Electrical properties of MAX phases

7

Electrical properties of MAX phases Y. Medkour, A. Roumili, D. Maouche, and L. Louail, University of Sétif, Algeria

Abstract: MAX phases have shown a series of interesting and sometimes unusual properties; among them electrical properties. In this chapter, based on previously reported studies, we will summarize the electric transport characteristic of these compounds. The electrical resistivity of MAX phases is weak and in general less than that of the corresponding binary transition metal carbides or nitrides. The resistivity increases with temperature and shows a metallic-like behaviour. In order to highlight the electrical conduction mechanism in the MAX phases, Hall Effect, Seebeck Effect and magnetoresistance measurement are presented. Most MAX phases have low Hall constant and Seebeck coefficients, with a quadratic non-saturating magnetoresistant coefficient. These observations lead us to assume that the MAX phases are compensated conductors. Moreover, the carriers’ densities and mobilities were estimated. Band structure calculations are in agreement with the experiment. Superconductivity is observed for various compounds. Key words: ternary transition metal carbides or nitrides, conduction mechanism, Hall Effect, Seebeck Effect, band structure calculations, superconductivity.

7.1 Introduction By the end of the last century, binary transition metal carbides and nitrides revealed various properties, making them potential candidates Published by Woodhead Publishing Limited 2012

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for use in various industrial applications (Pierson, 1996); hightemperature semiconductor devices, cutting tools, coatings on high-speed steel drill bits, passivating and electrically insulating coatings for semiconductor devices. In addition, they showed promising optical, electronic and magnetic properties useful for optical coatings, electrical contacts and diffusion barriers. In 2000, Barsoum (Barsoum, 2000a) presented a review article on new ternary transition metal carbides or nitrides materials, named MAX phases. This nomenclature is based on the chemical composition of these compounds. M refers to an early transition metal, A is an A group element in the Periodic Table, while X is either C or N. Considering the close chemical composition between the binary transition metal carbides or nitrides and their corresponding MAX phases, these compounds show the best properties of both ceramics and metals. They are elastically stiff, good thermal and electrical conductors, light-weight, thermal shock resistant, machinable and oxidation resistant (Barsoum et al. 2006, Barsoum, 2004, Wang et al. 2009, Wang et al. 2010). This chapter summarizes the electrical transport behavior within MAX phases; electrical resistivity, its temperature dependence and conduction mechanism according to the magnetization measurements and thermopower effect. We end this chapter with an overview of the critical low temperature behaviour.

7.2 Resistivity Up to now, the resistivity of all studied MAX phases shows metallic behaviour: the resistivity increases linearly with increasing temperature. This behaviour can be described by a linear fit according to the relation (Barsoum, 2000a, Barsoum et al. 2006): ρ(T)= ρ0(1− β(T − TRT))

[7.1]

Where ρ0 is the resistivity at room temperature, β is the temperature coefficient of resistivity expressed in K−1, T and TRT are respectively the measured and the room temperature expressed in Kelvin. The available room temperature resistivities are listed in Table 7.1 for the M2AX, M3AX2 and M4AX3 phases. The main result from these data shows the good electrical conductivity of all MAX phases, with the exception of Ti4AlN3 (or Ti4AlN2.9) that presents the highest measured resistivity (2.6 μΩm) among the studied MAX phases. The resistivity of Ti-containing

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0.22

0.14

0.28

Zr2SnC

0.07

Ti2SnC

Zr2SnC

0.28

(Ti Hf)2InC

Ti2SnC

0.19

Hf2InC

0.78

(Ti, Nb)2AlC

0.2

0.39

Nb2AlC

Ti2InC

0.74

Cr2AlC

0.3

0.26

V2AlC

0.25

0.36

Ti2Al C0.5N0.5

Ta2AlC

0.25

Ti2GeC

0.36

Ti2AlN

0.36

Ti2AlC

Ti2AlC

ρ0 μΩm

3.2

1.3

2.86

8.5

4.8

4.9

RRR

45.6

−3.9

−28

−27

RH 10−11 m3C−1

3.8

3.4

4.6

5.9

12

9

5.1

m /VS

2

μμn 10−3

3.1

3.6

3.9

5.9

12

8.2

5.1

m /VS

2

μp 10−3

Summary of electrical constants of MAX phases

Compd.

