**Preface to "Prosthetic Joint Infection: The Challenges of Prevention, Diagnosis and Treatment and Opportunities for Future Research"**

Joint replacement is a common and increasingly performed surgical procedure. The most commonly replaced joints are the hip and knee, although virtually all extra-axial joints can be replaced. Prosthetic joint infections (PJIs) are devastating complications with significant patient morbidity and mortality and considerable healthcare and societal costs. Although the percentage of PJIs in patients with joint replacements could be considered low (1–3% for elective primary arthroplasties), the increasing frequency of such procedures transforms an apparently low risk into a substantial and growing burden of infection. Nevertheless, the risk of PJIs is higher in revision procedures and in specific groups of patients. Indeed, in most developed countries, PJIs are considered a major public health problem.

PJI is a paradigm of biofilm-associated infection. The presence of biofilm influences and complicates the prevention, diagnosis, and treatment of PJI. Eradication of the infection requires surgery and antimicrobial therapy. Close collaboration between all medical and surgical specialists involved is a critical component of the care of patients with PJI.

In this complex scenario, despite the considerable amount of research conducted in recent decades on the prevention, diagnosis, treatment, and outcome of PJIs, many questions remain unanswered. Indeed, most recommendations in this area are based on expert opinion due to the limitations of the available information.

This Special Issue aimed to advance knowledge and broaden our perspectives on the prevention, diagnosis, management, and outcomes of PJI.

> **Natividad Benito, Oscar Murillo, and Jaime Lora-Tamayo ´** *Editors*


**4. Elastic properties**

Knowledge of elastic constants provides more information about mechanical properties and understanding of the usefulness of the materials. Mechanical stability requires that its independent elastic constants should satisfy the following Born's stability criteria.

For a tetragonal crystal

$$\left| \mathbf{C}\_{44} > \mathbf{0}, \mathbf{C}\_{66} > \mathbf{0}, \mathbf{C}\_{11} > \left| \mathbf{C}\_{12} \right|, \left( \mathbf{C}\_{11} + \mathbf{C}\_{12} \right) \mathbf{C}\_{33} > \mathbf{2}, \mathbf{C}\_{13} \tag{2}$$

For a hexagonal crystal

$$\left| \mathbf{C}\_{44} > \mathbf{0}; \mathbf{C}\_{11} - \left| \mathbf{C}\_{12} \right| > \mathbf{0}; \left( \mathbf{C}\_{11} + 2\mathbf{C}\_{12} \right) \mathbf{C}\_{33} - 2\mathbf{C}^{2}\_{13} > \mathbf{0} \tag{3}$$

For a cubic structure

$$\mathbf{C}\_{11} + \mathbf{2}\,\mathbf{C}\_{12} > \mathbf{0}; \quad \mathbf{C}\_{11} - \mathbf{C}\_{12} > \mathbf{0}; \mathbf{C}\_{44} > \mathbf{0} \tag{4}$$

According to the symmetry of crystalline systems, some elastic constants are null. In this part, **Table 2** gives an overview of the expression of the stiffness tensors corresponding to each crystal system studied (cubic, hexagonal and tetragonal). The cubic structure has the simplest elastic matrix, with only 3 independent

**Table 2.**

*The stiffness tensors of the elastic constants corresponding to the systems: cubic, hexagonal and tetragonal.*

**103**

compound.

*Titanium Aluminide Coating: Structural and Elastic Properties by DFT Approach*

94.90 *74.1* [29] *83* [24]

98.75 *88.7* [30] *83* [31]

constants, while the elastic matrices of the hexagonal and tetragonal structures have

B2-TiAl 76.04 118.26 — — 71.98 —

84.63 *74.4* [29] *84* [24]

78.23 *62.3* [30] *63* [31]

**C11 (GPa) C12 (GPa) C13 (GPa) C33 (GPa) C44 (GPa) C66 (GPa)**

167.96 *178* [29] *168* [24]

237.27 *220* [30] *231* [31]

113.84 *105* [29] *111* [24]

59.30 *62.2* [30] *57* [31]

72.12 *78.4* [29] *75* [24]

> -- -- --

**Table 3** clearly shows that all elastic constants satisfy well the required stability conditions, indicating that both TiAl and Ti3Al compounds are mechanically stable. In addition, our elastic constants calculated fit the experimental and theoretical values. As known, the elastic constants C11 and C33 measure the resistance of alloys under uniaxial stress along *a*- and *c-axis*. The results obtained allow us to predict that these alloys are more resistant to deformation along a and c-axis. Moreover, the C66 value is significantly lower than C44 suggesting; thus, that the (001)[100] deformation would be easier than (010)[100] deformation for these alloys. On the other hand, we can see that the elastic constants of B2 structure do not required the Born-Huang's stability criteria. This indicates that B2-TiAl phase is mechanically

It is well-known that the physical properties of a material are strongly correlated to its electronic structure nature. So, by applying the obtained equilibrium structural parameters, the total and partial densities of states (TDOS and PDOS) were calculated along the principal symmetry directions in the Brillouin zone to further understand the reasonable relationship between the mechanical behavior and bonding characteristics of γ-TiAl based alloys. The total and partial DOS of pure

We can see that Ti-DOS typically Ti-d states play a very important role in the total density of TiAl in L10 structure. In this compound, the total state density has two regions in the valence band: a deep region dominated by Al-s states, the second one is constituted by Al-p and Ti-d states, which are separated by a strong hybridization where Al-p states forming a peak at about −1.5 eV which is more localized contributes to the strong covalence in Ti-d-Al-p bonds. Al the Fermi level, the density of states is not zero, dominated mainly by Ti-d states, attesting to the weak metallic character of this intermetallic class. Hence, the interactions of the strong covalent bond with the weak metallic bond cause an unequal distribution of these forces leading to a cleavage fracture in the direction of the metallic interactions. From **Figure 2**, the interactions between Al-3p and 3d-Ti take place in the Ti-Al binary compounds, leading to the enhancement of the covalent bonding. By the way, it can be found that Al-3p plays an important role in the pseudogap of Ti-Al

Through the further analysis of PDOS, the peaks of the PDOS of Ti-3d and Al-3p are exactly overlapped, indicating the strong covalent bonding originates

unstable, although it is energetically stable as mentioned above.

L10-TiAl, α2-Ti3Al, and B2-TiAl compounds are depicted in **Figure 2**.

