Phase transitions in chrome

In astronautics, stainless steel is widely used for the manufacture of spacecraft. Rocket fuel tanks are now made of stainless steel. In order for steel to be stainless, for example, grades 08X13 and 12X13, it must contain up to 13% chromium. In pure chromium and its alloys, phase transitions occur under temperature fluctuations and mechanical loads, during which the plastic, strength, and magnetic characteristics of steel alloys change. The article describes distinguishes between phase transformations of the 1st and 2nd kind in chromium and the inconsistency in the definition of the type of transition by different authors. The change in the form of the crystal lattice during the transition from an antiferromagnet to a paramagnet at the Neel point T C N = ° 38 85, is described. An analysis of the relationship between the type of phase transition and the type of symmetry is given. An explanation is given for the difficulties in studying phase transitions in chromium due to the imperfection of the model of the electronic configuration in the 3d layer of the chromium atom.


Introduction
In astronautics, stainless steel is widely used for the manufacture of spacecraft.Rocket fuel tanks are now made of stainless steel.In order for steel to be stainless, for example, grades 08X13 and 12X13, it must contain up to 13% chromium.In pure chromium and its alloys, phase transitions occur under temperature fluctuations and mechanical loads, during which the plastic, strength, and magnetic characteristics of steel alloys change.The study of the physical properties of chromium alloys during phase transitions is topical.
The article describes some methods for testing and measuring the characteristics of chromium, as well as physical models that explain the magnetic and structural transitions in the chromium crystal lattice.The author's approach is proposed to explain the separate study of structural and magnetic phase transformations in chromium and its alloys.

Theoretical methods
Transitions of the 1st and 2nd kind.Chromium belongs to the d-transition metals.It is generally accepted that in chromium at T C N = °38 85 , (Néel point) there is a phase transition antiferromagnetparamagnet .The opinion on which transition is divided, some experts believe that this is a transition of the 1st kind, others -of the 2nd kind.For pure chromium, most experts tend to think this is the transition of the 2nd kind, and it is more diffuse over the temperature range than the transition of the 1st kind.It is believed that this is a transition of the second kind for doped chromium with impurities of other metals.
In Fig. 1 [1] , the temperature dependence of the heat capacity C cal g atom deg p / ⋅ ⋅ ( ) shows that This issue has not been finally resolved.Vonsovsky [2] : draws attention to the effect on: «The interection of an exchange type between internal 3dand 4f-electrons on one sideands-electrons on the other leads for the latter to the effect of magnetization, which in turn changes their equilibrium statistical and kinetic physical properties, i.e. leads to ferro-or antiferromagnetic anomalies of these properties».
A characteristic physical quantity in phase transitions for chromium is the change in the heat capacity of chromium heating and cooling at the Néel point.
The question arises which effect causes such a sharp change in the heat capacity -change in the crystal lattice or magnetic transformation when the electron configuration in the atom changes?
At the same time, it is known that in metals, the electric heat capacity is an order of magnitude less than the lattice.
The author proposes to divide the consideration of phase changes in lattice and magnetic structure.
The following approach is proposed: to consider separately the models of magnetic and structural changes in the lattice and, once the models have been Van Vleck notes [2] : in Langevin's theory, he did not apply classical statistics to the «internal» or electronic degrees of molecules freedom but only to their «external» coordinates, which determine their orientation as a whole.
Thus [2] , in the usual classical derivation of the Langevin formula, the Boltzmann distribution applies only to generalized coordinates and momenta.
Based on this, it follows that the question of symmetry during a phase transition in a crystal lattice is more complicated and not unambiguous.
Grazhdankina N. F. [3] reports: all magnetic phase transitions of the first kind can be divided into two groups: order-order and transitions of the order-disorder type.Order-order transitions are called transitions with exchange interaction inversion [4] (Kittel).
Transitions of the order-disorder type are due to the destruction of spin ordering and are observed during the antiferromagnetism → paramagnetism transformations.
According to the theory of Kittel, as well as Wien and Rodbell [5] , the main reason for the 1-st order transitions is a strong change in exchange interactions depending on interatomic distances, as well as a change in the elastic energy of matter associated with this (exchange-striction mechanism).
If we assume that the lattice transformations and the magnetic transition do not occur simultaneously, then periodically heating and cooling the chromium samples and measuring the parameters of the changes, we can try to determine whether these transitions are delayed from one another in the vicinity of T N .
© 2021 Measurements infrastructure tions in the measured signals during ultrasonic and mechanical measurements.
And in general, what is a gas of paramagnets, are they atoms or are molecules or crystals or dipoles?
These can be: a -a gas of free electrons in which spins are chaotically arranged; b -electrons located in a crystal lattice with different spins; c -socialized electrons in the lattice; d -exchange interaction.

