Luminescence decay-based Y2O3:Er phosphor thermometry: Temperature sensitivity governed by multiphonon emission with an effective phonon energy transition

Accepted Manuscript Luminescence decay-based Y2O3:Er phosphor thermometry: Temperature sensitivity governed by multiphonon emission with an effective phonon energy transition Jeffrey I. Eldridge PII:

S0022-2313(19)30674-X

DOI:

https://doi.org/10.1016/j.jlumin.2019.116535

Article Number: 116535 Reference:

LUMIN 116535

To appear in:

Journal of Luminescence

Received Date: 4 April 2019 Revised Date:

15 May 2019

Accepted Date: 3 June 2019

Please cite this article as: J.I. Eldridge, Luminescence decay-based Y2O3:Er phosphor thermometry: Temperature sensitivity governed by multiphonon emission with an effective phonon energy transition, Journal of Luminescence (2019), doi: https://doi.org/10.1016/j.jlumin.2019.116535. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Luminescence decay-based Y2O3:Er phosphor thermometry: Temperature sensitivity governed by multiphonon emission with an effective phonon energy

Jeffrey I. Eldridge

NASA Glenn Research Center

RI PT

transition

SC

21000 Brookpark Rd., Cleveland, OH 44135, USA

Abstract

M AN U

To shift the onset of thermal quenching by multiphonon emission to higher temperatures, thermographic phosphors for high-temperature applications are usually selected with a large energy gap between the radiatively emitting energy level and the next lowest energy level. An alternate approach is presented where Y2O3:Er, with a relatively small energy gap of 2795 cm-1 between the 4S3/2 emitting level and the 4F9/2 level below it, provides effective temperature measurements from room temperature to

TE D

1200 °C. The smaller energy gap results in an expanded temperature measurement range because (1) it results in a lower temperature onset of thermal quenching by multiphonon emission and (2) the smaller number of phonons required to bridge the energy gap produces a weaker temperature-dependent increase in multiphonon emission rates with

EP

temperature. Utilizing the intense hypersensitive 4I15/2 → 2H11/2 Er3+excitation at 522 nm offsets the temperature precision reduction due to the decreased decay time temperature

AC C

sensitivity. Two distinct temperature sensitivity ranges are observed due to a crossover in multiphonon emission relaxation from high to low effective phonon energies at about 950 °C. The implications of this transition from high to low effective phonon energies for selection of dopant hosts for high-temperature thermographic phosphor applications are discussed.

Keywords: luminescence, phosphor thermometry, multiphonon emission, nonradiative decay

1

ACCEPTED MANUSCRIPT

1. Introduction Phosphor thermometry has attracted significant interest for noncontact temperature measurement applications in high-temperature environments because it is not susceptible to the temperature errors associated with emissivity uncertainty and reflected radiation

RI PT

that are encountered by pyrometry or infrared thermographic imaging [1-6]. These

advantages are especially relevant for turbine engine environments, where a significant fraction of detected radiation from a high-pressure turbine or blade is due to reflected

radiation [7-8]. Much of the focus of thermographic phosphor development to meet the

SC

requirements of high-temperature applications has been to select or design phosphors with sufficient luminescence lifetime temperature sensitivity in the range of interest

M AN U

because luminescence lifetime is usually more temperature-sensitive than emission band intensity ratio measurements at temperatures above 1000 °C [4-6]. Because of the demand for extending luminescence decay-based phosphor thermometry to higher temperature applications, considerable effort has been devoted to meet the challenges encountered at higher temperatures: (1) higher background thermal radiation (including reflected radiation), (2) decreasing luminescence emission intensity, and (3) decreasing

TE D

luminescence lifetime [3]. These trends impede successful high-precision temperature measurements because the noise associated with the intense thermal radiation background can overwhelm the decreased high-temperature phosphor emission intensity, and the luminescence decay time can become too short to be easily measured. Therefore, the

EP

desired attributes for a thermographic phosphor for high-temperature applications are a short emission wavelength (where thermal radiation background is less intense) and

AC C

adequate retention of both emission intensity and decay time duration for sufficient temperature measurement precision in the temperature range of interest. To meet the last two requirements, rare-earth dopant ions are usually selected for their desirably weaker electron-phonon coupling strengths compared with transition-metal dopant ions. Selection from among rare earth dopant ion candidates is typically accomplished by referring to a Dieke energy diagram to seek emitting levels with a sufficiently large energy gap, ∆E, between the dopant ion emitting level and the next lower energy level so that ∆E cannot be bridged by multiphonon emission until the high temperature range of interest is reached. While this objective has been met by YAG:Dy and YAG:Tm, with 2

ACCEPTED MANUSCRIPT

relevant ∆E values of 7640 [9] and 6510 [10] cm-1, respectively, the delayed onset of temperature sensitivity (at about 1100 and 1000 °C, respectively) along with a very steep decay-time temperature dependence restricts temperature measurements using these thermographic phosphors to a fairly narrow temperature range. In this paper, a different

RI PT

strategy is presented where selecting a phosphor with a much smaller ∆E allows for a

much greater temperature measurement range. This strategy is implemented by selecting the thermographic phosphor Y2O3:Er, which has a much smaller ∆E of 2795 cm-1

between the 4S3/2 emitting level and the 4F9/2 energy level below it. It will be shown that

SC

luminescence decay-based temperature measurements using Y2O3:Er cover a much greater temperature range (from room temperature to 1200 °C) than thermographic

M AN U

phosphors with much larger ∆E values, without loss in temperature measurement precision due to more efficient excitation via a hypersensitive transition.

1.1 Temperature dependence of nonradiative relaxation by multiphonon emission The temperature dependence of luminescence decay is a result of temperaturedependent nonradiative relaxation processes that compete with radiative decay:
() =  ( ) 

TE D





 ( )

(1)

where τ is the decay time, Wr(T) is the temperature-dependent observed radiative decay

EP

rate, and Wnr(T) is the temperature-dependent nonradiative decay rate at temperature T. While Wr is usually considered to be temperature-independent, when there is

AC C

thermalization between two closely spaced radiatively emitting electron energy levels, the thermally coupled radiative decay rate Wr(T) will be temperature dependent [2]. The Wr(T) temperature dependence arises because the thermally coupled radiative decay becomes increasingly weighted by the higher energy level radiative decay rate with increasing temperature, as is the case for the 4S3/2 and 2H11/2 electron energy levels of Er3+considered here. There are several mechanisms for nonradiative decay, including multiphonon emission, cross-relaxation, and crossovers to low-lying charge transfer states or 4fn-15d1 levels. Cross-relaxation is usually undesirable for phosphor thermometry because it complicates the decay behavior and reduces emission intensity 3

ACCEPTED MANUSCRIPT

and decay time duration at low temperatures. Crossover to low-lying charge transfer states and 4fn-15d1 levels can be effective but is restricted to special cases of those rareearth dopant ions where one of those levels is especially low lying, like the charge transfer state of Eu3+ or the 4f75d1 level of Tb3+. The most frequently used nonradiative

RI PT

decay mechanism associated with luminescence decay-based phosphor thermometry

measurements is multiphonon emission. If multiphonon emission is the only nonradiative relaxation process considered, then Wnr = Wmp, where Wmp is the multiphonon emission rate. It has been shown that Wmp can be estimated using a single effective phonon

SC

frequency (ωeff) model [11-13]:  =  ( + 1)

M AN U

(2)

where W0 is the spontaneous multiphonon emission rate, p = ∆E/ħωeff is the number of phonons with effective phonon energy ħωeff needed to bridge ∆E, and neff is the phonon occupation number for phonon with energy ħωeff: ℏ 

− 1) = (1 − 

ℏ 

TE D

 = (

) − 1

(3)

where k is Boltzmann’s constant. The increase in Wmp above W0 with increasing

EP

temperature is due to stimulated phonon emission. The spontaneous multiphonon emission rate W0 has been shown to follow pth order multiphonon relaxation process

AC C

[11,13]:

 = 



=  !

