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Journal of Non-Crystalline Solids 354 (2008) 360–364

Electronic state of sulfide-based lithium ion conducting glasses

Y. Kowada a,*, M. Tatsumisago b, T. Minami c, H. Adachi d

a Hyogo University of Teacher Education, Department of Science, Technology, and Human life, 942-1 Shimokume, Kato-shi, Hyogo 673-1494, Japanb Department of Applied Chemistry, Osaka Prefecture University, Sakai 599-8531, Japan

c Osaka Prefecture University, Sakai 599-8531, Japand Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan

Available online 5 November 2007

Abstract

Electronic states of the sulfide-based lithium ion conducting glasses were calculated by the DV-Xa cluster method. The cluster modelswere constructed by the coordination number reported by experimental methods and the bond length estimated from the ionic radii ofeach ion. The movement of the Li ion was simulated by several model clusters with different positions of the moving ion. The relationshipbetween ionic conductivity and the differential total bond overlap population (DBOP) was discussed for the sulfide-based glasses in thesystems Li2S–SiS2–Al2S3 and Li2S–SiS2–P2S5. In these glasses, the DBOP with the movement of the lithium ion had good negative cor-relations with the ionic conductivities and positive correlations with the activation energies obtained by the experimental measurements.In any cases, the smaller change of the total bond overlap population of the moving cations played an important role for the fast ionmovement in the superionic conducting glasses. This bonding state of the moving cations is one of the characteristics of the electronicstate in the sulfide-based lithium ion conducting glasses.� 2007 Elsevier B.V. All rights reserved.

PACS: 31.15.A; 31.15.ae; 31.15.E; 66.10.Ed; 71.15.Ap; 71.23.�k

Keywords: Fast ion conduction; Ab initio; Density functional theory; Molecular orbital

1. Introduction

Recently about 10 years, we have paid attention to therelationship between fast ion movement and covalentbonding in the super ionic conducting materials [1–4]. Inthe AgI-based superionic conducting glasses, there was acertain covalent bonding between the moving Ag ion andthe neighboring Ag ions. This bonding interaction madethe moving Ag ion stable and the change of the covalentinteraction between the moving Ag ion and the surround-ing ions was very small in the course of the movementthrough the path. This result was the characteristic of theAgI-based superionic conducting glasses.

In the present work, we have tried to estimate the rela-tionship between the ionic conductivity and chemical bond-

0022-3093/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2007.07.085

* Corresponding author.E-mail address: ykowada@hyogo-u.ac.jp (Y. Kowada).

ing of the moving Li ions in the sulfide-based superionicconducting glasses. Usually it is difficult to calculate elec-tronic state of inorganic materials. Among various calcula-tion techniques, the DV-Xa cluster method is one of themost appropriate methods to analyze the chemical bondingof Li ions in the sulfide-based superionic conducting glasses[5]. This method has been widely applied to the electronicstate calculations in the fields of metals, ceramics, glassesand so on [6–9].

In the present study we have calculated the electronicstate of sulfide-based superionic conducting glasses by theDV-Xa cluster method.

2. Calculation method

The DV-Xa cluster method has been used to calculate theelectronic state of the sulfide-based superionic conductingglasses. This method is one of the linear combination of

Y. Kowada et al. / Journal of Non-Crystalline Solids 354 (2008) 360–364 361

atomic orbital (LCAO) molecular orbital methods. In thismethod the exchange potential [10] VXC is described by

V XCðr"Þ ¼ �3a3

4pq"ðrÞ

� �13

;

where q is the electron density of the cluster and a is a con-stant. a is fixed to be 0.7 throughout the present work,which was found empirically as the most appropriate.[11] The Mulliken population analysis was used for theevaluation of the bond overlap population between atoms.

