**High Resolution Infrared Spectroscopy of Phonons in the II-VI Alloys — The Temperature Dependencies Study**

E.M. Sheregii

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/59050

#### **1. Introduction**

The cubic II-VI systems HgTe, CdTe and ZnTe are extremely interesting technologically materials with many applications such as infrared as well as quantum electronics devices [21, 29, 5, 44; 26]. The phonon frequencies of these alloys belong to the far-infrared region and investigation of their phonon spectra was one of more important problem in the infrared spectroscopy during 70-th years. The temperature dependence of the phonon HgTe-mode frequencies in binary HgTe, ternary HgCdTe (MCT) and HgZnTe (MZT) materials has been the subject of an intense debate in the last three decades [16, 14, 2,1, 29, 4; Kozyrev et al., 1996; 31, 12, 35, 28], due to contradictory results regarding in particular the abnormal temperature shift of the HgTe-like TO-phonon frequency. The latter is opposite to the normal phonon frequency temperature shift of many alkali compounds as well as most of semiconductors. In fact, the HgTe-like TO-phonon frequency increases when temperature increases while the normal temperature shift associated with a crystal lattice expansion, has to be opposite: the frequency decreases when temperature is raised.

The different behaviour has been qualitatively explained by an electron-phonon (*e-p*) interac‐ tion contribution in work of [29] as the *e-p*-interaction would produce positive frequency shifts as the temperature is raised whose magnitude would exceed the negative shifts due to anharmonicity. However, the claiming that the *e-p*-coupling in the temperature shift of the optical phonon modes has a significant role should be better and quantitatively verified.

The *e-p* interaction is the main mechanism of charge carriers scattering in semiconductor crystals and low-dimensional structures together with impurities and defects. Particularly, the scattering on long wave longitudinal optical (LO(Γ)) phonons have an universal character because the latter generates a macroscopic polarized pole, and electrons experience very

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effective interaction. Several resonance effects also occur such as the pinning of magnetooptical inter-band transitions observed in InSb by Johnson and Larsen (Johnson & Larsen, 1966). They affect the energy spectrum of electrons via the interaction with LO(Γ)-phonons. Effects produced by the direct polarized e-p-interaction, i.e., phonons affect the electron energy spectrum, are described in few review articles and books [22, 13]. In addition, the role of effects due to a direct non-linear polarized e-p-interaction has been shown in [32, 33].

On the other hand, reverse effects, i.e., how light electrons affect the phonon spectrum are much less known. Recently, we have shown [35] that the singularity in an electron energy spectrum induces a discontinuity in the phonon frequency temperature dependence of the Hg1−x CdxTe alloys. That means the appearance of an unexpected effect of strong resonance influence on oscillations of heavy atoms by the electron subsystem. In our short communica‐ tion [36] we called this effect as returnable e-p interaction. It was shown that even though the returnable e-p-coupling has a non-polarized character, yet a deformation mechanism takes place [35, 36, 19]. It is necessary to note that singularity in the electron spectrum that induced the resonance returnable *e-p* interaction, is point of total zero of energy gap (Eg≡Γ6−Γ8=0) well known in the Hg1−x CdxTe alloys (Dornhaus & Nimtz, 1985) and called later as a Dirac point.

It is then important to test the occurrence of this or similar effects in other semiconductor compounds. Moreover, it seems that the abnormal temperature dependence of the HgTe-like phonon modes can be solved in this framework, because the presence of a returnable e-p interaction could explain the positive temperature shift of the optical phonon frequencies. On the other hand, the positive temperature shift of the phonon frequency is characteristic for the HgTe-like modes in different Hg-based alloys such as the abovementioned HgCdTe, the HgCdSe [40, 39] and the HgZnTe as shown in the sequel. Data suggest that a spin-orbit relativistic contribution, larger for heavy atoms, play an important role in this phenomenon because of its effect on the chemical bond [42,17, 30].

The aim of this contribution is to generalize experimental data on the temperature dependence of the TO-phonon modes in the Hg1−x CdxTe and Hg1−x ZnxTe alloys of different compositions and analyze the influence of the resonance returnable e-p-interaction in case when the temperatures are close to singular Dirac point (Eg≡ Γ6− Γ8=0) and far from this point for alloys where the Dirac point exists. Such analyses should be performed on a background of obligatory anharmonic contribution caused by the temperature extension of the crystal lattice. That analyses should be distributed on the alloy compositions where the Dirac point exists not, also.

The rich experimental reflectivity data in the far IR region of MCT and MZT alloys that were collected during 2002-2006 years for different compositions and in a wide temperature range using a synchrotron radiation source [34, 27, Cebulski et al., 2008; 35, 36, 28] allow unique opportunity for such investigation.

#### **2. Experiment**

In order to investigate the temperature behaviour of the phonon modes for HgZnTe and HgCdTe alloys, several optical reflectivity measurements were performed in the far-IR region at the DAΦNE-light laboratory at Laboratori Nazionale di Frascati (Italy) using a synchrotron radiation source (details on the experimental set-up are available in work(Cestelli Guidi et al., 2005)). A BRUKER Equinox 55 FT-IR interferometer modified to collect spectra in vacuum, was used. As IR sources both the synchrotron radiation from the DAΦNE storage ring and a mercury lamp were used. Measurements were performed from 20 to 300 K and in the wave‐ number range 50-600 cm−1. In order to provide the spectral resolution of 1 cm−1 (2 cm−1 in some cases), we typically collected 200 scans within 600 s of acquisition time with a bolometer cooled to 4.2 K. The reflectivity was measured using as a reference a gold film evaporated onto the surface of the investigated samples. This method enabled us to measure the reflectivity coefficient R(ω, T) with an accuracy of 0.2%. The

effective interaction. Several resonance effects also occur such as the pinning of magnetooptical inter-band transitions observed in InSb by Johnson and Larsen (Johnson & Larsen, 1966). They affect the energy spectrum of electrons via the interaction with LO(Γ)-phonons. Effects produced by the direct polarized e-p-interaction, i.e., phonons affect the electron energy spectrum, are described in few review articles and books [22, 13]. In addition, the role of effects

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

On the other hand, reverse effects, i.e., how light electrons affect the phonon spectrum are much less known. Recently, we have shown [35] that the singularity in an electron energy spectrum induces a discontinuity in the phonon frequency temperature dependence of the Hg1−x CdxTe alloys. That means the appearance of an unexpected effect of strong resonance influence on oscillations of heavy atoms by the electron subsystem. In our short communica‐ tion [36] we called this effect as returnable e-p interaction. It was shown that even though the returnable e-p-coupling has a non-polarized character, yet a deformation mechanism takes place [35, 36, 19]. It is necessary to note that singularity in the electron spectrum that induced the resonance returnable *e-p* interaction, is point of total zero of energy gap (Eg≡Γ6−Γ8=0) well known in the Hg1−x CdxTe alloys (Dornhaus & Nimtz, 1985) and called later as a Dirac point. It is then important to test the occurrence of this or similar effects in other semiconductor compounds. Moreover, it seems that the abnormal temperature dependence of the HgTe-like phonon modes can be solved in this framework, because the presence of a returnable e-p interaction could explain the positive temperature shift of the optical phonon frequencies. On the other hand, the positive temperature shift of the phonon frequency is characteristic for the HgTe-like modes in different Hg-based alloys such as the abovementioned HgCdTe, the HgCdSe [40, 39] and the HgZnTe as shown in the sequel. Data suggest that a spin-orbit relativistic contribution, larger for heavy atoms, play an important role in this phenomenon

The aim of this contribution is to generalize experimental data on the temperature dependence of the TO-phonon modes in the Hg1−x CdxTe and Hg1−x ZnxTe alloys of different compositions and analyze the influence of the resonance returnable e-p-interaction in case when the temperatures are close to singular Dirac point (Eg≡ Γ6− Γ8=0) and far from this point for alloys where the Dirac point exists. Such analyses should be performed on a background of obligatory anharmonic contribution caused by the temperature extension of the crystal lattice. That analyses should be distributed on the alloy compositions where the Dirac point exists not, also.

The rich experimental reflectivity data in the far IR region of MCT and MZT alloys that were collected during 2002-2006 years for different compositions and in a wide temperature range using a synchrotron radiation source [34, 27, Cebulski et al., 2008; 35, 36, 28] allow unique

In order to investigate the temperature behaviour of the phonon modes for HgZnTe and HgCdTe alloys, several optical reflectivity measurements were performed in the far-IR region

due to a direct non-linear polarized e-p-interaction has been shown in [32, 33].

because of its effect on the chemical bond [42,17, 30].

opportunity for such investigation.

**2. Experiment**

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64

Hg1−x Cdx Te crystals were grown at the Institute of Physics of the Polish Academy of Sciences in Warsaw (Poland) while the Hg1−x Znx Te ones at the CNRS-Groupe dEtude de la Matire Condense (Meudon, France). The reflectivity curves R(ω, T) for Hg0.90Zn0.10Te in the frequency range from 80 cm−1 to 220 cm-1 and in the temperature range 30-300 K are shown in Fig. 1.

Data show that the main phonon band consists of two subbands: a HgTe-like band in the range 118-135 cm−1 and a ZnTe-like band in the range of 160-180 cm−1. Both of them are characterized by a fine structure. A non-monotonic temperature dependence of the reflectivity maxima can be also recognized. Similar R(ω, T) curves are showed in Fig.2 for the Hg0.763Zn0.237Te. The maxima on reflectivity curves in Fig. 2 are shifted with increase of temperature towards lower phonon frequencies monotonically.

To recognize the real frequency positions of a phonon mode, it is however necessary to calculate for each obtained experimental curve R(ω, T) the imaginary part of the dielectric function Im[(ω, T)] as function of frequency and temperature. That ones were calculated from the reflectivity spectra shown in Fig. 1 and 2 by means of the Kramers-Kronig (KK) procedure. This procedure is described in details in the work of [6]; was applied to experimental results presented in several papers, for example [35, 28, 25]. An estimated uncertainty of 1.5% takes place at calculation the Im[(ω, T)] curves for all experimental data. The Im[(ω, T)] curves at different temperatures are shown in Fig. 3 a,b for the Hg0.90 Zn0.10 Te sample as well as in Fig. 4 a,b for the Hg0.763 Zn0.237 Te sample. In Fig. 3 the Im[(ω, T)]-curves are presented separately for HgTe-band (Fig. 3a) and for ZnTe-band (Fig.3b).

It is necessary to underline here that the maximum of the HgTe-like sub-band (Fig. 3a) shifts towards higher frequencies when the temperature increases from 30 K to 80 K while at temperature higher than 85 K the maximum shifts to lower frequencies. A non-monotonic temperature dependence of the ZnTe-like sub-band (Fig. 3b) with maximum frequency position near 85 K is also observed.

The frequency positions of HgTe-like and ZnTe-like sub-band maxima determined from the Im[(ω, T)] curves at different temperatures in the range 30-300 K are shown for the sample Hg0.90 Zn0.10 Te in Fig. 5a and 5b, respectively.

