# Metallurgist (v.61, #3-4)

The reduction in the specific consumption of deoxidizers in a furnace is due to the effective use of the reducing energy of the gas flow. The efficiency of the reduction processes can be increased by optimizing the BF charging parameters. A numerical procedure for BF charging optimization is developed using a mathematical three-factor model based on the performance analysis of blast-furnace smelting. The optimization procedure based on regression and correlation analysis makes it possible to determine the optimal charging parameters: the number of direct feeds, feed weight, stockline. This decreases the degree of direct reduction of iron. The optimal charging parameters allow formulating recommendations on the intensification of the reduction processes and improving the smelting process as a whole.
Keywords: charging parameters; direct reduction of iron; three-factor model; optimization procedure

Using the Upper-Bound Method to Calculate the Upsetting Forces for Oil Pipes by M. V. Erpalov; H. Dyja; A. A. Bogatov (179-182).
The upper-bound method is used to calculate the upsetting force. Novelty is the realism of the modeled velocity field of metal in the deformation zone. The calculated upsetting force is shown to be in agreement with available industrial data. The analytical expression derived is used in the press control algorithm and software to determine the rational upsetting force for various tool designs and pipe dimensions.
Keywords: drill pipe; pipe upsetting; upsetting force; upper-bound method

The data on the energy intensity, carbon dioxide emission, and end-to-end emission (carbon footprint) for the production of vanadium iron in coke-fired blast furnaces with injection of either natural gas or both natural gas and pulverized coal are presented. Energy intensity is represented by end-to-end process fuel number. Mean values, variance, standard deviation, range of variation of process fuel number, emission, and end-to-end emission of carbon dioxide are calculated using published data on the consumption of coke, natural gas, and pulverized coal in a blast furnace. It is shown that the process with injection of pulverized coal has better performance in terms of energy intensity. Carbon footprint is minimum when injecting natural gas only.
Keywords: blast furnace; coke; natural gas; pulverized coal; carbon dioxide emission

Effect of Tungsten on Precious Metal Extraction During Processing of Radio-Electronic Scrap by T. A. Aleksandrova; N. M. Telyakov; A. N. Telyakov; D. V. Gorlenkov (188-192).
An increase in demand for metal creates a requirement for finding new ways of supply. Toughening of ecological requirements for ore recovery necessitates ways for intensifying treatment processes with the aim of more complete extraction of economic components. In the forefront is secondary metallurgy technology making it possible to extract nonferrous and precious metals from waste. Ecological standards become an important condition for processing radio-electronic engineering scrap. Enrichment product compositions obtained from radio-electronic industry scrap are provided and results are described for melting radio-electronic scrap and dissolution of anodes prepared from this waste. The compositions of concentrates entering processing are provided. These compositions are analyzed in a Lab Center XRF-1800 x-ray fluorescence spectrometer. Anode potential measurements are given. The degree of tungsten oxidation in relation to temperature is analyzed. Kinetics of tungsten oxidation are studied and tungsten apparent oxidation activation energy is determined. It is concluded that tungsten may be a collector for gold. Tungsten oxidation is a required condition for reducing gold loss.
Keywords: secondary metallurgy; waste; radio-electronic scrap; metals; gold; silver; platinum; copper-nickel anodes; electrolyte

Effect of Slag Regime on Alkaline Compound Behavior in a Blast Furnace by A. A. Polinov; A. V. Pavlov; S. N. Pishnograev; G. N. Logachev; N. A. Spirin (193-197).
The effect of alkaline compounds on blast furnace operation is studied. It is shown that the main mass of alkaline compounds enters a blast furnace with sinter, coke ash, and pellets, and the main part of alkali emerges from a blast furnace with slag. A quantitative effect is established for an increase in the emergence of alkali with slag with a reduction in final slag basicity. The periodic nature of alkali removal with slag is established. It is found that it is necessary no less frequently that once every 4–5 days in each blast furnace to carry out two to three operating shifts with final slag reduced basicity (CaO/SiO2) (lower by 0.05–0.15 units than prescribed by the production chart). The technology proposed for alkaline compound removal is protected by an RF patent and implemented at the Magnitogorsk Metallurgical Combine since 2012.
Keywords: blast furnace process; alkaline compounds; balance; slag regime; frequency; removal; coke consumption

