Alkaline Chemistry in Crystallography

#### **Chapter 5**

## Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction in Annealed Crystals

*Yohichi Kohzuki*

#### **Abstract**

Combination method of strain-rate cycling tests and application of ultrasonic oscillations was conducted for KCl:Sr2+ (0.035, 0.050, 0.065 mol.% in the melt) single crystals at low temperatures. The measurement of strain-rate sensitivity (*λ*) of flow stress under the application of ultrasonic oscillatory stress provides useful information on the interaction between a mobile dislocation and impurities (Sr2+ ions) during plastic deformation and the variation of *λ* with stress decrement (Δ*τ*) due to oscillation has stair-like shape: The first plateau place ranges below the first bending point (*τ*p1) at low stress decrement and the second one extends from the second bending point (*τ*p2) at high stress decrement. The value of *λ* decreases with the Δ*τ* between the two bending points. The *τ*p1 is considered to represent the effective stress due to impurities when a dislocation begins to break-away from the impurities with the help of thermal activation during plastic deformation. Annealing the impure crystal by heat treatment, *τ*p1 decreases obviously at low temperature and the critical temperature *T*c, at which *τ*p1 is zero, also becomes slightly smaller. Furthermore, it was investigated whether a change in the state of a small amount of impurities has an influential factor of the flow parameters (e.g., the activation energy, the density of forest dislocations) from the data analyzed in terms of Δ*τ* vs. *λ* curve.

**Keywords:** heat treatment, dislocation, ultrasonic oscillatory stress, activation energy, divalent ion

#### **1. Introduction**

A large number of investigations on strength of materials have been made with alkali halide crystals so far [1–4]. This will be because the crystals have some advantages [5]: A small number of glide systems on account of rock salt structure, low dislocation density in grown crystal (e.g., 10<sup>4</sup> cm<sup>2</sup> order for NaCl [6] and KCl [7] single crystals) as against that of annealed metals (around 107 cm<sup>2</sup> [8], e.g., 1 to <sup>5</sup> <sup>10</sup><sup>6</sup> cm<sup>2</sup> in pure Cu single crystals [9], 1 to 5 <sup>10</sup><sup>6</sup> cm<sup>2</sup> in *<sup>α</sup>*-brass single crystals [10], and 10<sup>7</sup> cm<sup>2</sup> order for pure Fe single crystals [11]), transparency, and further readily available single crystal, etc. Alkali halide crystals, therefore, are excellent materials for an investigation on mechanical properties of crystals.

#### *Alkaline Chemistry and Applications*

When alkali halide crystals are doped with divalent impurities (divalent cations), the impurities induce positive ion vacancies in order to conserve the electrical neutrality and are expected to be paired with the vacancies. They are often at the nearest neighbor sites forming a divalent impurity-vacancy (I-V) dipole, which attract them strongly [12], for crystals quenched from a high temperature. Then asymmetrical distortions are produced around the I-V dipoles.

The greatest hardness occurs for the highest concentration of isolated I-V dipole and the decrease of hardness is attributed to precipitation in KCl:Sr2+ single crystals [13]. The state of impurities in a crystal affects its hardness. Chin et al. have obtained the following experimental results: KCl:Sr2+ (840 ppm) crystals soften on annealing at temperatures up to 773 K; the hardness of NaCl:Ca2+ (below 2000 ppm) crystals starts to increase rapidly after aging at 100 °C for 30 min and decreases on further annealing [14]. And also, it was reported that the change in their state strongly influences the resistance to movement of the dislocations when a small amount of impurities aggregates or diffuses into the crystal in various impure alkali halide crystals (e.g., NaCl: Ca2+ or Mn2+, KCl: Sr2+ or Ba2+, LiF:Mg2+) by heat treatment [15]. Annealing an impure crystal by heat treatment, this will lead to the change in various deformation characteristics.

Mobile dislocations on a slip plane interact strongly only with these defects lying within one atom spacing of the glide plane [16]. Dislocation motions are related to the plasticity of crystal in a microscopic viewpoint. Solution hardening depends on the dislocation motion hindered by the atomic defects around impurities in crystals and is namely influenced by the dislocation-point defects interaction. Annealing KCl:Sr2+ single crystals here, the study on the interaction between a dislocation and impurities was made by the combination method of strain-rate cycling tests and application of ultrasonic oscillations. This method seems to provide the information on dislocation-impurities interaction in ionic crystal during plastic deformation [17, 18].

#### **2. Combination method of strain-rate cycling tests and application of ultrasonic oscillations**

KCl:Sr2+ (0.035, 0.050, 0.065 mol.% in the melt) specimens were prepared by cleaving the single crystalline ingots to the size of 5 <sup>5</sup> 15 mm<sup>3</sup> . The specimens were kept immediately below the melting point for 24 h and were gradually cooled to room temperature at a rate of 40 Kh<sup>1</sup> . This heat treatment was carried out for the purpose of reducing dislocation density as much as possible. Further, the specimens were held at 673 K for 30 min and were rapidly cooled by waterquenching in order to disperse the impurities (Sr2+) in the specimens immediately before the following tests. The specimen KCl:Sr2+ (0.050 mol.%) is termed the quenched specimen in this article.

The specimens were compressed along the <100> axis at 77 K to the room temperature and the ultrasonic oscillatory stress (*τ*v) was intermittently superimposed in the same direction as the compression. The strain-rate cycling test under the ultrasonic oscillation is illustrated in **Figure 1**. Superposition of oscillatory stress causes a stress drop (Δ*τ*) during plastic deformation. The strain-rate cycling between strain-rates of *<sup>ε</sup>*\_ <sup>1</sup> (2.2 <sup>10</sup><sup>5</sup> <sup>s</sup> 1 ) and *<sup>ε</sup>*\_<sup>2</sup> (1.1 <sup>10</sup><sup>4</sup> <sup>s</sup> 1 ) was performed keeping the stress amplitude of *τ*<sup>v</sup> constant. Then, the variation of stress due to the strain-rate cycling is Δ*τ*'. The strain-rate sensitivity (Δ*τ*'/Δln*ε*\_) of the flow stress, which is given by Δ*τ*'/1.609, was used as a measurement of the strain-rate sensitivity (*λ*). The details was described in the article [19].

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

**Figure 1.**

*Explanatory diagram of a change in applied shear stress, τ*<sup>a</sup> *, for the strain-rate cycling test between the strain rates, <sup>ε</sup>*\_<sup>1</sup> *(2.2 <sup>10</sup><sup>5</sup> <sup>s</sup> 1 ) and <sup>ε</sup>*\_<sup>2</sup> *(1.1 <sup>10</sup><sup>4</sup> <sup>s</sup> 1 ), under superposition of ultrasonic oscillatory shear stress, τ*v*.*

#### **3. Effective stress due to agglomerates in the crystals**

Relation between Δ*τ* and *λ* for KCl:Sr2+ (0.050 mol.% in the melt) at the shear strain of 10% is shown in **Figure 2**. The measuring temperature is 103 K. Δ*τ* vs. *λ* curve reflects the effect of ultrasonic oscillation on the dislocation motion on the slip plane containing many weak obstacles such as impurities and a few forest dislocations during plastic deformation [20]. Open circles in the figure represent the relation for the specimen quenched from 673 K to room temperature, and open triangles for the specimen obtained by storing the quenched specimen at room temperature for a half year. The second one is termed the stored specimen here. As can be seen from **Figure 2**, the variation of *λ* with Δ*τ* has stair-like shape (there are two bending points on each curve, and there are two plateau regions: the first plateau region ranges below the first bending point (*τ*p1) at low stress decrement and the second one extends from the second bending point (*τ*p2) at high stress decrement) for the quenched specimen. *λ*

**Figure 2.**

*Relation between the strain-rate sensitivity (λ) and the stress decrement (Δτ) at 103 K for (○) the quenched specimen and (*Δ*) the stored specimen.*

**Figure 3.** *Dependence of (○) τp1 and (*Δ*) τp2 on temperature for (*a*) the quenched specimen and (b) the stored specimen.*

decreases with the stress decrement between the two bending points. *λ*<sup>p</sup> denoted in **Figure 2** is introduced in section 6 of this article. The *τ*p1 (Δ*τ* value at the first bending point) for the stored specimen is smaller than that for the quenched specimen. *τ*p1 is considered to be the effective stress due to the impurities (Sr2+) which lie on the dislocation when a dislocation begins to break-away from the impurities with the help of thermal activation during plastic deformation, because the value of *τ*p1 has been reported to be depend on temperature (*τ*p1 shifts in the direction of lower Δ*τ* as the temperature becomes larger), and on the type and the density of weak obstacle [21]. The *τ*p2 (Δ*τ* value at the second bending point) for the stored specimen, however, does not appear within the measurement, because high stress amplitude could not be applied to the specimen during the strain-rate cycling tests. Furthermore, *τ*p1 and *τ*p2 of the quenched and the stored specimens were investigated at various temperatures. **Figures 3(a)** and **(b)** show the results for the quenched specimen and for the stored one, respectively. The *τ*p1 for the stored specimen is smaller than that for the quenched specimen at a given temperature. On the other hand, the *τ*p2 for the stored specimen is a little smaller than that for the quenched one as compared with *τ*p1. In the following sections of this article, the state of impurities in the specimen is clarified and its influence on the interaction between a dislocation and the impurities will be described.