=  "#$

(4a) (4b) (4c)

where C is a host-dependent constant, ε is an electron-phonon coupling constant

associated with dopant ion host, β = -ln(1/ε), and α = β/ħωeff. Because ε ≪ 1, Eq. (4b) is

the justification for assigning p = ∆E/ħωeff to be the fewest number of phonons needed to 4

ACCEPTED MANUSCRIPT

bridge ∆E, as there is an exponential dropoff in the contributions from higher phonon order processes to spontaneous multiphonon relaxation. Therefore, ħωeff will be close to the maximum phonon energy of the dopant ion host for spontaneous multiphonon emission and has led to a rule of thumb that radiative relaxation will be greater than

RI PT

multiphonon relaxation for ∆E > 5ħωeff [12-13]. When stimulated phonon emission is included, this rule of thumb is relaxed: Eq. (2) indicates that as neff increases in

temperature, the (neff + 1)p term will lead to a rapidly increasing Wmp and will result in

Wmp overtaking Wr even for ∆E > 5ħωeff. At this point, the temperature sensitivity of τ

SC

given in Eq. (1) will be dominated by Wmp.

The vast majority of luminescence decay-based phosphor thermometry studies

M AN U

based on temperature-dependent multiphonon relaxation assume that ħωeff remains close to the maximum host phonon energy at all temperatures. However, at a sufficiently high temperature, the higher phonon occupation number for lower phonon energies (Eq. (3)) will result in a greater Wmp in Eq. (2) for lower ħωeff values (higher p), outweighing the lower W0 for higher p given in Eq. (4b). This possibility was recognized as early as 1967, when Kisliuk and Moore [14] proposed “…that [while] the nonradiative decay at low

TE D

temperatures is almost entirely due to the high-frequency modes, there is some higher temperature at which the low-frequency mode will pass the high-frequency one in importance…” Weber [12] also predicted that assigning ħωeff to close to the maximum host phonon energy will only hold at low temperatures where spontaneous phonon

EP

emission dominates and will shift to lower phonon energies when stimulated phonon emission becomes dominant at higher temperatures. This potential transition from high

AC C

frequency to low frequency ωeff at high temperature has been largely ignored with only a couple of exceptions [15-16] in the phosphor thermometry literature. Heyes [15] presented a convincing argument similar to that of Kisliuk and Moore [14] that higher order, lower effective phonon frequency multiphonon relaxation processes become more favored at higher temperatures due to higher phonon occupation numbers at high temperature. Similarly, Kennedy and Djeu [16] also predicted a high-temperature transition in ħωeff from 840 to 120 cm-1 for phonon-assisted energy transfer from Yb3+ to Tb3+ in co-doped YAG:Tb,Yb. Kennedy [17] later showed that a dual effective phonon energy model could account for a transition temperature from high to low ωeff: 5

ACCEPTED MANUSCRIPT

 =  (()*( + 1)+,-+ + . (/01 + 1)234

(5)

where W10 and W20 are the spontaneous multiphonon emission rates for the high and low

RI PT

phonon energy relaxation processes, respectively, nhigh and nlow are the occupation numbers for the effective high energy (ħωhigh) and low energy (ħωlow) phonons,

respectively, given by Eq. (3), and phigh and plow are the number of high and low effective phonon energy phonons, respectively, needed to bridge ∆E. The inclusion of only two

SC

phonon energies can be justified because the high phonon energy term in Eq. (5) will dominate below the transition temperature while the low phonon energy term will

M AN U

dominate above the transition temperature. In terms of the temperature dependence of Wmp, temperature sensitivity will greatly increase above the transition temperature because both nlow and the exponent plow in Eq. (5) are greater than nhigh and phigh, respectively.

1.2 Decay time temperature sensitivity and temperature measurement precision

TE D

Using Eqs. (1) to (3) for relaxation by a combination of temperature-independent Wr and single effective phonon energy multiphonon relaxation Wmp, the absolute temperature sensitivity of the decay time measurement, Sabs, can be determined: 9:

9

=

#$; < =

EP

5678 =

>?

( >? )=

(6)

AC C

and the relative sensitivity, Srel, can be expressed: 5@/ =

5@/ ≈

 9:

: 9

=

#$;

#$; < =

< =

>?

 >?

for  ≫ @

(7a) (7b)

Note that for a given ħωeff, Srel increases with increasing ∆E. In contrast, increasing temperature has counteracting effects on Srel as both neff in the numerator and T2 in the

6

ACCEPTED MANUSCRIPT

denominator of Eq. (7a) increase with temperature. While Srel is often given as a figure of merit for decay time-based temperature measurements, the signal-to-noise ratio also factors into the temperature measurement precision. Amiel et al. [18] showed that the concept of noise equivalent temperature difference (NETD), typically applied to thermal

RI PT

imaging cameras, can be usefully applied to phosphor thermometry as a measurement of temperature measurement precision. For decay time-based phosphor thermometry, NETD can be expressed as: IJ

KLMN

=

< = IJ [ >? ]=

#$;

>?

(8)

SC

FGH =

M AN U

where στ is the standard deviation determined for τ. NETD is the temperature range associated with an uncertainty in τ. It is clear that large temperature uncertainties will

occur for Wmp ≪ Wr. Therefore, good temperature precision cannot be obtained until the

onset of temperature sensitivity when Wmp approaches Wr. NETD also shows that

temperature measurement precision will improve by more efficient excitation, which will

pure shot noise:

TE D

decrease στ. As an example, Heeg [19] has shown that for a single-shot measurement with R: = S

:

;TU V

W

X =

(9)

where I0 is the measured quantity corresponding to light intensity at the start of the

EP

luminescence decay (typically voltage, current, or count rate), c is the ratio between the measured quantity and the actual photon counting rate, and n is the number of laser

AC C

pulses being averaged (n = 1 for single-shot measurements). Considering Eqs. (8) and (9), increasing the rate of photons being detected, I0c, will reduce NETD (improving temperature measurement precision) by a multiplicative factor of (1/I0c)½. While this can be accomplished by increasing the excitation pulse energy or increasing n, I0c can also be increased by selecting an excitation with a higher absorption line L (S conventionally denotes line strength, but L is used here to avoid confusion with sensitivity) without increasing the excitation photon “budget” since I0c ∝ L. This consideration is the basis for selecting a strong hypersensitive transition for the excitation. 7

ACCEPTED MANUSCRIPT

1.3 Strategy of reduced ∆E and excitation by hypersensitive transition using Y2O3:Er Y2O3:Er was selected, not only because it has a significantly lower ∆E between its radiating electron energy level and the next lower energy level than YAG:Dy or

RI PT

YAG:Tm, but also because it possesses a hypersensitive transition that can be used to

populate the radiating energy level. Referring to the electron energy level diagram for an Er3+ dopant ion in Y2O3 (Fig. 1), the hypersensitive 4I15/2 → 2H11/2 transition can be used to populate the 4S3/2 emitting level that is only 860 cm-1 [20] below the 2H11/2 level.

