Mechanoluminescence of ZnS:Mn phosphors excited by hydrostaticpressure steps and pressure pulses

V.K. Chandra a, B.P. Chandra b,n,1, Piyush Jha b

a Department of Electrical and Electronics Engineering, Chhatrapati Shivaji Institute of Technology, Shivaji Nagar, Kolihapuri, Durg 491001, C.G., Indiab Department of Postgraduate Studies and Research in Physics and Electronics, Rani Durgavati University, Jabalpur 482001, M.P., India

a r t i c l e i n f o

Article history:Received 27 November 2013Received in revised form27 June 2014Accepted 29 June 2014Available online 5 July 2014

Keywords:MechanoluminescenceTriboluminescenceHydrostatic pressureSensorZnS:Mn

a b s t r a c t

When a hydrostatic pressure step is applied rapidly on ZnS:Mn phosphor introduced into a pressure cellas oil suspension, initially the mechanoluminescence (ML) intensity increases linearly with time, attainsa peak value for a particular time, and then it decreases with time (G. Alzetta, N. Minnaja, S. Santucci,Nuovo Cimento 23, 1962, 910). When a hydrostatic pressure pulse is applied onto ZnS:Mn phosphor, thentwo ML pulses of equal intensity are emitted; one during the application of pressure and the otherduring the release of pressure. In case of ZnS:Mn phosphor, at low hydrostatic pressure the energyproduced during the electron–hole recombination excites the Mn2þ centres; however, at highhydrostatic pressure, the impact of accelerated electrons with the Mn2þ centres causes the lightemission. Considering the piezoelectrically-induced detrapping model of ML at low pressure and thepiezoelectrically-induced impact excitation model of ML at high pressure, expressions are derived fordifferent characteristics of ML, in which a good agreement is found between the theoretical andexperimental results. At low hydrostatic pressure in the range from 3 MPa to 40 MPa, piezoelectrically-induced detrapping model of ML becomes applicable in ZnS:Mn phosphors; while at high hydrostaticpressure beyond 40 MPa, the piezoelectrically-induced impact excitation model of ML becomesapplicable. The ML induced by hydrostatic pressure can be used for sensing both the magnitude andrise time of applied hydrostatic pressure.

& 2014 Published by Elsevier B.V.

1. Introduction

Mechanoluminescence (ML) is the phenomenon of cold lightemission induced by any mechanical action on solids. The lightemissions induced by elastic deformation, plastic deformation andfracture of solids are called elastico ML (EML), plastico ML (PML)and fracto ML (FML), respectively [1,2]. As ZnS:Mn phosphorexhibits intense elastico ML, plastico ML and fracto ML, it hasbeen a model material for ML studies and considerable works havebeen reported on its ML [3]. It has been shown that the ML of ZnS:Mn phosphors has potential for their use in stress sensor, damagesensor, impact sensor, light sources, ML displays, etc. [2,4–12].

The ML induced by hydrostatic pressure is interesting becauseof the following reasons: (i) hydrostatic pressure provides a verysystematic and simple technique for inducing ML in solids [13],(ii) the ML induced by hydrostatic pressure provides a simple andlow cost method to determine the amplitude and rise time of the

hydrostatic pressure (shown in the present paper), (iii) the ML inII–VI semiconductors arises due to charged dislocation movementsand also due to piezoelectrification, whereby the ML measurementin the hydrostatic pressure eliminates the ML emission arising dueto the movement of charged dislocations [1,2], (iv) least studieshave been made on the ML induced by hydrostatic pressure andthe salient features of the hydrostatic pressure induced ML are notunderstood till now [1,2], and (v) the ML induced by hydrostaticpressure has not been studied on the basis of the newly developedmechanism of ZnS:Mn [11].

Alzetta et al. [13] have reported interesting experimentalresults on the hydrostatic pressure induced ML of ZnS:Mn phos-phors. They have mentioned that, as the variation of pressurecauses shift of the equilibrium co-ordinate to a smaller value, it ispossible that during such a pressure variation transitions to highervibrational levels may be expected, and consequently ML mayappear during the application of hydrostatic pressure. The mea-surement of the pressure—coefficient of shift of the energycorresponding to the peak of the photoluminescence suggeststhat the ground and excited states will be within an energy of kTfrom each other at hydrostatic pressures ranging from 50 to70 GPa (or from 500 to 700 kbar) [14,15]. However, in ZnS:Mn

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Physica B

http://dx.doi.org/10.1016/j.physb.2014.06.0380921-4526/& 2014 Published by Elsevier B.V.

n Corresponding author. Tel.: þ91 771 2263650.E-mail address: bpchandra4@yahoo.co.in (B.P. Chandra).1 Present Address: Emeritus Professor, School of Studies in Physics and

Astrophysics, Pt. Ravishankar Shukla University, Raipur 492010, C.G., India.

