Journal of Luminescence 139 (2013) 91–97

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Journal of Luminescence

0022-23

http://d

n Corr

51014 T

E-m

journal homepage: www.elsevier.com/locate/jlumin

Fluctuation kinetics of fluorescence hopping quenchingin the Nd3þ:Y2O3 spherical nanoparticles

Yu.V. Orlovskii a,b,n, A.V. Popov a,b, V.V. Platonov c, S.G. Fedorenko d, I. Sildos a, V.V. Osipov c

a Institute of Physics, University of Tartu, 142 Riia Str., 51014 Tartu, Estoniab General Physics Institute RAS, 38 Vavilov Str., 119991 Moscow, Russiac Institute of Electrophysics UBRAS, 106 Amundsen Str., Ekaterinburg 620016, Russiad Institute of Chemical Kinetics and Combustion SB RAS, Novosibirsk 630090, Russia

a r t i c l e i n f o

Article history:

Received 21 December 2012

Received in revised form

25 January 2013

Accepted 12 February 2013Available online 21 February 2013

Keywords:

Y2O3:Nd3+ monoclinic nanocrystals

Laser ablation4F3/2 laser level

OH� molecular groups

Direct nonradiative energy transfer

Fluctuation kinetics of fluorescence

hopping quenching

13/$ - see front matter & 2013 Elsevier B.V. A

x.doi.org/10.1016/j.jlumin.2013.02.029

esponding author at: Institute of Physics, Uni

artu, Estonia. Tel.: þ3727374666.

ail address: yury.orlovskiy@ut.ee (Yu.V. Orlov

a b s t r a c t

We study the peculiarities of energy transfer kinetics from the 4F3/2 laser level in the Nd3þ doped Y2O3

spherical nanoparticles of monoclinic phase synthesized by laser ablation of solid targets with

subsequent recondensation in flow of air at atmospheric pressure comparing to the similar bulk

crystal. We show that the fluorescence quenching in the nanoparticles is determined by two processes

depending on Nd3þ concentration and the degree of dehydration. At concentrations less than 1% the

fluorescence quenching is mainly determined by direct (static) quenching by vibrations of OH�

molecular groups associated with oxygen vacancies. At concentrations greater than 1 at % quenching is

due to energy migration over neodymium ions, followed by the Nd3þ–OH� quenching. In the latter

case, the first time in a solid-state impurity laser medium we observe non-stationary kinetics on the

entire length of a time-dependent luminescence quenching, starting from static decay and ending with

fluctuation kinetics of fluorescence hopping quenching.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Materials consisting of spherical crystalline nanoparticlesdoped by rare-earth (RE) ions and transition metal (TM) ionsuniformly distributed in optically transparent amorphous, glass–ceramics or polymer matrix, are perspective for development ofphotochromic coatings, chemical sensors, nonlinear opticaldevices and, primarily, highly effective luminescent and lasermedia. The most attractive feature of such materials is apossibility to control spontaneous emission lifetimes t andabsorption and emission cross-sections s of induced transitionsby varying the volume fraction of the nanoparticles and therefractive index of the surrounding medium [1,2]. Most impor-tantly, that it is possible to increase a product st, which is asignificant laser parameter, several times. This enables achievingthe population inversion in nanocomposite laser mediumalready at reduced pumping power compared to bulk crystaldue to the decrease of spontaneous emission losses. The reducedlasing threshold permits employing less expensive laser diodesfor pumping without a decrease in the output power. However,

ll rights reserved.

versity of Tartu, 142 Riia Str.,

skii).

