	25.71	I	25.29	Misc	26.63

Table 6 Estimation of C_p,298 for LiAlO₂

Step	LiAlO2
1	Element	Δa,j	Element	Δb,j	Element	Δc,j
2	Li	23.25	Al	18.07	O	2×13.42
3	∑jnjΔi,j		68.16 J·mol-1·K-1

1.2 Verification of the model

The group contribution method was used to estimate the ΔH^θ_f,298 and ΔG^θ_f,298 of 56 solid inorganic compounds to determine the reliability and applicability of the model. The estimated and reported values of ΔH^θ_f,298 were compared^[31]. The absolute values of relative errors were within 4%, and the absolute values of the relative errors of 43 kinds of solid inorganic compounds were less than 2%. The estimated and reported values of ΔG^θ_f,298 were also compared. The absolute values of relative errors were within 4%, the absolute values of the relative errors of 42 kinds of solid inorganic compounds were less than 2%. The C_p,298 values of 54 solid inorganic compounds were likewise estimated^[32]. The absolute values of the relative errors of C_p,298 were within 5% of the values in the literature. The absolute values of the relative errors of 43 kinds of solid inorganic compounds were less than 2%. The C_p,298 values of 54 selected solid inorganic compounds were estimated in accordance with Kopp's rule. The absolute values of relative errors of C_p,298 were within 11% of those reported in the literature, and the absolute values of the relative errors of 33 solid inorganic compounds were less than 3%. Among them, the absolute values of the relative errors of 12 kinds of solid inorganic compounds were 3%~5%. This method has a better calculation effect than Kopp's rule estimation. The results show that the mathematical model of the correlation between group parameters and physical properties is correct, the experimental data selected by fitting the group parameters are accurate and reliable, and the group division method is appropriate.

2 Results and Discussion

Three main types of lithium-rich cathode materials are currently available: (1) lithium-rich layered xLi₂MnO₃· (1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) cathode material; (2) lithium-rich manganese-based xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) solid solution material; (3) layered spinel xLi[Li_1/3Mn_2/3]O₂· (1-x)LiMn₂O₄ (0<x<1) composite solid solution material and layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄ (0<x<1) composite solid solution material. The mathematical models for estimating ΔH^θ_f,298, and ΔG^θ_f,298, and C_p of three types of lithium-rich materials were constructed in accordance with the satisfactory results, and the ΔH^θ_f,298, and ΔG^θ_f,298 and C_p,298 of the common 63 lithium-rich materials were estimated.

2.1 Mathematical models for estimating ΔH^θ_f,298, ΔG^θ_f,298, and C_p of the lithium-rich layered xLi₂MnO₃· (1-x)LiMO₂ cathode materials

The chemical valences of Li, O, Mn, and M in the lithium-rich layered xLi₂MnO₃·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) materials are +1, -2, +4, and +3, respectively. The most studied systems of the lithium-rich xLi₂MnO₃·(1-x)LiMO₂ material are M=Co, Fe, and Ni-Mn. Common lithium-rich layered materials include xLi₂MnO₃·(1-x)LiCoO₂, xLi₂MnO₃·(1-x)LiFeO₂, and xLi₂MnO₃·(1-x)Li[Ni_0.5Mn_0.5]O₂. The mathematical models for estimating ΔH^θ_f,298, ΔG^θ_f,298, and C_p of lithium-rich layered xLi₂MnO₃·(1-x)LiMO₂ materials using the group contribution method are shown Eq.(5~7), respectively:

∆H^θ_f,298(xLi₂MnO₃·(1-x)LiMO₂)=2x∆H^θ_f,298(Li⁺)

+x∆H^θ_f,298(Mn⁴⁺)+3x∆H^θ_f,298(O^2-)+(1-x)∆H^θ_f,298(Li⁺)

+(1-x)∆Hθf,298(M3+)+2(1-x)∆Hθf,298(O2-)

(5)

∆G^θ_f,298(xLi₂MnO₃·(1-x)LiMO₂)=2x∆G^θ_f,298(Li⁺)

+x∆G^θ_f,298(Mn⁴⁺)+3x∆G^θ_f,298(O^2-)+(1-x)∆G^θ_f,298(Li⁺)

+(1-x)∆Gθf,298(M3+)+2(1-x)∆Gθf,298(O2-)