**Figure 1.** Reflectivity *R*(*ω, T)* for Hg0*.*90 Zn0*.*10 Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the tem‐ perature interval 30 K-300 K

**Figure 2.** Reflectivity *R*(*ω, T)* for Hg0*.237* Zn0*.763* Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the temperature interval 40 K-300 K

The KK-transformation was also performed for the R(ω, T) curves shown in Fig.2 (the Hg0.763 Zn0.237 Te sample). The Im[(ω, T)] curves at different temperatures for this sample are shown in Fig. 4, while the positions of the Im[(ω, T)]-maxima are shown in Fig.6 a,b for the HgTe-like mode and the ZnTe-like mode, respectively.

Analogous investigations of the temperature dependence of the phonon frequencies for different modes were performed for another semiconductor alloy contained the mercury as one of component, namely: HgCdTe. The results were published earlier: [35, Sheregii et al. (2010), 28]. The measured curves of R(ω,T) for Hg0.885 Cd0.115 Te in the frequency region from 80 cm-1 to 170 cm-1 and the temperature interval 40 K – 300 K are shown in Fig. 7. From Fig. 7 it is clearly seen, that the main phonon band consists of two subbands: a HgTe-like band in the range of 118-13 cm-1 and a CdTe-like band in the range of 140-160 cm-1 both characterized by a fine structure well known for the alloy phonon spectra [43, Kozyrev and Vodopynov 1996, 25]. A non-monotonic dependencies of the reflectivity maxima are seen too. The Im[ε(ω,Τ)] curves calculated from the reflectivity spectra are showed in Fig. 8 a,b. We have also to underline here that maximum of the HgTe-like sub-band is shifted towards higher frequencies when the temperature increases from 170 K to 240 K while for temperature higher than 240 K the maximum is shifted to lower frequencies. The similar temperature behaviour demonstrates the CdTe-like sub-band maximum.

The Verleur-Barker model [43] with five structural cells together with the statistical approach developed recently [26] is applied to the Hg1−x Znx Te solid solutions. According to this model each of the two sub-bands: HgTe-like and ZnTe-like in the case of the Hg1−x Znx Te alloys, consists of not more the four modes due to the oscillations of the Hg-Te or Zn-Te dipole pairs in each of the five tetrahedra Tn, where n is the number of Zn-atoms in the cell. Therefore, the maximum of each sub-bands can be associated to one of these four modes depending on the composition of alloy. In the case of the Hg0.90 Zn0.10 Te alloy we combine the T0-mode with the HgTe-like sub-band and the T1-mode with the ZnTe-like mode, similarly to the Hg0.85 Cd0.15 Te alloy. Regarding the Hg0.763 Zn0.237 Te alloy the maximum of the HgTe-like sub-band is attributed to the T1-mode, while the maxi-mum of the ZnTe-like subband, to the T2-mode. A comparison of the temperature dependence of the TO-mode frequencies showed in Fig.3 and 6 point out a monotonic behaviour of the curves of the Hg0.763Zn0.237Te sample (Fig.6 a,b), while discontinuities occur in the curves of the semimetallic composition Hg0.9 Zn0.1 Te (Fig.4 and 5) with a positive temperature shift of the HgTe-like mode frequency and a negative temperature shift, for both compositions, of the ZnTe-like mode. In the sample Hg0.763 Zn0.237 Te a similar temperature dependence of the HgTe-like and ZnTe-like TO-modes as in the sample Hg0.80 Cd0.20 Te are observed the HgTe-like and CdTe-like TO-modes as shown in Fig. 10 a and b, respectively. For the sample Hg0.763Zn0.237 Te, the frequency of the HgTe-like mode is practically independent of the temperature.

In Fig. 9 are shown the frequency positions of the HgTe-like and CdTe-like sub-band maxima on the Im[ε(ω,Τ)] curves for sample Hg0.885Cd0.115Te. It is seen from Fig. 9 that discontinuity is taken place precisely at 245 K for both HgTe-and CdTe modes. General‐ ly, for CdTe-mode is observed negative temperature shift of the phonon frequency, while for HgTe-mode is positive one.

**Figure 2.** Reflectivity *R*(*ω, T)* for Hg0*.237* Zn0*.763* Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the

**Figure 1.** Reflectivity *R*(*ω, T)* for Hg0*.*90 Zn0*.*10 Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the tem‐

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The KK-transformation was also performed for the R(ω, T) curves shown in Fig.2 (the Hg0.763 Zn0.237 Te sample). The Im[(ω, T)] curves at different temperatures for this sample are shown

temperature interval 40 K-300 K

perature interval 30 K-300 K

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**Figure 3.** The Im[(ω, T)] curves of the Hg0.90 Zn0.10 Te obtained from the reflectivity curves of Fig.1: a) the Im[(ω, T)] curves for the HgTe-like mode; b) the Im[(ω, T)] curves for the ZnTe-like mode.

**Figure 4.** The Im[є(*ω, T)*] curves of the Hg0*.*763 Zn0*.*237 Te obtained from the reflectivity curves of Fig.2.

**Figure 5.** The frequency positions of ZnTe-like a) and HgTe-like b) sub-band maxima on the Im[(ω, T)] curves for the Hg0.90 Zn0.10 Te at different temperatures in the range 30 300 K.

**Figure 3.** The Im[(ω, T)] curves of the Hg0.90 Zn0.10 Te obtained from the reflectivity curves of Fig.1: a) the Im[(ω, T)]

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68

**Figure 4.** The Im[є(*ω, T)*] curves of the Hg0*.*763 Zn0*.*237 Te obtained from the reflectivity curves of Fig.2.

curves for the HgTe-like mode; b) the Im[(ω, T)] curves for the ZnTe-like mode.

It is interesting to compare the temperature dependences of the phonon modes for another alloy of HgCdTe. As was shown in Fig. 6b for the sample Hg0.763 Zn0.237 Te, the frequency of the HgTe-like mode is practically independent of the temperature. Similar behaviour takes place for CdTe-mode in alloy Hg0.80Cd0.20Te as it is seen in Fig. 10 where are shown the temperature dependences for the phonon mode frequencies for this alloy.

So, it is possible to generalise the obtain experimental results on temperature behaviour of the phonon spectra for four alloys contained the mercury – Hg1-x Znx Te and Hg1-x Cdx Te. If composition x is near the value where the particularity in energy structure takes place, namely the Dirac point (Eg ≡ Γ6 − Γ8=0), for example in the case of the Hg1-x Cdx Te alloys that is x=0.1 – 0.17 and in the case of the Hg1-x Znx Te alloys it is x=0.06 – 0.11, then positive temperature shift is observed for the HgTe-modes with discontinuity the temperature where the Dirac point takes place.

**Figure 6.** The positions of the Im[(ω, T)]-maxima for the Hg0.763 Zn0.237 Te sample a) the ZnTe-like mode and b) the HgTe-like mode.

**Figure 7.** Reflectivity *R*(*ω, T)* for Hg0*.885* Cd 0*.115* Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the temperature interval 40 K-300 K

High Resolution Infrared Spectroscopy of Phonons in the II-VI Alloys — The Temperature Dependencies Study http://dx.doi.org/10.5772/59050 71

**Figure 8.** Reflectivity *R*(*ω, T)* for Hg0*.885* Cd 0*.115* Te in the frequency region from 80 cm−1 to 220 cm −1 and in the temperature interval 40 K-300 K

**Figure 6.** The positions of the Im[(ω, T)]-maxima for the Hg0.763 Zn0.237 Te sample a) the ZnTe-like mode and b) the

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**Figure 7.** Reflectivity *R*(*ω, T)* for Hg0*.885* Cd 0*.115* Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the

HgTe-like mode.

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temperature interval 40 K-300 K

**Figure 9.** Reflectivity *R*(*ω, T)* for Hg0*.885* Cd 0*.115* Te in the frequency region from 80 cm*−*1 to 220 cm *−*1 and in the temperature interval 40 K-300 K

**Figure 10.** The positions of the Im[(ω, T)]-maxima for the Hg0.80 Cd0.20 Te sample a) the CdTe-like mode and b) the HgTe-like mode.


**Table 1.** Parameters of alloys necessary to calculate the anharmonic contribution to the phonon frequency change


**Table 2.** Parameters of alloys necessary to calculate the e-p contribution to the phonon frequency change

In the case of compositions apart from that areas where Dirac point cold be presence (for x>0.17 for Hg1-xCdxTe alloys as well as for x>0.11 for the Hg1-xZnxTe alloys) an ambivalence behaviour for the temperature dependences of the HgTe-modes is observed – could be or strong positive temperature shift or complete independency on the temperature takes place.

#### **3. Discussion**

#### **3.1. Basic theory**

**Figure 10.** The positions of the Im[(ω, T)]-maxima for the Hg0.80 Cd0.20 Te sample a) the CdTe-like mode and b) the

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

**Table 1.** Parameters of alloys necessary to calculate the anharmonic contribution to the phonon frequency change

**Alloys mode A (cm-1) B (cm-1) C (cm-1)**

HgTe-like 121.8 -3.7 1.9 CdTe-like 152.0 -2.3 -0.4

HgTe-like 118.0 4 -0.6 CdTe-like 152.4 -2 -0.4

HgTe-like 119.2 3.6 -1.04 ZnTe-like 171.2 -0.26 -1.87

HgTe-like 126.03 0.001 0.005 ZnTe-like 177.0 -10 2

HgTe-like mode.

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Hg0.85Cd0.15Te

Hg0.80Cd0.20Te

Hg0.90Zn0.10Te

Hg0.763Zn0.237Te

In view of the most general assumptions, it is possible to start from the following equation for the temperature shift of the TOi -phonon mode frequencies νT Oi [18]:

$$
\Delta\nu\_{\mathcal{T}\mathcal{O}\_i} \left( T \right) = \left( \frac{\partial \nu}{\partial T} \right)\_P dT + \left( \frac{\partial \nu}{\partial T} \right)\_V dT \tag{1}
$$

The first term in Eq. (1) corresponds to the crystal expansion and to an anharmonic contribution to the harmonic crystal potential. This anharmonic term has been analyzed in detail by different authors in the last decades. The theory developed by Maradudin and Fein (Maradudin & Fein, 1962) as well as by [14] is based on the classical anharmonic oscillator. The potential energy is:

$$V(\mathbf{x}) = c\mathbf{x}^2 - \mathbf{g}\mathbf{x}^3 - \mathbf{f}\mathbf{x}^4 \tag{2}$$

where, the cubic term gx3 gives a thermal expansion but no change in the frequency at the first order. The quartic term fx4 and the cubic term to the second order (gx2 ) <sup>2</sup> may induce a change in the frequency of the modes. The role of these terms was estimated [10] by assuming for Si atoms a covalent interatomic bond within the Morse potential:

$$V(r) = D[(e^{-\vartheta(r-r\_0)} - 1)^2 - 1] \tag{3}$$

where the constants D, a and r0 are determined, respectively, by bonding energy, stiffness of bond and interatomic spacing. Using the Morse potential to determine the coefficients of the Taylor series expansion of the potential, [14] find that the quartic term is positive, i.e., it increases with the frequency, but accounts for only 3/5 respect to the cubic term to the second order that is negative. The result is then a net decrease in the frequency.

