利用异常X射线散射对无序材料结构表征的新应用

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"《新型异常（共振）X射线散射在无序材料结构表征中的应用》是Yoshio Waseda撰写的一本物理学术著作，由Springer-Verlag出版社于1984年出版。这本书探讨了利用异常X射线散射技术来分析和理解无序材料的结构特性。" 在物理学领域，尤其是在材料科学中，对无序材料的研究具有重要的意义。无序材料通常指的是那些原子排列不规则或无晶格结构的材料，如玻璃、非晶态金属、高分子材料等。这些材料的性质往往与有序材料大相径庭，因此理解和表征它们的微观结构是一项挑战。异常X射线散射（Anomalous X-ray Scattering, AXS），也称为共振X射线散射，是一种利用X射线与物质相互作用时发生的能量依赖性散射现象来获取材料内部信息的技术。当X射线的能量接近材料内特定原子的吸收边缘时，散射截面会出现显著变化，这就是所谓的“异常”。这种技术可以提供关于材料中原子位置、电子密度分布以及化学环境等信息。 Waseda教授在这本书中详细阐述了如何运用异常X射线散射技术进行无序材料的结构表征。他可能涵盖了以下关键知识点： 1. 异常X射线散射的基本原理：包括X射线的吸收和散射机制，以及能量依赖性的物理基础。 2. 无序材料的结构特点：讨论无序材料与有序材料的结构差异，以及这些差异对材料性能的影响。 3. 实验方法和技术：介绍如何设计实验以优化AXS测量，包括X射线源的选择、探测器的使用以及数据处理方法。 4. 数据分析和结果解释：解释如何从散射数据中提取结构信息，包括各种参数的计算和解析模型的应用。 5. 应用实例：展示AXS技术在无序材料研究中的具体应用案例，可能包括不同类型的无序材料，如非晶合金、高分子复合材料等。 6. 挑战与未来趋势：分析AXS技术在实际应用中面临的挑战，以及未来的发展方向和技术进步。这本书对于理解无序材料的微观结构以及开发新的表征方法具有很高的学术价值，适合材料科学家、物理学家和工程师阅读，有助于推动无序材料研究领域的进步。

O-IAPTER 3

DEFINITION OF PARTIAL STRUCIIJRE FACTORS /~D ~ITIONAL SHORT

Rnbr~ ORDER (CSRO)

Sincethe surrounding of each atom in disordered materials are

generally different from those of other atoms as easily seen in

Fig.2.1(a), the interpretation of RDF for the multi-component case is

more complicated. In this respect, the partial RDFs for the individual

pairs of chemical constituents are of particular importance and almost

the only unique items for quantitatively describing the atomic scale

structure of multi-component disordered materials. The partial radial

density function Pij(r) can mathematically defined by,

NiN5 ÷ ÷ ÷

Pie (r) = ejPogij (r) =@E E~{r-(re-r~) } - ~ ~ (~

(3.1)

where N i is the number of i-type atoms in the volume V and gij(r) is

the so-called partial pair distribution function. The surrrnation of i

and j over the chemical constituents whereas the summation of sand

is over all atoms in the system. The following relations have also

been used.

CiPij (r) = cjpji(r)

(3.2)

NiPij (r) = Njpji(r)

(3.3)

Therefore it follows irrrnediately that gij(r) = gji(r). Since the long-

range atomic correlations disappear in disordered materials such as

liquids and amorphous solids, the probability of finding a pair of

atoms, of course, approaches the average value with an increase in

distance. Thus,

-- = C.p gij (r) + I (r + ~) (3.4)

Pij (r) ÷ V 3 o

Hence, the basic features of the partial RDFs themselves are very

similar to those of the RDF for the simple case containing only one

kind of atoms. However, the number of partial RDFs, corresponding to

the possible atomic pairs, drastically increases, as the number of

constituent atoms in the system increases. It follows that there are

n(n+l)/2 possible pairs in the system containing n-components and thus

three partial RDFs in a binary system and six partial RDFs in a

ternary system are required to describe completely the atomic scale

structure in disordered materials.

