**2. Modification of titanium alloys defect structure by plastic deformation method**

The progress of modern engineering and technology is closely related to the achievements in science of metals, which before taking a specified form and properties usually undergo plastic deformation. Not only is the deformation process one of the effective methods for giving the required form to a material but it is also an important means for modifying its structure and properties. Yet defect formation and defects influence on metals physico-mechanical proper‐ ties is one of the important problems in metal physics. For investigation of modification processes in metals structures the titanium binary alloys, alloyed with Zr, Al, Sn, V, Ge and In within the range of solid solution, were prepared. The elements content in alloys was defined more precisely by chemical and spectral analysis.

Zirconium Zr is an analog of Ti and forms with it a substitutional solid solution of complete solubility. As far as concentration of Zr is increased the temperature of the allotropic trans‐ formation of Ti slightly drops and reaches the minimum at equiatomic ratio (50 at.% and 545ºС). Thus, Zr is a weak β–stabilizer for Ti. Usually β–phase is not preserved in this system at the room temperature. Al is a substitutional element for Ti with limited solubility in α- and β-phase at presence of peritectoid breakup of the β–solid solution. The Ti-Al system plays the same role as the Fe-C system for steels in physical metallurgy.

While alloying Ti by Sn, the eutectic systems are formed. Sn forms the system with limited solubility of alloying elements at presence of the eutectic breakup of β–solid solution. Sn considerably differs from Ti by its properties and it is restrictedly soluble in both Ti modifi‐ cations. Ti-In is one of those systems that are most insufficiently explored due to considerable difficulties related to preparation of alloys. In slightly reduces the temperature of alloy polymorphic transformation and is therefore a weak β–stabilizer.

When alloying titanium with vanadium a solid solution in β-Ti is formed, with complete solubility. Ti-V phase diagram strongly depends on the method of obtaining Ti (iodide, hydride-calcic or magnesium-thermic). The V solubility in *α*−Ti at 650ºС does not exceed 3.5 weight %. Alloying with V leads to Ti lattice spacing decrease, therefore the с/αratio consec‐ utively decreases with increase of V content in alloy.

#### **2.1. Structural transformations in plastically deformed alloys of the Ti-Zr system**

temperature. The true content of the components in the check samples of the material was determined by chemical and spectral analysis methods. Then the surfaces of these samples were thoroughly burnished, and the samples were polished electrochemically in the solution of the following composition: HF – one part, HNO3 – three parts and H2O – two parts. The prepared samples were flushed with flowing water and wiped with alcohol. The temperature measurement of samples at irradiation and annealing was performed by thermometry methods. All measurement processes of annihilation characteristics of investigated materials after different kinds of influences (plastic deformation, radiative and other complex physico‐

**2. Modification of titanium alloys defect structure by plastic deformation**

The progress of modern engineering and technology is closely related to the achievements in science of metals, which before taking a specified form and properties usually undergo plastic deformation. Not only is the deformation process one of the effective methods for giving the required form to a material but it is also an important means for modifying its structure and properties. Yet defect formation and defects influence on metals physico-mechanical proper‐ ties is one of the important problems in metal physics. For investigation of modification processes in metals structures the titanium binary alloys, alloyed with Zr, Al, Sn, V, Ge and In within the range of solid solution, were prepared. The elements content in alloys was defined

Zirconium Zr is an analog of Ti and forms with it a substitutional solid solution of complete solubility. As far as concentration of Zr is increased the temperature of the allotropic trans‐ formation of Ti slightly drops and reaches the minimum at equiatomic ratio (50 at.% and 545ºС). Thus, Zr is a weak β–stabilizer for Ti. Usually β–phase is not preserved in this system at the room temperature. Al is a substitutional element for Ti with limited solubility in α- and β-phase at presence of peritectoid breakup of the β–solid solution. The Ti-Al system plays the

While alloying Ti by Sn, the eutectic systems are formed. Sn forms the system with limited solubility of alloying elements at presence of the eutectic breakup of β–solid solution. Sn considerably differs from Ti by its properties and it is restrictedly soluble in both Ti modifi‐ cations. Ti-In is one of those systems that are most insufficiently explored due to considerable difficulties related to preparation of alloys. In slightly reduces the temperature of alloy

When alloying titanium with vanadium a solid solution in β-Ti is formed, with complete solubility. Ti-V phase diagram strongly depends on the method of obtaining Ti (iodide, hydride-calcic or magnesium-thermic). The V solubility in *α*−Ti at 650ºС does not exceed 3.5 weight %. Alloying with V leads to Ti lattice spacing decrease, therefore the с/αratio consec‐

chemical and thermal treatments) were conducted at room temperature.

more precisely by chemical and spectral analysis.

same role as the Fe-C system for steels in physical metallurgy.

polymorphic transformation and is therefore a weak β–stabilizer.

utively decreases with increase of V content in alloy.

