Medium-range order in amorphous substances: A modified layer model

Pergamon

Solid State Communications, Vol. 91, No. 2, pp. 101-104, 1994 Copyright © 1994. Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098(94)E0289-N 0038-1098/94 $7.00+.00

MEDIUM-RANGE ORDER IN AMORPHOUS SUBSTANCES: A MODIFIED LAYER MO~EL

E. A. 0 h e c h e t k i n a institute of General and Inorganic Chemistry, Leninsky Pr.31, Moscow 117907, Russia (Received at 30 March by V.~.Agranovich) A conventional layer model for the first sharp diffraction peak (FSDP), a signature of medium-range order typical for a wide range of amorphous substances, is revised. It is proposed t h a t t h e layers responsible f o r FSDP are based on alternative bonds, which are inherently connected with the basic bonds responsible f o r common s h o r t - r a n g e o r d e r in non-crystalline structure. B a s e d on e x p e r i m e n t a l FSDP d a t a and simple chemical bond arguments the origin of alternative bonds is established in definite groups of amorphous substances: glasses, amorphous metals, liquids of different nature.

{. Introduction A w e l l known f e a t u r e o f meny a m o r p phous substances is the so called first sharp diffraction peak (FSDP) which is considered as the evidence of ch-~acteristic m e d i u m - r a n g e o r d e r (MRO) e x i s t ing there (see [t,2~ as reviews). There a r e two w a y s o f e v a l u a t i o n o f t h e MR0 d i m e n s i o n s f r o m FSDP d a t a , f i r s t , the distance d = 2

~/QI

FSDP/MRO which appeal to the 21) fragments in glass like in parent crystal (e. g. As2S ~ so that for glass eq.(~) gives a distance close to a real one between covalent fragments linked by "intermolecular" bonds, L in eq.(2) being considering as the region of structural correlation between neighbouring layera The problem is the unknown nature of layers in glasses of ~D or 3D structur-

(1),

al motif (e.g. SexPI_x and Si02), amorphous metals and semiconductors, and, especially, in liquids. The synergetlc model of FSDP proposed recently [3] solves this problem in general since it considers collective excitations in the form of bond wave whose wavefronts populated with alternative bonds gives reflecting planes in amorphous network c0mposed of basic bonds, thus, the motif o£ the basic network is of no significance. However, this model in its initial form [3] is too abstract and may be considered only as a hypothesis that overcomes the contradictions of the conventional layer model of FSDP, but needs further concretization and justification. This is the goal of the present

where QI = ~ s i n @ / ~ is the FSDP position, a n d , s e c o n d , t h e l e n g h t T. ~ 2 " ~ / ' i I

(2),

where W I is the FSDP halfwidth. However due to the lack of translational symmetry the usage of Bragg equation (1) or the Scherer equation (2) is very questionable. Even assuming a conventional character of d named "equivalent distance" and L n-ned "the length of structural correlations" and substituting equ-!ity for approximation one should answer what value corresponds to MRO dimensions: d ~ 4-6 ~ or L ~ 20-30 ~ , or the both? The situation is somewhat better in frames of the layer model of 101

102

MEDIUM-RANGE ORDER IN AMORPHOUS SUBSTANCES

communication, in which experimental FSDP data are used to establish the nature of alternative bonds in very different amorphous substances with ~RO. 2- Empirical Laws for Further Analysis Let consider two boundaries of a layer populated with alternative bonds (AB) as a pair of reflecting planes which give the reflex at QI' the FSDP maximum. Then the layer thickness, d = = 2 ~ / ~ [eq.(1)~, may be connected with the geometry of AB, which, in turn, may be correlated with the geometry of the basic bonds (BB), namely, with its lenght obtained from radial distribution function as r I, the first interatomSc distance. Reall~, such correlations are shown to be exist [4 I, as it is seen in Fig.~ represented here for the convenience of the reader since just these empirical laws are used below to determine the AB nature. ~. Glasses and Glassforming Liquids Here BB are covalent bonds, the two-centre and two-electron ones. Let AB be three-centre bonds (TCB) after [5-7]. The simplest layer based on TCB is shown in Fig.2. Its thickness is d ~ 2 r ~ since TCB is weaker and so longer than two related covalent bonds. It means

