Computer simulation of surface reconstruction and relaxation of Ni single crystal faces in ferro- and paramagnetic states

Vacuum/volume 43lnumber Printed in Great Britain

8/pages 785 to 78911992

0042-207x/92$5.00+.00 Q 1992 Pergamon Press Ltd

Computer simulation of surface reconstruction and relaxation of Ni single crystal faces in ferro- and paramag.netic states A S Mosunov, Russia

Research

Computer

Center of the Russian Academy

of Sciences,

Pushchino,

Moscow

Region,

and 0 P Ivanenko, 7 19899,

M V Kuvakin

and V E Yurasova,

Department

of Physics, Moscow

State University,

Moscow

Russia

received for publication

4 February 1992

The variational method is used to calculate the atomic binding energy and the surface relaxation of the (001) and (I 7 1) Ni vicinal faces cut at a 70” angle to the [Of7 / axis. The one- and two-atom step crystal surfaces in ferroand paramagnetic states are studied for which a difference in the atomic binding energies of the upper layers and a curvature of the ( 1 IO) close-packed chains of atoms emerging on the crystal surface have been obtained. A possible change of the Wehner spot pattern for smooth and step-like surfaces in the ferro- and paramagnetic states is estimated.

1. Introduction The aim of the present work is to calculate the equilibrium structure of vicinal step-like faces close to (111) and (001) surfaces of the Ni single crystal in the ferro- and paramagnetic states. It is well-known that any (even a low-index) face exhibits a step-like structure’ and may suffer morphological changes when exposed to external factors. An interesting structural phase transition was observed, for example, when a Ni single crystal was heated near the Curie point’.‘. It was found that the IO and 5’ Ni(ll1) vicinal faces consisted, respectively, of two- or four-atom steps at temperatures T< T, and consisted of one-atom steps only at T > T,. It should be noted that many other characteristics of the near-surface layers also show anomalous behaviour in a temperature interval near T, (refs 48). With respect to sputtering, it is of great importance to assess the effect of the vicinal face surface structure reconstruction on the anomalous behaviour of Ni sputtering yield within a temperature interval including the Curie point. This work presents the results of a calculation of the surface layer relaxation and the atomic binding energy on the surfaces of the (111) and (001) Ni vicinal faces cut at a 10” angle with respect to the [Oll] axis, which can contain one- and two-atom steps at different temperatures2,3. For comparison, calculations were also carried out for the (111) and (001) Ni perfect faces.

movable part (matrix) for which the potential energy minimum is not calculated, but which are involved in interactions with the atoms of the movable part. The dimensions of the matrix were selected (in conformity with the cut-off radius of interaction potential) in such a way that the existence of the crystallite boundaries would not affect the atoms of the movable part. In its initial state, the crystallite was a parallelepiped with a (001) or (111) face having a size of 17 x 15 atoms. The number of layers in depth was varied from 13 to 17, depending on the particular calculation version. The movable part consisted of 8 x 8 atoms in a four-face plane and of up to 10 layers in depth. The borders of the steps in the faces were parallel to the [Oil] direction. 4.54.4 -

0

g

4.3 -

8 s g

,,2_Ni(OOl) .

e

4.1-

0

I 5

I 6

.

.

4-

2. Crystal model and calculation techniques

3.9 t Ni(ll1)

In order

3.81

to find the surface structure of the studied face, the potential energy of perfect crystal was minimized. The examined structure (crystallite) was broken into two parts, namely, (i) the atoms for which the potential energy is calculated (the upper movable part of the crystal) and (ii) the atoms surrounding the

w

.

0

$ 5ii

0

0

T

I 2

I 3

I 4

J 7

Layer number Figure 1. Difference in binding energy between the atoms of relaxed surfaces of the (001) and (I 11) faces in ferro- and paramagnetic states versus the number of layers. 785

A S Mosunov et al: Computer simulation The interaction by the potential I/@,,)

between

= U,,(r,,) +A&

3.1. Perfect face

the ith and jth atoms was described

h”(l

- (S,S,)).

X1.1. Relaxation. The changes of the face spacing (relaxation) for the ferro- and paramagnetic states on the (001) and i I I I ) surfaces can be found in Table 1. From the tabulated data it can bc seen that the first plane spacing (ic. the distance between the first and second layers of atoms) increases substantially in either of the faces and that the increase is greater for the ferromagnetic state compared with the paramagnetic state. In the cast of (001) fact. for example. the increase is 8.94% for the fcrro-, and 8.40% for the paramagnetic state. In the case of the ( I I I) face the increases are 4.34 and 3.99%. respectively.

