Neutron Rietveld analysis of structural changes in NASICON solid solutions Na1+xZr2SixP3−xO12 at elevated temperatures: x=1.6 and 2.0 at 320°C

Solid State h)nics 18 & 19 ( I'480 ) 944-~158 North+Holland. Amsterdam

944

NEUTRON RIETVELD ANALYSIS OF STRUCTURAL CHANGES IN NASICON SOLID SOLUTIONS Nal+~r2SixP3-xOl2x AT ELEVATED TEMPERATURES: x = 1.6 and 2.0 at 320°C J.-J.

*+

DIDISHEIM

*

, E. PRINCE~, and B. J. WUENSCH

*Department of Materials Science and Engineering, Massachusetts I n s t i t u t e o f Technology, Can~mridge, Massachusetts 02139, U.S.A. I n s t i t u t e o f Materials Science and Engineering, U.S. National Bureau of Standards, Gaithersburg, Maryland 02899, U.S.A. Neutron R i e t v e l d analyses of the structures of NASICON s o l i d s o l u t i o n s as a f u n c t i o n of composition have been extended to 320°C f o r the h i g h - c o n d u c t i v i t y compositions x = 1.6 and 2.0. The t r a n s f o r m a t i o n from the room temperature monoclinic C2/c s t r u c t u r e to the hexagonal R3c high temperature phase involves small atomic displacements, ranging from 0.385~ f o r Na(2) down to s h i f t s of only a few hundredths of an Angstrom f o r several framework ions. The Na(1) i n t e r s t i c e remains f u l l y occupied to the temperature presently examined. No evidence f o r p a r t i a l occupancy of the Zr octahedron is found, a non-stoichiometry which is possible but not o b l i g a t o r y f o r NASICON. The d i s t o r t i o n s of the framework are l a r g e s t at x = 2.0 as at room temperature. The radius of the windows between Na s i t e s at 320°C remain l a r g e s t at the composition w i t h x = 2.0 f o r both a Na(1)-Na(2) jump and a Na(2)-Na(2) jump. The r a d i i are s i g n i f i c a n t l y l a r g e r than the maximum value a v a i l a b l e among the three symmetry-independent paths in the room-temperature monoclinic structures f o r both types of d i f f u s i o n paths.

I.

INTRODUCTION

hedral s t r u c t u r e , the monoclinic c e l l axes

Fast-ion conduction in s o l i d s o l u t i o n s

being r e l a t e d to the hexagonal by the m a t r i x

between sodium zirconium phosphate and

[ l - l

sodium zirconium s i l i c a t e , Nal+xZr2SixP3_xOl2 ( 0 ~ x % 3 ) , was reported by Goodenough, Hong

composition in NASICON s o l i d s o l u t i o n s

and Kafalas I in 1976.

appeared to be c l o s e l y coupled w i t h struc-

The system is remark-

O/l l 0 / - I / 3 I / 3 I / 3 ] .

The marked v a r i a t i o n in c o n d u c t i v i t y with

able in t h a t the i o n i c c o n d u c t i v i t y o f the

t u r a l change.

intermediate compositions rose from the

hexagonal a axis increases monotonically

modest c o n d u c t i v i t i e s of the endmember

with x.

phases by f o u r orders of magnitude to reach

c a x i s , in c o n t r a s t , rises to a maximum

a maximum (0.2 ohm-lcm- l at 300°C) near

near x = 2 beyond which i t anomalously

x = 2.

decreases upon f u r t h e r s u b s t i t u t i o n of the

Phases near e i t h e r end of the s o l i d

s o l u t i o n series are hexagonal, space group R3c.

The i n t e r m e d i a t e phases o f high con-

ductivity 1.6
are monoclinic 2, space

but transform to the hexagonal

s t r u c t u r e at elevated temperature (ca.150°C3).

The hexagonal (or pseudo-

The hexagonal (or pseudohexagonal)

l a r g e r Si ion f o r P and, in a d d i t i o n , despite the i n s e r t i o n o f f u r t h e r chargecompensating Na ions in the s t r u c t u r e .

The

c e l l volume, as a consequence, a t t a i n s a

The monoclinic phases are s t r o n g l y pseudo-

maximum value at a composition close to t h a t at which maximum c o n d u c t i v i t y is observed. 2

hexagonal and c l o s e l y r e l a t e d to the rhombo-

In s p i t e of t h i s c o r r e l a t i o n , i t has been

+Present address: Switzerland.

Institut

de C r i s t a l l o g r a p h i e , U n i v e r s i t e de Lausanne, CH-IOI5 Lausanne,

0 167-2738/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes argued 4 that the enhanced c o n d u c t i v i t y arises

945

the results of our Rietveld analysis in an

from i n t e r a c t i o n s between the mobile Na ions,

under-occupancy of the Zr s i t e (0.891), in

the framework of the structure serving merely

the details of the d i s t r i b u t i o n of Na ions

to define conduction channels.

among i n t e r s t i c e s , and in the i n t e r p r e t a t i o n

This i n t e r -

pretation was supported by one-dimensional

of the transport mechanism.

calculations using stochastic Langevin

differences could well be due, however, to

dynamics.

The l a t t e r two

a dependence of these features upon tempera-

Crystal structure determinations by singlecrystal methods have been performed for a

tureo The present work is part of an e f f o r t to

number of phases w i t h the NASICON s t r u c t u r e

extend to elevated temperatures Rietveld

type, several studies having been conducted

analyses of neutron powder d i f f r a c t i o n data

p r i o r to the discovery of f a s t - i o n transport

obtained from the NASICON s o l i d - s o l u t i o n

in t h i s s t r u c t u r e type.

series.

Examples are

The objectives are to (a) detect

NaZr2(P04)3 ,2'5 Na4Zr2(Si04)3 ,6-8 Na4Zr2(Ge04)3 ,g Na3Sc2(P04)310-13 and

possible order-disorder transformations in

Na4.5Ybl.5(P04)314. The monoclinic structure in the NASICON system ( o r , in f a c t ,

found f o r Na3Scp(P04) 3 by Susman, Delbecq, Brun and Prince 21 and Sc, Cr and Fe phos-

the s t r u c t u r e of any s o l i d s o l u t i o n ) was not

phates by de la Rochere et a l . ; 22 (b) dis-

f u l l y determined u n t i l recently due, in part,

t i n g u i s h positional disorder from time-

to the fact that the preparation of single

averaged thermal Vibration of the a l k a l i

c r y s t a l s is d i f f i c u l t : before melting.

the a l k a l i ion d i s t r i b u t i o n s i m i l a r to those

NASICONdecomposes

Wuensch, Schioler and

ions through the temperature dependence of the temperature-factor c o e f f i c i e n t s ;

Prince 15 reported the results of Rietveld

(c) establish the atomic displacements which

analysis of room-temperature neutron powder

accompany the monoclinic to rhombohedral

d i f f r a c t i o n data obtained from compositions extending across the system (x = 1.0, 1.6, 2.0, 2.5).

In addition to e s t a b l i s h i n g the

monoclinic s t r u c t u r e , they found d i s t o r t i o n s of the framework which explained the anomalous v a r i a t i o n in the length of the c axis.16-18 Moreover, the d i s t o r t i o n s were found to open the saddlepoint c o n f i g u r a t i o n of oxygen ions between neighboring Na sites to a maximum size, close to the i o n i c radius of Na, at the composition of maximum c o n d u c t i v i t y . Conc u r r e n t l y , Kohler and Schulz 19 reported a s i n g l e - c r y s t a l x-ray analysis at 222°C of a small flux-grown crystal whose composition was deduced from the s t r u c t u r e determinat i o n 20 to be Na3.1ZrI.78SiI.24PI.76012" Twinning of the monoclinic structure precluded an analysis at room temperature.