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~ > 2, as it is really observed - see ! curves G and G in Fig.I. Note that the d~mension of covalent network (e.g. ~D in Fig.2) is -nmeterial because TCB may realize in glassy covalent network of any dimension [5]. However, as long as ~ 4 3 (Fig.I) the TCB which are elongated more th~n in 1.5 times in comparison with two covalent bonds are unstable, at least in a collective form of reflecting layer. The fact that there are two correlated curves (G and G') with instability at r K ~- 2.3 ~ is of a particular interest. It indicates that there exist a serious difference between TCB realizing in substances belonging to different curves, and the nature of the difference need further investigation. : LiQuid Halogens S i n c e TCB f o r t h e f i r s t time were proposed just for halogens (I~, ICI-2, etc.) [8] it is naturally to pPopose that AB=TCB in this case too. However, the fact that the H curve lies below G ! and G curves, and ~ may be lower than 2 say that the structure of layer is different, namely, instead of perpendicular TCB (Fig.2) there are inclined

•

01

2.5

2.0

1.5~

/ 1.0

1.5

2.0

A/ 2.5

"rl,

Fig.~. The scale of MRO, ~ = d/r~, in, glasses and glassforming liquids (G,G), amorphous metals and semiconductors(A), liquid halogens (H) and liquid ASn and AFo where A=Na,K,Rb,Cs (S and P) by [@]

FiK.2. tissue pating

Reflecting l ayers~ based on ~B (springs) and amorphous 2 ~ b e t w e e n t h e m . Atoms p a r t i c i in TCB are blackened.

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MEDIUM-RANGE ORDER IN AMORPHOUS SUBSTANCES

TCB within the layer. This is rather possible because TCB in halide and polihalide species are often crossed [9~. If the simple crossing takes place:

: io

(here O is Y,Ci,Br or I, and : are p-electrons of lone-pairs) and if such TCB are organized into layers, then d = 2rlsin c~ , and when o( @50-~90 ° and l>2r~, one obtains ~ ~.~-~2.2. This agrees well with the experimantally observed ~ (Fig.~,H) which falls from 2.2 (F2) t o ~[.6 (I2). ~. Amorphous metals and semiconductors The fact that the both belong to one and the same correlation line (A in Fig ~) indicates that, irrespectively of the c~racter of conductivity, the structure forming bonds are similar. Since amorphous metals (a-Pes~20 , CU3oZr70 , etc.) are known to have a strong covalent character of bonding together with the ability for hybridization with participation of d-electrons (e .g. [~0] ), one may suppose that in both amorphous metals and semiconductors (a-Si, etc.) BB and AB represent different covalent hybrids, e.g. sp 3 and sp2d2 in a-Si:

Note that such extracoordlnated hybrids are well known in coordination chemistry of Si [ ~ ] . On the othe~ hand, although central atom has five nelghbours its first coordination number is 3 because in these hybrids equatorial bonds are shorter ~b~n axial ones [12~, and it is known ~hat in amorphous forms o f

103

Si and Ge the averaged first coordination number is 3.5-3.9 instead of @ in crystal. Unequality of bonds in alternative hybrid leads t o t h e possible existence of two types of lyers: with d a = 2~a~ 2 r l and w i t h d e i , C 3 / 2 ) r e ~ t . S r ~ . The o b s e r v e d v a l u e s ~ < t . 6 indicate that equatorial packing is preferable. However, the -w!al packing cannot been excluded completely: it has been shown that in a-Ge films prepared in special conditions an additional weak peak at Q~ .2 LI3] can be attributed to ~ a = 2.X (r~ = 2.5 ~), so the layers of two types coexist in this material. B~m~larly, an additional low-Q peak(s) may be obtained in amorphous metal - if it has assymetric alternative hybrid and the sample prepared in conditions favouring long-bond packing. 6. Liquid ASn and AFo (A=Na, K,Rb,Cs ~ They occupy a large-r I region in the -r~ plot and demonstrate very high

~

(see s P in ig.I), what points to a principally new mechanism of bond alteration. As previously, let BB be the same as in parent crystal, here the tetrahedral Zintl ion (Sn~-or - T Pb~-) surrounded b~ A + ions positioned in the corners of larger tetrahedron. The bond is covalent (sp3-hybrld [~@] ) within Zintl ion and ionic outside it. Let AB to be a d~mer of Zintl ions:

In the case of ideal tetrahedra d = 2h= 1.63r I , i.e. ~id = 1.63. Prom Fig.I (S,P) it is seen that ~ is usually higher, i.e. the tetrahedra should be stretched. It is quite cles~ because to keep electroneutrali~y the islet must contain equivalent amount of A + ions, B

104

MEDIUM-RANGE ORDER IN AMORPHOUS SUBSTANCES

which "burst ou~" it in the extent roughly proportional to the ion dimension. The row of ionic radii (0.99, 1.33, I.@8, 1.67 ~ for A--Na+,K+,Rb+,Cs +) corresponds tO the ~ rows ( t . 5 ~ ,

2.06, 2.~3, 2.~7 for AFo and 1.97, 2.20, 2.32, 2.37 for ASn) that confirms the assumed structure o f reflecting layer. 7. Conclusions There are significant distinctions between the conventional and the modified layer model (MLM) for FSDP. First, since in MLM the FSDP is considered as a true Bragg reflex (Fig.2) then d in eq.(1) is a real distance strictly corresponding to the layer thickness, but not an"equivalent" (approximate) distance b e t w e e n the layers. Second, in contrast to conventional model, eq.(2) in MLM has no a physical sense, as length of interlayer correlation is c o in frames of underlaying bond wave model (the layers represent wavefronts) or, at least, of macroscopic scale for real bond wave restricted by the sample dimensions. On the other hand, the FSDP halfwidth W. and intensity S(Q[) really characterlze medium-range order (i.e. the layers) since they are determined by the layer smoothness (both halfwidth and intensity)

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and the layer concentration in a sample (intensity). Third, the layers in conventional model are associated with the bonds similar to those in parent crystal and, what is more, the existence of crystal-like 2D fragments in amorphous state needs for FSDP. In MLM the layers are formed by alternative bonds, which are not typical for crystalline counterpart and thus the existence of FSDP irrespectively of the parent crystal structure finds an explanation. Using d as the layer thickness and d vs r T dependencies it was succeeded in *establishing the nature of alternative bonds in concrete cases. Forth, if MRO (layers) is the conseuence of specific long-range order ond wave) then the LRO dimension the wavelength#i>>d should be found by both common methods (extra-low-Q diffraction, electron microscopy,etc.) and unusual ones (e.g. the formation of "gigantic lattices" after[15] m a y b e considered as the long-scale secondary formations based on bond waves). A@knowledgments. The author wish to tb-n~s Prof. S.A.Dembovsky for helpful discussions. This work was partially supported by Russian Foundation for Fundsmental Research (Grant No.93-03-456) and the Grant of International Scientific Foundation awarded by American l ~ sical Society.

References [. S.R.Elliott. J.Phys:Cond.Matt. 4, 766I (I992) • 2. S.C.Moss, D.L.Price. In: Physics of Disordered Materials. N-Y, Plenum, I985. P.77. 3. E.A.Chechetkina. Sol.St.Comm. 87, 171 (I993) • 4. E.A.Chechetkina. J.Phys:Cond.Matt. 5, L527 (I993). 5. S.A.Dembovsky, E.A.Chechetkina. Glass ~rmation. Moscow, Nauka,I990. 6. S.A.Dembovsky. Sol.St.Comm. 83, 76I (I992). 7. S.A.Dembovsk-y. Sol.St.Comm. 87, 179 (I993) • 8. G.C.Pimentel. J.Chem.P~ys. I9, ~46 (I95I).

9. G.C.Pimentel, R.D.Spratley. Chemical Bonding Clarified Through Quantum Mechanics. San Franslsco, Holden-Day, I970. ~0. J.Hafner, S.S.Jaswal. Phys.Rev. B38, 7320 (I988). ~I. S.N.Tandura. In: Structural Chemistry of Boron and Silicon. Berlin, Springer, I986. P.IOI. ~2. E.Huheey. Inorganic Chemistry. 3rd ed. N-Y, Harper & Row, I983. 13. P.Vi~6or. J. Non-Cryst.Solids IOI, I56 (I988). J.Hafner, W.Jank. Phys.Rev. B44, II662 (I99I). ~5. S .A .Dembovsky, P.A .Koz 'min. So].St.Commun. 86, 623 (I993).