(6)

C_p(xLi₂MnO₃·(1-x)LiMO₂)=∑_jn_jΔ_a,j+(∑_jn_jΔ_b,j×10^-3)T

+(∑_jn_jΔ_c,j×10⁶)/T²+(∑_jn_jΔ_d,j×10^-6)T²∑_jn_jΔ_a,j

=2xΔ_a,j(Li⁺)+xΔ_a,j(Mn⁴⁺)+3xΔ_a,j(O^2-)

+(1-x)Δ_a,j(Li⁺)+(1-x)Δ_a,j(M³⁺)+2(1-x)Δ_a,j(O^2-)∑_jn_jΔ_b,j

=2xΔ_b,j(Li⁺)+xΔ_b,j(Mn⁴⁺)+3xΔ_b,j(O^2-)

+(1-x)Δ_b,j(Li⁺)+(1-x)Δ_b,j(M³⁺)+2(1-x)Δ_b,j(O^2-)∑_jn_jΔ_c,j

=2xΔ_c,j(Li⁺)+xΔ_c,j(Mn⁴⁺)+3xΔ_c,j(O^2-)

+(1-x)Δ_c,j(Li⁺)+(1-x)Δ_c,j(M³⁺)+2(1-x)Δ_c,j(O^2-)∑_jn_jΔ_d,j

=2xΔ_d,j(Li⁺)+xΔ_d,j(Mn⁴⁺)+3xΔ_d,j(O^2-)

+(1-x)Δd,j(Li+)+(1-x)Δd,j(M3+)+2(1-x)Δd,j(O2-)

(7)

When M is Co, the mathematical models for estimating the ∆H^θ_f,298, ∆G^θ_f,298, and C_p of lithium-rich layered xLi₂MnO₃· (1-x)LiMO₂ materials using the group contribution method are shown in Eq.(8~10), respectively:

∆Hθf,298(xLi2MnO3·(1-x)LiCoO2)=-514.463x-678.200

(8)

∆Gθf,298(xLi2MnO3·(1-x)LiCoO2)=-508.336x-615.100

(9)

C_p(xLi₂MnO₃·(1-x)LiCoO₂)=6.040x+106.101

+(80.290x-13.865)×10^-3T+(0.038x-1.650)×10⁶/T²

+(13.808x-4.687)×10-6T2

(10)

When M is Fe, the mathematical models for estimating the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of lithium-rich layered xLi₂MnO₃·(1-x)LiMO₂ materials using the group contribution method are shown in Eq.(11~13), respectively:

∆Hθf,298(xLi2MnO3·(1-x)LiFeO2)=-429.598x-763.065

(11)

ΔGθf,298(xLi2MnO3·(1-x)LiFeO2)=-404.872x-718.564

(12)

C_p(xLi₂MnO₃·(1-x)LiFeO₂)=23.580x+88.561

+(34.887x+31.538)×10^-3T+(-0.193x-1.419)×10⁶/T²

+(4.192x+4.929)×10-6T2

(13)

When M is Ni_1/2Mn_1/2, the mathematical models for estimating the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of lithium-rich layered xLi₂MnO₃·(1-x)LiMO₂ materials using the group contribution method are shown in Eq.(14~16), respectively:

∆H^θ_f,298(xLi₂MnO₃·(1-x)LiNi_1/2Mn_1/2O₂)

=-463.816x-728.847

(14)

∆G^θ_f,298(xLi₂MnO₃·(1-x)LiNi_1/2Mn_1/2O₂)

=-446.979x-676.458

(15)

C_p(xLi₂MnO₃·(1-x)LiNi_1/2Mn_1/2O₂)=30.746x+81.395

+(30.527x+35.899)(10^-3)T+(-0.422x-1.191)(10⁶)/T²

+(3.455x+5.666)(10-6)T2

(16)

2.2 Mathematical models for estimating ΔH^θ_f,298, and ΔG^θ_f,298, and C_p of lithium-rich manganese-based xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂ solid solution materials

The chemical valences of Li, O, Mn, and M in the lithium-rich manganese-based solid solution materials of xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) are +1, -2, +4, and +3, respectively. The most studied systems of the lithium-rich manganese-based xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂ material are Ni-Mn, Ni-Co-Mn. Common layered lithium-rich materials include xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/3Co_1/3Mn_1/3O₂ and xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/3Co_1/3Mn_1/3O₂.