Table 7.1

1.6±0.3

2.7

1.2

2.7

1.1

1.02

∼1

1.39

n 1027 m−3

1.6±0.3

2.7

1.2

2.7

1.8

1.05

∼1

1.2

p 1027 m−3

3.5

17

20

2.6

m4V−2s−2

α (T−2) 10−5

El-Raghy et al. 2000 (Continued)

Barsoum et al. 1997

El-Raghy et al. 2000

Barsoum et al. 1997

Barsoum et al. 2002b

Barsoum et al. 2002b

Barsoum et al. 2002b

Scabarozi et al. 2008b

Hu et al. 2008

Barsoum et al. 2002a

Hettinger et al. 2005

Hettinger et al. 2005

Hettinger et al. 2005

Scabarozi et al. 2008a

Scabarozi et al. 2008a

Hettinger et al. 2005

Scabarozi et al. 2008a

Reference

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0.25

0.45

0.41

0.45

0.36

0.07

0.22

0.27

0.26

0.35

0.4

2.61

2.61

0.75

0.44

0.68

Nb2SnC

Hf2SnC

Hf2SnC

Zr2PbC

Hf2PbC

Ti3SiC2

Ti3(Si0.5 Ge0.5)C2

Ti3GeC2

Ti3AlC2

Ti3Al(C0.5N0.5)2

Ti4AlN2.9

Ti4AlN3

Nb4AlC3

Nb4AlC3

TiC

ρ0 μΩm

1.1

1.5

1.95

4.7

3.1

7.3

RRR

90±5

90

17.4

−1.2

18

8

30

RH 10−11 m3C−1

0.55

2.5

6.3

0.34

0.55

2.5

6.3

8

∼5

∼5 9

6

m /VS

2

μp 10−3

5

m /VS

2

μμn 10−3

0.8

2.5

1.41

1.5

2

2.5

n 1027 m−3

Summary of electrical constants of MAX phases (Contd)

Nb2SnC

Compd.

Table 7.1

7

3.51

3.5

1.4

1.5

2

2.5

p 1027 m−3

Pierson, 1996

Hu et al. 2009

Hu et al. 2008

Finkel et al. 2003

∼0.03

Scabarozi et al. 2008a

Scabarozi et al. 2008a

Finkel et al. 2004

Finkel et al. 2004

Finkel et al. 2004

El-Raghy et al. 2000

El-Raghy et al. 2000

El-Raghy et al. 2000

Barsoum et al. 1997

El-Raghy et al. 2000

Barsoum et al. 1997

Reference

Scabarozi et al. 2008a

−2

0.03

0.65

3.7

−2

mV s

4

α (T−2) 10−5

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0.2–0.25

0.43

0.37

0.6

0.25

0.35

TiN

ZrC

HfC

VC

TaC

NbC

Pierson, 1996

Pierson, 1996

Pierson, 1996

Pierson, 1996

Pierson, 1996

Pierson, 1996

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M2AX is about two or three times lower than the corresponding binary TiC resistivity. The lowest measured resistivity for M2AX is 0.07 μΩm for the unstable Hf2PbC while the highest is 0.74 μΩm for Cr2AlC. Also, we note that the resistivity of Hf2SnC is higher than that of the binary HfC. As an illustration, we have presented in Figure 7.1 the resistivity versus temperature for various M2AX and M3AX2 samples (Scabarozi et al., 2008a). The linear relationship is well established, the resistivity of the solid solution MAX phases is higher than the corresponding one of the end members. Moreover, the effect of substitution in M sites is

Figure 7.1

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Variation of resistivity with temperature for M2AXphases; Ti2AlNa, Ti2AlC, Ti2AlNb, Ti2AlC0.5N0.5 and M3AX2 phases: Ti3AlC2, Ti3AlCN. Reprinted from Scabarozi T, Ganguly A, Hettinger J D, Lofland S E, Amini S, Finkel P (2008), ‘Electronic and thermal properties of Ti3Al(C0.5N0.5)2, Ti2Al(C0.5N0.5) and Ti2AlN’, J Appl Phys, 104, 73713–73719. With permission from the American Institute of Physics (AIP)