**method**

122 Titanium Alloys - Advances in Properties Control

Influence of plastic deformation on the structural damages formation was investigated on the alloys that contained 0; 2.7; 8.3; 17.0; 22.0 and 39.0 at.% Zr. Plastic deformation *ε* = 50% considerably changes shape of the curves by decreasing width on the half height (FWHM) and increase of counting rate at maximum of *N*(0) relative to the initial (annealed) state, which is the effect of crystal structure defects occurrence in the material (Fig.4). For interpretation of investigation results the above mentioned annihilation parameters *F*=SP/Sg, *θ*F = *P*F/*mc* and their relative changes Δ*F* and Δ*θ*F were used.

In order to establish regularities of changes of annihilation parameters depending on the structure damages level, Ti and its alloy Ti – 2.7 at.% Zr underwent plastic deformation by different degrees in the range from *ε* = 5 up to 80 %. It is determined that main changes of the annihilation parameter occur when *ε* takes values up to 30%, whereupon it reaches saturation. Though for Ti–2.7 at.% Zr alloy it reaches saturation considerably quicker than for pure Ti (Fig. 5). Evidently it can be stated that with an increase of deformation degree the defects concentration in metals also increases and at certain level virtually all positrons are captured and annihilated in defects. In such state the annihilation parameters are typical for deformation defects. In other words, in the conditions of ultimate strains the EPA characteristics contain information about structure of the crystal regions, in which the vast majority of positrons annihilation occurs.

**Figure 5.** The influence of deformation degree and alloying element concentration on titanium alloys structural-sensi‐ tive characteristics: 1-Ti; 2- Ti-2.7 at.% Zr; 3- N(0)/S0 relationship; 4- the β-phase content in alloy

In order to determine the phase composition, titanium and Ti–2.7at.% Zr alloy underwent Xray analysis using the DRON-2 diffractometer in the filtered CuK<sup>α</sup> radiation with the help of the special methods of accuracy enhancement. Then the β−phase concentration in the lattice structure can be determined by the equation [5]:

$$C\_{\beta} = \frac{100\%}{1 + 2.33(I\_{\alpha}/I\_{\beta})} \text{ } \tag{9}$$

Therefore, one should consider two main factors that are responsible for initiation of the polymorphic transformation in the Ti-Zr alloys: plastic deformation, which leads to the formation of packing defect with the BCC-phase structure in the HCP-phase matrix, and positron interaction with lattice instability. Separation of contribution pertaining to each factor to annihilation parameters change is as yet an impracticable problem for employed experiment

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**Figure 6.** Concentration dependencies of annihilation characteristics for Ti-Zr system alloys.

In order to obtain additional information about the nature of positrons interaction with the structure damages in the plastically deformed metals the second group of binary titanium alloys was prepared. These alloys contain alloying elements from the III group of the periodic system, namely Al in concentrations 0; 5.2; 10.2; 12.5 and 16.5 at.%, and also In with concen‐ trations 0; 1.4; 2.9; 5.1; 8.5 and 10.3 at.%. The maximum concentration of alloying element in each of these systems meets the requirements of mandatory occurrence of alloys in the solid

All alloy samples with the specified concentrations of alloying elements were deformed by the cold rolling method by *ε* =50%. Concentration dependencies of the Δ*F* and Δ*θ*F annihilation parameters for the investigated materials are presented in Fig. 7. One can see that relative changes of the *F* parameter for these alloys are also considerable as in the previous case and reach 130% for Ti–5.2 Al alloy and 250% for Ti–1.4 In alloy. At the same time the Fermi angle decrease for the first case reaches Δθ = 17% and 12.7% - for the second case. For Ti-In system the ΔF concentration dependence is of complex nature with two maximum points with In

solution region, where the chemical compounds formation is ruled out in advance.

**2.2. Structure modification in the Ti-Al and Ti-In alloys**

conditions.

concentrations 1.4 and 7.4 at.%.

where *Ι*α and *Ι*β are X-ray radiation integral intensity for α- and β–phases of the alloy, respec‐ tively. It has been established that the cold deformed Ti at any deformation degrees has only a single-phase structure. Also after plastic deformation in the alloy there is a two-phase α+β microstructure is observed, where the β−phase content changes monotonically with the deformation degree (Table 1 and Fig.5).