In the quantum-mechanical approach each power of x correspond to a creation or an annihi‐ lation operator for a phonon, and the frequency shift of the optical mode is calculated as the self-energy of the mode [24]. Using this technique [10] performed detailed numerical calcula‐ tions for the diamond structure using eigenvectors and eigenfrequencies of the harmonic model deduced by fitting the parameters of the dispersion curves obtained by inelastic neutron scattering data. The appropriate anharmonic interaction was determined by fitting experi‐ mental thermal expansion data. Later, Ipatova I.P. et al. (Ipatova et al., 1967) working on ionic crystals and Schall M. et. al. (Schall et al., 2001) in the CdTe and ZnTe semiconductors applied this theory to explain the temperature dependence of the dielectric function in the far IR frequency range.

The second term in equation (1) is due to the e-p interaction and it is interesting to underline that an analogue expression takes place for the temperature dependence of the energy gap in semiconductors (Yu & Cardona, 1996) where two contributions also occur: the anharmonic one and that induced by the e-p interaction.

#### *3.1.1. Anharmonic contribution*

An expression was derived by Ipatova I.P. et al. [16] for the temperature dependence of the phonon mode frequency νT O or the damping of an oscillator γT O in the quartic anharmonic force constant approximation:

$$Y(T) = A + B\left(\frac{T}{\Theta}\right) + C\left(\frac{T}{\Theta}\right)^2\tag{4}$$

where Y(T) is one of the measured quantities νTO or γTO, Θ is the characteristic temperature of the phonon subsystem Θ=hνT O /kB (kB is the Boltzmann constant), A, B, C are the parameters obtained by fitting and for the CdTe phonon frequency (Ref. 12): A=4.361 THz (or 150 cm−1), B=-0.0298 THz (or-1.00 cm−1), C=-0.0348 THz (or-1.16 cm−1). The same parameters for the ZnTe are: 5.409 THz (or 190 cm−1),-0.0457 THz (or-1.52 cm−1) and-0.0341 THz (or-1.37 cm−1), respec‐ tively. In this case, it is clear that A is the frequency νTO(0) of the TO-phonon mode at T=0 and the first term in the equation (1) can be rewritten as:

$$
\Delta \nu\_{TO}^{I} \left( T \right) = B \left( \frac{T}{\Theta} \right) + \mathcal{C} \left( \frac{T}{\Theta} \right)^{2} \tag{5}
$$

Because A and B are usually negative parameters, equation (5) always points out a frequency decrease, i.e., a softening of the phonon frequency on increasing the temperature. This behaviour has been observed in many ionic crystals and wide-gap semiconductors.

#### *3.1.2. The e-p interaction contribution*

where the constants D, a and r0 are determined, respectively, by bonding energy, stiffness of bond and interatomic spacing. Using the Morse potential to determine the coefficients of the Taylor series expansion of the potential, [14] find that the quartic term is positive, i.e., it increases with the frequency, but accounts for only 3/5 respect to the cubic term to the second

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

In the quantum-mechanical approach each power of x correspond to a creation or an annihi‐ lation operator for a phonon, and the frequency shift of the optical mode is calculated as the self-energy of the mode [24]. Using this technique [10] performed detailed numerical calcula‐ tions for the diamond structure using eigenvectors and eigenfrequencies of the harmonic model deduced by fitting the parameters of the dispersion curves obtained by inelastic neutron scattering data. The appropriate anharmonic interaction was determined by fitting experi‐ mental thermal expansion data. Later, Ipatova I.P. et al. (Ipatova et al., 1967) working on ionic crystals and Schall M. et. al. (Schall et al., 2001) in the CdTe and ZnTe semiconductors applied this theory to explain the temperature dependence of the dielectric function in the far IR

The second term in equation (1) is due to the e-p interaction and it is interesting to underline that an analogue expression takes place for the temperature dependence of the energy gap in semiconductors (Yu & Cardona, 1996) where two contributions also occur: the anharmonic

An expression was derived by Ipatova I.P. et al. [16] for the temperature dependence of the phonon mode frequency νT O or the damping of an oscillator γT O in the quartic anharmonic

T

( )

 A B

( )

TB

I

n

TO

YT

the first term in the equation (1) can be rewritten as:

2

2

 T

 C

èø èø Q Q (4)

èø èø Q Q (5)

 T

 C æö æö =+ + ç÷ ç÷

where Y(T) is one of the measured quantities νTO or γTO, Θ is the characteristic temperature of the phonon subsystem Θ=hνT O /kB (kB is the Boltzmann constant), A, B, C are the parameters obtained by fitting and for the CdTe phonon frequency (Ref. 12): A=4.361 THz (or 150 cm−1), B=-0.0298 THz (or-1.00 cm−1), C=-0.0348 THz (or-1.16 cm−1). The same parameters for the ZnTe are: 5.409 THz (or 190 cm−1),-0.0457 THz (or-1.52 cm−1) and-0.0341 THz (or-1.37 cm−1), respec‐ tively. In this case, it is clear that A is the frequency νTO(0) of the TO-phonon mode at T=0 and

T

æö æö D =+ ç÷ ç÷

order that is negative. The result is then a net decrease in the frequency.

frequency range.

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one and that induced by the e-p interaction.

*3.1.1. Anharmonic contribution*

force constant approximation:

As mentioned in the Introduction, the returnable e-p interaction could be responsible for the abnormal temperature dependence of the phonon frequency in both HgCdTe as well as HgZnTe. This kind of e-p interaction induces a discontinuity in the temperature dependence of the phonon frequencies in the resonant case, i.e., Dirac points. Actually, it is possible to assume that far from a Dirac point the returnable e-p interaction may overcome the anharmonic contribution and reverse the sign of the phonon frequency temperature dependence associated with the lattice dilatation.

As shown in [19], the preferred mechanism explaining the influence of the electronic structure of the crystal on its phonon spectrum is a deformation potential that mediates the interaction of electrons with the transverse optical phonons (TO-phonons). The TO-phonons are clearly recognized in optical reflectivity experiments, therefore the deformation potential is respon‐ sible for the interaction of electrons with TO-phonons. We are interested only in the terms of the deformation potential matrix that correspond to the energy region between the valence and the conduction band. Therefore, the self-energy of the TO-phonons with a small wavevector q is given by the formula [19, 35]:

$$
\omega\_{\rm TO}^{\star 2} = \omega\_{\rm TO}^2 - \int dE F(E) \left\{ \frac{1}{E + E\_{\rm g} + \hbar \alpha\_{\rm TO}} + \frac{1}{E + E\_{\rm g} - \hbar \alpha\_{\rm TO}} \right\} \tag{6}
$$

where Eg is the energy gap and

$$F(E) = \frac{2}{2\pi^3} \int \frac{\rho\_{TO}}{\hbar} \left( V\_{cv}\left(k, q\right)^2 \cdot \delta\left(E - E\_c\left(k + q\right) - E\_v\left(k\right)\right) dk \right) \tag{7}$$

Vcν (k, q) does not depend on the wave vector of the long-wave optical phonons (q 0); thus, Ec (k+q) − Eν (k)=Eg.

We can identify two kinds of singularities in Eq. (6): the first is obtained when Eg is equal to, and the second occurs when Eg equals zero. In the second case, if the temperature increases, the Eg (T) dependence approaches zero from the negative side of the energy gap (the in-version band-structure). On the other hand, decreasing the temperature, the Eg (T) dependence approaches zero from the positive side of the energy gap (normal band structure), hence, a discontinuity in ωT O (T) may occur also at Eg (T)=0.

In order to describe the e-p contribution to the phonon frequency temperature dependence we may use an equation derived from Eq. (6) to determine the frequency change:

$$
\alpha\_{TO}^{\*2} = \alpha\_{TO}^2 \pm \frac{4\Xi\_{CV}^2}{M\pi^2 \mathcal{W}} \ln \frac{\mathcal{W}}{2E\_F + \left| E\_g \right|} \tag{8}
$$

where Ξ(k, q) is the optical deformation potential, EF is the Fermi energy measured from the band edge, W is the sum of the conduction and the valence bands width, *a* is the lattice constant and Eg ≡ Γ<sup>6</sup> − Γ8 is the energy gap between the Γ6 band, which is the conductive band in a normal semiconductor and the Γ<sup>8</sup> band, which is usually the top of the valence band. After a simple trans-formation from Eq. (8) we can obtain an expression for ∆νII (T), the phonon frequency change associated to the returnable e-p interaction:

$$
\Delta \nu^{\rm II} \left( T \right) = \pm 2 \frac{\Xi\_{\rm CV}}{a} \sqrt{\frac{1}{MW} \ln \frac{W}{2E\_{\rm F} + \left( E\_{\rm g} \right)}} \tag{9}
$$

Looking at ∆νII (T) we may recognize the sign of this contribution through the correspond‐ ing sign of the deformation potential Ξ(k, q) : the sign is "-" when the energy gap (Eg ≡ Γ<sup>6</sup> − Γ8) is positive (usually Eg > 0, in a normal semiconductor the deformation potential is negative) or the sign is "+" when Eg < 0 (that takes place before a Dirac point). Therefore, before the resonance case (Eg ≡ Γ6 − Γ8=0) when Eg < 0, Ξ(k, q) > 0 and the contribution of the returnable e-p interaction to the temperature change of the phonon frequency has a reversed sign with respect to the anharmonic contribution which is always negative. At some temperature a full reverse sign of the frequency could occur, i.e., when the phonon contribution overcomes the anharmonic one, on increasing the temperature also the frequency starts increasing. It enables us to explain the abnormal temperature depend‐ ence of the optical phonon frequency.

A different scenario occurs after the resonance: the sign is-for the phonon contribution to the temperature change of the phonon frequency when Ξ(k, q) < 0. The phonon frequen‐ cy suddenly decreases and a discontinuity takes place at the Dirac point. However, on increasing the temperature the Eg ≡ Γ6 − Γ8 also increases, and the negative phonon contribution to the temperature change of the phonon frequency is reduced that implies a decrease of the negative change of this frequency. Therefore, the magnitude of the phonon frequency increases with the temperature after the Dirac point only if the phonon contribu‐ tion overcomes the anharmonic one, a condition occurring not far from the resonance. As a consequence, the abnormal temperature dependence of the optical phonon frequency may occur also after the resonance.

