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On the interrelation between the microscopic and macroscopic properties of materials
Crystal Engineering 5 (2002) 163–167 www.elsevier.com/locate/cryseng
On the interrelation between the microscopic and macroscopic properties of materials Anatolii Ya Gubenko ∗ Moscow Institute of Steel and Alloys, Festival’naya 17-138, 125195 Moscow, Russia
Abstract The origin of the correlation between the microscopic and macroscopic material properties that are formed as a result of large-scale fluctuations in the process of evolution of the material to a new state was investigated. Each value of the state parameter corresponds to a certain set of large-scale fluctuations and microscopic states. It was established that the correlations between the dependences of the microscopic and macroscopic properties of the materials are determined by the interatomic interactions and the spatial arrangement of atoms. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Evolution; Correlation; Interaction; Properties
1. Introduction It was established in our previous works that all phase transformations and other transitions in materials (substances) occur in an interval of a variable state parameter [1,2] and time [3]. Within these intervals, the material evolves via large-scale fluctuations (LSFs) that arise spontaneously and disappear after the material reaches a state with a smaller free energy as compared to the initial state. The LSFs, along with a feedback, lead to the formation of oscillations, which consist of microscopic states differing from one another in interatomic interactions [1,2]. Along one of the branches of an oscillation, the interatomic interactions decrease, and, after they reach a minimum value, they begin increasing. The character of the changes to the opposite. Such a cycle can repeat until a state with a smaller free energy is formed. This
∗
Tel./fax: +7-095-458-0720. E-mail address: [email protected] (A.Y. Gubenko).
1463-0184/02/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1463-0184(02)00025-4
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peculiarity of the evolution to an attractor makes it possible to establish a relation between microscopic and macroscopic properties.
2. Results and discussion The methods of obtaining experimental data that will be given below have been described in the papers cited. In order to clarify the causes of the interrelation between microscopic and macroscopic properties of materials, we compare the dependences of properties and states of materials formed via LSFs upon the occurrence of a PT and other transitions in the temperature, concentration, and time intervals. Consider how the properties of solid solutions change in phase diagrams with a so-called retrograde solidus. The peculiar shape of such a solidus line can be explained by the fact that it corresponds to one-cycle oscillation formed upon PT [4]. In this case, along the solidus line, which represents an oscillation branch, the interatomic interactions and the density decrease with increasing temperature T, while the equilibrium concentrations of the alloying impurity and intrinsic point defects (vacancies), as well as the vapor pressures of the basic component of the solid solution increase up to T = T extr. At this temperature, the properties have a minimum or a maximum value. At T ⬎ T extr, the law of the variation of these quantities changes to the opposite. The electrophysical properties change in the same manner. In Si and Ge doped with Au, the Au ions are negative (Au-), i.e., manifest acceptor properties, up to Textr; at T ⬎ T extr, they become positive, which was established from the electrical transport properties [5,6]. The same occurs in Si and Ge doped with Ag and in Si doped with As above or below Textr. In pure Si, Ge, and other semiconductor materials, there also exists an extremal temperature Textr at which there is observed a sharp change in the interatomic interactions, and the law of their variation is similar to the law of the variation of macroscopic properties such as the density, vapor pressures, or electrophysical properties. In this case, the Textr temperature is somewhat higher than that observed in the solidus lines in binary systems. Phase transformations of the above types also occur in binary systems with unlimited solubility of the components, such as Fe–Ni or Ge–Si. One of such transformations in the first system occurs in a concentration interval from ~25 to 40 at.%. The maximum change in the interatomic interactions occurs at Ni concentrations of ~35 at.%. In the above interval, the lattice parameter changes nonmonotonically, passing through a maximum at ~35 at.% Ni. At this concentration, the arising LSFs lead to the formation of a well-known invar alloy possessing unique properties. In the Ge– Si system, there is a whole number of PTs. In the concentration intervals in which they occur, the interatomic interactions and the spatial arrangement of atoms change in an oscillating manner, judging from the character of the variation of the lattice parameter and density, and at the extremal points (at maxima and minima) of the oscillations alloys are formed with unique properties. The character of changes in the interatomic interactions was judged from the Debye temperature and density. In