(1)

The tirst term of equation (I) depends on the distance between the ith and,jth atoms; C’, is the Morse potential’; A = 5.16 eV; h = 0.81 I2 A ’ (ref IO) ; b,(~,,) = D(e ““~~ ‘/I’ -2e ~‘(‘,J ‘~~‘).In the cast of Ni, we have /I = 0.4205 eV. z = 1.4199 A ‘, and I’,, = 2.78 A (ref 9). The second term in equation (I) allows for spinspin orientation ; (SJ’,) is the two-spin correlator (in this case the mean cosine of the angle between the spin orientations in the ith and jth lattice points) ; the angular brackets designate the averaging over the ensemble. At T = 0 K we have (S,S,) = I, i.e. I/’ = I:, (Y,,) describes the ferromagnetic state of the crystal. At T > r, we have (S,S,) = 0. i.c. I! = C:, (Y,,)+ .ilr “? describes the paramagnetic state. The binding energy of the ith atom on the surface was calculated by the formula Eh = c U(r,,), where the summation is

3.1.2. Binding energy. The surface relaxation having been allowed for. the binding energy of the atoms in the upper layers proves to be somewhat lower compared with the case of the pcrfcct crystal”. in agrcemcnt also with the data of ref 13. The binding energy variation AE, calculated, making allowance I‘OI and disregarding the rclaxatmn. proved to be non-monotonic from layer to layer. The greatest variations occur in the second layer ( - 3% for the (001) face and - 5% for the (1 II) face). The variations A& in the first and third layers are not substantial ( - 0.4 “,G in the first layer of the (I I I) face and -0.9% for the (001) face). The variations A& due to the change of the magnetic state ix -4% (set Figure I). From Figure I it can be seen that the variations AE, in different layers of the (I I I ) face are alike and that the variation AE, in the upper layer of the (001) face ix greater compared with the second layer. Such an anomaly arises from the smallness of the binding energy of the first layer atoms in the (001) fact and. hence. from a greater rclativc variation 01 E,, for the ferro- and pammagnetic states.

with respect to I8 coordination spheres of the ith atom. The position was found for each of the atoms of the movable part of the crystal where the potential energy of an atom proved to bc minimum. The calculations were stopped when the displacement of the ith atom in thejth iteration got smaller than IO- ’ A. The energy minimum was determined by the Newton method and by the simplex method’ ‘. Thermal vibrations were disregard&. 3. Calculation results and discussion Table 1 summarises the results of calculation of the relaxation of surface layers and the atomic binding energies for the perfect (001) and (I I I) Ni faces and for the vicinal step-like faces in the ferro- and paramagnetic states cut at a IO’ angle to the perfect faces. We shall discuss the tabulated data and estimate the changes of the sputtering yield and of the Wehner spot pattern in the cases where the one- and two-atom steps occur on the (001) and (I I I) vicinal faces.

Table I.

Atomic binding energy E,_in (eV) and shifts of atoms and layers (in b.1 for smooth and stepped (001) and (I I I) faces of Ni single crystal in

ferro- and paramagnetic

No

of

layer at oni

3 4 5

states. Z is the normal

shift

; .x-is the tangential

shift in the (0

face

5.596

i.613

7.832 X.312 8.446 8.484

8.035 x.417 X.4X6 x.497

0. IO6 0.018 0.003 u.001 0.000

5.757 3.807 5.769

0.1 I9 0.073 0.109

0.27 I 0.x45 0. I43

5.4% 4.741 5.497

0 IX ~ 0.004 0. I I4

5.673 4.294 7.989 5.696

0. I25 ~ 9.007 -0.086 0.151

0.08 I

5.344 4.075 7.641 5.389

0. I72 0. I62 0.044 0. I64

One-atom

step

._.3

0.19Y 0.210 0.202

0.00 I 0.087 0.007

5.357 4.476 5.356

0. I59 0.170 0.158

0.003

0 4

5.558 4.680 5.559

Two-atom -3 0 2 5

step 5.584 4.476 7.991 5.590

0.161 0.194 -0.025 0. I64

-0.005 0.029 0.008 -0.009

5.337 4.298 7.671 5.351

--0.166 0.1x3 -0.025 0.158

o.ouo

786

I I ) plane

f-err0 ~ E,,

Perfect smooth

I 2

3. I .3. Sputtering. The Eb variations due to relaxation slightly affect the integral sputtering yield. At the same time. the fT+ variation under the transition from the ferro- to the paramagnetic state in Ni results in a -4% increase of the sputtering yield.