Use of High-Magnesia Flux Flumag in Steelmaking by A. P. Vozchikov; K. N. Demidov; T. V. Borisova; V. I. Nosenko; A. N. Filatov (198-204).
Research results are given for use of FluMag high-magnesia flux mainly containing brucite Mg(OH)2 during steel production in oxygen converters and electric steel smelting furnaces. Data are provided for FluMag flux physicochemical properties. The effect of using the flux in different periods of converter smelting on molten slag chemical composition and other process parameters, and also the increase in efficiency of applying a slag skull the converter lining are determined. Comparative analysis is carried out for molten slag foaming during steel smelting in electric furnaces and formation of a slag skull on the furnace lining with the use of magnesia fluxes of different compositions.
Keywords: converter; steel smelting arc furnace; lining; slag skull; magnesium oxide in slag; magnesia fluxes; FluMag flux; brucite; application technology

Modification of the TPA-220 Piercing Mill for Rolling Concast Billets and Long Tubes at the Pervouralsk New Pipe Plant by Yu. M. Chernyshev; A. V. Bolotov; E. A. Novikov; V. R. Gainanov; Yu. B. Chechulin; Yu. V. Pesin (205-209).
The results of modifying the TPA-220 piercing mill are described. The energy and force characteristics of the mill are evaluated. The dependence of the torque on the tube dimensions and feed angles is established. The performance of the mill after modification and introduction of experimental tool designs is estimated.
Keywords: modification; feed angle; piercing mill; concast billet; energy and force characteristics; tool design

Effect of Cooling Lubricants on Welded Steel Pipe Quality by N. G. Manokhina; R. L. Shatalov; I. V. Chursin; A. V. Lyubimov (210-216).
The main properties of domestic (Karbon-2) and three overseas (HAKUFORM 50-65-2, Multan 7040, ToolWay ST) cooling lubricants (coolant) are studied, making it possible to evaluate quantitatively their efficiency in welded pipe manufacture. The effect of different coolant grades on depth of score marks and surface roughness of welded steel pipes at the Filit Moscow Pipe Plant is studied. An integral method is proposed for evaluating coolant quality under plant conditions.
Keywords: cooling lubricant; coolant concentration; welded steel pipe; pipe electric welding unit (PEWU); score mark depth; surface roughness; pipe quality

Innovative Equipment for Producing Cost-Effective Hollow Billets for Mechanical-Engineering Parts of Small Diameter by B. A. Romantsev; Yu. V. Gamin; A. V. Goncharuk; A. S. Aleshchenko (217-222).
A technology and equipment for producing cost-effective hollow billets 30 to 60 mm in diameter for mechanicalengineering parts are described. The developed automated line provides high productivity and is relatively light. The line allows making axisymmetric billets with a through or blind hole with a depth/diameter ratio of up to 8.
Keywords: hollow billet; piercing mill; screw rolling; mechanical press; broaching; automated line

Studying the Deformation During Variable-Channel Direct Extrusion by P. M. Vinnik; K. M. Ivanov; G. A. Danilin; E. Yu. Remshev; M. Yu. Silaev (223-229).
Products made from wire and bars with uprated physical and mechanical characteristics are widely used in mechanical engineering. Such characteristics cannot be achieved by classical thermal and mechanical techniques. The use of new materials motivates development of new methods of hardening and achieving the required mechanical properties. Bulk nanomaterials, including those resulting from severe plastic deformation, whose mechanical properties are predetermined by ultrafine-grained structure, combine high strength, good ductility, and other properties. The purpose of severe plastic deformation is to accumulate plastic strain in the workpiece. This requires certain conditions, such as nonmonotonicity of deformation.
Keywords: direct extrusion; strain rate; mechanical properties; ultrafine-grained microstructure

The effect of molybdenum in an amount of 0.15% on the microstructure and properties of low-alloy pipe steel plate prepared by controlled rolling technology with accelerated cooling is studied. A favorable effect is established for molybdenum on increasing strength properties and sheet hydrogen induced cracking resistance.
Keywords: low-alloy pipe steel; rolled plate; molybdenum; accelerated cooling; microstructure; mechanical properties; hydrogen induced cracking

