Neutron diffraction study on the short-range order in a VD0.81 single crystal

Journol of

ALLOYS AND COMIPO~ND5 ELSEVIER

Journal of Alloys and Compounds 231 (1995) 126-131

Neutron diffraction study on the short-range order in a VD081 single crystal Yasuaki Sugizaki 1, Sadae Yamaguchi* Institute for Materials Research, Tohoku University, Sendai 980-77, Japan

Abstract

Short-range order parameters for deuterium arrangement in a single crystal of VD..sa at room temperature, which is about 90°C above To, were determined by measurements of elastic neutron diffuse scattering. The results show reduced occupation probabilities for the first-, second- and third-neighbor tetrahedral interstices around a given D atom, whereas the deuteriumdeuterium atom pair occurs preferentially at the fourth-neighbor site. These features are similar to those in the ordered structure below Tc. The first-order atomic displacement parameters for D-D pairs indicate that the D atoms in the first- and second-neighbor pair configurations move away from each other.

Keywords: Metal-hydride systems;Vanadium; Diffuse scattering; Neutron diffraction; Short range ordering

1. Introduction It is well established that the interstitial atoms arrange regularly in certain interstitial sites of the host metal lattice at a specific composition and temperature [1]. The crystal structures of hydride (deuteride) in group V metals (V, Nb and Ta) have been studied extensively by neutron diffraction [2-4]. Hydrogen atoms distribute in an ordered fashion over the tetrahedral holes in the b.c.c, metal lattice except in the [3 phase of the V - H system, in which the hydrogen atoms occupy regularly certain octahedral interstice, Such an ordering of hydrogen atoms should characteristically be associated with one type of interaction, namely with interactions between the interstitial hydrogen atoms, while the choice of a particular interstitial site (octahedral or tetrahedral) is governed by the interaction of the interstitial atoms with the matrix atoms, One can obtain valuable information on such interactions by study of diffuse scattering of neutrons, because the diffuse scattering gives us the local arrangement of interstitial atoms in the metal lattice, Finding the position of the interstitial H atoms by ordinary X-ray analysis, however, is difficult because * Corresponding author, 1Present address: Materials Research Laboratory, Kobe Steel

Ltd., Kobe 651-22, Japan. 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0 9 2 5 - 8 3 8 8 ( 9 5 ) 0 1 7 8 6 - 0

of their weak scattering power compared with that of the matrix atoms. Neutron diffraction, on the contrary, does not have this drawback; the scattering amplitude of deuterium is comparable with those for most metals. The purpose of the present study is to characterize, by diffuse neutron scattering, the short-range order (SRO) of the a-VD phase above the o r d e r - d i s o r d e r transition temperature T¢. It has b e e n established that the o r d e r - d i s o r d e r transition occurs in V D 0 s at 210 K with the formation of a superstructure, in which the deuterium atoms occupy special tetrahedral interstices of the b.c.c, metal lattice as shown in Fig. 1 [5]. Also, the SRO is revealed at room temperature in the powder diffraction pattern of ot-WD0.75 in the form of background modulation [6,7]. However, there are few complete sets of experiments on the SRO in the m e t a l - h y d r o g e n (deuterium) systems, except for the study on or-TaD055 by Kaneko et al. [8]. Hitherto, the analysis on the SRO in interstitial alloy or compound systems has been limited to the non-stoichiometric carbides and oxides having the rocksalt-type crystal structure [9-12]. The transition metal hydrides based on the b.c.c, lattice have a nonBravais lattice, in which the sublattices have their own local symmetry. Therefore it is necessary first to establish the intensity formulae for such a non-Bravais case. Following the general intensity formulae for the crystals with multiple sublattices derived by Hayakawa

Y. Sugizaki, S. Yamaguchi / Journal of Alloys and Compounds 231 (1995) 126-131

,p,,x. ~' G% i i

]/~0

~-\.