The

results of Kohler et al. at 222°C d i f f e r from

FIGURE 1 The "lantern" u n i t in the NASICON structure type: Three (Si,P) tetrahedra span the corners of a pair of Zr octahedra which are arranged such that a pair of t r i a n g u l a r faces are normal to the hexagonal c axls and approximately p a r a l l e l to one another.

J.-J. Didisheim et aL / Neutron Rietveld analysis o/structural ehanges

946

phase t r a n s f o r m a t i o n and (d) determine the

between l a n t e r n s at the e l e v a t i o n o f the cen-

e x t e n t to which the phase t r a n s f o r m a t i o n or

t e r o f the f i r s t

a n i s o t r o p i c thermal expansion may i n f l u e n c e

on a 2 - f o l d axis in (001) which passes through

the composition at which optimum window s i z e

the t e t r a h e d r a l c a t i o n and the c e n t e r o f the

occurs between neighboring a l k a l i

l a n t e r n as w e l l .

ion s i t e s .

The present paper r e p o r t s r e s u l t s f o r high-

lantern.

The s i t e is l o c a t e d

The R i e t v e l d analyses o f the s t r u c t u r e s a t

c o n d u c t i v i t y compositions near the middle o f

room temperature 15-17 showed t h a t the o r i e n -

the s e r i e s , x = 1.6 and 2.0, a t 320°C, a

t a t i o n o f the S i , P t e t r a h e d r a r o t a t e from the

temperature a t which the phases have under-

i d e a l o r i e n t a t i g n described above as Si re-

gone the monoclinic to rhombohedral phase

places P.

transformation.

from on the o r d e r o f 5 ° at x = 0 to a maximum

The t i l t

p r o g r e s s i v e l y increases

o f 20 ° f o r one o f the two symmetry-independent 2. CHANGES WITH COMPOSITION OF THE NASICON STRUCTURE AT ROOM TEMPERATURE The s t r u c t u r e s in the NASICON system con-

t e t r a h e d r a in the monoclinic s t r u c t u r e .

The

t e t r a h e d r a r e t u r n toward t h e i r o r i g i n a l

orien-

t a t i o n upon f u r t h e r s u b s t i t u t i o n

o f Si.

Rota-

t a i n a p a i r o f Zr octahedra arranged w i t h

t i o n o f the v e r t i c a l

opposed t r i a n g u l a r

acts to decrease the Z r - Z r s e p a r a t i o n across

llel

faces a p p r o x i m a t e l y para-

to one a n o t h e r , Fig. I .

These faces

edge o f the t e t r a h e d r a

the c e n t e r o f the l a n t e r n (an e n e r g e t i c a l l y

are normal to c in the hexagonal s t r u c t u r e

unfavorable change which is p a r t i a l l y

t y p e , but only a p p r o x i m a t e l y normal to the

sated by the increased s i z e o f the t e t r a h e -

pseudohexagonal c axis in the monoclinic

dron).

s t r u c t u r e type as a r e s u l t o f the lower

to s t r e t c h the h e i g h t o f the Na(1) octahedron

symmetry.

along c (a change which is compounded by

The corners o f t h i s p a i r o f faces

Rotation o f the h o r i z o n t a l

compen-

edge acts

are b r i d g e d by t h r e e S i , P t e t r a h e d r a which,

increased length o f the t e t r a h e d r a l edge).

a c c o r d i n g l y , have one " v e r t i c a l "

The extension and subsequent c o n t r a c t i o n o f

imately parallel

edge approx-

to c and an opposed " h o r i -

z o n t a l " edge a p p r o x i m a t e l y normal to c.

Two

such " l a n t e r n s " occur along the edge o f the c e l l w i t h i n the t r a n s l a t i o n a l c.

A first

periodicity

of

type o f c a v i t y a v a i l a b l e f o r Na,

t h i s dimension of the Na(1) c a v i t y was found to account almost e n t i r e l y

f o r the anomalous

change in length o f the c a x i s . The r o t a t i o n o f the t e t r a h e d r a l u n i t s also r e s u l t s in a d i s t o r t i o n

o f the network

designated Na(1), is a d i s t o r t e d octahedral

which, in t u r n , causes an expansion o f the

void which occurs on the c e l l

radius o f the sphere o f maximum s i z e which

lanterns.

As the l a t t i c e

edge between

i s rhombohedral

can j u s t pass through the s a d d l e - p o i n t con-

( o r pseudo-rhombohedral), e q u i v a l e n t chains

figuration

o f l a n t e r n s a l t e r n a t i n g w i t h Na(1) s i t e s

n e i g h b o r i n g Na(1)-Na(2) s i t e s and also the

o f oxygen ions which separate

are repeated by t r a n s l a t i o n a t 2/3 I / 3 I / 3 + z

n e i g h b o r i n g Na(2) p o s i t i o n s .

and I / 3 2/3 2 / 3 + z .

Each t e t r a h e d r a l u n i t

both "windows" was found to a t t a i n maximum

a t the c e n t e r o f a l a n t e r n shares a corner

v a l u e , close to the i o n i c radius o f Na+, at

o f i t s h o r i z o n t a l edge w i t h the corner o f the top and bottom edge of a l a n t e r n , respectively,

i n these two n e i g h b o r i n g chains.

second s i t e f o r a l k a l i w i t h an i r r e g u l a r

i o n s , Na(2), occurs

lO-fold coordination

A

The radius o f

x = 2, the composition o f maximum c o n d u c t i vity.

In response to the increased window

s i z e , the values found f o r the e q u i v a l e n t i s o t r o p i c temperature f a c t o r s o f both Na ions

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

rise to sharp maxima at x = 2, suggesting a softening of the p o t e n t i a l wells in which they reside.

The thermal motion of Na(1) (a

947

3. EXPERIMENTAL The NASICON s o l i d - s o l u t i o n powders employed f o r measurement were prepared by

highly oblate e l l i p s o i d of r o t a t i o n with max-

Schioler 17 by decomposition and s o l i d -

imum displacement normal to c) was judged to

state reaction of appropriate mixtures of

be only apparent, however.

The d i l a t i o n of

(NH4)2HPO4, Na2CO3, SiO2 and e i t h e r ZrO2 or

the Na(1) cavity resulted in i n t e r i o n i c dis-

Zr(C5H702) 4.

tances which were considerably l a r g e r than

viously employed in the Rietveld analyses

The specimens were those pre-

the sum of the i o n i c r a d i i of NaVI and O.

performed on the room-temperature data.

Moreover, Fourier syntheses revealed a

A q u a n t i t a t i v e x-ray analysis had revealed

t o r r o i d a l d i s t r i b u t i o n o f scattering density

no detectable free ZrO2 in the s o l i d solu-

f o r Na(1) in the rhombohedral phases and two

t i o n with x = 1.6 and <1.8 wt% in the

discreet maxima in the monoclinic struc-

NASICON composition, x = 2.0.

tures. 17

Distances from these local maxima

All ZrO2

d i f f r a c t i o n peaks of perceptible i n t e n s i t y

to three of the neighboring oxygen ions

occurred in regions o f the d i f f r a c t i o n pat-

agreed well with the sum of the i o n i c r a d i i .

tern which were free from overlap with the

The Na(1) ion thus appeared to be p o s i t i o n -

NASICON spectrum.

a l l y disordered and displaced from the center of i t s octahedral cavity.