SC

Hypersensitive 4f-4f transitions are induced electric dipole transitions that follow electric quadrupole selection rules where the most intense transitions typically occur when ∆J =

M AN U

±2 [21-22], where J is the total (orbital + spin) angular momentum, a criterion that is met by the 4I15/2 → 2H11/2 transition. Unlike most 4f-4f transitions, the hypersensitive transitions are very sensitive to the dopant ion environment and are especially intense for highly non-centrosymmetric environments. Y2O3 is an excellent host for producing a strong hypersensitive 4I15/2 → 2H11/2 transition in Er3+. The Y2O3 sesquioxide crystal structure contains C2 and centrosymmetric C3i cation symmetry sites in a ratio of 3:1 that

TE D

are occupied by the Er3+ dopant ions [20]. Induced electric dipole radiative transitions have not been observed from Er3+ ions occupying the C3i sites due to their inversion symmetry [23-25]. In contrast, the C2 sites are in an eightfold cubic structure with two oxygen vacancies along a face diagonal resulting in a highly non-centrosymmetric

EP

environment. The Y2O3 C2 site has been utilized in the past in lamp phosphors for its very strong hypersensitive radiative emission transition 5D0 → 7F2 from Eu3+ dopant ions [26]. Y2O3:Er luminescence has been studied extensively, and the absorption line strength, L,

AC C

of the hypersensitive 4I15/2 → 2H11/2 transition was determined to be 4.02 x 10-20 cm-2 [27], 5.9 and 22.5 times greater than the non-hypersensitive 4I15/2 → 4F7/2 and 4I15/2 → 4

S3/2 absorption line strengths, respectively. In comparison, L = 0.61 x 10-20 cm-2 [9] for

the excitation transition for YAG:Dy near the commonly used 355 nm excitation wavelength. If all else were equal, the larger L for the Y2O3:Er excitation would result in a reduced στ that is 39% of the value for the YAG:Dy excitation (Eq. (9)). This reduced στ in the numerator of Eq. (8) comes close to offsetting the smaller ∆E (2795 cm-1) for the relevant Y2O3:Er multiphonon transition that is 36% of the value for the corresponding 8

ACCEPTED MANUSCRIPT

YAG:Dy transition (7640 cm-1). Therefore, the higher absorption line strength nearly cancels out the effect of lower Srel on NETD (Eq. (8)), while the less steep decay time temperature dependence associated with a low Srel will allow Y2O3:Er to cover a much wider temperature range than YAG:Dy.

RI PT

This article demonstrates the implementation of a thermographic phosphor with a relatively small ∆E between its radiatively emitting energy level and the level below it for decay time-based temperature measurements over a wide temperature range without sacrificing temperature measurement precision. In particular, it is demonstrated that

SC

Y2O3:Er, with ∆E = 2795 cm-1 between the radiatively emitting 4S3/2 level and the 4F9/2

level below it, can be used to obtain temperature measurements from room temperature to

M AN U

1200 °C, and a strong hypersensitive excitation compensates for a lower Srel. A secondary objective is to definitively demonstrate the previously proposed [14-16] occurrence of a high-temperature transition in multiphonon emission from high to low effective phonon energies. While this transition was used for modeling high-temperature multiphonon emission by YAG:Dy [15], the transition itself could not be observed because the crossover from ħωhigh to ħωlow dominated multiphonon process occurred at temperatures

TE D

below the onset of detectable thermal quenching so that only the small ħωlow dominated behavior is observed. Because Wmp surpasses Wrad for Y2O3:Er even at room temperature [12], this provides an opportunity to examine and verify the crossover from ħωhigh to ħωlow dominated multiphonon emission and to model this behavior by a dual effective

EP

phonon energy model.

AC C

2. Experiment

Sintered disk specimens were fabricated from Y2O3:Er powder (Phosphor

Technology Ltd., UK) produced by solid-state reaction. Because undesirable depopulation of the 2H11/2 and 4S3/2 emitting states of Er3+ is known to occur by crossrelaxation at modest Er3+ concentrations [28-29], a dilute 0.1 mol% dopant concentration Y2O3:Er(0.1 mol%) with stoichiometry Y1.998Er0.002O3 was selected to minimize contributions from cross-relaxation. For comparison purposes, one higher dopant concentration specimen Y2O3:Er(0.8 mol%) with stoichiometry Y1.984Er0.016O3 was also

9

ACCEPTED MANUSCRIPT

prepared. Unless specifically stated otherwise, all measurements reported were from the Y2O3:Er(0.1 mol%) specimens. Fig. 2 shows the setup for performing the decay time versus temperature measurements. The Y2O3:Er disk specimen was placed inside a box furnace with two

RI PT

access holes in the back. Reference temperatures were obtained from a Type R (Pt/Pt-Rh) thermocouple pressed against the disk surface. A 20 Hz pulsed 522 nm excitation beam

provided by a wavelength-tunable optical parametric oscillator (OPO) (Opolette HE 355 LD, Opotek, USA) was aimed at the disk specimen through one of the furnace access

SC

holes. The luminescence emission was collected by an optics assembly with a 125 mm

working distance that was aimed at the specimen through the other furnace access hole. A

M AN U

532 nm longpass filter was mounted inside the collection optics assembly in order to prevent any scattered OPO excitation from being transmitted to the detection assembly. The delivered excitation energy was about 200 µJ/pulse and the excitation beam spot diameter was approximately 4 mm. The collected emission was transmitted via an optical fiber to the detection assembly. The detection assembly consisted of collimating optics to collimate the collected light so as to pass through a bandpass filter centered at 556 nm

TE D

with a full width half maximum (FWHM) of 20 nm before being detected by a photomultiplier tube (PMT) (H6780-20, Hamamatsu, Japan). The PMT was operated at control voltages between 260 and 320 mV (minimum recommended voltage was 250 mV). The unamplified output of the PMT was recorded using a 500 MHz oscilloscope

EP

with a 50 ohm input impedance. Each emission intensity versus decay time curve consisted of 10000 points, averaged over 512 excitation pulses for improved signal to

AC C

noise. A background subtraction was performed by subtracting the average of 900 prepulse intensity values from each point. Luminescence emission and excitation spectra were acquired by replacing the

detection optics and PMT in Fig. 2 with a spectrograph and replacing the collection fiber by a fiber bundle with a round fiber array input and rectangular slit pattern array output. Time-averaged spectra were acquired with a PMT and slit aperture at one spectrograph output, and time-resolved spectra were acquired with an intensified charged couple device (ICCD) detector (PI-MAX 1024RB, Princeton Instruments, USA) at the other exit port. Emission spectra intensities were corrected by referencing to a spectrum obtained 10

ACCEPTED MANUSCRIPT

from a calibrated tungsten lamp. Excitation spectra were obtained by replacing the 522 nm OPO excitation with the collimated output of a monochromator.