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the region of one of the extremal points of the oscillating dependence of the alloy properties on the concentration of Si in the alloy, the interatomic interactions, which decreased at Si concentrations less than 12.5 at.%, reach a minimum value at this concentration and increase at greater concentrations. The electrophysical properties change in the same manner. In the region of the concentration equal to 12.5 at.% Si in Ge, there occurs a transition from the ⬍111⬎ direction of the conduction-band minimum characteristic of the undoped Ge to the direction ⬍100⬎, as in pure Si [7]. At the same concentration of Si, the derivatives of the electron properties of the alloys with respect to the Si concentration varied in an oscillating manner. In Ge doped with Si to concentrations reaching a few tenths of an atomic percent, the values of the lattice parameter, energy gap, and density changed in an oscillating manner and correlated with one another. The effect of interatomic interactions and the spatial arrangement of atoms on the macroscopic properties of a substance can be traced on ultrathin films. For example, in ultrathin films of Au on Si, when the binding energy in them was higher than in the bulk material, compounds such as SiAu3 were revealed, which were absent in the equilibrium phase diagram. When the thickness of the ultrathin film reaches a value at which the binding energy becomes equal to that in the bulk material, no such compounds can be found in the ultrathin films. A brilliant example of the interrelation discussed is the PT in which a ferromagnetic material becomes paramagnetic, e.g., in Co. As was shown by measurements, the temperature dependencies of the rate of evaporation (j) of Co and of the pressure of its vapors calculated from this rate (pCo) consist of two maxima and one minimum (Fig. 1). One of the maxima is located at the Curie temperature (TC). Along one of the branches of this maximum, both j and pCo increase with temperature first slowly then rapidly. The interatomic interactions in Co, which are proportional to pCo,
Fig. 1. Temperature dependence of the rate of evaporation of cobalt. The rate of heating in the case of 1 is smaller than that in 2.
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change in the same manner. As is known, the magnetism of Co also changes in the same manner. The correlations of the dependences of all these quantities are due to the fact that the Co states in the temperature interval considered, in which the PT occurs, are formed via LSFs. On both sides of TC, the LSFs differ only a little from one another [1,2]. Therefore, the magnetism is retained at a temperature T somewhat greater than TC. A decrease in the magnetism is observed, as is known, at low temperatures. This effect is related to changes in the interatomic interactions along the branches of the second maximum (Fig. 1). Thus, a change in the quality of the same material is due to changes in the interatomic interactions. The same occurs upon PTs in other materials, but changes are not so radical. In Ge doped with Au and Sb, PTs occur at temperatures of 780– 850 °C. Beginning from ~780 °C, the interatomic interactions decrease progressively up to 850 °C, and the equilibrium solubilities of Au and Sb and the concentration of vacancies increase up to 850 °C, judging from the increase in the vapor pressure of Ge. At low temperatures in the same temperature range, a complex with an ionization energy of 0.05 eV is formed in Ge; the concentration of this complex decreases with temperature, but, instead, a complex with an ionization energy of 0.16 eV is formed, which consists of Au and Sb atoms and vacancies. The concentration of this complex increases with temperature up to 850 °C; at higher temperatures, this concentration decreases, like the equilibrium solubilities of Au and Sb and the concentration of vacancies, while the interatomic interactions increase. Such changes took place in an n-type silicon film with r⬇15 ⍀ cm quenched from 1000 °C upon subsequent annealing depending on the annealing time. In such a material the time dependences of the concentration of thermodonors, their composition, and ionization energy varied in an oscillating manner. In the Al–5% Cu alloy quenched from 550 °C, the dependence of interatomic interactions and the mechanical properties on the time of annealing at a temperature of 200 °C varied in an oscillating manner. In the vicinity of one extremal point of the oscillation, inclusions were revealed; on the next oscillation, they were absent; on the third oscillation, they were revealed again, but they had a different chemical composition [3]. The quenched, i.e., strongly supersaturated, solid solutions evolved upon annealing to a new state with a smaller free energy. In the process of the evolution, the interatomic interactions and the whole body of properties of the material changed in an oscillating manner, and compositions were formed with inclusions or complexes and without them. In all the cases that were described above and in other cases [1,3,4], the changes occurring in the material obey the following rule. If some interatomic (intermolecular) changes occur in a material (substance), these changes are accompanied by changes in the type of particles existing in the material and in the macroscopic properties of the material. And, vice versa, if particles of a new sort arise in the material, this means that interatomic (intermolecular) changes occur in it. All attempts to consider reactions that occur in a solid without allowance for this rule are unjustified. Correlations between various macroscopic properties observed by many researchers are a result of such changes in the interatomic interactions in a given material. Upon any change in an independent variable, each value of this
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variable corresponds to certain interatomic interactions and macroscopic properties. Such an interrelation makes it possible to estimate interatomic (intermolecular) interactions and the regularities of their changes from the character of changes in the macroscopic properties without resorting to complex investigations on the atomic (molecular) level.