### **4. State of impurities (Sr2+) in KCl:Sr2+ single crystals**

Measurements of the I-V dipole concentration and of the flow stress for KCl:Sr2+ (0.023 mol.%) were reported as a function of annealing time at 403 K after

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

quenching from 673 K by Dryden et al. [15]. Observing the concentration of isolated I-V dipoles in the crystal before and after the annealing and also the change of flow stress with it, the dipole concentration decreases and the flow stress becomes lower at a longer annealing time above 10 h.

Here is clarified the state of impurities in the specimen and is referred to the influence of the state of impurities on the dislocation-impurities interaction, especially on the relation between temperature and the effective stress. The crystals used here are two kinds of specimens. The first is KCl:Sr2+ (0.050 mol.% in the melt) at the preceding section 3 and is named the quenched specimen. The second is prepared by keeping the quenched specimen at 370 K for 500 h and gradually cooling in a furnace for the purpose of aggregating impurities in it [22]. This is hereafter termed the annealed specimen.

Dielectric absorption of an I-V dipole causes a peak on the tan*δ*-frequency relation. A relative formula which gives the proportionality between the concentration of I-V dipoles and a Debye peak height is expressed by [23].

$$\tan \delta = \frac{2\pi e^2 c}{3\epsilon' akT}, (\text{maximum}) \tag{1}$$

where *e* is the elementary electric charge, *c* the concentration of the I-V dipole, *ε*<sup>0</sup> the dielectric constant in the matrix, *a* the lattice constant and *kT* has its usual meaning.

**Figure 4** shows the influence of this heat treatment on the tan*δ*-frequency curves for KCl:Sr2+ at 393 K. The upper solid and dotted curves correspond to the

**Figure 4.**

*Dielectric loss in KCl:Sr2+ (0.050 mol.% in the melt) at 393 K: (○) for the quenched specimen, (*Δ*) for the annealed specimen. (*� � *- -) losses coming from the dipoles (reproduced from ref. [24] with permission from the publisher).*

quenched specimen and the lower curves the annealed specimen. Dotted lines show Debye peaks obtained by subtracting the d.c. part which is obtained by extrapolating the linear part of the solid curves in the low-frequency region to the highfrequency region. Introducing the peak heights of the dotted curves into Eq. (1), the concentration of the isolated dipole was determined to be 98.3 ppm for the quenched specimen and 21.8 ppm for the annealed specimen. On the other hand, the atomic absorption gave 121.7 ppm for the Sr2+ concentration in the quenched specimen and 96.2 ppm for the annealed specimen. Therefore, it should be considered that 71.9% of the I-V dipoles turn into the aggregates in KCl:Sr2+ single crystal and form at least trimers [22] by the heat treatment. The trimers (Sr2+-vacancy-Sr2+ vacancy-Sr2+-vacancy) have a structure in which three dipoles are arranged hexagonally head to tail in a (111) plane, as suggested by Cook and Dryden [22].

#### **5. Effective stress and critical temperature**

**Figure 5** shows the variation of *λ* with Δ*τ* at a shear strain of 8% for the annealed specimen at 125 K. The curve in the **Figure 5** has two bending points and two plateau regions at a given shear strain and temperature. The first plateau region ranges below the first bending point at low stress decrement and the second one extends from the second bending point at high stress decrement. The *λ* decreases with the Δ*τ* between the two bending points. The values of Δ*τ* at the first and the second bending points are referred to as *τ*p1 and *τ*p2, respectively.

The dependence of *τ*p1 and *τ*p2 on temperature for the quenched specimen is shown in **Figure 6(a)**, while that for the annealed specimen is shown in **Figure 6(b)**. The value of *τ*p1 becomes small by forming into the aggregates in the crystal and this result is clearer at lower temperature. This may be caused by the result that the separation between the weak obstacles lying on the mobile dislocation becomes wider as the I-V dipoles turn into aggregates. In addition, it is supposed that the decrease in *τ*p1 due to agglomerate of the I-V dipoles, i.e. softening, would be attributable to the loss of tetragonality in terms of the Fleischer's model [16], as suggested by Chin et al.

#### **Figure 5.**

*Relation between the strain-rate sensitivity (λ) and the stress decrement (Δτ) at a shear strain of 8% for the annealed specimen at 125 K (reproduced from ref. [24] with permission from the publisher).*

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

**Figure 6.**

*Dependence of (○) τp1 and (*Δ*) τp2 on temperature for KCl:Sr2+ (0.050 Mol.% in the melt): (a) for the quenched specimen and (b) for the annealed specimen (reproduced from ref. [24] with permission from the publisher).*

[14]. The decrease in the effective stress due to agglomerates of I-V dipoles has been reported for alkali halide crystals doped with divalent cations so far [14, 15, 25–27].

As for *τ*p2, no great difference is seen for the two kinds of specimens. Accordingly, as the I-V dipoles turn into the aggregates by the heat treatment, the difference between *τ*p1 and *τ*p2 obviously becomes wider at lower temperature. This may be caused by the wider distribution of Sr2+ obstacles on mobile dislocation in the annealed specimen as against that in the quenched one.

The critical temperature *T*<sup>c</sup> at which *τ*p1 is zero and a dislocation breaks away from the impurities only with the help of thermal activation is around 210 K for the annealed specimen. This *T*<sup>c</sup> value is small in contrast to *T*c≈240 K of the quenched specimen as can be seen from **Figures 6(a)** and **(b)**.

#### **6. Activation energy for the dislocation breaking-away from the defects**

The thermally activated deformation rate (*ε*\_) is expressed by an Arrhenius-type equation:

$$
\dot{\varepsilon} = \dot{\varepsilon}\_0 \exp\left(\frac{-\Delta G}{kT}\right),
\tag{2}
$$

where *ε*\_<sup>0</sup> is a frequency factor and is unique for a particular dislocation mechanism. And the change in Gibbs free energy, Δ*G*, is expressed for square forcedistance relation (SQ) between a dislocation and an impurity as follows.

$$
\Delta G = \Delta G\_0 - \tau^\* Lbd,\tag{3}
$$

where Δ*G*<sup>0</sup> is the Gibbs free energy for the break-away of the dislocation from the impurity in the absence of an applied stress, *τ* \* the effective shear stress due to the impurities, *L* the length of dislocation, *b* the magnitude of the Burgers vector and *d* the activation distance. The Gibbs free energy for the SQ is given by

$$
\Delta G = \Delta G\_0 - \beta \tau^{\*2/3} \tag{4}
$$

$$
\beta = \left(2\mu b^4 d^3 L\_0^2\right)^{1/3},\tag{5}
$$

where *μ* is the shear modulus and *L*<sup>0</sup> the average spacing of impurities on the slip plane. Differentiating the substitutional equation of Eqs. (4) and (5) in Eq. (2) with respect to the shear stress, we find

$$
\pi\_{p1} \left( \frac{\partial \ln \dot{\varepsilon}}{\partial \tau^\*} \right) = \left( \frac{2 \Delta G\_0}{3kT} \right) + \frac{2}{3} \ln \left( \frac{\dot{\varepsilon}}{\dot{\varepsilon}\_0} \right). \tag{6}
$$