/

~_ R

ISRo(h,heh3) = E E E l

w

,dL

i

X COS [ 2 ~ ( h l l

\

|

N \

× sin

J:;"

h2m +

+

h3n)]

(2)

"Ylmn

C) z = o \ v

h2m + h 3 n ) ]

[2'rr(hl/+

(3)

where the subscript lmn indicates an interatomic vector defined as rimn = la I + ma 2 + na 3 ( a l , a 2 and a 3 are translational vectors along the cube axes of the b.c.c, unit cell). According to the general equation for crystals with multiple sublattices derived by Hayakawa and Cohen [13], the Laue monotonic scattering is

• ( o z=~\ -/ D ° ¼J

Fig. 1. Projection of the o r d e r e d V D structure on (001) plane.

and Cohen [13], we derive the expression for the metal hydride based on the b.c.c, lattice. Using this expression, we analyse the neutron diffuse scattering intens/ties of VD0.8~ and obtain the SRO parameters for deuterium arrangement,,; as well as the first-order atomic displacement parameters for D - D pairs.

ILM = N ~ ~ ~ x f f x J ( b i - b y Ix i>j

]

2

i/

~lmn= E i>j E XIx XIx (b i -ILMby)iNol~ (lmn)

Diffuse scattering intensity formula

(4)

where N is the number of lattice points under the neutron beam, G, i the fraction of the ith element on the /zth sublattice and b~ the scattering amplitude of the ith element corrected for the temperature factor. The Fourier coefficient fflmn in Eq. (2) is expressed as follows: i

2.

o~-imn

n

IAD(hlh2h3) = - E hp E E E

i

[ N~'

m

127

(5)

The diffuse intensity ID(hlh2h3) consists of the contribution ISRO from local order of the deuterium atoms and the contribution lAD from local static displacements of atoms from the average structure. It

where %~i/(lmn)is defined as

is expressed as

where Pix~iJ(Imn) is the probability of finding a j-type atom on the ~,th sublattice separated by the vector r,, n from an /-type atom on the /zth sublattice. The coefficient %mn in Eq. (3) is given as

ID(hlh2h3)-IsRo(hlh2h3)+IAD(h~h2h3)

(1)

ILM

where ILM is the Laue monotonic scattering. Each term in (1) can be written as a Fourier series in terms of the reciprocal-space coordinates h~, h 2, h 3 :

PIxies(Iron) %~i/(lmn) = 1

/

2'IT(E\°E FIxviJ(AtxvPQ))

Ytm~P=

J where

Table 1 Sublattice vectors and sublattice fractions T y p e of sublattice

Sublattice vector (o, o, o; ' 1 ½) + 7, 7,

Sublattice fractions Vanadium

Deuterium D

Vacancy

11

¼, O, ½

XII v = 0

Xll

I2

l, ~,0

xl2V=0

Xl2D = x

xi2 V= 1 - x

13

0, 1, I

Xl3 V = 0

xi3 D = x

X13v = 1 -

i4

3 i l ~-,C,~

X14

v

D

15

1, _].,0

xis v = 0

xl5 D = x

10

0, ~, 3

xI6 v = 0

Xl6 D = x

xl6 v = 1 - x

Vanadium M

0, 0, 0

xM v = 1

xM o = 0

xM v = 0

Deuterium

" x = 0.81/6 = 0.135 for VDo.sv

:0

(6)

x~

XI4

= X

=X

Xll v = 1

Xl4

v

- x

x

=l-x

xl5 v = 1 - x

(7)

Y. Sugizaki, S. Yamaguchi / Journal of Alloys and Compounds 231 (1995) 126-131

128

F,,'= x,x~ jbibj(1- o%,q (lmn) ILM/N ..