3.1 Y2O3:Er excitation and emission spectra

RI PT

3. Results Fig. 3 shows the room temperature excitation spectrum of Y2O3:Er for the 4S3/2 → 4

I15/2 radiative emission at 564 nm. Based on this excitation spectrum, the intense

excitation peak at 522 nm associated with the hypersensitive 4I15/2 → 2H11/2 transition was

SC

selected to efficiently populate the 4S3/2 emitting level for the luminescence decay measurements.

M AN U

The effect of temperature on the emission spectra was investigated by acquiring timeresolved emission spectra so that time gating suppressed the high temperature thermal radiation background. These emission spectra were acquired by excitation via the 4I15/2 → 4

F7/2 transition at 489 nm rather than the 4I15/2 → 2H11/2 transition at 522 nm in order to

allow observation of the full 2H11/2 → 4I15/2 emission band that would have been obscured by the filtering used with 522 nm excitation. Fig. 4 shows the effect of temperature on the

TE D

time-resolved emission spectra collected by multipulse averaging to detect emission for 10 µs after each excitation pulse. It is evident from these emission spectra that the higher energy 2H11/2 → 4I15/2 emission band becomes much more prominent relative to the 4S3/2 → 4I15/2 emission band with increasing temperature. This occurs because thermal

EP

equilibrium is maintained between the thermally coupled 4S3/2 (which acts as a reservoir level) and the 2H11/2 level separated by energy difference ∆Ec; therefore, the relative

AC C

populations of those levels follow a Boltzmann distribution [30]. In addition, the rich emission band fine structure associated with transitions between Stark levels of the excited and ground state manifolds exhibits significant thermal broadening with increasing temperature. The vertical dashed lines in Fig. 4 indicate the wavelength range (FWHM) of the bandpass filter used for the luminescence decay measurements, which includes the uniformly decaying 4S3/2 → 4I15/2 emission band and the long wavelength tail of the thermally coupled 2H11/2 → 4I15/2 emission band. 3.2 Y2O3:Er luminescence decay measurements 11

ACCEPTED MANUSCRIPT

Luminescence decay measurements with 522 nm excitation were collected at approximately 50 °C intervals from room temperature to 500 °C and at 25 °C intervals from 500 to almost 1200 °C. Fig. 5 shows the subsets of the luminescence decay curves using 522 nm excitation obtained at the lower and upper end of the tested temperature

RI PT

range. The intensity is plotted on a logarithmic scale to more easily reveal departures from single exponential decay. Fig. 5a shows the close to single exponential decay

observed at lower temperatures, while Fig. 5b shows the biexponential decay observed at higher temperatures. The lack of significant departure from single exponential decay for

SC

Y2O3:Er(0.1 mol%) at temperatures less than 600 °C, shown in Fig. 6 at 575 °C, indicates an absence of contributions from nonradiative decay by cross-relaxation at this low

M AN U

dopant concentration. Therefore, at temperatures below 600 °C, a single exponential with decay time, τsingle, provides a good fit (dashed line in Fig. 6) to the decay curves: Y (Z) = Y  [/:N,-2

(10)

where I is the intensity, I0 is the initial intensity, and t is time. In contrast, Fig. 6 shows

TE D

initial substantial deviation from single exponential decay for Y2O3:Er(0.8 mol%) that asymptotically approaches the decay rate of Y2O3:Er(0.1 mol%) at long post-excitation times. This substantial contribution from nonradiative decay by cross-relaxation at this higher dopant concentration is undesirable for luminescence decay-based phosphor

EP

thermometry because it makes the decay behavior more complex and provides a nonradiative relaxation path that competes with the multiphonon emission mechanism used for temperature sensing.

AC C

Above 600 °C, despite low Er3+ dopant concentration, Y2O3:Er(0.1 mol%)

exhibits significant departure from single exponential decay (Fig. 5b), and a biexponential with decay times τ1 and τ2 provides a better fit to the decay curves: Y (Z) = Y  [/:X + Y.  [/:=

(11)

where τ1 is the shorter and τ2 is the longer decay time, and I1 and I2 are constants. Because Eq. (11) does not provide stable solutions for both decay constants when there is 12

ACCEPTED MANUSCRIPT

little deviation from single exponential decay, the biexponential fit values were only considered when there was more than 10% difference between τ1 and τsingle. The Levenberg-Marquardt nonlinear least squares regression method was applied for fitting both the single exponential (Eq. (10)) and biexponential (Eq. (11)) models to

RI PT

the luminescence decay data. A flexible yet consistent fitting window range selection was required to accommodate the several orders of magnitude change in decay constants that occurs over the tested temperature range. The intensity-threshold fitting window range

selection method that has been applied previously [31-33] was utilized with only minor

SC

modification. Advantages of the intensity-threshold approach over the iterative decay

time-based selection of the fitting window time interval developed by Brübach et al. [34]

M AN U

have been discussed [31-32,35-36]. For the Y2O3:Er decay measurements reported here, intensity-threshold crossings at 90% and 2% of the initial intensity, I0, were selected to be the start and end of the fitting window range, respectively, as illustrated in Fig. 7. The 90% intensity threshold for the start of the fitting window was chosen to be closer to the start of the luminescence decay than the 60% intensity threshold previously employed [31-32] because of the desire here to accurately determine both τ1 and τ2 as true

TE D

biexponential decay constants relating to nonradiative decay mechanisms, whereas the objective of the earlier work was only to accurately determine τ2. As performed previously [32-33], a 100 point locally estimated scatterplot smoothing (LOESS) was used to minimize the bias effect of intensity signal noise on the intensity threshold

EP

crossover points. The first point from the smoothed data that was below either the 90% or 10% intensity thresholds was selected as the start and end of the fitting window range,

AC C

respectively. Smoothing was only performed for determining intensity-threshold crossings, and the subsequent curve fit was performed on the original unsmoothed data. Fig. 7 shows the fitting window range determined by intensity-threshold crossings at 90% and 2% of initial intensity for a decay measurement at 1015 °C along with the fit determined by fitting Eq. (11) to the data within the fitting window. Decay times determined using the procedures described above are plotted as a function of temperature in Fig. 8. Values of the biexponential decay times τ1 and τ2 are plotted for temperatures above 600 °C, the temperature above which there is a greater than 10% difference between τ1 and τsingle. Values of τsingle are plotted from room 13

ACCEPTED MANUSCRIPT

temperature to 850 °C, including an overlap region with the τ1 and τsingle values between 600 and 850 °C. A typical 95% confidence interval (confidence intervals too small to be plotted on Fig. 8) on the least squares estimates of the decay time values was 1.58 x 10-6 ± 1.07 x 10-8 s for τ2 at 1015 °C, and the largest relative confidence interval for τ2 was

4. Discussion 4.1 Modeling luminescence decay temperature dependence

RI PT

3.62 x 10-7 ± 4.47 x 10-8 s at 1164 °C (highest tested temperature).