the processes of fluorescence quenching because of nonradiativedirect energy transfer to the acceptors which can be the sameunexcited ions (self-quenching) or molecular groups like OH�

associated with oxygen vacancies, or energy migration from theexcited laser ions over unexcited ions to the acceptors maynullify the advantages of the nanocomposite materials. At thesame time decreasing the crystallite to nanoscale object maydecrease an efficiency of quenched energy transfer to theintrinsic acceptors compared to the same bulk material leadingto an increased fluorescence quantum yield. One of the reasonsis that the fluorescence quenching rate of donors may depend ontheir position in the volume of nanocrystallites and in theabsence of surface defects it can be lower near the surfacecompared to being in the center of nanoparticles [3,4]. As aresult the fluorescence quenching of donors in the ensemble ofnanospheres can be lower than in the bulk crystal. Analysis ofsuch effects is very important for the development of new highlyconcentrated laser nanocomposites. A goal of this study is toobserve the peculiarities of energy transfer kinetics from the 4F3/

2 laser level in the Nd3þ doped Y2O3 spherical nanoparticlescomparing to the same bulk material. As a result, the first time ina solid-state impurity laser medium we observe non-stationaryenergy quenching kinetics on the entire length of a time-dependent luminescence quenching, starting from static decay

1250parti

cles

150017502000

Yu.V. Orlovskii et al. / Journal of Luminescence 139 (2013) 91–9792

and ending with fluctuation kinetics of fluorescence hoppingquenching.

In doing so we prepare monoclinic crystalline Nd3þ:Y2O3

spherical nanoparticles (NPs) of 12 nm mean size by laser abla-tion of solid targets with subsequent recondensation in flow of airat atmospheric pressure. By site-selective laser spectroscopy ofthe NPs we find two types of optical centers with differentspontaneous emission lifetimes t. We measure the fluorescencekinetics versus Nd3þ concentration and find the kinetics ofenergy transfer dividing the measured kinetics to exp(�t/t). Thenwe show that the fluorescence quenching in the synthesized NPsis determined by two processes depending on Nd3þ concentra-tion: direct (static) quenching by vibrations of OH� moleculargroups and Nd3þ–Nd3þ energy migration with subsequentNd3þ–OH� quenching. We find that at 0.11% of Nd3þ concentra-tion the process of static quenching by vibrations of OH�

molecular groups dominates for two types of optical centersdetected. In the 1.07% Nd3þ:Y2O3 spherical NPs for both typesof optical centers we observe non-stationary energy quenchingkinetics on the entire length of a time-dependent luminescencequenching, starting from static decay and ending with fluctuationkinetics of fluorescence hopping quenching.

1000

Num

ber o

f nan

o

0250500750

0diameter, nm

50 6010 20 30 40 70 80

Fig. 2. TEM image of Nd3þ:Y2O3 nanoparticles and their size distribution directly

counted on TEM image.

2. Material and methods

Crystalline Y2O3 nanoparticles (NPs) doped by two concentra-tions of the Nd3þ ions 0.11 and 1.07 at% are prepared using highaverage power pulsed periodic CO2 laser ablation of solid targetswith subsequent recondensation in flow of air at atmosphericpressure [5]. After sedimentation the nanopowders are dried firstat 80 1C in a vacuum evaporator and then annealed for 2 h at 790or 870 1C to remove water. XRD analysis (diffractometer Smar-tLab, Rigaku

TM

), performed after each stage of temperature treat-ment, detected nanocrystalline monoclinic Y2O3 (phase groupC2/m) in all samples as a single phase (Fig. 1). A size distributionand average diameter of 12 nm is counted directly on TEM image(Fig. 2). However, XRD gives the values between 20 and 24 nm,which is the volume weighted mean size. Concentration of Nd3þ

is determined by atomic-emission method with highly induc-tively coupled plasma with OPTIMA 4300DV spectrometer. Thefluorescence spectra and kinetics of Nd3þ in the NPs at 10 K is

Fig. 1. XRD pattern of the Nd3þ:Y2O3 nanoparticles measured after each stage of

temperature treatment at Rigaku SmartLab X-Ray difractometer—from top to

bottom: dried at 80 1C—green solid line, annealed for 2 h at 790 1C—red line,

annealed for 2 h at 870 1C—blue line, and JCPDS standard for monoclinic

phase—pink line. (For interpretation of the references to color in this figure

legend, the reader is referred to the web version of this article.)

measured in the near-IR spectral range using pulsed laser excita-tion of OPO-laser Ekspla NT342/1/UVE (tp¼5 ns, f¼10 Hz). Fluor-escence is dispersed by MDR-23 monochromator (LOMO) anddetected at the 4F3/2-

4I9/2 transition of Nd3þ by single-photoncounting technique using red-sensitive PMT Pheu-79 and multi-channel analyzer (MCA Series/P7882) with 100 ns timeresolution.