it 2{

Fi.tg ii -x- /~ D i ~X AC E

~/ X.JO%,'J(Imn)//(ILMIN)

i~j

In Eq. (7), (A,~ pi~) = (A~,Pi-A~ pi) is the deviation of the displacement vector from the average, where A,u.p~ is a p c o m p o n e n t of the displacement vector of an /-type atom from the lattice point o f / z . The sublattice vectors and the occupation probTable 2 Components of interatomic vectors for intersublattices and intrasub-

lattices Type of

l

vectors

(0, 0, 0; ~, I ~, ~ ½) +

A

p"

B

m

n

q~

Possible sublatticepairs

r~

4p+2

4q+2

4r+2

4

4

4

4p+l 4

4q+l 4

4 4q + 1

I2-I~, L-L

4 4p

4

4p+l 4

4p + 1 4 4p + 2 4 4p + 1

I3-12' I5-16

1'-15'12-14

4 4q + 3 4

4 4r + 1 4 4r+ 1 4 4r+l 4

I3-I1'I4-I6

4q + 1 4

4r + 2 4

I1-I2' 15-14

4q + 1 4 4q + 3

4r + 1 4

C

4 4q

4q+2 4

4r + 2 4

4

4

4p + 3 4

4q + 2 4

4r + 4

4p + 2 4 4p + 2 4 4p 44p -44p+2 4 4p+2 4 4p 4-

4q + 1 4

4r + 3 4

4q 4 4q + 2 4 4q 44q+2 4

4r 44r 4 4r + 2 4 4r 4

4q 4 4q+2 4

4r+2 4 4r+2 4

4q+l 4

4r 4

4p+2 4

I1-13, L - L

4

4 4p + 3

D

~ X14

D

~ X15

D

~ X16

1

~ X.

The interatomic vectors of intrasublattices and intersublattices in the present alloy are described in terms of the parameters 1, m and n given in Table 2. There are three types of interatomic vector in this structure which can be distinguished in terms of integers p, q and r. It will be noticed that s o m e sublattice pairs are forbidden for non-Bravais case. With these expressions, the parameters o~,,n and ~lmn for each interatomic pairs are derived and are given in Table 3.

3. Experimental procedures

4r 4

4r

D

XI3

M - M , lj-Ij (j = 1-6)

4p + 1 4q 4r + 1 4 4 4 4p 4q + 1 4r + 1

44p + 3

abilities for each sublattice in V D o 8 ) are shown in Table 1. The sublattice M corresponds to the b.c.c. lattice of vanadium, and I ~ - I 6 correspond to the tetrahedral interstices which are partially filled by deuterium atoms. The occupation probability x M for vanadium is 1, and those for deuterium are assumed to be equal for the six sublattices, i.e. x~ ° = x ) D =

I6-I~'I4-I3

I~-L, 13-I~

A crystal of pure vanadium (6 m m in diameter and 6 m m in length) was prepared by z o n e melting in an electron beam furnace. The specimen was prepared by the reaction of the vanadium crystal with deuterium gas using a Sieverts-type apparatus. The specimen was loaded with deuterium at 600°C and then cooled slowly to r o o m temperature. The deuterium content of the specimen was evaluated from the amount of deuterium gas absorbed by the specimen as well as from the weight increase of the specimen after the charging. The ( D ) / ( V ) ratio of the specimen determ i n e d w a s 0.81 _+ 0.01.

12-I~' 16-I5

It-I~'I2-I4

1

Neutron diffraction experiments were carried out at room

about

I1-I~' I3-I4 13-15' I2-I6

temperature using an automated four-circle

T O G diffractometer in JRR-2 at the Japan A t o m i c Energy Research Institute with a neutron beam of 1

A wavelength.

