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EN
Measurement of thermophysical properties of steel is possible by using different thermal analysis techniques. In the field of metallurgy the most relevant methods are Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC). The paper presents the results of thermophysical properties which are necessary to carry out numerical simulation of continuous casting of steel. The study was performed for two steel grades S320GD and S235JR. The main aim of the research was to determine the dependence of specific heat on temperature. On the basis of obtained results the thermal effects of phase transformations and characteristic transition temperatures were also identified. Both the specific heat of steel and thermal effects of phase transformations are included in the Fourier-Kirchhoff equation, as the material properties necessary to obtain the numerical solution. The paper presents the research methodology, analysis of results and method of determining the specific heat of steel based on the results of DSC analysis.
PL
Pomiar właściwości termofizycznych stali możliwy jest dzięki wykorzystaniu różnych technik analizy termicznej. W metalurgii najszersze zastosowanie znalazły różnicowa analiza termiczna (DTA) oraz różnicowa kalorymetria skaningowa (DSC). W pracy przedstawiono wyniki badań właściwości termofizycznych koniecznych do przeprowadzenia symulacji numerycznej procesu ciągłego odlewania stali. Badania wykonano dla dwóch gatunków stali S320GD i S235JR. Głównym celem badań było wyznaczenie funkcyjnej zależności ciepła właściwego analizowanych gatunków stali od temperatury. Na podstawie przeprowadzonych badań określono również efekty cieplne przemian fazowych oraz charakterystyczne temperatury przemian. Zarówno ciepło właściwe stali jak i efekty cieplne przemian fazowych wchodzą w skład równania Fouriera-Kirchhoffa, jako właściwości materiałowe konieczne do uzyskania rozwiązania numerycznego. W pracy przedstawiono metodykę badań, analizę uzyskanych wyników oraz sposób wyznaczania ciepła właściwego stali w oparciu wyniki analizy DSC.
2
Content available remote Kalorymetria skaningowa przemian austenitu w ferrytycznym żeliwie sferoidalnym
PL
Przeprowadzono próby wykorzystania kalorymetrii skaningowej (aparat SDT Q600 firmy Thermal Analysis) do oceny kinetyki przemian fazowych w żeliwie sferoidalnym w zakresie temperatury 600 - 1000°C. Celem było oszacowanie wpływu szybkości nagrzewania na położenie pików przemian fazowych dla żeliwa sferoidalnego o osnowie ferrytycznej, wyznaczenie entalpii przemian fazowych (ferryt - austenit, austenit - ferryt), porównanie kinetyki przemian fazowych podczas nagrzewania i studzenia próbki. Wyniki wskazują na istotny wpływ szybkości nagrzewania tworzywa na położenie punktów przemiany, jej kinetykę, a także na wartość ciepła przemiany.
EN
Ability of Differential Scanning Calorimetry (Q600 device of TA Instruments) was checked for the study of the phase transformation kinetics in the ductile cast iron in the temperature interval 600 - 1000°C. The main aims of this study are the estimation of heating rate influence on the temperature profile of transformation in the ferritic ductile cast iron, the estimation of the austenitisation and austenite decomposition enthalpy, comparison of the phase transformation rate during the heating and cooling processes. It was shown that the heating rate has an essential influence on the transformation rate, on the temperature of the transformation end and enthalpy of the transformation.
PL
Metodą kalorymetrii wysokotemperaturowej i skaningowej kalorymetrii różnicowej zbadano właściwości termodynamiczne (temperatury i entalpie przemian fazowych, ciepło molowe fazy stałej i ciekłej) osiemnastu halogenków lantanowców i trzydziestu związków pośrednich tworzących się w układach LnX3-MX (Ln = lantanowiec, X = Cl, Br, I). Wyznaczono diagramy fazowe układów podwójnych TbBr3-MBr (M = Na, K, Rb, Cs), LaI3-RbI i NdI3-RbI. Określono związek pomiędzy właściwościami termodynamicznymi badanych halogenków lantanowców i ich strukturą krystaliczną. Wyznaczono funkcje termodynamiczne badanych halogenków lantanowców i termodynamiczne funkcje ich tworzenia. Dokonano podziału kongruentnie topiących się związków M3LnX6 istniejących w układach LnX3-MX na dwie grupy: grupę związków tworzących się w podwyższonych temperaturach i grupę związków stabilnych lub metastabilnych w niskich temperaturach. Przedyskutowano specyficzną zależność ciepła molowego i przewodnictwa elektrycznego fazy stałej związków M3LnX6 od temperatury i zaproponowano jej wyjaśnienie jako efekt zaniku uporządkowania podsieci kationowej tworzonej przez kationy litowca. Wykonano pomiary entalpii mieszania w pełnym zakresie składów dla trzydziestu czterech ciekłych układów podwójnych LnX3-MX. Wykazano zależność efektu energetycznego procesu mieszania od promienia jonowego lantanowca, promienia jonowego litowca i promienia jonowego fluorowca. W oparciu o uzyskane wyniki przedyskutowano możliwość tworzenia się kompleksów w ciekłych układach halogenki lantanowców-halogenki litowców.