**Table 1.** The β−phase content in Ti–2.7at.% Zr alloy

Hence, one can do the following conclusion. For those alloys that undergo transformation, plastic deformation at room temperature initiates phase transformation since energy rise in the crystal introduced by the defects may thereby decrease. In this case, the boundary with matrix regions of new phase nucleus should be assumed as the most likely positrons capture centers.

In such metals as Ti and Zr, in which the phase transformations from HCP to BCC-structure occur at relatively low temperatures, the packing defect formation energy in prismatic plane must be small [6]. With this in mind one cannot help noticing the nature of dependence of the relative change Δ*F* = (*Fdef* – *Frel*)/*Frel* parameter on alloys composition (Fig.6).

The maximum changes Δ*F* are observed for alloys with 2.7 and 3.9 at.% Zr, while for other concentrations this value is significantly lower. By individual cases, possible role of other factors is indicated by this behavior of the parameter *F*; one of such factors can be interaction of localized-in-defects positrons with lattice instability. In other words, it is pertaining to the different degrees of alloys lattice stability towards transformation initiation. It is evident that the maximum deviation of the parameter *F* related to Zr concentration nearly corresponds to the minimum value of the α→β transformation temperature.

Experimentally obtained value of Δ*θ*F=(*θ*ε-*θ*F0)/*θ*F0 parameter reaches ~9,5%, which is higher by order of magnitude than expected. This testifies that the positrons are annihilated in the defect regions, in which electron density is significantly lower than in the matrix. Thus the most likely positrons capture centers in this case are the new phase regions on its boundaries with the matrix. The structure of these new phase regions differs by far from that of the matrix.

**Figure 6.** Concentration dependencies of annihilation characteristics for Ti-Zr system alloys.

Therefore, one should consider two main factors that are responsible for initiation of the polymorphic transformation in the Ti-Zr alloys: plastic deformation, which leads to the formation of packing defect with the BCC-phase structure in the HCP-phase matrix, and positron interaction with lattice instability. Separation of contribution pertaining to each factor to annihilation parameters change is as yet an impracticable problem for employed experiment conditions.

#### **2.2. Structure modification in the Ti-Al and Ti-In alloys**

the special methods of accuracy enhancement. Then the β−phase concentration in the lattice

100% , 1 2.33( / )

*I I*

<sup>=</sup> <sup>+</sup> (9)

a b

where *Ι*α and *Ι*β are X-ray radiation integral intensity for α- and β–phases of the alloy, respec‐ tively. It has been established that the cold deformed Ti at any deformation degrees has only a single-phase structure. Also after plastic deformation in the alloy there is a two-phase α+β microstructure is observed, where the β−phase content changes monotonically with the

Ε (%) 0 5 10 20 30 40 50 60 70 80 Сβ (%) - 2,66 3,61 3,76 4,85 5,90 6,96 7,25 8,05 8,77

Hence, one can do the following conclusion. For those alloys that undergo transformation, plastic deformation at room temperature initiates phase transformation since energy rise in the crystal introduced by the defects may thereby decrease. In this case, the boundary with matrix regions of new phase nucleus should be assumed as the most likely positrons capture

In such metals as Ti and Zr, in which the phase transformations from HCP to BCC-structure occur at relatively low temperatures, the packing defect formation energy in prismatic plane must be small [6]. With this in mind one cannot help noticing the nature of dependence of the

The maximum changes Δ*F* are observed for alloys with 2.7 and 3.9 at.% Zr, while for other concentrations this value is significantly lower. By individual cases, possible role of other factors is indicated by this behavior of the parameter *F*; one of such factors can be interaction of localized-in-defects positrons with lattice instability. In other words, it is pertaining to the different degrees of alloys lattice stability towards transformation initiation. It is evident that the maximum deviation of the parameter *F* related to Zr concentration nearly corresponds to

Experimentally obtained value of Δ*θ*F=(*θ*ε-*θ*F0)/*θ*F0 parameter reaches ~9,5%, which is higher by order of magnitude than expected. This testifies that the positrons are annihilated in the defect regions, in which electron density is significantly lower than in the matrix. Thus the most likely positrons capture centers in this case are the new phase regions on its boundaries with the matrix. The structure of these new phase regions differs by far from that of the matrix.

relative change Δ*F* = (*Fdef* – *Frel*)/*Frel* parameter on alloys composition (Fig.6).

the minimum value of the α→β transformation temperature.

structure can be determined by the equation [5]:

124 Titanium Alloys - Advances in Properties Control

deformation degree (Table 1 and Fig.5).

**Table 1.** The β−phase content in Ti–2.7at.% Zr alloy

Accuracy ±0,05

centers.