The mathematical models for estimating the ∆H^θ_f,298, ∆G^θ_f,298, and C_p of lithium-rich manganese-based xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) solid solution materials by the group contribution method are shown in Eq.(17~19):

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂)=4/3x∆H^θ_f,298(Li⁺)

+2/3x∆H^θ_f,298(Mn⁴⁺)+2x∆H^θ_f,298(O^2-)+(1-x)∆H^θ_f,298(Li⁺)

+(1-x)∆Hθf,298(M3+)+2(1-x)∆Hθf,298(O2-)

(17)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂)=4/3x∆G^θ_f,298(Li⁺)

+2/3x∆G^θ_f,298(Mn⁴⁺)+2x∆G^θ_f,298(O^2-)+(1-x)∆G^θ_f,298(Li⁺)

+(1-x)∆Gθf,298(M3+)+2(1-x)∆Gθf,298(O2-)

(18)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂)=∑_jn_jΔ_a,j+(∑_jn_jΔ_b,j×10^-3)T

+(∑_jn_jΔ_c,j×10⁶)/T²+(∑_jn_jΔ_d,j×10^-6)T²

∑_jn_jΔ_a,j=4/3xΔ_a,j(Li⁺)+2/3xΔ_a,j(Mn⁴⁺)+2xΔ_a,j(O^2-)

+(1-x)Δ_a,j(Li⁺)+(1-x)Δ_a,j(M³⁺)+2(1-x)Δ_a,j(O^2-)

∑_jn_jΔ_b,j=4/3xΔ_b,j(Li⁺)+2/3xΔ_b,j(Mn⁴⁺)+2xΔ_b,j(O^2-)

+(1-x)Δ_b,j(Li⁺)+(1-x)Δ_b,j(M³⁺)+2(1-x)Δ_b,j(O^2-)

∑_jn_jΔ_c,j=4/3xΔ_c,j(Li⁺)+2/3xΔ_c,j(Mn⁴⁺)+2xΔ_c,j(O^2-)

+(1-x)Δ_c,j(Li⁺)+(1-x)Δ_c,j(M³⁺)+2(1-x)Δ_c,j(O^2-)

∑_jn_jΔ_d,j=4/3xΔ_d,j(Li⁺)+2/3xΔ_d,j(Mn⁴⁺)+2xΔ_d,j(O^2-)

+(1-x)Δd,j(Li+)+(1-x)Δd,j(M3+)+2(1-x)Δd,j(O2-)

(19)

When M is Ni_1/2Mn_1/2, the mathematical models for estimating the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of lithium-rich manganese-based xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂ solid solution materials by the group contribution method are shown in Eq.(20~22):

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/2Mn_1/2O₂)

=-66.262x-728.847

(20)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/2Mn_1/2O₂)

=-72.500x-676.458

(21)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/2Mn_1/2O₂)

=-6.634x+81.395+(8.385x+35.899)(10^-3)T

+(0.116x-1.191)(106)/T2+(0.415x+5.666)(10-6)T2

(22)

When M is Ni_1/3Co_1/3Mn_1/3, the mathematical models for esti-mating the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of lithium-rich manganese-based xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMO₂ solid solution materials by the group contribution method are shown in Eq.(23~25):

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/3Co_1/3Mn_1/3O₂)

=-83.145x-711.964

(23)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/3Co_1/3Mn_1/3O₂)

=-92.952x-656.005

(24)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_1/3Co_1/3Mn_1/3O₂)

=-14.869x+89.630+(24.973x+19.311)(10^-3)T

+(0.269x-1.344)(106)/T2+(3.866x+2.215)(10-6)T2

(25)

2.3 Mathematical models for estimating ΔH^θ_f,298, ΔG^θ_f,298, and C_p of the layered spinel composite solid solution material

The chemical valences of Li, O in layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄ (0<x<1) composite solid solution material are +1, -2, respectively. The Mn element present in Li[Li_1/3Mn_2/3]O₂ has a valence of +4, and LiMn₂O₄ has a Mn³⁺ and Mn⁴⁺ content of 50%.