*DOI: http://dx.doi.org/10.5772/intechopen.97409*

*183* [29] *173* [24]

*175* [30] *185* [31]

*Elastic constants for B2-TiAl,* γ*-TiAl and* α*2-Ti3Al compounds.*

five and six constants respectively.

γ-TiAl 179.20

α2-Ti3Al 217.36

**Table 3.**

**5. Electronic properties**

*Titanium Aluminide Coating: Structural and Elastic Properties by DFT Approach DOI: http://dx.doi.org/10.5772/intechopen.97409*

#### **Table 3.**

*Transition Metal Compounds - Synthesis, Properties, and Application*

Knowledge of elastic constants provides more information about mechanical properties and understanding of the usefulness of the materials. Mechanical stability requires that its independent elastic constants should satisfy the following Born's

According to the symmetry of crystalline systems, some elastic constants are null. In this part, **Table 2** gives an overview of the expression of the stiffness tensors corresponding to each crystal system studied (cubic, hexagonal and tetragonal). The cubic structure has the simplest elastic matrix, with only 3 independent

**Crystal System Point symmetry group Stiffness Tensor**

m-3 432 -43 m m-3 m

−6 6/m 622 6 mm -62 m 6/mmm

4 mm −42 m 4/mmm 4 -4 4/m

*The stiffness tensors of the elastic constants corresponding to the systems: cubic, hexagonal and tetragonal.*

( ) 2 C 0,C 0,C C , C C C 2C 44 66 11 12 11 12 33 13 >>> + > (2)

( ) 2 C 0;C C 0; C 2C C – 2C 0 44 11 12 > −> + 11 12 33 13 > (3)

C 2C 0; C – C 0;C 0 11 12 +> > > 11 12 44 (4)

11 12 12 11 12 11

11 12 13 11 13 33

11 12 13 11 13 33

*CCC C C C*

*CCC C C C*

*CCC C C C*

44

44

44

*C*

*C*

*C*

44

44

44

*C*

*C*

*C*

44

66

66

*C*

*C*

*C*

**4. Elastic properties**

For a tetragonal crystal

For a hexagonal crystal

For a cubic structure

Cubic 23

Hexagonal 6

Tetragonal 422

stability criteria.

**102**

**Table 2.**

*Elastic constants for B2-TiAl,* γ*-TiAl and* α*2-Ti3Al compounds.*

constants, while the elastic matrices of the hexagonal and tetragonal structures have five and six constants respectively.

**Table 3** clearly shows that all elastic constants satisfy well the required stability conditions, indicating that both TiAl and Ti3Al compounds are mechanically stable. In addition, our elastic constants calculated fit the experimental and theoretical values. As known, the elastic constants C11 and C33 measure the resistance of alloys under uniaxial stress along *a*- and *c-axis*. The results obtained allow us to predict that these alloys are more resistant to deformation along a and c-axis. Moreover, the C66 value is significantly lower than C44 suggesting; thus, that the (001)[100] deformation would be easier than (010)[100] deformation for these alloys. On the other hand, we can see that the elastic constants of B2 structure do not required the Born-Huang's stability criteria. This indicates that B2-TiAl phase is mechanically unstable, although it is energetically stable as mentioned above.

#### **5. Electronic properties**

It is well-known that the physical properties of a material are strongly correlated to its electronic structure nature. So, by applying the obtained equilibrium structural parameters, the total and partial densities of states (TDOS and PDOS) were calculated along the principal symmetry directions in the Brillouin zone to further understand the reasonable relationship between the mechanical behavior and bonding characteristics of γ-TiAl based alloys. The total and partial DOS of pure L10-TiAl, α2-Ti3Al, and B2-TiAl compounds are depicted in **Figure 2**.

We can see that Ti-DOS typically Ti-d states play a very important role in the total density of TiAl in L10 structure. In this compound, the total state density has two regions in the valence band: a deep region dominated by Al-s states, the second one is constituted by Al-p and Ti-d states, which are separated by a strong hybridization where Al-p states forming a peak at about −1.5 eV which is more localized contributes to the strong covalence in Ti-d-Al-p bonds. Al the Fermi level, the density of states is not zero, dominated mainly by Ti-d states, attesting to the weak metallic character of this intermetallic class. Hence, the interactions of the strong covalent bond with the weak metallic bond cause an unequal distribution of these forces leading to a cleavage fracture in the direction of the metallic interactions.

From **Figure 2**, the interactions between Al-3p and 3d-Ti take place in the Ti-Al binary compounds, leading to the enhancement of the covalent bonding. By the way, it can be found that Al-3p plays an important role in the pseudogap of Ti-Al compound.

Through the further analysis of PDOS, the peaks of the PDOS of Ti-3d and Al-3p are exactly overlapped, indicating the strong covalent bonding originates

**Figure 2.** *The total and partial density of states (DOS) for: (a)* α*2-Ti3Al, (b) B2-TiAl, (c)* γ*-TiAl.*

from the interaction between Ti-3d and Al-3p. Sometimes, a high DOS value at Fermi level means unstable structures in some degree. In this work, the values of total DOS at Fermi level of Ti3Al, B2-TiAl, and γ-TiAl compounds are 10.8 eV, 3.4 eV,

**105**

**Author details**

Ouahiba Ouadah

*Titanium Aluminide Coating: Structural and Elastic Properties by DFT Approach*

and 3.0 eV, respectively. From this point of view, Ti3Al compound is considered to

In this chapter, we have studied the structural, elastic, and electronic properties of titanium aluminide intermetallic compounds using first-principles calculations based on density functional theory (DFT). The use of the GGA-PBE approximation for the exchanging correlation potential allowed us to obtain good results of the electronic structure. B2-TiAl, γ-TiAl, and α2-Ti3Al are thermodynamically stable according to both thermodynamical and mechanical criteria. Whereas, B2-TiAl compound is mechanically unstable. Besides, elastic properties showed that these alloys are more resistant to deformation along *a-* and *c-axis*. Moreover, the C66 value is significantly lower than C44 suggesting; thus, that the (001)[100] deformation would be easier than (010)[100] deformation for these alloys. Based on the electronic structure, titanium aluminide binary compounds are composed of both metallic bonds and covalent bonds. α2-Ti3Al shows the strongest metallic bonding

Division of Materials Discovery (DEPM), Unit of Research of Materials and Renewable Energies (URMER), University Abou Bekr Belkaid, Tlemcen, Algeria

© 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,

\*Address all correspondence to<EMAIL_ADDRESS>
provided the original work is properly cited.

