COMPUTER CALCULATION OF SCATTERING INTENSITY FOR DISORDERED MOLYBDENUM DISULFIDE

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COMPUTER CALCULATION OF SCATTERING INTENSITY FOR DISORDERED MOLYBDENUM

DISULFIDE

F. Chien, S. Moss, K. Liang, R. Chianelli

To cite this version:

F. Chien, S. Moss, K. Liang, R. Chianelli. COMPUTER CALCULATION OF SCATTERING IN-

TENSITY FOR DISORDERED MOLYBDENUM DISULFIDE. Journal de Physique Colloques, 1981,

42 (C4), pp.C4-273-C4-276. �10.1051/jphyscol:1981458�. �jpa-00220915�

CoZZoque C4, suppZ6ment au nOIO, Tome 42, octobre 1981 page C4-273

COMPUTER CALCULATION OF SCATTERING INTENSITY FOR DISORDERED MOLYBDENUM DISULFIDE

* *

F.Z. Chien, S.C. Moss, K.S. Liang and R.R. Chianelli

University o f Houston, Houston, TX 77004, U.S.A.

*

Emon Corporate Research-Science Laboratories, Linden, NJ 07036, U. S. A.

Abstract

-

We present computer c a l c u l a t i o n s of t h e Deybe i n t e r f e r e n c e function of "poorly c r y s t a l 1 ine" MoS2 f o r several model cases assigning s p e c i f i c f e a t u r e s of t h e measured i n t e n s i t y t o s p e c i f i c model aspects.

Most obvious among t h e s e i s t h e number of MoS2 sandwich l a y e r s . In a d d i t i o n both l a y e r s e x t e n t and r e l a t i v e r o t a t i o n or t i l t appear t o be neccessary s t r u c t u r a l parameters. The measured i n t e r f e r e n c e p a t t e r n s , which change c o n t i n u a l l y on anneal ing t h e as-prepared m a t e r i a l , may thereby be understood through t h e progressive increase in both t h e in plane and perpendicular c o r r e l a t i o n range and t h e attendant removal of d e f e c t s .

Introduction

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The c r y s t a l l i n e t r a n s i t i o n metal dichalcogenides a r e t y p i c a l l y pre- pared by vapor t r a n s p o r t from t h e melt of the metal and chacogen mixture. Recently, our i n t e r e s t has been on m a t e r i a l s prepared by chemical routes o t h e r than t h e vapor t r a n s p o r t . These a1 t e r n a t i v e methods include t h e thermal decomposition of t h e corresponding sal t s l and t h e low temperature p r e c i p i t a t i o n of t h e solution.2

Materi a1 s obtained by t h e s e routes have amorphous or poor1 y c r y s t a l 1 i n e s t r u c t u r e s , depending on t h e temperature of preparation, and a r e found t o have unique p r o p e r t i e s not present in t h e i r corresponding c r y s t a l 1 in e phases3-5. This paper d e a l s with t h e s t r u c t u r e of poorly c r y s t a l l i n e MoS2 through a d i r e c t a n a l y s i s of t h e d i f f u s e x-ray d i f f r a c t i o n p a t t e r n s . Such d i f f u s e i n t e n s i t y d i s t r i b u t i o n i s not p r o f i t a b l y

analyzed as a s e r i e s of separable Bragg peaks because t h e p a r t i c l e s a r e too small and t o o defective. I t i s a l s o not useful t o perform t h e usual r a d i a l density a n a l y s i s because one already knows t h e d i s t r i b u t i o n of near neighbors.

Description of Sample

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A t y p i c a l s e t of t h e observed x-ray d i f f r a c t i o n p a t t e r n s of poorly c r y s t a l 1 i n e MoSz i s shown in Fig. 1. These samples were prepared by thermal decomposition of ammonium thiomolybdate following t h e r e a c t i o n ,

where la-' stands f o r amorphous and 'px-' f o r poorly c r y s t a l 1 ine. The decomposition of (NH4)2MoS4 in flowing dry N2 a t 250°C f o r 4 hours r e s u l t s in amorphous MoS3. The The subsequent decomposition in flowing 15% H2S/H2 a t 400°C, 600°C, and 800°C f o r 4 hours r e s u l t in MoS2 samples of d i f f e r e n t degrees of c r y s t a l l i n i t y . The d i f f r a c t i o n p a t t e r n of powdered c r y s t a l l i n e (c-) MoS2 of a natural m l y b d e n i t e i s a l s o included f o r comparison.

