Contents

1. Intention of FAQ
2. Generic questions(in Japanese)
3. F3 Input system
4. Input data
5. Parameters refined/fixed in Rietveld analysis
6. Results of Rietveld refinement
7. Superfluity

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1. FAQの意図

FAQとはインターネットの世界でよく使われる用語で,Frequently Asked Questionsの略です.ソフトウェアの使用法に関する質問のうち上位10数種に対する回答を公開しておけば,疑問点のほとんどが解決してしまう --- という経験則があります.また,マニュアルなどにきちんと記載してあることでも,どこに書いてあるのか見つけられない人やろくに読まずに質問を浴びせてくる人がきわめて多いのも事実です.

このページはリートベルト解析とRIETANの普及に資するとともに,わが身に断続的にふりかかってくる火の粉 --- 電話,手紙,メールよる質問の集中砲火とそれに伴う時間の喪失 --- を振り払うために作成しました.リートベルト法のユーザーばかりでなく私のためにも貢献してくれるのですから,本ホームページの目玉商品といってよいでしょう.

このように,個人,組織(大学,研究所など)が種々のデータ,知識,ノウハウなどを出し惜しみせずに発信するように努めれば,インターネットの世界は充実・拡大の一途をたどり,閉鎖社会や管理社会に風穴を開け,オープンかつ自由な社会を建設するのに貢献していくことでしょう.情報を一方的に受け入れるだけのブラックホールのような人ばかり多くなっては,WWWの健全な発展は望めません.重要な情報は独占し,もっぱら自己の利益に直結させるというのが,競争社会における鉄則でした.インターネットはこのような唾棄すべき「社会常識」を破壊する可能性さえ秘めています.

いろいろ迷った末,将来,本ホームページの英語版を作成する時に備え,FAQは英語で書くことにしました.初心者,とくに学生にとっては専門的な文章を英語で読むというのは,想像以上に敷居が高いようです.しかし,くたびれかけた(くたびれちゃった?)中年オジンには,英語・日本語版,両方とも書く気力などありません.どちらか一方を選ぶとなると,マニュアル同様,英語だということになってしまうのです.どなたか,翻訳してくださるボランティアはいらっしゃいませんか?

このページで私に答えてもらいたい質問,あるいはすでに解決済みだが他の方々にとって助けになりそうな疑問がございましたら,私あてに

をお送りください.一般的に役に立ちそうな質疑応答はこのFAQに追加します.

なお以下の英文では"β"は"beta","Å"は"A"と書かれています.日本語フォントでも英文フォントでも読めるようにするためです.多少読みにくいですが,ご容赦ください.

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2. Generic questions

Q: Can you help us use RIETAN by answering our questions?

A: No, basically. RIETAN can be obtained free of charge and redistributed without any permission, which is my pleasure. However, I will be very troubled if too many questions come with a rush. RIETAN is free, but service for a specific person is not my business because I am a researcher at a national institute. Part of users of RIETAN do not read various documents carefully and ask me questions directly, which is somewhat troublesome for me. The most important purpose of this FAQ, "Know-how and Techniques of Rietveld analysis," "Fundamental knowledge indispensable for Rietveld refinement," and a book entitled "A Practical Guide for X-Ray Powder Analysis --- Introduction to the Rietveld Method" is to reduce such questions as many as possible. Please send me any questions by mails and e-mails (never by phone!) after reading through FAQ, manuals, and various documents carefully. Attaching *.ins and *.int to mails would sometimes be helpful to me. Note that I may not answer them to secure enough time for my research. I am, nevertheless, willing to answer part of questions when they are related to bugs in RIETAN and when my collaborators request me to help them use RIETAN.



Q: To my regret, I lack crystallographic knowledge. How can I obtain fundamental knowledge of crystallography to use the Rietveld method?

A: Certainly, most students, scientists and engineers have hardly learned crystallography when they were students. This makes it difficult to apply the Rietveld method to various compounds in which they are interested. Please search for a person who is familiar with crystallography or an expert at Rietveld analysis. If you fail, it is a good idea to read three Japanese documents entitled "Fundamental experimental and crystallographic information indispensable for Rietveld refinement", "Know-how and techniques of Rietveld refinement", and "Stabilities of structures and evaluation for inorganic compounds". These texts were created for lectures at various short courses and graduate schools. They were converted to PDF files and distributed through this home page. I also recommend to read the following famous book

"The Rietveld Method," ed. by R. A. Young, Oxford University Press, Oxford (1993).