0.08X 0.004

0.023 0.007 -0.005

0.4OY -0.017 -0.002

0 I45

0.6 I4 (I.060 --0.0’1 0.234 - 0.00

I - 0.050

A S Mosunov

et al: Computer simulation

Since the close-packed chains get curved by relaxation at their ends emerging on surface, the angular distributions of particles sputtered from the (001) and (111) faces, namely, the Wehner spots{ 110) shift aside to the normal of these faces. The relevant calculations have shown that the shift can range from 3 to 7”, depending on the energy of a focuson which moves along a closepacked chain and on a given magnetic state of the specimen. At a 20 eV focuson energy for the ferromagnetic state, the [I lo] spot shift is -6” for the (001) face and -4” for the (111) face. In the case of the paramagnetic state the spot shift is -4.5” for the (001) and -3” for the (111) face.

_45 ,’

Ni(001)

I

c

-

I

I

3

0

3.2. One-atom step -4

3.2.1. Relaxation. In the case of the (001) face with a oneatom step, an atom at the step border relaxes to a position farther from the face [Figure 2(a)], while the rest of the atoms become shifted but insignificantly. The shifts of atoms towards a surface normal are the same as in the case for the perfect face, but atoms 1 and 3 [see Figure 2(a)] relax towards each other, thereby smoothening the step. The calculations for the paramagnetic state give qualitatively the same shift of atoms, which is, however, smaller in value than in the case of the ferromagnetic state (see Table 1). In the case of the (111) face in the ferromagnetic state [Figure 2(b)] the shifts of atoms near the step edge are much greater than in the case of the (001) face. The step height decreases by - 10%. so that the obtuse angle at the ba.se turns into an acute angle. The effect diminishes for the paramagnetic state.

-4.6-

-3

-2

-1

ib

. Ni (111)

-5

-4.6 1

g

-5.2j

t -5.4 1 E -5.6 3$ 5

-5.6 _1

a

-6 ! -6.2

para n

.

n

q

0

=

I I

3 c!

ferro

I

-

--+-0

3.2.2. Binding energy. Whereas all the surface same binding energy on a perfect low-index crystal, the binding energies of the atoms which positions with respect to step edge are different

atoms are of the face of a single occupy different on a vicinal face

1

2

3

n

Figure 3. Binding energies of different atoms numbered from - 3 through to + 3 for crystal in ferro- and paramagnetic states on the surfaces of the (001) (a) and (111) (b) faces with a one-atom step. The number n = 0 corresponds to the atom in the step edge (atom 0 in Figure 2).

[see Table 1 and Figures 3(a) and (b)]. The atoms located in the base and in the edge of the step are, respectively, of the highest and lowest binding energies which differ by -2.5 eV in the calculated cases. The allowance for relaxation of step-like surfaces gives rise to substantial changes of the vicinal face structure and of the atomic binding energy. Figure 3(a) shows the difference in the binding energies of the surface-layer atoms for ferro- and paramagnetic states. On average, the binding energy of paramagnetic state surface atoms is 3% lower than in the ferromagnetic state. In the case of the (001) and (111) vicinal faces, the binding energy of atom 0 in the step edge [Figure 2(a)] in the ferromagnetic state is 4% higher than in the paramagnetic state. The greatest difference (which reaches 8%) in the binding energies occurs for the second-layer atoms and for the first-layer atoms not adjacent to the step, rather than for the atom in the step edge [Figure 3(b)].

(b)

Figure 2. One-atom step on the (001) (a) and the (111) (b) faces. Projection onto the (110) plane. Open circles (0) represent the position in the ideal lattice. Closed circles (0) represent atoms in the first layer of the (110) plane after relaxation. Hatched circles (6) after relaxation but for the atoms in the second layer of the (110) plane.

3.2.3. Sputtering. The change of the integral sputtering yield of a vicinal face compared with a perfect face cannot be determined accurately without making some additional calculations, but estimates based on the values of atomic binding energy are quite feasible. The mean binding energy of surface atoms on a vicinal face is lower compared with the perfect face because the binding energy of the atoms in a step edge is much (by up to 25%) lower than the binding energy of the atoms in a perfect surface. We obtained rough estimates of the integral sputtering yield S of 787

A S Mosunov et al: Computer simulation vicinal step-like

l’xus

rciation

\vcll-known

appr~‘“imatiuli.