As the Na(1) dis-

Neutron d i f f r a c t i o n data were collected with the f i v e - d e t e c t o r powder diffractometer

placements appear not to represent dynamic

at the U.S. Nation~l Bureau of Standards

thermal v i b r a t i o n , we proposed a Na(2)-

Research Reactor.

Na(2) jump as the predominant transport

was recorded in steps of 0.05 ° 20 f o r the

The d i f f r a c t i o n p r o f i l e

mechanism as previously suggested by Tran

range 12 ° ~ 2e ~ 120° using 1.5500~ thermal

Q u i e t al. 8

neutrons monochromated by r e f l e c t i o n from

This view is supported by our

f ind ing that (a) the Na(1) s i t e remains

(220) of a Cu c r y s t a l .

f u l l y occuped at a l l compositions, Na(2)

tained at 320°C in an e l e c t r i c a l resistance

filling

heater.

progressively with increasing x;

The sample was main-

A few l i m i t e d regions of the

Na(1) accordingly must have lower s i t e

recorded p r o f i l e which contained powder

energy

d i f f r a c t i o n maxima from the A1 sample holder

(b) the two symmetry-independent

sites of the Na(2) type in monoclinic

and furnace were deleted from the subsequent

structures were found to have equal occu-

refinements.

pancy (and hence equal s i t e energy) near

using the procedure and computer program of

the composition of maximum conductivity

Rietveld 23 as modified f o r the mult idet ec t o r

and (c) the thermal e l l i p s o i d fo r Na(2)

diffractometer by Prince.

appeared to describe true thermal vibra-

adjustable parameters were required f or the

t i o n with maximum displacement directed

model:

toward a neighboring Na(2) p o s i t i o n .

9 p o s i t i o n a l and 24 thermal parameters and

In con-

The analyses were performed

A t o t a l of 51

a scale f a c t o r , 2 l a t t i c e constants,

t r a s t , Kohler and Schulz 19 favor the Na(1)-

Na occupancy (constrained so that the t o t a l

Na(2) jump ( o r i g i n a l l y proposed by Hong2) at

corresponded to the known value of x) to

222°C on the basis of electron density

describe the structure and instrumental var-

bridges between these s i t e s .

iables consisting of I0 parameters to describe background i n t e n s i t y , the zero-point of the 28 readings and 3 parameters to specify a

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

948

Gaussian peak shape.

where I B is the i n t e g r a t e d i n t e n s i t y of the

The q u a l i t y of the refinements was assessed by three conventional r e s i d u a l s :

i n d i v i d u a l Bragg d i f f r a c t i o n

the weighted

peaks evaluated,

in regions where maxima overlap in the powder

p r o f i l e residual

p a t t e r n , by p a r t i t i o n i n g the observed i n t e n s i t y in p r o p o r t i o n to the values c a l c u l a t e d f o r the

RWp = { w i ~ i ( ° b s )

i n d i v i d u a l maxima.

- c-lyi(cal)]2/Ewi[Yi(obs)]2}½

4. RESULTS AND DISCUSSION

where Yi(obs) and Y i ( c a l ) are the i n d i v i d u a l i n t e n s i t i e s in the step-scanned p r o f i l e which

4.1. L a t t i c e Constants and Atomic Coordinate~

are observed and c a l c u l a t e d , r e s p e c t i v e l y ; C

Refined l a t t i c e

constants f o r s o l i d solu-

is the scale f a c t o r , and the weight, wi ,

t i o n s with x = 1.6 and 2.0 at 320°C are com-

applied to each observation is the r e c i p r o c a l

pared in Table 1 with values obtained e a r l i e r

o f the square of the standard d e v i a t i o n of

f o r these compositions 15-17 at room temperature.

the measurement and thus equal to Yi(obs) - I .

The comparison is not s t r a i g h t f o r w a r d because

This residual may be compared w i t h the expected

of the phase t r a n s f o r m a t i o n which the samples

residual

have undergone. the l a t t i c e

Table 1 accordingly presents

constants expressed in terms of

both the monoclinic and hexagonal c e l l s whose

RE = {[n - p ] / Z w i [ Y i ( o b s ) ] 2 } ½

edges are r e l a t e d v e c t o r i a l l y by the t r a n s f o r where n is the nun~)er o f i n t e n s i t y measure-

mation m a t r i x given above.

ments and p is the number o f parameters in the

320°C f o r x = 2.0 continues to be l a r g e r than

model.

t h a t at x = 1.6 by e x a c t l y the same amount as

A t h i r d residual o f i n t e r e s t is the

The c e l l volume at

Bragg residual which is analogous to the con-

at room temperature.

ventional residual o f s i n g l e crystal a n a l y s i s :

f o r x = 1.6, u n l i k e the s i t u a t i o n at room tem-

The l a t t i c e

constant c

perature, now exceeds t h a t f o r x = 2.0.

same e f f e c t i v e volume expansion c o e f f i c i e n t

RB = ZllB(Obs ) - c - l l B ( C a l ) I / Z I B ( O b s )

Table I .

Comparison o f L a t t i c e Constants at 23°C and 320°C f o r NASICON S o l i d Solutions w i t h x = 1.6 and 2.0 x = 1.6 23°C(C 2/c)

Hexagonal axes

x = 2.0 320°C(R3c)

23°C(C 2/c)

320°C(R3c)

a(X)

8.9954

9.0038(5)

9.0351

9.0535(7)

c(~)

22.9716

23.0794(16)

22.9810

23.0677(27)

90.445

90.

90.953

90.

y V(A 3) Monoclinic axes

The

89.555

90.

89.047

90.

119.999

120.

119.892

120.

1609.8

1620.4(2)

1626.7

1637.4(4)

a(A)

15.5805(9)

15.5950

15,6407(6)

15.6811

b(~)

8.9946(5)

9.0038

9.0498(3)

9.0535

c(~) 6

9.2137(5) 123.795(4)

9.2848 124.047

9.2102(4) 123.709(3)

9.2976 124.207

Z-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

949

Table 2. Comparison of Atomic Positions at 23°C and 320°C f o r NASICON Solid Solutions with x = 1.6 and 2.0 (Estimated standard deviations in parentheses) x = 1.6

Atom and hexagonal equipoint

Parameter

23°C(C2/c) *

320°C(R~c)

1.0

1.01(7)

occupancy x Y z

0.533+ 0.6429 0.0091 0.2657

0.53(2) 0.6261(32) 0.0 0.25

x y z

0.0040 0.0014 0,1476

0.0 0.0 0,1482(3)

x y z

0.2898 0,0054 0.2456

x y z

0(2)

x

36 f 1 xyz

Na(1) 6 b 3 000

occupancy

Na(2) 18 e 2 xO~

IAI(A)

x = 2.0 Axi

23°C(C2/c) 1.0

o.o~

320°C(R~c) 1.01(7)

Axi

o.o~

0.667 + 0.6231 -0.0145 0.02531

0.66(2) 0.6292(28) 0.0 0.25

-0.0040 -0,0014 0.0006 0.0346~

0.0008 -0.0032 0.1481

0.0 0,0 0.1469(5)

-0.0008 0.0032 -0.0012 0.0432~

0.2897(8) 0.0 0.25

-0.0001 -0.0054 0.0044 0.I124X

0.2840 0,0022 0.2441

0.2883(13) 0.0 0.25

0.0043 -0.0022 0.0059 o 0.1456A

0.1780 -0.0432 0.1890

0.1735(6) -0.0349(7) 0.1944(2)