3. Theory

The energy transfer kinetics N(t) in bulk solid solutions is arather complicated multistage process that depends essentiallyon the character of the interaction between donors and acceptors,and concentration of impurity centers [6,7]. The necessity ofperforming configuration averaging over random location ofimpurity optical centers hinders considerably the theoreticaldescription of the phenomenon. However, there are two specificcases where configuration averaging may be carried out to theend so as to obtain the solution of a many-particle problem. Thefirst case is when the donor concentration nD is vanishingly small,and excitation decays at the same donor where it arises. Then thesolution is the well-known static kinetics [8]. The second case isthe hopping quenching realizing when the average step l� nD

�1=3

of excitation migration over donors exceeds significantly the RW

radius of effective quenching of the excitation by acceptors:lbRW. In this situation for the kinetics of energy transfer N(t)we have the closed integral [9,10]:

NðtÞ ¼N0ðtÞR0ðtÞ�

Z t

0N0ðt

0Þ _R0ðt0ÞNðt�t0Þdt0 ð1Þ

Yu.V. Orlovskii et al. / Journal of Luminescence 139 (2013) 91–97 93

Here � _R0ðtÞdt defines the time distribution between sequentialuncorrelated excitation jumps.

As it is known, the distribution is not exponential in solid bulksolutions, and depends on the character of resonance interactionbetween donors. In particular, in the simplest approximation nottaking into account the excitation return from the nearestneighbors the kinetics of the excitation emigration from thedonor where it originated is [11,12]

R0ðtÞ ¼ expf�nD

Zd3r½1�e�uðrÞt�g ð2Þ

Here u(r) is the probability of energy transfer per unit timebetween two donors separated by the distance r.

The solution of Eq. (2) for dipole–dipole interaction, when thefunctions N0(t) (static quenching) and R0(t) (emigration kinetics)take the form

N0ðtÞ ¼ expf�gA

ffiffitpg ð3Þ

R0ðtÞ ¼ expf�gD

ffiffitpg ð4Þ

with the macroparameters of energy quenching and migration

gA ¼ ð4=3Þp3=2ðnA

ffiffiffiffiffiffiffiffiCDA

pÞ, ð5Þ

gD ¼ ð4=3Þp3=2nD

ffiffiffiffiffiffiffiffiCDD

p, ð6Þ

where nA is the acceptor concentration, and donor and acceptorare different ions, as given in Ref. [13]. The microparameters ofenergy transfer CDA and CDD are defined by the expressions forprobability of energy transfer between donor and acceptorand donor and donor (w(r)¼CDA/r6; u(r)¼CDD/r6). It is shownthere that from the very beginning the quenching develops in astatic way: N(t)EN0(t). At this stage the excitations havingfavorable acceptor surroundings are quenched. The binary para-meter a is an average number of acceptors in a volume of strongquenching around the excited donors determining a type oftransfer kinetics:

a¼ nAð4pR3w=3Þ ¼ gA=gD ¼

nA

ffiffiffiffiffiffiffiffiCDA

pnD

ffiffiffiffiffiffiffiffiCDD

p ð7Þ

At small values of parameter a¼gA/gD51 and sufficientlylarge time tb(gAþgD)�2 the kinetics in bulk crystal may berepresented as two independent components

NðtÞ �NeðtÞþNmðtÞ ð8Þ

The first component is determined by migration acceleratedquenching at the constant rate W depending non-linearly ondonor and acceptor concentration:

NeðtÞ ¼1þa

1þ3aexpð�WtÞ, W ¼

aðgAþgDÞ2

2ð1þ3aÞð9Þ

It is valid in the time interval

4ð1þaÞ2

ðgAþgDÞ2¼ ts5t5tf ¼

4

a2ðgAþgDÞ2

ð10Þ

This component describes the decay of excitations arisen inthe regions filled with donors, and having the possibility ofeffective reaching the acceptors by a series of jumps. ExpandingEq. (9) in a series over small a and retaining the linear terms weobtain the well-known binary migration accelerated stage ofkinetics [14–17] which follows just after initial static stage andis commonly used for experimental data interpretation in bulk

crystals [18]:

NbinðtÞ ¼ ð1�2aÞexpð�WbintÞ � expð�2a�WbintÞ, Wbin ¼gAgD

2ð11Þ

The value of 2a is a part of excitations decayed at the initialstatic quenching stage t5ts before approaching exponentialkinetics (Eq. (9)).

The second component of the kinetics Nm(t) (Eq. (8)) describesthe processes of non-stationary quenching in the regions depletedwith donors. It includes initial static kinetics in the regions wellfilled with acceptors and final stage of fluctuation kinetics in theregions depleted with donors and acceptors. These donors can befound in isolation due to fluctuation of concentration; so thiskinetics was defined in Ref. [13] as fluctuation kinetics. Due to thelarge distance between donors the excitation migration is slow inthese regions. So the overall kinetics is non-exponential begin-ning with the initial interval of static quenching N0(t) (Eq. (3)) at

t5ts ¼ ð1þaÞ2=gAþgD

2

� �2

ð12Þ

and ending with quenching of excitations at isolated donorcenters that determines the kinetics at large times:

NmðtÞpNf ðtÞ ¼1þaa

� �expð�ðgAþgDÞ

ffiffitpÞ, tbtf ¼

4

a2ðgAþgDÞ2

ð13Þ

It is easily seen that with increasing binary parameter a theboundaries ts and tf approach each other, and at a-1 the intervalof migration accelerated quenching

4 ð1þaÞ2

ðgAþgDÞ2¼ ts5t5tf ¼

4

a2ðgAþgDÞ2

ð14Þ

goes to zero leaving no room at all for exponential kinetics ofEqs. (9) and (11). In this case slow migration of excitations fails toform time independent quenching rate W , so the kinetics of energyquenching is non-stationary from the beginning up to the end.Experimental confirmation of the existence of such kinetics is obtainedin Ref. [19]. However, we do not find elsewhere an analytical expressionfor the kinetics of fluorescence hopping quenching in nanoparticles.

4. Results

We measure site-selective fluorescence spectra of the 0.11%Nd3þ:Y2O3 NPs at 10 K at two excitation wavelengths 577.8 nmand 589.5 nm after direct excitation into the 4G5/2 level of Nd3þ . Wedetect fluorescence of Nd3þ in the near IR spectral range on the4F3/2-

4I9/2 transition from the 4F3/2 metastable level after fastmultiphonon relaxation of optical excitation. Spectral peaks in thelong wavelength range of the fluorescence spectra for differentexcitation wavelengths are well separated (905.5 nm and 907.5 nm)and appear to belong to different optical centers: center A and centerB, respectively (Fig. 3). Fluorescence kinetics is measured for the x at%Nd3þ:Y2O3 NPs, where x¼0.11 and 1.07 with double spectralselection at different excitation and detection wavelengths. Longerexcitation wavelength (589.5 nm) at shorter detection wavelength(905.5 nm) of fluorescence recording gives faster fluorescence kineticsdecay (Fig. 4, curve 1) than at shorter excitation wavelength(577.8 nm) and longer detection wavelength (907.5 nm) (Fig. 4, curve3). For both the centers the kinetics exhibits non-exponential decay atthe initial stage and exponential decay at the late stage. We find thatfor the 1.07 at% Nd3þ:Y2O3 NPs fluorescence kinetics acceleratessignificantly (Fig. 4, curves 2, 4). We do not reveal any evidence ofenergy transfer between two different types of optical centers at 10 Kusing excitation wavelengths of one center and detection wave-lengths of fluorescence spectrum of another center.

nm885 890 895 900 905 910

Fluo

resc

ence

, a.u

.