I wrote Chapter 13 of this book. Chapter 1 written by Young must be useful for obtaining minimum information about the Rietveld method. In addition,

F. Izumi, "The Rietveld Method and Its Applications to Synchrotron X-Ray Powder Data," in "Applications of Synchrotron Radiation to Materials Analysis," ed. by H. Saisho and Y. Gohshi, Elsevier Science, Amsterdam (1996), Chap. 7.

is very useful for those who wish to obtain fundamental information about the Rietveld method.



Q: What is the difference between Rietveld analysis and simulation of powder patterns?

A: Rietveld analysis is a pattern-fitting structure-refinement method where lattice and structure parameters are extracted from digital powder diffraction data using nonlinear least-squares methods. On the other hand, powder diffraction patterns are merely calculated from background, profile, structure, and other parameters and displayed/printed in simulation; no measured diffraction data are processed at all. Simulation is usually applied prior to Rietveld analysis to confirm the validity of a structural model.



Q: How can I analyze TOF neutron diffraction data taken on the Vega or Sirius diffractometer at KENS?

A: Refer to the page of RIETAN-2001T.

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3. F3 input system

Q: I believe that input files of RIETAN are too tedious. How can I shorten them?

A: I hate both hierarchic menu systems and fixed-column, formatted inputs, which is the reason why I developed the F3 (Flat, Flexible, and Friendly) input system. Menu operations are too tedious, regardless of user interfaces, for power users who analyze diffraction data by the Rietveld method routinely. Editing formatted input files is too old-fashioned and painful even for those who are familiar with various formats of FORTRAN. The F3 input system directly reflects my preferences for an input manner. In this innovative input system, a compromise is reached between the readiness to use and the compactness of input files. Nevertheless, you can cut comments lines starting with '#' or containing '!', and comments starting with ':'. They are usually removed by the preprocessor TINK, but you may delete them by yourself, of course. For example, the following lines

NBEAM = 0! Neutron powder diffraction.
NBEAM = 1: Conventional X-ray powder diffraction (characteristic X rays).
NBEAM = 2! Synchrotron X-ray powder diffraction.

may be replaced with

NBEAM = 1

Even inputting only '1' has not any problems; the part of 'NBEAM = ' is removed by TINK. Referring to the source code of rietan1.f, you can learn how to input only values of real and integer variables and characters with or without quotation marks. Because most data are input with list-directed input statements, you do not mind troublesome fixed-column formats in FORTRAN.



Q: Can I use Japanese, Chinese, or Hankul characters as comments?

A: Yes, you may. You can write any characters after '#', ':', or '!' used to show the beginnings of comments. This feature is very convenient not only for Asian people but other ones whose mother tongues are not English.



Q: Can I nest 'If ... then' and 'end if?'

A: No. I judged that nesting 'If ... then' and 'end if' blocks would make part of input files too complex for most users. If you use 'and' or 'or' in logical expressions between 'If' and 'then,' such nesting is not necessary in almost all the cases.



Q: What is the role of '}' in input files *.ins?

A: The preprocessor TINK judges that a series of input lines ends with '}.' In the several template input files distributed with RIETAN-94, pairs of braces '{' and '}' are included. Optional lines containing '{' are regarded as comment lines but useful to show the starting point of a series of input lines. For example, in the following lines

Imaginary species {
'M1' 'Ba' 0.633 'Nd' 0.367 /
'M2' 'Nd' 0.675 'Ce' 0.325 /
} Imaginary species

The first line is regarded as a comment line, two imaginary species are input in the second and third lines, and the fourth line is used to indicate the termination of imaginary species. The first line and a comment after '}' are optional.

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4. Input data

Q: In the Rietveld analysis of X-ray powder diffraction data, we must input appropriate chemical species from two or more ones, e.g., Ti, Ti2+, Ti3+, and Ti4+ for titanium. Which species should we choose?

A: The atomic scattering factors, f, of chemical species with different oxidation states are nearly the same except for those in a very low sinθ/λ region. The final solution would be essentially identical regardless of selected chemical species. It should also be indicated that chemical bonds are more or less of covalent character. Therefore, the selection of metals with somewhat lower oxidation states is more reasonable than formal ones. A similar discussion holds for anions; not O2- but O- is supplied in the database file asfdc.



Q: How can we input anomalous dispersion corrections in Rietveld analysis of synchrotron X-ray powder diffraction data?