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more severe than in X sites on the resistivity (Scabarozi et al. 2008a, Barsoum et al. 2002a, Barsoum et al. 2002b). To illustrate the effect of synthesis procedures and the sample shape, we give the example of Ti2GeC in Figure 7.2; bulk sample and two films A and B synthesized by different methods (Scabarozi et al. 2008b). It was found that sample a has higher crystalline quality than b, that leads to a low resistivity of the sample a. The resistivity increases in the following rank Ti2GeCA, Ti2GeCB, bulk Ti2GeC. The temperature coefficient of the resistivity is an essential factor; it provides information about the speed of resistivity dependence on temperature. The curves of Ti2AlN, Ti2AlC and Ti2Al(C0.5N0.5) are parallel. However, Ti2AlNb shows less dependence on temperature with regards to neighbouring phases. For the Ti3AlC2, it appears that the solid solution Ti3AlCN is more temperature dependent (Scabarozi et al. 2008a). In the series of M2SnC with M = Ti, Zr, Nb and Hf (El-Raghy Figure 7.2

Variation of resistivity with temperature for different Ti2GeC samples. Reprinted from Scabarozi T H, Eklund P, Emmerlich J, Hogberg H, Meehan T, Finkel P, Barsoum M W, Hettinger J D, Hultman L, Lofland S E (2008), ‘Weak electronic anisotropy in the layered nanolaminate Ti2GeC’, Solid State Commun, 146, 498–501. With permission from Elsevier

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et al. 2000), the resistivity of Nb2SnC was the lowest dependent on temperature with β = 2.1 × 10−3 K−1 while Zr2SnC has the highest value with β = 3.5 × 10−3 K−1. The physical properties of ceramics are very sensitive to synthesizing process and crystal quality. It is known that at very low temperatures lattice defects and impurity atoms affect the resistivity, rather than thermal lattice vibrations. This type of resistivity is called the residual resistivity. It is important to note that it is relatively temperature independent (Mitchell, 2004). The high value of the residual resistivity reflects the high degree of defects or impurities in crystal. However, for the residual resistivity ratio (RRR = ρ(300)/ρ(5)), high value of the RRR is accompanied by low degree of defects or impurities (Scabarozi et al. 2008a). From Figures 7.1 and 7.2, one can observe that the resistivity is temperature independent in the range of temperature from ≈10 to 40 K. The residual resistivity, which provides a measure or an estimation of the degree of defects or impurities in the crystal could be obtained. It is very easy to see that the residual resistivity increases in the sequence Ti2AlNa, Ti2AlC, Ti2AlNb and Ti2AlC0.5N0.5. For Ti2AlN, sample A was prepared to have a high crystal quality, which is confirmed by the lower residual resistivity (Scabarozi et al. 2008a). Due to the absence of periodicity on X sites for the solid solution Ti2AlC0.5N0.5, more electron scattering will appear and this increases the resistivity (Barsoum et al. 2002a, 2002b, Finkel et al. 2004). The residual resistivity of the solid solution Ti3AlCN shifted to a higher level compared to the ordinary Ti3AlC2 phase. Figure 7.2 shows the effect of both synthesizing process and the sample size. It can be observed that the resistivity of the bulk sample is greater than that of thin films. However, sample A characterized by higher crystalline quality (Scabarozi et al. 2008b) is less resistant than sample B. These results can be extended for the residual resistivity. The observed disagreement between the reported results for the same phases, as shown in Table 7.1, can be explained on the basis of the residual resistivity values, and the synthesis methods. The latter can be examined by the Nb4AlC3 samples (Hu et al. 2008, Hu et al. 2009). The measured resistivity of a sample prepared using an in situ reaction hot pressing is 0.75 μΩm compared to 0.44 μΩm for the same phase obtained by spark plasma sintering. On the other hand, residual resistivity which is an additional term to ρ0, significantly affects the measured resistivity (Mitchell, 2004, Barsoum et al. 1997, El-Raghy et al. 2000). Moreover, these discrepancies can be expected from the X-ray diffraction patterns. In order to understand the deviations in the measured resistivity, it is worth performing a microscopic analysis that yields more fundamental

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parameters, such as the type of carriers, their mobilities and their concentrations (Barsoum, 2003).