SC

The dual effective phonon energy model (Eq. (5)) was used as the basis for the

temperature dependence of the observed decay time, τ, of the thermally coupled 4S3/2 + H11/2 → 4I15/2 emission. The total relaxation rate will include the temperature-dependent

M AN U

2

radiative relaxation rate from the thermally coupled 4S3/2 and 2H11/2 energy levels (modeled previously [37-38]) in addition to the multiphonon relaxation rate:



ge ?234 



)234 h

=

∆ef  b 

=

+  (1 − 

ℏ+,-+ 

)+,-+ + . (1 −

TE D


= ( @ +  ) = ]

∆e

f  ^ _K` a b ^ =cXX a 

(12)

EP

where Wr(4S3/2) is the temperature-independent radiative relaxation rate from the 4S3/2 level, Wr(2H11/2) is the temperature-independent radiative relaxation rate from the 2H11/2

AC C

level, and ∆Ec is the energy difference between the thermally coupled 2H11/2 and 4S3/2 levels. The temperature-independent radiative decay times τr(4S3/2) and τr(2H11/2) are the inverses of Wr(4S3/2) and Wr(2H11/2), respectively. For simplicity, the multilevel manifolds are treated in Eq. (12) as single energy levels. To approximate the manifold-averaged radiative relaxation rate, Wr, ∆Ec is assigned to the energy difference between the centers of gravity of the 2H11/2 and 4S3/2 manifolds. To approximate the manifold-averaged multiphonon relaxation rate, ∆E is assigned to the energy difference between the lowest Stark level of the 4S3/2 manifold and the highest Stark level of the 4F9/2 manifold because

14

ACCEPTED MANUSCRIPT

the probability of multiphonon emission is highly weighted for transitions with smaller ∆E values (Eq. (4c)). Calculating the decay time using Eq. (12) requires determination of eight parameters: Wr(4S3/2), Wr(2H11/2), ∆Ec, ∆E, W10, W20, phigh, and plow (phonon energies, ħω, can be

RI PT

substituted for p through the relationship ħω = ∆E/p). While these eight parameters could be theoretically determined by making them all adjustable parameters in a fit of Eq. (12) to the data, significant parameter correlations would make a reliable inverse solution of Eq. (12) difficult [39]. Fortunately, the dynamics of Y2O3:Er have been extensively

SC

studied [11-12, 20] and parameters could be assigned constant values from the literature (see Table 1), except for W10, W20, and plow, which remained as the three adjustable

M AN U

parameters for fitting Eq. (12) to the data.

Eq. (12) corresponds to a single exponential decay process with decay time τ. However, a transition from single to biexponential decay was observed to begin at about 600 °C in Fig. 8, beyond which the application of Eq. (12) is less straightforward. Because the decay of Y2O3:Er(0.8 mol%) was observed to asymptotically approach the long-term decay (τ2) from Y2O3:Er(0.1 mol%), it was concluded that τ2 represented a

TE D

dopant concentration independent decay process and was a continuation of the τsingle single exponential decay observed from Y2O3:Er(0.1 mol%) below 600 °C. The faster decay associated with τ1 would then be associated with either a faster Wmp from a different symmetry site or with an additional relaxation process not represented in Eq.

Section 4.2.

EP

(12). These possible sources for the biexponential decay behavior are discussed in

AC C

The temperature range selection of decay values to be fit by Eq. (12) is complicated by nonrobustness of the decay values determined in the single to biexponential decay transition between 600 and 850 °C where the values of τ1 and τ2 are relatively close. Lakowicz [40] has indicated that it is difficult to determine biexponential decay times when τ2 < 2τ1 because the coefficients and decay times in Eq. (11) are highly correlated when τ1 and τ2 are close. The twofold criterion τ2 > 2τ1 is met only at temperatures greater than 850 °C; therefore, the decay time values within the 600 to 850 °C transition region were not included when fitting Eq. (12) to the decay time data. A fit of Eq. (12) to the combined set of τsingle and τ2 values, excluding values in the 600 to 850 °C range, was 15

ACCEPTED MANUSCRIPT

performed using the Levenberg-Marquardt nonlinear least squares regression method, and the residuals were taken as the differences between the natural logarithms of the data and the fit values. The natural logarithm was applied as a variance-stabilizing transformation because the standard error for the decay times was much closer to a

RI PT

percentage of the decay time than a constant value. The values of W10, W20, and plow and their 95% confidence intervals determined by the fit are presented in Table 2, and the fit is plotted as a solid line in Fig. 8. It should be noted that a relatively small uncertainty in plow correlates with a much larger relative uncertainty in W20 as seen in Table 2. This

SC

occurs because plow has a much stronger effect on Wmp than does W20 over the limited high temperature range where relaxation is dominated by low phonon energy

multiphonon emission. As a result, only order-of-magnitude precision is obtained for W20.

M AN U

The resulting value of plow = 18.8 indicates that there was a transition from a 550 cm-1 effective phonon energy five-phonon emission process at low temperatures to a 149 cm-1 phonon energy nineteen-phonon emission relaxation process at high temperatures. The transition to a higher order phonon emission process at high temperature represents an effective phonon energy transition from ħωhigh to ħωlow, where ħωhigh is

TE D

close to the largest Y2O3 phonon energy and ħωlow is close to the smallest Y2O3 phonon energy. This interpretation of ħωlow is supported by the close agreement of ħωlow = 149 cm-1 to the two lowest energy Y2O3 Raman peaks at 129 and 162 cm-1 [41]. The effect of the transition in effective phonon energy for multiphonon relaxation is seen more clearly

EP

in Fig. 9 by the decomposition of the total relaxation rate into the separate terms given in Eq. (12). The contributions from the coupled radiative relaxation from the 2H11/2 and 4S3/2

AC C

levels (first term), the high effective phonon energy multiphonon relaxation rate (second term), and the low effective phonon energy multiphonon relaxation rate (third term) are plotted separately. Fig. 9 shows a crossover of the ħωhigh and ħωlow multiphonon emission rates at about 950 °C, beyond which the more temperature-sensitive ħωlow multiphonon emission starts to dominate the total relaxation rate. While either the high or low effective phonon energy process in Eq. (12) is expected to dominate over most of the full temperature range, it is likely that intermediate effective phonon energies contribute to multiphonon emission processes in a temperature interval around the 950 °C transition. Note that although the ratio of the 2H11/2 → 4I15/2 to the 4S3/2 → 4I15/2 emission intensities 16

ACCEPTED MANUSCRIPT

has been shown to be a sensitive temperature indicator [42-48], Fig. 9 shows that their thermally coupled relaxation rates have only a minor effect on the total relaxation rate, consistent with previous studies [12,38]. Contrary to the previously proposed [2,53] important role of this thermally coupled radiative emission to the two distinct ranges of

RI PT

Er3+ emission decay temperature dependence, Fig. 9 shows that this coupled radiative

decay has no appreciable role in producing the two distinct temperature sensitivity ranges observed in Fig. 8.