#### *3.1.3. Full temperature shift of the TO-phonon frequency*

According to the above, the full temperature shift of the TO-phonon frequency in the semi‐ conductor crystals is ∆ν(T)=∆νΙ (T)+∆νII(T) (T) and the temperature dependence of the TOphonon mode νT O (T) can be written as:

High Resolution Infrared Spectroscopy of Phonons in the II-VI Alloys — The Temperature Dependencies Study http://dx.doi.org/10.5772/59050 77

$$\nu\_{\rm TO}(T) \equiv \nu\_{\rm TO}(0) + \Delta\nu\_{\rm TO}(T) = \nu\_{\rm TO}(0) + B\left(\frac{T}{\Theta}\right) + C\left(\frac{T}{\Theta}\right)^2 + 2\frac{\Xi\_{\rm CV}}{a} \sqrt{\frac{1}{MW} \ln \frac{W}{2E\_{\rm F} + \left(E\_g\right)}}\tag{10}$$

From the comparisons of Eqns (5), (9) and (10) the anharmonic contribution exhibits for all crystals a monotonic function vs. temperature and, because the B and C constants are usually negative, the phonon frequency decreases (Ipatova et al., 1967; Schall et al., 2001). Actually, the e-p contribution depends dramatically on the temperature because Eg(T) crosses through a point where Eg=0. In this point a singularity occurs and, because the e-p contribution is huge, a discontinuity in the temperature dependence of the phonon mode frequency is observed for Hg0.89 Cd0.11 Te at 245 K (Sheregii et al., 2009). When Eg < 0, the ∆νII (T) is positive and leads to the hardening of the phonon mode with increase of temperature. However, this contribution quickly reduces decreasing the temperature. Indeed, when temperature decrease the value of |Eg | increases and ∆νII(T) becomes smaller than ∆ν<sup>I</sup> (T) what means a softening of the phonon mode at low temperatures. In the semiconductor case at (Eg > 0), the ∆νII(T) is negative and | ∆νII(T) | > |∆ν<sup>I</sup> (T) | is fulfilled, because at Eg ~ 0 the e-p contribution is large. However, the increase of |Eg | when temperature increase, leads to a decrease of the total negative change of the phonon frequency that implies a positive temperature shift of the magnitude of the phonon mode frequency already observed in the Hg1−x CdxTe as well as in another mercury contained alloys. So, it seems to be possible to explain this positive temperature shift of the phonon frequency by the e-p contribution Nevertheless, concerning the role of the returnable e-p coupling, it is necessary to carry out a reliable experimental test of the above theoretical assumptions on the temperature dependence of the phonon mode frequency.

In what follows, we will present the analysis of the experimental data which are described above. Data allow to answer if the returnable e-p coupling contribution is enough to explain the abnormal temperature dependence of the HgTe-like mode frequency in both MCT and MZT alloys.

#### **3.2. Analyses and Interpretation of experimental results**

#### *3.2.1. Alloy Hg0.85Cd0.15Te*

2

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

X

CV

2 4

<sup>Ξ</sup> <sup>1</sup> 2 ln

*<sup>W</sup> T ±*

Ma W ln 2

where Ξ(k, q) is the optical deformation potential, EF is the Fermi energy measured from the band edge, W is the sum of the conduction and the valence bands width, *a* is the lattice constant and Eg ≡ Γ<sup>6</sup> − Γ8 is the energy gap between the Γ6 band, which is the conductive band in a normal semiconductor and the Γ<sup>8</sup> band, which is usually the top of the valence band. After a simple trans-formation from Eq. (8) we can obtain an expression for ∆νII (T), the phonon frequency

F

 E E

W

+

 g

( )

(9)

*F g*

2

*a MW E+E*

Looking at ∆νII (T) we may recognize the sign of this contribution through the correspond‐ ing sign of the deformation potential Ξ(k, q) : the sign is "-" when the energy gap (Eg ≡ Γ<sup>6</sup> − Γ8) is positive (usually Eg > 0, in a normal semiconductor the deformation potential is negative) or the sign is "+" when Eg < 0 (that takes place before a Dirac point). Therefore, before the resonance case (Eg ≡ Γ6 − Γ8=0) when Eg < 0, Ξ(k, q) > 0 and the contribution of the returnable e-p interaction to the temperature change of the phonon frequency has a reversed sign with respect to the anharmonic contribution which is always negative. At some temperature a full reverse sign of the frequency could occur, i.e., when the phonon contribution overcomes the anharmonic one, on increasing the temperature also the frequency starts increasing. It enables us to explain the abnormal temperature depend‐

A different scenario occurs after the resonance: the sign is-for the phonon contribution to the temperature change of the phonon frequency when Ξ(k, q) < 0. The phonon frequen‐ cy suddenly decreases and a discontinuity takes place at the Dirac point. However, on increasing the temperature the Eg ≡ Γ6 − Γ8 also increases, and the negative phonon contribution to the temperature change of the phonon frequency is reduced that implies a decrease of the negative change of this frequency. Therefore, the magnitude of the phonon frequency increases with the temperature after the Dirac point only if the phonon contribu‐ tion overcomes the anharmonic one, a condition occurring not far from the resonance. As a consequence, the abnormal temperature dependence of the optical phonon frequency may

According to the above, the full temperature shift of the TO-phonon frequency in the semi‐ conductor crystals is ∆ν(T)=∆νΙ (T)+∆νII(T) (T) and the temperature dependence of the TO-

(8)

\*2 2

 w

= ±

TO TO

w

Applications

76

change associated to the returnable e-p interaction:

ence of the optical phonon frequency.

occur also after the resonance.

phonon mode νT O (T) can be written as:

*3.1.3. Full temperature shift of the TO-phonon frequency*

( )

D = n

*II CV*

The analysis of the observed temperature dependence of the TO-phonon modes for these semimetallic and semiconductor alloys is based on Eq. (10).

In order to calculate the *e-p* contribution to the temperature shift according to Eqns.(9,10) we need to know the temperature dependence of the energy gap *Eg(T)*. An empirical formula for *Eg(x,T)* is presented in (Sheregii et al., 2009) derived for the Hg1−xCdx Te alloy. According this empirical formula the Dirac point (Eg ≡ Γ<sup>6</sup> − Γ8=0) takes place for sample Hg0.85 Cd0.15 Te at temperature 245 K. In Table 1 values of other important parameters are presented such as the optical deformation potential *Ξ(k, T)*, the Fermi energy *EF*, the sum of the conduction, and the valence bands width as well as the lattice constant *a* for the HgCdTe and HgZnTe alloys. The *A*, *B* and *C* parameters for the anharmonic contribution for each sample are listed in Table 2.

**Figure 11.** The CdTe-like (a) and HgTe-like (b) TO-mode positions in the frequency scale at different temperatures for the sample Hg0.85Cd0.15Te – the same experimental pointa as in Fig. 9; solid curves are calculated according the Eqn. 10.

Result of the *e-p* contribution calculation according Eqn. (9) is shown by solid curve in Fig. 9. The discontinuity at 245 K is displayed by theoretical curve in narrow region of temperature very impressible and agree with experimental dependences very well. However, we need to confirm that Eq. (10) satisfactorily describes the experimentally observed temperature dependence of both HgTe-like and CdTe-like mode frequencies in wide temperature region together with the discontinuity observed at 245 K. Anharmonic and e-p terms in Eq. (10) match the experimental dependence of HgTe-mode in the whole temperature range from 40 K to 300 K for this sample as it is shown in Fig. 11b. The anharmonic contribution dominates at low temperature from 40 K to 120 K and the temperature shift of the HgTe-like T*0*-mode is negative. After the minimum at 121 K, the *e-p*-contribution overcomes the anharmonic one, and the HgTe-like T0-mode frequency start increasing up to resonance at 245 K. At the resonance (Dirac point) the *e-p*-contribution change sign and the phonon frequency suddenly decreases: the discontinuity takes place and the following increase of the temperature leads to a decrease of the negative *e-p*-contribution that induces the increase of the phonon frequency up to room temperature. It is important to note that theoretical curve in Fig. 11b is calculated with a positive value of the constant C. In the case of the CdTe-like mode (see Fig. 11a) both B and C parameters are negative similarly to the CdTe-binary but the linear constant B is slightly larger than nonlinear while C is slightly smaller compared to the binary one. On the contrary, in the case of the HgTe-like mode it is impossible to have a satisfactorily theoretical agreement with experimental curves using negative values of both B and C constants. As a consequence, we take positive sign for the C constant what implies that *the thermal expansion can lead to an ambivalent effect in the frequency temperature dependence of the HgTe-like mode*.

#### *3.2.2. Alloy Hg0.80Cd0.20Te*

In the case of the Hg0.80 Cd0.20 Te-alloy the singularity in the second term of Eq. (10) is very far (formally should exist at temperature closed to absolute zero) and the effect of the returnable e-p interaction is negligible. That is shown in Fig. 10b where we show experimental data and theoretical curves of the HgTe-like mode. Here the solid curve is calculated with the *e-p* term while the dotted one without it. Parameters are listed in Tables 1 and 2. A good fit of the experimental data was obtained with B > 0. It is clear from their behaviour that the phonon frequency of the HgTe-like mode strongly increases with the temperature, almost linearly, so that B must be large and positive.

The CdTe-like mode frequency has an opposite behavior vs. temperature with respect to the HgTe-like one: the frequency strongly decreases vs. temperature. It is a classical behavior where the anharmonic contribution dominates in the phonon frequency. The parameters B and C are close to that of the sample Hg0.85 Cd0.15Te and also of the binary CdTe.

#### *3.2.3. Alloy Hg0.90Zn0.10Te*

Result of the *e-p* contribution calculation according Eqn. (9) is shown by solid curve in Fig. 9. The discontinuity at 245 K is displayed by theoretical curve in narrow region of temperature very impressible and agree with experimental dependences very well. However, we need to confirm that Eq. (10) satisfactorily describes the experimentally observed temperature dependence of both HgTe-like and CdTe-like mode frequencies in wide temperature region together with the discontinuity observed at 245 K. Anharmonic and e-p terms in Eq. (10) match the experimental dependence of HgTe-mode in the whole temperature range from 40 K to 300 K for this sample as it is shown in Fig. 11b. The anharmonic contribution dominates at low temperature from 40 K to 120 K and the temperature shift of the HgTe-like T*0*-mode is negative. After the minimum at 121 K, the *e-p*-contribution overcomes the anharmonic one, and the HgTe-like T0-mode frequency start increasing up to resonance at 245 K. At the resonance (Dirac point) the *e-p*-contribution change sign and the phonon frequency suddenly decreases: the discontinuity takes place and the following increase of the temperature leads to a decrease of the negative *e-p*-contribution that induces the increase of the phonon frequency up to room temperature. It is important to note that theoretical curve in Fig. 11b is calculated with a positive value of the constant C. In the case of the CdTe-like mode (see Fig. 11a) both B and C

**Figure 11.** The CdTe-like (a) and HgTe-like (b) TO-mode positions in the frequency scale at different temperatures for the sample Hg0.85Cd0.15Te – the same experimental pointa as in Fig. 9; solid curves are calculated according the Eqn. 10.

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

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78

To calculate according to Eqns. (9, 10) the *e-p* contribution to the temperature shift of the temperature dependence of the energy gap *Eg*(*T)* of the Hg1*−x* Zn*<sup>x</sup>* Te, it is necessary to write an empirical formula *Eg* (*x,T)* similar to that of the Hg1*−x* Cd*x* Te (Talwar, 2010):

$$E\_g(\mathbf{x}, T) = -0.302 + 2.731\mathbf{x} + 3.2410 - 2\mathbf{x} - 0.629\mathbf{x} \mathbf{2} + 0.533\mathbf{x} \mathbf{3} + 5.310 - 4(0.76\mathbf{x} 0.5 - 1.29\mathbf{x})T \tag{11}$$

From the above *equation* calculated for the Hg0*.*<sup>9</sup> Zn0*.*1 Te and shown in Fig. 12, the zero-gap state should take place at 85 K.