*DOI: http://dx.doi.org/10.5772/intechopen.97409*

be the least stable Ti-Al binary compound.

The authors declare no conflict of interest.

**6. Conclusion**

character.

**Conflict of interest**

*Titanium Aluminide Coating: Structural and Elastic Properties by DFT Approach DOI: http://dx.doi.org/10.5772/intechopen.97409*

and 3.0 eV, respectively. From this point of view, Ti3Al compound is considered to be the least stable Ti-Al binary compound.


**Abstract**

Activities such as development of industrialisation, urbanisation is a part of our life in the present scenario. During this phase we face a lot of health issues due to noise pollution. Growing of vehicle traffic is one of the major causes towards noise pollution and it affects significantly on the environment. The impact of such pollution had been assessed in 20 major squares (Commercial, residential and silence area) of the Balasore town during and after lockdown imposition of Covid-19. During lockdown period, the noise level of the town was within the permissible limit set by CPCB while before and after lockdown period it was beyond the permissible limit. The demographics and psychophysiological (annoyance, sleeping problem, tiredness, headache, and depression) responses of the participants were collected using standard questionnaires. It was also observed that there were better health conditions among the public (150 participated in the questionnaire) during the lockdown period, then before and after the lockdown phase. It was revealed that socio-demographic factors have no effects on the annoyance level.

**Keywords:** noise pollution, health issues, Covid-19, equivalent noise level, Balasore


**1. Introduction**

Over the last decade, pharmacy has seen a large shift in the role of both the pharmacist and pharmacy technician. For instance, pharmacists have increasingly focused on providing clinical care, and gradually fallen away from the traditional dispensing role [1]. Pharmacy technicians are personnel "working in a pharmacy who, under the supervision of the licensed pharmacist, assists in pharmacy activities that do not require the professional judgment of a pharmacist [1]." However, as pharmacists have decreased their focus on dispensing, pharmacy technicians have been given the opportunity to fill the traditional dispensing role in the pharmacist's place. These new changes have progressively become the normal pharmacy model, and many studies have shown the added value of this model in both improved quality of patient care and pharmacy efficiency [2–8]. This shift is a huge building block for the future, yet at the same time, it has resulted in the formation of unique and evolving roles for pharmacy technicians. These new roles are still in the development process, and research is beginning to roll out on the safety and efficacy of advanced pharmacy technician positions [9–12]. These changes, in due course, may be considerable innovations, but at the same time, they may pose poignant risks to patient safety. This study helps to define pharmacy technicians' new roles through the use of pharmacy technician job advertisements.

Understanding the way pharmacy technicians are recruited through job advertisements is helpful in defining the evolving role of pharmacy technicians. The recruitment process through job listings on social forums is an important and commonly-used tool by employers to convey job requirements and responsibilities. Additionally, job advertisements a ffect the number, type, and talent of possible hires. If e ffectively used, employers can use job advertisements to increase the quality and quantity of applicants by giving applicants a clear snapshot of future roles and responsibilities as well as the requirements for the job. While advertisements do not represent the formal contractual responsibilities and requirements of a technician, they do represent what the employer needs in a technician. Ultimately, looking at pharmacy technician advertisements can serve as an indicator of both the duties and qualifications desired for pharmacy technicians.

The roles and responsibilities of pharmacy technicians have been evolving from basic pharmacy organization and prescription assembly skills to complex dispensary, verification, immunization, education, and medication synchronization skills in the past decade [13]. Recently, the American Society of Health-System Pharmacists (ASHP) has defined the role of pharmacy technicians in three categories: entry-level, advanced, and specialized [13]. The listed skills needed for entry-level roles include pharmacology for technicians, pharmacy law and regulation, compounding including low- or medium-risk sterile compounding and non-sterile compounding, basic safe medication practices, pharmacy quality assurance, medication order entry and distribution, pharmacy inventory management, pharmacy billing and reimbursement, and medication-use system technology [13]. Interestingly, many of what the ASHP calls "entry-level skills" are what used to traditionally define the role of pharmacy technician [1]. However, as the pharmacy model has evolved, pharmacy technicians are now receiving new roles that are attained through additional education, training, and competency testing. These new advanced roles are supervised by pharmacists and/or approved by each state's Board of Pharmacy [1]. According to the ASHP, pharmacy technicians need to have certain skills to be included in this advanced category [13]. These skills include advanced medication systems including "tech-check-tech" programs, purchasing or fiscal management, management or supervision of other pharmacy technicians, medication history assistance, medication therapy management assistance, quality improvement, immunization assistance, hazardous drug handling, patient assistance programs, pharmacy technician education and training, community outreach, drug utilization evaluation and/or adverse-drug-event monitoring, industry, and informatics [13]. Furthermore, the ASHP says that some technicians receive even more specialized roles which are dependent upon each technician's individual situation [13]. They define these specialized roles as roles that require extra certification as specified by the Pharmacy Technician Certification Board (PTCB) [13]. These advanced and specialized roles contain many unique and innovative changes for pharmacy technicians which could ultimately improve patient care [13].

Despite the fact that these new technician roles may help alleviate a pharmacist's workload and allow for a more streamlined pharmacy, they may, at the same time, present safety and e fficacy issues in patient care. For instance, many of these new roles are still in the research and development process and, therefore, require strict certification, regulation, and supervision by each state's Board of Pharmacy [9–12,14]. These innovative roles require exemptions as can be seen in the research studies done by Frost, Adams. McKeiran, Henriksen, and Bailey [9–12,14]. However, employers may knowingly or unknowingly try to utilize the added e fficiency of these new roles in their pharmacies without receiving proper exemption status. Unfortunately, without the provided exemption, many of the strict protocols and regulations put into place by Boards of Pharmacy as safeguards may be ignored or improperly implemented. Without proper regulation, there is a higher chance of errors and mistakes. As a result, employers may run into legal issues, and, more importantly, patient safety and e fficacy of care will be put at risk. A previous study on pharmacy technician training programs found that of 216 training programs, 29.6% were accredited and 46% had pharmacists as faculty of the program. It was concluded that there is little to no oversight of and consistency in pharmacy technician training [15].