The collimation of 1 5 ' - h o l e - 1 5 ' was kept througho u t t h e experiments. The intensity d i s t r i b u t i o n o f t h e diffuse scattering was measured over the v o l u m e in the

II-I4' I4-I~ I2-I5, I5-I z I3-I6' 16-13

Table 3 d ~ , and

Type of

~lmn parameters for each interatomic vector dtm n

~lmnp

I3-I 6, I6-I 3

vector

12-15' Is-I2

A

au Dv

12~" - x [x + (1 - x)an Dv] (AHP t)D)

B

, Dv ~trH

27r [ x + ( 1 --x)aHDV](An pDD ) 3(1 x)

C

0

3(1-x)

I4-I~' 11-14 -

M-I/, I j - M (i, j = 1-6) 2~"

p, q and r are integers.

bv b D (/lIMP

DV)

Y. Sugizaki, S. Yamaguchi / Journal of Alloys and Compounds 231 (1995) 126-131

OOZ-

/~ 4 0

/x

I .

r

129

/,,

Fig. 4. Reciprocal lattice of the ordered VD0. 8.

Fig, 2. Volume in reciprocal space in which the diffuse intensity was measured. 4. R e s u l t s a n d d i s c u s s i o n

reciprocal space shown in Fig. 2 at intervals Gh = 0.05a*. The resolution in the reciprocal space estimated from the width at the half-height of Bragg reflections were Ah 1 = 0.03a*, Ah 2 = 0.03a* and A h 3 = 0.05a*, which are much smaller than the scanning intervals. The intensities obtained were corrected for instrumental background and absorption and were converted into Laue units by comparison with the incoherent scattering of vanadium•

'

-

'

(a)

Figs. 3(a) and 3(b) show the diffraction intensity 11 curves along the ~ h and hhl lines. The diffuse 11 scattering intensities are observed near ~-~1 and their equivalents, which are the reciprocal-lattice positions for the ordered VD structure as shown in Fig. 4. The total scattering intensity, the first-order atomic displacement scattering and the SRO intensity along ~7 I 1h are shown in Fig. 5. Since the scattering amplitude of vanadium is very small, the intensity due to the static displacement is very weak and of the same order of magnitude as the measurement error. Figs. 6(a) and 6(b) show the diffraction curves obtained along the h00 and hhO lines in reciprocal space. There exists SRO diffuse scattering near 200

o ~o10000_ ~ , ~ , ~ , ~ , ~ , , ~ 4.

0

o= 500(3

"

..... . . . .

....

....

.....

,

(a) 2

I

1/2112

1

I

I

112 112 3

=

0000

0 o.

~_

000000 O0000000c

°0°0°°0

0.000.00

.

0

t

~,0

o"

o

/

t

[

,

(b) Oz

,

(b)

,

0000

O0

t~

7: ,

O0 O0

~

j

<001:~

It,

q

xo

_oO

~°-o_

o-o

- --%o~-o' -'o ~o-o' --o. \

°°°

0 O0.00 00'

~-4

&ooo~

~ -0.4

g

~

,

,

,

D O

u 5o0c

ooOOOOoo

2 O0 O0

001

I

1121121

0

I11

3123~2 I

221

Fig. 3. (a) Diffuse scattering intensities on the ~11h line. The open triangle indicate instrumental resolution. (b) Diffuse scattering intensities on the hhl line.

oooOO Ooo 000 O0000

l

1/2112 I

I

000

O0 O0 I

112112 3

Fig. 5. Comparison of (a) the total diffuse scattering, (b) the first-

order atomic displacement scattering and (c) SRO scattering inten11 sities along the ~ h line.

Y. Sugizaki, S. Yamaguchi / Journal of Alloys and Compounds 231 (1995) 126-131

130

'~

(a)

-

-Observed .

.

.

(b)

.

.

.

.

a.e4o.e.d

S R O p a r a m e t e r s •lmn DV for the disordered VD0~t and perfectly

.

g 8L

VDt •

l

Shell

~'

i -~

1

m

n

Observed Dv

Perfectly o r d e r e d VD,, ~l 8

Distance (,~)