EN
The present paper is the author's contribution to international scientific project devoted to investigations on thermodynamic properties, structure and electrical conductivity of lanthanide and actinide halides and binary systems: lanthanide (actinide) halides-alkali metal halides. The project was initiated in the early 90s with a cooperation between the Institute of Inorganic Chemistry and Metallurgy of Rare Elements at the Technical University of Wroclaw and the Institut Universitaire des Systems Ther-miques Industriels Universite de Provence in Marseille. As the years went by, research groups from Japan (Research Laboratory for Nuclear Reactors - Tokyo Institute of Technology and Chiba University) and Great Britain (University of Abertay - Dundee) joined to realize the above project. And so an international research team was formed. It has at its disposal a wide range of experimental methods (thermal analysis, calorimetry, differential scanning calorimetry, X-ray diffraction, neutron diffraction, Raman spectroscopy, density and electrical conductivity measurements in fused salts) and is capable of solving theoretic problems (optimization of experimental data, molecular dynamic simulation). The ultimate goal pursued by the team has been to create a complete database for lanthanide and actinide halides. The database is created step by step as the investigations continue, with the support of the National Institute of Standards and Technology (NIST, USA) and Centre National de la Recherche Scienti-fique (CNRS, France). Following the division of tasks scheduled in the international scientific project mentioned above, the author of this work investigates thermodynamic properties and electrical conductivity of both the pure lanthanide halides (chlorides, bromides, iodides) and the binary systems, i.e., lanthanide (actinide) halides-alkali metal halides. The results obtained by the author so far have been presented in this work. The investigations were not commenced until a thorough analysis of the existing literature data had been performed. It turned out that the available data were often extremely scant and incomplete, pretty often inconsistent with one another. Depending on source of information, great discrepancies were noted even for such basic quantities as fusion temperature and enthalpy for pure lanthanide halides. The reason of 174 those discrepancies could not lie only in the measurement methods applied. Considering the fact that different results were obtained while using the same research method (e.g. differences in fusion temperatures would come up to several dozen degrees), it was accepted that the purity of lanthanide halides used in investigations would be a decisive factor for the quality of results. In this connection, prior to starting any investigation, enormous amount of time was spent on developing synthesis methods, selecting suitable materials and methods of verifying the chemical composition and purity of the lanthanide halides obtained. As a result the synthesis methods were developed that would yield in high purity (min. 99,9%), oxyhalide contamination-free lanthanide halides (chlorides, bromides, iodides). Those compounds were used in examinations aimed at determination of thermodynamic properties of both the pure lanthanide halides and the binary systems of lanthanide halides-alkali metal halides. Thermodynamic properties (phase transition temperatures and enthalpies, heat capacity of solid phase and liquid phase) for eighteen lanthanide halides (LaCl3, CeCl3, PrClj, NdCl3, SmCl3, EuCl3, GdCl3, TbCl3, DyCl3, TmCl3, YbCl3, LaBr3, NdBr3, TbBr3, Lal3, Ndl3, EuCl2, and YbCl2) were determined. The lanthanide(III) halides were divided into groups taking into account the relationships between fusion temperature plus enthalpy and atomic number of the respective lanthanide. Such a division was reflected in crystal structure of the halides under investigation. A correlation between the crystal structure of lanthanide(III) halides and their respective entropy of fusion or the sum of the entropy of fusion and the entropy of the solid-solid phase transition was found from consideration of the above-mentioned relationships. Fusion of halides having the hexagonal, UCl3-type, and the orthorhombic, PuBr3-type, structures entails a change in the entropy of fusion (or the sum of the entropy of phase transition and the entropy of fusion) by 50 š 4 J moF(-1)K(-1). Analogical entropy change within the group of halides having the rhomboedric, FeCl3-type structure is lower and equal to 40 š 4 J mol(-1)K(-1). Halides of