.Y do no1 change taken

I E,, ri.c. aswming

that.

ii5 2 iit-st

all the paramctcrs other than E,. which dctcrmlw \vhcn

binding cncrgy for \\a’\

c~~mparcd u~th :! smn~lth I’xc LISIII~ rhc S’ _

on \icin;il

steps arc formed

IO i~toiiis localcci

to bc the E,, V;IIIIC

The

fuccs)

i.hc

at the top ~i~itl 1x1s~ 01‘ ;I step sztimates

shop n th;~t ~hc

ha\c

nitcgral sputtcring yield of Ihc one-atoni step (001

) I’xc incrc;isc5

in bl _ 7”,,, compurcd with the pcrrccl Il~cc and I\ x d”,, lo\\~ctthe Ii-roni~ignctic state wmparcrl Mith thy paramagnctic \lalc. The ~ntcgrzl sputterin higher

lx

g_ cicld

_ 3? 0 comparai

IowcI- in llicI‘crroniapnctic

hlcp (I

01‘ Ihc one-aroni

wlh

\t:~lc coinpal-cd

vbith the paraniagnciic

stale. The change of’ the ,tngular distributlnn !crcd I’rvm the step-like ((Ml 1s not substantial

(the

distt-ihtition

amwig

chains near lhc step cdpe vurics slightly. close-pxked bv hearing spots

the Ibllo\ving

cl793

This

rpot

tu ~ttom 0 (the binding cncrg ;ln tlv;~I spot ol’gc:lt

to the prcx ious c;ixs)

the rcrroniagneCic state).

I IO

7( b)]. tlxrc-

01‘lhc Wchnci-

on the po\ition,

.4s ;I rcbtilt.

(contrar!

l:izurc

t\>the t.h;ingc ol‘ the M’ehncr

pattci-n is l‘roni the ch:lins aii~accnt

Jircction

namely. tlccrca\~~ ;3\

chains get cur\~cdnoticcabl! [xl:

of the chains is Ioucr).

I’:IN I IO

Ilic

(I I I) Licinal I’ucc. hov+cvc~-.the

: the highest contribution

dinicnsions

ol’ pat-tick\ hput-

) ii~cc comp;lrod \\ith ii smooth

angular

_ 2 i. In the C‘;ISL‘01‘ the

I I ) I;ky I\

I’x~c 2nd I\ _ 5” (,

the pdcct

salcll~tc

fat-id

i\

spot

:ingul;i~-

( . IO 1‘01 1ii the

~211 Jiilted

opposite to the shirt 01‘ spots I’r~~m the‘ pcr!‘ccl

:hurl’:~~x.

i.c. in tlic direction from ;I nol-in,11 to the hurllicc. Bcsidc~. 21\po! 01‘ ;I much lower

Intcnsitq

xt qprosimatcly

the sanx place as the spot I‘I-ml

The relaxation

ma:. IKCLI~ in the Ihrnxl-

of aloms

near the step cdgo is cluxlitati\cl~

sonic as in the p:~raniagnctic state. altllollgll of

the shilis

satcllilc

perdition. i.c.

pcrl~cc~ surl’xc.

of atoms will

bc somcwlial

IllC ahsolu1c

Thci-cl’orc.

Imu.

spot will bc 01 grcatcr angular dinicnsions

par;iniagnctic

staCc. Clear14.

the occurrcncc

the \,IIUC

the

( - 7 ) in the

01‘ the satellite

is dcfincd by step spacing. Since ;I step in prxticc

ywt

does not IXII

any clli’ct on the atoms located at three atomic spacings

1‘1.on:

the

step cdgs. it may bc cxpccted in the ciisc 01‘ small \tcp sp;icinph that the spot inherent with

8 satellite

dimensions

lowcr

intcnsitq.

;ingul:ii-

step A step with an obtuse angle at its base IS ;I

Relaxation.

stable I‘orm of two-atom steps (Figure present the results (001) and

appca~- tvgethcl

but UC greater

(which is due to the sputtcrin g of corner atoms).