Really, at this temperature 85 K a discontinuity of the temperature dependences of the HgTelike and ZnTe-like modes is observed (see Fig. 5a and 5b). These discontinuities are smaller than in the Hg0*.*85 Cd0*.*<sup>15</sup> Te sample. In the case of the HgTe-like mode for the sample Hg0*.*9 Zn0*.* 1 Te (Fig. 5a), Eq. (10) describes quite well the experimental behavior with the discontinuity at 85 K but with a value *B=3.6* which is positive that points out a strong increase of the phonon frequency with the temperature. So, the returnable *e-p*-interaction contribution in the second term in Eq. 10 describes the discontinuity in the phonon frequency temperature dependence but on top of a general increase of the frequency. A third factor, connected with the expansion but included not in Eqn. (10) openly, should cause this increase. The ZnTe-like mode temper‐

**Figure 12.** Temperature dependence of the energy gap (Eg ≡ Γ<sup>6</sup> − Γ8) for the Hg0*.*9 Zn0*.*1 Te alloy calculated according to the Eq.11 (see text).

ature behavior (Fig. 5b) can be interpreted by Eq.10 with the anharmonic constants *B=-0.26* and *C=-1.87* with a discontinuity always at 85 K.

#### *3.2.4. Alloy Hg0.237Zn0.763Te*

The sample Hg0.763 Zn0.237 Te is characterized by the HgTe-like phonon frequency practically independent of the temperature as showed in Fig. 6b, and constants B and C close to zero. The *e-p* contribution is then negligible similarly to the Hg0.80 Cd0.20 Te. Therefore, the two contri‐ butions are compensated in this system: one due to the anharmonicity that induces a negative frequency shift while the second, an unknown yet, induces positive temperature shift but the latter one is connected with thermal expansion too.

The temperature dependence of the ZnTe-like mode frequency in the case of the Hg0.763 Zn0.237 Te alloy points out a maximal negative shift among all the alloys we investigated: *B*=-10 while *C*=2 is positive. The latter is due to the character of the mode frequency temperature depend‐ ence we observed. This character is different from the temperature dependence of the same mode for the Hg0.90 Zn0.10 Te (Fig. 5a and 5b) as well as the CdTe-like TO-phonon frequency temperature dependence of both HgCdTe samples (Fig. 9 and 10a). In the binary ZnTe the temperature dependence of the ZnTe mode frequency is significantly smaller [14].

#### *3.2.5. The relativistic contribution to vibrational effects*

From the above data the positive temperature shift is characteristic in different alloys only of the HgTe-like modes. It means that contribution of Hg-atoms to the chemical bonds mainly affects the abnormal temperature dependence of the HgTe-like phonon frequencies. It is then useful to consider the peculiarities of the chemical bonds in the case of the II-VI compounds with Hg.

Using a simple chemical picture of these compounds, Hg atoms contribute to bonds with two s electrons while Te atoms with two s and four p electrons. In comparison with Ca, Sr, and Ba chalcogenides, the ionicity of Hg chalcogenides is reduced. The Hg-d-electrons are partially delocalized, and, therefore, the effective nuclear charge, experienced by the valence electrons, increases. This generates a more tightly bound of Hg valence s electrons and, hence, a less ionic and more covalent bond. In this respect, Hg-atoms in the II-VI compounds are similar to the isoelectronic Cd and Zn in the same semiconductors. However, the d-shell delocalization is stronger in Hg than in Cd or Zn and, in fact, enough strong to pull the s level below the chalcogen p level10. As a con-sequence, an inverted band structure is obtained. The role of delectrons in II-VI compounds is discussed in more detail by Wei and Zunger, [42], while the contribution of the spin-orbit interaction to chemical bonds and electronic structure is consid‐ ered in [12]. This contribution increases with the number of atoms, and it is larger for Hg atoms with respect to Cd and Zn ones. In HgTe, the Γ8 band is higher in energy than the Γ<sup>6</sup> one, whereas the situation is reversed in CdTe and ZnTe. Actually, this is because the energy difference between the Γ8 and Γ<sup>6</sup> levels is determined by three factors: i) the chalcogen p-spinorbit splitting, ii) the Hg-d-spin-orbit splitting and iii) the coupling strength among these states – so-called pd-coupling. For the p states, the Γ8 symmetry is higher in energy than the Γ7, whereas for d-states the situation is reversed. Thus, if the p-spin-orbit coupling with the Hgd-spin-orbit split states becomes reasonably small as in CdTe (ZnTe), the order of the Hg-dspin-orbit split states drives the sequence order of Γ8 and Γ6 levels. Alternatively, if due to large pd-coupling the d character dominates in these bands, the Γ8 level may also end up higher than the Γ6 level.

ature behavior (Fig. 5b) can be interpreted by Eq.10 with the anharmonic constants *B=-0.26* and

**Figure 12.** Temperature dependence of the energy gap (Eg ≡ Γ<sup>6</sup> − Γ8) for the Hg0*.*9 Zn0*.*1 Te alloy calculated according

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

The sample Hg0.763 Zn0.237 Te is characterized by the HgTe-like phonon frequency practically independent of the temperature as showed in Fig. 6b, and constants B and C close to zero. The *e-p* contribution is then negligible similarly to the Hg0.80 Cd0.20 Te. Therefore, the two contri‐ butions are compensated in this system: one due to the anharmonicity that induces a negative frequency shift while the second, an unknown yet, induces positive temperature shift but the

The temperature dependence of the ZnTe-like mode frequency in the case of the Hg0.763 Zn0.237 Te alloy points out a maximal negative shift among all the alloys we investigated: *B*=-10 while *C*=2 is positive. The latter is due to the character of the mode frequency temperature depend‐ ence we observed. This character is different from the temperature dependence of the same mode for the Hg0.90 Zn0.10 Te (Fig. 5a and 5b) as well as the CdTe-like TO-phonon frequency temperature dependence of both HgCdTe samples (Fig. 9 and 10a). In the binary ZnTe the

From the above data the positive temperature shift is characteristic in different alloys only of the HgTe-like modes. It means that contribution of Hg-atoms to the chemical bonds mainly affects the abnormal temperature dependence of the HgTe-like phonon frequencies. It is then

temperature dependence of the ZnTe mode frequency is significantly smaller [14].

*C=-1.87* with a discontinuity always at 85 K.

latter one is connected with thermal expansion too.

*3.2.5. The relativistic contribution to vibrational effects*

*3.2.4. Alloy Hg0.237Zn0.763Te*

to the Eq.11 (see text).

Applications

80

However, how the difference between CdTe (ZnTe) and HgTe electronic structures translates into a temperature dependence of the phonon frequency? As it was underlined in the Subsec‐ tion 3.1, a similar equation to Eq.(1) takes place for the temperature dependence of the energy gap in semiconductors where two contributions, the anharmonic one and that associated to ep interaction, interplay with each other. It is interesting to note that the energy gap of HgCdTe and HgZnTe alloys have the same positive shift (Dornhaus & Nimtz, 1985) as the HgTe-like modes frequencies, actually opposite to the temperature shift observed for the energy gap of both CdTe and ZnTe [41, 23]. This difference in the Eg(T) dependences for binary CdTe(ZnTe) and ternary HgCd(Zn)Te is due to the Hg-d-spin-orbit split states and, probably, is translated into the νTO(T) also due to a large pd-coupling of the chemical bonds. Although, the temper‐ ature dependence of the expansion coefficients in CdTe(ZnTe) and HgTe are similar (Bagot, 1993), the role of the lattice expansion on the νTO(T) dependences is different, similarly to the Eg(T). It is possible to claim that the role of the quartic term in the potential of the Eq.(2) (see Subsection 3.1) is different for a Hg-Te bond compared to Cd-Te and Zn-Te ones because of the Hg-d-spin-orbit split states: overcomes others terms and positive temperature shift of the phonon frequency takes place.

#### **4. Conclusion**

It was performed an extensive experimental investigation of the temperature dependence of the phonon mode frequencies for Hg-based semiconductor alloys of II-VI compounds using the synchrotron radiation as a source in the far-infrared region. In the case of the Hg0.9 Zn0.1Te alloy we found a discontinuity of the temperature dependence of HgTe-like T0-mode and ZnTe-like T1-mode similarly to the Hg0.85 Cd0.15 Te alloy firstly found five years ago by [35]. A theoretical expression (Eqn. (10) in subsection 3.1) for the temperature shift of the phonon mode frequency has been derived including an anharmonic contribution as well as a term of a returnable electron-phonon interaction. It was shown that this expression including both abovementioned contributions satisfactorily describes the temperature shift of Hg0.85Cd0.15Te and Hg0.90 Zn0.10 Te alloys containing a Dirac point (Eg ≡ Γ6 − Γ8=0) if one of the two constants B and C describing the anharmonic shift of the HgTe-like mode, is positive. Moreover, in the case of the semiconductor alloys Hg0.80Cd0.20Te and Hg0.763 Zn0.237 Te the role of the returnable *e-p* contribution is negligible but a positive temperature shift for the HgTe-like modes takes place. The result cannot be explained as summing an *e-p* interaction as pointed out by (Rath et al., 1995).

The difference between the temperature behaviour of HgTe-like modes and CdTe-or ZnTelike ones can be explained by the Hg-d-spin-orbit split contribution to the chemical bond. This contribution is responsible of the positive temperature shift of the energy gap of ternary HgCdTe and HgZnTe alloys with a narrow gap because the relativistic contribution to chemical bonds is also at the origin of the abnormal temperature shift of electron states in Hgbased semiconductors – inverse band structure. Similar effect is reasonably expected that the Hg-d-spin-orbit split contribution leads to an abnormal temperature shift of the HgTe-like phonon mode frequency.

#### **Acknowledgements**

Author is greatly indebted to staff of the Laboratori Nazionale di Frascatti for possibility to perform several Project in framework of the TARI-contract in the years 2002 – 2006. This work was partly supported by the EU Foundation by the TARI-contract HPRI-CT-1999-00088.

#### **Author details**

E.M. Sheregii

University of Rzeszow, Centre for Microelectronics and Nanotechnology, Poland

#### **References**

**4. Conclusion**

Applications

82

et al., 1995).

phonon mode frequency.

