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苏 玉 长,石墨,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,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,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=h,2,A+k,2,B+l,2,C+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.,Indexing Programs,The methods currently implemented are shown bold.They are selected 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 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.,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.,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.,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/d,2,=(4 sin,2,Q,)/,l,2,Q can be represented as a quadratic form of the(hkl)s.,Q=h,2,A+k,2,B+l,2,C+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 powder pattern.Other forms are the angle,Q,or 2,Q,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 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 the 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 parameters,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 structure 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
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