Physica B 452 (2014) 23–30

phosphors the ML starts appearing from very low value of theapplied stress of the order of 3 MPa [11] whereby the orbitals ofthe ground and excited states cannot be significantly affected.Therefore, the ML of ZnS:Mn phosphors may not arise due to thepressure variation transitions to higher vibrational levels. It hasbeen reported that the total ML intensity IT can be expressed bythe relation, IT¼ I0exp[γ(ΔP2)], where ΔP is the change in pressure,and I0 and γ are constants [13]. This equation indicates no thresh-old pressure for the ML emission, and moreover, it shows that thetotal ML intensity IT should increase exponentially with the squareof the applied pressure P. Practically, it has been found that the MLemission starts after a threshold pressure of nearly 3 MPa [11] andfor high values of pressure the total ML intensity tends to attain asaturation value [13] (see Fig. 5 of the present paper). Further-more, the ML model based on pressure variation transitions tohigher vibrational levels is also not able to explain the MLemission during release of pressure. Thus, there is a need ofinvestigating the hydrostatic pressure dependence of the totalML intensity of ZnS:Mn phosphors on the basis of recentlyinvestigated suitable model for the ML of ZnS:Mn phosphor. Thehydrostatic pressure dependence of the ML of ZnS:Mn phosphor isnot understood till now. The present paper explores the mathe-matical studies made on the ML induced by the application ofhydrostatic pressure steps and pressure pulses to ZnS:Mn phos-phors on the basis of the piezoelectrically-induced detrappingmodel of ML. Furthermore, a comparison between the mathema-tical and experimental results is made, in which a good agreementis found. The present paper reports for the first time that, for thehigh value of the hydrostatic pressure, the ML in ZnS:Mn phosphorarises due to the impact excitation of Mn2þ ions.

In recent years, ZnS:Mn phosphors have been found to be amost important mechanoluminescent material, which has poten-tial for many mechano-optical devices [2,4–12], and therefore, aclear understanding of the pressure dependence of the MLintensity of ZnS:Mn phosphors is required. Recently, Jeong et al.[9,10] have demonstrated highly bright and durable mechanolu-minescent flexible composite films with a brightness of E120 cd/m2 and durability over E100,000 repeated mechanical stresses byusing a combination of ZnS:Cu particles and polydimethylsiloxane(PDMS). They have shown that the degradation of composite filmfor high values of stretching can be caused by the reduced stresstransfer ratio between PDMS and phosphor particles due to thepermanent weakening of contact between the components. It isexpected that the use of hydrostatic pressure technique for the MLexcitation in phosphors introduced into a pressure cell either as anoil suspension or with other liquids may solve the problem relatedto the degradation of composite film for high values of stretching.

2. Piezoelectrically-induced detrapping model of ML

When a hydrostatic pressure is applied the dislocations cannotmove, therefore, the ML emission in ZnS:Mn may not be due to themovement of charged dislocations. Chandra et al. [11] havereported that the ML in ZnS:Mn phosphors is caused by thepiezoelectrification of ZnS crystals [11]. The piezoelectrically-induced detrapping model of ML in ZnS:Mn phosphors can beunderstood with respect to the following points:

(i) As ZnS:Mn crystal is non-centrosymmetric, the application ofpressure produces piezoelectric field in the crystals [16],whereby the piezoelectric field near activator ions or otherimpurities may be high due to the change in the localstructure [17,18] and due to the presence of the photo-generated electric dipoles formed by the trapping of chargedcarriers in the crystals [11].

(ii) The local piezoelectric field may reduce the trap-depth of thecarriers [19,20] or it may cause the band bending [19,21,22].

(iii) In the case of decrease in trap-depth of the carriers, thermaldetrapping of the carriers may be produced [19,20]. In thecase of band bending, the trapped charge carriers may tunnelto the respective band [19,21,22].

(iv) In the case of ZnS:Mn phosphor, at low hydrostatic pressureless piezoelectric field is produced, in which the detrapping oftraps takes place and the detrapped electrons move in theconduction band. Subsequently, the energy produced duringthe electron–hole recombination may excite the Mn2þ cen-tres and the de-excitation may give rise to the luminescence.At high hydrostatic pressure, high piezoelectric field will beproduced, in which the electrons in the conduction band willbe accelerated and their subsequent impact with the Mn2þ

centres may cause the excitation and subsequently lightemission will take place during the de-excitation [11].