SC

4.2 Source of biexponential decay

The typical source of biexponential decay behavior described by Eq. (11) is emission

M AN U

from two distinct crystallographic sites resulting in two decay time constants, τ1 and τ2. However, while Y2O3 does have the two distinct symmetry sites C2 and C3i, radiative emission from the 2H11/2 and 4S3/2 energy levels of Y2O3:Er has only been observed from the C2 symmetry site [23-25], as emission from the C3i site is forbidden due to its inversion symmetry. While radiative emission from these energy levels by the C3i site has not been previously observed, it is conceivable that mixing of odd-parity vibrational

TE D

modes with the 2H11/2 or 4S3/2 electronic levels could allow for otherwise parity-forbidden excitation or emission at high temperatures [49]. To search for spectral evidence of radiative emission from C3i or other possible symmetry sites responsible for biexponential decay, time-resolved emission spectra were acquired at temperatures where

EP

biexponential decay is clearly observed. Time-resolved emission spectra were acquired during intervals of the emission decay that were dominated by either the fast initial

AC C

decay, τ1, or the slower long-term decay, τ2. Fig. 10 compares a time-resolved emission spectrum acquired at 971 °C over the first 1.5 µs of emission decay (with no delay after the excitation pulse) with a spectrum acquired over an interval of 2 µs starting with a 4 µs delay after the excitation pulse. As the Fig. 10 inset shows, the first spectrum (solid line) is collected over an interval where decay is dominated by relaxation processes associated with τ1, and the second spectrum is collected over an interval where decay is dominated by relaxation processes dominated by τ2. Because no significant spectral differences are observed, it can be concluded that radiative emission continues to originate exclusively

17

ACCEPTED MANUSCRIPT

from the C2 symmetry site at the high temperatures where biexponential decay is observed. Another potential source for non-monoexponential decay is cross-relaxation. The single exponential decay observed below 600 °C indicates that the 0.1 mol% Er3+ dopant

RI PT

concentration was sufficiently dilute to avoid cross-relaxation effects. However, crossrelaxation processes may become more likely at higher temperatures because the

increasingly thermally populated 2H11/2 energy level is substantially more susceptible to both cross-relaxation and energy migration than the 4S3/2 energy level in Y2O3:Er due to

SC

the higher oscillator strengths associated with transitions to and from the 2H11/2 energy level [27]. In particular, the primary cross-relaxation process that depopulates the 2

H11/2 + 4I15/2 → 4I9/2 + 4I13/2

M AN U

thermally coupled 2H11/2 and 4S3/2 excited levels has been identified to be [28-29]: (13)

Therefore the excited level depopulation will be enhanced by the increasing thermal population of the 2H11/2 energy level that occurs with increasing temperature. While the reverse direction process of Eq. (13) (upconversion) could contribute to reducing the decay rate, its occurrence would be exceedingly unlikely, as it would require the close

TE D

proximity of two transient cross-relaxation products from a dilute Er3+ dopant concentration. Without energy migration, the cross-relaxation process described by Eq. (13) cannot produce the observed biexponential decay behavior (Fig. 7), because the distribution of Er3+ inter-ion distances will produce the nonexponential decay behavior

EP

modeled by Inokuti and Hirayama [50]. Single exponential decay, however, can be observed for the special case when fast energy migration occurs among Er3+ dopant ions before depopulation of excited energy levels occurs by Eq. (13) [51-52]. Energy

AC C

migration from the 2H11/2 excited state, with no net excited energy level depopulation, is favored for Er3+ dopant ions due to the strong hypersensitive transitions 2H11/2 ↔ 4I15/2 involved in the cross-relaxation process responsible for energy migration: 2

H11/2 + 4I15/2 → 4I15/2 + 2H11/2

(14)

Because the resonant energy migration process given by Eq. (14) consists of strong hypersensitive transitions, it is much more likely to occur than the excited state depopulating cross-relaxation given by Eq. (13); therefore, energy migration can occur over greater inter-ion distances than excited state depopulating cross-relaxations. Energy 18

ACCEPTED MANUSCRIPT

migration via Eq. (14) will, however, only produce nonradiative relaxation if there is an energy trap within the energy migration dopant ion network. In the case considered here, the energy trap is considered to be a location where the Er3+ dopant ion is sufficiently close to another Er3+ ion that the excited state depopulating cross-relaxation has

RI PT

significant probability. Huber [52] has shown that when energy migration is fast enough, the excitation is effectively delocalized and experiences a spatially averaged energy trap environment. Under these conditions, fast energy migration in the presence of energy traps results in a temperature-dependent energy trap relaxation rate, Wtrap(T). When

SC

combined with the modified dual effective phonon energy multiphonon relaxation model (Eq. (12)), single exponential decay behavior will be observed with decay time τ1 given


 = [: + [@6 ()] 

=

M AN U

by:

(15)

where τ2 is given by the right-hand side of Eq. (12). Note that Wtrap(T) will increase with temperature, both because energy migration (Eq. (14)) increases with increased thermal population of the 2H11/2 energy level and because the energy traps become more effective

TE D

as the energy mismatches associated with nonresonant cross-relaxations such as Eq. (13) (and others with greater energy mismatches) become more easily compensated for at higher temperatures. The observed biexponential decay behavior could then be explained by a bimodal distribution of Er3+ dopant ions at C2 symmetry with one subset of ions

EP

belonging to energy migration networks with energy traps (Er3+ ions with close Er3+ neighbors) and the other subset consisting of ions effectively isolated from energy traps.

AC C

The subset in networks with energy traps would exhibit single exponential decay behavior with decay time given by Eq. (15), while the subset of isolated ions would exhibit slower single exponential decay behavior with decay time given by Eq. (12). A possible explanation for a bimodal distribution of regions with and without close Er3+ ion pair energy traps is that it is difficult to produce a uniformly random distribution of dopant ions at low dopant concentration by solid state reaction. The possibility that fast energy migration in the presence of energy traps at 0.1 mol% dopant concentration could be responsible for the fast initial decay observed at temperatures above 600 °C requires further validation along with modeling of the temperature dependence of Wtrap(T). 19

ACCEPTED MANUSCRIPT

While the mechanism underlying the faster decay associated with τ1 was unclear, the temperature dependence remains useful for phosphor thermometry. To this end, a fit of Eq. (12) to the combined set of τsingle and τ1 values, again excluding values in the 600 to 850 °C range, was performed. This approach may be physically unrealistic as Eq. (12)

RI PT

neglects potential contributions from cross-relaxation contributions to the faster decay

associated with τ1. The values of W10, W20, and plow determined by the fit are presented in Table 2, and the fit is plotted as a dashed line in Fig. 8. While the physical meaning of the results of the fit to the combined set of τsingle and τ1 parameters is unclear, they are

M AN U

4.3 Thermographic phosphor performance of Y2O3:Er

SC

included as a potentially useful parametric characterization of τ1 temperature dependence.

The performance of Y2O3:Er as a luminescence lifetime-based thermographic phosphor can be divided into different temperature ranges due to both a crossover in multiphonon emission relaxation from high to low effective phonon energies at about 950 °C and a transition from single to biexponential decay that occurs between 600 and 850 °C. The transition in multiphonon emission from high to low effective phonon energies

TE D

greatly increases the decay time temperature sensitivity. The relative sensitivity, Srel = (1/τ)(dτ/dT), can be evaluated by taking the temperature derivative of τ from Eq. (12) determined from the fit to the combined set of τsingle and τ2 values shown in Fig. 8. Srel is plotted in Fig. 11 in units of % K-1 versus temperature. Fig. 11 shows that a fairly stable

EP

Srel of about 0.35 % K-1 is observed below 600 °C where relaxation is dominated by high phonon energy multiphonon emission (see Fig. 9). Above 600 °C, Srel rapidly increases

AC C

up to 1.1 % K-1 as the relative contribution of low phonon energy multiphonon emission increases until becoming dominant at about 1100 °C (see Fig. 9). These results therefore show a large benefit in temperature sensitivity produced by the transition in multiphonon emission from high to low effective phonon energies. It should be noted that two distinct temperature sensitivity ranges have been previously observed for Er3+-doped yttriastabilized zirconia that was chosen as a candidate for temperature sensing applied to thermal barrier coatings [2,53]. While yttria-stabilized zirconia is an ideal nonintrusive dopant host for integration into thermal barrier coatings that are composed of yttriastabilized zirconia, compared with Y2O3, it is not a good general-purpose thermographic 20