The shape of t h e d i f f r a c t i o n p a t t e r n s of px-MoS2 i s q u i t e d i f f e r e n t from t h a t of c r y s t a l l i n e MoS2 i n t h e region containing 100

-

105 Bragg peaks. Going from t h e c r y s t a l l i n e t o t h e poorly c r y s t a l l i n e s t a t e , t h e 103 and 105 peaks become so d i f - f u s e t h a t t h e i r peak i n t e n s i t i e s a r e g r e a t l y reduced. Limited s t r u c t u r a l information, mainly on t h e c r y s t a l l i t e s i z e , may be determined using x-ray l i n e broadening analy- s i s on t h e 002, 100 and 110 peaks. However, t h e d i f f u s e nature of t h e 103,

105 and o t h e r higher order peaks remains t o be explained. In f a c t , comparison of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981458

C4-274 JOURNAL DE PHYSIQUE

t h e d i f f r a c t i o n p a t t e r n s o f px-MoSp w i t h t h a t o f c-MoS2 r e v e a l s other features such as s h i f t i n g o f t h e peak p o s i t i o n s and asymmetric broadening o f t h e peaks.

Most Bragg peaks i n t h i s case are not amenable t o d e t a i l e d l i n e p r o f i l e analysis (Figs. l c o r I d ) and a strong d i f f u s e background i s present i n t h e 100-103-105 r e g i o n (as marked by t h e d o t t e d l i n e ) . These f e a t u r e s are t y p i c a l o f d e f e c t i v e l a y e r m a t e r i a l s , o f t e n described as quasi-two dimensional, i n which t h e r e i s a progressive l o s s o f c o r r e l a t i o n along t h e c a x i s (normal t o t h e layer).6 We have, t h e r e f o r e , chosen t o compute t h e d i f f r a c t i o n p a t t e r n from an assumed s t r u c t u r e using the Debye S c a t t e r i n g equation.7

s i n

I S [

rmn 'eu =

E fi Ifi 8

I S I rmn

where fm is r;ne x-ray atomic s c a t t e r i n g f a c t o r o f m-type atoms, S i s t h e x-ray scat- t e r i n g vector w i t h

/g

⁼ 4 ~ s i n e / X , and t h e vector rmn i s t h e disTance vector con- n e c t i n g atom rn and atom n. For a s t r u c t u r e i n whirh a l l o f the atomic p o s i t i o n s have been specified, t h e d i f f r a c t i o n i n t e n s i t y i s d i r e c t l y c a l c u l a t e d using Eq. (1).

While t h i s i s not a w i d e l y used method f o r c r y s t a l l i n e s o l i d s i t has advantages f o r a random aggregate o f very small c r y s t a l l i t e s i n which d e f e c t s and d i s o r d e r may be introduced.

Results o f Computer C a l c u l a t i o n

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The c a l c u l a t e d d i f f r a c t i o n p a t t e r n s o f micro- c r y s t a l l i t e 2H-MoS2 w i l l be discussed f i r s t . We w i l l then examine t h e o r i g i n o f t h e observed d i f f r a c i t o n peaks and the e f f e c t s o f d i f f e r e n t s t a c k i n g order on these peaks. F i n a l l y , t h e e f f e c t o f stacking d i s o r d e r w i l l be presented i n comparison w i t h t h e experimental d i f f r a c t i o n patterns.

A. M i c r o - C r y s t a l l i t e Model o f 2H-MoS2 and Variants

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C r y s t a l l i n e MoS2 occurs w i t h a layered s t r u c t u r e . W i t h i n a s u l f u r sandwich, t h e metal atoms i s coordinated by s i x s u l f u r atoms i n a t r i g o n a l p r i s m a t i c arrangement. There e x i s t two polytypes o f t h e s t a c k i n g sequence o f t h e sandwiched layers, t h e hexagonal (2H) and the rhom- bohedral (3R) forms o f MoS2. MoS2, which occurs i n nature as the mineral molybdenite has the hexagonal s t r u c t u r e .