3. Mathematical approach to the ML induced by application ofhydrostatic pressure on ZnS:Mn phosphors

3.1. Low values of the applied pressure

The unique property of ZnS:Mn and ZnS:Cu microcrystals isthat, for low value of applied pressure their ML is repetitive[5,13,23–25]. Alzetta et al. [13] have measured the ML inducedby the application of hydrostatic pressure on ZnS:Mn phosphors,in which the phosphor was introduced into a pressure cell eitheras an oil suspension or with other liquids, and subjected to rapidcompression through a piston acted on with electromagnets.

It has been found that the elastico ML of ZnS:Mn is directlyrelated to the mechanical energy given to the materials [26]. Asthe mechanical energy cannot directly excite the luminescencecentres, it seems that the ML of ZnS:Mn should be related to theconversion of mechanical energy into electrical energy, followedby the conversion of electrical energy into light energy. In the MLmeasurement induced by the hydrostatic pressure, ZnS:Mn phos-phors of micron size are introduced into a pressure cell as oilsuspension, in which each microcrystallite may be considered as amechanoluminescence cell. When a pressure P is applied, thencharges are developed on the surfaces of all the crystallites due tothe bulk piezoelectrification and local piezoelectrification, and theaverage surface charge Q developed on the surface of each crystal-lite will be given by, Q¼d0P, where d0 is the local piezoelectricconstant of the crystal. It has been reported that, in the thin filmelectroluminescence of ZnS:Mn, the total number of photonsemitted is directly related to the total electrostatic energy[27,28]. Thus, the total elastico ML of ZnS:Mn phosphors in oilsuspension may also be related directly to the total electrostaticenergy of the crystallites. This will become possible if the totalnumber nt of electrons detrapped from the filled electron trapswill be directly proportional to the electrostatic energy of themechanoluminescent system. In hydrostatic pressure cell thecrystallites of ZnS:Mn phosphors are suspended in oil, in whicheach crystallite acts as a mechanoluminescence cell. If Q is theaverage surface charge density of a crystallite at any time t, C theaverage capacity of a crystallite, Nc the total number of crystallitesin the pressure cell, then the total number of the detrapped chargecarriers can be expressed as

nt ¼DNcðQ�QthÞ2

2C

" #or;nt ¼ aNcðQ�QthÞ2 ¼ aNcd

2oðP�PthÞ2 ð1Þ

where D is a constant, Qth the threshold charge for the MLemission, d0 the local piezoelectric constant, P the applied

V.K. Chandra et al. / Physica B 452 (2014) 23–3024

pressure, Pth the threshold pressure for the ML emission, Q¼d0P,Qth¼d0Pth, and a¼D/2C.

In fact, the piezoelectric field F¼BQ (where B is a correlatingfactor between F and Q) produced during the application ofpressure causes the detrapping of charge carriers. As thedetrapped electrons reach the conduction band, the rate dnt/dt ofdetrapping of electrons will be equal to the rate of generation g ofelectrons in the conduction band. Thus, by differentiating Eq. (1),we get

g ¼ dnt

dt¼ 2aNcd

2oðP�PthÞ _P ð2Þ

where _P¼dP/dt.If τr is the time constant for the rise of the hydrostatic pressure,

then the rise of pressure with time can be expressed as

P ¼ P0½1�expð�ξtÞ� ð3Þwhere ξ¼1/τr is the rate constant for the rise of pressure and P0 isthe final value of pressure in the case of pressure steps and peakvalue of the pressure in the case of pressure pulses.

From Eq. (3), dP/dt can be expressed as

dPdt

¼ _P ¼ ξP0expð�ξtÞ ð4Þ

If td is the time to attain the threshold pressure Pth or the delaytime between the time of application of pressure and the time ofonset of ML emission, then using Eq. (3), we can write

Pth ¼ P0½1�expð�ξtdÞ� ð5ÞSubstituting the values of P, _P and Pth, from Eqs. (3)–(5),

respectively in Eq. (2), we get

g ¼ 2aNcd2oξexpð�2ξtdÞP2

0½expf�ξðt�tdÞg�expf�2ξðt�tdÞg� ð6Þ

If τ is the lifetime of electrons in the conduction bands, then wecan write the following rate equation

dðΔnÞdt

¼ g�Δnτ

¼ 2aNcd2oξP

20expð�2ξtdÞ½expf�ξðt� tdÞg�expf�2ξðt� tdÞg��βΔn

ð7Þwhere β¼1/τ, and Δn is the change in the number of electrons inthe conduction band at any time t.

