The application of X-Ray diffraction and computer experiments in the studies of structure of liquids and amorphous solids P-15

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ISSRNS 2016: Abstracts / Extended abstracts / Synchrotron Radiation in Natural Science Vol. 15, No. 1-2 (2016)

71

P-15

The application of X-Ray diffraction and computer experiments in the studies of structure of liquids and amorphous solids

M. Śliwińska-Bartkowiak^1,2*, H. Drozdowski^1,2 and E. Robak^1,2

1Adam Mickiewicz University,Umultowska 85, 61-614 Poznań, Poland

2NanoBioMedical Centre, Adam Mickiewicz University,Umultowska 85, 61-614 Poznań, Poland

Keywords: X-ray diffraction, computer experiments, coordination numbers for liquids

e-mail: msb@amu.edu.pl

The application of the X-ray diffraction method for study the structure of liquids and amorphous solids is described. The main sources of errors are discussed.

A numerical analysis is performed of the influence of X-ray data termination on the normalization constants, radial distribution functions (RDF), and on interatomic distances and coordination numbers determined from these functions. Computations are carried out for liquid dichloroalkanes [1,2], carbon tetrachloride [3,5]

and naphthalene [4]. The strong dependence of coordination number on the termination angle, observed by other authors, is confirmed. An approximately linear dependence of coordination numbers on wave vector S is found.

Use of RDF, to compute a coordination number, N₁, for liquids is discussed for four methods:

1/ symmetrizing the first peak in RDF; 2/ symmetrizing the first peak in r² RDF(r); 3/ decomposition of r² RDF(r) into shells; 4/ computation of area to the first minimum in r² RDF(r).

Figure 1 shows the calculated RDF of 1,12-dichloroalkanes decomposed into the various atomic peaks. These composite peaks are resolved into atomic peaks on the assumptions that the shape of an atomic peak can be represented by an equation of the form:

e

^^x²^/^c where c is a constant, i. e. that the curve is Gaussian, and also that the area under an atomic peak formed by two atoms multiplied by the distance between the two atoms is proportional to the product of the scattering powers of the two atoms.

The coordination numbers and interatomic and intermolecular distances in a liquid are mean values and undergo fluctuations. Therefore, it seems that the best method to estimate the total experimental uncertainty of

RDF determination is a comparison of results obtained independently by X-ray diffraction [4].

K(r)4r2 j,kjk K4r2 jjo

28 000 24 000 20 000 16 000 12 000 8 000 4 000 0

C(1)-C(5) 5.07 4.20 C(1)-H(41)

5.20 C(1)-H(51)

5.24 C(4)-Cl

C(6)-Cl 7.78

1.12 C(1)-H(12)

1.76 C(1)-Cl C(1)-C(2)

1.54

C(1)-C(4) 3.91

4.11 C(3)-Cl

C(1)-C(6) 6.38 C(5)-Cl

6.76

0 1 2 3 4 r [A]^o 6

C(1)-C(3) 2.54

1.83 H(12)-H(13) 1.12

C(1)-H(12)

2.36 H(12)-Cl 2.18 C(1)-H(21)

2.77 C(1)-H(31)

2.70 C(2)-Cl

C(1)-C(2) 1.54

1.12 C(1)-H(12)

1.76 C(1)-Cl

r [A]^o

0 1 2 3 4

-2000 0 2000 4000 6000 8000 10 000

K(r)4r2 j,kjk Cl(1)

H(13)

C(1) C(2) H(31) H(32)

C(3)

H(21) H(22) C(4)

H(41) H(12)

C(5) H(51)

H(42) H(52)

C(6) H(71) H(72)

C(7)

H(61) H(62) C(8)

H(81) C(9)

H(82) H(92)

C(10) H(111) H(112)

C(11)

H(101) H(102) C(12)

H(121) H(91)

Cl(2)

H(122)

a)

b)

Figure 1. The experimental RDF of 1,12-dichlorododecane decomposed into its atomic peaks.

Acknowledgments: This work was supported by Grant NCN Opus Nr. Dec – 2013/09/B/ST4/03711

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[1] H. Drozdowski, J. Mol. Liquids 122 (1–3) (2005) 32.

[2] H. Drozdowski, Phys. Chem. Liquids 42 (6) (2004) 577.

[3] M. Śliwińska-Bartkowiak, H. Drozdowski,

M. Kempiński, M. Jażdżewska, Y. Long, J. C. Palmer, K. E. Gubbins, Phys. Chem. Chem. Physics 14 (19) (2012) 7145.

[4] H. Drozdowski, Acta Phys. Slovaca 54 (5) (2004) 447.

[5] Y. Long, M. Śliwińska-Bartkowiak, H. Drozdowski, M. Kempiński, K.A. Phillips, J.C. Palmer, K. Gubbins, Coll. Surf. A: Physicochem. Engineer. Aspects 437 (2013) 33.