The X-ray d i f f r a c t i o n p a t t e r n s o f m i c r o - c r y s t a l l i t e s o f 2H-MoS2 are c a l c u l a t e d by v a r y i n g the sizes o f the c r y s t a l l i t e s . A symbol, Nw(LlxL2) i s used t o designate t h e s i z e o f the c r y s t a l . N i s t h e number o f t h e sandwiched l a y e r s and L1 and L2 are t h e numbers o f Mo atoms along t h e a and b c r y s t a l l i n e axes, r e s p e c t i v e l y , i n one sandwiched MoS2 layer. I n most cases we choose L1 equal t o L2. We have c a l c u l a t e d mainly i n t h r e e series: No(6x6) w i t h t h e number o f l a y e r s N=l t o 10; 1-(LxL) w i t h L=6 t o 12 and 2.(LxL) w i t h L=2 t o 12.

We f i r s t examine t h e e f f e c t o f the thickness o f t h e s t a c k i n g layers. Fig. 2 shows the c a l c u l a t e d p a t t e r n s o f Na(6x6) 2H-MoS2 w i t h N i n c r e a s i n g from 1 t o 4. This corresponds t o a c r y s t a l l i t e s i z e o f about 208, x 20A i n the basal plane.

There are f i v e major peaks i n t h e c a l c u l a t e d range o f S= 0 t o 5A-1. For the con- venience o f discussion, these peaks are assigned as 002, 100, 103, 105 and 110. S t r i c t l y speaking, o f course, a l l these peaks, except 002, are mixtures o f several Bragg peaks c l o s e t o t h e assigned ones. The l i n e s marked on t h e f i g u r e are t h e p o s i t i o n s o f t h e Bragg peaks o f c r y s t a l l i n e 2H-MoS2.

Several i n t e r e s t i n g features are evident i n the f i g u r e . The 100 and 110 peaks (2=O) are o b v i o u s l y l i t t l e a f f e c t e d as t h e number o f l a y e r s increases. The most s t r i k i n g v a r i a t i o n appears w i t h the l a r g e change o f t h e d i f f r a c t i o n p a t t e r n i n t h e 100

-

105 r e g i o n between one and two layers. The presence o f two MoS2

sandwiches i s r e q u i r e d t o produce s u b d s t a n t i a l 103 and 105 peaks w i t h o n l y a slow change o f these peaks beyond two l a y e r s ( i n c o n t r a s t t o t h e 100 and 110 peaks.) The 002 i n t e r l a y e r peak i s present, o f course, o n l y when t h e r e are two or more sandwich l a y e r s present. As t h e number o f l a y e r s increases, t h e peak continues t o sharpen and move up t o the proper Bragg p o s i t i o n .

obtained w i t h Cu Ka r a d i a t i o n from (a) : n a t u r a l molybnite ( b ) - ( d ) : p o o r l y c r y s t a l l i n e MoS2 prepared a t 800°C, 600°C and 400°C, r e s p e c t i v e l y .

p a t t e r n s o f small c r y s t a l l i t e s o f 2H-MoS2. The number o f s t a c k i n g l a y e r s i s v a r i e d from 1 t o 4 w i t h each sandwiched l a y e r c o n t a i n i n g 6x6 Mo atoms.