Integrating Eq. (7) and taking Δn¼0, at t¼td, for β44ξ, we get

Δn¼ 2aNcd2oξP

20expð�2ξtdÞ½expf�ξðt�tdÞg�expf�2ξðt�tdÞg�

βð8Þ

It has been shown that the local piezoelectric field F producednear the defects in ZnS crystals for the threshold pressure is of theorder of 104 V/cm [11], and the electron mobility m of ZnS crystal is165 cm2/V s [29,30]. Thus, the drift velocity of electrons in theconduction band will be, vd¼mF¼1.65�106 cm/s. For the lifetime τof electrons in the conduction band to be of the order of 10�8 s, thedistance travelled is, vdτ¼0.016 cm¼1.6�10�2 cm, which is muchgreater than the average size l¼10�4 cm of the phosphors. Thus, inthis case, the mean free path λ of the electrons in the conductionband will be limited by the size of the crystallites of the phosphors,and it will be equal to the average size l¼10�4 cm of the phosphors.If σ is the area of the cross-section of the hole centres, λ the meanfree path of an electron in the conduction band, and Nh theconcentration of hole centres in the phosphors, then the rate ofelectron–hole recombination R can be expressed as

R¼ σλNhβΔn

¼ 2σλNhaNcd2oξP

20expð�2ξtdÞ½expf�ξðt� tdÞg�expf�2ξðt�tdÞg� ð9Þ

If η is the luminescence efficiency of Mn2þ centres producedduring their excitation by the energy released during the electron–hole recombination, then the ML intensity can be expressed as

I¼ ηR

¼ 2σλNhηaNcd2oξP

20expð�2ξtdÞ½expf�ξðt�tdÞg�expf�2ξðt�tdÞg�

ð10Þ

3.1.1. Rise of ML intensityFor ξ t{1, Eq. (10) can be expressed as

Ir ¼ 2ησλNhaNcd2oξ

2P20expð�2ξtdÞðt�tdÞ ð11Þ

The above equation shows that for low value of time the MLemission will start after a particular time period td, and then theML intensity will increase linearly with time upto the periodslightly less than tm, at which the ML intensity attains amaximum value.

3.1.2. Evaluation of tmDifferentiating Eq. (10) and equating it to zero, the time tm at

which the ML intensity will be maximum can be expressed as

tm ¼ tdþ1ξln 2 ð12Þ

For P0 comparable to Pth, there will be a time delay td betweenthe applied pressure pulse and the corresponding ML pulsebecause the ML will appear when P will be greater than Pth. Fora given rise time the pressing rate will increase with the increasingvalue of the final pressure P0 applied on to the phosphors, andtherefore, td, the time for attaining the threshold pressure Pth willdecrease with the increasing value of P0. For P0bPth, td willbecome negligible and tm will be given by Eq. (12).

3.1.3. Estimation of tmSubstituting the value of tm from Eq. (12) in Eq. (10), the ML

intensity Im corresponding to the peak of ML intensity versus timecurve is given by

Im ¼ 2ησλNhaNcd2oξexpð�2ξtdÞP2

0

4ð13Þ

As expð�ξtdÞ ¼ 1�Pth=P0, Eq. (13) can be written as

Im ¼ 2ησλNhaNcd2oξP

20ð1�Pth=P0Þ2

4¼ 2ησλNhaNcd

2oξðP0�PthÞ24

ð14Þ

For high value of P0, P0bPth, Eq. (14) can be written as

Im ¼ 2ησλNhaNcd2oξP

20

4ð15Þ

When the applied pressure increases from zero to P0, theninitially detrapping starts from the shallow traps and latter ondetrapping of charge carriers takes place from deeper and deepertraps with increasing value of the applied pressure. As theelectrons up to certain trap depth are thermally detrapped, thedetrapping and consequently the ML emission starts from thethreshold pressure Pth. The linear dependence of Im on ξd20 P2

0(1�Pth/P0)2¼ξd20 (P0�Pth)2¼ξ (Qo�Qth)2 [Eq. (14)], indicates thatthe detrapping rate is proportional to the rate of change ofelectrostatic energy, because ξ (Qo�Qth)2¼(Eel0�Eelth)/τr, is theenergy increased in time (τr�τd) or Eel0, is the energy increased intime τr, where Eel and Eelth are the electrostatic energy at τr and td,respectively, after the application of pressure. Thus, the physicalreason for the increase of Im with ξd20 P2

0 (1�Pth/P0)2 in Eq. (14) canbe understood.

As the number Nc of crystallites in the sample increases linearlywith the volume of the sample and ξ remains a constant, it is

V.K. Chandra et al. / Physica B 452 (2014) 23–30 25

evident from Eq. (14) that Im should increase linearly with thevolume of sample.

