Applicability of the Meyer-Neldel rule to selected single crystal, ceramic and glassy superionic conductors

Sohd State lomcs 36 (1989) 239-241 North-Holland, Amsterdam

APPLICABILITY OF THE M E Y E R - N E L D E L RULE TO SELECTED SINGLE CRYSTAL, CERAMIC AND GLASSY S U P E R I O N I C C O N D U C T O R S J GARBARCZYK, P KUREK, J NOWIlqSKI and W JAKUBOWSKI Instttute of Physws, WarsawUmversttyof Technology, ul Koszykowa 75, 00-662 Warszawa,Poland Received 18 July 1988, accepted for pubhcatmn 21 December 1988

The apphcabfl~tyof the Meyer-Neldei (M-N) rule to several crystaihne and amorphous supermmc conductors is exammed The mterpretatmn of the constant ct in the M-N dependence ts proposed

1. Introduction For a variety of solids, including semiconductors, runic conductors and supenonic conductors [ 1 - 3 ] , the so-called Meyer-Neldel rule is fulfilled Accordmg to that rule the following, linear relationship holds lnao=Ot AE+fl,

a, fl=const

(1)

For the (super)ionic conductors ao and AE are the preexponential factor and the acUvatlon energy of ion motion respecuvely, which stand In the Arrhenms formula a T = a o e x p ( - A E / k T ) The MeyerNeldel rule, m fact, is a semiempmcal relationship so far, although some attempts have been undertaken to explain it theoretically [ 3 ] The application of the M - N rule is especmlly adequate to the conductors of variable chemical composition or preprepared in various conditions, for which the ranges of ao and AE are wide enough The extrapolated straight hnes of the Arrhenius plots for those conductors, usually cross together at a common focal point at a characteristic temperature To Comparing the conducuwties of two compositions at that point, it IS easy to show that the temperature To equals 1/kot, where ot ~s the slope of the straight line given by eq ( 1 ) It is also valid for linear parts of those Arrhenius plots which exhibit curvatures So, it seems that a has a clear geometric interpretation In this work we have examined several single crystals, ceramic and glassy supelaonic conductors and checked the applicability

of the M - N rule for them For analysis we used our own conductivity data [4-8 ] as well as the values reported In the literature

2. Results and discussion 2 1 Smgle crystals Curve a in fig 1 shows the M - N dependence for single crystals of Na+13"-alumlna prepared by various authors in various conditions [ 9-12 ]. The slope a, found from the least square fit, gives the temperature To=(154_+45)°C It is interesting to notice that such a value is within the range of temperature 150-220°C, where the curvature of the Arrhenxus graphs for Na+~"-alumlna occurs [9,10] Usually that curvature is interpreted m terms of order-disorder transition or melting of a mobile ion sublattlce

2 2 Ceramws ceramic samples of Lll6_2vZnr(GeO4)4 i e LISICON and LIl35Zn125(GeO4)4_v(ZrO4)v i e ZrO2 doped LISICON are shown in fig lb and c The temperatures which correspond to the slopes of the presented lines are equal to (226+ 100)°C and ( 1 6 0 + 3 0 ) ° C respectively Our conductivity measurements showed that both compounds, similarly to ~"-alumma, exhibit curvatures of the Arrhenius plots which occur

0 167-2738/89/$ 03 50 © Elsevier Science Publishers B V ( North-Holland Physics Publishing Division )

The

M-N

lines

for

240

J Garbarczyk et al IApphcabthty of the Meyer-Neldel rule

16

16 c

14

14

6

v

½ 12 "T

9_. 10

-q 10 Q

Q

6

0

i

i

0'2 '

0'2

'

0'4

'

O~

i

i

04 aE [eV]

0'6

aE [eV] Fig 1 The Meyer-Neldel dependences for single crystals of Na+13"-alumma (a), ceramic samples of LISICON (b) and zlrcoma doped LISICON (c)

at the temperatures around the corresponding values of To Depending on the composition, this occurs at about 200-240°C for LtSICON [4] and at 190230°C for ZrO2 doped LISICON [8] Those bends also may be interpreted as the effect of L~+ mobile ions sublattlce melting

Fig 2 The M-N dependences for some supenonlc glasses xAg( I -x)AgPOa (a), xAgI 0 5( 1-x)Ag~O 0 5( 1-x)P205 (b) xCul 0 5( l - x ) C u 2 0 0 5( l -x)P2Os (c) and xL1Cl 0 45L120 0 55B203 (d)

14 !