In order to calculate the electronic state of the Li ion inthe sulfide-based superionic conducting glasses, there is ahurdle to construct a model cluster, since it is difficult toobtain the details of the structure around Li ions in theglasses by experimental methods. The coordination num-ber of sulfide ions to the Li ion and the distances betweenthe Li ion and the first neighboring ions were reportedabout several kinds of the sulfide glasses [12–14]. As basedon these studies, we have modeled a tetrahedral structureand estimated the bond length from the ionic radius of eachion reported by Shannon [15], to calculate electronic statenear Li ions. Fig. 1 shows a schematic diagram of themodel cluster to calculate the electronic state around theLi ion in the present work. In this model, a lithium ion islocated in the center and four sulfide ions are coordinatedto the center atom. Each sulfide ion forms a SiS4 unit,which has regular tetrahedron structure. The outside sul-fide ions of SiS4 units are terminated by lithium ions. Thedistances of Si–S, Li–S, P–S, and Al–S are 2.10, 2.43,2.01, and 2.23 A, respectively. Near the center tetrahedralunit, three lithium ions are located on the outside to keepthe cluster neutral. The movement of the center Li ionwas simulated by shifting the Li ion to different positionsof the five clusters. The Li ion is moved along with the con-duction path through a face of the tetrahedron of sulfideions coordinated to the Li ion. The length of the movementof the Li ion was 0.810 A. The SiS2 content was changedwith exchange of Si in SiS4 units with the other elements,such as Al and P. In this case, the neutrality of the modelclusters was adjusted by the number of the outside Li ions.Then the contents of Al and P in the clusters could become

Fig. 1. Schematic diagram of th

25, 50, 75, and 100 mol% in the present work. To comparethe theoretical results with the experimental ones, the bondoverlap population calculated for the composition corre-sponding to the experimental samples was obtained byinterpolation of the results of these four compositions.

As previously reported, the covalency of bonding naturebetween the moving cations and surrounding ions werevery important to realize the fast movement of the ions.We investigated the total bond overlap population to esti-mate total of covalent interactions of moving cations and itwas suggested that the cations, which could move easily,had small change of the total bond overlap population inthe course of the movement. In the present work we wouldlike to introduce differential total bond overlap population(DBOP), to evaluate the relationship between the covalentinteraction and the fast movement of the moving Li ions.DBOP is obtained by subtracting the minimum from themaximum of the total bond overlap population throughoutthe movement of the lithium ion along the path. Thoughthe net charge of the moving Li ion is also very importantto discuss the ionic conductivity, the changes of the netcharge of the moving Li ions were very small in all systems.Then we have omitted for the page limitation. In this studythe electronic state of the moving lithium ions were calcu-lated in the systems Li2S–SiS2–Al2S3 and Li2S–SiS2–P2S5 tocompare with the ionic conductivity.

3. Results

The composition dependences of the DBOP and theionic conductivity at 25 �C in the system Li2S–SiS2–Al2S3

are shown in Fig. 2. In this figure, closed diamonds showthe results of ionic conductivity reported in Ref. [16] andclosed rectangles show DBOP in the 60Li2S Æ 0.4(xAl-S1.5 Æ (100�x)SiS2) glasses. The ionic conductivity isdecreased with an increase in the compositional parameterx up to x = 50 and then gradually decreased with furtherincrease in x. On the other hand, the DBOP shows oppositetendency with the Al2S3 content. The DBOP at x = 0 is0.017 and shows increasing tendency with the Al2S3

content to 0.057 at x = 100. As mentioned above, the faster

e Li16Si4S16 model cluster.

Fig. 2. The composition dependence of ionic conductivity and DBOP inthe 60Li2S Æ 40(xAlS1.5 Æ (100�x)SiS2) glasses. The lines are drawn as aguide to the eye.

Fig. 4. The composition dependence of ionic conductivity and DBOP inthe 60Li2S Æ 40(xPS2.5 Æ (100�x)SiS2) glasses. The lines are drawn as aguide to the eye.

362 Y. Kowada et al. / Journal of Non-Crystalline Solids 354 (2008) 360–364

movable cations in the superionic conducting glassesshowed smaller DBOP with the movement. In this system,the DBOP becomes smaller at the composition with thehigher ionic conductivity. Furthermore, there seems to bea correlation between the ionic conductivity and theDBOP.

Fig. 3 shows the composition dependences of the activa-tion energy for conduction and the DBOP. In this system,activation energy is increased with the Al2S3 content, corre-sponding to the decrease of the ionic conductivity. TheDBOP is also increased with x and might be found to cor-relate with activation energy. Then, we have estimated cor-relations of the DBOP with the ionic conductivity and theactivation energy.

Fig. 3. The composition dependence of the activation energy of the ionicconductivity and DBOP in the 60Li2S Æ 40(xAlS1.5 Æ (100�x)SiS2) glasses.The lines are drawn as a guide to the eye.