The Gibbs free energy for the interaction between a dislocation and the impurity is expressed from the Eq. (2), namely

$$
\Delta G = akT, \left( a = \ln \left( \frac{\dot{\varepsilon}\_0}{\dot{\varepsilon}} \right) \right) \tag{7}
$$

and the Δ*G* for the Fleischer's model [16] taking account of the Friedel relation [28] (F-F) is also expressed by

$$
\Delta G = \Delta G\_0 \left\{ 1 - \left( \frac{\tau^\*}{\tau\_0^\*} \right)^{1/3} \right\}^2, (\Delta G\_0 = F\_0 b) \tag{8}
$$

where *τ* \* <sup>0</sup> is the value of *τ* \* at absolute zero and *F*<sup>0</sup> the force acted on the dislocation at 0 K. It is well known that the Friedel relation [28] between the effective stress and the average length of dislocation segments can be applied to most weak obstacles to dislocation motion at low solute concentration. Differentiating the combination of Eqs. (7) and (8) with respect to the shear stress gives

$$\frac{\partial \ln \dot{\varepsilon}}{\partial \tau^\*} = \left(\frac{2\Delta G\_0}{3kT\tau\_0^\*}\right) \left(\frac{\tau\_0^\*}{\tau^\*}\right)^{2/3} \left\{ 1 - \left(\frac{\tau^\*}{\tau\_0^\*}\right)^{1/3} \right\} + \frac{\partial \ln \dot{\varepsilon}\_0}{\partial \tau^\*}.\tag{9}$$

Further, substituting the following Eq. (10) in Eq. (9) gives Eq. (11)

$$\left(\frac{\tau\_{p1}}{\tau\_{p0}}\right)^{1/3} = \mathbf{1} - \left(\frac{T}{T\_c}\right)^{1/2} \tag{10}$$

namely,

$$\frac{\partial \ln \dot{\varepsilon}}{\partial \tau^\*} = \left(\frac{2\Delta G\_0}{3kT\tau\_{p0}}\right) \left\{ 1 - \left(\frac{T}{T\_c}\right)^{1/2} \right\}^{-2} \left(\frac{T}{T\_c}\right)^{1/2} + \frac{\partial \ln \dot{\varepsilon}\_0}{\partial \tau^\*},\tag{11}$$

where *τ* \* <sup>0</sup> is replaced by *τ*p0 (*τ*p1 value at absolute zero). Eq. (10) represents the relative formula of *τ*p1 and temperature, which will reveal the force-distance

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

**Figure 7.**

*Linear plots of Eq. (11) for the quenched specimen: KCl:Sr2+ ((○) 0.035 mol.%, (*Δ*) 0.050 mol.%, (*□*) 0.065 mol.% in the melt) (reproduced from ref. [30] with permission from the publisher).*

**Figure 8.**

*Linear plots of Eq. (6) for the annealed specimen (reproduced from ref. [31] with permission from the publisher).*

relation between a dislocation and an impurity. The result of calculations of Eq. (11) for the F-F is shown in **Figure 7** for the quenched specimen. The open symbols correspond to the inverse of *λ*<sup>p</sup> for the quenched specimen, which are derived from the difference between *λ* values at first plateau place and at second one on the relative curves of Δ*τ* vs. *λ* as shown in **Figure 2**. *λ*<sup>p</sup> is considered to be due to the impurities [29]. On the basis of the slope of straight line, the Gibbs free energy is 0.39 eV. The F-F is suitable for the force-distance profile for the quenched specimen but not for the annealed one [30, 31]. As for the annealed specimen, SQ seems to be most suitable of the three profiles: a square force-distance relation, a parabolic one and a triangular one, taking account of the Friedel relation [31]. The Gibbs free energy for the interaction between a dislocation and the aggregate in the annealed specimen, which is obtained through the slope of straight line in **Figure 8**, is 0.26 eV. The open circles in **Figure 8** show the results of calculations for Eq. (6). Here, the *<sup>∂</sup>* ln *<sup>ε</sup>*\_ *∂τ* <sup>∗</sup> in Eq. (6) is obtained from *λ*p. The Gibbs free energy for the annealed specimen is smaller than that of the quenched one.

#### **7.** *λ* **at second plateau place on Δ***τ* **vs.** *λ* **curve**

Influence of the heat treatment on the density of forest dislocations is treated in detail for the two kinds of KCl:Sr2+ (0.050 mol.% in the melt) single crystals (i.e., the quenched and the annealed specimens). This is examined from the variation of *λ* (see the marked part with gray circle in **Figure 9**) at the second plateau place on the Δ*τ* vs. *λ* curve with shear strain, where the obstacles to the dislocation motion are only forest dislocations and the impurities no longer act as obstacles [21]. A general Δ*τ* vs. *λ* at a given strain is schematically drawn in **Figure 9**, where the curve has two bending points and two plateau regions. The *λ* at second plateau place on the Δ*τ* vs. *λ* curve is considered to be due to dislocation cuttings [21]. The variation of *λ* at second plateau place with shear strain (Δ*λ*/Δ*ε*) is considered to be the increase of forest dislocation density with the shear strain [32]. In **Figure 10**, the Δ*λ*/Δ*ε* dependence of temperature is shown in the different plastic deformation regions of stress–strain curve for the two kinds of specimens: the quenched and the annealed

#### **Figure 9.**

*Illustration of relationship between the strain-rate sensitivity (λ) of flow stress and the stress decrement (Δτ) at a given strain, ε. (ε*<sup>1</sup> <*ε*2*).*

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

**Figure 10.**

*Dependence of Δ λ/Δε on the temperature in the different plastic deformation regions: (○) for the quenched specimen and (*●*) for the annealed specimen in stage I; (*Δ*) for the quenched specimen and (*▲*) for the annealed specimen in stage II (reproduced from ref. [32] with permission from the publisher).*

specimens. Δ*λ*/Δ*ε* in stage I (easy glide region) and in stage II (linear hardening region) are represented by a circle and a triangle, respectively. The open symbols correspond to that for the quenched specimen and the solid ones that for the annealed specimen. The curves in **Figure 10** are to guide the reader's eye. Unfortunately, the Δ*λ*/Δ*ε* could not be obtained at low temperature. Three-stage strain hardening is obtained for KCl [33, 34] and impure KCl single crystals doped with monovalent or divalent cations [35, 36]. Two phenomena are observed for both the specimens in **Figure 10**. That is, the first phenomenon is that the Δ*λ*/Δ*ε* in stage II is obviously larger than that in stage I at a given temperature. The other phenomenon is that the Δ*λ*/Δ*ε* in stage I and in stage II increases with decreasing temperature. **Figure 10** also shows that the Δ*λ*/Δ*ε* for the annealed specimens is considerably large in contrast to that for the quenched specimens in the two stages within the temperature. This may result from a rapid increase in forest dislocation density with shear strain in the annealed specimen. Accordingly, the increase in forest dislocation density in the annealed specimen seems to be remarkable in the two stages under the compression test, compared with it in the quenched specimen.

#### **8. Conclusions**

The following conclusions were derived from the data analyzed in terms of the Δ*τ* vs. *λ* curves for KCl:Sr2+ single crystals.

1.The plots of Δ*τ* vs. *λ* have two bending points and two plateau regions for the quenched specimen and similar result is observed also for the specimen stored at room temperature for a half year. On the basis of the relative curve of Δ*τ* vs. *λ*, it was found that *τ*p1 due to the impurities in the stored specimen is smaller than that of the quenched specimen within the temperatures.


### **Conflict of interest**

The author declares no conflict of interest.

### **Author details**

Yohichi Kohzuki

Department of Mechanical Engineering, Saitama Institute of Technology, Fukaya, Japan

\*Address all correspondence to: kohzuki@sit.ac.jp

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

#### **References**

[1] Urusovskaya AA, Darinskaya EV, Voszka R, Jansky J. Defect structure and the nature of the obstacles for dislocations in NaCl(Ca) crystals. Kristall und Technik. 1981;**16**:597-601. DOI: https://doi.org/10.1002/ crat.19810160511

[2] Suszyńska M, Nowak-Woźny D. Mechanical characteristics of the NaCl: Eu2+ crystal system. Crystal Research and Technology. 1990;25: 855–861. DOI: https://doi.org/10.1002/ crat.2170250721

[3] Boyarskaya YS, Zhitaru RP, Palistrant NA. The anomalous behaviour of the doped NaCl crystals compressed at low temperatures. Crystal Research and Technology. 1990; 25:1469–1473. DOI: https://doi.org/ 10.1002/crat.2170251219

[4] Sprackling MT. The plastic deformation of simple ionic crystals. In: Alper AM, Margrave JL, Nowick AS, editors. Materials Science and Technology. London New York San Francisco: Academic Press; 1976.

[5] Kataoka T. Studies on plastic deformation of alkali halide crystals [thesis]. Osaka: Osaka University; 1975, p 2 (in Japanese).

[6] Argon AS, Nigam AK, Padawer GE. Plastic deformation and strain hardening in pure Nacl at low temperatures. Philosophical Magazine. 1972;25:1095–1118. DOI: https://doi.org/ 10.1080/14786437208226855

[7] Kohzuki Y. Studies on interaction between a dislocation and impurities in KCl single crystals [thesis]. Kanazawa: Kanazawa University; 1994, pp 12–13.