**Acknowledgements**

**Author details**

E.M. Sheregii

It was performed an extensive experimental investigation of the temperature dependence of the phonon mode frequencies for Hg-based semiconductor alloys of II-VI compounds using the synchrotron radiation as a source in the far-infrared region. In the case of the Hg0.9 Zn0.1Te alloy we found a discontinuity of the temperature dependence of HgTe-like T0-mode and ZnTe-like T1-mode similarly to the Hg0.85 Cd0.15 Te alloy firstly found five years ago by [35]. A theoretical expression (Eqn. (10) in subsection 3.1) for the temperature shift of the phonon mode frequency has been derived including an anharmonic contribution as well as a term of a returnable electron-phonon interaction. It was shown that this expression including both abovementioned contributions satisfactorily describes the temperature shift of Hg0.85Cd0.15Te and Hg0.90 Zn0.10 Te alloys containing a Dirac point (Eg ≡ Γ6 − Γ8=0) if one of the two constants B and C describing the anharmonic shift of the HgTe-like mode, is positive. Moreover, in the case of the semiconductor alloys Hg0.80Cd0.20Te and Hg0.763 Zn0.237 Te the role of the returnable *e-p* contribution is negligible but a positive temperature shift for the HgTe-like modes takes place. The result cannot be explained as summing an *e-p* interaction as pointed out by (Rath

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

The difference between the temperature behaviour of HgTe-like modes and CdTe-or ZnTelike ones can be explained by the Hg-d-spin-orbit split contribution to the chemical bond. This contribution is responsible of the positive temperature shift of the energy gap of ternary HgCdTe and HgZnTe alloys with a narrow gap because the relativistic contribution to chemical bonds is also at the origin of the abnormal temperature shift of electron states in Hgbased semiconductors – inverse band structure. Similar effect is reasonably expected that the Hg-d-spin-orbit split contribution leads to an abnormal temperature shift of the HgTe-like

Author is greatly indebted to staff of the Laboratori Nazionale di Frascatti for possibility to perform several Project in framework of the TARI-contract in the years 2002 – 2006. This work was partly supported by the EU Foundation by the TARI-contract HPRI-CT-1999-00088.

University of Rzeszow, Centre for Microelectronics and Nanotechnology, Poland

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[26] Orlita M., Basko D. M., Zholudev M. S.,Teppe F., Knap W., Gavrilenko V. I., Mikhai‐ lov N. N., Dvoretskii S. A., Neuebauer P., Faugeras C., Barra A-L., Martinez G. & M. Potemski, (2014) Observation of three-dimensional massless Kane fermions in a zincblende crystal, *Nature Physics*, Vol. 10, No.3 (March 2014), pp. 233-238, 1745-2473

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[15] Ingale A., Bansal M.L. & Roy A.P., (1989) Resonance Raman scattering in HgTe: TOphonon and forbidden-LO-phonon cross section near the E1 gap, *Phys. Rev. B* Vol. 40,

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[17] de Jong W. A., Visscher L., & Nieuwpoort W. C., *J.* (1997) Relativistic and correlated calculations on the ground, excited, and ionized states of iodine, *The Journal of Chem.*

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[20] Kozyrev S.P., L.K. Vodopyanov & R.Triboulet, (1998) Structural analysis of the semi‐ conductor-semimetal alloy Cd 1-x Hg x Te by infrared lattice-vibration spectroscopy,

[21] M.Konig, S. Wiedmann, C. Brne, A. Roth, H. Buhmann, L.W. Molenkamp, X. L. Qi & S. C. Zhang, (2007) Quantum Spin Hall Insulator State in HgTe Quantum Wells, *Sci‐*

[22] Levinson Y.M. & Rashba E.I., (1973), Electron-phonon and exciton-phonon bound states, *Rep. Progr. Phys.* Vol. 36, No12 (December 1973), pp.1499-1524, 1361-6633

[23] Madelung O., (1996), *Semiconductor Basic Data, 2nd revised Edition*, Springer-Verlag,

[24] Maradudin A.A. & Fein A.E., (1962) Scattering of Neutrons by an Anharmonic Crys‐ tal, *Phys. Rev.*, Vol. 128, No12 (15 December 1962), pp. 2589-2596, 1550-235X

[25] M. Marchewka, M. Wozny, J. Polit, V. Robouch, A.Kisiel, A. Marcelli & E.M. Sheregii, (2014), The stochastic model for ternary and quaternary alloys: Application of the Bernoulli relation to the phonon spectra of mixed crystals, *J. Appl. Phys*., Vol. 115, No

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(January 1985), pp.105-111, 0734-2101

1521-3951

Applications

86

## **Chapter 5**

## **An FT-IR Spectroscopic Study of Metastatic Cancerous Bones**

J. Anastassopoulou, Μ. Kyriakidou, S. Kyriazis, T.H. Kormas, A.F. Mavrogenis, V. Dritsa, P. Kolovou and T. Theophanides

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/58910

#### **1. Introduction**

Breast cancer is the most frequently diagnosed cancer in women aged 40 to 65 years, with more than 464,000 new cases (13.5% of all cancer cases) per year in Europe [1,2]. Approximately 5% of breast cancer patients have advanced (metastatic) disease at diagnosis. Despite important progress in adjuvant and neoadjuvant therapies, up to 90% of cancer deaths are due to complications arising from metastatic dissemination of the disease [3,4].For patients with established metastatic disease, therapy is usually for palliation.

Metastasis is a complex process, entailing tumor cells acquiring a set of features that allow them to develop new foci of the disease. Its exact mechanism remains unclear. Metastasis has been described as the migration of tumor cells from the primary tumor, followed by intrava‐ sation, survival, extravasation of the circulatory system, and progressive colonization of a distant site [5-7]. In a second definition, tumor cell genomic instability occurs that enables invasion and distant organ colonization [8].In another definition, metastasis is described in terms of seed and soil [9]. Tumor cells (seeds) spread widely through the body, but grow only in supportive locations (congenial soil). Thus the various microenvironments (soils) of metastases contribute to the observed heterogeneity [9].

The most common sites of breast cancer metastases are the bones, brain, adrenal glands and other parts of the body [10,11]. Metastatic bone disease alters the mechanical properties of the involved bones, produces painful osteolysis, microfractures, and eventually complete frac‐ tures.The extent to which metastases are site specific and the transformation of healthy cells into cancer cells also remain poorly understood. A hallmark of breast cancer metastasis is the redundancy of pathways that mediate the process or its component steps, and theabound of promoting genes [3]. Some pathways contribute to bone metastasis, while other pathways have

© 2015 The Author(s). Licensee InTech. 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 eproduction in any medium, provided the original work is properly cited.

been reported to mediate lung and liver metastasis. Advanced next-generation sequencing techniques have also been used to interrogate whole cancer genomes at the single-nucleotide level and have distinguished between mutations in breast cancer metastases [12,13]. However, one metastasis may be distinct from another within the same patient accurate prediction of the molecular profile of metastatic disease by profiling the primary tumor is not feasible. In this setting, novel detection techniques are necessary [14].

Fourier transform infrared spectroscopy is a physicochemical, non-destructive, sensitive and reproducible method which provides important information about changes in the molecular structure of the bone due to the disease [15-29]. The advantage of the method is that it needs small amounts of the sample (only few micrograms) and we could study the sample without any preparation, such as coloring or demineralization as it is done in histopathology, since the spectra are based on individual chemical characteristics of the bone. Another important advantage of the infrared spectroscopy is that the method does not require any preparation of the sample, such as coloring or decalcification, as in methods like histopathology, where the samples are decalcified and labeled with color and are analyzed only the changes in the organic phase of the tissues.In infrared spectroscopy, the spectrum is the sum of all the frequencies of the components present and provides information on all components simultaneously [15-21].

Here within it is presented the influence of cancer on the molecular structure of the constituents of the bone (Hydroxyapatite, Collagen and Protein) and the characterization of the spectral differences between healthy and cancerous bones, in order to have a better insight of the process of the disease.

## **2. Materials and methods**

#### **2.1. Sample preparation**

Although breast cancer metastases to skeleton bones are frequent sites of first distant relapse,however the bone samples are not easy to be obtained. Six bone sections from breast metastatic cancer patients (39 and 65 years), who suffered from breast cancer and under‐ went a reconstruction with an osteoarticular allograft, were used for the present study. Small amount of fresh bones (cancellous or/compact), were immersed successively in hydrogen peroxide solution (H2O2) and in acetone, according to a modification method [15-17, 20,30]. Hydrogen peroxide and acetone processing is known to reduce the fat tissue and blood chromophores of fresh bone, but it does not remove the organic components completely.

#### **2.2. Sample analysis**

#### *2.2.1. Infrared spectroscopy*

The conformational and molecular changes of healthy and cancerous bones were recorded using a Nicolet 6700 thermoscientific Transform Infrared (FT-IR) spectrometer, which was connected to an attenuated total reflection (ATR) accessory. This technique is convenient in this case for the cancerous bones since it is almost impossible to powderize these tissues.More‐ over, impregnated with PMMA bone appears less suited, because when remove the plastic there is dangerous to loose important components.

Each absorption spectrum of the samples was consisted of 120 co-added spectra at a resolution of 4 cm−1 and all spectra were obtained in the same way in absorption mode in the spectral region 4000-400 cm-1.The interpretation of the spectra was done by analyzing the spectra and comparing the spectral data between cancerous and healthy tissues in order to follow and show the characteristic pattern of the disease. Data analysis was performed with the OMNIC 7.3 software.

#### *2.2.2. Scanning electron microscope*

been reported to mediate lung and liver metastasis. Advanced next-generation sequencing techniques have also been used to interrogate whole cancer genomes at the single-nucleotide level and have distinguished between mutations in breast cancer metastases [12,13]. However, one metastasis may be distinct from another within the same patient accurate prediction of the molecular profile of metastatic disease by profiling the primary tumor is not feasible. In this

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

Fourier transform infrared spectroscopy is a physicochemical, non-destructive, sensitive and reproducible method which provides important information about changes in the molecular structure of the bone due to the disease [15-29]. The advantage of the method is that it needs small amounts of the sample (only few micrograms) and we could study the sample without any preparation, such as coloring or demineralization as it is done in histopathology, since the spectra are based on individual chemical characteristics of the bone. Another important advantage of the infrared spectroscopy is that the method does not require any preparation of the sample, such as coloring or decalcification, as in methods like histopathology, where the samples are decalcified and labeled with color and are analyzed only the changes in the organic phase of the tissues.In infrared spectroscopy, the spectrum is the sum of all the frequencies of the components present and provides information on all components simultaneously [15-21]. Here within it is presented the influence of cancer on the molecular structure of the constituents of the bone (Hydroxyapatite, Collagen and Protein) and the characterization of the spectral differences between healthy and cancerous bones, in order to have a better insight of the

Although breast cancer metastases to skeleton bones are frequent sites of first distant relapse,however the bone samples are not easy to be obtained. Six bone sections from breast metastatic cancer patients (39 and 65 years), who suffered from breast cancer and under‐ went a reconstruction with an osteoarticular allograft, were used for the present study. Small amount of fresh bones (cancellous or/compact), were immersed successively in hydrogen peroxide solution (H2O2) and in acetone, according to a modification method [15-17, 20,30]. Hydrogen peroxide and acetone processing is known to reduce the fat tissue and blood chromophores of fresh bone, but it does not remove the organic components

The conformational and molecular changes of healthy and cancerous bones were recorded using a Nicolet 6700 thermoscientific Transform Infrared (FT-IR) spectrometer, which was connected to an attenuated total reflection (ATR) accessory. This technique is convenient in

setting, novel detection techniques are necessary [14].

process of the disease.

Applications

90

**2.1. Sample preparation**

completely.

**2.2. Sample analysis**

*2.2.1. Infrared spectroscopy*

**2. Materials and methods**

Scanning electron microscopy (SEM) is also a non-destructive method, which allows the investigation of the surfaces of cancerous bone tissues, without any decalcification, coloring or coating. Under these conditions, there is not any change in chemical bonds between mineral and organic phase of the sample.

