The INDICIR program package is designed for solving the main problem of the first stage of X-ray diffraction analysis– determination of the polycrystal elementary cell by the X-ray diffractometry method. The basic ideas, realized in the algorithms and programs of the packet, are presented in the review [1], in the following publications [2] – [7], and in the methodical issues.

By the type of these algorithms all the programs can be divided into universal (INKGTROM, MONOKLIN, TRIKLIN, TRIKDUBL), special (INDSPEC, MONOK) ones and the program of processing the full-profile spectrum obtained by the angular-scanning method (INDPSE).

Universal algorithms suppose the presence in the small angle domain of reflexes with indices of general view (h, k, l). Special algorithms imply the filling of this domain with reflexes such as (hk0), (h0l) and (0kl). A characteristic feature of the spectra suitable for processing by the program INDPSE is the presence of wide diffraction maxima which in the first approximation can be described in the cubic system. Interpretation of the integral diffraction pattern should be started from the call to the program INKGTROM, which analyzes the set of interplanar distances {d_i} in the approach of cubic, tetragonal, hexagonal and rhombic systems. To set up the program in the proper mode the symbol n is used. To set up the program the n symbol is used presenting simultaneously a full number of reflexes in the experimental array: 1) n≤7 − the limitation by a cubic system, 2) n≤11− limitation by cubic, hexagonal and tetragonal cells, 3)   n≥12 − analysis of all the systems from the cube to the rhomb inclusive.

In the cases when the reflex array does not reach required sizes its completion is admitted by replication of a minimum element {d_i}. To handle the program there used are the symbols vmax and dq presenting the limiting volume of an elementary cell and the absolute identification error 1/d²_exp − 1/d²_cal, respectively. In the case of giving vmax=0 its value is determined automatically, but the time of calculations can be increased. It is recommended to limit v=max in the case of indexing the diffraction patterns to a high accuracy.

An approximate value of dq can be determined starting from the order of the last digit in the fractional part of d_exp:

dq≤.0001 − the third digit arises beginning from d<5. For example, d=4.957.

dq≤.0003 − the third digit arises for d≤4. For example, d=3.934.

dq≤..0005 − the three-digit fractional part begins from d≤3.

q≤.001 − the third digit arises only for d≥2 or do not arise at all.

The operator can exceed the recommended values of dq. Then, as a rule, the invalidations of some identifications p_i and the absolute errors of the elementary cell parameters are increasing.

The program is not related by the strict single-phase conditions, therefore the diffraction indices can not attached to the reflexes. Near these reflexes the message «no index» and the nearest calculated value d_cal are printed. After receiving such message one should consider the following variants:

1. The `singled-out reflex does not refers to the main phase of the material under investigation;
2. The value of vmax is  excessively limited
3. The corridor of dq identification is too “narrow”. The closeness of experimental and calculated values of d argues in favor of this supposition. If this is the case, one should not overly expand dq; the obtained result can be lost. It is more correct to generate the whole spectrum using the preset periods of the elementary cell.
4. The investigated material is referred to the monoclinic or triclinic system.

The input information

 is presented by the known symbols n, vmax and dq, as well as, by the set of interplanar distances d_i.

The calculation results contain (Dexp., Dcal., d(D), h, k, l, p)_i, i=1,…n, i.e. the experimental and calculated d values, the difference between them, the diffraction indices and the invalidation factor in %. In conclusion printed are the periods of the elementary cell, its volume and the validation criterion of the obtained result.

Estimating the performed indexing one should try to get the value of d(D) not exceeding the unity in the last sign of d_exp., and the invalidation factor p_i (%) <<100.

If any varying of vmax and dq did not gave the correct results one should pass to the analysis of the diffraction pattern in order to determine whether the investigated material belongs to the monoclinic system. Such analysis is performed with the help of the programs “MONOKLIN”, “MONOK” and “INDSPEC”.

The first of these programs supposes the presence, in the small-angle spectral region, of   reflexes with the indices of a general form (hkl).  This is possible if the elementary cell periods are approximately equal. The algorithm, realized by this program belongs to the algorithm of a universal type. Generally the required number of reflexes does not exceed 16.

The above mentioned recommendations hold their validity, however, the passage to the lower symmetry requires a higher accuracy: the use of dq=.001 involves some problems.

Preparation of the input information is performed similarly to the foregoing case. The calculated monoclinc cell is presented in the arrangement B.