[8] Suzuki H. Introduction to Theory of Dislocations. Tokyo: AGNE; 1989, p 70 (in Japanese).

[9] Young Jr. FW. Etch pits at dislocations in copper. Journal of Applied Physics. 1961;32:192–201. DOI: https://doi.org/10.1063/1.1735977

[10] Meakin JD, Wilsdorf HGF. Dislocations in deformed single crystals of alpha brass. I. General observations. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers. 1960;218:737–745.

[11] Takeuchi S. Solid-Solution Strengthening in Single Crystals of Iron Alloys. Journal of the Physical Society of Japan. 1969;27:929–940. DOI: https:// doi.org/10.1143/JPSJ.27.929

[12] Pick H, Weber H. Dichteänderung von KCl-Kristallen durch Einbau zweiwertiger Ionen. Zeitschrift für Physik. 1950;128:409–413. DOI: https:// doi.org/10.1007/BF01339441

[13] Green M. L, Zydzik G. Effect of heat treatment on the microhardness of some mixed and doped alkali halides. Scripta Metall. 1972;6:991–994. DOI: https://doi. org/10.1016/0036-9748(72)90159-7

[14] Chin G. Y, Van Uitert L. G, Green M. L, Zydzik G. J, Kometani T. Y. Strengthening of alkali halides by divalent-ion additions. J. Am. Ceram. Soc. 1973;56:369–372. DOI: https://doi.org/10.1111/j.1151-2916.1973. tb12688.x

[15] Dryden J. S, Morimoto S, Cook J. S. The hardness of alkali halide crystals containing divalent ion impurities. Philosophical Magazine. 1965;12:379– 391. DOI: https://doi.org/10.1080/ 14786436508218880

[16] Fleischer RL. Rapid solution hardening, dislocation mobility, and the flow stress of crystals. Journal of Applied Physics. 1962;33: 3504–3508. DOI: https://doi.org/ 10.1063/1.1702437

[17] Ohgaku T, Takeuchi N. The relation of the Blaha effect with internal friction for alkali halide crystals. Physica Status Solidi A. 1988;105:153–159. DOI: https:// doi.org/10.1002/pssa.2211050115

[18] Ohgaku T, Takeuchi N. Relation between plastic deformation and the Blaha effect for alkali halide crystals. Physica Status Solidi A. 1989;111:165– 172. DOI: https://doi.org/10.1002/ pssa.2211110117

[19] Kohzuki Y. Study on dislocationdopant ions interaction during plastic deformation by combination method of strain-sate cycling tests and application of ultrasonic oscillations. In: Singh D, Condurache-Bota S, editors. Electron Crystallography. IntechOpen: London; 2020. DOI: 10.5772/intechopen.92607

[20] Kohzuki Y. Bending angle of dislocation pinned by an obstacle and the Friedel relation. Philosophical Magazine. 2010;90:2273–2287. DOI: 10.1080/14786431003636089

[21] Kohzuki Y, Ohgaku T, Takeuchi N. Interaction between a dislocation and impurities in KCl single crystals. Journal of Materials Science. 1993;28:3612–3616. DOI: https://doi.org/10.1007/ BF01159844

[22] Cook J. S, Dryden J. S. An investigation of the aggregation of divalent cationic impurities in alkali halides by dielectric absorption. Proceedings of the Physical Society. 1962;80:479–488. DOI: 10.1088/ 0370-1328/80/2/315

[23] Lidiard A. B. Handbuch der Physik, Berlin: Springer; 1957, Vol. 20, p 246.

[24] Kohzuki Y, Ohgaku T, Takeuchi N. Influence of a state of impurities on the interaction between a dislocation and impurities in KCl single crystals. Journal of Materials Science. 1993;28:6329–6332. DOI: https://doi.org/10.1007/ BF01352192

[25] Johnston, W. G. Effect of Impurities on the Flow Stress of LiF Crystals. Journal of Applied Physics. 1962;33; 2050–2058. DOI: https://doi.org/ 10.1063/1.1728892

[26] Gaiduchenya V. F, Blistanov A. A, Shaskolskaya M. P. Thermally activated slip in LiF crystals. Soviet Physics Solid State 1970;12;27–31.

[27] Buravleva M. G, Rozenberg G. K, Soifer L. M, Chaikovskii E. F. Changes in the flow stress of LiF:Mg2+ and LiF: Co2+ crystals during precipitation of solid solutions. Soviet Physics Solid State. 1980;22;150–152.

[28] Friedel J. Dislocations, Oxford: Pergamon Press; 1964, p 224.

[29] Kohzuki Y, Ohgaku T, Takeuchi N. Interaction between a dislocation and various divalent impurities in KCl single crystals. Journal of Materials Science. 1995;30:101–104. DOI: https://doi.org/ 10.1007/BF00352137

[30] Kohzuki Y. Study on the interaction between a dislocation and impurities in in KCl:Sr2+ single crystals by the Blaha effect Part IInteraction between a dislocation and impurity for the Fleischer's model taking account of the Friedel relation. Journal of Materials Science. 2000;35:3397–3401. DOI: https://doi.org/10.1023/A: 1004889203796

[31] Kohzuki Y, Ohgaku T. Study on the interaction between a dislocation and impurities in in KCl:Sr2+ single crystals by the Blaha effect Part IIInteraction between a dislocation and aggregates for various force-distance relations between a dislocation and an impurity. Journal of Materials Science. 2001;36:923–928. DOI: https://doi.org/10.1023/A: 1004807403566

[32] Kohzuki Y. Study on the interaction between a dislocation and impurities in KCl:Sr2+ single crystals by the Blaha

*Study on Influence of a State of Dopants on Dislocation-Dopant Ions Interaction… DOI: http://dx.doi.org/10.5772/intechopen.96395*

effect-Part IV influence of heat treatment on dislocation density. Journal of Materials Science. 2009;44: 379–384. DOI: https://doi.org/10.1007/ s10853-008-3150-8

[33] Alden T. H. Latent hardening and the role of oblique slip in the strain hardening of rock-salt structure crystals. Transactions of the Metallurgical Society of AIME. 1964;230:649–656.

[34] Davis L. A, Gordon R. B. Plastic deformation of alkali halide crystals at high pressure: Work-hardening effects. Journal of Applied Physics. 1969;40: 4507–4513. DOI: https://doi.org/ 10.1063/1.1657224

[35] Kohzuki Y. Interaction between a dislocation and impurities in KCl doped with Li<sup>+</sup> or Na<sup>+</sup> . Journal of Materials Science. 2000;35:2273–2277. DOI: https://doi.org/10.1023/A: 1004735128091

[36] Kohzuki Y. Influence of various divalent impurities on dislocation density in KCl:Mg2+, Ca2+, Sr2+ or Ba2+ single crystals. Journal of Materials Science. 2003;38:953–958. DOI: https:// doi.org/10.1023/A:1022373124795

#### **Chapter 6**

## Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide Materials

*Amira Marzouki, Ameni Brahmia, Riadh Marzouki, Mosbah Jemmali, Ismat H. Ali and Mohamed Faouzi Zid*

#### **Abstract**

In this chapter, the correlation between structure and electrical properties of Na2*M*P1.5As0.5O7 (*MII* = Co and Cu) are treated. The structural study shows that the cobalt and copper isotype materials can be crystallized in the tetragonal and monoclinic systems, respectively. The electrical study using impedance spectroscopy technique showed that these mixed diphosphate diarsenates are fast electrical conductors; however, the cobalt material exhibited more conductive property than the copper compound. In addition, the powder perovskite manganites La0.7*M*0.2*M*'0.1MnO3 (*M* = Sr, Ba and *M*' = Na, Ag and K) have been prepared using the conventional solid-state reaction. The structural, magnetic, and magnetocaloric properties of these perovskite manganites compounds were studied extensively by means of X-ray powder diffraction (XRD) and magnetic measurements. These samples were crystallized in the distorted rhombohedral system with R3c space group. The variation of magnetization (M) vs. temperature (T) reveals that all compounds exhibit a second-order ferromagnetic to paramagnetic phase transition in the vicinity of the Curie temperature (TC). A maximum magnetic entropy change, Δ*SM Max*, of 4.07 J kg<sup>1</sup> K<sup>1</sup> around 345 K was obtained in La0.7Sr0.2Na0.1MnO3 sample upon a magnetic field change of 5 T. The Δ*SM Max* values of La0.7Ba0.2M'0.1MnO3 are smaller in magnitude compared to La0.7Sr0.2*M'*0.1MnO3 samples and occur at lower temperatures.