ACCEPTED MANUSCRIPT

phosphor host candidate because of its known low excitation efficiency and lower temperature range associated with its disordered oxygen vacancy network [54]. While the transition in multiphonon emission from high to low effective phonon energies at high temperature produced a desirable increase in temperature sensitivity, the

RI PT

transition from single to biexponential decay that begins at about 600 °C complicates

analysis of the decay curves. Below 600 °C, the very close to single exponential decay is ideal behavior for thermographic phosphor purposes, in particular, allowing for accurate temperature measurements based on rapid lifetime determination (RLD) from only two

SC

time intervals during the decay [55]. With RLD enabled by single exponential decay behavior, luminescence lifetime-based phosphor thermometry can be extended from

M AN U

PMT-based spot temperature measurements to dual-gate CCD-based temperature imaging [56]. Beyond 600 °C, an increasing number of gates would be required to capture enough decay intervals to uniquely represent the non-monoexponential decay. While deviations from single exponential decay begin at about 600 °C, clear biexponential decay (when τ2 > 2τ1) does not begin until 850 °C. Therefore, for phosphor thermometry purposes (where quantifying physical processes responsible for relaxation is

TE D

not important), it is recommended that decay curves should be fit by a single exponential decay (Eq. (10)) up to 850 °C. Above 850 °C, fit by a biexponential decay (Eq. (11)) is preferred because the measured decay can be decomposed unambiguously into two distinct exponential decay components. Applying a different decay model at low versus

EP

high temperatures will not create a problem as long as the temperature range of interest is fully below or above 850 °C, but may be a complication if the temperature range of

AC C

interest spans that temperature.

4.4 Implications for phosphor thermometry The shift from high to low effective phonon energies for multiphonon relaxation at

high temperatures has important implications for luminescence decay-based phosphor thermometry when multiphonon emission is the primary mechanism for temperaturedependent nonradiative relaxation. Heyes [15] has shown that while spontaneous multiphonon emission rates are higher for dopant hosts with higher maximum phonon energies, stimulated multiphonon emission rates at high temperatures are higher for hosts 21

ACCEPTED MANUSCRIPT

with lower maximum phonon energies (leading to lower luminescence quenching temperatures). This discrepancy is explained by a shift from high to low effective phonon energies for multiphonon relaxation. The high luminescence quenching temperatures and steep decay time temperature dependence beyond the onset of quenching were well

RI PT

modeled by stimulated multiphonon emission via a large number of low-energy phonons as opposed to an energy equivalent lower number of high-energy phonons. The

occurrence of the transition from high to low effective phonon energies was not observed for Y2O3:Eu or YAG:Dy [15] because radiative decay rates dominated relaxation at lower

SC

temperatures. In contrast, the luminescence decay behavior observed here for Y2O3:Er

clearly exhibits a crossover from high to low effective phonon energy at about 950 °C

M AN U

and further validates the occurrence of a transition to lower effective phonon energies for stimulated multiphonon emission at high temperatures. Observation of this crossover for Y2O3:Er is possible because the much smaller ∆E of 2795 cm-1 between the 4S3/2 emitting level and the 4F9/2 energy level below it allows high effective phonon energy multiphonon emission rates to dominate radiative relaxation rates below the crossover temperature. The validation of a crossover suggests that the shift at high temperature to multiphonon

TE D

emission by a large number of low energy phonons is responsible for the high quenching temperature and very steep temperature dependence of thermographic phosphors successfully used at very high temperatures, such as YAG:Dy and YAG:Tm [33,57-61]. The results reported here for Y2O3:Er show that a thermographic phosphor with a

EP

relatively small ∆E (2795 cm-1) between its emitting level and the next lower energy level can be effective from room temperature to 1200 °C even though multiphonon emission

AC C

already dominates total relaxation rates at room temperature. Although Y2O3:Er exhibits lower Srel than phosphors with larger ∆E such as YAG:Dy, it covers a much wider temperature range without a sacrifice in temperature measurement precision due to more efficient excitation via a hypersensitive transition. Therefore, a larger ∆E is not always beneficial for high temperature measurements; rather, tradeoffs between temperature measurement range and sensitivity should be considered toward an optimal ∆E. In addition, when very strong reflected thermal radiation is present (such as reflections of combustor radiation from first stage vanes and blades), it may be necessary to select a thermographic phosphor that emits at short wavelengths where there is less competition 22

ACCEPTED MANUSCRIPT

from reflected thermal radiation. In this regard, YAG:Dy (emits at 456, 484, and 496 nm [57-61]) and YAG:Tm (emits at 365 and 456 nm [33]) retain an advantage over Y2O3:Er, which emits at longer wavelengths (556 nm in the results reported here). Y2O3:Er is also limited to low dopant concentrations, as are YAG:Dy and YAG:Tm, to minimize

RI PT

nonradiative decay by cross-relaxation.

The shift at high temperature to an effective phonon energy of 149 cm-1 (close to the lowest energy available phonons in Y2O3) reverses several of the criteria normally used

for selecting dopant hosts to minimize nonradiative relaxation. Usually, a host is selected

SC

with a low maximum phonon energy so that nonradiative relaxation by multiphonon

emission will be minimized, resulting in higher onset temperatures for luminescence

M AN U

quenching. To this end, hosts with heavier anions and less covalent bonding are typically selected; lower covalency explains why halides are preferred over oxides for dopant hosts at lower temperatures [62-63]. In contrast, when low phonon energy multiphonon relaxation rates dominate nonradiative relaxation at high temperatures, a dopant host should be selected for a low phonon density of states at low phonon energies. Therefore, to increase the energy of low energy phonon modes, stronger (not weaker) covalent

TE D

bonding is desired (oxides preferred over halides). In addition, because lower energy phonon modes are associated with vibrations of the metal cations [41], decreasing the cation mass will increase the energy of the low energy phonons [ω ≈ (k/M)½ where k is the bond strength and M is the phonon reduced mass]. In this regard, the high Al content

AC C

Conclusions

EP

in YAG (Y3Al5O12) is desirable for increasing the energy of the low energy phonons.

While thermographic phosphors for high temperature measurements are usually

selected for a high temperature onset of thermal quenching, this work shows that successful luminescence decay-based thermometry measurements can be obtained from room temperature to almost 1200 °C using a thermographic phosphor Y2O3:Er that already exhibits significant thermal quenching by multiphonon emission at room temperature. This wide temperature range relies on the choice of a relatively small ∆E (2795 cm-1) between the 4S3/2 emitting energy level and the next lower energy level 4F9/2. Because the small ∆E both lowers the onset of thermal quenching by multiphonon 23

ACCEPTED MANUSCRIPT

emission (according to Eqs. (1) and (2)) and decreases the decay time temperature sensitivity (according to Eq. (7a)), a much larger temperature measurement range is achieved than for phosphors with larger ∆E values. Therefore, a tradeoff between temperature measurement range and precision should always be part of a consideration of

RI PT

optimal ∆E. Both wide measurement range and high precision can be achieved with

Y2O3:Er by utilizing its intense hypersensitive 4I15/2 → 2H11/2 excitation at 522 nm that offsets the measurement precision reduction produced by the decreased decay time temperature sensitivity.

