*3.4.3 Electrical resistivity measurements*

*Metallic Glasses*

**34**

**Figure 6.**

*Microhardness values of the Fe73.5Cu1Nb3Si15.5B7, Fe75Ni2Si8B13C2, and Fe81B13Si4C2 alloys after annealing at different temperatures (a) and the first derivative of the curve of temperature dependence of electrical* 

Fe75Ni2Si8B13C2 and Fe81B13Si4C2 exhibit similar values of the first Curie temperature, as a result of similarities in their chemical composition including high Fe content, and equal percentages of B and C. The lowest values of the first Curie temperature are observed for the Fe73.5Cu1Nb3Si15.5B7 and Fe40Ni40P14B6 alloys. In the case of Fe73.5Cu1Nb3Si15.5B7 alloy, low value of the first Curie temperature is provoked by the presence of Nb. It is well known that the addition of Nb reduces the Curie temperature of the amorphous phase by around 25% per atomic percent of Nb, while the influence of Cu is negligible [39]. Relatively low Fe content, relatively high Ni content, and the presence of P in the amorphous Fe40Ni40P14B6 alloy result in low value of the Curie temperature of this alloy. This is a consequence of the facts that Ni has lower Curie temperature and lower magnetic moment than Fe and the P

The beginning of crystallization process (**Figure 7**), as a result of formation of various magnetic crystalline phases, leads to an increase in magnetic moment of polycrystalline alloys. The manner of magnetic moment growth during the

*resistivity for Fe81B13Si4C2 alloys (reprinted from ref. [29] with permission of Elsevier) (b).*

addition has a decreasing effect on magnetic moment [40].

Electrical resistivity measurements performed on the alloys containing 73–81 atomic % of iron [15, 27, 29, 42], at room temperature, reveal that the as-prepared Fe79.8Ni1.5Si5.2B13C0.5 and Fe81B13Si4C2 alloys exhibit slightly lower electrical resistivity values, and better electronic conductivity, than the Fe73.5Cu1Nb3Si15.5B7 and Fe75Ni2Si8B13C2 alloys (**Table 3**), which is attributed to their somewhat higher iron content. As expected, after heating at different temperatures, each structural transformation is followed by certain changes in the trend of temperature dependence of electrical resistivity [15, 27, 29, 42].

**Figure 7.** *Thermomagnetic curves recorded at 4°C/min.*


#### **Table 3.**

*Electrical resistivity of the as-prepared alloys containing 73–81 atomic % of iron at room temperature.*

The influence of thermally induced structural transformations on electrical resistivity of amorphous alloy can be illustrated with the example of Fe75Ni2Si8B13C2 alloys [27]. In the temperature range 20–500°C, thermal treatment causes an increase in electrical resistivity (**Table 4**), where the slightly faster growth in the region 250–400°C corresponds to the structural relaxation, while the sharp increase occurs near the Curie point (400–430°C) [27]. Crystallization process, which starts at around 500°C, involves the sudden decline in electrical resistivity, since the ordered structure possesses lower electrical resistivity than the amorphous one. The second heating of the crystallized alloy results in linear growth of electrical resistivity with temperature [27], which is typical behavior of electronic (metal) conductors.

Measurement of electrical resistivity of the Fe81B13Si4C2 alloy after thermal treatment represents a good example of the situation when the functional properties are more sensitive to microstructural changes than thermal analysis. Derivative curve of the temperature dependence of electrical resistivity exhibits two well-defined maxima in the crystallization region (**Figure 6b**) [29], indicating that the crystallization in this case is a multistep process, although it occurs as a single peak in the DSC curve.

### **3.5 Crystallization kinetics**

The knowledge of crystallization kinetics, besides thermal stability, is very important for usage of these alloys in modern technology, in order to estimate their applicability. The increase in heating rate leads to a shift in DSC peak temperature toward the region of higher temperatures [19, 21–24], showing that the observed processes are thermally activated, allowing the application of Arrhenius equation for kinetic description of the examined processes.