A: I will show an example. If the real chemical species are input as

If NBEAM > 0 then
# Real chemical species and '/'.
   'Y'  'Ba'  'Cu'  'O' /
end if

the corresponding lines for anomalous dispersion corrections are

If NBEAM = 2 then
   # Read pairs of anomalous dispersion corrections, Delta-f' and Delta-f''
   -0.2670  2.0244  # Y
   -1.0456  8.4617  # Ba
   -1.9646  0.5888  # Cu
    0.0492  0.0322  # O
end if
for a wavelength of 0.1540520 nm (cf. International Tables, Vol. C, pp. 219-222). In this case, '}' is not required before the 'end if' line because the number of real chemical species is known: 4.



Q: What is "imaginary chemical species?"

A: "Imaginary chemical species" are used when dealing with solid solutions where two or more kinds of atoms occupy one site. Its atomic scattering factors f (X-ray diffraction) or coherent scattering lengths bc (neutron diffraction) are calculated from the fractions of constituent atoms. Defining such a species, we need to input only a group of structure parameters for a mixed-atom site. Of course, this feature is not effective when refining the occupation factors of constituent atoms.



Q: How can I determine a preferred-orientation vector?

A: The trial and error method is not very effective. Examining the tendency of integrated intensities in the reflection list (obtained when NPRINT > 0) in the output file is very helpful for the determination of the preferred-orientation vector. For example, if the observed integrated intensities of 00l reflections are larger than the calculated ones, the preferred-orientation vector may be [001] with the flat-plate cleavage plane. Similar procedures are required when determining the axis of anisotropic profile broadening; observed, calculated, and difference patterns must be very useful for learning this axis in this case. Anyway, preferred orientation is corrected only semi-empirically. Try to reduce the preferred-orientation effect as much as possible. The use of neutron powder diffraction is recommended to obtain accurate structure parameters if you fail in suppressing it.

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5. Parameters refined/fixed in Rietveld analysis

Q: What should we note in the input of refinable parameters?

A: The most important point is that fairly precise lattice parameters have to be input as initial parameters. With initial lattice parameters distant from real ones, the refined parameters are often trapped into false minima. In addition, initial profile parameters specific for your diffractometer and its setting conditions (e.g., focal-spot dimension, tube-specimen distance, slit widths, sample height, and monochromator) should be determined in advance using standard samples such as NIST SRM 640c (Si) and 674a (alpha-Al2O3, ZnO, TiO2, Cr2O3, and CeO2). With these initial parameters, you will be able to attain smooth convergence by setting NAUTO at 2 unless the final solution is trapped into a false minimum.



Q: What do Ds and Ts mean?

A: Ds is related to displacement of the specimen surface from the diffractometer axis of rotation. Ts is associated with the specimen-transparency aberration, which is caused by diffraction from below the surface of the specimen and asymmetrically broadens the profile. Refer to the following reference for both types of the aberrations:

W. Parrish, "International Tables for Crystallography," Vol. C, ed. by A. J. C. Wilson, Kluwer, Dordrecht (1992), pp. 48-50.

Z (zero-point shift), Ds, Ts, and lattice constants are highly correlated with each other and should be refined and/or fixed carefully by taking into account such high correlations. Rietveld analysis of a sample in which a standard sample such as NIST SRM 640c is mixed enables us to refine both lattice and peak-shift parameters by fixing the lattice parameters of the standard sample. The resulting highly accurate lattice parameters of the sample may then be fixed in a subsequent Rietveld refinement using intensity data of the pure sample. Such strict treatment is, however, seldom carried out.



Q: RIETAN can refine up to 12 background parameters. How should we determine the total number of refinable background parameters?

A: I increased the maximum number of background parameters to 12 so as to fit complex background patterns. For example, samples containing amorphous or very poorly crystallized compounds have usually "humps," which makes it hard to fit the background with a small number of background parameters. If the background changes smoothly and simply with 2θ, 6-8 background parameters are usually adequate. Increasing the total number of background parameters, more or less, decreases R factors, leading to higher correlations between background parameters despite the use of Legendre polynomials as a background function. If estimated standard deviations of background parameters are partly too large in comparison with their own values, the total number of background parameters must be decreased.



Q: Which lattice parameters should be refined when using RIETAN?

A: Two or more lattice parameters may be equal to each other, which depends on the crystal system. Refinable lattice parameters are listed below:

Crystal systemRefinable parameters
Cubica
Hexagonala and c
Rhombohedrala and alpha
Tetragonala and c
Orthorhombica, b, and c
Monoclinic (b-axis unique)a, b, c, and beta
Monoclinic (c-axis unique)a, b, c, and gamma
Triclinica, b, c, alpha, beta, and gamma

Other lattice parameters are constrained automatically, if necessary. Input correct values for the constrained parameters. For example, the b value in a tetragonal compound must be set equal to a.