References [1] A.Y. Gubenko, Kistallografiya 46 (2001) 81. [2] A.Y. Gubenko, in: The Seventh Scientific and Business Conference, 7–10 November 2000, Rozˇ nov pod Radhostem, Czech Republic. [3] A.Y. Gubenko, Izv. Ross. Akad. Nauk, Met. (1) (2000) 87. [4] A.Y. Gubenko, Izv. Ross. Akad. Nauk, Met. (4) (1997) 99. [5] B.N. Boltaks, Diffuziya v poluprovodnikakh (Diffusion in Semiconductors), Fizmatlit, Moscow, 1958. [6] O.N. Gromova, K.M. Khodunova, Fiz. Khim. Obrab. Mater. (5) (1968) 150. [7] N.M. Bogatov, E.N. Khabarov, Vysokochist, Veshchestva (5) (1968) 15.
On the interrelation between the microscopic and macroscopic properties of materials Anatolii Ya Gubenko ∗ Moscow Institute of Steel and Alloys, Festival’naya 17-138, 125195 Moscow, Russia
Abstract The origin of the correlation between the microscopic and macroscopic material properties that are formed as a result of large-scale fluctuations in the process of evolution of the material to a new state was investigated. Each value of the state parameter corresponds to a certain set of large-scale fluctuations and microscopic states. It was established that the correlations between the dependences of the microscopic and macroscopic properties of the materials are determined by the interatomic interactions and the spatial arrangement of atoms. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Evolution; Correlation; Interaction; Properties
1. Introduction It was established in our previous works that all phase transformations and other transitions in materials (substances) occur in an interval of a variable state parameter [1,2] and time [3]. Within these intervals, the material evolves via large-scale fluctuations (LSFs) that arise spontaneously and disappear after the material reaches a state with a smaller free energy as compared to the initial state. The LSFs, along with a feedback, lead to the formation of oscillations, which consist of microscopic states differing from one another in interatomic interactions [1,2]. Along one of the branches of an oscillation, the interatomic interactions decrease, and, after they reach a minimum value, they begin increasing. The character of the changes to the opposite. Such a cycle can repeat until a state with a smaller free energy is formed. This
∗
Tel./fax: +7-095-458-0720. E-mail address: [email protected] (A.Y. Gubenko).
1463-0184/02/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1463-0184(02)00025-4
164
A.Y. Gubenko / Crystal Engineering 5 (2002) 163–167
peculiarity of the evolution to an attractor makes it possible to establish a relation between microscopic and macroscopic properties.