monoclinic, AlCl3-type, crystal structure belong to the third group. Their entropy change during fusion is considerably lower, only 31 š 4 J mol(-1)K(-1). Molar heat capacities of the solid as well as of the liquid phase of the lanthanide halides mentioned earlier were measured. Those are the only experimental results for eleven of the halides (respective literature data were only estimated values). The molar heat capacity measurements for DyCl3 and TbCl3 have confirmed the occurrence of a solid-solid phase transition for those compounds. At the same time additional thermal effects, invisible on the DTA curves, have been found for DyCl3 and TbCl3. Their occurrence is probably connected with a complicated crystal structure of those compounds (possible formation of metastable phases at lower temperatures). Thermodynamic data obtained (temperature and enthalpy of phase transitions as well as molar heat capacity dependence on temperature) were used to determine the thermodynamic functions of both solid and liquid lanthanide halides, and also thermodynamic functions of formation of those halides. The temperature dependence of lanthanide(III) halides entropy was used to determine a S1300(LnX3(c)) - S298(LnX3(S) difference. This difference is evidently connected with the crystal structure of lanthanide(III) halides. It is equal to 216 š 4 J mol(-)K(-1) for halides having the UC13- or PuBr3-type crystal structure, 200 š 5 J mol(-1)K(-1) for halides having the FeCl3-type structure, and 190 š 4 J mol(-1)K(-1) for halides having the AlCl3-type structure. The same value of the difference for chlorides, bromides and iodides of similar structure indicates that the entropy differences, resulting from the anion presence and magnetic effects, reveal at low temperatures and affect the value of the S298(LnX3(s)) -S0(LnX3(s)) difference. Indeed, the entropy of S298(LnX3(s)) decreases, starting from iodides, through bromides, to chlorides. The Si3oo(LnX3(C)) _ S298(LnX3(S)) difference for halides of the FeCl3-type structure is smaller compared to the difference for the UC13- and PuBr3-type structure, although clearly greater than the one corresponding to the AlCl3-type structure. This means that the degree of order in fused halides increases from light lanthanide halides to heavy lanthanide halides, and reaches the maximum for halides having the AlCl3-type crystal structure in solid phase. Thermodynamic properties (temperature and enthalpy of phase transitions, molar heat capacity) have been determined for M3LnX6 compounds that are formed in LnX3-MX binary systems (Ln = La, Ce, Pr, Nd, Tb; M = K, Rb, Cs; X = Cl, Br, I). These compounds can be divided into two groups. Compounds having only a high-temperature modification, cubic, elpasolite-type (Fm3m, Z = 4) crystal structure, belong to the first group (K3CeCl6, K3PrCl6, K3NdCl6, Rb3LaCl6, K3NdBr6, Rb3LaBr6). They are form at elevated temperatures, and their formation is a reconstructive phase transition. The K2LnX5 compounds of the K2PrCl5-type structure (Pnma, Z = 4) react at temperature Tform with KX to form the K3LnX6 compounds of cubic, elpasolite-type (Fm3m, Z = 4) crystal structure. The process proceeds with a high molar enthalpy, ranging from 44 to 55 kJ mol(-1). When being cooled, they decompose to initial substances at temperature being clearly lower than the temperature of formation. The compounds of the second group (K3TbCl6, Rb3CeCl6, Rb3PrCl6, Rb3NdCl6, Rb3TbCl6, K3TbBr6, Rb3TbBr6, Rb3NdBr6, Rb3NdI6, and all Cs3LnX6 compounds) have both the high-temperature, cubic, elpasolite-type, and the low-temperature, monoclinic, Cs3BiCl6-type structures. Transition from the low- to high-temperature modification is a non-reconstructive phase transition. The molar enthalpy corresponding to this transition is considerably smaller than the formation enthalpy of the compounds of the first group and ranges from 6 to 10 kJ mol(-1). The compounds of the second group are stable or metastable at room temperature. The above-presented classification of M3LnX6 compounds into two groups manifests itself in the dependence of their molar heat capacity on temperature. In the first group (compounds with high-temperature modification only), the molar heat capacity of stoichiometric mixture, corresponding to a composition of this compound, increases monotonically as the temperature rises until the formation temperature of the M3LnX6 compound (Tform) is reached. Once the compound is formed, its molar heat capacity decreases as the temperature rises further, and attains a minimum at the temperature range of 100-150 K, above the