3.1.4. Estimation of total ML intensity ITUsing Eq. (10), the total ML intensity IT, i.e., area below the ML

intensity versus time curve can be expressed as

IT ¼Z 1

tdIdt

¼ 2ησλNhaNcd2oξexpð�2ξtdÞP2

0½expf�ξðt�tdÞg�expf�2ξðt�tdÞg�dt

or,

IT ¼Z P0

Pth2ησλNhaNcd

2oðP�PthÞdP ¼ ησλNhaNcd

2oðP0�PthÞ2 ð16Þ

For P0bPth, the increase of IT will be given by

IT ¼ ησλNhaNcd2oP

20 ð17Þ

Since the number Nc of crystallites in the sample increaseslinearly with the volume of the sample and ξ remains a constant, itis evident from Eq. (17) that IT should increase linearly with thevolume of sample. As IT is directly proportional to d20ðP0�PthÞ2, itseems that the total ML intensity is directly related to the totalelectrostatic energy given to the phosphors.

3.1.5. Fast decay of ML intensityEq. (10) can be written as

I¼ 2ησλNhaNcd2oξexpð�2ξtdÞP2

0½exp �ξðt�tdÞ� �

�exp �2ξðt�tdÞ� �� I

½1�expf�ξðt�tdÞg�¼ 2ησλNhaNcd

2oξexpð�2ξtdÞP2

0expð�ξtmÞexpf�ξðt�td�tmÞgð18Þ

For ξ (t�td)b1, Eq. (18) can be expressed as

Idf ¼ 2ησλNhaNcd2oξexpð�2ξtdÞP2

0expð�ξtmÞexpf�ξðt�td�tmÞgð19Þ

Eq. (18) shows that the semilog plot of I/[1�exp{�ξ(t�td)}]versus (t�td�tm) should be a straight line, in which the slope willbe equal to ξ¼1/τr. Eq. (19) shows that for ξ(t�td)b1, the semilogplot of I versus (t�td�tm) should be a straight line, in which theslope will be equal to ξ¼1/τr.

3.1.6. Slow decay of ML intensityIn ZnS:Mn crystal, the local piezoelectric constant near the

defect centres is high as compared to the piezoelectric constant inthe normal region of the crystal [11]. Therefore, for a given value ofthe applied pressure, the local piezoelectric field near the defectcentres will be high as compared to the piezoelectric field in thenormal region of the crystal. As the high local piezoelectric fieldnear the defect centres will cause the detrapping of shallow traps,the trapped electrons in the shallow traps may exist only in thenormal region of the crystal where the piezoelectric field will beless, and consequently, the thermal release of such trappedelectrons in shallow traps lying in the normal piezoelectric regionwill be responsible for the slow decay of ML.

During the deformation of the crystals some of the detrappedelectrons moving in the conduction band may get trapped at theshallow traps lying in the normal piezoelectric region of thecrystals where the piezoelectric field is less and later on suchtrapped electrons will be thermally released from the traps andthe energy released during the electron–hole recombination willexcite Mn2þ and subsequent de-excitation may give rise to thelight emission characteristic of the Mn2þ ions. In this case, the

slow decay of ML intensity is given by

Ids ¼ I0sexp �ðt�tcÞτs

� �¼ I0sexp½�χðt�tcÞ� ð20Þ

where tc is the time at which the fast decrease of ML intensitybecomes negligible, I0s is the ML intensity at t¼tc, and τs¼1/χ, isthe lifetime of electrons in the shallow traps lying in the normalpiezoelectric region of the crystals.

3.2. High values of the applied pressure

In the past, Destriau [31], Henderson [32], and Lehmann [33]have made the theoretical analysis of electroluminescence (EL).For the excitation of electroluminescence the following conditionsmust be satisfied [34]: (i) Electrons from donor levels or fromelectron traps must be transported to the conduction band, (ii) inthe presence of external electric field, some electrons obtainenergy and their kinetic energy increases faster than it is lost asthe result of collisions with phonons, and (iii) some electrons mustobtain the energy which is needed for the excitation of lumines-cence centres.

In ZnS:Mn, the important scattering mechanisms includephonon scattering and impurity scattering. After the electronsfrom donor levels or from electron traps are emitted into theconduction band by the applied electric field, for the duration τreof the relaxation process the acceleration of electrons takes placein which the electron drift velocity increases with the electric fieldstrength. For t4τre, the thermal dispersion or scattering of anelectron takes place due to electron–phonon collision. The disper-sion or scattering of an electron also takes place due to electron-impurity collision. While the electrons will be accelerated by thehigh electric field, they lose energy by phonon scattering andimpact ionization. In fact, the mean free path λ is the averagedistance travelled by electrons before collisions.

If F is the electric field strength, e is the electron charge, λ is theaverage distance between two thermal dispersions for an electronand L is the geometrical dimension of an electroluminescent cell inthe direction of the electric field vector, then the maximum energyvalueW of electrons in external electric field which can be used forthe excitation or ionization of atom inside the electroluminescentcell can be expressed as

W ¼ eU ¼ eFL ð21Þ

where U is the applied voltage, L is the thickness of the lumino-phore, and F is the electric field that is, F¼U/L.