0

200

400

600

800

1000

1200

1400

1600

1800

1

2

Fig. 3. Site-selective fluorescence spectra of the 0.11% Nd3þ:Y2O3 nanocrystals at 10 K annealed for 2 h at 790 1C. 1—center A, excitation 589.5 nm—red solid line;

2—center B, excitation 577.8 nm—blue solid line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

t, µs40003000200010000

fluor

esce

nce,

a.u

.

0.0001

0.001

0.01

0.1

1

1

2

345

6

Fig. 4. Site-selective measurements of the fluorescence kinetics decay of two types of optical centers in the 0.11% Nd3þ:Y2O3 and the 1.07% Nd3þ:Y2O3 nanoparticles at

10 K annealed for 2 h at 790 1C. Center A, excitation 589.5 nm, detection 905.5 nm: 1—red—0.11%:Nd3þ and 2—pink—1.07% Nd3þ broken lines; center B, excitation

577.8 nm, detection 907.5 nm: 3—blue—0.11% Nd3þ and 4—cyan—1.07% Nd3þ broken lines; 5—exponential decay with t¼415 ms—green solid line, and 6—exponential

decay with t¼562 ms—yellow solid line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Yu.V. Orlovskii et al. / Journal of Luminescence 139 (2013) 91–9794

5. Discussion

When considering quenching of optical excitation of the 4F3/2

level of the Nd3þ ion in crystalline matrixes one should be awarethat donors and acceptors of energy are the same ions. As a resultthe case of direct (static) Nd–Nd quenching without energymigration cannot be realized even at very low concentrationsfor the following reason. Always, an electronic excitation of thedonor may either migrate to an other donor or may be quenchedby the same ion as an acceptor. According to the literature acriterion of hopping quenching for the 4F3/2 metastable level ofNd3þ in doped crystal matrixes CDDbCDA is usually performed[20,21]. This means that for any concentration of Nd3þ a prob-ability of energy migration from the excited ion (donor) to theunexcited ion as new donor greatly exceeds the probability of

quenching on the same unexcited ion as on the acceptor. Forexample, in a complex phosphate NdxLa1�xP5O14 crystal theCDD/CDA ratio is higher than one hundred even at room tempera-ture (CDD¼5�10�39 cm6/s (5 nm6/ms), CDA¼3.7�10�41 cm6/s(0.037 nm6/ms)) [20]. Analysis and direct calculation of theenergy migration interaction microparameter CDD in the Nd3þ

doped YAG crystal at room temperature reveals that the energymigration rate between Nd3þ ions in the YAG laser crystal isabout one order of magnitude faster than the energyquenching rate (CDD¼2.73�10�39 cm6/s (2.73 nm6/ms),CDA¼1.79�10�40 cm6/s (0.179 nm6/ms)) [21]. As a result aprobability of energy migration over the Nd3þ donors is muchhigher than a probability of energy quenching to the Nd3þ

acceptors. This fact can be easily explained by the Forster–Dexter theory of resonant multipolar interaction [22]. It assumes

Fig. 5. The energy transfer kinetics from the 4F3/2 manifold of the Nd3þ ion N(t)¼ I(t)/exp(�t/t) in the 0.11% Nd3þ:Y2O3 nanoparticles at 10 K annealed for 2 h at 790 1C:

(a) excited at 589.5 nm and detected at 905.5 nm measured: 1—just after annealing—brown broken line and 2—after 2 weeks of storage in a desiccator—red line;

(b) excited at 577.8 nm and detected at 907.5 nm measured: 3—just after annealing—cyan broken line and 4—after 2 weeks of storage in a desiccator—blue line.