Tform. In the second group (compounds having both the high- and low-temperature modifications), a distinct increase in the molar heat capacity is observed as early as during low-temperature modification. This increase coincides with the first-order phase transition (low-temperature modification - high-temperature modification). The molar heat capacity of the high-temperature modification decreases as the temperature rises, and attains a minimum at the temperature range of 100-150 K, above the temperature of phase transition (rtrans), i.e. in the same way as in the case of a high-temperature modification of the first group of compounds. The specific dependence of the molar heat capacity of M3LnXc compounds on temperature correlates well with electrical conductivity of their solid phase (measurements were made for M3LnCl6 and M3LnBr6 compounds). Formation of compounds of the first group at elevated temperatures (Tform) results in abrupt increase of electrical conductivity. Second, much lower but a distinct jump in the electrical conductivity (or a kink on a curve of electrical conductivity versus temperature related to a change in activation energy of conductivity) takes place at the temperature corresponding well to the minimum of the molar heat capacity of the high-temperature modification. The phase transition from low- to high-temperature modification, which is specific to the second group of M3LnX6 compounds, is also connected with a jump in electrical conductivity. The magnitude of this jump depends on the ionic radius of alkali metal (bigger jump for rubidium compounds than for cesium compounds). An additional effect appears on the curves representing the electrical conductivity versus temperature of solid phase (a noticeable kink) at the temperature corresponding to the minimum on the curves of molar heat capacity versus temperature. The specific behaviour of the relationships: molar heat capacity - temperature, and electrical conductivity of a solid phase - temperature for the compounds under consideration is most likely connected with a disordering of cationic sublattice formed by alkali metal ions. The high-temperature modification of M3LnX6 compounds has a cubic, elpasolite-type crystal structure (Fm3m). Taking into account the location of alkali metal ions within a unit cell, the correct formula of those compounds should be M2M'LnX6. The lanthanide ions are surrounded by six halogen ions to form regular octahedra (LnX6). One-third of alkali metal cations (M') occupy octahedral holes while the remaining two-thirds of alkali metal ions (M) occupy the tetrahedral holes formed by closely packed octahedra (LnX6). And so, each of M' ions is surrounded by six ions, and each of M ions - by twelve halogen ions. At low temperatures the (LnX6) octahedra are slightly deformed and have been markedly rotated out of their ideal positions. These rotations result in a decrease of difference in the coordination number between the M and M' ions. In the monoclinic, Cs3BiCl6-type structure obtained, one of the (M') alkali metal ions is surrounded by eleven ions, while the other two (M) ions - by eight halogen ions. A disordering of cationic sublattice within the group of M3LnX6 compounds that have only a high-temperature modification (cubic, elpasolite-type structure) most likely takes place in a discontinuous way. Their formation from the M2LnX5 and MX compounds is a transition from the K2PrCl5-type structure, specific to M2LnX5 compounds (monocapped trigonal prisms linked to chains via common edges ([PrCl3Cl4/2]2-), to the elpasolite-type structure. This transition results in formation of anionic sublattice composed of (LnX6) octahedra and cationic sublattice formed by the M and M' ions. The anionic sublattice is a cubic, face-centered structure, while the alkali metal cations are most probably in great part randomly distributed over a unit cell between the (LnX6) octahedra. The transition perfectly correlates with a change in electrical conductivity. A jump in the electrical conductivity at the temperature of compound formation (Tform) is linked to emerging migration possibilities for alkali metal ions, as the carriers of electrical charge, within the unit cell space. Additional jump in the electrical conductivity (or kink on the curve of the conductivity-temperature dependence, resulting from change of the activation energy) in the high-temperature modification of the compounds under discussion, that occurs at the temperature corresponding to a minimum on the molar heat capacity curve, may be attributed to the state of complete "structural