The mathematical models for estimating the ∆H^θ_f,298, ∆G^θ_f,298, and C_p of the layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄ composite solid solution materials using the group contribution method are shown in Eq.(26~28), respectively:

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄)=4/3x∆H^θ_f,298(Li⁺)

+2/3x∆H^θ_f,298(Mn⁴⁺)+2x∆H^θ_f,298(O^2-)+(1-x)∆H^θ_f,298(Li⁺)

+2×0.5(1-x)∆H^θ_f,298(Mn³⁺)+2×0.5(1-x)∆H^θ_f,298(Mn⁴⁺)

+4(1-x)∆Hθf,298(O2-)

(26)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄)

=4/3x∆G^θ_f,298(Li⁺)+2/3xΔG^θ_f,298(Mn⁴⁺)

+2x∆G^θ_f,298(O^2-)+(1-x)∆G^θ_f,298(Li⁺)+

2×0.5(1-x)∆G^θ_f,298(Mn³⁺)+2×0.5(1-x)∆G^θ_f,298(Mn⁴⁺)

+4(1-x)∆Gθf,298(O2-)

(27)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄)

=∑_jn_jΔ_a,j+(∑_jn_jΔ_b,j×10^-3T+(∑_jn_jΔ_c,j×10⁶)/T²

+(∑_jn_jΔ_d,j×10^-6)T²

∑_jn_jΔ_a,j=4/3xΔ_a,j(Li⁺)+2/3xΔ_a,j(Mn⁴⁺)+2xΔ_a,j(O^2-)

+(1-x)Δ_a,j(Li⁺)+2×0.5(1-x)Δ_a,j(Mn³⁺)

+2×0.5(1-x)Δ_a,j(Mn⁴⁺)+4(1-x)Δ_a,j(O^2-)

∑_jn_jΔ_b,j=4/3xΔ_b,j(Li⁺)+2/3xΔ_b,j(Mn⁴⁺)+2xΔ_b,j(O^2-)

+(1-x)Δ_b,j(Li⁺)+2×0.5(1-x)Δ_b,j(Mn³⁺)

+2×0.5(1-x)Δ_b,j(Mn⁴⁺)+4(1-x)Δ_b,j(O^2-)

∑_jn_jΔ_c,j=4/3xΔ_c,j(Li⁺)+2/3xΔ_c,j(Mn⁴⁺)+2xΔ_c,j(O^2-)

+(1-x)Δ_c,j(Li⁺)+2×0.5(1-x)Δ_c,j(Mn³⁺)

+2×0.5(1-x)Δ_c,j(Mn⁴⁺)+4(1-x)Δ_c,j(O^2-)

∑_jn_jΔ_d,j=4/3xΔ_d,j(Li⁺)+2/3xΔ_d,j(Mn⁴⁺)+2xΔ_d,j(O^2-)

+(1-x)Δ_d,j(Li⁺)+2×0.5(1-x)Δ_d,j(Mn³⁺)

+2×0.5(1-x)Δd,j(Mn4+)+4(1-x)Δd,j(O2-)

(28)

In Eq.(28), the values of the group contribution can be considered as the contributions in the layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄ composite solid solution material. The mathematical models of ∆H^θ_f,298, ∆G^θ_f,298, and C_p are shown in Eq.(29~31), respectively:

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄)

=446.175x-1241.284

(29)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄)

=454.248x-1203.205

(30)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄)

=-58.806x+133.567+(-33.131x+77.414)(10^-3)T

+(0.823x-1.898)(106)/T2+(3.508x+2.573)(10-6)T2

(31)

In the layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄ (0<x<1) composite solid solution material, the chemical valences of Li and O are +1 and -2, respectively. The ma-thematical models for estimating the ∆H^θ_f,298, ∆G^θ_f,298, and C_p of the layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄ com-posite solid solution materials using the group contribution method are shown in Eq.(34), respectively:

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄)

=4/3x∆H^θ_f,298(Li⁺)+2/3x∆H^θ_f,298(Mn⁴⁺)

+2x∆H^θ_f,298(O^2-)+(1-x)∆H^θ_f,298(Li⁺)

+0.5(1-x)∆H^θ_f,298(Ni²⁺)+1.5(1-x)∆H^θ_f,298(Mn⁴⁺)

4 (1-x)∆H^θ_f,298(O^2-)

(32)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄)

=4/3x∆G^θ_f,298(Li⁺)+2/3x∆G^θ_f,298(Mn⁴⁺)