**Keywords:** diphosphate-diarsenate, crystal structure, electrical properties, perovskite, magnetic materials, magnetocaloric effect

#### **1. Introduction**

The exploration of new alkali-based materials, especially Na-ion compounds, has become an area of intense activity [1–3]. In fact, these materials have the potential to replace lithium-based cathodes in the new generation of batteries. This trend can be explained by the global increase in demand for lithium and its toxicity compared to the low cost of sodium and its abundance in nature [4].

The two main methods of developing new cathodes, which are currently being explored, are either by researching new crystalline materials or by improving known materials by improving their electrical properties and electrochemical performance. In either case, crystallography remains the key to the development of these electrochemical systems as a determination of crystal structure and ion transport followed by electrochemical properties.

In this context, the exploration and investigation of phosphates, arsenates, and molybdates of transition metals and monovalent cations (Li, Na, K, Ag, etc.) have a promising field for various applications: electrical, piezoelectric processes, ferroelectric, magnetic, catalytic [5, 6]. Moreover, taking into account their remarkable structural richness, in particular the melilite structure [7], the olivine structure [8], and the sodium super ionic conductor (NaSICON) structure [9], these materials show several interesting physical properties, in particular, the ionic conduction and ion exchange [8, 9]. Many sodium-based materials have recently been prepared and tested for their electrical and/or electrochemical properties, including Na2CoP2O7 [10], LiCoAsO4 [11], Na1.86Fe3(PO4)3 [12], etc. These physicochemical properties are linked on the one hand to their structural wealth and on the other hand to the degree of openness of their anionic frameworks which can be dense, open, or microporous.

Thus, the investigation of this type of material requires a good correlation between crystal structure and electrical properties taking into account factors influencing the electrical conductivity such as porosity and the temperature range of stability of the crystal structure of the sample. In this chapter, the first part comprises a structural study of alkali metals (especially Na elements) transition metals (Co, Cu) phosphates-arsenates and their correlations with electrical properties.

On the other hand, alkaline atoms have an electronic procession, composed of a set of inert internal layers, having the structure of a rare gas, and an additional electron, or valence electron, which orbiting an s-type orbital. The study of ionization potentials shows that this electron is easily torn off, the heavier the atom is the lesser the energy is required for ionization. The chemistry of alkali metals is essentially constituted by the study of the transition to the ionized state M<sup>+</sup> and by the properties of this ion. Most alkaline compounds, therefore, have a purely ionic structure; this peculiarity, together with the fact that the most stable ionic edifices are constituted by ions of similar volume, makes it possible to predict that as a general rule hydrides, nitrides, carbides, and simple oxides, that is to say compounds possessing fairly small anions, will be all the more stable the lighter the alkali metal, while the salts corresponding to large anions, peroxides (OdO)<sup>2</sup>, superoxides (OdO), oxacids, and halides will be more stable with heavy alkali metals.

The dangers of the impact of synthetic refrigerants on the environment are central to the global ecological scene. Global warming, by its complexity and magnitude, poses several challenges to the ecological future of the earth. One of the solutions proposed to slow down this process is to reduce the production of greenhouse gases. While demand is growing, the areas of refrigeration and air conditioning are trying to renew themselves to meet the new ecological requirements. Such developments will lead to new technologies applicable to domestic and industrial uses of microtechnologies, HVAC systems refrigerators, heat pumps and affecting the automotive, railway, aeronautical, and aerospace industries. Magnetocaloric cooling (MCE) is a possible solution and becomes a promising attempt. Magnetic refrigeration is a technology that relies on the magnetocaloric effect, similar to compressibility refrigerant for gas refrigeration.

The magnetocaloric effect being present in all magnetic substances gives a large field of research activity to find active materials suitable for every utility [13, 14]. Gadolinium is the reference material for magnetic cold at room temperature. This

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

element also has the advantage of being an easy compound to obtain through its purity. It finds its technological development, thanks to the ease of implementation reflected by its high ductility and suitability. This is why it is used in most current magnetic refrigeration devices at room temperature. However, its prohibitive price (up to 3500 €/kg) and its limited reserves preclude it from possible magnetocooling materials for consumer applications. It is, therefore, important to find another magnetocaloric material. Manganese is an energetically clean alternative to address this problem and may be potential material for magnetic refrigeration.

The compounds LnMnO3, Ln2MnO4 (where Ln is a rare earth) are antiferromagnetic insulators. The partial substitution of Ln3+ by a divalent element A2+ (A2+ = Ca2+; Sr2+; Ba2+; Pb2+ … ), monovalent A+ (A+ = Ag<sup>+</sup> , Na<sup>+</sup> , K<sup>+</sup> … ), trivalent A3+ (A3+ = Nd3+, Sm3+, Pr3+ … ), or a gap in Ln1�xAxMnO3 results in oxidation or partial reduction of Mn3+/Mn4+ ions, a structural transition (cubic \$ rhombohedral \$ orthorhombic) and an antiferromagnetic order change TN = 125 K in LaMnO3) ferromagnetic with Tc > 360 K depending on the composition [15–22].

The manganese oxides, which we are interested in given the importance of their electrical and magnetic properties [23, 24], crystallize in a perovskite-like structure. For this structure, of general formula ABO3, the Bravais network of sites B (octahedral site), whose species are generally transition cations (Mn3+, Mn4+, Ti4+, Al3+ … ) occupying the eight vertices of the cube, is simple cubic. Oxygen ions occupy the midpoints of the ridges, and species A in coordination 12 (cuboctahedral site) occupying the center of the cube are alkaline ions (K+ , Na<sup>+</sup> , Ag+ … ). Alkaline earth (Sr2+, Ca2+, Pb2+ … ) or rare earths (La3+, Pr3+, Nd3+ … ). Site B is, therefore, occupied by an ion of octahedral coordination, manganese in the case of manganites, thus forming the MnO6 octahedra (**Figure 1**(**a**) and (**b**)).

It should be noted that the cations A and B must allow the electroneutrality of the compound; that is, the sum of the charges of the cations A and B must be equal to the total charge of the anions. Three types of ternary oxides can be found: cation A is monovalent (A+ B5+ O2� 3), bivalent (A2+ B4+ O2� 3), or trivalent (A3+ B3+ O2� 3).

**Figure 1.** *Unit cell ABO3 (a), octahedral environment of species B and (b) cuboctahedral environment of species A.*

#### **2. Structure, characterization, and electrical properties of Na2***M***P1.5As0.5O7 (***MII* **= Co and Cu).**

#### **2.1 Structural characterizations**

The X-ray powder diffractograms were recorded in the range 10–70° at 20°C with 0.02° step (**Figures 2** and **3**). GSAS software [25] using Rietveld method was used to confirm the crystallinity and purity of the obtained powders. The final reliability factors are Rp = 1.4%, Rwp = 1.9%, and Rp = 5.4%, Rwp = 6.9%, of the Co and Cu samples, respectively.

In this case, the difference between the two diffractograms is noticeable. Indeed, the Na2CoP1.5As0.5O7 [26] material crystallizes in the tetragonal system of the space group P42/mnm with the unit cell parameters a = 7.764 (3) Å; c = 10.385 (3) Å.

**Figure 2.** *Rietveld refinement pattern of Na2CoP1.5As0.5O7 powder.*

**Figure 3.** *Rietveld refinement pattern of Na2CuP1.5As0.5O7 powder.*

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

While the compound Na2CuP1.5As0.5O7 [27] crystallizes in the monoclinic system of the C2/c space group with the unit cell parameters a = 14.798 (2) Å; b = 5.729 (3) Å; c = 8.075 (2) Å; β = 115.00 (3)°.

In fact, the structural unit of the compound Na2CoP1.5As0.5O7 is formed by a site occupied by a cobalt atom, a site occupied by a phosphorus atom partially substituted by arsenic, two sites for the sodium atoms and three sites for the sodium atoms ten oxygen atoms. The asymmetric unit is shown in **Figure 4**.

(i) y + 1/2, x 1/2, z + 1/2; (ii) x + 1, y, z; (iii) y + 1/2, x + 1/2, z + 1/2].

The projection of the structure in the b direction (**Figure 5**) illustrates the layered nature of the anionic framework with two alternating orientations of anion

**Figure 4.** *Structural unit of Na2CoP1.5As0.5O7 with atom labeling scheme.*

**Figure 5.** *Projection of the Na2CoP1.5As0.5O7 along* b *direction.*

**Figure 6.** *Structural unit projection of Na2CuP1.5As0.5O7.*

sheets [Co(P/As)2O7] <sup>2</sup> per unit cell parallel to the *ab* plane where sodium cations are sandwiched between layers. Compared to Na2CoP2O7 [28] crystal structure, the substitution of the phosphorus ions by arsenic cations decreases the size of the interlayer space and decreases in binding NadO distance.