The kinetics of single-step solid-state phase transformation can be described using the equation:

 $\mathbf{e}^{\mathbf{a}} = \mathbf{e}^{\mathbf{a}}$ ,  $\mathbf{e}^{\mathbf{a}} = \mathbf{e}^{\mathbf{a}}$ ,  $\mathbf{e}^{\mathbf{a}} = A$   $\exp\left(\frac{-E\_a}{RT}\right)$ f(a) \tag{1}

**37**

tion energy (**Table 5**).

**Table 4.**

*temperatures.*

*Thermal Stability and Phase Transformations of Multicomponent Iron-Based Amorphous Alloys*

**Temperature (°C) Electrical resistivity (μΩm)**

20 2.268 100 2.282 150 2.296 200 2.310 250 2.331 350 2.408 400 2.492 410 2.548 440 2.576 530 2.604 540 2.604 545 2.492 550 2.352

using various methods [19, 21–24], are in agreement with the literature overall *Ea*

*Electrical resistivity measurements performed on the Fe75Ni2Si8B13C2 alloy after thermal treatment at different* 

The alloys containing 73–81 atomic % of Fe, except the Fe81B13Si4C2, have lower crystallization apparent activation energy for the Fe2B phase than that of the α-Fe(Si) phase by approximately 25%. This is a consequence of the creation of favorable conditions for crystallization of Fe2B phase by enrichment of amorphous matrix with B caused by crystallization of α-Fe(Si) grains. The similar values of apparent activation energy of crystallization for the α-Fe(Si) and Fe2B phases in the Fe81B13Si4C2 alloy can be explained by the presence of crystalline phase in amount of around 5% in the as-prepared structure acting as crystallization seeds and facilitating the crystallization of the α-Fe(Si) phase from the amorphous matrix. Higher value of apparent activation energy of crystallization of α-Fe(Si) can be observed for the Fe79.8Ni1.5Si5.2B13C0.5 alloy due to the high thermal stability of this alloy, which originates from its optimal chemical composition. In the case of the alloy with high Ni content, formation of the bcc structure entails somewhat higher apparent activa-

Kinetic analysis [19, 21–24] reveals that the conditions for application of the JMA model, most commonly used for kinetic description of transformations that consisted of nucleation and crystal growth processes, are not entirely fulfilled for any crystallization step in the alloys examined. Actually, for all crystallization steps, the shape of the Málek's curves [52] corresponds to the JMA model, but the maxima of the z(*α*) functions are shifted toward lower *α* values. Nucleation, which does not occur only in the early stages of transformations, and hard impingement effects corresponding to anisotropic crystal growth are the main contributors to such behavior. Anisotropic crystal growth is also indicated by the appearance of preferential orientation, observed during microstructural analysis [17]. Considering good accordance among the Málek's curves obtained at different heating rates, it can be concluded that the mechanism of the studied process does not change with heating rate in the range of heating rates examined.

Autocatalytic Šesták-Berggren model, in two-parameter form f(*α*) = *α*

*<sup>M</sup>*(1 − *α*)*<sup>N</sup>*,

values corresponding to the similar systems [36, 50, 51].

*DOI: http://dx.doi.org/10.5772/intechopen.88260*

where *T* is the temperature, *R* is the gas constant, *α* is the conversion degree, *β* is the heating rate, f(*α*) is the conversion function representing the kinetic model, *Ea* is the activation energy, and *A* is the pre-exponential factor. The two last mentioned parameters are Arrhenius parameters, while the set including *Ea*, *A* and f(*α*) represents the kinetic triplet. For full kinetic description of a process, determination of kinetic triplet is required. Practical significance of kinetic triplets is determination of material lifetimes related to structural stability of materials and process rates [43].