+2x∆G^θ_f,298(O^2-)+(1-x)∆G^θ_f,298(Li⁺)

+0.5(1-x)∆G^θ_f,298(Ni²⁺)+1.5(1-x)∆G^θ_f,298(Mn⁴⁺)

+4 (1-x)∆Gθf,298(O2-)

(33)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄)

=∑_jn_jΔ_a,j+(∑_jn_jΔ_b,j×10^-3)T+(∑_jn_jΔ_c,j×10⁶)/T²

+(∑jnjΔd,j×10-6)T2

(34)

∑_jn_jΔ_a,j=4/3xΔ_a,j(Li⁺)+2/3xΔ_a,j(Mn⁴⁺)+2xΔ_a,j(O^2-)

+(1-x)Δ_a,j(Li⁺)+0.5(1-x)Δ_a,jNi²⁺)+1.5(1-x)Δ_a,j(Mn⁴⁺)

+4 (1-x)Δ_a,j(O^2-)

∑_jn_jΔ_b,j=4/3xΔ_b,j(Li⁺)+2/3xΔ_b,j(Mn⁴⁺)+2xΔ_b,j(O^2-)

+(1-x)Δ_b,j(Li⁺)+0.5(1-x)Δ_b,j(Ni²⁺)+1.5(1-x)Δ_b,j(Mn⁴⁺)

+4(1-x)Δ_b,j(O^2-)

∑_jn_jΔ_c,j=4/3xΔ_c,j(Li⁺)+2/3xΔ_c,j(Mn⁴⁺)+2xΔ_c,j(O^2-)

+(1-x)Δ_c,j(Li⁺)+0.5(1-x)Δ_c,j(Ni²⁺)

+1.5(1-x)Δ_c,j(Mn⁴⁺)+4(1-x)Δ_c,j(O^2-)

∑_jn_jΔ_d,j=4/3xΔ_d,j(Li⁺)+2/3xΔ_d,j(Mn⁴⁺)+2xΔ_d,j(O^2-)

+(1-x)Δ_d,j(Li⁺)+0.5(1-x)Δ_d,j(Ni²⁺)

+1.5(1-x)Δ_d,j(Mn⁴⁺)+4(1-x)Δ_d,j(O^2-)

In Eq.(34), the values of the group contribution can be ob-tained as the layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄ composite solid solution material. The mathematical models of ΔH^θ_f,298, ∆G^θ_f,298, and C_p are shown in Eq.(37), respectively:

∆H^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄)

=366.851x-1161.960

(35)

∆G^θ_f,298(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄)

=320.593x-1069.550

(36)

C_p(xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄)=-59.345x+

134.106 +(-37.749x+82.033)(10^-3)T+(0.967x-2.042)

(106)/T 2+(3.217x+2.864)(10-6)T2

(37)

The ∆H^θ_f,298, ∆G^θ_f,298, and C_p of the common 63 lithium-rich materials were estimated by the mathematical models, as show in Table 7.

Table 7 Estimation results of ∆H^θ_f,298, ∆G^θ_f,298 and C_p,298 for lithium-rich materials