The results of the DBOP analysis in the system Li2S–P2S5–SiS2 are shown in Fig. 4. This figure shows the com-position dependence of DBOP and ionic conductivity at25 �C in the 75Li2S Æ 0.25(xPS2.5 Æ (100�x)SiS2) glasses.[17,18] In this system, the ionic conductivity is0.64 · 10�4 S cm�1 at x = 60 and is increased with increas-ing of the P2S5 content. The conductivity becomes1.60 · 10�4 S cm�1 at x = 75. Contrary to this, DBOP ofthe moving Li ion is 0.031 at x = 50 and is decreased withthe P2S5 content. The composition dependence of the acti-vation energy for conduction in this system is shown inFig. 5. The activation energy is 35.0 KJ mol�1 at x = 60and is almost flat up to x = 80. Further increase in x resultsin a decrease in the activation energy. This change is corre-sponding to the increase of ionic conductivity. The DBOPof the Li ion shows similar variation with x, whereas theDBOP is decreased in the range of x larger than 75. Since

Fig. 5. The composition dependence of the activation energy of the ionicconductivity and DBOP in the 60Li2S Æ 40(xPS2.5 Æ 100�x)SiS2) glasses.The lines are drawn as a guide to the eye.

Y. Kowada et al. / Journal of Non-Crystalline Solids 354 (2008) 360–364 363

the change of the activation energy and the DBOP are alsosimilar in this system, we have estimated the correlationbetween the experimental results and the DBOP.

Fig. 7. The relationship between the ionic conductivity, the activationenergy and DBOP in the 60Li2S Æ 40(xPS2.5 Æ 100�x)SiS2) glasses. The lineswere obtained by the least-squares method.

4. Discussion

The ionic conductivity at 25 �C and the activationenergy for conduction in the 60Li2S Æ 0.4(xAlS1.5 Æ (100�x)-SiS2), as a function of the DBOP, are shown in Fig. 6. It isnoteworthy that the ionic conductivity is decreased and theactivation energy is increased linearly with an increase inthe DBOP. The evaluated correlation coefficient betweenthe ionic conductivity and DBOP is �0.91 and thatbetween the activation energy and DBOP is 0.90. Thisresult suggests that the DBOP significantly has a goodpositive correlation with the activation energy and a goodnegative correlation with the ionic conductivity in this sys-tem. This is very interesting because the model clusters forthis calculation were constructed without no strict struc-tural informations obtained by experimental measure-ments. Furthermore, these good correlations of DBOPsupport quantitative relations between DBOP and ionicconductivity.

Fig. 7 shows the DBOP dependence of ionic conductiv-ity at 25 �C and activation energy for conduction. In thissystem the correlations of the DBOP with ionic conductiv-ity and activation energy are very similar in the systemLi2S–SiS2–Al2S3, i.e. a positive correlation of the DBOPwith activation energy and a good negative one with ionicconductivity are observed, while the increase of activationenergy with the DBOP is smaller than that in the case ofthe addition of Al2S3. The correlation coefficient for theionic conductivity is �0.92 and that for the activationenergy is 0.51. The small correlation coefficient of activa-tion energy would be due to the difference of the composi-tion where the DBOP and the activation energy start todecrease. This difference of the composition between the

Fig. 6. The relationship between the ionic conductivity, the activationenergy and DBOP in the 60Li2S Æ 40(xAlS1.5 Æ (100�x)SiS2) glasses. Thelines were obtained by the least-squares method.

experimental and the theoretical results might be depen-dent on the long range structures of the conduction pathsof the moving Li ions. Nevertheless, there are good corre-lations of the DBOP with the ionic conductivity and theactivation energy in the both systems Li2S–SiS2–Al2S3

and Li2S–SiS2–P2S5. This result suggests that the DBOPcalculated by the DV-Xa method has a certain relationshipwith the ionic conductivity and the activation energy in thesulfide-based superionic conducting glasses.

5. Conclusion

Electronic states of the sulfide-based superionic con-ducting glasses in the systems Li2S–SiS2–Al2S3 and Li2S–SiS2–P2S5 were calculated by the DV-Xa method. The dif-ferential total bond overlap population (DBOP) wasobtained from the model clusters constructed with no strictstructural parameters by experimental measurements. TheDBOP had good correlations with the ionic conductivityand activation energy in the both systems. This result sug-gests that the covalent interaction of the moving lithiumions is very important to understand the fast movementof the lithium ions in the sulfide-based superionic conduct-ing glasses. The DBOP estimated by the DV-Xa methodcould be applied to design new sulfide-based superionicconducting glasses.

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