Our results concerning glasses AgI-Ag20-P2Os [ 5 ], LiC1-L120-B203 [ 6 ] and C u I - C u 2 0 - P 2 0 5 [ 7 ] are presented m fig 2 The corresponding temperatures To are equal to (594_+60)°C, (565+_85)°C and (655_+200)°C respectively These temperatures are close to the melting point temperatures of AgI, L1C1 and CuI which are equal to 558 ° C, 613 °C and 605°C respecUvely It is compatible with the interpretation g~ven above for single crystals and ceramics if we assume that AgI-hke m~croregtons are responsible for fast ion transport in those glasses It would be consistent with the ~deas of other authors, e g [ 13 ], who postulate the existence of such regions m Ag+-conductlve glasses

i \

,,,- 12 O

2 3 Glasses

i

"#'--......

,'t" ,/" ~

,g q

a

\o c

b\ | i

0'4

'

0'6

'

0'8 aE [eV]

I

I

10

Fig 3 The M-N dependences for selected glassy conductors xLl20 ( l -X)B203 (a), xNa20 ( 1-x)GeO2 (b) and xNa2S( 1-x)GeS2 (c)

2 4 Negattve slope in the M - N dependence All of the aforemenuoned conductors exhibit positive value of constant a However, among the examined glasses e g LI20-B203, [ 6,14,15 ], we also

J Garbarczyket al /Apphcabthty of the Meyer-Neldel rule f o u n d t h o s e for w h i c h ot is n e g a t i v e o r changes its sign d e p e n d i n g o n c o m p o s i t i o n (fig 3) T h i s has n o clear i n t e r p r e t a t i o n up to d a t e O u r p r e l i m i n a r y exp l a n a t i o n is b a s e d o n the fact that tro i n c l u d e s the f u n c t i o n f ( c ) = c ( 1 - c), e g [ 3 ], w h i c h m a y c h a n g e its m o n o t o n i c i t y d e p e n d i n g o n t h e o c c u p a t i o n f a c t o r c T h e ao i n c l u d e s also t h e e n t r o p y t e r m e x p ( A S / k ) , w h i c h d e c r e a s e s w h e n e n t r o p y S goes d o w n t h a t c o n s e q u e n t l y m a y p r o d u c e a n e g a t i v e cz It s e e m s that n e g a t i v e A S can be u n d e r s t o o d i f the o r d e r i n g o f the m o b i l e i o n s (1 e c o l l e c t i v e m o t i o n ) occurs d u n n g transport

Acknowledgement T h e w o r k was s u p p o r t e d C P B R 3 20 60

by R e s e a r c h P r o j e c t

References [ I ] T DosdaleandR Brook, J Mat Scl 13 (1978) 167

241

[ 2 ] D Almond and A West, Sohd State Iomcs 18 / 19 (1986) 1105 [3] D Almond andA West, Solid State Iomcs 23 (1987) 27 [4] P Kurek and W Bogusz, Phys Status Sohdl a 78 (1983) Kl17 [ 5 ] J Novafiskl, B Wn~trzewskl and W Jakubowskl, Sohd State Iomcs 28-30 (1988) 804 [ 6 ] P Kurek, J Nowmskl and W Jakubowskl, m 37th Meeting of ISE, Vllmus 1986, USSR, Extended Abstracts vol 3 p 125 [ 7 ] J Nowlfiskl, P Kurek, J Garbarczyk and W Jakubowskl, Rept Inst Phys WUT, 37 (1989), to be pubhshed [ 8 ] T Ayuub, Thesis (Warsaw Umverslty of Technology, 1987 ) [9] G Famngton and J Bnant m Fast ion transport in sohds, eds P Vashlshta, J N Mundy, G K Shenoy (NorthHolland, Amsterdam, 1979) p 395 [ 10] J Bates, H Engstrom, J Wang, B Larson, N Dudney and W Brundage, Sohd State IOnlCS5 ( 1981 ) 159 [ 11 ] W R o t h , R Benson, V Tlkku and B Dunn, Sohd State Iomcs 5 ( 1981 ) 163 [12] D White, S Chen, M Sankararaman and H Sato, Sohd State lomcs 18/19 (1986) 608 [13] T Mmaml, J Non-Cryst Sohds 56 (1983) 15 [ 14] M Thomas and N Peterson, Sohd State Iomcs 14 (1984) 297 [ 15 ] M Rtbes, B Barran and J Souqet, J Non-Cryst Sohds 38/ 39 (1980) 271