2. Results and discussion The methods of obtaining experimental data that will be given below have been described in the papers cited. In order to clarify the causes of the interrelation between microscopic and macroscopic properties of materials, we compare the dependences of properties and states of materials formed via LSFs upon the occurrence of a PT and other transitions in the temperature, concentration, and time intervals. Consider how the properties of solid solutions change in phase diagrams with a so-called retrograde solidus. The peculiar shape of such a solidus line can be explained by the fact that it corresponds to one-cycle oscillation formed upon PT [4]. In this case, along the solidus line, which represents an oscillation branch, the interatomic interactions and the density decrease with increasing temperature T, while the equilibrium concentrations of the alloying impurity and intrinsic point defects (vacancies), as well as the vapor pressures of the basic component of the solid solution increase up to T = T extr. At this temperature, the properties have a minimum or a maximum value. At T ⬎ T extr, the law of the variation of these quantities changes to the opposite. The electrophysical properties change in the same manner. In Si and Ge doped with Au, the Au ions are negative (Au-), i.e., manifest acceptor properties, up to Textr; at T ⬎ T extr, they become positive, which was established from the electrical transport properties [5,6]. The same occurs in Si and Ge doped with Ag and in Si doped with As above or below Textr. In pure Si, Ge, and other semiconductor materials, there also exists an extremal temperature Textr at which there is observed a sharp change in the interatomic interactions, and the law of their variation is similar to the law of the variation of macroscopic properties such as the density, vapor pressures, or electrophysical properties. In this case, the Textr temperature is somewhat higher than that observed in the solidus lines in binary systems. Phase transformations of the above types also occur in binary systems with unlimited solubility of the components, such as Fe–Ni or Ge–Si. One of such transformations in the first system occurs in a concentration interval from ~25 to 40 at.%. The maximum change in the interatomic interactions occurs at Ni concentrations of ~35 at.%. In the above interval, the lattice parameter changes nonmonotonically, passing through a maximum at ~35 at.% Ni. At this concentration, the arising LSFs lead to the formation of a well-known invar alloy possessing unique properties. In the Ge– Si system, there is a whole number of PTs. In the concentration intervals in which they occur, the interatomic interactions and the spatial arrangement of atoms change in an oscillating manner, judging from the character of the variation of the lattice parameter and density, and at the extremal points (at maxima and minima) of the oscillations alloys are formed with unique properties. The character of changes in the interatomic interactions was judged from the Debye temperature and density. In
A.Y. Gubenko / Crystal Engineering 5 (2002) 163–167
165
the region of one of the extremal points of the oscillating dependence of the alloy properties on the concentration of Si in the alloy, the interatomic interactions, which decreased at Si concentrations less than 12.5 at.%, reach a minimum value at this concentration and increase at greater concentrations. The electrophysical properties change in the same manner. In the region of the concentration equal to 12.5 at.% Si in Ge, there occurs a transition from the ⬍111⬎ direction of the conduction-band minimum characteristic of the undoped Ge to the direction ⬍100⬎, as in pure Si [7]. At the same concentration of Si, the derivatives of the electron properties of the alloys with respect to the Si concentration varied in an oscillating manner. In Ge doped with Si to concentrations reaching a few tenths of an atomic percent, the values of the lattice parameter, energy gap, and density changed in an oscillating manner and correlated with one another. The effect of interatomic interactions and the spatial arrangement of atoms on the macroscopic properties of a substance can be traced on ultrathin films. For example, in ultrathin films of Au on Si, when the binding energy in them was higher than in the bulk material, compounds such as SiAu3 were revealed, which were absent in the equilibrium phase diagram. When the thickness of the ultrathin film reaches a value at which the binding energy becomes equal to that in the bulk material, no such compounds can be found in the ultrathin films. A brilliant example of the interrelation discussed is the PT in which a ferromagnetic material becomes paramagnetic, e.g., in Co. As was shown by measurements, the temperature dependencies of the rate of evaporation (j) of Co and of the pressure of its vapors calculated from this rate (pCo) consist of two maxima and one minimum (Fig. 1). One of the maxima is located at the Curie temperature (TC). Along one of the branches of this maximum, both j and pCo increase with temperature first slowly then rapidly. The interatomic interactions in Co, which are proportional to pCo,
Fig. 1. Temperature dependence of the rate of evaporation of cobalt. The rate of heating in the case of 1 is smaller than that in 2.