*C*

b

In order to obtain additional information about the nature of positrons interaction with the structure damages in the plastically deformed metals the second group of binary titanium alloys was prepared. These alloys contain alloying elements from the III group of the periodic system, namely Al in concentrations 0; 5.2; 10.2; 12.5 and 16.5 at.%, and also In with concen‐ trations 0; 1.4; 2.9; 5.1; 8.5 and 10.3 at.%. The maximum concentration of alloying element in each of these systems meets the requirements of mandatory occurrence of alloys in the solid solution region, where the chemical compounds formation is ruled out in advance.

All alloy samples with the specified concentrations of alloying elements were deformed by the cold rolling method by *ε* =50%. Concentration dependencies of the Δ*F* and Δ*θ*F annihilation parameters for the investigated materials are presented in Fig. 7. One can see that relative changes of the *F* parameter for these alloys are also considerable as in the previous case and reach 130% for Ti–5.2 Al alloy and 250% for Ti–1.4 In alloy. At the same time the Fermi angle decrease for the first case reaches Δθ = 17% and 12.7% - for the second case. For Ti-In system the ΔF concentration dependence is of complex nature with two maximum points with In concentrations 1.4 and 7.4 at.%.

**Figure 7.** The concentration dependencies of annihilation parameters for Ti-In (1) and Ti-Al (2) deformed alloys systems.

On the basis of the findings related to studying Ti alloys one can state the following. For the deformed Ti alloys the sharply expressed anomalies are typical, which become even stronger with certain concentrations of the alloying elements and when the initial lattice is fully reconstructed as a result of considerable shortening of material interatomic distance. Conse‐ quently it is not possible for crystal lattice to preserve initial electron structure. Therefore, probably for the investigated Ti binary alloys we should adopt a concept of autonomy of delectron matrix subsystem relative to the alloying elements interstitial atoms conduction band, when the wave functions of the matrix atoms d-electrons are overlapped with the wave functions of impurity atoms conduction electrons. The latter is probably correlated somehow with the lattice instability. With this in mind the largest lattice instability are displayed by the investigated Ti alloys systems that contain 1.2 at.% Sn, due to which the maximum change of

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**Figure 8.** The concentration dependencies of annihilation parameters for Ti-Sn system.

**2.4. Restoration of structure damages in plastically deformed titanium alloys**

In many metals, the structure damages generated at low temperatures are usually "frozen", which enables investigation of their spectrum by measuring some macroscopic properties of the crystal with its subsequent heating. Among the most applicable are the methods of residual electrical resistance measurement, crystalline lattice period measurement, X-ray line profile measurement, etc. For dislocation structure investigation, electron microscopic and neutron

The main task of investigating metals modified by cold deformation is the differentiation between effects that are related to the presence of the structure defects ensemble in them. These effects can be more or less successfully determined while investigating the processes of recovery and recrystalization of deformed metals by annealing. The most important structure imperfection annealing mechanisms are absorption of point defects by dislocations, mutual destruction of vacancy and interstitial atoms, breakup of point defects aggregations into individual one, etc. As a result of these mechanisms, while heating, the structure damages are partially or fully annealed in different temperature ranges. Eventually the annealing process can be interrupted after recrystallization, due to which full removal of the defect structure and

Δ*F* annihilation parameter is observed.

diffraction methods were most effective [7, 8].

the initial structure restoration is observed.

If a strongly deformed alloy is to be considered as a two-phase system, then on the basis of positrons capture models one can define approximate bulk defect size therein: *R*V = 10 Å. Therefore, one can assume that strong deformation of titanium alloys is accompanied, along with the new phase, by the formation of vacancy clusters and their aggregations, which can serve as deep potential wells for positrons.

#### **2.3. Peculiarities of positrons annihilation in the deformed Ti-Sn alloys**

These alloys contained the following concentrations of alloying element: 0; 1.2; 2.5; 4.3; 6.2 and 7.6 at.% Sn. All alloys were deformed by cold rolling by *ε* = 50 %. The investigation results are presented in Fig.8. The observed changes of parameters in this case, as in the earlier one, are substantial and possess a complex nature dependent on alloy composition. Thus, the relative change of annihilation probability Δ*F* for Ti–1.2 at.% Sn alloy passes through maximum and reaches 135 % and then reaches minimum value (Δ*F* = 85 %) at the concentration of 6.2 at. % Sn. For comparison, in the case of Ti-Ge alloys system this factor also passes through maximum at the concentration of 0.8 at.% Ge, but with Δ*F* =185 %.