Low-Temperature Pressure Leaching of Converter Matte in Sulfuric Acid Solutions by K. A. Karimov; A. V. Kritskii; L. G. Elfimova; S. S. Naboichenko (238-242).
During treatment of copper-cobalt ores with a high nickel content of one of the domestic deposits by standard technology, it is expected to obtain converter matte containing, wt.%: 60–68 Ni, 7–9 Cu, 4–6 Fe, 2–3 Co, 21–23 S. It has been established for a model sample (wt. %: 62 Ni, 7.1 Cu, 3.7 Fe, 2.2 Co, 18 S) that processing converter matte under conditions of increased oxygen pressure is much more effective than under atmospheric conditions, and this is indicated by a reduction in the duration of pressure leaching (1.3–1.5 h) compared with leaching under atmospheric conditions (4–8 h), and also indices for extraction of economic components into solution (wt. %: 67 Ni, 99 Cu, 99 Fe). Due to the use of special experiment planning programs, a more complete study is achieved for the effect of oxygen pressure and temperature on leaching nickel, and also determination of the most effective production parameters for performing the process. In view of the low copper content, flotation separation of this converter matte is ineffective. Separation of copper and nickel is accomplished by selective pressure leaching of nickel from converter matte. It is established that as a result of selective leaching of nickel from copper-nickel converter matte the initial acid concentration has a considerable effect. It is possible to extract nickel into solution at the level of 50–55% and copper and iron are concentrated in cake (concentration in final solution is mg/dm3: 0.06 Cu and 0.62 Fe). A method is proposed for processing leaching products.
Keywords: converter matte; atmospheric leaching; pressure leaching; nickel; copper; iron; extraction

Provision of Stable Operation of a Combined Casting–Extrusion Unit for Nonferrous Metals by Yu. V. Gorokhov; S. V. Belyaev; I. Yu. Gubanov; I. V. Uskov; A. G. Ivanov; E. M. Lesiv (243-248).
The object studied is the contemporary Castex process of continuous casting–extrusion of nonferrous alloys implemented in a Conform unit with a wheel-crystallizer vertical axis of rotation. The aim of research is to establish relationships for planning equipment structural elements providing implementation of a stable process of continuous feeding of molten metal into a crystallizer channel, its solidification and extrusion into a die orifice. The problem is set of revealing and calculating the main process parameters determining observation of conditions for constancy of second-by-second volumes of metal during its movement from a dispenser with melt to emergence of an extruded object from the die orifice. An original technical solution is provided for implementing metal combined casting–extrusion in a Conform unit with a horizontal wheel-crystallizer. Dispenser dimensions are calculated in relation to the level of melt within it and wheelcrystallizer rotation rate providing stable accomplishment of the test process in a laboratory unit. Test results for continuous casting and extrusion of aluminum alloy AD 31 confirm the correctness of calculated data.
Keywords: Castex; Conform unit; continuous metal casting–extrusion; extrusion; molten metal dispenser; carousel crystallizer

Gold Electrowinning from Cyanide Solutions Using Three-Dimensional Cathodes by K. D. Naumov; V. G. Lobanov; Ya. D. Zelyakh (249-253).
Work is devoted to studying electrowinning of precious metals, in particular gold, in rich cyanide solutions on three-dimensional cathodes of electronegative metals. The object studied is production solution obtained during cyanide leaching of gravitation concentrates containing about 95 g/m3 of gold, 30 g/m3 of silver, and 6.5 g/dm3 CN–. The effect of current density, electrolyte volume consumption, and cathode material on the degree of gold extraction are studied. An operating regime is established making it possible to extract more than 99% gold with a residual concentration below 0.1 g/m3.
Keywords: electrowinning; precious metals; gold; cyanide solutions

Studying the Nonstationary Stages of Screw Rolling of Billets with Profiled Ends by B. V. Karpov; M. M. Skripalenko; S. P. Galkin; M. N. Skripalenko; S. V. Samusev; Tran Ba Huy; S. A. Pavlov (257-264).
The rolling of VT-6 alloy billets with profiled ends in a screw rolling mill is studied to determine the geometry of the end sections minimizing the funnel depth after rolling. The rolling experiment conducted is of 23 factorial design. The nonstationary stages of the process are simulated using Deform-3D software. The results of the simulation are used to find the shape and dimensions of the end sections of the billet that minimize the funnel depth.
Keywords: three-high screw rolling; screw rolling minimill; nonstationary stage; funnel; end; profiling; computer simulation; full factorial design