disorder". Completely disordered cationic sublattice can be considered as a quasi-liquid. In the group of M3LnX6 compounds having both: the high-temperature elpasolite-type and the low-temperature modifications of Cs3BiCl6-type (K3TbCl6, Rb3CeCl6, Rb3PrCl6, Rb3NdCl6, Rb3TbCl6, K3TbBr6, Rb3TbBr6, Rb3NdBr6, Rb3NdI6 and all Cs3LnX6 compounds), the disordering of cationic sublattice formed by alkali metal ions proceeds in a continuous way. It starts already in the low-temperature modification, at temperature significantly lower than the phase transition temperature. As a result an unusual increase of the molar heat capacity is observed. The dependence of molar heat capacity on temperature assumes a X shape and is in a good correlation with the change in electrical conductivity. The end of the X transition (complete "structural disorder" of cationic sublattice) corresponds to a visible kink on the electrical conductivity curve. As opposed to compounds from the first group (the high-temperature modification only), where the first-order phase transition, i.e. the compound formation, initiated the order-disorder transition, here the first-order phase transition (low-temperature-high-temperature modification) superimposes on the order-disorder (X) transition. Unknown earlier the phase diagrams of TbBr3-MBr (M = Na, K, Rb, Cs), Lal3-Rbl and NdI3-RbI binary systems have been determined. The characteristic feature of these systems, similarly as that of other LnX3-MX systems, is the occurrence of congruently melting M3LnX6 compounds (M = K, Rb, Cs). Their fusion temperature increases with an increase in the ionic radius of alkali metal. The dependence of the ratio of ionic potential of the alkali metal cation to ionic potential of the lanthanide cation on the shape of the phase diagram of LnCl3-MCl, LnBr3-MBr and LnI3-MI binary systems has been found. All these systems can be divided into three groups: - simple eutectic systems (ionic potential ratio higher or equal to 0.448, 0.325 and 0.330 for chloride, bromide and iodide systems, respectively), - systems including only incongruently melting compounds (ionic potential ratio within the range of 0.416-0.280, 0.315-0,284 and 0.352-0,306 for chloride, bromide and iodide systems, respectively), - systems including both incongruently and congruently melting compounds (ionic potential ratio equal to or less than 0.256). In the third group, i.e. in the systems including both the congruently and incongruently melting compounds, one can find close similarities as well as noticeable differences between chloride, iodide and bromide systems. The common features are as follows: - in all systems, the identical value of the ionic potential ratio at which the congruently melting compounds occur, - the first congruently melting compound that occurs at IPM+/IPLn3+ = 0.256 is K2LnX5 (X = Cl, Br, I), - congruently melting M2LnX5 compounds exist within a narrow range of the ionic potential ratio values (0.256-0.249), - at smaller values of the ionic potential ratio (IPM+/IPLn3+ < 0.249) the M2LnX5 compounds melt incongruently, - congruently melting compounds M3LnX6 form at smaller IPM+/IPLn3+ values (0.249). The common characteristic of chloride and bromide systems is also the occurrence of MLn2X7 compounds (X = Cl, Br; M = K, Rb, Cs) that melt congruently or incongruently, and form in the systems where IPM+/IPLn3+ < 0.244. Essential differences between chloride, bromide and iodide systems are as follow: - M2LnI5 compounds occur within a narrow range of ionic potential ratio values (0.256-0.222), while the M2LnCl5 and M2LnBr5 occur in all chloride and bromide systems whose IPM+/IPLn3+ ratio is 0.256, - MLn2X7 compounds that occur in chloride and bromide systems at the value of the ionic potential ratio equal to or less than 0.244 practically are not found in iodide systems (with exception of RbNd2I7), -M3Ln2X9 compounds that occur in chloride (rPM+/IPLn3+ < 0.175) and in iodide (IPM+/IPLn3+ < 0.198) systems practically are not present in bromide systems (except for Cs3Dy2Br9). Mixing enthalpy measurements were performed over the whole composition range for NdClr-MCl, PrCl3-MCl, DyCl3-MCl, TbCl3-MCl, LaBr3-MBr, NdBr3-MBr, TbBr3-MBr and NdI3-MI liquid systems. Selection of the binary systems for the mixing enthalpy measurements gave possibility to determine the influence of lanthanide ionic radius, alkali metal ionic radius and halide ionic radius on thermodynamic properties of lanthanide halide -alkali metal halide liquid systems All the systems under investigation are characterised by negative enthalpies of