Sample	∆Hθf,298/kJ·mol-1	∆Gθf,298/kJ·mol-1	Cp,298 predicted by the group contribution method/ J·mol-1·K-1	Cp,298 predicted by the Kopps rule/ J·mol-1·K-1
0.1Li2MnO3·0.9LiCoO2	-729.65	-665.93	86.13	79.70
0.2Li2MnO3·0.8LiCoO2	-781.09	-716.77	89.30	83.60
0.3Li2MnO3·0.7LiCoO2	-832.54	-767.60	92.46	87.51
0.4Li2MnO3·0.6LiCoO2	-883.99	-818.43	95.62	91.41
0.5Li2MnO3·0.5LiCoO2	-935.43	-869.27	98.78	95.31
0.6Li2MnO3·0.4LiCoO2	-986.88	-920.10	101.95	99.21
0.7Li2MnO3·0.3LiCoO2	-1038.32	-970.94	105.11	103.11
0.8Li2MnO3·0.2LiCoO2	-1089.77	-1021.77	108.27	107.02
0.9Li2MnO3·0.1LiCoO2	-1141.22	-1072.60	111.43	110.92
0.1Li2MnO3·0.9LiFeO2	-806.02	-759.05	85.64	82.74
0.2Li2MnO3·0.8LiFeO2	-848.98	-799.54	88.85	86.30
0.3Li2MnO3·0.7LiFeO2	-891.94	-840.03	92.07	89.87
0.4Li2MnO3·0.6LiFeO2	-934.90	-880.51	95.29	93.43
0.5Li2MnO3·0.5LiFeO2	-977.86	-921.00	98.51	97.00
0.6Li2MnO3·0.4LiFeO2	-1020.82	-961.49	101.72	100.56
0.7Li2MnO3·0.3LiFeO2	-1063.78	-1001.97	104.94	104.13
0.8Li2MnO3·0.2LiFeO2	-1106.74	-1042.46	108.16	107.69
0.9Li2MnO3·0.1LiFeO2	-1149.70	-1082.95	111.38	111.26
0.1Li2MnO3·0.9LiNi1/2Mn1/2O2	-775.23	-721.16	82.73	80.65
0.2Li2MnO3·0.8LiNi1/2Mn1/2O2	-821.61	-765.85	86.27	84.44
0.3Li2MnO3·0.7LiNi1/2Mn1/2O2	-867.99	-810.55	89.80	88.24
0.4Li2MnO3·0.6LiNi1/2Mn1/2O2	-914.37	-855.25	93.34	92.04
0.5Li2MnO3·0.5LiNi1/2Mn1/2O2	-960.76	-899.95	96.88	95.84
0.6Li2MnO3·0.4LiNi1/2Mn1/2O2	-1007.14	-944.65	100.42	99.63
0.7Li2MnO3·0.3LiNi1/2Mn1/2O2	-1053.52	-989.34	103.96	103.43
0.8Li2MnO3·0.2LiNi1/2Mn1/2O2	-1099.90	-1034.04	107.50	107.23
0.9Li2MnO3·0.1LiNi1/2Mn1/2O2	-1146.28	-1078.74	111.04	111.02
0.1Li[Li1/3Mn2/3]O2·0.9LiNi1/2Mn1/2O2	-735.47	-683.71	78.91	76.82
0.2Li[Li1/3Mn2/3]O2·0.8LiNi1/2Mn1/2O2	-742.10	-690.96	78.63	76.79
0.3Li[Li1/3Mn2/3]O2·0.7LiNi1/2Mn1/2O2	-748.73	-698.21	78.35	76.76
0.4Li[Li1/3Mn2/3]O2·0.6LiNi1/2Mn1/2O2	-755.35	-705.46	78.07	76.73
0.5Li[Li1/3Mn2/3]O2·0.5LiNi1/2Mn1/2O2	-761.98	-712.71	77.79	76.70
0.6Li[Li1/3Mn2/3]O2·0.4LiNi1/2Mn1/2O2	-768.60	-719.96	77.51	76.67
0.7Li[Li1/3Mn2/3]O2·0.3LiNi1/2Mn1/2O2	-775.23	-727.21	77.23	76.64
0.8Li[Li1/3Mn2/3]O2·0.2LiNi1/2Mn1/2O2	-781.86	-734.46	76.95	76.61
0.9Li[Li1/3Mn2/3]O2·0.1LiNi1/2Mn1/2O2	-788.48	-741.71	76.67	76.58
0.1Li[Li1/3Mn2/3]O2·0.9LiNi1/3Co1/3Mn1/3O2	-720.28	-665.30	80.04	76.50
0.2Li[Li1/3Mn2/3]O2·0.8LiNi1/3Co1/3Mn1/3O2	-728.59	-674.60	79.64	76.49
0.3Li[Li1/3Mn2/3]O2·0.7LiNi1/3Co1/3Mn1/3O2	-736.91	-683.89	79.23	76.49
0.4Li[Li1/3Mn2/3]O2·0.6LiNi1/3Co1/3Mn1/3O2	-745.22	-693.19	78.83	76.48
0.5Li[Li1/3Mn2/3]O2·0.5LiNi1/3Co1/3Mn1/3O2	-753.54	-702.48	78.42	76.48
0.6Li[Li1/3Mn2/3]O2·0.4LiNi1/3Co1/3Mn1/3O2	-761.85	-711.78	78.01	76.47
0.7Li[Li1/3Mn2/3]O2·0.3LiNi1/3Co1/3Mn1/3O2	-770.17	-721.07	77.61	76.47
0.8Li[Li1/3Mn2/3]O2·0.2LiNi1/3Co1/3Mn1/3O2	-778.48	-730.37	77.20	76.46
0.9Li[Li1/3Mn2/3]O2·0.1LiNi1/3Co1/3Mn1/3O2	-786.79	-739.66	76.80	76.46
0.1Li[Li1/3Mn2/3]O2·0.9LiMn2O4	-1196.67	-1157.78	129.58	127.40
0.2Li[Li1/3Mn2/3]O2·0.8LiMn2O4	-1152.05	-1112.36	123.67	121.75
0.3Li[Li1/3Mn2/3]O2·0.7LiMn2O4	-1107.43	-1066.93	117.76	116.10
0.4Li[Li1/3Mn2/3]O2·0.6LiMn2O4	-1062.81	-1021.51	111.85	110.45
0.5Li[Li1/3Mn2/3]O2·0.5LiMn2O4	-1018.20	-976.08	105.94	104.80
0.6Li[Li1/3Mn2/3]O2·0.4LiMn2O4	-973.58	-930.66	100.03	99.15
0.7Li[Li1/3Mn2/3]O2·0.3LiMn2O4	-928.96	-885.23	94.12	93.50
0.8Li[Li1/3Mn2/3]O2·0.2LiMn2O4	-884.34	-839.81	88.21	87.85
0.9Li[Li1/3Mn2/3]O2·0.1LiMn2O4	-839.73	-794.38	82.30	82.20
0.1Li[Li1/3Mn2/3]O2·0.9LiNi0.5Mn1.5O4	-1125.27	-1037.49	129.87	126.23
0.2Li[Li1/3Mn2/3]O2·0.8LiNi0.5Mn1.5O4	-1088.59	-1005.43	123.93	120.71
0.3Li[Li1/3Mn2/3]O2·0.7LiNi0.5Mn1.5O4	-1051.90	-973.37	117.99	115.19
0.4Li[Li1/3Mn2/3]O2·0.6LiNi0.5Mn1.5O4	-1015.22	-941.31	112.04	109.67
0.5Li[Li1/3Mn2/3]O2·0.5LiNi0.5Mn1.5O4	-978.53	-909.25	106.10	104.15
0.6Li[Li1/3Mn2/3]O2·0.4LiNi0.5Mn1.5O4	-941.85	-877.19	100.16	98.63
0.7Li[Li1/3Mn2/3]O2·0.3LiNi0.5Mn1.5O4	-905.16	-845.13	94.22	93.11
0.8Li[Li1/3Mn2/3]O2·0.2LiNi0.5Mn1.5O4	-868.48	-813.08	88.28	87.59
0.9Li[Li1/3Mn2/3]O2·0.1LiNi0.5Mn1.5O4	-831.79	-781.02	82.34	82.07