The distribution of the morphology of samples and bone mineral content were obtained using the (SEM) equipped with a microanalyzer probe EDX (Electron Dispersive X-rays analysis) from Fei Co, Eindhoven, The Netherlands

#### *2.2.3. X-Ray diffraction*

X-Ray diffraction, XRD, was used to identify the crystal structure of hydroxyl apatite and the presence of other calcium phosphate salts, which were produced with the progress of the cancer metastasis and development.

Powdered bone diffraction patterns were recorded using a Siemens D-500 X-Ray diffractom‐ eter based on an automatic adjustment and analysis system. The diffraction interval was of 2θ 5-80o and scan rate of 0.030o /s.

#### **3. Results and discussion**

#### **3.1. Infrared spectroscopic analysis**

In the treatment of breast cancer, the occurrence and growth of distant metastases is the major cause of morbidity and mortality. Long distant metastasis of breast cancer to bones induces micro-fractures changing the patients' quality of life. To understand the mecha‐ nism of the cancer cell dispersive and damaging effects which are induced to bone structure is of high interest in order to study the disease. Figure 1 shows the FT-IR spectra of a) healthy radius bones and b) of cancerous bones from a woman (59 years old) with a primary breast cancer.

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical Applications 92

**Figure 1.** FT-IR spectra of a) healthy bone and b) cancerous bone from a 59 years woman with metastatic bone cancer from breast cancer the original site

Comparison of the two spectra showed considerable changes in the whole spectral range of 3600-400 cm-1. The intensity of the shoulder band near 3550 cm-1 for healthy bones was reduced or disappeared in all cancerous bones. Deconvolution of this band showed that it was double with maxima at 3515 cm-1 and 3400 cm-1, which are dominated by the absorption of stretching vibration of *v*OH functional groups of water and hydroxyapatite, respectively [15-17, 19,20]. The intensities of these bands are sensitive at the demineralization of the bones due to disease cancer and they can show the progress of osteolysis. The broad band in the region 3300-3000 cm-1is made up from the two bands at 3209 cm-1 and 3187cm-1, assigned to NH vibrations [15-30]. In cancerous bone spectra the band at 3209cm-1 shifted to higher wavenumbers at 3277 cm-1 and the 3187 cm-1 was reduced in intensity, but it was not shifted. It seems that in cancerous bones the binding of proteins changed in structure and they did not give neither inter-nor intra-molecular hydrogen bonding of the NH hydrogen bonding leading to the result that decalcification takes place and finally the disease changes the secondary molecular structure of the proteins.

The absorption bands of the symmetric and asymmetric stretching vibrations of methyl (*v*asCH3 and *v*sCH3) groups were found at 2965 cm-1 and 2880 cm-1 and of methylene (*vas*CH2and *vs*CH2) were near 2926 cm-1 and 2854 cm-1, respectively [15-31]. These bands did not shift but their intensities increased for cancerous bones. These changes indicated that the environment of lipids, phospholipids and proteins has changed and that the permeabil‐ ity and fluidity of the membranes have increased, due to the damage induced by the disease and demineralization [15-30].

Interesting was the appearance of a new band in the spectra of cancerous bones at about 1745 cm-1, which was assigned to *v*C=O carbonyl stretching vibration of ester carbonyl groups (RO-C=O) and was attributed to formation of aldehydes [31,32]. It is known that aldehydes are recognized as native "cancer markers" [33]. This carbonyl band was also proposed to charac‐ terize the apoptotic cells [34]. This particular band indicates that lipid peroxidation was one of the pathways during the process of metastasis of bone cancer and could be used as "marker band" for the progression of the disease.This fact leads also to the hypothesis that the immunelike systemis a contribution to the development of metastasis, in agreement with literature data [34].

Considerable changes were also observed in the region 1700-1500 cm-1. This region is known to be characteristic of proteins and is sensitive in order to evaluate the secondary structure of proteins and to distinguish that collagen exists as α-helix [15-17,30-32]. A shift to lower frequencies of the absorption band of Amide I of proteins from about 1650 cm-1 in healthy bones to 1630 cm-1 in cancerous bones was observed. This shift to lower frequencies suggests that the proteins changed their secondary structure from α-helix to random coil due to cancer processing. These results were confirmed also from SEM analysis.

Figure 2 shows the morphology of the cancerous bone. One can see that the bone is rich in fibrils, concerning the damage of collagenous and non-collagenous proteins, as well as the demineralization of the bone. The proteins changed their native structure as shown from the arrows on the points of damaged proteins (Fig. 2C). Image J analysis gives the relative intensity of the pixels which correspond to electron density of the proteins (Fig. D & E). The curves show the analyzed regions at the misfolding points.

**Figure 1.** FT-IR spectra of a) healthy bone and b) cancerous bone from a 59 years woman with metastatic bone cancer

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

Comparison of the two spectra showed considerable changes in the whole spectral range of 3600-400 cm-1. The intensity of the shoulder band near 3550 cm-1 for healthy bones was reduced or disappeared in all cancerous bones. Deconvolution of this band showed that it was double with maxima at 3515 cm-1 and 3400 cm-1, which are dominated by the absorption of stretching vibration of *v*OH functional groups of water and hydroxyapatite, respectively [15-17, 19,20]. The intensities of these bands are sensitive at the demineralization of the bones due to disease cancer and they can show the progress of osteolysis. The broad band in the region 3300-3000 cm-1is made up from the two bands at 3209 cm-1 and 3187cm-1, assigned to NH vibrations [15-30]. In cancerous bone spectra the band at 3209cm-1 shifted to higher wavenumbers at 3277 cm-1 and the 3187 cm-1 was reduced in intensity, but it was not shifted. It seems that in cancerous bones the binding of proteins changed in structure and they did not give neither inter-nor intra-molecular hydrogen bonding of the NH hydrogen bonding leading to the result that decalcification takes place and finally the disease changes the secondary molecular structure

The absorption bands of the symmetric and asymmetric stretching vibrations of methyl (*v*asCH3 and *v*sCH3) groups were found at 2965 cm-1 and 2880 cm-1 and of methylene (*vas*CH2and *vs*CH2) were near 2926 cm-1 and 2854 cm-1, respectively [15-31]. These bands did not shift but their intensities increased for cancerous bones. These changes indicated that the environment of lipids, phospholipids and proteins has changed and that the permeabil‐ ity and fluidity of the membranes have increased, due to the damage induced by the disease

Interesting was the appearance of a new band in the spectra of cancerous bones at about 1745 cm-1, which was assigned to *v*C=O carbonyl stretching vibration of ester carbonyl groups (RO-C=O) and was attributed to formation of aldehydes [31,32]. It is known that aldehydes are recognized as native "cancer markers" [33]. This carbonyl band was also proposed to charac‐

from breast cancer the original site

Applications

92

of the proteins.

and demineralization [15-30].

**Figure 2.** SEM morphology of metastatic breast cancerous bone (scale 500 μm, Mag. 100x). B Selected region rich in proteins, C: Higher magnitude 800x (scale 50 μm), which shows the misfolding of proteins. D & E ImageJ analysis of the folding regions

The Amide II band at 1555 cm-1, which is consisted from δNH in-plane and *v*CN stretching vibrations, is very sensitive to environmental changes. It was found that the intensity of this band decreases and in almost all patients and sifts to lower wavenumbers.The ratio of the bands of [Amide I1650]/[Amide II1550] decreases with increasing the grade of cancer and it was found in the patients healthy bones to be equal to 1.11,whereas in the cancer it was 1.3. Although the differences are very small they are significant and it was found also in breast

cancer and colon cancer [18;21].These changes represent the "structural change and abnor‐ mality" of proteins, induced from cancer disease, which decrease the probability of remineralization of the bones and thus increases the fragility of the bones.

Figure 1 clearly shows the absorption band at 1418 cm-1, which is assigned to stretching vibration of carbonate anions (*v*CO3 2-) of hydroxyapatite containing carbonate ions. Thisband is also reduced in intensity confirming the substitution of phosphate anions with carbonates in hydroxyapatite following the total demineralization of cancerous bones [17,20].

The band at about 1040 cm-1 refers to stretching vibrations of *v*C-O coupled with the bending vibration of δC-OH groups of glycogenic bonds [36,37]. We found that the intensity of this band increases in the spectra of cancerous bones. The *v*OH absorption bands are sensitive upon isotopic substitution (deuteration), concerning the substitution of hydrogen atoms with deuterium in the C-OH groups of glucose (spectra not shown here). The increasing amount of glycogenic materials inhibits the mineralization of the bones [38]. From the conformational protein folding changes in combination with the increase glycogenic bonds (starch) it is suggested the production of amyloid-like proteins [39]. The formation of fibrils is also well shown in SEM morphology (Figure 2).

Furthermore, the spectra show characteristic differences between healthy and cancerous bone in the regions 1200-900 cm-1and 600-500 cm-1, where the phosphate groups (*v*3PO4 3-) of hydrox‐ yapatite absorb. The characteristic bands of *v*3PO4 3-and *v*4PO4 3-in cancerous bones have been dramatically decreased due to cancer, proving that osteolysis of the bones is taking place. These findings show that in cancerous bone a progressive mineral deficiency occurs in agreement with clinical and histological analyses indicating that the bone destruction is mediated by the osteoclasts [40]. Moreover, in the fingerprint region of the cancerous spectra between 1200-900 cm-1 are coupled also the bands which are assigned to phosphodiester C-O-PO2 of DNA [23-25,41-43]. These bands were not observed in normal bone tissue, maybe they were masked because of high concentration of hydroxyapatite.

#### **3.2. FT-IR spectra after removal of organic components**

To understand further the mechanisms of osteolysis of bone from metastatic cancer the boneswere washed using organic solvents to eliminate the organic mass of the bones. Figure 3 shows the spectra of the bone before (spectrum a) and after elimination of dissolved organic components (spectrum b).

Comparison of the two spectra shows that after treatment with hexane all the organic com‐ ponents with low molecular weight have been dissolved and disappeared from the sample and are not shown in their spectra. It is interesting to note that the bands in the region 1100-900 cm-1 and 700-500 cm-1, where the bands of hydroxyapatite absorb, the bands of *v*PO4 3-have almost disappeared after treatment with hexane. From these findings it was suggested that the bands haveresulted from other phosphate proteins, which also have phosphate groups with hydroxyapatite or fragments of phospholipids. However, these bands do not show that there is present biological hydroxyapatite. In addition, XRD analysis revealed that cancerous bones were not consisted from biological hydroxyapatite, but there was apatite rich in organic phase.