-0.0045 0.0083 0.0054 0.1606~

0.1805 -0.0459 0.1869

0.1762(9) -0.0360(9) 0.1944(3)

-0.0043 0.0099 0.0075 0.2073~

y z

0.1942 0.1780 0.0926

0.1947(6) 0.1705(6) 0.0916(2)

0.0005 -0.0075 -0.0010 0.0736X

0.1974 0,1754 0,0941

0.1939(8) 0.1707(7) 0.0929(3)

-0.0035 -0.0047 -0.0012 0.0473X

Bragg residual

RB

5.93%

4.41%

9.61%

Weighted prof i l e residual

RWp

6.45

6.22

9.18

IAI(A)

Zr 12 c 300z

IAI/~) T (Si ,P) 18 e z xO~

IAI(A) o(I) 36 f 1 xyz

IAI(~)

I~I(~)

-0.0168 -0.0091 -0.0157 0.3854X

10.61% 8.41

0.0061 0.0145 -0.0031o 0.1347A

Expected RE 5.20 5.02 5.28 6,50 residual +Average combined occupancy per s i t e for two types of symmetry-independent positions. *The monoclinic room-temperature structures (Ref, 17) have been referred to pseudohexagonal axes to permit comparison o f 2.2 I0-5°C -I is obtained fo r both phases on

provide a volume expansion c o e f f i c i e n t of

the basis of the change in c e l l volume.

3.7 I0-5°C - I .

With

results presently a v a i l a b l e f o r the rhombo-

The corresponding l i n e a r thermal

expansion coefficients--normal to c and para-

hedral phase at only one temperature i t is

llel

not possible to divide this into any discon-

1.6 I0-5°C -I f o r x = 1.6, and 6.9 10-6 and

to c, r es p e c t iv e ly - - ar e 3.1 10-6 and

tinuous change which accompanies the phase

1.3 I0-5°C -I f o r x = 2.0 in the present work.

transformation and the portion due to thermal

The crystallographic data 8 f o r the s i l i c a t e ,

expansion.

x = 3.0, provide <2 10-7 and 3.7 I0-5°C -I

Lattice constant determinations to

620°C f o r the s i l i c a t e endmember8 x = 3.0

respectively.

(which is rhombohedral at a l l temperatures)

suggests that much of the change observed in

The s i m i l a r i t y in magnitudes

950

J.-J. Didisheim et al. / Neutron Rietveld analrsis o f structural change.s

the present work is due to thermal expansion

stants.

The l a r g e s t displacement (0.385~) is

r a t h e r than displacements which accompany the

f o r a Na(2) ion.

phase t r a n s f o r m a t i o n .

t h i s ion is presumably l o c a t e d i n a shallow potential well,

Residuals f o r the present refinements are summarized in Table 2.

The values o f

This is not s u r p r i s i n g as the l o c a t i o n o f whose minimum

should be s e n s i t i v e to s l i g h t

dual, RE, and somewhat less than the values

ion O(1) undergoes a s h i f t

o f ca. 10% which are t y p i c a l l y

magnitude.

neutron d i f f r a c t i o n

profile

encountered in

analysis.

changes in the

p o s i t i o n s of c o o r d i n a t i n g ions.

RWp are w i t h i n 2 to 3% o f the expected r e s i -

llel

The

The oxygen

of slightly

smaller

This ion forms the s e t o f para-

interior

faces o f the Zr octahedron at

refinements are not as p r e c i s e , however, as

the c e n t e r o f the l a n t e r n .

those obtained by S c h i o l e r 17 w i t h data obtained

t h a t these ions move i n t o a common (OOl) o r i -

at room temperature and which are i n c l u d e d in

e n t a t i o n ; the p o s i t i o n of t h i s ion also

Table 2 f o r comparison.

determines the t i l t atoms contained in

the Zr ion and 0(2) s h i f t

edge o f

In c o n t r a s t

by only a few hun-

dredths of an ~ngstrom.

the asymmetrical u n i t are also presented in Table 2.

o f the v e r t i c a l

the t e t r a h e d r o n r e l a t i v e to c.

The r e f i n e d s i t e occupancies f o r the Na ions and coordinates o f a l l

Symmetry r e q u i r e s

The phase t r a n s f o r m a t i o n again com4.2.

p l i c a t e s d i r e c t comparison w i t h the roomtemperature s t r u c t u r e s . 15-17

Interionic

Interionic

To f a c i l i t a t e

Distances

distances f o r the room temper-

comparison, the coordinates o f the atom in the

a t u r e and 320°C s t r u c t u r e s are compared in

monoclinic s t r u c t u r e which corresponds to each

Table 3.

atom in the asymmetric u n i t o f the rhombohedral

Na(2) i o n - - w h i c h i n v o l v e s ten independent

phase

d i s t a n c e s - - h a s been o m i t t e d from the l i s t -

have been transformed to the pseudo-

hexagonal reference axes given in Table I .

The

(For b r e v i t y ,

a second type o f

ings f o r the monoclinic s t r u c t u r e s ) .

As the

d i f f e r e n c e in c o o r d i n a t e s , because o f the d i f -

shifts

f e r i n g basis v e c t o r s , gives the displacement

two sets o f i n t e r i o n i c

o f an ion in the rhombohedral phase from i t s

similar.

corresponding l o c a t i o n in a s t r u c t u r e which is

vated temperature tend g e n e r a l l y to be more

homogeneously deformed to the monoclinic axes.

regular--in

As the deformation is s l i g h t ,

metry, [Na(1), f o r example].

the displacement

in atomic p o s i t i o n s are s m a l l , the distances are q u i t e

The c o o r d i n a t i o n polyhedra at e l e p a r t because o f increased symEven when per-

components were then converted to an a p p r o x i -

m i t t e d by symmetry, however, the range of bond

mate magnitude of a displacement v e c t o r using

distances tends to be s m a l l e r .

the l a t t i c e

cially

constants o f the h i g h - t e m p e r a t u r e

This is espe-

t r u e f o r the t e t r a h e d r a l groups, f o r

which the room-temperature r e s u l t s revealed

phase. The atomic displacements i n v o l v e d in the

unexpected l a r g e d i f f e r e n c e s in bond lengths.

m o n o c l i n i c - t o - r h o m b o h e d r a l phase t r a n s f o r m a -

The t e t r a h e d r a l bond angles we found to be

t i o n plus those a r i s i n g from thermal expan-

w i t h i n a few degrees, at most, o f those in a

sion are r e l a t i v e l y

r e g u l a r t e t r a h e d r o n ranging I 0 6 . 4 ( 2 ) - I I I . 9 ( 6 ) °

s m a l l - - a s had been p r e v i -

ously suspected from the close correspondence

and 1 0 6 . 7 ( 2 ) - 1 1 4 . 1 ( 9 ) ° f o r x = 1.6 and 2.0,

o f monoclinic and rhombohedral l a t t i c e

respectively.

con-

Virtually

the same range of

*For an exhaustive comparison, s i x a d d i t i o n a l independent atoms in the monoclinic s t r u c t u r e - - o n e sodium ion o f the Na(2) t y p e , 1 t e t r a h e d r a l ion and 4 0 i o n s - - s h o u l d also be transformed and compared w i t h an a p p r o p r i a t e atom in the rhombohedral s t r u c t u r e which is r e l a t e d to one in the asymmetric u n i t by symmetry.