Special a t t e n t i o n i s a l s o c a l l e d t o the r e l a t i v e peak h e i g h t s o f 100, 103 and 105 as shown i n Fig. 2. The c a l c u l a t e d p a t t e r n s w i t h more than one l a y e r (N>l) resemble t h a t o f c r y s t a l l i n e 2H-MoS2 i n s t e a d o f those o f t h e observed p o o r l y c r y s t a l l i n e samples (Fig. 1). I n f a c t , no c a l c u l a t e d p a t t e r n based simply on a m i c r o c r y s t a l l i n e s t r u c t u r e i s close t o t h a t observed f o r px-MoS2. This leads us t o conclude t h a t t h e s t r u c t u r e o f p o o r l y c r y s t a l l i n e MoS2 cannot be described as a per- f e c t m i c r o c r y s t a l l i t e of 2H-MoS2. Our d e t a i l e d c a l c u l a t i o n s f o r a1 1 o f these p o s s i b l e v a r i a n t s o f m i c r o c r y s t a l 1 in e MoS2, i n c l u d i n g octahedral (as opposed t o tri- gonal p r i s m a t i c ) c o o r d i n a t i o n f a i l e d t o improve t h e f i t t o experiment. We s h a l l t h e r e f o r e only present t h e r e s u l t s o f t h e d e f e c t i v e 2H-MoS2 model

.

B. Imperfect C r y s t a l l i t e Models

-

The c e n t r a l issue f o r t h e modeling i s t o reduce t h e peak i n t e n s i t y o f 103 and 105 peaks by broadening. Since these peaks a r e s t r o n g l y associated w i t h the i n t e r l a y e r i n t e r f e r e n c e c o n t r i b u t i o n t o t h e scat- t e r i n g pattern, i t i s n o t d i f f i c u l t t o imagine t h a t d e f e c t s i n stacking might play an important r o l e i n f i t t i n g these s t r u c t u r e s . I n f a c t , such defects as s t a c k i n g f a u l t s and t h e bending o f t h e l a y e r s already have been observed i n t h e e l e c t r o n

m i ~ r o ~ r a ~ h s . 3 The e f f e c t o f a l i n e a r s h i f t between layers, however, does not produce e f f e c t s sirnil a r t o experimental observation and w i l l not be f u r t h e r addressed here. Although t h e l a y e r s o f MoS2 appear h i g h l y f l e x i b l e , i t i s also not c l e a r t o what extent the f l e x e d l a y e r would a f f e c t the d i f f r a c t i o n pattern. As i t t u r n s out, i n t r o d u c i n g a modest bending o f t h e l a y e r s produces o n l y a small e f f e c t i n t h e i n t e r - ference f u n c t i o n and cannot account f o r the observed d i f f r a c t i o n p a t t e r n s o f px-MoS2.

F i n a l l y , t h e e f f e c t o f i n t e r l a y e r r o t a t i o n may be treated. This may be i n t r o - duced as a r o t a t i o n e i t h e r about t h e a a x i s o r about t h e c axis. R o t a t i n g about t h e a a x i s produces a fanning o f t h e planes and an attendant s h i f t and broadening of 002.

It also changes t h e p a t t e r n a t higher

IsI

i n accord w i t h t h e data. R o t a t i o n about

C4-276 JOURNAL DE PHYSIQUE

t h e c-axis, o f course, leaves 002 unchanged and q u i c k l y b r i n g s t h e r e s t o f t h e pat- t e r n i n t o agreement w i t h t h e experiment. Fig. 3 shows t h e d i f f r a c t i o n p a t t e r n s o f a 2.(8x8) s t r u c t u r e w i t h t h e two sandwich l a y e r s r o t a t e d about the c-axis w i t h respect t o each o t h e r through an angle o f 0.0, 0.02, 0.04, 0.08 and 0.1 radian, r e s p e c t i v e l y . These s t r u c t u r a l changes have l i t t l e e f f e c t on t h e 002 and 110 peaks. However, t h e e f f e c t on t h e 100

-

¹⁰³

-

105 r e g i o n i s q u i t e evident. I n f a c t f o r 1.0 r a d i a n

(5.73') r o t a t i o n , t h e p a t t e r n i n t h i s r e g i o n i s q u i t e close t o t h a t o f the s i n g l e l a y e r s t r u c t u r e shown i n Fig. 2. The degree o f t h i s i n t e r l a y e r r o t a t i o n can there- f o r e be one o f t h e most important s t r u c u t r a l parameters i n t h e determination o f t h e d i f f u s e x--ray d i f f r a c t i o n p a t t e r n o f px-MoS2. Combining t h i s simple d i s o r d e r para- meter w i t h t h e o t h e r 2 parameters N and L (L1 and Lp) should, i n p r i n c i p l e , permit a good q u a n t i t a t i v e fit t o the various stages o f px-MoS2 i n Fig. 1.