7.3 Conduction mechanisms Resistivity (ρ) is the reciprocal of conductivity (σ). The latter can be defined as the ability of materials to transport the electrical charge. Besides, it is proportional to the density of carriers and their mobility (Ashcroft et al. 1967). In order to connect the macroscopic measurement (resistivity) and the microscopic characteristics, more decisive measurements need to be carried out, such as the Hall Effect, the Seebeck Effect and magnetoresistance (MR) measurements. The Hall Effect gives an important and accurate way to determine the dominant carrier. The sign of the Hall constant, RH, indicates whether electrons or holes predominate in the conduction process. RH is negative (positive) when electrons (holes) are the predominant charge carriers. The Seebeck Effect measures the thermoelectric power (μV/K) when one of the sides is brought to a higher temperature than the other. When a conductor is exposed to a magnetic field that is perpendicular to an electric field and in addition to the Hall Effect, the relative change in the resistivity (MR) is proportional to the square value of the magnetic field strength. For more details see Hummel, 2000. In Table 7.1 there is a summary of the available Hall constants for MAX phases. With the exception of Ti4AlN3 or the close phase Ti4AlN2.9, all studied MAX phases have low Hall constant values (Barsoum, 2006). Moreover, the temperature effect shows that Hall constant is more or less temperature dependent, as can be seen in Figure 7.3. Going from 0 up to 300 K, the Hall constant fluctuates around a medium value and appears to be temperature independent (Scabarozi et al. 2008a). At low temperatures, Ti3SiC2 shows a strong temperature dependence, and exhibits weak dependence above 100 K (Finkel et al. 2001). For Ti4AlN3, the Hall constant is positive, so the electrical conduction is dominated by hole carriers (Barsoum et al. 2000b, Finkel et al. 2003, 2004, Scabarozi et al. 2008a). Nevertheless, the other reported values are weak, from which it can be expected that electrical conduction in these compounds is provided by both electrons and holes (Finkel et al. 2001, Hettinger et al. 2005, Scabarozi et al. 2008a). In general, the Seebeck coefficient of MAX phases is weak (Barsoum, 2006). For the example in Figure 7.4, and below 40 K, all coefficients are positive, except for Ti2AlC. However, as the temperature increases, the Seebeck voltage increases in a different Published by Woodhead Publishing Limited 2012

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Figure 7.3

Temperature dependence of the Hall coefficient for M2AXphases; Ti2AlNa, Ti2AlC, Ti2AlNb, Ti2AlC0.5N0.5 and M3AX2 phases: Ti3AlC2, Ti3AlCN. Reprinted from: Scabarozi T, Ganguly A, Hettinger J D, Lofland S E, Amini S, Finkel P (2008), ‘Electronic and thermal properties of Ti3Al(C0.5N0.5)2, Ti2Al(C0.5N0.5) and Ti2AlN’, J Appl Phys, 104, 73713–73719. With permission from the American Institute of Physics (AIP)

manner, Ti3AlCN solid solution gets the highest dependence, while Ti2AlC has the lowest one (Scabarozi et al. 2008a). Another example is for Ti3SiC2, Ti3GeC2 and Ti3Si0.5Al0.5C2 where the Seebeck coefficient fluctuates around ±2 μV/K and is less temperature dependent (Finkel et al. 2001, 2004). The magnetoresistance coefficients (α) of some MAX phases are listed in Table 7.1. They range from between 20 × 10−5 m4V−2 s−2 for Ti2AlC (Scabarozi et al. 2008a) and 3 × 10−7 m4V−2 s−2 for Ti4AlN3 (Scabarozi et al. 2008a, Finkel et al. 2003). The temperature effect on the magnetoresistance coefficient is shown in Figure 7.5. For various Ti2GeC phases, the magnetoresistance coefficients are positive. Apart from Ti2GeCA, they are quadratic and non-saturating. The magnetoresistance coefficients of both thin films A (α = 2.5 × 10−2) and B (α = 4 × 10−3 m4V−2 s−2), are higher

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Electrical properties of MAX phases