On the other hand, the structural unit of Na2CuP1.5As0.5O7 (**Figure 6**) contains two P2O7 units connected by the corner with two CuO4 with square plane geometry. The charge neutrality of the structural unit is ensured by four sodium ions.

The Cu2P4O15 groups of the structural unit are linked by oxygen peaks to give infinite chains, wavy sawtooth in the [001] direction (**Figure 7**). Na<sup>+</sup> ions are located in the inter-chain space.

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

#### **2.2 Electrical study of Na2CoP1.5As0.5O7**

The electrical properties of the cobalt compound were studied using complex impedance spectroscopy [29] in the temperature range from 240 to 360°C after stabilization at each step of 30°C between 1 Hz and 13 MHz frequency range. The electrical parameters are concluded using the conventional electrical circuit: R//CPE-R//CPE, where Rest is a resistance and CPE is a constant phase element:

The electrical parameters are summarized in **Table 1**.

The electrical measurements show that the electrical conductivity of Na2CoP1.5As0.5O7 increases from 4.0 <sup>10</sup><sup>6</sup> S cm<sup>1</sup> at 240°C to 3.69 <sup>10</sup><sup>5</sup> S cm<sup>1</sup> at 360°C. On the other hand, the activation energy which follows Arrhenius' law is 0.56 eV.

#### **2.3 Electrical study of Na2CuP1.5As0.5O7**

The Na2CuP1.5As0.5O7 sample was sintered at 550°C for 2 h with 5°C/min of heating and cooling. The relative density of the obtained pellet is D = 88%. Electrical measurements in the temperature range of 260–380°C were performed using complex impedance spectroscopy. The recorded spectra are shown in **Figure 8**.

The best refinements of impedance spectra were obtained when using a conventional electrical circuit Rg//CPEg-Rgb//CPEgb.


#### **Table 1.**

*Results of electrical parameters of Na2CoP1.5As0.5O7.*

**Figure 8.** *Impedance spectra of Na2CuP1.5As0.5O7 recorded at 240–360°C.*


**Table 2.**

*Results of electrical parameters of Na2CuP1.5As0.5O7.*

The values of the electrical parameters calculated at different temperatures are presented in **Table 2**.

The conductivity of Na2CuP1.5As0.5O7 (**Table 2**) increase from 0.35 <sup>10</sup><sup>5</sup> S cm<sup>1</sup> at 260°C to 3.13 <sup>10</sup><sup>5</sup> S cm<sup>1</sup> at 380°C. On the other hand, the porosity of 12% of our sample prompted us to estimate the conductivity values of the fully dense sample of Na2CuP1.5As0.5O7 using the empirical formula proposed by Langlois and Couret [30].

Taking into account the porosity factor P = 0.12, the conductivity value of the dense material will be σ<sup>d</sup> = (4σ/0.88). The conductivity values of a dense sample, calculated at different temperatures, are summarized in **Table 2**. In this case, the experimental conductivity of 3.5 <sup>10</sup><sup>6</sup> S cm<sup>1</sup> corresponds to the corrected value of 1.59 <sup>10</sup><sup>5</sup> S cm<sup>1</sup> to 260°C.

The activation energy calculated from the slope of the linear curve Ln(σ T) = f(1000/T) is linear (**Figure 9**), with a slope that gives the value of Ea = 0.60 eV, satisfying Arrhenius law LnσT = Lnσ<sup>0</sup> Ea/kT (k = Boltzmann constant).

The electrical study shows that the activation energy decreases for Na2CuP1.5As0.5O7 compared to that of Na2CuP2O7 [27], i.e., 0.60 eV and 0.89 eV, respectively. Therefore, the effect of P/As substitution increases the electrical conductivity of the parent phase Na2CuP2O7 at a lower temperature [31]. Overall, a comparison of the conductivity values of the material studied Na2CuP1.5As0.5O7 (at T = 350°C, <sup>σ</sup><sup>d</sup> = 88% = 2.28 <sup>10</sup>–<sup>5</sup> S cm<sup>1</sup> ; <sup>σ</sup><sup>d</sup> = 2.28 <sup>10</sup><sup>4</sup> S cm<sup>1</sup> and Ea = 0.60 eV) with those found in the literature shows that our material can be classified as fast ionic conductors.

**Figure 9.** *Arrhenius plot of conductivity of the Na2CuP1.5As0.5O7 sample.*

#### **3. Structure, magnetic, and magnetocaloric of La0.7Sr0.2K0.1MnO3 and La0.7Ba0.2Na0.1MnO3 compounds**

#### **3.1 Structural characterization**

Before proceeding with the magnetic study, it was necessary to ascertain the structure of the materials. Using the X-ray diffraction technique, it was possible to confirm that all the samples analyzed in this work have only one type of structure (single-phase) and that they corresponded to the given stoichiometry. The samples were reduced to powdered form, with a grinding time of 2 min, which was sufficient to obtain the random effect of orienting the structures without destroying them.

To check the nature and purity of the synthetic products, X-ray diffraction patterns were recorded at room temperature using the Panalytical X'Pert PRO diffractometer which is equipped with a copper anticathode (λKα1 = 1.54056 Å, λKα2 = 1.54439 Å) and provides good quality diffractograms.

**Figure 10** presents the experimental X-ray diffraction spectra of La0.7Sr0.2Na0.1MnO3 compound refined via the WinPlotr graphical interface of FullProf\_Suite which has been studied by W. Cheikh-Rouhou Koubaa et al. [32].

The Rietveld analysis of X-ray diffraction patterns shows that the La0.7Sr0.2K0.1MnO3 and La0.7Ba0.2Na0.1MnO3 compounds are single-phase and crystallize in the rhombohedral Th2Zn17-type structure (space group, R\_3m).

**Figure 11** shows the evolution of the unit cell volume compared to hrAi for the two series. For La0.7Sr0.2M0.1MnO3 samples, an observed increase of hrAi occurred with a slight decrease in the volume of the unit cell from 352.5 Å for *M* = Na to 351.1 Å for *M* = K. While in the compounds La0.7Ba0.2M0.1MnO3, the evolution of unit cells is rather governed by <sup>h</sup>rA<sup>i</sup> than by <sup>σ</sup><sup>2</sup> observed increase in unit cell volume. It should be noted that, although the ionic radius of site A and the size of the mismatch are similar for both samples, La0.7Sr0.2K0.1MnO3 and La0.7Ba0.2Na0.1MnO3, the unit cell volume has different values. This behavior highlights the effects of the difference in electronegativity between the A-site ions in our compounds [33]. With increasing hrAi, the MndOdMn binding angle decreases from 166.7° for sample La0.7Sr0.2Na0.1MnO3 to 165.9° for the sample La0.7Ba0.2Na0.1MnO3. However, the MndO bond length increases from 1.957 Å to

**Figure 10.** *X-ray diffraction patterns of La0.7Sr0.2Na0.1MnO3 sample.*

**Figure 11.** *Unit cell volume versus* h*rA*i *for La0.7M0.2M'0.1MnO3 (M = Sr, Ba and M' = Na, Ag and K) samples.*

1.968 Å, which influences the dual force of exchange. Effects of monovalent doping on the structural, magnetic, and magnetocaloric properties in La0.7*M*0.2*M*'0.1MnO3 manganese oxides (*M* = Sr, Ba and *M*' = Na, Ag, K) has been studied to control the value evaluation of magnetic entropy and cooling capacity.

#### **3.2 Study of magnetic properties**

The magnetic behaviors are subjected to two variables, which are the temperature and the applied magnetic field. It is possible to control these two factors experimentally and, thus, to keep one constant while studying the influence of the other on the magnetization M. The magnetic measurements were carried out on the two magnetometers BS2 and BS1 of the NEEL Institute used in the low/hightemperature configuration. The evolution of the magnetization as a function of the temperature and of the M(H, T) field was carried out on either side of the Curie temperature for each compound. The temperature of transition from the ferromagnetic state to the paramagnetic state was determined from the thermomagnetic curve M(T). TC corresponds to the minimum value of (dM/dT). The change in magnetic entropy was evaluated from the M(H, T) matrix based on the corresponding Maxwell equation.

Magnetic measurements of these compounds La0.7Sr0.2K0.1MnO3 and La0.7Ba0.2Na0.1MnO3 as a function of temperature in the temperature range 20–350 K under an applied magnetic field of 50mT show that all substituted samples show a magnetic transition from paramagnetic to ferromagnetic with decreasing temperature, as shown in **Figure 12**.