The partial RDF is known to connect with the partial structure

factor (often called partial interference function) of corresponding

pair correlation determined from the diffraction experiments of x-rays

and neutrons. However, the definition of the partial structure factors

are not unique and three different equations have been used in the

literature, although they are combined by linear relations (see for

example, Waseda 1980). For convenience, the essential points of these

different sets of the partial structure factors are given below, using

a binary disordered system as an example.

Let us consider a binary disordered material containing two types

of atoms, 1 and 2. Thus three different partial RDFs, related to

Pll(r), P22(r) and Pl2(r), are required to describe this structure.

The total number of atoms N in a volume V consists of N 1 and N 2 where

N I and N 2 are the number of atoms 1 and 2 and then the atomic frac-

tions are defined by c 1 = N1/N and c 2 = N2/N , respectively. The

coherent x-ray scattering intensity IC°h(q), analogous to ~ eq.(2.5) may

be written by the following form.

2 .÷ -~ 2> 2 ÷

IC°h(q) = fl<IE exp(-lq'rij) ] + f2<l~2exp(-i~-r2k ) 1 2

k=l

N I N2 -~ ÷ +

+ 2flf2< £ ~ exp(-iq- (rij-r2k) }>

j=l k=l

(3.5)

Here, the q-dependence of the atomic scattering factor fi(q) is

excluded for simplification, because it depends only upon the intra-

atomic interference effect. The three double sums in eq.(3.5) corres-

ponds to the partial structure factors of the respective atomic pairs,

1-1, 2-2 and 1-2.

Faber and Ziman (1965) used the following definition, analogous

to eq.(2.14), for the partial structure factors aij(q);

aij (q) = I + Pol~i " (r)-1] exp(-i~-~)d~

(3.6)

Excluding the forward scattering term, the Faber-Ziman (hereafter

tion. Using eqs.(3.13) and (3.18), the following relation could be

made regarding the total structure factors:

_ ClC2(fl-f2 )2

SAL(q) - 1 <f>___22 - I (3.20)

aFZ(q) - I <f2> <f2>

Thus,

SAL (q) < aFZ (q)

SAL (q) = aFZ (q) = I

SAL(q) > aFz(q)

when aFZ(q) > I

when aFZ(q) = I I (3.21)

when aFZ(q) < I

An additional set of partial structure factors were proposed by

Bhatia and Thornton (1970). Their approach provides a useful link

between the mean square thermal fluctuatio~ in local number density

and concentration in disordered materials on the one hand and macro-

scopic thermodynamic properties on the other, which is strictly

correct only in the long wavelength limit (q+0). However, the Bhatia-

Thornton (hereafter referred to as BT) partial structure factors

themselves correspond to the Fourier transforms of the mean square

fluctuations in the particle number, the concentration and their cross

term. This formalism is superior to the FZ and AL forms, when dis-

cussing.several specific topics of disordered materials such as the

relation between structure and thermodynamic quantities or some kinds

of atomic ordering effect arising from different physico-chemical

properties of Constituent atoms in multi-component system. The

detailed description for the BT partial structure factors and their

physical significance in the long wavelength limit are given in

Appendix 1 for future reference. However, we give here some essential

points of the Bhatia and. ThorntonVs expression for comparison with the

FZ or AL f0rm.

Bhatia and Thornton (1970) proposed three partial structure fac-

tors SNN(q) , SCC(q) and SNC(q) using the concept of the local fluctua-

tions in disordered materials. SNN(q) is the spatial correlation

between number density (related to the topological arrangement of

atoms) and its Fourier transform corresponds to the usual RDF. S(x:(q)

is the correlation of the concentration fluctuation for chemical con-

stituents and its Fourier transform gives the so-called radial concert-

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