At high electric fields, the charge carriers can gain a substantialamount of energy from the field and this would show itself as anincrease of the average velocity above the value characteristic ofthe thermodynamic temperature of the material structure. In aballistic acceleration process an electron can attain the energy, Em,required to excite or ionize a molecule already over its mean freepath, λ, and the probability of the electron experiencing a pathgreater than lc ¼ Em=eF , is given by, pe¼exp(�Em=eFλÞ ¼expð�b=FÞ, where b¼ Em=eλ [35]. If the part of electrons inconduction band, which meet this condition is f, then, according tothe Boltzmann’s statistics, the component f can be expressed as [36]

f ¼ exp �bF

� �ð22Þ

In addition to f, the electroluminescence (EL) intensity I(F) alsodepends on the electron concentration n(F) in the conductingband, the probability pc of an electron collision with the lumines-cence centre and the efficiency η0 of quantum energy emissionarising from one impact ionization [36,37]. In fact, the EL intensityis proportional to the product of all these probabilities and it can

V.K. Chandra et al. / Physica B 452 (2014) 23–3026

be expressed as

IðFÞ ¼ nðFÞpcf ðFÞη0 ð23Þ

In high electric field, all the trapped electrons trapped in shallowtraps or interface in the case of EL cell tunnel to the conductionband, and therefore, n(F) may be considered as a field independent.If σl is the impact cross-section of the luminescence centres, λh themean free path of an electron at high electric field, and Nl is theconcentration of luminescence centres (Mn2þ), then the probabilitypc of an electron collision with the luminescence centres is given by,pc¼σl λh Nl. The values of σl and Nl do not depend on the electricfield F; however, at high electric field λh for ZnS increases withincreasing value of the electric field F [38], and therefore, at highelectric field pc should increase with increasing F.

It has been reported that the efficiency η0 is given by [39]:η0¼EmσlNl/(eF), in which Eem is the photon energy of the emittedradiation, σl the cross-section for impact excitation, Nl the con-centration of luminescent centres, and F the electric field applied.If η1 is the efficiency for the radiative decay of excited Mn2þ ion,then more correctly η0 can be expressed as, η0¼Em/(eF) η1. Theefficiency η1 is given by, η1¼α1/(α1þα2), in which α1 and α2 are therate constants for the radiative and non-radiative transitions,respectively. The efficiency η1 decreases slightly with the increas-ing value of the applied electric field F, for example, it decreasesnearly 3% when the value of the applied electric field is doubled[40]. As the unit of σl is cm2 and the unit of Nl is cm�3, thedimensional analysis shows that (σlNl)�1 has the unit [cm]. Thephysical meaning of (σlNl)�1 is the mean distance that an electrontravels through the luminescent material between two excitationevents, and we can take, (σlNl)�1¼ le. Thus, we can write,η0¼EmσlNl/(eF)¼Em/(eFle).

By substituting the above mentioned relations for pc and η0,Eq. (23) can be written as

IðFÞ ¼ nðFÞσlλhNlEmη1expð�b=FÞeFle

ð24Þ

The mean free path of electrons λh in ZnS at high electric fieldincreases linearly with the square root of electron energy [38].As the drift velocity of electrons increases linearly with F, and theelectron energy increases quardratically with the drift velocity ofelectrons, a linear increase of λh with F is expected upto the period,at which the deformation of the sample ceases. Thus, the ratio ofλh and F in Eq. (24) may be taken to be a constant. As n(F) remainsnearly a field independent, σ1, N1, Em, and le are constants,and η1 decreases slightly with F, the field dependence of½nðFÞσlλhNlEmη1=eFle� in Eq. (24) can be neglected as compared tothe rapid increase of exp(�b/F) with F. Thus, using Eq. (24) thefield dependence of EL intensity can be expressed as

I ¼ A0expð�b=FÞ ð25Þ

where A0 ¼ nðFÞσlλhNlEmη1=eFle.

When a pressure P0 is applied on to a piezoelectric crystal, inwhich the local piezoelectric constant is d0, the electric fieldF¼BQ0¼Bd0P0, where B is the correlating factor between F andQ0, that is, F¼BQ0. Thus, using Eq. (25), the pressure dependenceof the ML intensity for high value of the hydrostatic pressure canbe expressed as

I ¼ A0exp � bBd0P0

� �¼ A0exp � b0

P0

� �ð26Þ

where b0 ¼ b=ðBd0Þ.