While, this topic should be of great interest to employers, there is a lack of literature studying the hiring requirements and expectations of pharmacy technicians. A review of state regulations

concerning entry-level pharmacy technicians in 2017 found that 86% of states required board registration or licensure. While only 16 states required any training programs for entry-level pharmacy technicians. This study reveals the legal requirements for the employment of pharmacy technicians, but did not study or discuss what employers actually look for in pharmacy technician candidates [16]. Therefore, the overall objective of this study was to look at the pharmacy technician advertisement database from the Pharmacy Week to find patterns and commonalities in the duties and qualifications of pharmacy technicians.

#### **2. Materials and Methods**

This study used a retrospective analysis study design to describe the current pharmacy technician job descriptions. Pharmacy technician job advertisements were obtained from Pharmacy Week for a 14 day period (26 November 2018–9 December 2018). PharmacyWeek.com was an online database of job advertisements for pharmacists, pharmacy technicians, and pharmacy interns started in 1990. Unfortunately, it is no longer maintained and can no longer be accessed. For all pharmacy technician job advertisements, the following items were obtained: (1) job title, (2) location of job (city and state), (3) what field of pharmacy job is in (hospital system, retail, [chain versus independent], long-term care, managed care, etc.), (4) position type (full or part time), (5) job duties, and (6) listed requirements for the position. Requirements within job advertisements were noted as being either required, preferred, not required, or not specified. Duties within job advertisements were noted as being either listed or not listed. Following data collection, related requirements and duties were combined into themes. These themes are detailed in Tables 1 and 2. The decision to code requirements and duties by themes verses individually was made by all researchers after listing were made of all the individual requirements and duties found in the position listing. The final themes agreed upon are depicted in the Tables 1 and 2.

**Table 1.** Job Requirements Themes.

#### **Table 1.** *Cont.*

Data were collected and entered into an Excel document. Data were de-identified prior to Excel entry. No information was recorded in a manner that could reveal the identity. Descriptive statistics were performed for all data in IBM© SPSS v 26.0 (Armonk, NY, USA). This included frequencies and percentages.

#### **Table 2.** Job Duties by Theme.

#### **Table 2.** *Cont.*

Provides PAP assistance

**Table 2.** *Cont.*


**Abstract**

This paper proposes a conceptual implementation model for small and medium enterprises (SMEs) to follow as part of their digital transformation. The conceptual model can be translated into a practical step-by-step guide for SMEs to apply during their digital transformation. The model is based on gradually developing industrial capabilities that can influence production processes performance. We employed a comparative case study approach to capture the lessons learned by SMEs in their journey to develop and implement a production digitalization system for deviation management and performance improvement. The model was validated in the cases of study capturing the actual SMEs' needs. Managerial capabilities of production processes such as monitoring and control demonstrate to influence the performance positively. The proposed model aims for a full digital transformation by following a gradual approach to being resource-efficient and integrating their business needs. This paper is an extension of work originally presented in APMS 2020, IFIP AICT 592.

**Keywords:** Managerial Capabilities, SME, Sustainable Production, Digitalization, Manufacturing Industry


**5. Conclusions**

This article was aimed at 4D printing adaptive metastructures with locally resonated and Bragg-type stop-bands. The FDM 4D printing technology was implemented to program shape-memory elements during the layer-by-layer deposition process in a functionally graded manner. Experiments

were conducted to explore 1D-to-2D self-bending features characterized in terms of 4D printer head speed. Boundary value problems were solved to explain thermomechanical mechanisms behind inducing prestrain during 4D printing and shape recovery after thermal activation. In this respect, a straightforward approach was introduced and implemented into the commercial FE software package of COMSOL Multiphysics, which is much simpler than writing a user-defined material model (UMAT) subroutine or an in-house FE code. The 4D-printed elements were simulated as functionally graded materials whose thermal expansion changed through the thickness direction. The excellent accuracy of the proposed technique was checked via a comparative study with experiments and computational results from the developed in-house FE MATLAB-based solution. Two periodic architected temperature-sensitive metastructures with adaptive dynamical characteristics were conceptually proposed. The COMSOL-based computational tool was then applied to dynamically analyze periodic metastructures with self-bending active elements 4D-printed at di fferent printing speeds. It was found that the metastructures have the capability of controlling elastic wave propagation by forming bandgaps or frequency ranges where the wave cannot propagate. It was observed that the bandgap size and frequency range could be controlled and broadened through local resonances by changing 4D printing speed and thermal excitation. Due to the absence of a similar concept and results in the specialized literature, this article is likely to advance the state-of-the-art tunable metastructures for vibration mitigation and sound attenuation.

**Author Contributions:** Conceptualization, M.B.; methodology, R.N., M.B. and H.J.; software, R.N. and H.J.; validation, R.N., M.B. and H.J.; investigation, R.N., M.B., H.J., A.Z. and M.F.; formal analysis, R.N., M.B., H.J., A.Z. and M.F.; resources, M.B.; writing—original draft preparation, R.N., M.B. and H.J.; writing—review and editing, R.N., M.B., H.J., A.Z. and M.F.; supervision, M.B.; project administration, M.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.


**4. Thermoelectric properties of Mg2X and its alloys**

## **4.1. Mg2X composites**

As it was already mentioned that the new wave of research activity on Mg2X-based thermoelectrics was initiated by work of Zaitsev et al., who demonstrated stable Mg2(Si-Sn) alloys with a maximum *ZT* value of about 1.1 at 800 K [2]. A systematic study of Mg2Si thermoelectric properties was performed by Tani et.al. They found (*ZT*)max for Mg2Si, doped with 2 at% of bismuth of about 0.86 at 820 K with samples, fabricated by SPS [54]. However, such large (*ZT*)max has been not supported by independent researchers [55]. Sb and P-doped Mg2Si was

investigated from 300 up to 900 K with the Sb content of up to 2% [56] and the P content up to 3% [57]. The samples were prepared from high-purity powder components by SPS. The maximum *ZT* = 0.56 was obtained at 860 K for sample with 2% of Sb due to the lowest thermal conductivity.

tionally heat treated for homogenization. Dense sinters can be produced by hot uniaxial pressing of the obtained powders under moderate temperature and pressure conditions.