Q: In general, there are two or more equivalent sites in the unit cell. Do we need to input structure parameters of all these sites?

A: No, only structure parameters of one site should be input. All the other equivalent sites are generated automatically by RIETAN using database files storing information on 230 space groups: spgri and spgra. It should also be pointed out that you need not input any translated positions in complex lattices, e.g., x+1/2, y+1/2, z+1/2 for a body-centered lattice. In connection with this question, it should be pointed out that, within a unit cell, (number of atoms occupying a site) = (occupation factor of the site) x (multiplicity of the site). Please check the numbers of atoms in the unit cell for all the sites in the output list after the refinement and confirm that they are right.



Q: What are differences among B, Q, Beq, betaij, and Uij?

A: These physical quantities are associated with thermal motion. Strictly speaking, the Debye-Waller factor is calculated from betaij and Uij with equations included in printer outputs (near the tail) created by RIETAN though B, Q, Beq, betaij, Uij, and the Debye-Waller factor are often referred to as "temperature factors." According to some documents of IUCr, they are designated as follows:

ParameterNameRemark
B/A2Isotropic atomic displacement parameterAssigned to each site
Q/A2Overall isotropic atomic displacement parameterB common to all the sites
Beq/A2Equivalent isotropic atomic displacement parameterConverted from betaij's
betaijAnisotropic atomic displacement parametersDimensionless
Uij/A2Anisotropic atomic displacement parametersUnit-cell dimensions are taken into account

Now, we must use the above authorized technical terms rather than the conventional words "temperature factor" and "thermal parameter." Q should be set at zero when B's and/or betaij's are assigned to each site (INDIV = 1). On the other hand, skip B's and/or betaij's when giving non-zero values for Q (INDIV = 0). Please note that Beq is not refined in Rietveld analysis but converted from betaij's after the refinement to estimate the degree of thermal motion when it is approximated to be isotropic. Uij's are more convenient than betaij's to consider the anisotropy of thermal vibration. It should also be noted that the International Union of Crystallography (IUCr) recommends to report not B but U (in the unit of A2) defined as U = B/(8 X pi2).



Q: How should I input fractional coordinates for special positions such as 1/3, 2/3, 1/2?

A: In that case, input 0.33333 33, 0.6666667, 0.5. Seven digits are enough because most real variables and arrays are implicitely declared as REAL*4 in RIETAN-2000. Never input approximate values such as 0.33, 0.67, 0.5, which will cause the generation of extra atoms in a unit cell because they are not regarded as overlapping with other equivalent atoms. Structure factors are, consequently overestimated.



Q: What are appropriate initial values of isotropic atomic displacement parameters, B?

A: You need not to be too nervous about inputting good estimates of atomic displacement parameters. Typically, 0.5 A2 for metals and 1.0 A2 for nonmetals. No serious problems usually occur with such values. It is also a good idea to use literature values of B for related compounds.



Q: Is there any useful tip in incremental refinement?

A: In general, parameters which are apt to diverge in least-squares calculations are not refined in early refinement stages but refined in later stages. Their estimated standard deviations are usually large. Such parameters include (1) structure parameters for atoms whose scattering amplitudes (atomic scattering factors or coherent scattering lengths) are small, (2) atomic displacement parameters, and (3) profile parameters related to anisotropic prifile broadening.



Q: How we should refine magnetic structures?

A: Please attach '*' just after the chemical species name of a magnetic atom, e.g., 'Fe*,' and input coefficients for the spherical spin-only form factor. Only collinear magnetic structures can be determined with RIETAN. Refer to "supple.doc" to learn how to input magnetic structure parameters.



Q: On what kinds of parameters can we impose linear constraints?

A: Linear constraints may be applied to structure parameters within one phase and profile parameters (U, V, W, P, X, Xe, Y, Ye, and As) between two or more phases. The latter constraints are usually used to set the profile parameters of two or more phases equal to each other. No linear constraints should be input for lattice parameters; such constraints (e.g., b = a in tetragonal and hexagonal systems) are applied automatically by the program. Linear constraints which should be imposed on anisotropic atomic displacement parameters, betaij's are compiled in

W. J. A. M. Peterse and J. H. Palm, Acta Crystallogr., Sect. A, 32 (1966) 751.

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6. Results of Rietveld refinement

Q: With X-ray diffraction data, we sometimes obtain negative isotropic atomic displacement parameters, B. How can I improve the accuracy of these parameters?