Computer Simulation in Developing the Technology of Welding High-Tensile Steel Sheets by G. A. Bilenko; R. U. Khaibrakhmanov; Yu. S. Korobov (265-270).
Finite-element simulation for automatic argon-arc welding of high-tensile steel sheets is considered. The mathematical model used to calculate the temperature distribution, changes in phase composition, strains, and stresses is described. SYSWELD and PROWELD software packages are used. Based on the results obtained, rational boundary conditions are chosen and an assembly-and-welding fixture is designed.
Keywords: welding simulation; welding equipment development; steel sheet welding; high-tensile steel; finite-element method; residual displacements; residual stresses and strains

Development of Innovations for Metallurgical Productions by V. I. Zolotukhin; E. I. Gordeev; D. A. Provotorov; A. G. Golovko (271-277).
The basic stages in the development of and the recent developments for metallurgy and foundry by the Vulkan-TM Scientific and Production Enterprise (Tula) are considered. The design features of unified VTseries slide gates of new generation are outlined.
Keywords: import substitution; innovations; slide gate; refractories; slide gate ceramics

Evaluating the Weight of Pig Iron Tapped from a Blast Furnace by A. D. Chernopol’skii; S. V. Ageev; A. A. Dmitriev; A. A. Blinnikov; E. S. Glebova; R. A. Kartashev (278-282).
A method of evaluating the tap weight during the production of iron in several blast furnaces simultaneously is proposed. The following systems developed by the NTTs Pribor for Severstal and underlying the method are considered: radar iron-level monitoring system, mixer positioning system, and automated rolling-stock accounting system. It is proposed to integrate the weighing system, hot-metal pouring control systems, and rolling-stock accounting system into an integrated information system. The method allows increasing the accuracy and efficiency of evaluating the tap weight.
Keywords: tap weight; marking; RFID label; iron level; level gage; mixer positioning

Effect of Converter Slag Consumption on Blast Furnace Operating Indices by A. A. Polinov; A. V. Pavlov; G. N. Logachev; O. P. Onorin; N. A. Spirin (283-290).
Results are provided for calculation of the predicted blast furnace operating regime using converter slag in the iron-ore part of the charge without implementing additional measures with the aim of evaluating its effect on process indices. Introduction into a blast furnace charge of fractionated converter slag may be performed in order to increase slag magnesia content and to use it as a basic for flux for increasing the proportion of pellets in a charge of an individual furnace without changing the prescribed sinter basicity for the whole workshop. An increase is provided in gas permeability of the dry part of a charge for a furnace with a limited upper zone in the case of distortion of its profile. Charging converter slag into a blast furnace gives rise to an increase in iron phosphorus content. Prolonged use of converter slag in all blast furnaces gives rise to accumulation of phosphorus in metal, and consequently to resolution of the problem of removing phosphorous during converter treatment. The choice of the ratio of charge components may be made by maintaining the iron content in a fluxed charge at a level relating to specifications of the technology and the task of providing an economic furnace regime. Solution of the question of the expediency of using converter slag in blast furnaces is possible with comprehensive analysis of the problem: evaluation of the economic expediency of its use as a fluxing additive; economic development of this question for a blast furnace – converter production complex; choice of a furnace operating regime in accordance with its operating conditions; analysis of the ecological problems of the operation of an enterprise and a region.
Keywords: blast furnace process; converter slag; slag regime; iron composition; melting indices; coke consumption

Monitoring Blast Furnace Lining Condition During Five Years of Operation by Yu. S. Semenov; E. I. Shumel’chik; V. V. Gorupakha; A. V. Nasledov; A. M. Kuznetsov; A. V. Zubenko (291-297).
Changes in lining temperature for the shoulders, bosh, and shaft, their mean-square deviation with respect to furnace surroundings, and also overall thermal loads of the cooling system for blast furnace No. 3 at the Enakievo Metallurgical Plant are analyzed for five years of operation: from December 2011 to September 2016. Limiting values of temperature are established that point to partial or complete shaft lining wear. Features are revealed for the effect of blast-furnace smelting production conditions on the change in blast-furnace lining temperature. The furnace well condition is evaluated.
Keywords: blast furnace; lining; thermocouples; coneless charging unit (CCU); coke quality; charge pellet content; cooling system thermal load; furnace well