Practical methods
Structural changes in the crystal lattice.The issue of structural changes in the crystal lattice of chromium has not been resolved.In some papers, the authors believe that the volume-centered cubic (VCC) lattice of chromium at Neel point converted to a volume-centered tetragonal (VCT) lattice at the lowtemperature point when turning spins to There is no reliable single method for investigating both changes or by different methods at the same time.
In the work of Polovov V. M. [6]  In [7] «The anomalies in the mechanical properties of antiferromagnetic (AFM) crystals, especially cubic ones, often turn out to be greater than the anoma-lies in the magnetic susceptibility».Conclusion -it is possible to separate the changes in the magnetic and crystalline systems separately.They may have different criteria for assessing the type of phase transition.
The crystalline cubic system has rotations (5 parameters) of symmetry (rotation), and the tetragonal one has less.
The magnetization of randomly located magnons in paramagnets is equal to zero, and in AFM is also zero due to the mutual compensation of two sublattices with opposite spins, if we take the magnetization as a symmetry parameter.In a mechanical crystal, as the temperature drops below the Néel point, the order of symmetry decreases, while in a magnetic system, it does not change."In the vicinity of the Néel point, the sound propagation anomalies are determined by the parameters of the transition domain structure of the first-order transition [7] .It is interesting to study which In some works with ultrasonic measurements, including the author of [8] , the onset of a phase transition is observed not at the Néel point 38,75 ºС, and at a temperature of 31,5 ºС.Moreover, the reflection curves ultrasound (US) [8] consist of troughs and peaks (fluctuations) of the signals.The heating and cooling curves are mirror symmetrical.In the works of Taborov V. F. [9] , when exposed to ultra- at the low-temperature point when turning spins to There is no reliable single method for investigating both changes or by different methods at the same time.Baklanova [10]  general interpretation of all second-order phase transitions as symmetry change points: above the transition point in the disordered phase, the system has a higher symmetry than below the transition point in the ordered phase [11] .In the magnet above the transition point, the directions of the spins are distributed randomly.Therefore, the simultaneous rotation of all spins does not change the physical properties of the system.Below the transition points, the backs have a preferential orientation.Their simultaneous rotation changes the direction of the magnetic moment of the system.The symmetry itself at the transition point changes abruptly.However, the value that characterizes the asymmetry, which is called the order parameter, can change continuously [11] .

Symmetry of transitions. Of interest is what
kind of symmetry at phase transition points and which chromium parameter should be considered as symmetry parameter in phase transitions.According to Landau [11] , using the example of a slow displacement of O (oxygen) and Ti atoms in BaTiO 3 , there is an This is true for changing the cubic structure to a tetragonal one.But for the magnetic transition in chromium, the high-temperature phase is distinguished by a chaotic arrangement of magnets, and below the temperature at the Néel points of the AFM, the magnets are oppositely directed, and the total magnetization is zero, and, accordingly, such a symmetry parameter is equal to zero.
Symmetry is missing in both cases.As the temperature increases, the crystal lattice transforms from VC to VCC, and the magnetic system transforms from an ordered AFM state to a disordered paramagnetic state.

Conclusion
The article provides an analysis of literary sources and the author's works on phase transitions in chromium.In studies of phase transitions in chromium, such points as the reliability of the type of phase transition in chromium have not been sufficiently investigated.How do the changes in the crystal lattice in a chromium crystal and their relationship relate to the phase magnetic transition of the two sublattice antiferromagnets?Hence, the criteria for classifying the type of phase transition according to the symmetry parameters in the lattice and in the magnetic structure are not correct.
established, generalize their mutual influence by correlating their parameters.Moreover, these two transformations (magnetic and structural) are investigated by different methods.It is not known what changes in time occur earlier -a change in the lattice or changes in the magnetic structure.In some works with ultrasonic measurements, including the author, there is an onset of phase interruption not at Neel point but earlier by a few degrees.Interesting studies, such methods are more sensitive to a particular change in the lattice or magnetic structure.Also interesting is the question of what is primary and what is secondary: first, a change in the structure of the lattice, and then a magnetic transition, or vice versa.The physics of structural changes in the chromium crystal lattice has not been sufficiently studied in relation to the atomic structure of the atom.Some studies have observed sharp fluctua-of heat capacity to the statistics of the distribution of molecules (phonons) vibrations and, accordingly, magnetic magnons, then we can say that the statistics of magnons on both sides of the T N point differ.In this case, the transition type may change from the 1st to the 2nd view to the right and left of the T N point.Accordingly, the symmetry will change to the left and right of the transition point.At present, it is unknown what determines the change in heat capacity, either from a magnetic transformation or from a rearrangement of the crystal lattice.