**Figure 13** shows that the Curie temperature varies according to the ionic rays. It goes to lower values with hrAi and varies from 340 K for hrAi = 1.182 Å to 311.5 K for hrAi = 1.247.

#### **3.3 Study of magnetic properties under an applied magnetic field**

In manganites, magnetism is essential of the localized type. A simple way to check, at low temperature, the ferromagnetic state, the fixed spin state, or the coexistence of a ferromagnetic and antiferromagnetic state of a sample, is to

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

**Figure 12.** *Temperature dependence of the magnetization under an applied magnetic field 50 mT.*

**Figure 13.** *Curie temperature versus* h*rA*i *for La0.7M0.2M'0.1MnO3 (M = Sr, Ba and M' = Na, Ag and K) samples.*

compare the value of the saturation magnetization with its calculated value assuming full alignment of the manganese spins of this compound. This procedure gives an estimate of the degree of alignment of the moments. For this, we present the study of the magnetic properties of these samples under an applied magnetic field up to the value of 7 tesla. As the study of the thermal variations of the magnetization under weak magnetic field (0.05 T) showed that the samples Pr0.6�xEuxSr0.4MnO3 (0.0 ≤ x ≤ 0.2) present a magnetic transition as a function of the temperature, it is then interesting to specify the nature of the magnetic order at low temperatures. M'nassri et al. [34] performed magnetization measurements as a function of the magnetic field applied at various temperatures.

The difference observed between the compounds La0.7Sr0.2K0.1MnO3 and La0.7Ba0.2Na0.1MnO3 is fully explained by the effects of the difference in electronegativity between the ions at site A for the two samples. The magnetization measurements as a function of the applied magnetic field up to 7 T at several temperatures confirmed the ferromagnetic behavior of these samples at low temperature, and the results are shown in **Figure 14**.

**Figure 14.** *(a) Isotherm magnetization curves M(H,T). (b) Temperature dependence of the spontaneous magnetization Msp and 1/χ for La0.7Sr0.2Na0.1MnO3 sample.*

The authors show that below TC, the magnetization M increases strongly with the magnetic field applied for H < 0.5 T then saturates above 1 T. The saturation magnet changes to higher values as the temperature decreases. This result confirms the ferromagnetic behavior of our sample at low temperature. **Figure 14b** shows the temperature dependence of the spontaneous magnetization Msp and 1/χ for the sample La0.7Sr0.2Na0.1MnO3. The experimental value of the spontaneous magnetization Msp(exp), deduced from the M(H) curves is 3.48 μB/Mn. The amplitude of the Msp(exp) is comparable to the theoretical value of 3.6 μB/mole calculated for full spin alignment. The critical exponent defined by.

$$\mathbf{Msp(T)} = \mathbf{Msp(0)} [\mathbf{1} - \mathbf{T}/\mathbf{T\_C}]^\nu \tag{1}$$

and deduced from the fit of the curve Msp(T) is 0.31, which confirms the ferromagnetic behavior of the samples from the group Cheikh-Rouhou team at low temperature

#### **3.4 Magnetocaloric effect**

Entropy is a measure of order in the magneto-thermodynamic system. High order is related to low entropy and vice versa. Dipoles, that is, electron spins, can take on different orientations. If these entities are oriented in the same direction in a paramagnetic material, a ferromagnetic or a diamagnetic material, the order and the magnetization are high. It is obvious that applying a magnetic field aligns the electronic spins and lowering the temperature (releasing energy from the system) also results in a more ordered arrangement. So the external magnetic field generates the stress parameter, while the magnetization determines the order parameter of such magnetic materials.

In order to obtain a maximum of information on the thermodynamic behavior and to observe the magnetocaloric effect in the manganites in the vicinity from

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

their magnetic transition temperature, we have studied the magnetocaloric behavior of the whole range of composition x.

After having studied magnetic measurements of magnetization as a function of temperature M(T) as well as magnetization as a function of the magnetic field at various temperature M(μ0H, T), we have calculated, the magnetic entropy change ΔSM of all our synthesized compounds as a function of temperature T and magnetic field H.

Based on the thermodynamic theory, magnetic entropy change is determined through the numerical integration of the magnetization isotherms, according to Maxwell's thermodynamic relation given by the following equation [34, 35]:

$$
\Delta \mathbb{S}\_{\mathcal{M}}(T, \Delta H) = \int\_0^H \mu\_0 \left(\frac{\partial \mathcal{M}}{\partial T}\right)\_{P,H} dH \tag{2}
$$

$$\Delta \mathbb{S}\_{\mathcal{M}}(T\_i, \Delta H) = -\sum\_{j} \frac{\mathcal{M}\_{i+1} \left(T\_{i+1}, H\_j\right) - \mathcal{M}\_i \left(T\_i, H\_j\right)}{T\_{i+1} - T\_i} \mu\_0 \delta H\_j \tag{3}$$

where Mi and Mi+1 are the magnetization values measured at the Hi field and at temperatures Ti and Ti+1, respectively [35].

We have shown in **Figure 15**, the variations in entropy (�ΔSM) as a function of temperature for different magnetic fields applied for these La0.7Sr0.2Na0.1MnO3 and La0.7*M*0.2*M*'0.1MnO3 sample (*M* = Sr, Ba and M' = Na, Ag and K) system. These curves show that the entropy value (�ΔSM) varies with temperature and has a peak around the transition temperature TC. The sample La0.7Sr0.2Na0.1MnO3 shows the highest value of ΔSM Max, 4.07 J kg�<sup>1</sup> K�<sup>1</sup> , around 345 K. For the sample La0.7Ba0.2Na0.1MnO3, we observed an asymmetric broadening of the peak ΔSM, which could be explained by a structural inhomogeneity. We can also notice that the magnetic and negative entropy for all our samples was due to the ferromagnetism encountered in these samples. The value of the entropy (�ΔSM Max) was also observed to increase when the applied magnetic field increased. Although these ΔSM Max values in these samples are lower than those observed in Gd or Gd-based compounds, the ΔSM Max curves as a function of temperature are significantly wider.

**Figure 15.** *Magnetic entropy change* �*ΔSM evolution versus temperature at (a) Several magnetic applied fields for La0.7Sr0.2Na0.1MnO3 sample (b) At 5 T for La0.7*M*0.2*M*'0.1MnO3 samples (*M *= Sr, Ba and* M*' = Na, Ag and K).*

This wider temperature range with a large change in magnetic entropy is useful for an ideal Ericsson refrigeration cycle. In addition, our samples are interesting in application as potential candidates in magnetic refrigeration because they are inexpensive, easier to manufacture, possess tunable TC, and have high chemical resistance stability.

### **4. Conclusion**

During our research on the investigation of new phosphates, arsenates of metals (Co, Cu) and alkali cations, we were able to isolate 2 crystalline phases. These compounds have shown remarkable structural diversity, even though they are isoformular. The synthesis method adopted was dry synthesis. In addition, P/As substitution showed conservation of structure in each material with variation in cation-oxygen distances. On the other hand, the effect of substitution is remarkable on the electrical properties. In fact, the sodium Co and Cu diphosphates-diarsenates are more conductive than the pure diphosphates. Alkaline atoms have an electronic procession, composed of a set of inert internal layers, having the structure of a rare gas, and an additional electron, or valence electron, which orbiting an s-type orbital. The magnetic and magnetocaloric study on the La0.7M0.2M'0.1MnO3 family shows that there is a Curie temperature in the vicinity of the room temperature and very high magnetic entropy values. We can conclude that these compounds are good candidates for magnetic refrigeration.