Results are provided for calculating arc efficiency of steel-smelting arc furnaces in various stages of charge melting with a change in slag layer thickness. Arc efficiency is at a maximum after cutting a well in a charge. Charge thickness decreases during melting and arc efficiency is reduced. An increase in slag layer thickness in the opening period leads to an increase in arc efficiency. Calculated data are confirmed by experimental studies in steel melting arc furnaces.
Keywords: electric arc; furnace; steel; radiation; efficiency

Analysis of Strain Hardening Mechanisms for Steel with a Bainitic Structure by V. E. Gromov; E. N. Nikitina; Yu. F. Ivanov; K. V. Aksenova (303-310).
Transmission electron diffraction microscopy is used to analyze strain hardening of steel with a bainitic structure. Contributions to strengthening are considered for lattice friction, interphase boundaries, dislocation substructure, carbide phases, alloying element atoms, and remote stress fields. It is established that substructural and solid solution strengthening make the greatest contributions. The reason for steel loss of strength with large degrees of deformation is connected with activation of deformation microtwinning.
Keywords: bainite; strengthening mechanism; microtwinning

Results are given for a study of metal deformation state with screw rolling in a three-roll mill by means of computer modeling. Quantitative characteristics are obtained for the unequal distribution of degree of deformation through a workpiece cross section. Features are established for the use of screw line pitch length, partial reduction, and penetration index for the plastic deformation zone to workpiece axis in relation to screw line pitch number. Recommendations are given according to which in calculating roll calibration the roll profi le should be selected so that deformation penetrates the whole workpiece depth over the whole deformation site length.
Keywords: screw rolling; fi nite-element modeling; deformation state

Effect of Cast Iron Structure and Properties on Contact Quality with an Aluminum Electrolyzer Carbon Anode by V. G. Babkin; V. A. Kukartsev; A. I. Cherepanov; G. V. Arkhipov; A. N. Savina (318-324).
Physicomechanical and casting properties are studied for high-phosphorus irons used in the assembly of aluminum electrolyzer baked anodes in RUSAL enterprises compared with gray cast iron containing a minimum amount of phosphorus and sulfur. It is shown that iron primary crystallization under conditions approaching pouring production parameters and iron cooling in the nipple – cast iron – carbon anode contact assembly proceeds with significant supercooling that causes the formation of a pearlite matrix in the cast iron structure with increased hardness. Iron with a lower carbon equivalent exhibiting high hardness has a better elasticity modulus and strength values. The presence of ternary phosphide eutectic within the iron structure with a high phosphorus content reduces the breaking strength considerably at high anode operating temperatures and this may be a reason for cast iron loss of strength and anode separation at the end of an operating cycle leading the electrolyzer stoppage. Iron with the minimum phosphorus content exhibits strength exceeding by more than a factor of two that of high-phosphorus cast iron and also the least electrical resistance in the range up to 500–600°C. In addition, iron with a high phosphorus content has an anomalous change in linear thermal expansion coeffi cient (LTEC) in the range 600–810°C that may also lead to degradation of “soft” metal (anode at the end of an operating cycle). The results obtained are explained drawing on thermal analysis data and metallographic studies.
Keywords: electrolyzer anodes; electrode discarded metal; anode assembly; iron casting; cast iron; chemical composition; physicomechanical properties; electrical resistance; casting properties; metallographic studies; thermal analysis

Analysis of Hydrogen Content in the Main Stages of Low-Alloy Aluminum Alloy Flat Ingot Manufacture by S. V. Belyaev; B. P. Kulikov; V. B. Deev; V. N. Baranov; E. M. Rakhuba (325-329).
Results are given for research aimed at improving the quality of large tonnage flat ingots under RUSAL Joint Company (Krasnoyarsk) conditions as a result of reducing the hydrogen content within them to less than 0.1 cm3/100g. For this purpose, under production conditions the change in molten aluminum alloys series 1XXX hydrogen content is analyzed in the main stages from the aluminum electrolyzer to the casting machine. Production operations are determined within which there is significant melt impregnation with hydrogen. Research precision is provided by using a developed procedure for molten sample collection in the main production operations and considering the specific nature of production. Technical solutions are proposed from research results aimed at reducing melt hydrogen expansion.
Keywords: low-alloy aluminum material hydrogen saturation; metal sample collection; equipment and production scheme for metallurgical production of flat ingots; degassing