1 A 2 →
with reference to the research of several authors, it is indicated with different research methods: neutrongraphic (Arott), magnetic (Strit, Pepper, Steinitz) and dilatometric (Matsumoto, Kondorsky) it has been established that the symmetry of the Cr lattice varies from VCC to orthorhombic (VCR) at Neel point and from VCR to VCT at spin rotation temperature T SF (Steinitz).There is no specific data on the phase transition temperature in this work.Finite jumps in neutron scattering intensity (Frrott), Cr at the T N and T sf phase transition temperatures suggest that both magnetic transformations in pure chromium are 1st kind transitions.Maybe one method is more sensitive to crystal lattice transformation and others to magnetic transition.There is no data in the work at what temperature the 1 A A transition occurs.One of the most reliable criteria for belonging to the phase transition of the 1st kind is the presence of latent heat, which is determined calorimetrically.
methods are more sensitive to one or another change in the lattice or magnetic structure.Also, the question of interest is what is primary and what is secondary: first, a change in the lattice structure, and then a magnetic transition, or vice versa.The physics of structural changes in the chromium crystal lattice has not been sufficiently studied in relation to the atomic structure of the atom.
sound at frequencies from 30 to 190 MHz at a temperature of 31,5 ºС, the speed jump is 2%, and the damping decrement reaches 5 10 2 ⋅ − .The maximum change in the damping decrement occurs earlier and in the opposite direction at 21,85 ºС.It is possible that ultrasound reacts first and faster to changes in the crystal lattice.The question of structural changes in the crystal lattice of chromium has not been resolved.In some papers, the authors believe that the volume-centered cubic (VCC) lattice of chromium at the Néel point transforms into a volume-centered tetragonal (VCT) © 2021 Measurements infrastructure considers the possibility of the existence of two VCC lattices with different parameters; as well as the possibility of the formation of VCR and VCT lattices.The diffraction structure of chromium below the Néel temperature corresponds to the tetragonal symmetry of its crystal lattice c a / , = 1 002) 300 K (where c, a -lat- tice parameters), and the VCC VCT → rearrangement is accompanied by polydominization of the initial single crystal.The formation of domains that are in twin orientation to each other according to the 011 011 { }→< > system is allowed.In the references to the structural studies available in the literature, no deviation from cubic symmetry was found at temperatures below the Néel point.It is possible that these transformations occur in time-shifted temperature regimes and occur differently during heating and cooling.That is, when heated, there is one transition mechanism, and when cooled, another.It is possible that there is a transition of the 1st kind of the crystal lattice of the VCC crystal at the Néel temperature to the tetragonal and then to the orthorhombic structure.Moreover, the time of the period of lattice changes and the magnetic period are divided both by time and by mechanism.During transitions of the 2nd kind, a sharp change in the heat capacity occurs.But the electron gas is not able to cause such a sharp transition since the heat capacity of the lattice is an order of magnitude greater than the heat capacity of the electron gas.It is possible that such changes in thermal effects occur due to the exchange interaction.As is known, electron gas in metals cannot be described by Boltzmann statistics, and Fermi-Dirac statistics are used for description.Without affecting the nature of the occurrence of magnetic moments in matter and the mechanisms of magnetic ordering, L. D. Landau in 1937 proposed a abrupt change in the crystallographic modification of the cubic lattice structure into a tetragonal one with decreasing temperature.For a clear understanding, it is necessary to know the critical parameters of these changes.The criterion for abruptness and transitions to another state and physical characteristics is set in the literature as the main difference between phase transitions of the 1st and 2nd order.Other parameters are also important for choosing the criterion for the type of phase transition.As a rule, the symmetry also changes during the transition.Therefore, it is more important to consider the relationship between changes in structure and symmetry rather than changes in state.An important fact is that the phase transition of the 1st kind of body in different states, and during the transition of the 2nd kind, they coincide.For example, the question of which transition of the 1st or 2nd kind is even more difficult for chromium.Since at the transition point, a magnetic transition occurs with a decrease in temperature from paramagnetic to antiferromagnetic, and at the same time, the cubic structure changes into a tetragonal one.The symmetry of the cubic structure is greater than the tetragonal one.Landau and Lifshitz believe that in the vast majority of cases of second-order phase transitions, the more symmetric phase corre-sponds to higher temperatures, and the less symmetric phase corresponds to lower temperatures.