One can make yet another observation which is typical for these alloys: the nature of change of the alloying elements parameters at small concentrations roughly coincide, whereas maximum decrease of the Fermi angle (Δ*θ*F = −17%) is detected for the Ti–1.5 at.% Ge alloy. In other words, it is facing a certain shift between maximum locations for two dependencies of one system of alloys.

Based on abnormally large changes of *F* and *θ*F annihilation parameters one can make an assumption that the positrons capture centers structure conform to the regions with average electron density, which is considerably lower than for general vacancy-dislocation defects. Since the deformation causes a considerable increase of the parameter *F* with the respective decease of the Fermi momentum, this indicates that with general decrease of average electron density in these defects the contribution of ion core electrons to the EPA process also decreases. This means that the annihilation occurs mainly with free electrons in the defects.

**Figure 8.** The concentration dependencies of annihilation parameters for Ti-Sn system.

**Figure 7.** The concentration dependencies of annihilation parameters for Ti-In (1) and Ti-Al (2) deformed alloys systems.

If a strongly deformed alloy is to be considered as a two-phase system, then on the basis of positrons capture models one can define approximate bulk defect size therein: *R*V = 10 Å. Therefore, one can assume that strong deformation of titanium alloys is accompanied, along with the new phase, by the formation of vacancy clusters and their aggregations, which can

These alloys contained the following concentrations of alloying element: 0; 1.2; 2.5; 4.3; 6.2 and 7.6 at.% Sn. All alloys were deformed by cold rolling by *ε* = 50 %. The investigation results are presented in Fig.8. The observed changes of parameters in this case, as in the earlier one, are substantial and possess a complex nature dependent on alloy composition. Thus, the relative change of annihilation probability Δ*F* for Ti–1.2 at.% Sn alloy passes through maximum and reaches 135 % and then reaches minimum value (Δ*F* = 85 %) at the concentration of 6.2 at. % Sn. For comparison, in the case of Ti-Ge alloys system this factor also passes through maximum

One can make yet another observation which is typical for these alloys: the nature of change of the alloying elements parameters at small concentrations roughly coincide, whereas maximum decrease of the Fermi angle (Δ*θ*F = −17%) is detected for the Ti–1.5 at.% Ge alloy. In other words, it is facing a certain shift between maximum locations for two dependencies of

Based on abnormally large changes of *F* and *θ*F annihilation parameters one can make an assumption that the positrons capture centers structure conform to the regions with average electron density, which is considerably lower than for general vacancy-dislocation defects. Since the deformation causes a considerable increase of the parameter *F* with the respective decease of the Fermi momentum, this indicates that with general decrease of average electron density in these defects the contribution of ion core electrons to the EPA process also decreases.

This means that the annihilation occurs mainly with free electrons in the defects.

**2.3. Peculiarities of positrons annihilation in the deformed Ti-Sn alloys**

serve as deep potential wells for positrons.

126 Titanium Alloys - Advances in Properties Control

at the concentration of 0.8 at.% Ge, but with Δ*F* =185 %.

one system of alloys.

On the basis of the findings related to studying Ti alloys one can state the following. For the deformed Ti alloys the sharply expressed anomalies are typical, which become even stronger with certain concentrations of the alloying elements and when the initial lattice is fully reconstructed as a result of considerable shortening of material interatomic distance. Conse‐ quently it is not possible for crystal lattice to preserve initial electron structure. Therefore, probably for the investigated Ti binary alloys we should adopt a concept of autonomy of delectron matrix subsystem relative to the alloying elements interstitial atoms conduction band, when the wave functions of the matrix atoms d-electrons are overlapped with the wave functions of impurity atoms conduction electrons. The latter is probably correlated somehow with the lattice instability. With this in mind the largest lattice instability are displayed by the investigated Ti alloys systems that contain 1.2 at.% Sn, due to which the maximum change of Δ*F* annihilation parameter is observed.

#### **2.4. Restoration of structure damages in plastically deformed titanium alloys**

In many metals, the structure damages generated at low temperatures are usually "frozen", which enables investigation of their spectrum by measuring some macroscopic properties of the crystal with its subsequent heating. Among the most applicable are the methods of residual electrical resistance measurement, crystalline lattice period measurement, X-ray line profile measurement, etc. For dislocation structure investigation, electron microscopic and neutron diffraction methods were most effective [7, 8].

The main task of investigating metals modified by cold deformation is the differentiation between effects that are related to the presence of the structure defects ensemble in them. These effects can be more or less successfully determined while investigating the processes of recovery and recrystalization of deformed metals by annealing. The most important structure imperfection annealing mechanisms are absorption of point defects by dislocations, mutual destruction of vacancy and interstitial atoms, breakup of point defects aggregations into individual one, etc. As a result of these mechanisms, while heating, the structure damages are partially or fully annealed in different temperature ranges. Eventually the annealing process can be interrupted after recrystallization, due to which full removal of the defect structure and the initial structure restoration is observed.