Combined Low-Frequency and Electro-Impulse Treatment of Molten Metal by I. E. Ignat’ev; V. V. Krymskii; P. V. Kotenkov; V. F. Balakirev; E. A. Pastukhov; E. V. Ignat’eva (330-333).
A method is given for preparing alloy using combined low-frequency and electro-impulse action on a melt. Metallographic comparison is provided for the result of using this procedure with results of preparing alloy with separate low-frequency and electro-impulse methods on the example of alloy of the Al–Ti–C system. It is established that melt treatment by the new method leads to a variety of aluminide growth shapes.
Keywords: melt; low-frequency treatment; electro-impulse treatment; aluminide growth shape; Al3Ti

Comparative Laboratory Tests of Methanesulfonate and Sulfamic Tinplate Tinning Electrolytes by V. P. Vinogradov; V. V. Levenkov; A. V. Papshev; P. E. Markov (334-343).
Comparative tests are performed under laboratory conditions in units modeling existing electrolytic tinning units for contemporary ecologically clean tinning electrolytes based on methanesulfonate (Niveostan 200 version) and sulfamic acids. The main comparison criteria are: adaptability (the range of tolerance for the main parameters); hydrolysis stability and the level of sludge formation; tinned coating qualitative properties. It is shown that both types of electrolytes meet the specifications laid down for tinplate industrial tinning electrolytes and make it possible to prepare high quality anticorrosion coatings over a wide temperature range from 30 to 60°C, and they may provide good electrolytic efficiency (tin current efficiency 95%) with sensible limitation of the current density limit. Sulfamic electrolyte provides a broader range of variation in current density. Methanesulfonate electrolyte without admixture of iron is hardly prone to sludge formation. With an identical iron content (10 g/liter), both electrolytes have about the same low level of tin loss in sludge, but the anticipated rate of iron accumulation is greater in methanesulfonate electrolyte. The main advantage of methanesulfonate tinning is the high electrolyte electrical conductivity making it possible to reduce electrical energy consumption. Maximum use of the technical possibilities of both types of electrolyte is possible in new tinning lines planned and constructed in accordance with features of the production processes used.
Keywords: white tinplate; tinning electrolyte; adaptability; hydrolysis resistance; coating quality; Hull cell

Production of Shapes for Electrical Engineering Purposes in a Rolling and Drawing Mill by P. A. Vasilevskii; L. M. Zheleznyak; R. R. Bekmansurov (344-347).
Industrial output of electrical engineering shapes, i.e., rectangular sections intended for preparing various components by cold forming, and wedge-shaped sections for electrical machine commutators, is assimilated using a contemporary rolling and drawing unit based on planned rolling regimes and repeated drawing with sliding. Contact wires are also produced for overhead town electrical transport networks (trolleybuses, tramways).
Keywords: rolling and drawing mill; electrical engineering copper sections; broad range; production treatment regimes; component industrial production

Selenium Leaching from Copper Anode Slimes Using a Nitric Acid–Sulfuric Acid Mixture by Xue-jiao Li; Hong-ying Yang; Zhe-nan Jin; Lin-lin Tong; Fa-xin Xiao (348-356).
Based on the Eh–pH diagram for the Se–H2O system, a new method is proposed for leaching selenium from copper anode slimes using a nitric acid–sulfuric acid mixture. The effects of solid/liquid ratio, HNO3 and H2SO4 concentrations, leaching temperature, and reaction time on the leaching efficiency of selenium were investigated. Samples were mineralogically characterized by x-ray diffraction and scanning electron microscopy with energy-dispersive spectroscopy to study the transformation of selenium-containing phases during the leaching process. The results showed that the optimal conditions comprised a solid/liquid ratio of 0.25 g/ml, HNO3 concentration of 0.5 M, H2SO4 concentration of 2 M, leaching temperature of 363 K, and reaction time of 3 h. A selenium leaching efficiency of 97.79% was obtained under these conditions. Mineralogical characterization indicated that selenium occurred as Cu–Ag selenide in the raw copper anode slimes. This was first converted to elemental selenium and then to selenite ions in solution.
Keywords: selenium; copper anode slime; acid leaching; nitric acid–sulfuric acid mixture; mineralogical characterization