Most of the observed crystallization DSC peaks are asymmetric as a result of complexity of crystallization processes involving more than one crystallization step. In order to study the kinetics of individual steps, complex crystallization peak deconvolution by application of appropriate mathematical procedure [19, 21–24] is required. For confirmation of single-step processes, isoconversional methods [43–49] are used.

Crystallization apparent activation energies for the formation of individual phases in the examined amorphous alloys, determined using Kissinger method [44], are presented in **Table 5**. The values obtained for the α-Fe(Si) phase are in the range 300–400 kJ/mol, while 200–350 kJ/mol are those determined for the Fe2B phase. For all the crystalline phases in all the alloys examined, relatively high *Ea* values are obtained, probably as a result of cooperative participation of a large number of atoms in each step of the transformations [36]. The *Ea* values, obtained *Thermal Stability and Phase Transformations of Multicomponent Iron-Based Amorphous Alloys DOI: http://dx.doi.org/10.5772/intechopen.88260*


#### **Table 4.**

*Metallic Glasses*

conductors.

DSC curve.

**3.5 Crystallization kinetics**

using the equation:

and process rates [43].

[43–49] are used.

for kinetic description of the examined processes.

β

The influence of thermally induced structural transformations on electrical resistivity of amorphous alloy can be illustrated with the example of Fe75Ni2Si8B13C2 alloys [27]. In the temperature range 20–500°C, thermal treatment causes an increase in electrical resistivity (**Table 4**), where the slightly faster growth in the region 250–400°C corresponds to the structural relaxation, while the sharp increase occurs near the Curie point (400–430°C) [27]. Crystallization process, which starts at around 500°C, involves the sudden decline in electrical resistivity, since the ordered structure possesses lower electrical resistivity than the amorphous one. The second heating of the crystallized alloy results in linear growth of electrical resistivity with temperature [27], which is typical behavior of electronic (metal)

Measurement of electrical resistivity of the Fe81B13Si4C2 alloy after thermal treatment represents a good example of the situation when the functional properties are more sensitive to microstructural changes than thermal analysis. Derivative curve of the temperature dependence of electrical resistivity exhibits two well-defined maxima in the crystallization region (**Figure 6b**) [29], indicating that the crystallization in this case is a multistep process, although it occurs as a single peak in the

The knowledge of crystallization kinetics, besides thermal stability, is very important for usage of these alloys in modern technology, in order to estimate their applicability. The increase in heating rate leads to a shift in DSC peak temperature toward the region of higher temperatures [19, 21–24], showing that the observed processes are thermally activated, allowing the application of Arrhenius equation

The kinetics of single-step solid-state phase transformation can be described

( \_ − *Ea*

where *T* is the temperature, *R* is the gas constant, *α* is the conversion degree, *β* is the heating rate, f(*α*) is the conversion function representing the kinetic model, *Ea* is the activation energy, and *A* is the pre-exponential factor. The two last mentioned parameters are Arrhenius parameters, while the set including *Ea*, *A* and f(*α*) represents the kinetic triplet. For full kinetic description of a process, determination of kinetic triplet is required. Practical significance of kinetic triplets is determination of material lifetimes related to structural stability of materials

Most of the observed crystallization DSC peaks are asymmetric as a result of complexity of crystallization processes involving more than one crystallization step. In order to study the kinetics of individual steps, complex crystallization peak deconvolution by application of appropriate mathematical procedure [19, 21–24] is required. For confirmation of single-step processes, isoconversional methods

Crystallization apparent activation energies for the formation of individual phases in the examined amorphous alloys, determined using Kissinger method [44], are presented in **Table 5**. The values obtained for the α-Fe(Si) phase are in the range 300–400 kJ/mol, while 200–350 kJ/mol are those determined for the Fe2B phase. For all the crystalline phases in all the alloys examined, relatively high *Ea* values are obtained, probably as a result of cooperative participation of a large number of atoms in each step of the transformations [36]. The *Ea* values, obtained

*RT* )f(α) (1)

\_ dα <sup>d</sup>*T* = *<sup>A</sup>* exp

**36**

*Electrical resistivity measurements performed on the Fe75Ni2Si8B13C2 alloy after thermal treatment at different temperatures.*

using various methods [19, 21–24], are in agreement with the literature overall *Ea* values corresponding to the similar systems [36, 50, 51].