Of course, in the given temperature range more than one independent or concurrent processes can occur. Then the overall picture of annealing kinetics can be presented as superposition of separate individual processes each of which is responsible for a certain return mechanism. In addition, it appears to be impossible to avoid formation of the complexes, mobility of which can significantly differ from that of the single defects. The annealing kinetics of structure damages in metals, provided that there is one type of defects, can be described by following equation [9, 10]:

$$dP \mid dt = -\mathcal{J}\_0 P^t = -A\_0 P^t(t) \exp\left[-E\_a \mid kT\right],\tag{10}$$

where *P*(*t*) is the change of some material's physical property; T is absolute temperature. Here the activation energy of migration *Е*а is a typical sign of each of the defects type [11, 12]. If there are several active processes in the crystal then the search of the respective *Е*а values becomes complicated. At the same time the determination of the physical meaning of each value of *Е*<sup>а</sup> also becomes nontrivial. Therefore, it is often assumed that in the given narrow temperature range only one active process is running.

The essence of conducting the isochronal annealing by EPA method is based on the ADAP curve return for a defect material up to annealed state. As a result, the defects annealing states are usually established and the respective activation energy is defined by the following equation [13]:

$$E\_a = kT\_0 \ln(\nu \cdot k / aE\_a),\tag{11}$$

lization gradually shifts towards low temperature: from 200ºС at *ε* = 5% down to 100ºС at *ε* = 20%. At the same time the I-stage part tends to increase depending on the deformation degree. This effectively confirms successive accumulation of vacancy defects. This stage with *Е*а1 = 1.65–1.75 eV, evidently corresponds to vacancy and vacancy-impurity complexes. The II stage of annealing for this alloy tends to narrowing along with an increase of the deformation degree. All narrowing processes of the II stage are also accompanied by an increase of its relative level. Based on these results it can easily be established that it is Zr that serves as the β-phase initiating element. The given high-temperature stage, for which the migration activation energy occupies the interval of *Е*а2=1.85eV, probably corresponds to the dislocation and packing defects

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annealing with β-phase with split dislocations initiated by plastic deformation.

temperature. In other words, the alloying element must be β−stabilizer.

ν = 0.1 J/m2

**Figure 9.** Annealing kinetics of Ti-Zr alloys

**2.5. The structure modification of Ti-V alloys system as a source of packing defects**

The positrons interaction with packing defects is of certain interest because some researchers tend to doubt that positrons can be captured by defects of this type [14]. Therefore, arrange‐ ment of special experiments with more precise methods for detecting the latter is the task of high importance. However, in order to ensure with the highest probability packing defects occurrence as a result of plastic deformation, the investigated titanium alloys have to be accordingly chosen. To this effect, the alloying elements must form a complete solubility of solid solution with titanium without eutectic and peritectic in the investigated concentration range of the second component with the successive decrease of the phase transformation

Packing defects are a voluminous lesion. The objective of this research was to study packing defects by virtue of comparing X-ray structural analysis results with positron annihilation data. Based on the aforementioned, vanadium (V) was chosen as an alloying element, which is located in the Y-group of the periodic system. The energy of V packing defects formation is

, that is five times greater than for Ti but considerably smaller than for other metals

where *ν* ≈1013*s* <sup>−</sup><sup>1</sup> is a Debye frequency; *k* =8.62⋅10−<sup>5</sup> eV/K is the Boltzmann constant; *Т*<sup>0</sup> is average temperature of annealing stage (K); *α* =*Δ*(*T* <sup>−</sup><sup>1</sup> ) / *Δt*; *Δ*(*T* <sup>−</sup><sup>1</sup> )=*TI* <sup>−</sup><sup>1</sup> <sup>−</sup>*TF* −1 ; *Т*I and *Т*<sup>F</sup> are initial and final temperatures of the stage; Δ*t* is annealing time at a given temperature (*Т*).

The results of annealing investigations for titanium deformed by *ε* = 50% and 2.7 at.% Zr titanium alloy at different degree of deformation (*ε* = 5, 10 and 20%) are presented in Fig. 9 as isochronal annealing curves, which are shifted one relative to another by a constant value downward along the Y-coordinate. Isochronal annealing of iodide titanium is implemented in two steps. The first one is a low-temperature stage in the temperature range of 150-350ºС, i.e. the recrystallization temperature threshold for this stage is 150ºС. This stage, which has defects migration energy activation *Е*а1 =1.35eV, corresponds to the vacancy complexes. The hightemperature stage is located between 350ºС and 650ºС with activation energy *Е*а2 = 1.9eV. It is obvious that in this stage the dislocation defects and the packing defects, as β-phase initiated by plastic deformation, are annealed.