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

951

Table 3. Comparison of I n t e r i o n i c Distances at 23°C and 320°C for NASICON Solid Solutions with x = 1.6 and 2.0 (Estimated standard deviations in parentheses. Designation of atoms pertains to the rhombohedral s t r u c t u r e . ) x = 1.6

x = 2.0

23°C

320°C

23°C

320°C

Na(1)-O(2)

2.578(8) 2X 2.726(10) 2X 2,710(11) 2X

2.684(5)

6X

2.559(7) 2.749(9) 2.751(7)

2X 2X 2X

2,711(7)

6X

Na(2)-O(2) 0(2) 0(I) 0(I) 0(I)

2,501(11) 2.605(9) 2.671(8) 2.715(10) 3,385(11)

2.471(9) 2.479(33) 2.789(8) 2.939(31) 3.437(31)

2X 2X 2X 2X 2X

2.469(10) 2,661(8) 2.615(8) 2.679(10) 3.440(8)

2X 2X 2X 2X 2X

2.489(8) 2.511(23) 2,785(8) 2.922(20) 3.439(21)

2X 2X 2X 2X 2X

Zr-O(2)

2.082(10) 2.106(9) 2.111(7) 2,027(8) 2.044(8) 2.092(10)

2.109(6)

3X

2.076(9)

3X

2.042(5)

3X

2.087(7) 2.107(8) 2,107(8) 2.033(8) 2.062(7) 2.067(8)

2.092(8)

3X

1.571(9) 1,573(8) 1.522(11) 1.631(9)

1.584(6)

2X

1,564(8)

2X

1.574(6)

2X

1.550(8) 1.557(8) 1.564(8) 1.671(8)

1,596(9)

2X

0(I)

T-O(1) 0(2) T'-O(1) 0(2)

1.538(9) 1.613(8)

2X 2X

1.609(8) 1.590(8)

2X 2X

bond angles occurs in the room temperature

cients d i f f e r e d in absolute magnitude, how-

structures despite the lower symmetry and

ever, and were subject to very large standard

greater range of bond distances.

deviations.

I t may be noted that the Na(1)-O(2) dis-

The present results confirm

t h i s experience.

Several of the thermal

o

tances are on the order of O.3A longer than

e l l i p s o i d s described by the c o e f f i c i e n t s of

the value of 2.39X anticipated on the basis of the sum of the i o n i c r a d i i 24 f o r NaVI and O.

Table 4 f o r x = 2 are n o n - p o s i t i v e - d e f i n i t e ,

The minimum Na(2)-oxygen separations on the

an amount which is but a small f r a c t i o n of a

other hand, are of an appropriate magnitude for NaVIII-o (2.53~) or NalX-o (2.69~).

large standard deviation ( f o r example, B33

but often because an element is negative by

4.3. Thermal Vibration Parameters

for Na(1) or B22 for the tetrahedral i o n ) . The general sense of the anisotropies corre-

The anisotropic temperature f a c t o r c o e f f i -

sponds to that found in most previous analyses

cients obtained in the refinement are summar-

of the NASICON structure type:

ized i n Table 4.

plays an oblate thermal v i b r a t i o n e l l i p s o i d

The Rietveld refinement of

room temperature data 16'18 f o r x = 3.0 had

Na(1) dis-

of r o t a t i o n w i t h very large mean-squared

provided temperature factor c o e f f i c i e n t s

displacement normal to c.

which were in good q u a l i t a t i v e agreement

motion of Na(2) corresponds to a prolate

In contrast, the

with the results produced by a refinement

e l l i p s o i d having the p r i n c i p a l axis of maxi-

of s i n g l e - c r y s t a l data 8 to R = 1.9%, and

mum displacement i n c l i n e d 11(3) ° to c for

described anisotropic thermal v i b r a t i o n (or

x = 1.6, in approximately the d i r e c t i o n of a

lack of same) of the same sort.

neighboring Na(2) s i t e .

The c o e f f i -

The framework ions

J.-J. Didisheim et al. / Neutron Rietveld attalysis o f structural change~

952

exhibit little

or only modest v i b r a t i o n a l

anisotropies. No attempt w i l l

should be p r o p o r t i o n a l to temperature.

The

present values should, a c c o r d i n g l y , be be made to compare the

approximately double the magnitude of the

i n d i v i d u a l c o e f f i c i e n t s of Table 4 d i r e c t l y

room temperature determinations as the tem-

w i t h the results f o r the s t r u c t u r e at room

peratures i n v o l v e d are roughly 300 and 600°K.

temperature (in p a r t because o f the large

The increase, as shown by Table 5, is not

standard d e v i a t i o n s , but also because the

this substantial.

tensors f o r the room temperature structures

average value of the e q u i v a l e n t i s o t r o p i c

Figure 2 compares the

are expressed r e l a t i v e to a d i f f e r e n t set of

temperature f a c t o r f o r selected framework

non-orthogonal basis vectors from which con-

ions (those f o r which the values found f o r

version would be t e d i o u s ) .

symmetry-independent ions of a given type in

Table 5 instead

compares e q u i v a l e n t i s o t r o p i c temperature

the monoclinic structures are spread over not

factors defined by Bo = I / 3 ( B I I + B22 + B33). The values of Bo f o r the framework ions

too large a range) at room temperature with

increase w i t h temperature as should be expec-

obtained f o r the corresponding ion at 320°C.

ted.

The v e r t i c a l bars shown f o r the room temper-

If it

is assumed t h a t no d i s c o n t i n u i t y

a l i n e extending from the o r i g i n to the r e s u l t

or change o f slope accompanies the phase

ature r e s u l t s range between the minimum i n d i -

t r a n s f o r m a t i o n , the i n d i v i d u a l c o e f f i c i e n t s

vidual value found f o r an atom less i t s

Table 4. A n i s o t r o p i c Temperature Factor C o e f f i c i e n t s (#2) at 320°C f o r NASICON S o l i d Solutions with x = 1.6 and 2.0 (Estimated standard d e v i a t i o n s in parentheses). Bll

B22

Na(1) x = 1.6

56.7(71)

BII

3.5(24)

½BII

O.

O.

x = 2.0

48.3(95)

BII

-0.I(27)

½Bll

O.

O.

Na(2) x = 1.6

T

0(I)

0(2)

Bij

Bl2

Bl 3

B23

1.6(12)

1.9(14)

52.2(91)

½B22

½B23

3.7(24)

l.l(9)

9.1(23)

22.3(57)

½B22

½B23

2.0(24)

x = 1.6

1.2(I)

BII

2.1(3)

½Bll

O.

O.

x = 2.0

0.9(2)

BII

2.2(5)

½BII

O.

O.

x = 2.0 Zr

B33

x : 1.6

1.4(3)

2.8(4)

2.6(4)

½B22

½B23

x = 2.0

0.7(4)

-0.I(5)

3.4(7)

½B22

½B23

0.4(4)

x = 1.6

1.5(3)

5.1(3)

1.7(2)

1.8(2)

-1.1(2)

-0.4(2)

x = 2.0

3.6(5)

4.9(4)

3.3(5)

3.3(4)

-3.7(4)

-1.9(4)

x = 1.6

1.8(3)

2.0(2)

3.0(3)

0.7(2)

0.6(2)

-0.I(2)

x = 2.0

3.3(4)

0.7(3)

1.5(4)

1.6(3)

-0.6(3)

-0.8(3)

Bij/~aia j

where the form o f the temperature f a c t o r employed is T = exp - h i h j ~ i j .