### **Author details**

Amira Marzouki<sup>1</sup> , Ameni Brahmia2,3, Riadh Marzouki2,4\*, Mosbah Jemmali4 , Ismat H. Ali<sup>2</sup> and Mohamed Faouzi Zid<sup>5</sup>

1 Laboratory of Signal Image and Energy Mastery, Engineering National Higher School of Tunis, Tunis, Tunisia

2 Chemistry Department, College of Science, King Khalid University, Abha, Saudi Arabia

3 Laboratoire des Materiaux et de l'Environnement pour le Developpement Durable, LR18ES10, University of Tunis El Manar, Tunisia

4 Faculty of Science, LSME, University of Sfax, Sfax, Tunisia

5 Faculty of Sciences of Tunis, Laboratory of Materials, Crystallochemistry and Applied Thermodynamics, University of Tunis El Manar, Tunisia

\*Address all correspondence to: rmarzouki@kku.edu.sa

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

#### **References**

[1] Brian LE, Nazar F. Sodium and sodium-ion energy storage batteries. Current Opinion in Solid State & Materials Science*.* 2012;**16**:168-177

[2] Shakoor RA, Seo DH, Kim H, Park YU, Kim J, Kim SW, et al. A combined first principles and experimental study on Na3V2(PO4)2F3 for rechargeable Na batteries. Journal of Materials Chemistry. 2012;**22**:20535

[3] Kim H, Shakoor RA, Park C, Yeon Lim S, Kim JS, Jo YN, et al. Na2FeP2O7 as a positive electrode material for rechargeable aqueous sodium-ion batteries. Advanced Functional Materials. 2013;**23**:1147

[4] Peng Y, Yang L, Ju X, Liao B, Ye K, Li L, et al. A comprehensive investigation on the thermal and toxic hazards of large format lithium-ion batteries with LiFePO4 cathode. Journal of Hazardous Materials. 2020;**381**:120916

[5] Goodenough JB, Hong HY-P, Kafalas JA. Fast Na<sup>+</sup> -ion transport in skeleton structures. Materials Research Bulletin. 1976;**11**:203-220

[6] Kanazawa T. Inorganic Phosphate Materials, Materials Science Monographs. Vol. 52. Amsterdam: Elsevier; 1989

[7] Erragh F, Boukhari A, Elouadi B, Holt EM. Crystal structures of two allotropic forms of Na2CoP2O7. Journal of Crystallographic and Spectroscopic Research. 1991;**21**:321-326

[8] Padhi AK, Nanjundaswamy K, Goodenough JB. Phospho‐olivines as positive‐electrode materials for rechargeable lithium batteries. Journal of the Electrochemical Society. 1997; **144**(4):1188-1194

[9] Durif A. Crystal Chemistry of Condensed Phosphates. US: Springer; 1995 [10] Barpanda P, Lu J, Ye T, Kajiyama M, Chung S-C, Yabuuchi N, et al. A layerstructured Na2CoP2O7 pyrophosphate cathode for sodium-ion batteries. RSC Advances. 2013;**3**: 3857-3860. DOI: 10.1039/C3RA23026K

[11] Satya Kishore MVVM, Varadaraju UV. Synthesis, characterization and electrochemical studies on LiCoAsO4. Materials Research Bulletin. 2006;**41**: 601-607

[12] Essehli R, Ben Yahia H, Maher K, Sougrati MT, Abouimrane A, Park J-B, et al. Unveiling the sodium intercalation properties in Na1.86□0.14Fe3(PO4)3. Journal of Power Sources. 2016;**324**: 657-664

[13] Tishin AM, Spichkin YI. The Magnetocaloric Effect and Its Applications. Bristol: Institute of Physics Publishing; 2003

[14] Tegus O, Brück E, Buschow KHJ, de Boer FR. Transition-metal-based magnetic refrigerants for roomtemperature applications. Nature. 2002; **415**:150

[15] Cherif K, Dhahri J, Dhahri E, Oumezzine M, Vincent H. Effect of indium substitution on structural, magnetic and magnetocaloric properties of La0.5Sm0.1Sr0.4Mn1xInxO3 (0 ≤ x ≤ 0.1) manganites. Journal of Solid State Chemistry. 2002;**163**:466

[16] Tlili MT, Chihaoui N, Bejar M, Dhahri E, Valente MA, Hlil EK. Charge ordering analysis by electrical and dielectric measurements in Ca2xPrxMnO4 (x = 0–0.2) compounds. Journal of Alloys and Compounds. 2011; **509**:6447

[17] Daoudi A, Le Flem G. Sur une série de solutions solides de formule Ca2xLnxMnO4 (Ln = Pr, Nd, Sm, Eu,

Gd). Journal of Solid State Chemistry. 1972;**5**:57

[18] Takahashi J, Kamegashira N. Lowtemperature structural phase transitions in rare earths substituted calcium manganese oxides [Ca2�xLnxMnO4, where Ln=Nd, Sm-Lu and Y]. Materials Research Bulletin. 1993;**28**:451

[19] Takahashi J, Kikuchi T, Satoh H, Kamegashira N. Phase transition of Ca2-xSmxMnO4 (x < 0.5). Journal of Alloys and Compounds. 1993;**192**:96

[20] Dhahri E, Guidara K, Cheikhrouhou A, Joubert JC, Pierre J. Monovalent effects on structural, magnetic and magnetoresistance properties in doped manganite oxides. Phase Transitions. 1998;**66**:99

[21] Teresa JMDE, Ibarra MR, Garcia J, Blasco J, Ritter C, Algarabel PA, et al. Spin-glass insulator state in (Tb-La)2/3Ca1/3MnO3 perovskite. Physical Review Letters. 1996;**76**:3392

[22] Ju HL, Kwon C, Li Q, Greene RL, Venkatesan T. Magnetic anisotropy and strain states of (001) and (110) colossal magnetoresistance thin films. Applied Physics Letters. 1994;**65**:2108

[23] Ziese M. Extrinsic magnetotransport phenomena in ferromagnetic oxides. Reports on Progress in Physics. 2002; **65**:143

[24] Shankar KS, Kar S, Raychaudhuri AK, Subbanna GN. Fabrication of ordered array of nanowires of La0.67Ca0.33MnO3La0.67Ca0.33MnO3 (x=0.33)(x=0.33) in alumina templates with enhanced ferromagnetic transition temperature. Applied Physics Letters. 2003;**84**(6):993

[25] Larson AC, Von Dreele RB. General Structure Analysis System (GSAS). Report LAUR 86–748. Los Alamos, NM: Los Alamos National Laboratory; 2000

[26] Marzouki R, Ben Smida Y, Sonni M, Avdeev M, Zid MF. Synthesis, structure, electrical properties and Na<sup>+</sup> migration pathways of Na2CoP1.5As0.5O7. Journal of Solid State Chemistry. 2020;**285**: 121058

[27] ALQarni OSA, Marzouki R, Smida YB, Avdeev M, Alghamdi MM, Zid MF. Synthesis, electrical properties and Na+ migration pathways of Na2CuP1.5As0.5O7. PRO. 2020;**8**:305

[28] MacDonald JR. Impedance Spectroscopy. New York: Wiley; 1987

[29] Sanz F, Parada C, Rojo JM, Ruiz-Valero C, Saez-Puche R. Studies on tetragonal Na2CoP2O7, a novel ionic conductor. Journal of Solid State Chemistry. 1999;**145**(2):604-611. DOI: 10.1006/jssc.1999.8249

[30] Langlois S, Couret F. Electrochemical measurements of mass transfer coefficients in a cell simulating tooth canals. Journal of Applied Electrochemistry. 1989;**19**:43

[31] Hafidi E, El Omari M, El Omari M, Bentayeb A, Bennazha J, El Maadi A, et al. Conductivity studies of some diphosphates with the general formula AI 2BIIP2O7 by impedance spectroscopy. Arabian Journal of Chemistry. 2013;**6**: 253-263

[32] Cheikh-Rouhou Koubaaa W, Koubaaa M, Cheikhrouhou A. Effect of monovalent doping on the structural, magnetic and magnetocaloric properties in La0.7M0.2M<sup>0</sup> 0.1MnO3 manganese oxides (M=Sr, Ba and M<sup>0</sup> =Na, Ag, K). Physics Procedia. 2009;**2**:989-996

[33] Koubaa WC, Koubaa M, Cheikhrouhou A. Structural, magnetotransport, and magnetocaloric properties of La0.7Sr0.3�xAgxMnO3 perovskite manganites. Journal of Alloys and Compounds. 2008;**453**:42

*Correlation between Structure, Electrical, and Magnetic Properties of Some Alkali-Oxide… DOI: http://dx.doi.org/10.5772/intechopen.102322*

[34] M'nassri R, Cheikhrouhou-Koubaa W, Koubaa M, Boudjada N, Cheikhrouhou A. Magnetic and magnetocaloric properties of Pr0.6-xEuxSr0.4MnO3 manganese oxides. Solid State Communications. 2011; **151**:1579

[35] Mc Michael RD, Ritter JJ, Shull RD. Enhanced magnetocaloric effect in Gd3Ga5xFexO12. Journal of Applied Physics. 1993;**73**:6946

### *Edited by Riadh Marzouki*

Alkaline elements are present in large quantities and in different forms in the Earth's layers. They are widely used in the manufacture of materials showing interesting physical properties that can be applied in several fields, including catalysis, biology, energy, and others. This book describes different methods of synthesis and treatment of certain alkaline materials and their applications in different fields. It discusses alkaline chemistry in catalysis, biology, polymers and composites, and crystallography.

Published in London, UK © 2022 IntechOpen © SimoneN / iStock

Alkaline Chemistry and Applications

Alkaline Chemistry and

Applications

*Edited by Riadh Marzouki*