The alloys containing 73–81 atomic % of Fe, except the Fe81B13Si4C2, have lower crystallization apparent activation energy for the Fe2B phase than that of the α-Fe(Si) phase by approximately 25%. This is a consequence of the creation of favorable conditions for crystallization of Fe2B phase by enrichment of amorphous matrix with B caused by crystallization of α-Fe(Si) grains. The similar values of apparent activation energy of crystallization for the α-Fe(Si) and Fe2B phases in the Fe81B13Si4C2 alloy can be explained by the presence of crystalline phase in amount of around 5% in the as-prepared structure acting as crystallization seeds and facilitating the crystallization of the α-Fe(Si) phase from the amorphous matrix. Higher value of apparent activation energy of crystallization of α-Fe(Si) can be observed for the Fe79.8Ni1.5Si5.2B13C0.5 alloy due to the high thermal stability of this alloy, which originates from its optimal chemical composition. In the case of the alloy with high Ni content, formation of the bcc structure entails somewhat higher apparent activation energy (**Table 5**).

Kinetic analysis [19, 21–24] reveals that the conditions for application of the JMA model, most commonly used for kinetic description of transformations that consisted of nucleation and crystal growth processes, are not entirely fulfilled for any crystallization step in the alloys examined. Actually, for all crystallization steps, the shape of the Málek's curves [52] corresponds to the JMA model, but the maxima of the z(*α*) functions are shifted toward lower *α* values. Nucleation, which does not occur only in the early stages of transformations, and hard impingement effects corresponding to anisotropic crystal growth are the main contributors to such behavior. Anisotropic crystal growth is also indicated by the appearance of preferential orientation, observed during microstructural analysis [17]. Considering good accordance among the Málek's curves obtained at different heating rates, it can be concluded that the mechanism of the studied process does not change with heating rate in the range of heating rates examined. Autocatalytic Šesták-Berggren model, in two-parameter form f(*α*) = *α <sup>M</sup>*(1 − *α*)*<sup>N</sup>*,

best describes the kinetics of crystallization, for all crystallization steps [19, 21–24]. Conversion functions of individual crystallization steps, in different alloys, are presented in **Table 5**. By introducing the kinetic triplets of individual crystallization steps into the equation for the solid-state transformation rate, with corresponding normalization and summation, simulated DSC curves can be obtained, which are, for the studied processes, in full accordance with experimental DSC curves [19, 21, 23], confirming the validity of the obtained kinetic triplets (**Figure 8**).

More information on crystallization mechanism can be obtained by considering values of local Avrami exponent, *n* [53]. Local Avrami exponent as well as the manner of its change with the progress of the process can indicate a certain transformation mechanism. For all crystallization steps of the examined alloys, decline in *n* value with the progress of transformation is observed (**Figure 9**) [19, 21]. This suggests the occurrence of impingement during the crystal growth, which was also indicated by microstructural analysis, as mentioned previously [19–21]. For non-isothermal measurements, at constant heating rates, conversion degree which corresponds to the position of the transformation rate maximum (*αp*) suggests the anisotropic crystal growth as the prevailing type of impingement [54]. This includes blocking effects of growing particles occurring earlier than those for the isotropic growth, leading to hard impingement and to deviation from the classical JMA model [54]. Anisotropic crystal growth was also suggested by the existence of preferential orientation [17].

