中南大学：《X射线衍射分析技术——晶体X射线衍射学基础》X-Ray与电镜_第6章 衍射花样指数化与应用概述（苏玉长）

衍射花样指数化 苏五长 有一太

苏 玉 长 衍射花样指数化

The first step in analysing unknown powder pattern is often an attempt to find a unit cell that explains all observed lines in the spectrum You do not need additional crystallographic data, although if it exists it makes for faster and more reliable results The material to be analysed must be single phased and the experimental material must be very accurate 苏五长 有一太

苏 玉 长 The first step in analysing unknown powder pattern is often an attempt to find a unit cell that explains all observed lines in the spectrum. You do not need additional crystallographic data, although if it exists it makes for faster and more reliable results. The material to be analysed must be single phased and the experimental material must be very accurate

Indexing programs use only the positional information of the pattern and try to find a set of lattice constants(a, b,c, a, B,y)and individual Miller indices (hkl) for each line The form of equations to solve is complicated for the general case(triclinic)in direct space but is straightforward in reciprocal space. In the latter the set of equations is 苏五长 有一太

苏 玉 长 Indexing programs use only the positional information of the pattern and try to find a set of lattice constants (a,b,c,a,b,g) and individual Miller indices (hkl) for each line. The form of equations to solve is complicated for the general case (triclinic) in direct space but is straightforward in reciprocal space. In the latter the set of equations is：

Q=hA+kB+1 C+ hkD+ hIE kIF where the Q-values are easily derived from the diffraction angle (. This set has to be solved for the unknowns.ABC.de f which are in a simple way related to the lattice constants. Finding the proper values for the lattice parameters so that every observed d-spacing satifies a particular combination of Miller indices is the goal of indexing. It is not easy even for the cubic system but it is very difficult for the triclinic system 苏五长 有一太

苏 玉 长 Q = h2A + k2B + l2C+ hkD + hlE + klF where the Q-values are easily derived from the diffraction angle Q. This set has to be solved for the unknowns, A, B, C, D, E, F, which are in a simple way related to the lattice constants. Finding the proper values for the lattice parameters so that every observed d-spacing satifies a particular combination of Miller indices is the goal of indexing. It is not easy even for the cubic system, but it is very difficult for the triclinic system

There are two general approaches to indexing, the exhaustive and the analytical approach. Both of these approaches require very accurate d-spacing data. The smaller the errors the easier it is to test solutions because there are often missing data points due to intensity extinctions related to the symmetry or the structural arrangement or due to lack of resolution of the d-spacing themselves The earliest approaches were of the exhaustive type and were done by graphical fitting or numerical table fitting 苏五长 有一太

苏 玉 长 • There are two general approaches to indexing, the exhaustive and the analytical approach. Both of these approaches require very accurate d-spacing data. The smaller the errors, the easier it is to test solutions because there are often missing data points due to intensity extinctions related to the symmetry or the structural arrangement or due to lack of resolution of the d-spacing themselves. The earliest approaches were of the exhaustive type and were done by graphical fitting or numerical table fitting

Indexing programs The methods currently implemented are shown bold. They are selected through the item Indexing in the main menu Program Author Type ITo Visser analytical TrEoR Werner exhaustive POWDER DICVOL CUBIC 苏五长 有一太

苏 玉 长 • Indexing Programs • The methods currently implemented are shown bold. They are selected through the item Indexing in the main menu. • Program Author Type • ITO Visser analytical • TREOR Werner exhaustive • POWDER • DICVOL • CUBIC

The programs use a set of common parameters, e.g. the wavelength and a method specific set. After you have clicked on a program with the left mouse button indexing is immediately started with the active parameter set. Depending on the problem and computer type the program run can take from seconds to many minutes. All solutions are computed and stored internally The"best" one is displayed at the top of the screen. the next to best at the bottom for an overview of all solutions select solutions in the main menu 苏五长 有一太

苏 玉 长 • The programs use a set of common parameters, e.g. the wavelength and a method specific set. After you have clicked on a program with the left mouse button indexing is immediately started with the active parameter set. Depending on the problem and computer type the program run can take from seconds to many minutes. All solutions are computed and stored internally. The "best" one is displayed at the top of the screen, the next to best at the bottom. For an overview of all solutions select Solutions in the main menu

Miller Indices Triplet of integer numbers uniquely assigned to a Bragg reflection. The notation is usually in the form of(hkl). Formally spoken. Miller Indices represent coordinates of lattice points in reciprocal space 苏五长 有一太

苏 玉 长 • Miller Indices Triplet of integer numbers uniquely assigned to a Bragg reflection. The notation is usually in the form of (hkl). Formally spoken, Miller Indices represent coordinates of lattice points in reciprocal space

Reciprocal Space Direct space is composed of unit cells and its contents whereas reciprocal space is a lattice whose lattice points are Bragg reflections. Direct and reciprocal space are ghtly coupled 分 苏五长 有一太

苏 玉 长 • Reciprocal Space Direct space is composed of unit cells and its contents, whereas reciprocal space is a lattice whose lattice points are Bragg reflections. Direct and reciprocal space are tightly coupled

attice constants A set of maximally six floating numbers representing the unit cell. As crystal symmetry grows the number of lattice constants needed to describe the metrics of a unit cell reduce. In the cubic system there is only one constant 分 苏五长 有一太

苏 玉 长 Lattice constants A set of maximally six floating numbers representing the unit cell. As crystal symmetry grows the number of lattice constants needed to describe the metrics of a unit cell reduce. In the cubic system there is only one constant