0 1 2 3 4

0 ~ ½ ½ t

0 ~ 0 41 L

0 0 0 ~ 0

1 -0.111 -0.106 -0.079 0.196

1 -0.154 -0.154 -0.154 0.313

0 1.121 1.584 1.939 2.240

5 6 7 8

] t2 ~4 1

~ ~ 21 0 4~

0 t 4~ 0 ¼

-0.052 0.042 0.033 0.010

-0.154 0.313 -0.154 0.139

2.506 2.743 2.962 3.168

~ 4

0 0 12 ~

0.017 -0.013 0.027

0.936 -0.154 0.313

3.548 3.707 3.865

0

0.008

-0.154

4.023

t

-0.005

-0.154

4.340

0

-0.004

-~

orrected

,

=

,

, ,

TT2

'°'o, , , , ,

002

I "~ °'°

112

22T

"°-7o , 220

22 ~

Fig. 6. Diffraction intensity curves along (a) the h00 and (b) hhO lines.

and 220 positions in addition to the Bragg peaks. This is expected because the intersublattice vectors connecting tetrahedral interstices, which are shown in Table 2, do not coincide with the translation vectors of the b.c.c, lattice. When the conditions hlh2h3; h~ = 4n, " h 2 = 4 n , h 3 = 4 n or h l = 4 n + 2 , h 2 = 4 n + 2, h 3 = 4 n + 2 (n is an integer) are satisfied, the scattered neutrons from each deuterium atoms in the tetrahedral interstices are "in phase" and contribute to the Bragg peak without producing the SRO diffuse scattering. The short-range order diffuse scattering / S R O is plotted in Fig. 7, where the intensity levels are given in Laue units. From this result, the SRO parameter dt,~,, is evaluated by Fourier inversion of the SRO diffuse scattering intensity in the unit volume of the reciprocal lattice by the following formula:

9

10 11 12 13

14 15

2

2

1 ~ 4 1 ~ 1 5 ~

½

~ 12 ~ ~ 4 ~ 1

~

1

0.021

-0.154

3.358

4

0.139

4.625

~ _~ 0.

1

4.o= f f f 'sRo h,h h ) 0

-0.

× cos [27r(lh~ + m h 2 + nh3) dh~ dh 2 dh 3

o

Ollmn D V v a l u e s , which are deduced from ff;m,, using the relations given in Table 3, are listed in Table 4 and plotted in Fig. 8, together with those for the ordered VD structure [5] shown in Fig. 1. The parameter a;m, ov oscillates up to about 4.A in the interatomic distance corresponding to the thirteenth-neighbor shell of the tetrahedral sites. The The

(a)

?,

h3=OZ,

plane

(b)

7'

z

INTERATOMIC DISTANCE (,'~)

Fig. 8. S R O p a r a m e t e r s

a;,,, Dv plotted

oscillation is similar to that in the ordered structure below T c. Accordingly, the deuterium configuration in the ordered state is partially maintained above T c. It is

h =I .3 plane

(c)

?'

h~=2plane

® ® @ ®

I

against the interatomic

distance:©,VD0.8~at room temperature (this work); @, ordered VD structure[5].

o-

! OOh~

~Oh3

'-- ~i

/.Oh3

OOh3

20h 3

--h~

&Oh]

002

202

0~.--h,

Fig. 7. Diffuse scattering distribution in the (00h3) plane for (a) h = 0 and 4, (b) h 3 = 1 and 3, artd (c) h 3 = 2: @, Bragg peaks. The intensity levels are given in Laue units.

Y. Sugizaki, S. Yamaguchi / Journal of Alloys and Compounds 231 (1995) 126-131

131

Table 5 First-order displacement coefficients ~/lmn p and displacement values Atmnp for D - D pairs Shell

l

m

n

a °v

yX

(/Ix )

,yy

(A y )

yz

( d z)

A

Distance

(A) 1 2 3 4

t I ½ ½ 4

2

!4 0 4~ ~

0 0 0 4~

-0.111 -0.109 _a --0.079

0.0069 0.0101 --0.0010 0.0068

0.028 0.040 0.074 0.025

0.0069 0 --0.0052 0.0015

0.028 0 0.038 0.006

0 0 0 0.0015

0 0 0 0.006

0.13 0.13 0.12 0.08

1.121 1.584 1.771 1.939

" The a values for D - V pairs are zero (see Table 4).