(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Yu.V. Orlovskii et al. / Journal of Luminescence 139 (2013) 91–97 95

that the interaction probability WDA in the donor–acceptor pair isproportional to an overlap integral of the donor fluorescence andthe acceptor absorption spectra. In the Nd3þ doped oxide crystalsthe donors fluorescence and absorption spectra overlap integral ishigh enough even at room temperature due to good resonancebetween the 4F3/2-

4I9/2 fluorescence and the 4I9/2-4F3/2 absorp-

tion transitions. Moreover, it increases at 10 K due to spectral linesnarrowing. In turn, the donor–acceptor fluorescence quenching,e.g. in the Nd3þ:Y2O3 crystal, can be realized through three non-resonant cross-relaxation channels (4F3/2-

4I15/2; 4I9/2-4I13/2�_o¼

400 cm�1); (4F3/2-4I13/2; 4I9/2-

4I15/2�_o¼400 cm�1); (4F3/2-4I15/2;

4I9/2-4I15/2þ_o¼209 cm�1). We calculate their energy mis-

matches from the energy levels diagram for the C2 site in theNd3þ:Y2O3 crystal of cubic phase [23]. They all require onephonon for compensation of energy mismatch between donorfluorescence and acceptor absorption transitions. The spectraloverlap integral for the quenched energy transfer has the oppositedependence on temperature. It considerably decreases from roomto liquid helium temperature. Thus the condition CDDbCDA musthold even stricter at 10 K. We assume that in case of monoclinicphase of the Nd3þ:Y2O3 crystal the energy mismatch for the samecross-relaxational transitions is similar to that for the cubic phasedue to weak electro-phonon coupling, so that the values of CDD

and CDA as well as the CDD/CDA ratio will be of the same order.At the beginning we find the energy transfer kinetics from the

kinetics of fluorescence decay for the 0.11%Nd3þ:Y2O3 dilutedsample. As it is stated above for low donor concentrations thequenching develops in a static way when donors and acceptorsare different ions or for the time interval shorter than ts whenthey are the same ions. In this case the fluorescence kinetics inbulk crystal is expressed as [8]

IðtÞ ¼ exp �t

t�gAt3=s

� �, ð15Þ

where s¼6 for the dipole–dipole interaction, s¼8 for the dipole–quadrupole interaction, s¼10 for the quadrupole–quadrupoleinteraction, and so on. The energy transfer kinetics N(t) can befound by division of the measured fluorescence kinetics I(t) by

exp(�t/t). We measure the intra center decay time t at the longstage of fluorescence kinetics in the 0.11 at% Nd3þ:Y2O3 dilutedsample. We fit exponential decay for the center A with t¼415 msand for the center B with t¼562 ms (Fig. 4, curves 1, 3, 5, 6).We find that the energy transfer kinetics in diluted sample isindependent on the optical center type under the same annealingconditions (Fig. 5, curves 1, 3 and 2, 4). However, the kineticsmeasured just after annealing (Fig. 5, curves 1, 3) decreasesslowly than that after 2 weeks of storage in a desiccator (Fig. 5,curves 2, 4). This allows us to assume the quenching by vibrationsof OH� molecular groups which can be trapped by oxygenvacancies [24].

By plotting the energy transfer kinetics � lg(� ln N(t)) for twodifferent centers A and B as a function of lg(t) for the 0.11%Nd3þ:Y2O3

NPs (Fig. 6, curves 1, 2), we determine from the slope of this graph theexponent of the time parameter tg j¼3/s (see Eq. (15)) and determinethe s parameter. We found that tg j eventually tends to 1/2, whichcorresponds to s¼6 and the dipole–dipole quenching interactionbetween the excited Nd3þ and OH� ions. Thus, in the case of quenchingby vibrations of OH�groups, on the measured depth of the kinetics wedo not observe any significant differences in the functional behavior ofthe static energy quenching kinetics in the Nd3þ:Y2O3 doped nano-particles from that in a bulk crystal or glass [25]. If we use now thedependence ln N(t) as a function of t1/2 (Fig. 7, curves 1, 2), these curvesare linearized, which proves Forster-like decay law and their slopes canbe used to determine the gA (Fig. 7, curves 3, 4). For the center A we fitgA¼0.0167 ms�1/2 (0.5265 ms�1/2).Wecanestimatetheconcentrationof OH� molecular groups trapped by oxygen vacancies using Eq. (5).The evaluation value of CDA(Nd–OH)¼0.6�10�39 cm6/s (0.6 nm6/ms)found in phosphate glass at 4.2 K is taken from Ref. [25]. As a resultnA¼0.0916 nm�3, which is approximately three times higher thanNd3þ impurity concentration nD¼0.03227 nm�3 in the 0.11 at%Nd3þ:Y2O3 NPs. We can explain insignificant contribution of Nd–Ndself-quenching to the measured kinetics of energy transfer by smallvalue of CDA(Nd–Nd)E10�40–10�41 cm6/s (0.1–0.01 nm6/ms) takingelsewhere [20,21].