A: Such meaningless B values often result when contributions of some atoms to structure factors are relatively small. Please check the estimated standard deviations (e.s.d.'s) of negative B. You will find that their e.s.d.'s are considerably large. B parameters have usually large correlations with other refinable parameters including background parameters and occupation factors. The value of the profile cutoff also affects B values. These are reasons why the e.s.d.'s of B are usually large. The use of neutron powder diffraction, which is more favorable for the determination of atomic displacement parameters, is recommended in such cases. If you impose linear constraints on part of B's (i.e., set two or more B values equal to each other), you may be able to get a positive B value.



Q: Fairly high R factors results from my Rietveld refinement, but I cannot understand the reason. How should I do?

A: Have you analyzed your intensity data by setting NAUTO at 2? If it is the case, the first and often the best way to learn the reason for such a bad fit is to plot observed, calculated, and difference diffraction patterns. You may be able to know the reason instantly. In addition, please check whether or not initial lattice parameters are too distant from actual values. With inaccurate initial lattice parameters, final parameters are often trapped into false minima. In addition, please check whether your solution has been trapped into a false minimum by the conjugate-direction method, which often enables us to escape from the false minimum and reach the global minimum. The availability of this quite efficient direct-search method is a great advantage of RIETAN over other Rietveld-refinement program.



Q: R factors become much worse after changing the 2θ range of intensity data. Why?

A: In RIETAN, 2θ's used in the calculation of background intensities are normalized between -1 and 1. Therefore, background parameters optimized for the previous 2θ range are no longer effective after changing it, and you may fall into false minima. In such a case, setting NAUTO at 2 easily solves the problem because background parameters are refined again in the first cycle.



Q: With RIETAN, either of two different types of estimated standard deviations (e.s.d's) can be output. Which is better to report in scientific journals?

A: E.s.d's of variable parameters calculated in the conventional way are considerably underestimated and usually about two/three times larger than real standard deviations. However, no satisfactory method of calculating e.s.d's has yet been devised. Scott's method is far from perfect but may give e.s.d's that are much nearer to real values. Anyway, you had better quote Scott's paper:

H. G. Scott, J. Appl. Crystallogr., 16 (1983) 159.

when using his method because those who read your paper may misunderstand that parameters refined by you have too large e.s.d's.



Q: In printer outputs, the following R factors are written: Rwp, Rp, RR, Re, RI, and RF. Please explain how to calculate them.

A: R factors except for RR are defined in the following reference:

R. A. Young, "The Rietveld Method," ed. by R. A. Young, Oxford Univ. Press, Oxford (1995), p. 22.

RI ('R-Integrated intensity') is the same as RB if no magnetic scattering is observed. RR ('R-Rietveld') is calculated as 100Σi|yi(obs)-yi(cal)| / Σi|yi(obs)-Bi|, where yi and Bi are the total intensity and background at the i'th step, respectively.



Q: How low are satisfactory R factors?

A: The most important R factor is Rwp because its numerator is equal to the sum of weighted squares of residuals minimized in Rietveld analysis. Nevertheless its absolute value cannot be used as a measure of the goodness of fit because it varies with the background level and reflection intensities. Re is the minimum Rwp expected statistically. Then, S (= Rwp/Re) is conveniently used to estimate the goodness of fit. S values less than 1.3 are usually satisfactory.



Q: I want to plot Fourier maps using *.hkl files created by RIETAN but have not any programs for Fourier/D synthesis. Will you present such an application program in future?

A: Many scientists requested me to distribute a Fourier-synthesis program for RIETAN, but nobody was kind enough to present such a kind of program to me. I consulted with Dr. Shintaro Kumazawa of the University of Tsukuba about this problem. He is an expert in computer programing. His specialty is studies of electron/nuclear densities by the maximum-entropy method, having his own Fourier-synthesis program, fousyn, and a program for drawing electron/nuclear density maps, mevius. I requested him to combine a graphics subroutine library, PGPLOT, with mevius. Because PGPLOT libraries for several major operating systems are available free of charge, we can easily transport the resulting mevius program to various platforms. He has recently finished this task and provided me with the source and executable programs for the Macintosh. Refer to "Software" of his home page to get them.

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7. Superfluity

Q: Should we send you a postcard as recommended at the tail of each template file?

A: Yes and no. If you like RIETAN-2000 very much and are willing to encourage me to continue its development, please send me a postcard, which is then regarded as a kind of "hommage" to me. If you do not like RIETAN or are unconcerned about its future, you need not send a postcard to me at all. Anyway, everybody may use RIETAN regardless of sending postcards.

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