I n t e r p r e t a t i o n o f Experimental P a t t e r n

-

For d e t a i l e d i n t e r p r e t a t i o n o f a p a r t i c u l a r set o f t h e d i f f r a c t i o n data, we r e q u i r e a q u a n t i t a t i v e f i t o f the p a t t e r n over the whole r e g i o n o f s c a t t e r i n g . I n i l l u s t r a t i o n we show here a comparison o f the calcu- l a t e d and experimental r e s u l t s using a d i f f r a c t i o n p a t t e r n o f MoS2 prepared a t 400°C.

This i s new data s i m i l a r t o Fig. Id. I n Fig. 4 t h e raw data i s used i n t h e p l o t w i t h o u t such c o r r e c t i o n s as Compton s c a t t e r i n g , p o l a r i z a t i o n , and absorption, and i t i s not p r o p e r l y scaled. These c o r r e c t i o n s u l t i m a t e l y are needed i n order t o y i e l d t h e coherent p a r t o f t h e s c a t t e r e d i n t e n s i t y f o r a d i r e c t comparison w i t h the calcu- l a t i o n . On t h e same f i g u r e a c a l c u l a t e d curve (Fig. 3 D) i s chosen f o r comparison and t h e two are a r b i t r a r i l y set equal a t S = 2.3 A-1. The f i t i s very good except a t S z 1 (002). This presents no problem as can be seen i n Fig. 2. As the number o f l a y e r s increases, t h e 002 peak i s sharpened and s h i f t e d t o higher IS1 w i t h o u t s e r i o u s l y a l t e r i n g t h e r e s t o f t h e p a t t e r n . It i s c l e a r from Fig. 4, both a t 002 and f o r t h e 100-103 s p l i t t i n g , t h a t we r e q u i r e c l o s e r t o 4 l a y e r s than the 2 used here.

The f a l l o f f a t l a r g e r IS1 (S = 4A-I) can be l a r g e l y a t t r i b u t e d t o t h e need f o r a p o l a r i z a t i o n and a b s o r p t i o n c o r r e c t i o n .

g

g ;

S t 2 0 I 6

1. DIEMANN, E. and Muller, A., Coord. Chem. 432 (1977) 127.

2. CHIANELLI, R. R. and Dines, M. B., 1norg.Tem. (1978) 2758.

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4. JA= A. J., C h i a n e l l i , R. R., Rich, S. M. and Whittingham, M. S., Mat.

Res. B u l l . 14 (1979) 1473.

5. JACOBSON, A. x , C h i a n e l l i , R. R. and Whittingham, M. S., J. Electrochem. Soc.

SOC.

126

(1979) 2277.

6. WILSON, A. J. C., X-Ra 0 t i c s , Methuen and Co. Ltd. London (John Wiley, N..) (1962) p.

7. GUINIER, A., X-Ray D i f f r a c t i o n i n Crystals, Imperfect C r y s t a l s and Amorphous Bodies, W. H. Freeman and Co., San Francisco (1963).

P" - M o l

C ^----

M I Q I M E N T A L -CALCULATED I I

1 I

-

I :

\,-;-,\

' ._, '

.. ^J

^':,

_'.-,-

0 I 2 3 4 5

3 t b - ' ~ 0-1

S 1 A 1

FIG. 3: The e f f e c t o f i n t e r l a y e r r o t a t i o n FIG. 4: Comparison o f t h e measured about t h e c-axis by 0.0, 0.02, x-ray s c a t t e r e d i n t e n s i t y o f px-MoS2 0.04, 0.08 and 0.10 radian, r e s p e c t i v e l y , (400°C) w i t h the c a l c u l a t e d i n t e n - o f a 2.(8x8) MoS2 structure. s i t y using a 2.(8x8) s t r u c t u r e and

0.04 r a d i a n in-plane r o t a t i o n r o t a t ion.