-I.I(3)

J.-Z Didisheim et al. / Neutron Rietveld analysis o f structural changes

Table 5. Comparison of Equivalent Isotropic Temperature Factor Coefficients Bo = (BII + B22 + B33)/3 (~2) at 23°C and 320°C f o r NASICON Solid Solutions with x = 1.6 and 2.0.

x = 1.6 23°C* 320°C Na(1) Na(2)

32.(2) 7.0(9)

37.(4) 18.(3)

3.(I)

23°CX * = 2.0 320°C 74.(6) 1.0(4)

953

ing of the height of the Na(1) octahedron along c and an increase in the size of the windows separating neighboring Na sites. Table 6 shows the angle of r o t a t i o n of the v e r t i c a l 0 ( I ) - 0 ( I ) tetrahedral edge r e l a t i v e to the c axis* and the horizontal 0(2)-0(2)

32.(6)

edge r e l a t i v e to (001).

10.(2)

tetrahedron through e i t h e r of these measures

The t i l t

of the

of o r i e n t a t i o n is larger at x = 2.0 than at

31.(3)

Zr

l.l(1)

1.5(1)

l.O(1)

1.4(2)

x = 1.6 at 320 ° as well as at room tempera-

T

2.7(3)

2.1(2)

1.0(2)

1.4(3)

ture.

4.5(4)

Na(1) octahedron remains largest f o r x = 2.0

1.8(2)

3.4(2)

at 320° .

2.0(4) O(1)

0(2)

2.0(2)

2.7(I)

Correspondingly, the height of the

2.1(2)

2.3(2)

I t is also of i n t e r e s t to evaluate the

1.8(2)

2.3(2)

maximum radius of the sphere which may pass

2.2(2)

2.4(I)

1.6(2)

2.2(2)

2.5(2)

1.1(2)

0.9(2)

1.6(2)

through the saddle-point configuration of 4.0

I

I

I

I

0(I) *M u lti p l e entries f o r an ion in the monoclinic room temperature structures represent values f o r symmetry-independent atoms which become equivalent in the high temperature rhombohedral phase.

o ho rr"

~

I

I

x = 2 ~

3,0

rf 0

0

2.0

standard deviation up to the maximum value plus i t s standard deviation.

~ z kd

tJ 122 ~

Given the

necessity of assuming a l i n e a r v a r i a t i o n

5~

between results f o r phases with two d i f f e r e n t

Ld

Lo

o

Ld I--

structures, the correspondence is not physic a l l y unreasonable.

The Na(1) ion exhibits

a change in thermal parameters which is quite d i s t i n c t from that o f the framework ions or Na(2):

Bo increases n e g l i g i b l y with tempera-

ture f o r the s o l i d s o l u t i o n with x = 1.6 and is found to decrease with increased temperature f o r x = 2.0. 4.4. D i s t o r t i o n of the Framework and Change in Window Sizes The r o t a t i o n of the tetrahedral units in the room temperature structure with change in composition was found to r e s u l t in stretch-

I

0.0

200

I

i

400

I

600

TEMPERATURE (OK) FIGURE 2 Plot of equivalent i s o t r o p i c temperature factors f o r selected framework ions as a function of temperature. The lines extend from the o r i g i n to the value obtained at 320°C. To be compared with t h i s v a r i a t i o n are the values obtained at 23°C f o r which each datum represents an average over symmetry-independent atoms (which become equivalent in the 320°C s t r u c t u r e ) ; v e r t i c a l bars extend from Bmin-O to Bmax+O. (Open syn~ols: x = 2.0, f i l l e d x = 1.6.)

*The o r i e n t a t i o n o f the vector between Zr ions in the lantern is taken as the reference d i r e c t i o n in the monoclinic structures.

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

954

oxygen ions which separates n e i g h b o r i n g Na

perature.

ion l o c a t i o n s .

change in composition appears to be s l i g h t l y

In e v a l u a t i n g t h i s radius i t

is assumed t h a t the c r i t i c a l

contact w i l l

occur when the m i g r a t i n g sphere is coplanar

The s e n s i t i v i t y

o f window s i z e to

more pronounced at 320°C than a t room temperature.

w i t h some t r i a n g l e o f oxygen ions which

4.5. D i s t r i b u t i o n

occurs in the a r r a y .

The temperature f a c t o r s f o r both types of

The c r i t i c a l

radius

o f Na S c a t t e r i n g Density

is thus computed by c o n s i d e r i n g a l l oxygen

Na ions are e x t r a o r d i n a r i l y

ions near a p o s s i b l e window t h r e e a t a time

v a l e n t i s o t r o p i c temperature f a c t o r s f o r

and s e l e c t i n g as the c r i t i c a l

Na(2) increase w i t h temperature as is to be

radius the

large.

The e q u i -

l a r g e s t value which does not o v e r l a p any o t h e r

expected, Table S.

oxygen ion in the a r r a y .

the s c a t t e r i n g d e n s i t y w i t h i n the c e l l

The values f o r the

F o u r i e r synthesis o f

sum R c r i t + R° so determined are presented i n

revealed a normal maximum a t the Na(2) loca-

Table 6 f o r jumps between a Na(1)-Na(2)

tion,

p o s i t i o n (Path I ) and also f o r a jump between

sponding to t h a t i n d i c a t e d by the aniso-

neighboring Na(2) s i t e s

t r o p i c temperature f a c t o r c o e f f i c i e n t s .

critical

(Path 2).

The

radius may be obtained by sub-

elongated along a d i r e c t i o n c o r r e -

The s c a t t e r i n g d e n s i t y at the Na(1) s i t e

t r a c t i n g an a p p r o p r i a t e radius f o r an oxygen

i s h i g h l y d e l o c a l i z e d , Fig. 3.

ion from t h i s i n t e r i o n i c

f o r Na(1) in the composition w i t h x = 2.0,

distance. ~

The low-

The d e n s i t y

ered symmetry o f the m o n o c l i n i c phases

shown between ±0.13 a I and a 2 in Fig. 3a,

r e s u l t s in t h r e e symmetry-independent paths

v a r i e s by only a f a c t o r o f two over t h i s

f o r both types o f d i f f u s i v e

region (see Fig. 4 f o r a maximum a t a normal

Table 6 shows t h a t ,

jumps.

f o r both x = 1.6 and

ion l o c a t i o n , contoured a t i n t e r v a l s which

2.0, the window r a d i i f o r both Na(1)-Na(2)

are 5 times l a r g e r ) .

and Na(2)-Na(2) jumps have expanded w i t h

occurs not at the o r i g i n where Na(1) is l o c a -

The maximum d e n s i t y

increased temperature by amounts which range

t e d , but in a t o r r o i d a l

0.019 to 0.046~ g r e a t e r than the maximum

location.

s i z e a v a i l a b l e among the t h r e e symmetry-

w i t h i n t h i s band; there is no l o c a l maximum.

independent room-temperature paths.

The diameter o f the t o r r o i d has increased in

The

volume about t h i s

The d e n s i t y is completely uniform

g r e a t e s t increase is f o r path 1 f o r x = 2.0.

the composition w i t h x = 1.6, Fig. 3b, and a

This occurs, in p a r t , because the d i s t o r t i o n s

l o c a l maximum ( o f magnitude i d e n t i c a l

in the oxygen ion a r r a y have caused a d i f f e r -

t h a t which occurs in Fig. 3a) occurs at 0.78

ent oxygen ion to become p a r t o f the t r i a n g l e

0.90 O.

of ions which defines the c r i t i c a l

000, is n e g a t i v e .