4. Correlation between the theoretical and experimentalresults

Alzetta et al. [13] have measured the ML induced by theapplication of hydrostatic pressure on ZnS:Mn phosphors. In thatexperiment, the phosphor was introduced into a pressure cell eitheras an oil suspension or with other liquids, and subjected to rapidcompression through a piston acted on with electromagnets. TheML emission through the glass window of the cell was detectedusing a photomultiplier tube with a conventional low-noise circuit,which was fed to the input of an oscilloscope, whereby the MLsignal appeared on the screen of the oscilloscope. The devices suchas pressure pick-ups were used to measure the hydrostatic pressure[13]. The rise time of the pressure steps was 4 ms.

Fig. 1 shows the growth and decay of ML in ZnS:Mn phosphorsfor three hydrostatic pressure steps of different amplitudes [13]. Itis seen that, when a hydrostatic pressure step is applied on to thephosphor, then initially the ML intensity increases linearly withtime, attains a peak value Im for a particular time tm, and later on itdecreases with time. It is evident that the peak ML intensity Imincreases with increasing value of the hydrostatic pressure. Fig. 2shows the semilog plot of the ML intensity versus (t�tm). It is seen

Fig. 1. Oscillogram showing the time dependence of ML intensity of ZnS:Mnphosphors for three pressure steps of different heights. Curves 1, 2 and 3 correspondto the pressure 4.9 MPa, 9.8 MPa, and 11.76 MPa, respectively (after Alzetta et al.Ref. [13]).

Fig. 2. Semilog plot of I/[1�exp{�ξ(t�td)}] versus (t�tm) of ZnS:Mn phosphors.Curves 1, 2 and 3 correspond to the pressure 4.9 MPa, 9.8 MPa, and 11.76 MPa,respectively.

V.K. Chandra et al. / Physica B 452 (2014) 23–30 27

that initially the ML intensity decreases at a fast rate and then itdecays at a slow rate. Table 1 shows the values of the delay time td,time tm corresponding to the peak of the ML intensity versus timecurve, rate constant ξ for the fast decay, rate constant χ for theslow decay, decay time τr (¼1/ξ) for the fast decay, and the decaytime τs for the slow decay of the ML intensity for different pressuresteps. It is to be noted that, in Table 1 we have shown tm for SNo. 3 as 2.60 ms. In this case, the value of tm has been determinedby extrapolating the rising part and decaying part of thecorresponding curve.

The values of the total ML intensity IT are determined for thepressure of 4.9, 9.8 and 11.76 MPa from the area below the MLintensity versus time plots of Fig. 1. Fig. 3 shows the total MLintensity IT versus applied pressure P plot for ZnS:Mn phosphor forlow values of the applied pressure. It is seen that the total MLintensity increases nonlinearly with the pressure applied ontoZnS:Mn phosphor. From the extrapolation of the plot that thethreshold pressure (Pth) for the ML emission in ZnS:Mn phosphorsis found to be E3 MPa.

Fig. 4 shows that for low pressure the plot of total ML intensityIT versus (P0�Pth)2 is a straight line with a positive slope. Thisresult is in accord with Eq. (16).

Fig. 5 shows the total ML intensity IT versus applied pressure P0plot for ZnS:Mn phosphor for low and high values of the appliedpressure. It is seen that the total ML intensity increases nonlinearlywith the pressure applied onto ZnS:Mn phosphor and for the highvalue of the applied pressure it tends to attain a saturation value.As the total ML intensity at low pressure shown in Fig. 3 and thetotal ML intensity at high pressure shown in Fig. 5 have beenplotted in different arbitrary units in Figs. 3 and 5, respectively, thenormalized values of the total ML intensity at low pressures areplotted in Fig. 5. For getting the normalized values at lowpressures the curve for higher values of the total ML intensity isextrapolated up to 11.76 MPa and by multiplying the total MLintensity at 11.76 MPa by a suitable factor the values of IT wasmade comparable to that obtained by the extrapolated value.

Subsequently, the values of IT for other two values of lowerpressures are also normalized by multiplying with the samenormalization factor. At low hydrostatic pressure in the rangefrom 3 MPa to 40 MPa, piezoelectrically-induced detrappingmodel of ML becomes applicable in ZnS:Mn phosphors; while athigh hydrostatic pressure beyond 40 MPa, the piezoelectrically—induced impact excitation model of ML becomes applicable. Suchfact occurs because the local piezoelectric field beyond 40 MPabecomes able to cause the impact ionization of Mn2þ ions in ZnS:Mn phosphors. It is to be noted that the pressure dependence ofphotoluminescence of ZnS:Mn phosphors has been studied up to5 GPa (50 kbar), in which no any transition has been found in thephotoluminescence spectral-shift versus pressure plot [15].

Fig. 6 shows the semilog plot of the total ML intensity IT versus1/P0 for ZnS:Mn for high pressure, in which the data were taken

Table 1Values of td, tm, ξ, τr, χ and τs for different values of hydrostatic pressure.