 If the results obtained at this stage do not satisfy then, besides the above-mentioned causes one should verify the possibilities of filling the small-angle region with reflexes (hk0), (0kl) or (h01). These verifications are performed by the programs MONOK and INDSPEC, respectively. The mentioned spectrum feature takes place when one of cell periods significantly exceeds two other. Therefore, it is necessary to introduce an additional quantity amax – a maximum value of the prolonged period. This value should satisfy the condition amax>(vmax)^1/3. The programs MONOK and INDSOEC are divided into two stages – analysis and selection of the planar inverse cell; the calculation of the three-dimensional Bravais parallelepiped. In the case of MONOK the planar cell is orthogonal. In the case of INDSPEC the planar cell is oblique. In connection with the latter fact this program can be used for the interpretation of the spectra of monoclinic and triclinic polycrystals. In this case the code-delimiter is one more additionally introduced quantity m=1 (monoclinic crystal), m=2 (triclinic crystal).

There are two universal programs for the analysis of triclinic polycrystals – TRIKLIN and TRIKDUBL. The indexing should be started by using the program TRIKLIN, which in most cases provides reasonable results. The object of calculations for this program are the spectra {d}_i, the small-angle elements of which have no great differences. For example, d₁=4.92, d₂=4.49, … . If   such differences take place, for example, d₁=10.2, d₂=4.34…, it is recommended to apply the   program TRIKDUBL. The analysis of the second-kind spectra can be also performed by the program TRIKLIN, but then the calculations may be too long.

Functionally, the program TRIKDUBL is based on the cyclic duplication of some stages of the algorithm TRIKLIN and operates enough reliably by determining the elementary cells of great volumes.

The recommended number of reflexes processed by these programs is 20. Sometimes, if the presence of a systematic error is possible this number may be decreased to n=12.  

As is noted above, the subject of investigation for the program INDPSEV is a full-profile diffraction spectrum recorded/in the mode of angular step SCAN. In the case of pseudocubic polycrystals this spectrum represents the wide diffraction maxima, which can be explained, to a first approximation, as reflexes from the cubic material with the period A. “Broadening” of these maxima ocurs as a result of A splitting into the periods of the tetragonal, rhombic or monoclinic cells: a=A/n, b=A/m, c=A/p with an angle β≈90º. Here m,n,p take, independently of one another, the integer values 1,2… .

A more precise definition of elementary cells and their subsequent selection is performed by the minimum value of the invalidation criterion.

Preparation of the input information begins from the line “NA, ghag iha alfa1 alfa2 iter amax”. Here

NA – number of scanning pitches, i.e. number of pairs (2Teta, Intens.)_k, where k=1,…NA;

ghag  - scanning pitch in degrees;

iha – minimum quantity of “points” above the background, which are interpreted as a diffraction maximum;

alfa1, alfa2 – are the doublet radiation components;

iter – number of iterations;

amax – maximum period of a pseudocube.

The following parcel of information corresponds to the standard output of the X-ray diffractometer and consists of the pair {2Teta, Intens}_k, where K=1,…,NA. This array should be recorded by skipping the background areas, i.e. by dividing the whole spectrum into the separate zones. A signal for passing to the next zone is the break between the nearest 2Teta, exceeding 2 ghag.

 At the program output printed are: list of computed zones, system, 2Teta split singlets, their intensities and Bravais cell periods.

When all the programs are operating, at the desktop the window opens permitting to observe the in-process computation. When the program operates normally, in the window a current value of the criterion of validation (or invalidation in the case of INDPSEV) is displayed. If such information is not displayed it means, most likely, that an error has been made during preparation of the initial information. A fast program stop usually occurs because of the erroneous definition of vmax and amax. Reliable limitations of these values provide a rather quick solving of the problem. The most laborious tests at a 1.8 GHz CPU clock were computed during the time not exceeding 5 min.

The Application INDICIR.ZIP contains 7 program directories, each of which comprises four files. Two of them − exe and txt − are the work files. Two other represent a test information suite.

REFERENCES

1. Serykh V.P. Zavodskaya laboratoriya. 2001. T.67. No 67. No1. P20. (in Russian)
2. Serykh V.P., ibidem. 2002. No10. V.68. P.32.
3. Serykh V.P., ibidem. 2004. No10. V.70. P.28.
4. Serykh V.P., Serykh L.M., ibidem. 2007. V.73. No3. P.45.
5. Serykh V.P., Serykh L.M.,  ibidem. 2007. V.68. No10, P.32.
6. Serykh V.P., Kristallografiya. 2002. V.47. No3. P.415. (in Russian)
7. Serykh V.P., Kristallografiya. 2005. V.50. No4. P.588

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