The c r i t i c a l

radius.

radius f o r P1 remains about

to

The d e n s i t y at the Na(1) l o c a t i o n , The s e c t i o n Ap(xyo) f o r

the d i f f e r e n c e d e n s i t y , Pobs(Xyo) - Pcal (xyo)

O.12X l a r g e r than P2 independent o f temper-

is e s s e n t i a l l y zero in regions s l i g h t l y

a t u r e f o r both x = 1.6 and 2.0.

placed from the nominal Na(1) l o c a t i o n , but

The s i z e o f

dis-

both types o f windows remains a maximum a t

confirms t h a t the model has placed excess

x = 2.0 at 320 ° as was the case a t room tem-

scattering density directly

+

at 000.

. . . . 17 The e f f e c t i v e radius o f oxygen i s dependent upon i t s c o o r d l n a t l o n number. S c h l o l e r emplo%ed a value f o r the c r y s t a l radius 24 o f oxygen which v a r i e d l i n e a r l y w i t h x between 1.215X at x = 0 and 1.245X at x = 3 to r e f l e c t the changing c o o r d i n a t i o n o f oxygen as a d d i t i o n a l Na ions are i n s e r t e d in the s t r u c t u r e . The sum of the r a d i i f o r NaIV and O, when values f o r the l a t t e r are assigned on t h i s b a s i s , range from 2.345~ at x = 0 to 2.375# at x = 3, values w i t h which the sums o f R c r i t and Ro in Table 6 may be compared.

Similar

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

'\\\\\

\

955

Table 6. Comparison o f Framework D i s t o r t i o n s and "Window" Sizes along D i f f u s i o n Paths in NASICON S o l i d S o l u t i o n s at Room Temperature and 320°C

,\

x \

\

\,

Height along c o f Na(1) octahedron

0.0 1.0 1.6 2.0 2.5 3.0

Rotation o f vertical 0(I)0(I) tetrahedral edge r e l a t i v e to c

0.0 1.0 1.6 2.0 2.5 3,0

Rotation o f horizontal 0(2)0(2) t e t r a h e d r a l edge r e l a t i v e to (001)

0.0 1.0 1.6 2.0 2.5 3.0

Distance from saddle-point p o s i t i o n to 3 surrounding 0 ( R c r i t + Ro) Path I [Na(l )-Na(2) ]

0.0 1.0 1.6

2.0

2.5 3.0 FIGURE 3 F o u r i e r synthesis o f the s c a t t e r i n g d e n s i t y at the Na(1) s i t e at 320°C. The contour i n t e r v a l s on a l l maps are at the same e q u a l , but a r b i t r a r y , i n t e r v a l s . (a) S c a t t e r i n g dens i t y section p(xyo} f o r x = 2.0. (b) Scattering density section p(xyo) f o r x = 1.6. (c) Difference density section Ap(xyo) = Pobs(Xyo) - Pcal(xyo) f o r x = 1.6. The region of the section which is depicted extends +0.13 a I and ±0.13 a2. Regions o f negative density are shaded.

Distance from saddle-point p o s i t i o n to 3 surroudning 0 ( R c r i t + Ro) Path 2 [Na(2)-Na(2) ]

0.0 1.0 1.6

2.0

2.5 3.0

23°C

3.985 4.074 4.209 4,233 4.059 3.771

320°C

4.228 4. 341

6.71 ° 10.16 ° 18.14°(2X) 9.38 ° 15.22 ° Av. 11.99 ° 20.I0°~2X} 7.72 ° 15.97 ° Av. 12.43 ° 10.72 ° 6.87 ° 4.37 ° 6.05 ° I0.42°(2X) 4.05 ° 8.30 ° Av. 12.04°(2X) 2.29 ° 8.79 ° Av. 6.15 ° 1.49 ° 2.218 2.245 2.201 2.256 2.356 2.271 Av. 2.168 2. 292 2.374 2. 278 Av. 2. 250 2.186 2.169 2.207 2,194 2,235 2.252 2. 227 Av. 2.158 2.237 2.257 2.217 Av, 2.172 2.105

8.50 ° 9.82 °

2.392

2. 420

2. 271

2,298

J.-J. Didisheim et al. / Neutron Rietveld analysis oJ structural changes

956

features were found fo r the Na(1) density f o r a l l of the rhombohedral compositions examined by Schioler 17 at room temperature.

[/

(The den-

s i t y was confined to two discreet maxima in the monoclinic phases.) The distance between the nominal Na(1) position and the surrounding oxygen neighbors i s , as noted above, s i g n i f i c a n t l y larger than the sum of the i o n i c r a d i i 24 f o r s i x coordinated Na and oxygen (2.39A).

The

distances from the local maximum in Fig. 3b to the three nearest neighbors are 2.31, 2.43 and 2.69~.

No local maximum is present

in the density f o r x = 2.0, Fig. 3a.

Dis-

tances from locations w i t h i n the uniform maximum of the t o r r o i d at 0.053 0.053 0 and

"\

0.06 0.03 0 (locations on [ I I 0 ] and [210], respectively) are 2.45, 2.58 and 2.63A and 2.48, 2.51 and 2.72~, respectively.

All

minimum distances f a l l close to the sum of the r a d i i for NaVI and oxygen.

The stretch-

ing of the height of the Na(1) cavity caused by t i l t i n g

of the Si, P tetrahedra thus

appears to r e s u l t in displacement of Na(1) from the center of i t s coordination octahedron. 4.6. Occupancy of the Zr Octahedron

/\,

Early attempts at synthesis and consolidation of NASICON powders commonly provided samples which contained s i g n i f i c a n t amounts of ZrO2.

This experience led eventually to

a proposal 25 that NASICONwas inherently d e f i c i e n t in Zr.

I t was suggested that com-

positions along the j o i n Nal+xZr2SixP3_xOl2 were not single phase for a l l values of x. Engell, Mortensen and Moller, 26 however, using sol-gel techniques and careful powder characterization methods, have recently demonstrated that single-phase ZrO2-free powders may be prepared.

Upon careful prepa-

r a t i o n and annealing, the samples used in the present work contained l i t t l e

(< 1.8 wt%)

or no detectable ZrO2 as has been previously

FIGURE 4 Fourier synthesis of the scattering density at the Zr s i t e at 320°C. The maps extend ~0.13 a. (a) Scattering density section p(x y 0.15) for x = 2.0. (b) Scattering density section p(x y 0.15) for x = 1.6. (c) Difference dens i t y section Pobs(X y 0.15) - Pcal(X y 0.15) fcr x = 1.6. All contours are at equal but a r b i t r a r y i n t e r v a l s ; negative regions are shaded. The contour i n t e r v a l s of (a) and (b) are equal (and 5 times the i n t e r v a l of Fig. 3). The difference map (c) is contoured at an i n t e r v a l 5 times f i n e r than the density maps.

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

noted.

Moreover, the temperature f a c t o r

957

culty in c o n t r o l l i n g the composition of a

c o e f f i c i e n t s found f o r Zr in the room tem-

flux-grown crystal 19 or hydrothermal

perature Rietveld analyses 15-17 were normal

product 27 rather than being an i m p l i c a t i o n

in magnitude and independent of composition.

that non-stoichiometry is required in a l l

There was no suggestion of the large values

such phases.

which would represent an attempt by the refinement to compensate f o r overpopulation of this s i t e . Sections p(x y 0.15) of a Fourier synthesis of the scattering density of the samples with x = 2.0 and 1.6, respectively, are presented in Fig. 4a and 4b.

These sections

pass close to the Zr positions at 0 0 0.1469 and 0 0 0.1482, respectively.

