第6章_衍射花樣指數(shù)化與應(yīng)用概述.ppt

1、衍射花樣指數(shù)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

2、 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,g) and individual Miller indices (hkl) for each line. The form of equations to solve is complicated for th

3、e general case (triclinic) in direct space but is straightforward in reciprocal space. In the latter the set of equations is：,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 a

4、re 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

5、 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 relate

6、d 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 se

7、lected through the item Indexing in the main menu. ProgramAuthorType ITOVisseranalytical TREORWernerexhaustive 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 im

8、mediately 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

9、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.,Reciprocal Space Direct space

10、 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.,Lattice constants A set of maximally six floating numbers representing the unit cell. As crystal symmetry grows the number o

11、f lattice constants needed to describe the metrics of a unit cell reduce. In the cubic system there is only one constant.,Q-value The Q-value is one of several possible forms to represent the positional information of peaks in powder pattern. They are defined as: Q = 1/d2= ( 4 sin2Q)/l2 Q can be rep

12、resented as a quadratic form of the (hkl)s. Q = h2A + k2B + l2C + hk D + hl E + kl F, where A, B, C, D, E, F are related to the lattice constants. In ITO each Q-value is multiplied by 10000.,d-Spacing The d-spacing is one of several possible forms to represent the positional information of peaks in

13、powder pattern. Other forms are the angle Q, or 2Q, or Q-values. Win_DIFFRAC assumes input in the form of d-spacings. They are internally converted, e.g. ITO works only with Qs.,TREOR This program uses the exhaustive approach. It is widely used for indexing of powder pattern throughout the world and

14、 is believed to be one of the most powerful engines for solving high and medium symmetries. It is useful as well for low symmetry at the cost of rather high time consumption.,We recommend that you start with a diffraction pattern whose result is well known to you. If you are already familiar with th

15、e TREOR program you may decide to straightforward indexing , using the default parameters. In case you are a novice user you should swiftly go through the parameters and change settings only when they are obviously wrong. With the results obtained you may then turn to the more sophisticated paramete

16、rs, e.g. Select Baseline Set. The parameters are described in detail under general and TREOR-specific parameters.,In contrast to ITO a multitude of non-systematic extinctions among the first lines may not appreciably affect the power of trial-and-error methods. However, powder indexing is not like s

17、tructure analysis, which works well on good data, and will usually get by on poor data given a little more time and attention. Powder indexing works beautifully on good data, but with poor data it will usually not work at all. (op.cit Ref.4).,The standard procedure using TREOR is to start with the h

18、igh symmetries: cubic, tetragonal, hexagonal and orthorhombic in one run. Next the monoclinic symmetry should be tried. More than one run may be necessary, successively increasing the number of baseline sets, the cell volume and cell edge. If the formula weight and density are known, they should be

19、used. The CPU-time needed will then usually be strongly reduced. Unfortunately they are mostly not well known and therefore not often usable. If all previous tests have failed the triclinic test remains for which in general we recommend ITO.,Analytical Approach The crystal is assumed to be triclinic

20、. Solutions are approached in three steps. In the first, one tries to find reasonable zones from the diffraction data. Each pair of lines, together with the origin forms a crystallographic zone. A zone is relevant to the solution finding algorithm if some other diffraction lines lie on it, if not it

21、 is discarded. In the second step the best zones are then tried in combinations to find complete lattices. This method is known as the ITO method. Once a lattice is found that satisfies the experimental d-spacing data, the geometry of the lattice is examined for possible higher metric symmetry. This

22、 is the final step.,衍射分析應(yīng)用,物質(zhì)對(duì)射線的衍射產(chǎn)生了衍射花樣或衍射譜，對(duì)于給定的單晶試樣，其衍射花樣與入射線的相對(duì)取向及晶體結(jié)構(gòu)有關(guān)；對(duì)于給定的多晶體也有特定的衍射花樣。衍射花樣具有三要素：衍射線（或衍射斑）的位置、強(qiáng)度和線型。測(cè)定衍射花樣三要素在不同狀態(tài)下的變化，是衍射分析應(yīng)用的基礎(chǔ)。,衍射分析應(yīng)用,基于衍射位置的應(yīng)用 點(diǎn)陣參數(shù)的精確測(cè)定，膨脹系數(shù)的測(cè)定； 第一類（即宏觀殘余）應(yīng)力的測(cè)定； 由點(diǎn)陣參數(shù)測(cè)定相平衡圖中的相界； 晶體取向的測(cè)定； 固溶體類型的測(cè)定，固溶體組分的測(cè)定； 多晶材料中層錯(cuò)幾率的測(cè)定； 點(diǎn)缺陷引起的Bragg峰的漂移。,衍射分析應(yīng)用,基于衍射強(qiáng)度測(cè)

23、量的應(yīng)用 （1）物相的定量分析，結(jié)晶度的測(cè)定 (2) 平衡相圖的相界的測(cè)定； (3) 第三類應(yīng)力的測(cè)定； (4) 有序固溶體長(zhǎng)程有序度的測(cè)定； (5) 多晶體材料中晶粒擇優(yōu)取向的極圖、反極圖和三維取向分布的測(cè)定； (6) 薄膜厚度的測(cè)定。,衍射分析應(yīng)用,基于衍射線型分析的應(yīng)用 (1) 多晶材料中位錯(cuò)密度的測(cè)定，層錯(cuò)能的測(cè)定，晶體缺陷的研究； (2) 第二類（微觀殘余）應(yīng)力的測(cè)定； (3) 晶粒大小和微應(yīng)變的測(cè)定；,衍射分析應(yīng)用,基于衍射位置和強(qiáng)度的測(cè)定 (1) 物相的定性分析 (2) 相消失法測(cè)定相平衡圖中的相界; (3) 晶體(相)結(jié)構(gòu),磁結(jié)構(gòu),表面結(jié)構(gòu),界面結(jié)構(gòu)的研究,衍射分析應(yīng)用,同時(shí)基

24、于衍射位置、強(qiáng)度和線型的Rietveld多晶結(jié)構(gòu)測(cè)定 需輸入原子參數(shù)（晶胞中各原子的坐標(biāo)、占位幾率和濕度因子）、點(diǎn)陣參數(shù)、波長(zhǎng)、偏正因子、吸收系數(shù)、擇優(yōu)取向參數(shù)等。,衍射分析應(yīng)用,Rietveld profile refinement What is the Rietveld method? A comprehensive, computer based method fro the analysis of X-ray and neutron powder diffraction patterns by least squares fitting of a calculated diffraction pattern to the observed