Several advantages were identified in the proposed technology: relatively short time of

Single crystals of Mg2X compounds can be easily produced by any methods of directed

It is hard to produce homogeneous solid solutions via a liquid phase through co-melting of the components. One of the problems is related to large difference in masses of magnesium, silicon, germanium, and tin atoms. Without stirring, segregation by specific weight occurs. The other problem relates to phase diagrams of solid solutions, which have large difference in liquidus and solidus curves in a wide range of compositions [33]. Therefore, compositional segregation occurs during crystallization as well. In order to homogenize alloys, a long-term annealing is necessary. The necessary homogenization annealing time is determined by diffusion processes, which depend on temperature and crystallite size. Temperature cannot be high due to magnesium evaporation. In order to shorten the annealing time, hot pressing can be utilized. Ingots of alloys are crushed into powder and then powder is pressed in a vacuum. The finer grain size the less time for homogenization is needed [47]. Annealing is not required

Recently, mechanical alloying in the ball mill followed by spark plasma sintering (SPS) has

As mentioned above, the figure of merit Z is function of free charge carriers' concentration. Optimal concentration yielding maximum *ZT* value is equal to about 1019 to 1020 cm−3. Theoretical and experimental investigations of a doping impurity effect in Mg2Si for a wide range of impurity elements (B, Al, N, P, Sb, Bi, Cu, Ag, Au) were made by Tani and Kido [48, 49]. As, P, Sb, Bi, Al, and N were suggested as n-type dopants whereas Ga is suggested as p-type dopant. For In, Ag, Cu, and Au, the doping effect, i.e. a resulting conduction type, depends on the site in lattice where a doping atom will occupy. Actually, Ag-doped samples show p-type of conductivity. In Mg2Sn-rich solid solutions, impurities Na, Li, Ga, Ag and at low concen-

As it was already mentioned that the new wave of research activity on Mg2X-based thermoelectrics was initiated by work of Zaitsev et al., who demonstrated stable Mg2(Si-Sn) alloys with a maximum *ZT* value of about 1.1 at 800 K [2]. A systematic study of Mg2Si thermoelectric properties was performed by Tani et.al. They found (*ZT*)max for Mg2Si, doped with 2 at% of bismuth of about 0.86 at 820 K with samples, fabricated by SPS [54]. However, such large (*ZT*)max has been not supported by independent researchers [55]. Sb and P-doped Mg2Si was

synthesis, possibility of *in-situ* or *ex-situ* doping and grain size control.

272 Thermoelectrics for Power Generation - A Look at Trends in the Technology

become the most popular preparation technique for this solid solution.

for the samples produced from nanosize particles.

tration Al and In act as p-type dopants [50–53].

**4.1. Mg2X composites**

**4. Thermoelectric properties of Mg2X and its alloys**

crystallization.

Samples of Mg2Si, undoped and doped with Bi and Ag, were grown by a vertical Bridgman method [58, 59]. The n-type Bi-doped samples have a maximum *ZT* of 0.65 at 840 K, while Agdoped samples are of p-type (below 650 K) and show a maximum *ZT* of 0.1 at 570 K.

A comprehensive study of a doping mechanism, i.e. location of dopants in Mg2Si was undertaken by Farahi et al. [60]. Samples of Sb- and Bi-doped Mg2Si were prepared via two-stage annealing of powder mixtures of individual components at 823 K for 3.5 days and at 873 K for 5 days, followed by hot pressing. It was shown that part of dopants replaces Si, while the rest forms, Mg3Sb2 and Mg3Bi2, found between the grains of doped Mg2Si particles. As doping of Sb and Bi only partly led to Si substitution, experimentally determined charge carriers' concentration was lower than originally expected.

Using a technique of incremental milling, phase pure Mg2Si was produced within a few hours with negligible oxygen contamination [61]. In this technique, to prevent agglomeration of ductile Mg during ball milling, Mg is added to Si + doped mixture by small portions followed a comparatively short milling period until the stoichiometric amount of Mg is attained. More effective Bi doping is achieved with higher mobility values at lower concentrations of dopant compared to previous work. A peak *ZT* value of about 0.7 is achieved at 775 K using an optimum doping level with only 0.15% of Bi, which is an order of magnitude lower than that mentioned in Ref. [54].

Temperature dependences of the figure of merit *ZT* of Mg2Si samples doped with different dopants are shown in **Figure 8**.

**Figure 8.** Figure of merit *ZT* temperature dependences of Mg2Si. 1—Mg2Si+0.15% Bi [61]; 2—Mg2Si+0.5% Sb [58]; 3— Mg2Si+2% Sb [54]; 4—Mg2Si+1% Bi [59]; 5—Mg2Si+2% Sb [56]; 6—Mg2Si+3% P [57].

#### **4.2. Figure of merit of n-type Mg2X-based solid solutions**

Analysis of transport properties and band structure features has shown that the Mg2Si-Mg2Sn system is the most promising for development of efficient n-type thermoelectrics. **Figure 9** shows the effect of high band degeneracy on *ZT*. Temperature dependences of *ZT* are shown for n-type Mg2Si0.4Sn0.6 (left) and Mg2Si0.6Sn0.4 (right) alloys. *CL* and *CH* subbands of the conduction band are close to each other in the Mg2Si0.4Sn0.6 alloy, as the result it has higher *ZT* at lower temperatures. In Mg2Si0.6Sn0.4,subbands *CL* and *CH*are separated by a narrow gap; therefore, at low temperatures *CH* subband gives no contribution to electronic transport. Therefore, *ZT* of Mg2Si0.6Sn0.4 at low temperatures is smaller in comparison with *ZT* of Mg2Si0.6Sn0.4. However, at higher temperatures, the *CH* subband in this alloy gives increasing contribution to electrical conductivity and thermopower, which gives rise to enhanced *ZT* values. Although both solid solutions have high maximum *ZT* values close to 1.2, the average value (*ZT*)*av* of Mg2Si0.4Sn0.6, in the temperature range of 400–850 K, is higher (about 0.83 and 0.78, respectively). This study revealed the best compositions of n-type solid solutions and allowed reproducible synthesis of thermoelectrics with *ZT*max ≈ 1.2 and higher [2, 5]. Comparison of obtained results with the data for the state-of-the-art thermoelectrics revealed that these materials are among the best thermoelectrics of n-type in the temperature range of 600–870 K.

**Figure 9.** Figure of merit *ZT* temperature dependences of alloys Mg2Si0.6Sn0.4 (right) and Mg2Si0.4Sn0.6 (left). *n*, 1020 cm−3: (right) 1—3.17; 2—3.30; 3—3.83; 4—4.54. *n*, 1020 cm−3: (left) 1—2.31; 2—2.52; 3—2.99; 4—3.10.