3 Conclusions

1) The ∆H^θ_f,298, ∆G^θ_f,298, and C_p,298 of the three types of lithium-rich cathode materials consist of the thermodynamic group contribution values of Li⁺, Ni²⁺, Fe³⁺, Co²⁺, Co³⁺, Mn³⁺, and Mn⁴⁺. Three main types of lithium-rich cathode materials are explored: (1) lithium-rich layered xLi₂MnO₃·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) cathode material, (2) lithium-rich manganese-based xLi_1/3MnO_2/3·(1-x)LiMO₂ (0<x<1, M=Ni, Co, Cr, Fe, Al, Mg, Ni-Co, Ni-Mn, Ni-Co-Mn···) solid solution material, and (3) layered spinel xLi[Li_1/3Mn_2/3]O₂·(1-x)LiMn₂O₄ (0<x<1) composite solid solution material and layered spinel

xLi[Li_1/3Mn_2/3]O₂·(1-x)LiNi_0.5Mn_1.5O₄ (0<x<1) composite solid solution material.

2) The mathematical models for estimating the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of three types of lithium-rich cathode materials are constructed for the first time by the group contribution method.

3) Based on the satisfactory results, the ΔH^θ_f,298, ΔG^θ_f,298, and C_p of three types of lithium-rich Li_1+xM_1-xO₂ cathode materials are calculated, and those of 63 common lithium-rich Li_1+xM_1-xO₂ materials can also be estimated by the mathematical models.