3.3. Two-atom X3.1.

to perfect surl’acc will

spot ol‘a

(I I I) facts. Qualitatively

pattern observed I,r

4(;1) and (I~)

of atoms for the

the pattern i\ close lo 111~

one-atom steps. naiiicl~.

atoms in the (001) LKC is sniull due to niolions

4). Figures

of calculating the rclaxatioll

(i)

Ihe

sh11‘t 01‘

: the step is smoothcned sonicwhat

of atoms 2 and 4 (i-igtirc 4) towards cxh

0th~

:

(ii) in the cast of the (I I I) Ir~co [Fipurc 4(b)] the \hilIs ol‘aiom\ near the step edge incrcascs sub~lantially leading

to marked

chains emcrginf 3.3.2.

Binding

changes

d

the pmmctry

(up to

I A). thcrchl

of the close-packed

on the surt’acc. energy.

The

data on the binding

dill’crcnt atoms for the (001) and (I bc found in Figure

5 and Table

cncrgy 01‘

I I) two-atom

step li1ccs can

I. Qualitatively

the pattern 01‘

binding cncrgy variations

of the two-atom steps is the

the case ol‘ the one-atom

steps. The only

between

the two casts IS that the mean

atoms ofthc

(I I I) face in the paramagnetic

the s;tmc I’or the pcrfcct 78%

and vicinal

liccz

diKcrcncc binding

S;IIW

in

as

in principle cnerg!

01‘ the

state is approximately and is practically

iw

A .S Mosunov -4

eta/:

Computer simulation

I=

Ni (001)

.

.

n

.

.

LJ

-

/

.

-6.5

I .

I .

7

/

.

rz

(- 9%) and greater in the ferro- than in the paramagnetic state of crystal. The difference in the binding energies of the atoms of upper layers of crystal in ferro- and paramagnetic states has been found to depend on the number of a particular layer and to reach 5%. The equilibrium configuration of one- and two-atom steps on the (001) and (Ill) Ni 10” vicinal faces in ferro- and paramagnetic states has been calculated, making allowance for relaxation. The binding energy of atoms in different crystal layers has been determined in these cases. The variations of the integral sputtering yield and of the spot pattern have been estimated for relaxed smooth and stepped surfaces as compared with a perfect crystal. The binding energy variations have been shown to result in an increase of sputtering yield by 45% in the paramagnetic state compared with the ferromagnetic state. The Wehner spot patterns have been found to vary substantially. In the case of smooth faces the (I IO) spots have been shown to get closer to each other by 12’ in ferro- and by 9” in paramagnetic state. Besides, in the case of the (111) vicinal face with one- and two-atom steps, the occurrence of a satellite spot is predicted at a - lO^ distance from [I lo] in the (110) plane. The satellite spot intensity has been found to depend on the length of terraces between steps, i.e. on the face cut angle (as the terrace length increases, the intensity of the satellite spot decreases compared with an ordinary spot). By virtue of a comparatively large spot spacing, the spots can probably be resolved experimentally under bombardment by slow ions which destruct the surface but little. In such a case the ordinary Wehner spotto-satellite spot intensity ratio could have been used to characterize the approximation of a given face to the perfect face. References

Figure 5. The same as in Figure 3 for the faces with a two-atom step.

of these) may be used to be the measure of surface perfection. The qualitative pattern of relaxation and binding energy variations in the case of the two-atom steps is the same as in the case of the one-atom step. 4. Conclusions

Studying relaxation of surface layers of the (001) and (111) Ni faces has shown that the increase of the interplane distance between the first and second layers of the two faces is substantial

’ J Golovchenko. Science, X34,48 (I 986). *J C Hamilton and J Terrens. Phvs Rev Left. 46. 745 (1982) ’ N S Dresselhaus, Nature, 292, 196 (1982). ‘J A Hedvall, K Hedin and 0 Persson, Z Phrs Chem, 27, 196 (1934). ’ D S Sales, J E Turner and M B Maple, Phw Rer Lrtf, 44, 586 (I 980). ‘V 0 Khandros and N A Bogolyubov, H&h-Tamp Thermal Phys, 21, 600 (1983).

’ V E Yurasova, Vacuum, 33, 565 (1983) ; 36, 630 (I 986). ’ H V Thapliyal and J M Blakely, J Vuc Tech, 15, 60 (1978). ’ L A Girifalco and V G Weizer. Phys Rezl, 114, 687 (1959). ‘“M V Kuvakin, Thesis, Moscow State University (1979). ’ ’ N N Kalitkin, In Numerical

Methods.

Nauka, Moscow (1978).

’ *V N Samoilov, V A Eltekov and V E Yurasova, Vestnil; MGU (USSR) SW Fiz Astron, 27, 87 (1986). ” D P Jackson, Radiat EJg; 18, 185

(I 973).

789