Several approaches have been used in order to maximize the figure of merit, including optimization of alloy composition and doping level, various types of nanostructuring. The nanostructuring is currently considered as the most promising and universal approach to enhance the thermoelectric performance. There are a number of technological approaches for producing different kinds of nanostructured materials. Most important among them are nanocrystalline materials, materials with nanoprecipitates of second phase and materials with nanoinclusions of foreign substance. All these approaches were applied with different degree of success to Mg2X compounds and related alloys.

**4.2. Figure of merit of n-type Mg2X-based solid solutions**

274 Thermoelectrics for Power Generation - A Look at Trends in the Technology

thermoelectrics of n-type in the temperature range of 600–870 K.

Analysis of transport properties and band structure features has shown that the Mg2Si-Mg2Sn system is the most promising for development of efficient n-type thermoelectrics. **Figure 9** shows the effect of high band degeneracy on *ZT*. Temperature dependences of *ZT* are shown for n-type Mg2Si0.4Sn0.6 (left) and Mg2Si0.6Sn0.4 (right) alloys. *CL* and *CH* subbands of the conduction band are close to each other in the Mg2Si0.4Sn0.6 alloy, as the result it has higher *ZT* at lower temperatures. In Mg2Si0.6Sn0.4,subbands *CL* and *CH*are separated by a narrow gap; therefore, at low temperatures *CH* subband gives no contribution to electronic transport. Therefore, *ZT* of Mg2Si0.6Sn0.4 at low temperatures is smaller in comparison with *ZT* of Mg2Si0.6Sn0.4. However, at higher temperatures, the *CH* subband in this alloy gives increasing contribution to electrical conductivity and thermopower, which gives rise to enhanced *ZT* values. Although both solid solutions have high maximum *ZT* values close to 1.2, the average value (*ZT*)*av* of Mg2Si0.4Sn0.6, in the temperature range of 400–850 K, is higher (about 0.83 and 0.78, respectively). This study revealed the best compositions of n-type solid solutions and allowed reproducible synthesis of thermoelectrics with *ZT*max ≈ 1.2 and higher [2, 5]. Comparison of obtained results with the data for the state-of-the-art thermoelectrics revealed that these materials are among the best

**Figure 9.** Figure of merit *ZT* temperature dependences of alloys Mg2Si0.6Sn0.4 (right) and Mg2Si0.4Sn0.6 (left). *n*, 1020 cm−3:

Several approaches have been used in order to maximize the figure of merit, including optimization of alloy composition and doping level, various types of nanostructuring. The nanostructuring is currently considered as the most promising and universal approach to enhance the thermoelectric performance. There are a number of technological approaches for producing different kinds of nanostructured materials. Most important among them are nanocrystalline materials, materials with nanoprecipitates of second phase and materials with

(right) 1—3.17; 2—3.30; 3—3.83; 4—4.54. *n*, 1020 cm−3: (left) 1—2.31; 2—2.52; 3—2.99; 4—3.10.

Effects of nanostructuring on Mg2Si were theoretically modeled and systematically analyzed in Ref. [62]. It was shown that nanostructuring limits the energy-dependent phonon mean free path in Mg2Si, which results in significant reduction (50%) in lattice thermal conductivity. However, it was also concluded that nanostructuring in both p-type and n-type Mg2Si increases significantly charge carrier scattering and leads to unfavorable reduction in electrical conductivity. A decrease in charge carriers' mobility of nanostructured Mg2Si strongly affects the power factor, resulting in only minor enhancement in the overall figure of merit. In the case of nanostructured n-type Mg2Si, an optimal doping concentration of 8.1 × 1019 cm−3 was estimated for achieving *ZT* of 0.83 at 850 K, which is less than 10% improvement in comparison with the maximum *ZT* of bulk Mg2Si. On the other hand, in the case of nanostructured p-type Mg2Si, a maximum *ZT* of 0.90 at 850 K was predicted, which is nearly 37% improvement over the maximum *ZT* of bulk Mg2Si. The predicted optimum dopant concentration for p-type Mg2Si was equal to 4.3 × 1020 cm3 . In practice, inherent challenge for p-type Mg2Si is a charge carriers' compensation effect that limits the maximum charge carriers' concentration by value 1018 cm−3.

A higher effect of nanostructuring on the efficiency of n-Mg2Si and n-Mg2Si0.8Sn0.2 alloys was predicted in another theoretical work [63]. It was shown that relatively higher depression of lattice thermal conductivity compared to decrease in electrical conductivity due to grain boundary scattering can lead to 10 and 15% increase of *ZT* at 850 K in nanostructured materials based on Mg2Si and Mg2Si0.8Sn0.2, respectively. A nanostructured alloy is more favorable for increase in the figure of merit than bulk Mg2Si.

The presence of nanoinclusions is considered as an alternative approach to achieve nanoscale effects. Theoretical estimate of additional scattering on nanoinclusions of Mg2Si and Mg2Ge in the n-Mg2Si0.4Sn0.6 matrix predicted a considerable increase in the figure of merit [64]. A small concentration of nanoparticles (about 3.4%) can lead to 60% reduction of thermal conductivity at 300 K and to 40% at 800 K with the optimal particle size of a few nanometers. The best value of *ZT* 1.9 at 800 K is predicted for Mg2Si or Mg2Ge nanoparticles in Mg2Si0.4Sn0.6, which is considerably higher than the best experimental value for these alloys.

Various material synthesis technologies and alloy compositions were used in experiments in order to increase the figure of merit. Combination of induction melting, melt spinning (MS), and spark plasma sintering (SPS) methods were used to produce n-type Mg2Si0.4Sn0.6 alloys doped with Bi [6]. Multiple localized nanostructures within the matrix containing nanoscale precipitates and mesoscale grains were formed, resulting in a remarkable decrease of lattice thermal conductivity, particularly for the samples with nanoscale precipitates having a size of 10–20 nm. Meanwhile, electrical resistivity was reduced and the Seebeck coefficient was increased by Bi-doping, causing improved electrical performance. Figure of merit *ZT* was significantly improved and the maximum value reaches 1.20 at 573 K for the Mg2Si0.4Sn0.6+3% Bi sample, which is higher than that of nondoped samples. In comparison to samples of a similar composition, prepared by a conventional procedure, these samples have very low thermal conductivity, larger thermopower, and lower electrical conductivity.

