1. BASIS FOR THE UNIFORM DESCRIPTION AND ORDERING OF CHEMICAL AND MINERAL COMPOSITIONS OF GEOLOGICAL OBJECTS
Tomas Petrov, and Natalia Krasnova
(Saint-Petersburg State University, Saint Petersburg, Russia)
rambler.ru;

2. Some epigraphs:
“The stability means absence of ideas”
Igor Huberman
“Using to think as before, you will receive former results” Patrick K. Porter
“Our first duty in this world is to settle arbitrary islands of order and system”
Norbert Wiener

3. The universal system for display of chemical and mineral compositions on the basis of information RHA language was worked out by Tomas Petrov since 1971, but its application stayed too long because of absence of appropriate computer software. Now the work using the RHA method is provided by the program Petros-2, author S. Moshkin (
RHA method gives the possibility for unique uniform description, systematisation and classification of compositions, their grouping, creation of databanks, and search of materials in them, and also for the decision of some mineralogical, geochemical and petrologic problems.

4. It is obvious that the composition is primary as a necessary condition of object’s occurrence. Therefore the composition as a mix of atoms or molecules (minerals) is accepted for the basis of universal substantial classifications of objects Depending on selected RHA components it is a system of co-ordinates in the whole chemical or mineral space. On a set of opportunities the RHA method has no analogues in the scientific literature known to us.
The description of any analytical data in RHA system consists of three components: R – rank formula; H – information entropy, which was defined by Shannon, is a measure of complexity; A – anentropy, which was defined by T. Petrov, is a measure of purity of composition - the negative mean of concentration’s logarithms. Using the R, H, and A, which can serve as a “object’s composition passport”, all objects can be simple (monosemantically) classified.

5. For lamprophyllite Na3Sr2Ti3(Si2O7 )2O3 (OH)
Rank formula - R is a sequence of symbols of components (chemical elements or minerals) on decreasing atomic % or, correspondingly, mol. %. R is identical to result of ordering of chemical elements on decrease of the sums of all their coefficients in crystal-chemical formula, without taking into account the valence of elements or their site position.
For lamprophyllite Na3Sr2Ti3(Si2O7 )2O3 (OH)
the R is: O Si Na= Ti Sr H
For osumilite-(Fe) K0.75Na0.25Fe2+1.5Mg0.5Al2.25Fe3+0.75Si9Al3O31
the R is: O Si Al Fe K Mg Na

6. Let’s show the example of calculation of R for paragonite
SiO2 TiO2 Al2O3 FeO Fe2O3 MnO MgO CaO Na2O K2O H2O+ H2O– Total
Rank formula of given analysis is a set of element symbols ranked in order of decreasing atomic %
O Si= Al H Na K Fe Ca Mg Mn Ti
Atomic coefficients calculated on the basis of 12 (O, OH)
– –
RHA system represents a way to curtail the information on rather full analyses, id est., is the integrated description of composition for the n first main components. Standard length of R is equal 10 for chemical- and 3-5 for mineral compositions.

7. For linear ordering of RHA-data R is accepted for a “word” in which symbols of components play a part of “letters”. The alphabet for chemical compounds is the Periodic Table, and for mineral mixtures (e.g. rocks) – a sequence of theoretical mineral composition in their chemical R classification. As a result a simple (monosematic), hierarchically and dictionary ordered classification of any composition set with increase of average atomic (or molecular) weights from the beginning to the end of a sequence is created.

8. Fragment of RHA table for chemical composition of phlogopites
Здесь видна структура упорядочения по первому – внутри – по второму. Знаки равенства

9. The RHA method enables decisions of following tasks: 1) for express diagnostics of object by results of its chemical and / or mineral analysis:

10. 2) for unequivocal specification of limits between chemical varieties of objects on presence of changes in their R (e.g. on rearrangements of elements). A good example of mineral nomenclature:
A possible specification of limits between ijolites and clinopyroxenites
Символов в формулах

11. 3. for improving of object’s nomenclature, in particular, for revealing synonyms or specification of structural differences at identity of their chemical composition, and to work out the general recommendations at confirmation of names to new objects (minerals, rocks) or updating of limits for application of old terms.
? Mn > Fe ?

12. Which principles where used for the nomenclature of holmquistite
minerals? Why magnesioholmquistite contains less Mg than the simple holmquistite?

13. In this fragment of detail R-classification of clintonites one can see the alternation of the name clintonite with synonyms

14. 4) for creation of some more detailed chemical classifications for separate groups of objects, and also to predict existence of new species.
Fragment of perovskite group R-classification
(analyses after Chakhmouradian and
Mitchell, 1997)

15. 5) for calculation of representativety, variability and novelty of the given group of compositions of natural objects.
Individual RHA catalogues of chemical composition for some groups of minerals were created (see Table).

16. In addition the R-catalogue of chemical composition of all minerals available in Mineralogical Database (its address: containing 4614 descriptions was compiled. In more than 75 % of cases it is possible to determine the name of a mineral directly by its chemical composition.
6) for uniform ordering and comparison of compositions, both minerals and rocks, and any other mixes of substances, i.e. for creation of the uniform, general for all national languages, catalogue of chemical composition of any objects.

17. For creation of R-mineral rock’s classification (CRmin) the sequence of minerals ranked in line on decreasing their molecular contents, i.e. Rmin, is accepted as a “word”, in which the minerals play a part of “letters”. Sequence of theoretical composition of minerals in the chemical R-catalogue is applied as the alphabet for ordering of this Rmin’s in a column.

18. Tables of RHA-descriptions of some rock types are submitted on the site
The listed opportunities of RHA method give the possibility to recommend it as a search attribute of substantial object’s composition at organisation of databanks for chemical composition of geological objects, and at creation of the uniform information system serving museums of a natural-historical specialisation.

19. As a result of postulating by D
As a result of postulating by D. Mendeleev in 1869 of the periodic law chemistry got the uniform method for ordering of chemical elements. RHA method provides the uniform hierarchic ordering of description for the chemical and mineral compositions of any objects by the same principle of periodicity and monosematicy.
Method is described in the book “Information-component analysis. RHA method.” Authors: Petrov T.G. & Farafonova O.I., S. Petersburg, 2005 (in Russian).
Everyone can be convinced of ample opportunities of method’s application itself, it is only necessary to begin!

20. Thank you for attention!