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A.Y. Gubenko / Crystal Engineering 5 (2002) 163–167
change in the same manner. As is known, the magnetism of Co also changes in the same manner. The correlations of the dependences of all these quantities are due to the fact that the Co states in the temperature interval considered, in which the PT occurs, are formed via LSFs. On both sides of TC, the LSFs differ only a little from one another [1,2]. Therefore, the magnetism is retained at a temperature T somewhat greater than TC. A decrease in the magnetism is observed, as is known, at low temperatures. This effect is related to changes in the interatomic interactions along the branches of the second maximum (Fig. 1). Thus, a change in the quality of the same material is due to changes in the interatomic interactions. The same occurs upon PTs in other materials, but changes are not so radical. In Ge doped with Au and Sb, PTs occur at temperatures of 780– 850 °C. Beginning from ~780 °C, the interatomic interactions decrease progressively up to 850 °C, and the equilibrium solubilities of Au and Sb and the concentration of vacancies increase up to 850 °C, judging from the increase in the vapor pressure of Ge. At low temperatures in the same temperature range, a complex with an ionization energy of 0.05 eV is formed in Ge; the concentration of this complex decreases with temperature, but, instead, a complex with an ionization energy of 0.16 eV is formed, which consists of Au and Sb atoms and vacancies. The concentration of this complex increases with temperature up to 850 °C; at higher temperatures, this concentration decreases, like the equilibrium solubilities of Au and Sb and the concentration of vacancies, while the interatomic interactions increase. Such changes took place in an n-type silicon film with r⬇15 ⍀ cm quenched from 1000 °C upon subsequent annealing depending on the annealing time. In such a material the time dependences of the concentration of thermodonors, their composition, and ionization energy varied in an oscillating manner. In the Al–5% Cu alloy quenched from 550 °C, the dependence of interatomic interactions and the mechanical properties on the time of annealing at a temperature of 200 °C varied in an oscillating manner. In the vicinity of one extremal point of the oscillation, inclusions were revealed; on the next oscillation, they were absent; on the third oscillation, they were revealed again, but they had a different chemical composition [3]. The quenched, i.e., strongly supersaturated, solid solutions evolved upon annealing to a new state with a smaller free energy. In the process of the evolution, the interatomic interactions and the whole body of properties of the material changed in an oscillating manner, and compositions were formed with inclusions or complexes and without them. In all the cases that were described above and in other cases [1,3,4], the changes occurring in the material obey the following rule. If some interatomic (intermolecular) changes occur in a material (substance), these changes are accompanied by changes in the type of particles existing in the material and in the macroscopic properties of the material. And, vice versa, if particles of a new sort arise in the material, this means that interatomic (intermolecular) changes occur in it. All attempts to consider reactions that occur in a solid without allowance for this rule are unjustified. Correlations between various macroscopic properties observed by many researchers are a result of such changes in the interatomic interactions in a given material. Upon any change in an independent variable, each value of this
A.Y. Gubenko / Crystal Engineering 5 (2002) 163–167
167
variable corresponds to certain interatomic interactions and macroscopic properties. Such an interrelation makes it possible to estimate interatomic (intermolecular) interactions and the regularities of their changes from the character of changes in the macroscopic properties without resorting to complex investigations on the atomic (molecular) level.
References [1] A.Y. Gubenko, Kistallografiya 46 (2001) 81. [2] A.Y. Gubenko, in: The Seventh Scientific and Business Conference, 7–10 November 2000, Rozˇ nov pod Radhostem, Czech Republic. [3] A.Y. Gubenko, Izv. Ross. Akad. Nauk, Met. (1) (2000) 87. [4] A.Y. Gubenko, Izv. Ross. Akad. Nauk, Met. (4) (1997) 99. [5] B.N. Boltaks, Diffuziya v poluprovodnikakh (Diffusion in Semiconductors), Fizmatlit, Moscow, 1958. [6] O.N. Gromova, K.M. Khodunova, Fiz. Khim. Obrab. Mater. (5) (1968) 150. [7] N.M. Bogatov, E.N. Khabarov, Vysokochist, Veshchestva (5) (1968) 15.