Another way to increase the *ZT* value is use of quasi-quaternary alloys Mg2Si-Mg2Sn-Mg2Ge. Although theoretical calculation did not predict noticeable influence of Ge on the lattice thermal conductivity of Mg2Si-Mg2Sn [65], it was demonstrated experimentally that *ZT* can be increased up to 1.4 in Bi-doped Mg2Si1−*x*−*y*Sn*x*Ge*y* (*x* = 0.4 and *y* = 0.05) alloys [3, 66]. Alloys were prepared by solid-state synthesis and sintering via hot pressing. Transmission electron microscopy (TEM) confirmed the coexistence of phases with different stoichiometry and yielded nanofeatures of the Mg2Si1−*x*−*y*Sn*x*Ge*y* phase. Thermoelectric properties of these materials were affected by different stoichiometry and the Sn-rich phase is believed to play a crucial role. High figure of merit could be attributed to a relatively high power factor that is related to contribution of the Sn-rich phase as well as low thermal conductivity that originates from nanostructuring.

Homogeneous alloys Mg2Si0.3Sn0.7 were successfully prepared by nonequilibrium synthesis (melt spinning) followed by hot pressing and a plasma-assisted sintering (MS-PAS) technique [7]. Microstructure homogenization promotes charge carrier transport and effectively enhances the power factor. As a result, the MS-PAS sample achieved the highest figure of merit *ZT* of 1.30 at 750 K. However, the Mg2Si0.3Sn0.7 alloy is intrinsically unstable at higher temperatures and tends to decompose into various Si-rich and Sn-rich phases even following the modest annealing at 773 K for 2 h.

The influence of grain size on thermoelectric properties of Mg2Si0.8Sn0.2 doped with Sb was investigated using samples prepared by hot-pressing synthesized powders with grain sizes in the range from 100 to below 70 nm [67]. Contrary to expectation, no significant reduction of thermal conductivity in nanograined samples was found. *ZT* showed very weak dependence on grain's size with maximum values of about 0.8–0.9 at 900 K.

The best *ZT* results for n-type of Mg2Si-based thermoelectrics are summarized in **Figure 10**.

## **4.3. Figure of merit of p-type Mg2X solid solutions**

To realize high performance of n-type Mg2X-based alloys in practical applications, one needs to have a matching p-type material, preferably of the same base material. Therefore, considerable efforts have been made to the development of p-type Mg2X-based alloys. However, progress with this development has been not so impressive as with n-type materials. At present, the maximum *ZT* of p-type Mg2X-based alloys is about 0.5. There are several reasons for this. The high *ZT* of the n-type Mg2(Si-Sn) alloys is connected in part with high valley degeneracy of the conduction band that increases in alloys due to the band inversion effect. The valley degeneracy effect is absent for the valence band, since the top of this band is located at the Γ-point of the Brillouin zone. Furthermore, hole mobility is lower than the electron mobility in all Mg2X compounds; hence, the onset of intrinsic conduction gives a negative impact on thermoelectric performance at lower temperatures in comparison with n-type alloys. The difference between hole and electron mobility is smallest in Mg2Sn, where the electron-tohole mobility ratio is about 1.5. Therefore, one can expect that the most efficient p-type alloy will contain a large fraction of Mg2Sn.

Efficient Thermoelectric Materials Based on Solid Solutions of Mg2X Compounds (X = Si, Ge, Sn) http://dx.doi.org/10.5772/65864 277

Another way to increase the *ZT* value is use of quasi-quaternary alloys Mg2Si-Mg2Sn-Mg2Ge. Although theoretical calculation did not predict noticeable influence of Ge on the lattice thermal conductivity of Mg2Si-Mg2Sn [65], it was demonstrated experimentally that *ZT* can be increased up to 1.4 in Bi-doped Mg2Si1−*x*−*y*Sn*x*Ge*y* (*x* = 0.4 and *y* = 0.05) alloys [3, 66]. Alloys were prepared by solid-state synthesis and sintering via hot pressing. Transmission electron microscopy (TEM) confirmed the coexistence of phases with different stoichiometry and yielded nanofeatures of the Mg2Si1−*x*−*y*Sn*x*Ge*y* phase. Thermoelectric properties of these materials were affected by different stoichiometry and the Sn-rich phase is believed to play a crucial role. High figure of merit could be attributed to a relatively high power factor that is related to contribution of the Sn-rich phase as well as low thermal conductivity that originates

Homogeneous alloys Mg2Si0.3Sn0.7 were successfully prepared by nonequilibrium synthesis (melt spinning) followed by hot pressing and a plasma-assisted sintering (MS-PAS) technique [7]. Microstructure homogenization promotes charge carrier transport and effectively enhances the power factor. As a result, the MS-PAS sample achieved the highest figure of merit *ZT* of 1.30 at 750 K. However, the Mg2Si0.3Sn0.7 alloy is intrinsically unstable at higher temperatures and tends to decompose into various Si-rich and Sn-rich phases even following the modest

The influence of grain size on thermoelectric properties of Mg2Si0.8Sn0.2 doped with Sb was investigated using samples prepared by hot-pressing synthesized powders with grain sizes in the range from 100 to below 70 nm [67]. Contrary to expectation, no significant reduction of thermal conductivity in nanograined samples was found. *ZT* showed very weak dependence

The best *ZT* results for n-type of Mg2Si-based thermoelectrics are summarized in **Figure 10**.

To realize high performance of n-type Mg2X-based alloys in practical applications, one needs to have a matching p-type material, preferably of the same base material. Therefore, considerable efforts have been made to the development of p-type Mg2X-based alloys. However, progress with this development has been not so impressive as with n-type materials. At present, the maximum *ZT* of p-type Mg2X-based alloys is about 0.5. There are several reasons for this. The high *ZT* of the n-type Mg2(Si-Sn) alloys is connected in part with high valley degeneracy of the conduction band that increases in alloys due to the band inversion effect. The valley degeneracy effect is absent for the valence band, since the top of this band is located at the Γ-point of the Brillouin zone. Furthermore, hole mobility is lower than the electron mobility in all Mg2X compounds; hence, the onset of intrinsic conduction gives a negative impact on thermoelectric performance at lower temperatures in comparison with n-type alloys. The difference between hole and electron mobility is smallest in Mg2Sn, where the electron-tohole mobility ratio is about 1.5. Therefore, one can expect that the most efficient p-type alloy

on grain's size with maximum values of about 0.8–0.9 at 900 K.

