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Publicly Available Published by De Gruyter May 29, 2018

Thermal Shifts and Electron-Phonon Coupling Parameters for the Three Luminescence Lines of 5DJ7FJ in SrFCl:Sm2+ Crystal

  • Yang Mei EMAIL logo , Hong-Gang Liu and Wen-Chen Zheng

Abstract

The thermal blue shifts of three spectral lines E1(5D07F0), E2(5D07F1), and E3(5D17F0) in SrFCl:Sm2+ crystal are investigated by a complete expression consisting of both the static contribution due to lattice thermal expansion and the vibrational contribution owing to electron-phonon interaction. The obtained true electron-phonon coupling parameters α′ in both sign and magnitude are considerably different from the apparent electron-phonon coupling parameters α acquired in the previous paper by considering only the vibrational contribution. It is suggested that differing from the simple expression including only the vibrational contribution (many authors thought that it cannot be used to explain the thermal blue shifts), the complete expression containing both the vibrational and static contributions is effective in the studies of thermal shift (whether red shift or blue shift) and true electron-phonon coupling parameter for a spectral line in crystals.

1 Introduction

There are many luminescence lines in crystals doped with rare-earth ions. So, they can be used as the phosphor, luminescence (including upconversion and downconversion), and laser materials [1], [2], [3], [4]. The spectral lines can be shifted under pressure and temperature, so these crystals can also be served as the pressure sensor and temperature sensor [5], [6], [7], [8], [9], [10]. For the sake of better applications, the temperature dependences (or thermal shifts) and pressure dependences of spectral lines in crystals doped with rare-earth ions have been widely studied [5], [6], [7], [8], [9], [10], [11], [12], [13]. For example, the temperature and also pressure dependences of the three spectral lines E1(5D07F0), E2(5D07F1), and E3(5D17F0) in SrFCl:Sm2+ crystal were measured by Kuznetsov et al. [12], [13]. They found that the three emission lines Ei (i=1, 2, 3) show the thermal blue shifts [13]. However, a lot of studies found that many spectral lines in crystals doped with transition-metal and rare-earth ions show the thermal red shifts [14], [15], [16], [17], [18], [19], [20], [21], [22]. These thermal red shifts are often explained or described by the simple expression based on the Raman two-phonon process concerning Debye model [20], [21], i.e.

(1)ΔE(T)=α(TTD)40TD/Tx3ex1dx

where TD is the Debye temperature and α is the electron-phonon coupling parameter. This expression takes account of only the vibrational contribution due to electron-phonon interaction to the thermal shift. In the above expression, the electron-phonon coupling parameter α in thermal red shift is negative [20], [23], [24] (note: in some papers [17], [18], [19], [21], [25], a very similar expression is applied except the coefficient changes from α to −α, or only the magnitude, i. e., the absolute value of thermal shift is considered; thus, the parameters α in thermal red shift are written as positive). For the thermal blue shift, the sign of parameter α in (1) should be positive, in contrary to that of thermal red shift. Because the vibrational contribution only results in the red shift and so the parameter α should be negative, many authors [17], [18], [21], [22] thought that (1) cannot be used to explain the thermal blue shift.

Actually, the observed thermal shift of a spectral line in crystals comes from two contributions, the above vibrational contribution and the static contribution due to lattice thermal expansion [13], [24]. By using the pressure dependences of the three spectral lines Ei in SrFCl:Sm2+ crystal [12] and the compressibility KT and thermal expansion coefficient αvol. of SrFCl, Kuznetsov et al. [13] calculated the static contributions (dEidT)st.=[αvib.KT(dEidP)T] for the three spectral lines Ei near room temperature. Based on these, the vibrational contributions (dEidT)vib. are also acquired from the observed temperature dependences (dEidT)obs.. The values of (dEidT)st. and (dEidT)vib. for the three spectral lines Ei in SrFCl:Sm2+ are listed in Table 1. From these values, they concluded that the thermal blue shifts of the three spectral lines Ei in SrFCl:Sm2+ are due to the static contribution being larger than the vibrational one [13]. Unsatisfactorily, they [13] still applied (1) to describe these thermal blue shifts, and so the obtained parameters α for the three spectral lines Ei in SrFCl:Sm2+ crystal are positive rather than negative (see Tab. 1). Obviously, these apparent electron-phonon coupling parameters α obtained in Ref. [13] in both sign and magnitude are doubtful because in (1), only the vibrational contribution is included. To get rid of these drawbacks, in this paper, we investigate the thermal blue shifts of the three spectral lines Ei in SrFCl:Sm2+ crystal by means of a complete and rational expression where both the vibrational and static contributions to thermal shift are contained. On the basis of the studies, the true electron-phonon coupling parameters α′ for the three spectral lines Ei in SrFCl:Sm2+ are estimated reasonably, and the results are discussed.