Figure 7.4

Temperature dependence of the Seebeck coefficient for M2AXphases; Ti2AlNa, Ti2AlC, Ti2AlNb, Ti2AlC0.5N0.5 and M3AX2 phases: Ti3AlC2, Ti3AlCN. Reprinted from Scabarozi T, Ganguly A, Hettinger J D, Lofland S E, Amini S, Finkel P (2008a), ‘Electronic and thermal properties of Ti3Al(C0.5N0.5)2, Ti2Al(C0.5N0.5) and Ti2AlN’, J Appl Phys, 104, 73713–73719. With permission from the American Institute of Physics (AIP)

than that of the bulk (α = 7 × 10−4 m4V−2 s−2) (Scabarozi et al. 2008b) and converged rapidly to 5 × 10−5 at room temperature. Among other data Scabarozi et al. observed that α decreases rapidly for Ti2AlC and Ti2AlN, while it is less dependent on temperature for the solid solution of Ti2AlC0.5N0.5 and Ti3AlCN, and it fluctuates around 3.7 × 10−5 m4V−2 s−2 for Ti3AlC2 (Scabarozi et al. 2008a). To make these results relevant and more significant, it is important to discuss them on the basis of mathematical relations relating these quantities to their origins. In general for MAX phases, the electric conduction is assured by electrons and holes and it is well described by the relation (McClure, 1958): Published by Woodhead Publishing Limited 2012

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Figure 7.5

Temperature dependence of the magnetoresistance coefficient for different Ti2GeC samples. Reprinted from Scabarozi T H, Eklund P, Emmerlich J, Hogberg H, Meehan T, Finkel P, Barsoum M W, Hettinger J D, Hultman L, Lofland S E (2008), ‘Weak electronic anisotropy in the layered nanolaminate Ti2GeC’, Solid State Commun, 146, 498–501. With permission from Elsevier

[7.2] Where e is the electronic charge, n and p are the electrons and hole densities, μn and μp are electron and hole mobilities. The Hall constant at low field limit and for the two band model is defined by (McClure, 1958): [7.3] The magnetoresistance behaviour is described by the following expression (McClure, 1958): [7.4]

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In which B is the magnetic field strength and α is the magnetoresistance coefficient. For two type of carriers, the two band model is required and α is given by (McClure, 1958): [7.5] In the simplest case, where the conduction is governed by either electrons or holes, these relations are simplified to: [7.6]

[7.7]

[7.8] According to the relatively low values reported in Table 7.1 for the Hall constant, it is noticed that the electrical conduction is governed by two type of carriers (electrons and holes) for all studied MAX phases (Barsoum, 2006), with the exception of Ti4AlN3. The single band model was applied for Ti4AlN3 (Finkel et al. 2003). Equations 7.6, 7.7 and 7.8 were applied to calculate the density of carriers, p (holes), and their mobility, μp. The results show that this compound is rich in carriers but their mobility is very low, which explains the higher measured resistivity. For the compounds with low value of Hall constant, a two band model should be used in order to calculate the four independent variables n, p, μn and μp, and the result is more complex than the single band model. We have three relationships, 2, 3 and 4, with four unknown variables. To proceed, we must add one more condition, either on n and p or μn and μp. Considering the weak dependence of RH on temperature and magnetic field (B), as well as the quadratic non-saturation MR behaviour, these observations lead us to assume that most MAX phases are compensated conductors; i.e. n ≈ p (Finkel et al. 2004, Scabarozi et al. 2008a). The assumption made on the mobilities consists of the restriction of μn and μp values (Barsoum et al. 2000b; Finkel et al. 2001; Scabarozi et al. 2008a). The results obtained from these assumptions are listed in Table 7.1. We observe all mobilities are close, as well as the carriers’ densities. Note that these values are very important in order to understand the macroscopic results, nevertheless, strong deviations due to the presence of impurity and vacancy are evident. Published by Woodhead Publishing Limited 2012

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The contribution of first principle methods to the study of the MAX phases cannot be ignored (Hug, 2006, Wang et al. 2009). All band structure calculations on MAX phases show that these compounds are good electrical conductors, with no band gap. The conduction is mostly governed by the Md electrons (Eklund et al. 2010). The predicted high electrical anisotropy for most MAX phases does not line up with experience. The available measured electrical anisotropy does not exceed 2.5 (Scabarozi et al. 2008b, Haddad et al. 2008 and Magnuson et al. 2008).