The results of annealing of Ti–2.7 at. % Zr alloy, which was exposed to different degrees of deformation, seems more interesting. It is easy to see that the annealing curves shape for alloy considerably differs from those of Ti that verifies the appropriate role of the alloying element Zr. With an increase of the plastic deformation degree the temperature threshold of recrystal‐

**Figure 9.** Annealing kinetics of Ti-Zr alloys

Of course, in the given temperature range more than one independent or concurrent processes can occur. Then the overall picture of annealing kinetics can be presented as superposition of separate individual processes each of which is responsible for a certain return mechanism. In addition, it appears to be impossible to avoid formation of the complexes, mobility of which can significantly differ from that of the single defects. The annealing kinetics of structure damages in metals, provided that there is one type of defects, can be described by following

> 0 0 / ( )exp / , *n n <sup>a</sup> dP dt P A P t E kT* =- =- -

é ù

where *P*(*t*) is the change of some material's physical property; T is absolute temperature. Here the activation energy of migration *Е*а is a typical sign of each of the defects type [11, 12]. If there are several active processes in the crystal then the search of the respective *Е*а values becomes complicated. At the same time the determination of the physical meaning of each value of *Е*<sup>а</sup> also becomes nontrivial. Therefore, it is often assumed that in the given narrow temperature

The essence of conducting the isochronal annealing by EPA method is based on the ADAP curve return for a defect material up to annealed state. As a result, the defects annealing states are usually established and the respective activation energy is defined by the following

> a

<sup>0</sup> ln( / ), *a a E kT k E* = × n

initial and final temperatures of the stage; Δ*t* is annealing time at a given temperature (*Т*). The results of annealing investigations for titanium deformed by *ε* = 50% and 2.7 at.% Zr titanium alloy at different degree of deformation (*ε* = 5, 10 and 20%) are presented in Fig. 9 as isochronal annealing curves, which are shifted one relative to another by a constant value downward along the Y-coordinate. Isochronal annealing of iodide titanium is implemented in two steps. The first one is a low-temperature stage in the temperature range of 150-350ºС, i.e. the recrystallization temperature threshold for this stage is 150ºС. This stage, which has defects migration energy activation *Е*а1 =1.35eV, corresponds to the vacancy complexes. The hightemperature stage is located between 350ºС and 650ºС with activation energy *Е*а2 = 1.9eV. It is obvious that in this stage the dislocation defects and the packing defects, as β-phase initiated

The results of annealing of Ti–2.7 at. % Zr alloy, which was exposed to different degrees of deformation, seems more interesting. It is easy to see that the annealing curves shape for alloy considerably differs from those of Ti that verifies the appropriate role of the alloying element Zr. With an increase of the plastic deformation degree the temperature threshold of recrystal‐

is a Debye frequency; *k* =8.62⋅10−<sup>5</sup>

average temperature of annealing stage (K); *α* =*Δ*(*T* <sup>−</sup><sup>1</sup>

ë û (10)

(11)

)=*TI*

) / *Δt*; *Δ*(*T* <sup>−</sup><sup>1</sup>

eV/K is the Boltzmann constant; *Т*<sup>0</sup> is

<sup>−</sup><sup>1</sup> <sup>−</sup>*TF* −1

; *Т*I and *Т*<sup>F</sup> are

l

range only one active process is running.

by plastic deformation, are annealed.

equation [9, 10]:

128 Titanium Alloys - Advances in Properties Control

equation [13]:

where *ν* ≈1013*s* <sup>−</sup><sup>1</sup>

lization gradually shifts towards low temperature: from 200ºС at *ε* = 5% down to 100ºС at *ε* = 20%. At the same time the I-stage part tends to increase depending on the deformation degree. This effectively confirms successive accumulation of vacancy defects. This stage with *Е*а1 = 1.65–1.75 eV, evidently corresponds to vacancy and vacancy-impurity complexes. The II stage of annealing for this alloy tends to narrowing along with an increase of the deformation degree. All narrowing processes of the II stage are also accompanied by an increase of its relative level. Based on these results it can easily be established that it is Zr that serves as the β-phase initiating element. The given high-temperature stage, for which the migration activation energy occupies the interval of *Е*а2=1.85eV, probably corresponds to the dislocation and packing defects annealing with β-phase with split dislocations initiated by plastic deformation.