After determining the kinetic triplets, the lifetime of the alloys against crystallization which reflects their thermal stability as well as the stability of their functional properties is estimated. For the conversion degree of 5%, at room temperature, the alloys exhibit high lifetime values (1027–1039 years) (**Table 6**), indicating that these materials are very stable at room temperature, in spite of their thermodynamic and kinetic metastability [21, 23]. Nevertheless, an increase in the


**39**

component (**Table 6**).

*Thermal Stability and Phase Transformations of Multicomponent Iron-Based Amorphous Alloys*

*Examples of comparison of experimental DSC curves at 8°C/min and the curves simulated with determined kinetic triplets of individual crystallization steps: Fe73.5Cu1Nb3Si15.5B7 alloy, peak 1 (a), and Fe79.8Ni1.5Si5.2B13C0.5*

temperature of thermal treatment leads to an exponential decline in the values of estimated lifetime against crystallization, which amounts to only several minutes at the temperature of the onset of crystallization process [21, 23]. At room temperature, the amorphous Fe79.8Ni1.5Si5.2B13C0.5 alloy shows lifetime value by several orders of magnitude higher than those of the other alloys containing 73–81 atomic % of Fe, which is in accordance with its higher thermal stability. In spite of crystallizing at lower temperatures than the alloys with 73–81 atomic % of Fe, the alloy containing 40 atomic % of Fe shows higher thermal stability at room temperature, manifested by higher lifetime values than those of the alloys containing Fe as the dominant

*Estimated values of the lifetime of the alloys against crystallization at room temperature, determined for* 

*Local values of Avrami exponent of α-Fe(Si) (a) and Fe2B (b) phases in different alloys at 5 °C/min.*

**Alloy Lifetime (year)** Fe81B13Si4C2 2.2 × 1029 Fe79.8Ni1.5Si5.2B13C0.5 3.6 × 1039 Fe75Ni2Si8B13C2 2.5 × 1027 Fe73.5Cu1Nb3Si15.5B7 2.2 × 1030 Fe40Ni40P14B6 3.3 × 1038

*DOI: http://dx.doi.org/10.5772/intechopen.88260*

**Figure 8.**

*alloy (b).*

**Figure 9.**

**Table 6.**

*conversion degree of 5%.*

#### **Table 5.**

*Kinetic triplets of individual crystallization steps determined for different alloys.*

*Thermal Stability and Phase Transformations of Multicomponent Iron-Based Amorphous Alloys DOI: http://dx.doi.org/10.5772/intechopen.88260*

#### **Figure 8.**

*Metallic Glasses*

triplets (**Figure 8**).

preferential orientation [17].

**Phase Alloy** *Еа*

best describes the kinetics of crystallization, for all crystallization steps

[19, 21–24]. Conversion functions of individual crystallization steps, in different alloys, are presented in **Table 5**. By introducing the kinetic triplets of individual crystallization steps into the equation for the solid-state transformation rate, with corresponding normalization and summation, simulated DSC curves can be obtained, which are, for the studied processes, in full accordance with experimental DSC curves [19, 21, 23], confirming the validity of the obtained kinetic

More information on crystallization mechanism can be obtained by considering values of local Avrami exponent, *n* [53]. Local Avrami exponent as well as the manner of its change with the progress of the process can indicate a certain transformation mechanism. For all crystallization steps of the examined alloys, decline in *n* value with the progress of transformation is observed (**Figure 9**) [19, 21]. This suggests the occurrence of impingement during the crystal growth, which was also indicated by microstructural analysis, as mentioned previously [19–21]. For non-isothermal measurements, at constant heating rates, conversion degree which corresponds to the position of the transformation rate maximum (*αp*) suggests the anisotropic crystal growth as the prevailing type of impingement [54]. This includes blocking effects of growing particles occurring earlier than those for the isotropic growth, leading to hard impingement and to deviation from the classical JMA model [54]. Anisotropic crystal growth was also suggested by the existence of