To evaluate macroparameter CDD does not necessarily know theconcentration of acceptors (OH�) and microparameter CDA. It is

Fig. 6. The energy transfer kinetics from the 4F3/2 manifold of the Nd3þ ion � lg[� ln(I(t)/exp(�t/t)] as a function of lg t in the x% Nd3þ:Y2O3 nanoparticles at 10 K

annealed for 2 h at 790 1C: (a) x¼0.11, 1—excited at 589.5 nm and detected at 905.5 nm (center A)—red broken line and 2—excited at 577.8 nm and detected at 907.5 nm

(center B)—blue broken line; (b) x¼1.07, 3—center A—pink broken line, 4—center B—cyan broken line. (For interpretation of the references to color in this figure legend,

the reader is referred to the web version of this article.)

Fig. 7. The energy transfer kinetics from the 4F3/2 manifold of the Nd3þ ion ln(I(t)/exp(�t/t) as a function of t1/2 in the x% Nd3þ:Y2O3 nanoparticles at 10 K annealed for 2 h

at 790C: (a) x¼0.11; 1—excited at 589.5 nm and detected at 905.5 nm (center A)red broken line (3—linear curve fit of the static stage—black solid line) and 2—excited at

577.8 nm and detected at 907.5 nm (center B)—blue broken line (4—linear curve fit of the static stage—yellow solid line); (b) x¼1.07; 5—center A—pink broken line

(7—linear curve fit of the fluctuation stage—dark gray solid line) and 6—center B—cyan broken line (8–linear curve fit of the fluctuation stage–gray solid line). (For

interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Yu.V. Orlovskii et al. / Journal of Luminescence 139 (2013) 91–9796

Yu.V. Orlovskii et al. / Journal of Luminescence 139 (2013) 91–97 97

enough to know macroparameter gA determined at the previousstage. We find energy transfer kinetics for the 1.07 at% Nd3þ:Y2O3

NPs the same way as for diluted sample keeping in mind Eqs. (11)and (13). Next, by plotting the energy transfer kinetics � lg(� ln N(t))as a function of lg(t) (Fig. 6, curves 3, 4), we determine from the slopeof this graph at the late stage the exponent of the time parametertg j¼1/2. We assume that this is a fluctuation stage, because it is inagreement with the dipole–dipole nature of Nd–OH energy transferand Nd–Nd energy migration over the 4F3/2 energy level of Nd3þ inthe Nd3þ:Y2O3 crystal (see Eq. (13)). At this stage in the1.07%Nd3þ:Y2O3 NPs we fit the slope of the energy transfer kineticsin coordinates 1n N(t) vs t1/2 with g¼gDþgA (Eq. (13)) (Fig.7, curves5–8). We find gD as the difference between g and gA.

As a result we have for the center A gA¼0.016649 ms�1/2

(0.52649 ms�1/2), g¼0.040722 ms�1/2 (1.28775 ms�1/2), andgD¼0.024073 ms�1/2 (0.76126 ms�1/2) and for the center BgA¼0.015103 ms�1/2 (0.47764 ms�1/2), g¼0.036578 ms�1/2

(1.1568 ms�1/2), and gD¼0.021475 ms�1/2 (0.67916 ms�1/2).According to Eq. (7) the parameter a¼gA/gDE0.7 for both

optical centers that is even higher than in Ref. [19] wherefluctuation kinetics of hopping quenching is detected experimen-tally for the first time.