#### **2.5. The structure modification of Ti-V alloys system as a source of packing defects**

The positrons interaction with packing defects is of certain interest because some researchers tend to doubt that positrons can be captured by defects of this type [14]. Therefore, arrange‐ ment of special experiments with more precise methods for detecting the latter is the task of high importance. However, in order to ensure with the highest probability packing defects occurrence as a result of plastic deformation, the investigated titanium alloys have to be accordingly chosen. To this effect, the alloying elements must form a complete solubility of solid solution with titanium without eutectic and peritectic in the investigated concentration range of the second component with the successive decrease of the phase transformation temperature. In other words, the alloying element must be β−stabilizer.

Packing defects are a voluminous lesion. The objective of this research was to study packing defects by virtue of comparing X-ray structural analysis results with positron annihilation data. Based on the aforementioned, vanadium (V) was chosen as an alloying element, which is located in the Y-group of the periodic system. The energy of V packing defects formation is ν = 0.1 J/m2 , that is five times greater than for Ti but considerably smaller than for other metals of the transition group. V is a β-stabilizing substitutional element for Ti with the atomic diameter of 2,72Å. The V alloys with 0; 0.5; 1.5; 2.0; 4.0 and 5.8 at. % content were prepared by the technique described above. The plastic deformation by *ε* = 80 % was implemented by rolling

at room temperature. (101 \_\_ 0), (0002) and (101 \_\_ 0) lines profiles were taken in the filtered CuK<sup>α</sup> radiation using the DRON-2 diffractometer. The packing defects formation on prismatic plane α(1010) probability calculation results along with the annihilation parameters are summarized in Table 2.


process is shaded by the bound vacancy-impurity complexes, which are caused by plastic

**Figure 10.** The concentration dependencies of annealing kinetics for deformed Ti-V alloys 1 – Ti; 2 – Ti – 2.0 at. %V; 3 –

Physicochemical and Radiation Modification of Titanium Alloys Structure

http://dx.doi.org/10.5772/55485

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The study of positrons behavior in the plastically deformed metals showed high sensitivity and selectivity of the EPA method to the structure damages in these materials. Therefore it is natural that investigators tend to use this method to learn about radiation effects in solids as a result of nuclear irradiations of a material. This irradiation is accompanied by a number of new phenomena. The most important among them are nuclear reactions and related to them change in the elemental composition, point defects formation and crystal integrity disturbance, point defects aggregations occurrence and matrix disturbance caused by atomic collisions

It is clear that without careful and detailed study of all aspects of nuclear radiation interaction with material and its consequences it is impossible to predict behavior of the materials in the field of strong ionizing radiation. The positron annihilation methods are promising and

As known, interaction of nuclear radiation with a material occurs by elastic and inelastic collisions channels. It is impossible to trace the process of radiation damage, which happens during 10-13–10-11s. Therefore, using different experimental methods the final structure of radiation damaged material is usually studied, which is in the state of equilibrium with an environment. Consequently, investigation and control of construction materials radiation

deformation, and the impurity atoms atmosphere formation around packing defects.

**3. Radiation modificationof the titanium alloys properties**

sufficiently informative for investigations of this kind.

**3.1. Problem statement**

Ti – 4.6 at.%V; 4 – V

cascades, etc.

**Table 2.** The packing defects probability and Ti-V alloys annihilation parameters

One can see that for all investigated alloys the plastic deformation leads to an increase of the parameter *F* by 25-50% with a simultaneous decrease of the Fermi angle *θ*F by 5-10%. The changes of the annihilation parameters depending on the composition are of monotonous nature. The packing defects probability on the basal plane both for Ti and alloys remains practically without changes and equals α(0001) = 2 10-3, whereas on the prismatic plane (1010) the probability monotonically increases from 4.2 10-3 up to 10.2 10-3 depending on V concen‐ tration. Thus, the packing defects formation under plastic deformation in Ti – V alloys became an established fact and alloying with V only facilitates this.

The results of the isochronal annealing for deformed Ti, V and Ti – V alloys are presented in Fig. 10.

On the basis of stage II annealing results analysis one can notice that among the investigated materials the packing defects are most pronounced only in the alloy with 2 at.% V, which corresponds to the temperature range 350 - 720ºС with *Е*а2 = 2.35eV. For all other alloys this

**Figure 10.** The concentration dependencies of annealing kinetics for deformed Ti-V alloys 1 – Ti; 2 – Ti – 2.0 at. %V; 3 – Ti – 4.6 at.%V; 4 – V

process is shaded by the bound vacancy-impurity complexes, which are caused by plastic deformation, and the impurity atoms atmosphere formation around packing defects.