mixing. The minimum of the molar mixing enthalpy is shifted towards the alkali halide-rich composition and located in the vicinity of xLnx3 ~ 0.3-0.4. It is evident that the ionic radius of the alkali metal influences the magnitude of mixing enthalpy as well as the minimum position. The smaller the alkali metal ionic radius, the smaller the absolute value of mixing enthalpy, and the minimum is more shifted towards the alkali metal halide-rich composition. The other factor that shows the influence on the mixing enthalpy value is the lanthanide ionic radius. Its decrease (with an increase of lanthanide atomic number Z) results in an increase of absolute value of the mixing enthalpy and in a shift of the enthalpy minimum towards the alkali halide-rich composition. Ionic radius of halide also influences considerably the value of mixing enthalpy. Absolute value of mixing enthalpy decreases with an increase of halide ionic radius (from chloride to iodide). In all LnX3-MX -systems, the value of the interaction parameter X is negative. Its absolute value increases significantly with an increase of ionic radius of alkali metal cation. All the systems show more negative values of interaction parameter at the alkali halide-rich compared to the lanthanide halide-rich compositions. The nature of the relationship between the interaction parameter and the composition depends on alkali metal halide, and practically is independent of the lanthanide halide. In the systems containing lithium halides, this relation is practically linear; in the systems containing sodium halides, a broad and blurred minimum is observed; and starting from potassium halides, a clear minimum appears to exist at a molar fraction of lanthanide halide (XLnx3) of about 0.2-0.3. This minimum can be undoubtedly ascribed to the formation of LnX6~ octahedral complexes in the systems under investigation. These complexes dominate in the mixtures rich in alkali metal halide. An increase of LnX3 concentration changes the structure of the melt. Pure LnX6 octahedra are replaced by polymeric forms, where the octahedra are linked across the halogen ions. Mixing the liquid lanthanide halide and liquid alkali metal halide leads to formation of LnX6~ octahedral complexes. So additional halogen ions need to be entered into a coordination shell of the Ln3+ ion. Possible source of those ions can be the alkali metal halide. Nevertheless, the alkali metal cations that are present in the system also tend to create a coordination shell consisting of halogen ions. The result of such "competition" depends on the relative attractive power of alkali metal cation. Within the group of alkali metals this force decreases following the sequence: Li+ > Na+ > K+ > Rb+ > Cs+, i.e. with an increase of ionic radius. Thus the possibility of forming octahedral lanthanide complexes as well as their stability will increase according to the sequence: LiX < NaX < KX < RbX < CsX. An increase in the stability of those complexes results in a higher absolute value of molar enthalpy of liquid mixtures (3 MX, LnX3) formation. The stability of complexes under consideration depends also on the halide ionic radius. The increase of ionic radius (Cl~ < Br~ < F) results in a lower stability of LnX6(-3) complexes, and also in a lower absolute value of molar enthalpy of liquid mixtures (3 MX, LnX3) formation. Molar enthalpies of liquid mixtures (3 MX, LnX3) formation determined from mixing enthalpy measurements were used for verifying the correctness and consistence of thermodynamic properties (temperatures and enthalpies of phase transitions, molar heat capacity) determined for pure lanthanide halides and M3LnX6 compounds.
4
Content available remote Wpływ przemiany fazowej na żaroodporność staliwa typu "Ferchroman"
PL
Zbadano wpływ przemian fazowych na żaroodporność staliwa w warunkach atermicznych. Za pomocą metody DSC określono temperaturę oraz entalpię przemiany fazowej \alfa-\ypsilon w staliwach Cr-Mn. Wykazano, że staliwo o strukturze \ypsilon wykazuje lepszą żaroodporność od staliwa o strukturze dwufazowej \alfa+\ypsilon.
EN
The effect of phase transitions on high-temperature corrosion resistance of steels in non-isothermal conditions has been examined. The phase transition \alfa-\ypsilon temperature and enthalpy in Cr-Mn steels have been determined by Differential Scanning Calorimetry (DSC). It has been proved that the austenitic steels have better high-temperature corrosion resistance than two phase \alfa+\ypsilon steels despite of their higher carbon content (0.5%C).
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