It must be emphasized that again we do not observe any significantdifference in the functional dependence of the fluctuation kinetics ofenergy quenching in the Nd3þ:Y2O3 doped nanoparticles from thedependence in the same bulk crystal. We use Eq. (6) to calculate the CDD.Taking into consideration the lifetimes and the areas under themeasured fluorescence spectra for different centers we assumethat concentrations of centers A and B are equal and is half of theconcentration of Nd3þ (nD¼0.313938 nm�3/2¼0.156969 nm�3).Under this assumption, we find CDD(A)¼0.427 nm6/ms and CDD(B)¼0.340 nm6/ms. The probability of spontaneous transitions in the Nd3þ

donor is higher in the center A than in B, whereas the strength ofabsorption transition in OH� acceptor is equal for both the centers. Thisis in agreement with the higher values of the gA(Nd–OH) macropara-meter and CDD(Nd–Nd) microparameters for the center A comparingto the center B found. The energy transfer microparameter CDA

(Nd–OH)¼0.6 nm6/ms taken from the literature is of the same orderof magnitude as the energy migration microparameters CDD(Nd–Nd)found. It may seem that the criterion of hopping quenching CDDbCDA isnot fulfilled as CDDECDA. However, the accuracy of estimating theconcentration of OH� in Ref. [25] is very low, because it was difficult todetermine the absolute values of the concentration of OH�ions fromthe infrared absorption spectra. Besides the spontaneous emissionlifetime is one and a half times shorter in phosphate glass (t¼375 ms)than in yttrium oxide that correlates with the value of CDD

(Nd–Nd)E10�38 cm6/s (10 nm6/ms) found in phosphate glass, whichis thirty times higher than the values obtained by us in yttrium oxide. Asa result the value of the microparameter CDA(Nd–OH) in Nd3þ:Y2O3

maybeoverestimated by anorderof magnitude.Therefore,weconsiderthe estimated value of CDA(Nd–OH) as the upper estimate. All estimatesof microparameters in no way affect the value of the parametera found,which is calculated from the slopes of the experimental curves in thecorresponding coordinates. Moreover, the calculated boundary timetsE6.9 ms is larger than tfE5.0 ms (Eqs. (12) and (13)) for both types ofoptical centers. This means that the interval of migration acceleratedquenching goes to zero leaving no room at all for exponential kinetics ofEqs. (9) and (11) that confirms the detection of fluctuation stage.However, the calculated values of ts and tf valid for bulk crystal arelonger than the measured time interval. We suppose that due to limitedgeometry the fluctuation stage in nanoparticles sets earlier than in bulkcrystal and we manage to observe it on the measured time scale.

6. Conclusions

We show that the fluorescence quenching in the Nd3þ dopedY2O3 nanoparticles of monoclinic phase is determined by twoprocesses depending on Nd3þ concentration: direct (static)quenching by vibrations of OH� molecular groups associatedwith the oxygen vacancies and Nd3þ–Nd3þ energy migrationwith subsequent Nd3þ–OH� quenching. We find that at 0.11% ofNd3þ concentration the process of static quenching by vibrationsof OH� molecular groups dominates for two types of opticalcenters detected. We observe for both types of optical centers inthe 1.07 at% Nd3þ:Y2O3 spherical NPs a non-stationary energyquenching kinetics on the entire length of a time-dependentluminescence quenching, starting from static decay and endingwith fluctuation kinetics of fluorescence hopping quenching.

Acknowledgments

This work is supported by European Social Fund (Projects #MTT50, MJD 167), the Centre of Excellence TK114 ‘‘Mesosystems:Theory and Applications’’; TK117 ‘‘High-Technology Materials forSustainable Development’’, Russian Fund for Basic Research (Pro-ject #11-02-00248 and 11-08-00005).

Authors are grateful to Dr. Hugo Mandar for XRD analysis ofthe samples, and Katrin Utt for her help in annealing the samplesand their preparation for XRD analysis.

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