Table 1:

The static and vibrational contributions of temperature dependence and their ratios t, the apparent and true electron-phonon coupling parameters α and α′, and the static parameters A for the three spectral lines E1(5D07F0), E2(5D07F1), and E3(5D17F0) in SrFCl:Sm2+ crystal.

Line(dEidT)st. (cm−1/K)a(dEidT)st. (cm−1/K)at (cm−1)α (cm−1)α′ (cm−1)A (cm−1)
E10.0749−0.0275−2.7236−2157
E20.0666−0.0421−1.5822−3860
E30.0745−0.0275−2.7132−1951
  1. aRef. [13].

2 Calculation

The complete expression of thermal shift of a spectral line in crystals composed by both the static and vibrational contributions is written as [24]

(2)ΔE(T)=(A+α)(TTD)40TD/Tx3ex1dx

where A is a parameter presenting the static contribution and α′ is the true rather than apparent electron-phonon coupling parameter. The ratio t=A/α′ implies the relative importance of static contribution, and according to the definitions of A and α′, it can be given as

(3)t=Aα=ΔEst.(T)ΔEvib.(T)=(dEidT)st.(dEidT)vib.

For the three spectral lines Ei in SrFCl:Sm2+ crystal, the calculated ratios t from the values of (dEidT)st. and (dEidT)vib. (see Tab. 1) are also collected in Table 1.

As (1) and (2) are basically the same except that the coefficient α is changed as (A+α′), we have

(4)α=(A+α)=tα+α=(t+1)α

From the values of α and t (see Tab. 1) for the three spectral lines in SrFCl:Sm2+ crystal, the true electron-phonon coupling parameters α′ and hence the static parameters A for the three spectral lines can be computed, and the outcomes are given in Table 1.

3 Discussion

From (1) and (2), one can find that the signs of parameters A, α′, and α are related to the direction of thermal shift; that is to say, the positive sign implies the blue shift, whereas the negative sign means the red shift. So, for the three spectral lines in SrFCl:Sm2+ crystal, even the observed thermal shifts are blue shifts, the negative signs of true electron-phonon coupling parameter α′ indicate that the vibrational contribution still results in the thermal red shift, as found for the thermal red shifts of many spectral lines in crystals [20], [23], [24]. This manifests that whether in thermal red shift or in blue shift, the true electron-phonon coupling parameter α′ should be negative (contrarily, the positive signs of the apparent electron-phonon coupling parameters α obtained from (1) in Ref. [13] imply that the vibrational contribution leads to the thermal blue shift; it is not suitable). The observed thermal blue shift for the three spectral lines in SrFCl:Sm2+ crystal is due to the static contribution (which results in the thermal blue shift because of the positive sign of static parameter A) being larger than the vibrational one (i.e. the static parameter A in magnitude is larger than the parameter α′; see Tab. 1). The drawback shown in Section 1 is therefore overcome.

As can be seen in Table 1, by using the complete expression in (2), the estimated true electron-phonon coupling parameters α′ in both magnitude and sign are different from the corresponding apparent parameters α obtained by considering only the vibrational contribution [i.e. from (1)]. It is suggested that the complete expression containing both the vibrational and static contributions is effective in the studies of thermal shift (whether red shift or blue shift) of a spectral line in crystals.

Acknowledgments

This work was financially supported by the Project of Education Department in Sichuan Province (Grant No. 17ZB0206) and the National Natural Science Foundation of China (Funder Id: 10.13039/501100001809, Grant No. 11404229).

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Received: 2018-03-15
Accepted: 2018-04-20
Published Online: 2018-05-29
Published in Print: 2018-07-26

©2018 Walter de Gruyter GmbH, Berlin/Boston

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