After determining the kinetic triplets, the lifetime of the alloys against crystallization which reflects their thermal stability as well as the stability of their functional properties is estimated. For the conversion degree of 5%, at room temperature, the alloys exhibit high lifetime values (1027–1039 years) (**Table 6**), indicating that these materials are very stable at room temperature, in spite of their thermodynamic and kinetic metastability [21, 23]. Nevertheless, an increase in the

α-Fe(Si) Fe81B13Si4C2 320 ± 10 48 ± 2 *α*0.69(1 − *α*)

Fe3B Fe81B13Si4C2 332 ± 5 50 ± 1 *α*0.69(1 − *α*)

Fe2B Fe81B13Si4C2 340 ± 20 50 ± 3 *α*0.78(1 − *α*)

Fe16Nb6Si7 Fe73.5Cu1Nb3Si15.5B7 490 ± 10 60 ± 2 *α*(1 − *α*)

Fe2Si Fe73.5Cu1Nb3Si15.5B7 470 ± 30 58 ± 5 *α*0.60(1 − *α*)

α-(Fe,Ni) Fe40Ni40P14B6 450 ± 20 82 ± 3 *α*0.53(1 − *α*)

γ-(Fe,Ni) Fe40Ni40P14B6 450 ± 30 80 ± 5 *α*0.50(1 − *α*)

(Fe,Ni)3(P,B) Fe40Ni40P14B6 460 ± 30 81 ± 6 *α*0.48(1 − *α*)

*Kinetic triplets of individual crystallization steps determined for different alloys.*

**(kJ mol<sup>−</sup><sup>1</sup> )**

Fe79.8Ni1.5Si5.2B13C0.5 399 ± 6 58 ± 2 *α*0.98(1 − *α*)

Fe75Ni2Si8B13C2 298 ± 7 44 ± 1 *α*0.51(1 − *α*)

Fe75Ni2Si8B13C2 230 ± 10 33 ± 3 *α*0.64(1 − *α*)

Fe75Ni2Si8B13C2 210 ± 20 29 ± 4 *α*0.62(1 − *α*) Fe73.5Cu1Nb3Si15.5B7 260 ± 20 37 ± 3 *α*0.51(1 − *α*)

Fe79.8Ni1.5Si5.2B13C0.5 300 ± 10 43 ± 2 *α*(1 − *α*)

Fe73.5Cu1Nb3Si15.5B7 335 ± 7 49 ± 1 *α*0.46(1 − *α*)

**lnA (A/min<sup>−</sup><sup>1</sup> )** **f(***α***)**

0.99

1.20

1.16

1.20

0.93

0.92

1.30

1.10

1.11

1.15

1.18

1.40

1.30

**38**

**Table 5.**

*Examples of comparison of experimental DSC curves at 8°C/min and the curves simulated with determined kinetic triplets of individual crystallization steps: Fe73.5Cu1Nb3Si15.5B7 alloy, peak 1 (a), and Fe79.8Ni1.5Si5.2B13C0.5 alloy (b).*

#### **Figure 9.**

*Local values of Avrami exponent of α-Fe(Si) (a) and Fe2B (b) phases in different alloys at 5 °C/min.*


#### **Table 6.**

*Estimated values of the lifetime of the alloys against crystallization at room temperature, determined for conversion degree of 5%.*

temperature of thermal treatment leads to an exponential decline in the values of estimated lifetime against crystallization, which amounts to only several minutes at the temperature of the onset of crystallization process [21, 23]. At room temperature, the amorphous Fe79.8Ni1.5Si5.2B13C0.5 alloy shows lifetime value by several orders of magnitude higher than those of the other alloys containing 73–81 atomic % of Fe, which is in accordance with its higher thermal stability. In spite of crystallizing at lower temperatures than the alloys with 73–81 atomic % of Fe, the alloy containing 40 atomic % of Fe shows higher thermal stability at room temperature, manifested by higher lifetime values than those of the alloys containing Fe as the dominant component (**Table 6**).