Sno.

Load td(ms)

tm(ms)

ξ(ms)�1

τr(ms)

χ(ms)�1

τs(ms)�1

1 4.9 MPa 0.90 2.10 0.243 4.111 0.082 12.192 9.8 MPa 0.70 2.30 0.236 4.230 0.081 12.343 11.76 MPa 0.40 2.60 0.235 4.250 0.079 12.654 39.2 MPa

(during pressing)0.00 3.00 0.251 3.980

5 39.2 MPa(during release)

0.00 3.00 0.241 4.140 0.083 12.04

Fig. 3. Dependence of the total ML intensity of ZnS:Mn phosphors on the low valueof applied pressure. The data were taken from Fig. 1.

Fig. 4. Dependence of the total ML intensity on (P�Pth)2 for ZnS:Mn phosphors forthe low value of applied pressure.

Fig. 5. Dependence of the total ML intensity of ZnS:Mn phosphors on the low andhigh values of applied pressure. The data for low values of pressure were takenfrom Fig. 1 and the data for low values of pressure were taken from Fig. 3 of Ref.[13].

Fig. 6. Semilog plot of the total ML intensity versus 1/P0 for ZnS:Mn phosphors forthe high value of applied pressure. The data were taken from Fig. 3 of Ref. [13].

V.K. Chandra et al. / Physica B 452 (2014) 23–3028

from Fig. 3 of Ref. [13]. It is evident that the plot is a straight linewith a negative slope. This result is in accord with Eq. (25). Theexperimental point related to the highest pressure is deviatedfrom the linearity because at this pressure the value of IT tendstowards the saturation.

Fig. 7 shows the oscillogram for the light emission for apressure pulse of 39.2 MPa. It is seen that, when a pressure pulseis applied, initially the ML intensity increases linearly with time,attains a peak value Im1 at a particular time tm1, and then the MLintensity decreases with time, and when the applied pulse isreleased the ML intensity rises again, attains a peak value Im2 attime tm2 and finally ML intensity decreases with time. Fig. 7 showsthat the peak ML intensity Im1 obtained during the application ofpressure pulse is equal to the peak ML intensity Im2 producedduring the release of pressure pulse. This result follows the factthat the piezoelectric field produced during the application ofpressure is equal to the piezoelectric field produced during therelease of pressure. It is to be noted that, for the ML emissionproduced due to the movement of charged dislocations, the MLintensity produced during the release of pressure is several timesless as compared to that produced during the application ofpressure. Such result is obtained because for the applied pressuregreater than the limit of elasticity, the dislocations are unpinned inwhich they move forward along the appropriate slip planes;however, when the applied pressure is released, then only alimited number of dislocations move in the backward direction[1,2]. Thus, it seems that for the hydrostatic pressure the piezo-electrification provides a dominating process for the ML emission.The value of the decay time for the fast decay of ML intensityproduced during the application of pressure pulse is nearly equalto the value of the decay time for the fast decay of ML intensityproduced during the release of pressure pulse. However, the value

of slow decay of ML obtained during the release of pressure pulseis nearly equal to the value of slow decay time obtained during theapplication of hydrostatic pressure steps on ZnS:Mn phosphor.

Thus, the expressions derived are able to explain satisfactorilythe characteristics of the ML produced during the application ofhydrostatic pressure on ZnS:Mn phosphors.

5. Conclusions

In ZnS:Mn phosphor, at low hydrostatic pressure the energyproduced during the electron–hole recombination excites theMn2þ centres; however, at high hydrostatic pressure the impactof accelerated electrons with the Mn2þ ions in presence of highpiezoelectric field causes the excitation of Mn2þ ions. The peak MLintensity Im2 produced during the release of pressure pulse is equalto the peak ML intensity Im1 obtained during the application ofpressure pulse. Considering the piezoelectrically-induced detrap-ping model of ML at low pressure and piezoelectrically-inducedimpact excitation model of ML at high pressure expressions arederived for different characteristics of ML, in which a goodagreement is found between the mathematical and experimentalresults. At low hydrostatic pressure in the range from 3 MPa to40 MPa, piezoelectrically-induced detrapping model of MLbecomes applicable in ZnS:Mn phosphors; while at high hydro-static pressure beyond 40 MPa, the piezoelectrically—inducedimpact excitation model of ML becomes applicable. The MLinduced by hydrostatic pressure can be used for sensing both themagnitude and rise time of applied hydrostatic pressure.

Acknowledgement

The authors are thankful to the reviewers for their suggestions.

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Fig. 7. Oscillogram showing the time dependence of ML intensity for a shortduration pressure pulse of magnitude 39.2 MPa (after Alzetta et al. Ref. [13]).

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