**4.3. Figure of merit of p-type Mg2X solid solutions**

276 Thermoelectrics for Power Generation - A Look at Trends in the Technology

will contain a large fraction of Mg2Sn.

from nanostructuring.

annealing at 773 K for 2 h.

**Figure 10.** The best figure of merit of the Mg2Si-Mg2Sn alloy. 1—Mg2Si0.4Sn0.6+Sb [2]; 2—Mg2Si0.3Sn0.7+0.6% Sb [5]; 3— Mg2Si0.4Sn0.6+1% Bi [6]; 4—Mg2Si0.53Sn0.4Ge0.05Bi0.02 [3]; 5—Mg2(Si0.3Sn0.7)0.98Sb0.02 [7].

There are several potential p-type dopants for Mg2X compounds. The most effective impurities for Mg2Sn-rich alloys are Ga and Li. Both of these dopants provide hole concentrations higher than 1020 cm−3. Our study shows that these impurities yield one hole per dopant atom up to 2.5% Ga and 1.5% Li. Alloy Mg2Si0.3Sn0.7 doped with these impurities has a maximum *ZT* of up to 0.45 at 650 K [4, 68].

Experimental and theoretical studies of effects related to Ga doping of the Mg2Si compound and the Mg2Si0.6Ge0.4 alloy by measurements of electrical resistivity, thermopower, Hall coefficient, and thermal conductivity, supplemented by electronic band structure calculations, have shown that p-type materials with the maximum *ZT* value of 0.36 at 625 K can be obtained for Mg2Si0.6Ge0.4:Ga (0.8%) [69].

Another p-type dopant is silver. The maximum figure of merit *ZT* of 0.38 was achieved at 675 K for Mg1.98Ag0.02Si0.4Sn0.6 [70]. It was found that the solubility of Ag in Mg2Si0.4Sn0.6 is about 2%. Oversaturated Ag doping in Mg2Si0.4Sn0.6 is unfavorable for the improvement of thermoelectric properties.

Investigation on the effect of Li doping on electrical and thermal transport properties of Mg2Si0.3Sn0.7 alloys indicated that Li is an efficient dopant occupying Mg sites. Theoretical calculations as well as experiments indicate that Li doping preserves high hole mobility. While overall thermal conductivity increases with an increase in the Li content (due to enhanced electrical conductivity) at low to mid-range temperatures, the beneficial effect of Li doping is shifting the onset of bipolar conductivity to higher temperatures and thus extending the regime, where thermal conductivity benefits from Umklapp phonon scattering. As a consequence, thermoelectric performance is significantly improved with the figure of merit *ZT* reaching a value of 0.50 at around 750 K at the Li doping level of 0.07 [71]. **Figure 11** summarizes *ZT* temperature dependences for the best p-type Mg2X-based alloys.

**Figure 11.** The figure of merit for the state-of-the-art p-type Mg2Si-Mg2Sn alloys. 1—Mg2(Si0.3Sn0.7)0.985Ga0.015 [4]; 2— Mg2Si0.6Ge0.4+0.8% Ga [69]; 3—Mg1.98Ge0.4Sn0.6Ag0.02 [70]; 4—Mg1.86Si0.3Sn0.7Li0.14 [71]; 5—Mg1.99Si0.3Sn0.7Li0.01 [68].

Known attempts to use nanostructuring have not yielded positive results for p-doped Mg2Xbased alloys. Another practically important problem with p-type alloys containing a large fraction of Mg2Sb is their intrinsic instability.

#### **5. Conclusion**

The last decade comprehensive study of Mg2X and Mg2X-based alloys has yielded rather impressive results. Mg2X-based n-type alloys are sufficiently stable at a temperature up to about 800 K and have maximum figure of merit close to 1.5. The combination of high-thermoelectric performance with low cost of raw elemental materials places these materials among the best thermoelectrics for temperature range from 300 to 800 K. However, there are still many problems to be solved in order to bring these alloys to the application stage. The most important problem is the failure to develop a matching p-type thermoelectric material. The best *ZT* value for p-type Mg2X-based alloys does not exceed 0.5. Moreover, the p-type alloys are not sufficiently stable. Another problem is the absence of technology for making stable, high quality electrical contacts with the alloys. However, this problem certainly can be solved with adequate efforts and resources.

## **Author details**

reaching a value of 0.50 at around 750 K at the Li doping level of 0.07 [71]. **Figure 11** summarizes

**Figure 11.** The figure of merit for the state-of-the-art p-type Mg2Si-Mg2Sn alloys. 1—Mg2(Si0.3Sn0.7)0.985Ga0.015 [4]; 2—

Known attempts to use nanostructuring have not yielded positive results for p-doped Mg2Xbased alloys. Another practically important problem with p-type alloys containing a large

The last decade comprehensive study of Mg2X and Mg2X-based alloys has yielded rather impressive results. Mg2X-based n-type alloys are sufficiently stable at a temperature up to about 800 K and have maximum figure of merit close to 1.5. The combination of high-thermoelectric performance with low cost of raw elemental materials places these materials among the best thermoelectrics for temperature range from 300 to 800 K. However, there are still many problems to be solved in order to bring these alloys to the application stage. The most important problem is the failure to develop a matching p-type thermoelectric material. The best *ZT* value for p-type Mg2X-based alloys does not exceed 0.5. Moreover, the p-type alloys are not sufficiently stable. Another problem is the absence of technology for making stable, high quality electrical contacts with the alloys. However, this problem certainly can be solved with

Mg2Si0.6Ge0.4+0.8% Ga [69]; 3—Mg1.98Ge0.4Sn0.6Ag0.02 [70]; 4—Mg1.86Si0.3Sn0.7Li0.14 [71]; 5—Mg1.99Si0.3Sn0.7Li0.01 [68].

fraction of Mg2Sb is their intrinsic instability.

**5. Conclusion**

adequate efforts and resources.

*ZT* temperature dependences for the best p-type Mg2X-based alloys.

278 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Vladimir K. Zaitsev1 , Grigoriy N. Isachenko1,2\* and Alexander T. Burkov1,2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Ioffe Institute, Politeknicheskaya ul., Saint Petersburg, Russia

2 ITMO University, Kronverkskiy pr., Saint Petersburg, Russia

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