An FT-IR Spectroscopic Study of Metastatic Cancerous Bones http://dx.doi.org/10.5772/58910 95

cancer and colon cancer [18;21].These changes represent the "structural change and abnor‐ mality" of proteins, induced from cancer disease, which decrease the probability of re-

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

Figure 1 clearly shows the absorption band at 1418 cm-1, which is assigned to stretching

is also reduced in intensity confirming the substitution of phosphate anions with carbonates

The band at about 1040 cm-1 refers to stretching vibrations of *v*C-O coupled with the bending vibration of δC-OH groups of glycogenic bonds [36,37]. We found that the intensity of this band increases in the spectra of cancerous bones. The *v*OH absorption bands are sensitive upon isotopic substitution (deuteration), concerning the substitution of hydrogen atoms with deuterium in the C-OH groups of glucose (spectra not shown here). The increasing amount of glycogenic materials inhibits the mineralization of the bones [38]. From the conformational protein folding changes in combination with the increase glycogenic bonds (starch) it is suggested the production of amyloid-like proteins [39]. The formation of fibrils is also well

Furthermore, the spectra show characteristic differences between healthy and cancerous bone

dramatically decreased due to cancer, proving that osteolysis of the bones is taking place. These findings show that in cancerous bone a progressive mineral deficiency occurs in agreement with clinical and histological analyses indicating that the bone destruction is mediated by the osteoclasts [40]. Moreover, in the fingerprint region of the cancerous spectra between 1200-900

[23-25,41-43]. These bands were not observed in normal bone tissue, maybe they were masked

To understand further the mechanisms of osteolysis of bone from metastatic cancer the boneswere washed using organic solvents to eliminate the organic mass of the bones. Figure 3 shows the spectra of the bone before (spectrum a) and after elimination of dissolved organic

Comparison of the two spectra shows that after treatment with hexane all the organic com‐ ponents with low molecular weight have been dissolved and disappeared from the sample and are not shown in their spectra. It is interesting to note that the bands in the region 1100-900 cm-1 and 700-500 cm-1, where the bands of hydroxyapatite absorb, the bands of *v*PO4

almost disappeared after treatment with hexane. From these findings it was suggested that the bands haveresulted from other phosphate proteins, which also have phosphate groups with hydroxyapatite or fragments of phospholipids. However, these bands do not show that there is present biological hydroxyapatite. In addition, XRD analysis revealed that cancerous bones were not consisted from biological hydroxyapatite, but there was apatite rich in organic phase.

3-and *v*4PO4

in the regions 1200-900 cm-1and 600-500 cm-1, where the phosphate groups (*v*3PO4

cm-1 are coupled also the bands which are assigned to phosphodiester C-O-PO2

in hydroxyapatite following the total demineralization of cancerous bones [17,20].

2-) of hydroxyapatite containing carbonate ions. Thisband

3-) of hydrox‐

 of DNA

3-have

3-in cancerous bones have been

mineralization of the bones and thus increases the fragility of the bones.

vibration of carbonate anions (*v*CO3

Applications

94

shown in SEM morphology (Figure 2).

yapatite absorb. The characteristic bands of *v*3PO4

because of high concentration of hydroxyapatite.

components (spectrum b).

**3.2. FT-IR spectra after removal of organic components**

**Figure 3.** FT-IR spectra of cancerous bone tissues in the region 4000-400 cm-1; a: without any preparation, b: after elimi‐ nation of the organic components of the bone. The arrow shows free calcium phosphate.

The size of the crystals at 2θ=25,85° was found to be 15 nm much smaller than the normal bone's hydroxyapatite which is 20-25 nm [44].

The SEM analysis of cancerous bones before treatment with hexane is given in Figure 4A. The relative element concentration of the white spot and of the dark region, are shown in the Figure.

**Figure 4.** SEM-EDXmorphology and composition of metastatic breast cancerous bone before treatment: A; on white spot and B; on black area. Scale 100 μm, Mag 400x

From EDX chemical analysis it was found that the extent area of the bone was poor in calcium and only the spread white spots were rich in minerals. By washing the bone with hexane the morphology of the surface changed (Figure 5). Figure 5 gives the SEM morphology of the bone after washing it with hexane. Figure 5Agives the relative concentration of the chemical elements of the white spots. It is obvious that the concentration of calcium of white spot is significantly reduced. The same picture was found for the extent area of the sample, where the calcium has almost disappeared (Figure 5B).

**Figure 5.** SEM-EDX results, composition of metastatic breast cancerous bone after treatment A; on white spot and B; on balk area and C SEM morphology of the tissue. Scale 100 μm, Mag 400x

These SEM results are in agreement with infrared spectroscopic results, which suggest that the mineral phase maybe a mixture of calcium salts of phosphate together with calcium carbonate, but not a biological hydroxyapatite. It was found from XRD analysis at 2θ=25,85ο that the crystal of hydroxya showed also that the size of the hydroxyapatite crystals is 15 nm. This size is smaller than in healthy bones, which in adults was found 20-25 nm [44, 45].

#### **4. Conclusions**

The results obtained here using FT-IR spectroscopy and SEM analysis have shown that cancerous bone from metastatic breast cancer leads to considerable changes in bone density, especially in the structure of biological apatite that decreases dramatically or even it is destroyed due to osteolysis.Proteins change their secondary structure from α-helix to random coil and aldehydes are produced during cancer metabolism.The intensity of the aldehyde band indicates the magnitude of the damage caused by the cancer. Furthermore, It is also noticed that the proportion of inorganic mass is reduced in comparison to the organic matrix upon cancer invasion of the bones.

Furthermore, FT-IR spectroscopy can provide more information than histopathology, since it does not need any decalcification for analysis. From a clinical point of view, major disadvan‐ tages of bone decalcification are the laborious procedure that proceeds only slowly with incubation times up to several weeks depending on the extent of mineralization, the frequent loss of immune-reactivity, and the acid hydrolysis of DNA. In addition, excessive decalcifica‐ tion may lead to negative or non-diagnostic biopsy of the bone specimen (Rey, 1991). In this case, FT-IR spectroscopy is a rapid technique and it provides much more information com‐ pared to histology for a fast diagnosis of bone tumors.

## **Author details**

From EDX chemical analysis it was found that the extent area of the bone was poor in calcium and only the spread white spots were rich in minerals. By washing the bone with hexane the morphology of the surface changed (Figure 5). Figure 5 gives the SEM morphology of the bone after washing it with hexane. Figure 5Agives the relative concentration of the chemical elements of the white spots. It is obvious that the concentration of calcium of white spot is significantly reduced. The same picture was found for the extent area of the sample, where the

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

**Figure 5.** SEM-EDX results, composition of metastatic breast cancerous bone after treatment A; on white spot and B; on

These SEM results are in agreement with infrared spectroscopic results, which suggest that the mineral phase maybe a mixture of calcium salts of phosphate together with calcium carbonate, but not a biological hydroxyapatite. It was found from XRD analysis at 2θ=25,85ο that the crystal of hydroxya showed also that the size of the hydroxyapatite crystals is 15 nm. This size is smaller than in healthy bones, which in adults was found 20-25 nm [44, 45].

The results obtained here using FT-IR spectroscopy and SEM analysis have shown that cancerous bone from metastatic breast cancer leads to considerable changes in bone density, especially in the structure of biological apatite that decreases dramatically or even it is destroyed due to osteolysis.Proteins change their secondary structure from α-helix to random coil and aldehydes are produced during cancer metabolism.The intensity of the aldehyde band indicates the magnitude of the damage caused by the cancer. Furthermore, It is also noticed

calcium has almost disappeared (Figure 5B).

Applications

96

balk area and C SEM morphology of the tissue. Scale 100 μm, Mag 400x

**4. Conclusions**

J. Anastassopoulou1\*, Μ. Kyriakidou1 , S. Kyriazis1 , T.H. Kormas2 , A.F. Mavrogenis3 , V. Dritsa1 , P. Kolovou1 and T. Theophanides1

\*Address all correspondence to: ianastas@central.ntua.gr

1 National Technical University of Athens, Chemical Engineering Department, Radiation Chemistry & Biospectroscopy, Athens, Greece

2 Anticancer Hospital "AgiosSavvas", Orthopaedic Department, Athens, Greece

3 First Department of Orthopaedics, Athens University Medical School, ATTIKON University Hospital, Athens, Greece

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[5] Steeg PS. Tumor metastasis mechanistic insights and clinical challenges. Nat Med

Infrared Spectroscopy - Anharmonicity of Biomolecules, Crosslinking of Biopolymers, Food Quality and Medical

[6] Welch DR. Do we need to redefine a cancer metastasis and staging definitions?

[7] Comen E, Norton L, Massagué J. Clinical implications of cancer self-seeding. Nature

[8] Klein CA. Parallel progression of primary tumours and metastases. Nat Rev Cancer

[9] Paget S. The distribution of secondary growths in cancer of the breast. Cancer Meta‐

[10] Shuker DEG. The Cancer Clock. In: Missailidis S.(ed), J Wiley & Sons, Ltd., 2007. p.

[11] Lu C, Onn A,Vaporciyan AA, Chang JY, Glisson BS, Wistuba II, Rothand JA, Herbst RS.Cancer Medicine. In: Hong WK, Bast RC, Hait WN, Kufe DW, Pollock RE, Weich‐ selbaum RR, Holland JF, Frei E.(eds). Holland-FreiPeople's Medical Publishing

[12] Shah SP, Morin RD, Khattra J, Prentice L, Pugh T, Burleigh A, Delaney A, Gelmon K, Guliany R, Senz J, Steidl C, Holt RA, Jones S, Sun M, Leung G, Moore R, Severson T, Taylor GA, Teschendorff AE, Tse K,Turashvili G, Varhol R, Warren RL, Watson P, Zhao Y, Caldas C, Huntsman D, Hirst M, Marra MA, Aparicio S. Mutational evolu‐ tion in a lobular breast tumour profiled at single nucleotide resolution. Nature 2009;

[13] Ding L, Ellis MJ, Li S, Larson DE, Chen K, Wallis JW. Genome remodelling in a basal-

[14] Marino N, Woditschka S, Reed LT, Nakayama J, Mayer M, Wetzel MP, Steeg PS. Breast cancer metastasis: issues for the personalization of its prevention and treat‐

[15] Petra M, Anastassopoulou J, Theologis T, Theophanides T. Synchrotron micro-FT-IR spectroscopic evaluation of normal paediatric human bone. Journal of Molecular

[16] Kolovou P, Anastassopoulou J. Synchrotron FT-IR spectroscopy of human bones.The effect of aging. In : V. Tsakanov and H. Wiedemann (eds), Brilliant Light in Life and

[17] Anastasssopoulou J, Kolovou P,Papagelopoulos P, Theophanides T. In:heophanides

[18] Anastassopoulou J, Boukaki E, Arapantoni P, Valavanis C, Konstadoudakis S, Conti C, Ferraris P, Giorgini G, Sabbatini, S, Tosi G. In: Tsakanov V. and Wiedemann H(eds), Brilliant Light in Life and Material Sciences, Springer, 2008. p. 273-278.

T.(ed). Infrared Spectroscopy/Book 2, Intech Publications.2012. p259-271

like breast cancer metastasis and xenograft. Nature 2010; 464: 999-1005.

ment. American Journal of Pathology 2013; 183(4):1084-95.

2006; 12: 895-904.

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2009; 9:302-312.

3-24.

461:809-813.

Structure 2005; 733: 101-110.

Material Sciences. Springer; 2007. p. 267-272

stasis Rev 1989;8:98-101.

Breast Disease 2006; 26: 3-12.

Reviews Clinical Oncology 2011; 8: 369-377.

House-USA: Shelton, CT, 2008. p999-1043.


> ALDH1 is a marker of normal and malignant human mammary stem cells and a pre‐ dictor of poor clinical outcome.Cell Stem 2007; 1: 555–567.