also noted that a~m, Dv has fairly large negative values at first-, second- and third-neighbor pairs. This shows that the first three coordination spheres around occupied interstices tend to be vacant. Thus a deuterium atom blocks the neighboring interstitial positions. Similar experimental results showing the blocking effect were obtained on a-VD0.75 [6,7] and et-TaD0.55 [8]. From the diffuse scatte,ring intensity lAD due to the atomic displacement, ~/h~np values and the average interatomic displacements Almn p for the D - D pairs were deduced. The results are given in Table 5, where a positive (negative) value of "Ylmnp means that the I m n interatomic separation is extended (contracted) in the p direction and vice ver,;a. The yx and ~/Y values are positive for the first-neighbor configurations of D - D pairs. For the second-neighbor D - D pairs the 3 / v a l u e is positive. These results suggest that a repulsive interaction exists between the neighboring deuterium atoms, which is consistent with the blocking effect

parameters for D-D pairs indicate that D atoms in the first- and second-neighbor configurations move away from each other.

Acknowledgements The present authors are grateful to Mr. K. Nemoto for technical assistance with the neutron diffraction experiment. This work was partly supported by the Grant-in-Aid for the Scientific Research from the Ministry of Education, Science and Culture of Japan.

References [1] M. Hirabayashi, S. Yamaguchi, H. Aasano and K. Hiraga, in H. Warlimant (ed.) Order-Disorder transformations in Alloys, Springer, Berlin, 1974, p. 266. [2] H. Asano and M. Hirabayashi, Z. Phys. Chem., N.F., 114 (1979) 1.

described above.

[3] V.A. Somenkov and S.S. Shil'stein, Z. Phys. Chem., N.F., 117 (1979) 125. [4] V.A. Somenkov and S.S. Shil'stein, Prog. Mater. Sci., 24 (1980)

5. Summary Elastic neutron diffuse scattering measurements have been made on a single crystal of VD0.8~ at room temperature, which is about 90°C above T c, to study the local atomic arrangements of deuterium atoms dissolved interstitially in the b.c.c, metal lattice. We derived the expression for the diffuse scattering intensity from crystals consisting of multiple sublattices, in which each sublattice has different local symmetry in the unit cell. The displacement effects are small for the present WD0.81 crystal. The SRO parameters up to the fifteenth neighbors were obtained by Fourier inversion of the local SRO intensity. The variation in the SRO parameter with distance shows that the first three coordination spheres around a deuterium atom tend to be vacant. The first-order atomic displacement

267. [5] A.Yu. Cheryakov, I.R. Entin, M.E. Kost, V.A. Somenkov, S.S. Shil'stein and A.A. Chertkov, Soy. Phys.--Solid State, 12 (1972) 2172. [6] V.A. Somenkov, Ber. Bunsenges. Phys. Chem., 76 (1972) 724. [7] U. Knell, H. Wipf, G. Lautenschlager, R. Hock, H. Weitzel and E. Ressouche, J. Phys.: Condens. Matter, 6 (1994) 1461. [8] H. Kaneko, T. Kajitani, M. Hirabayashi and M. Sakamoto, Mater. Trans. Jpn. Inst. Met., 32 (1991) 567. [9] M. Sauvage, E. Parte and W.B. Yelon, Acta Crystallogr., Sect. A, 30 (1974) 597. [10] v. Moisy-Maurice, C.H. de Novion, A.N. Christensen and W. Just, Solid State Commun., 39 (1981) 661. [11] H. Terauchi and J.B. Cohen, Acta Crystallogr., Sect. A, 35 (1979) 646. [12] M. Morinaga and J.B. Cohen, Acta Crystallogr., Sect. A, 35

(1979) 975.

[13] M. Hayakawa and J.B. Cohen, Acta Crystallogr., Sect. A, 31 (1975) 635.