The maxima

5. CONCLUSIONS A comparison of structure refinements performed by Rietveld analysis of neutron powder d i f f r a c t i o n data obtained from NASICON samples at room temperature and 320°C f o r x = 1.6 and 2.0 shows: (a) Only small atomic displacements are involved in the monoclinic to rhombohedral

are completely normal, symmetric peaks sur-

phase transformation, ranging from a few

rounded by a weak negative ring o f series

tenths or hundredths of an Xngstrom f o r the

termination r i p p l e .

framework ions up to a maximum of 0.385X

A difference density

section ~p(x y 0.15) for x = 1.6 shows a

for the Na(2) ion in i t s loosely-coordinated

p o s i t i v e density at the Zr p o s i t i o n which

shallow p o t e n t ia l w e l l .

amounts to only 4.5% of the maximum density and which is not considered s i g n i f i c a n t . (The anomaly, in any case, would have to be

Ib) The Na(1) i n t e r s t i c e remains f u l l y occuoied at 320°C. (c) There is no evidence f o r underoccu-

negative i f the s i t e were underpopulated.)

pancy of the Zr p o s i t i o n in the present

Fig. 4c shows no anomalies other than a

powder samples.

s l i g h t h i n t of possible anharmonicity in the v i b r a t i o n a l motion.

The present work

(d) The r o t a t i o n of Si, P tetrahedra and stretching of the Na(1) octahedron appear to

accordingly provides no evidence f o r under-

remain largest at x = 2.0 f o llo w in g the phase

occupancy of the Zr position.

transformation.

I t is important to distinguish between excess ZrO2 which represents an e q u i l i b r i u m

(e) The size of the windows between neighboring Na sites displays a greater dependence

assemblage of phases and that which arises

upon composition at 320°C than in the mono-

in samples as a r e s u l t of incomplete s o l i d -

c l i n i c room-temperature structures.

state reaction o f the r e f r a c t o r y ZrO2 pre-

of the windows remain largest at x = 2.0 f or

cursor or from decomposition during consoli-

both a Na(1)-Na(2) jump and a Na(2)-Na(2)

dation o f a powder by s i n t e r i n g at high tem-

jump at 320°C and both windows are appre-

perature.

ciably l a r g e r than the maximum opening

The octahedral s i t e in the NASICON-

The size

type framework may be only p a r t i a l l y occupied

a v a i l a b l e among the three symmetry indepen-

by Zr and ~ p a r t i a l l y

dent paths in the room-temperature mono-

contain Na, as had

been shown by the sinQle-crystal study of Na4.5YbI.5(P04)3 .14

c l i n i c structures.

NASICONs o l i d solutions

with Zr deficiencies do e x i s t as demonstrated by recent structure analyses 1g'27.

But the

non-stoichiometry probably r e f l e c t s d i f f i -

ACKNOWLEDGEr~,ENTS This work was supported by the Office of Energy System Resources, Energy Storage

J.-J. Didisheim et al. / Neutron Rietveld analysis o f structural changes

958

Division, of the U.S. Department of Energy under Contract DE-ACO3-76SFO0098, Subcont r a c t No. 4528610, with the Lawrence Berkeley Laboratory. (J.-J.

The c o n t r i b u t i o n of one of us

D.) was supported in part by a f e l l o w -

ship from the Swiss National Science Foundation. REFERENCES I. J. B. Goodenough, H. Y.-P. Hong and J. A. Kafalas, Mat. Res. Bull. I I (1976) 203. 2. H. Y.-P. Hong, Mat. Res. Bull. I I 173.

(1976)

3. J. P. B o i l o t , J. P. Salani~, G. Desp!anches and D. LePotier, Mat. Res. Bull. 14 (lg79) 1469. 4. S. H. Jacobsen, M. A. Ratner and A. Nitzan, Phys. Rev. B 23 (1981) 1580. 5. L.-O. Hagman and P. Kierkegaard, Acta. Chem. Scand. 22 (1968) 1822. 6. R. G. Sizova, A. A. Voronkov, N. G. Shumyatskaya, V. V. l l y u k i n and N. V. Below, Sov. Phys. Dokl. 17 (1973) 618. 7. D. Tran Qui, J. J. Capponi, M. Gondrand, M. Saib. J. C. Joubert and R. D. Shannon, Solid State Ionics 3/4 (1981) 219. 8. D. Tran Qui, J. J. Capponi, J. C. Joubert and R. D. Shannon, J. Solid State Chem. 39 (1981) 219. 9. R. G. Sizova, V. A. Blinov, V. A. Kuznetsov, A. A. Voronkov, V. V. l l y u k i n and N. V. Below Sov. Phys. Dokl. 23 (1978) I03.

14.R. Salmon, C. Parent, M. Vlasse and G. LeFlem, Mat. Res. Bull. 14 (1979) 85. 1 5 . B . J . Wuensch, L. J. Schioler and E. Prince, Neutron Rietveld analysis of structural changes in the f a s t - i o n conducting NASICON s o l i d - s o l u t i o n system, Program and Abstracts American Crystallographic Assoc. l l [ l ] , Winter Meeting, March 1983, 34. 1 6 . B . J . Wuensch, L. J. Schioler and E. Prince, Relation between structure and conductivity in the NASICON s o l i d solut i o n system, in: Proceedings of the Conference on High Temperature Solid Oxide Electrolytes August 16-17, 1983. Vol. I I - Cation Conductors, ed. F. J. Salzano (Brookhaven National Laboratory Report BNL-51728, Upton, Long Island, New York, 1983) pp. 55-71. 1 7 . L . J . Schioler, Relation between structural change and conductivity in the fastion conducting NASICON s o l i d solution system, Na~+xZr2SixP3 ~012, Sc.D. Thesis, Dept. ot Materials-~clence and Engineering Mass. Inst. of Tech., Cambridge, MA, January 1983. 1 8 . L . J . Schioler, B. J. Wuensch and E. Prince, Solid State Ionics, in press. 19.H. ~ehler and H. Schulz, Solid State Ionics 9/I0 (1983) 795. 20.H. Kohler, H. Schulz and O. Melnikov, Mat. Res. Bull. 18 (1983) I143. 21.S. Susman, C. J. Delbecq, T. O. Brun and E. Prince, Solid State Ionics 9/I0 (1983) 839. 22.M. de la Rochere, F. d'Yvoire, G. C o l l i n , R. Comes and J. P. B o i l o t , Solid State Ionics 9/I0 (1983) 825.

l O . V . A . Efremov and V. B. K a l i n i n , Sov. Phys. Crystallogr. 23 (1978) 393.

23.H.M. Rietveld, J. Appl. Cryst. 2 (1969) 65.

l l . H . Y . - P . Hong, Crystal structure and ionic conductivity of a nm~ superionic conductor, Na3Sc2P3012, in: Fast Ion Transport in Solids, eds. P. Vashista, J. N. Mundy and G. K. Shenoy (Elsevier North Holland, New York, 1979) pp. 431433.

24.R.D. Shannon and C. T. Prewitt, Acta Cryst. B25 (1969) 925.

1 2 . J . P . B o i l o t , G. C o l l i n and R. Com~s, Solid State Ionics 5 (1981) 307. 13.D. Tran Qui, J. J. Capponi, M. Gondrand and J. C. Joubert, Solid State Ionics 5 (1981) 305.

25.U. von Alpen, M. F. Bell and H. H. Hoefer, Solid State Ionics 3/4 (1981) 215. 26.J. Engell, S. Mortensen and L. Moiler, Solid State Ionics 9/IO (1983) 877. 27.P.R. Rudolf, M. A. Subramanian, A. C l e a r f i e l d and J. D. Jorgensen, Mat. Res. Bull. 20 (1985) 643.