7.4 Superconductivity The resistance can be small but it is always finite for normal conductors. For some materials, the resistivity drops to zero under very low temperature. In this case, the conductor can carry very high current densities with zero resistive losses and zero heating. The temperature below which superconductivity occurs is called the transition or the critical temperature (TC) (Solymar et al. 2004). The earlier studies on the superconductivity of MAX phases was by Toth, who studied Mo2GaC and shows that the superconducting appears below 4.1 K (Toth, 1967). Available works on this behaviour are few: Bortolozo et al. have studied the low temperature resistivity of Nb2SnC, Ti2InC, Nb2InC and Ti2InN. All of them are superconductors with a critical temperature respectively at: 7.8, 3.1, 7.5 and 7.3 K (Bortolozo et al. 2006, 2007, 2009, 2010). The critical temperature of the superconductor is strongly affected by the synthesis method (Bortolozo et al. 2006). The available results of the magnetization versus magnetic field show that these compounds are of type II superconductivity. These primary results emphasize a new class of interstitial superconductors.

7.5 Conclusions MAX phases are good electrical conductors, with metallic like resistivity. The lowest resistivity measured so far is 0.19 μΩm for Hf2InC at and the highest is 2.6 μΩm for Ti4AlN3. The good conductivity of MAX phases is related to richness on carriers and their relatively high mobilities, and most of them are considered as compensated conductors. The weakest conductivity of Ti4AlN3 was explained by the low mobility of its hole

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carriers. Weak anisotropy was measured for the conductivity, and is mainly governed by the Md electrons. In general the magnetoresistance and Seebeck coefficient are weak and temperature independent. In addition to their unusual properties, the MAX phases present a new class of superconducting materials, with highest measured TC = 7.8 K for Nb2SnC.

Acknowledgement We gratefully acknowledge Elsevier and American Institute of Physics (AIP) for permission to reproduce figures from their publications.

References Ashcroft, N.W., Mermin, N.D. (1967), Solid State Physics, Saunders College Publishing, Philadelphia. Barsoum, M.W., Yaroschuk, G. (1997), ‘Fabrication and characterization of M2SnC (M= Ti, Zr, Hf, and Nb)’, Scrip. Mater., 37, 1583–91. Barsoum, M.W. (2000a), The MAX phases: New class of solids; ‘Thermodynamically stable nanolaminates’, Prog Solid St Chem, 28, 201–81. Barsoum, M.W., Yoo, H.I., Polushina, I.K., Rud, V.Y., El-Raghy, T. (2000b), ‘Electrical conductivity, thermopower, and Hall effect of Ti3AlC2, Ti4AlN3, and Ti3SiC2’, Phys Rev B, 62, 10194–8. Barsoum, M.W., Salam, I., El-Raghy, T., Golczewski, J., Porter, W.D., Wang, H., Seifert, H.J., Aldinger, F. (2002a), ‘Thermal and electrical properties of Nb2AlC, (Ti, Nb)2AlC and Ti2AlC’, Metall. Mater. Trans. A, 33A, 2775–9. Barsoum, M.W., Golczewski, J., Seifert, H.J., Aldinger, F. (2002b), ‘Fabrication and electrical and thermal properties of Ti2InC, Hf2InC and (Ti,Hf)2InC’, J. Alloys Compd., 340, 173–9. Barsoum, M.W. (2003), ‘Fundamentals of ceramics’, Institute of Physics Publishing, Bristol and Philadephia. Barsoum, M.W., Radovic, M. (2004), ‘Mechanical properties of the MAX phases’, in Encyclopedia of Materials Science and Technology, 1–16, Edited by Cahn K R W, Buschow K H J, Flemings M C, Kramer E J, Mahajan S, Veyssiere P, Elsevier, Amsterdam. Barsoum, M.W. (2006), ‘Physical properties of the MAX phases’, Encyclopedia of Materials: Science and Technology, 1–11, Edited by Buschow K H J, Cahn R W, Flemings M C, Kramer E J, Mahajan S, Veyssiere P, Elsevier, Amsterdam. Bortolozo, A.D., Sant’Anna, O.H., da Luz, M.S., dos Santos, C.A.M., Pereira, A.S., Trentin, K.S., Machado, A.J.S. (2006), ‘Superconductivity in the Nb2SnC compound’, Solid State Commun, 139, 57–9.

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