SC

The dominance of multiphonon emission over the room temperature to 1200 °C measurement range for Y2O3:Er allowed observation of the transition in multiphonon

M AN U

emission from high to low effective phonon energies at about 950 °C. The occurrence of this transition has not been previously observed for other high temperature thermographic phosphors with larger ∆E values because the onset of thermal quenching by multiphonon emission does not occur for those phosphors until beyond the temperature for the crossover between high and low phonon energy multiphonon emission rates. For Y2O3:Er, a dual effective phonon energy model was used to fit the temperature

TE D

dependence of the decay time and was based on high and low effective phonon energy multiphonon emission dominating temperature dependence below and above the transition temperature, respectively. This transition in the effective phonon energy results in two distinct ranges of temperature sensitivity (Figs. 8 and 11) because the multiphonon

EP

emission rate by a larger number of lower energy phonons is more strongly temperature dependent than the emission rate by a smaller number of higher energy phonons.

AC C

The luminescence emission decay behavior for Y2O3:Er exhibited a gradual transition from single to biexponential decay between 600 and 850 °C. The source of the biexponential behavior above 600 °C is unclear, as no changes occurred in time-resolved emission spectra acquired at different delay times after the excitation pulse, precluding emission from a second symmetry site as the source of the additional exponential decay component. An argument was made that the faster decay component could be due to fast energy migration in the presence of energy traps consisting of close Er3+ ions that could undergo a nonradiative cross-relaxation process. Further investigation is required to

24

ACCEPTED MANUSCRIPT

verify whether this fast energy migration among Er3+ ions can occur at a dilute dopant concentration of 0.1 mol% at temperatures above 600 °C. Finally, the transition in multiphonon emission from high to low effective phonon energies has important implications for selection of dopant hosts for high temperature

RI PT

thermographic phosphor applications. Usually, dopant hosts are chosen for low maximum phonon energies so that the onset of thermal quenching by multiphonon emission occurs at higher temperatures. However, at temperatures beyond the transition from high to low effective phonon energies, dopant hosts should be selected for a low density of states of

SC

low energy phonons, favoring stronger covalent bonding and lower metal cation masses.

M AN U

Acknowledgments

The author gratefully acknowledges the support of the NASA Transformational Tools and Technologies Project.

References

[1] S.W. Allison, G.T. Gillies, Remote thermometry with thermographic phosphors:

TE D

Instrumentation and applications, Rev. Sci. Instrum. 68 (1997) 2615-2650. [2] M.D. Chambers, D.R. Clarke, Doped oxides for high-temperature luminescence and lifetime thermometry, Annu. Rev. Mater. Res. 39 (2009) 325-359. [3] A.H. Khalid, K. Kontis, Thermographic phosphors for high temperature

EP

measurements: Principles, current state of the art and recent applications, Sensors 8 (2008) 5673-5744.

AC C

[4] M. Aldén, A. Omrane, M. Richter, G. Särner, Thermographic phosphors for thermometry: A survey of combustion applications, Prog. Energy Combust. Sci. 37 (2011) 422-461.

[5] J. Brübach, C. Pflitsch, A. Dreizler, B. Atakan, On surface temperature measurements with thermographic phosphors: A review, Prog. Energy Combust. Sci. 39 (2013) 37-60. [6] N. Fuhrmann, J. Brübach, A. Dreizler, Phosphor thermometry: A comparison of the luminescence lifetime and the intensity ratio approach, Proc. Combust. Inst. 34 (2013) 3611-3618.

25

ACCEPTED MANUSCRIPT

[7] E. Suarez, H.R. Przirembel, Pyrometry for turbine blade development, J. Propul. Power 6 (1990) 584-589. [8] C. Kerr, P. Ivey, An overview of the measurement errors associated with gas turbine aeroengine pyrometer systems, Meas. Sci. Technol. 13 (2002) 873-881.

RI PT

[9] A. Lupei, V. Luppi, C. Gheorghe, A. Ikesue, M. Enculsecu, Spectroscopic

characteristics of Dy3+ doped Y3Al5O12 transparent ceramics, J. Appl. Phys. 110 (2011) 083120.

[10] J.B. Gruber, M.E. Mills, R.M. Macfarlane, C.A. Morrison, G.A. Turner, G.J.

SC

Quarles, G.J. Kintz, L. Estorowitz, Spectra and energy levels of Tm3+:Y3Al5O12, Phys. Rev. B 40 (1989) 9464-9478.

M AN U

[11] L.A. Riseberg, H.W. Moos, Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals, Phys. Rev. 174 (1968) 429-438.

[12] M.J. Weber, Radiative and multiphonon relaxation of rare-earth ions in Y2O3, Phys. Rev. 171 (1968) 283-291.

[13] B.H. Henderson, G.F. Imbusch, Optical Spectroscopy of Inorganic Solids, Oxford University Press, Oxford, 1989.

TE D

[14] P. Kisliuk, C.A. Moore, Radiation from the 4T2 state of Cr3+ in ruby and emerald, Phys. Rev. 160 (1967) 307-312.

[15] A.L. Heyes, On the design of phosphors for high-temperature thermometry, J. Luminescence 129 (2009) 2004-2009.

EP

[16] J.L. Kennedy, N. Djeu, Energy transfer in rare earth doped Y3Al5O12 at very high temperatures, J. Luminescence 101 (2003) 147-153.

AC C

[17] J.L. Kennedy, Investigations of fiber optic temperature sensors based on Yb:Y3Al5O12, Ph.D Thesis, University of South Florida, 2006. [18] S. Amiel, E. Copin, T. Sentenac, P. Lours, Y. Le Maoult, On the thermal sensitivity and resolution of a YSZ:Er3+/YSZ:Eu3+ fluorescent thermal history sensor, Sensors Actuators A 272 (2018) 42-52. [19] B. Heeg, Precision of least-squares mono-exponential decay time estimates from optical measurements with both photon shot noise and background noise, Meas. Sci. Technol. 24 (2013) 125201.

26

ACCEPTED MANUSCRIPT

[20] P. Kisliuk, W.F. Krubke, J.B. Gruber, Spectrum of Er3+ in single crystals of Y2O3, J. Chem. Phys. 40 (1964) 3606-3610. [21] F.S. Richardson, Selection rules for lanthanide optical activity, Inorg. Chem. 19 (1980) 2806-2812.

Materials, Springer-Verlag Berlin Heidelberg, 2005.

RI PT

[22] M. Gaft, R. Reisfeld, G. Panczer, Luminescence Spectroscopy of Minerals and

[23] J.B. Gruber, K.L. Nash, D.K. Sardar, U.V. Valiev, N. Ter-Gabrielyan, L.D. Merkle, Modeling optical transitions of Er3+ (4f11) in C2 and C3i sites in polycrystalline Y2O3, J.

SC

Appl. Phys. 104 (2008) 023101.

[24] P.A. Tanner, X. Zhou, F. Liu, Assignment of electronic transitions and electron-

M AN U

phonon coupling of Er3+ doped into Y2O3, J. Phys. Chem. A 108 (2004) 11521-11525. [25] D. den Engelsen, G.R. Fern, T.G. Ireland, J. Silver, Reassignment of electronic transitions in the laser-activated spectrum of nanocrystalline Y2O3:Er3+, J. Luminescence 196 (2018) 337-346.

[26] T. Kano, Principal phosphor materials and their optical properties, in Phosphor Handbook, S. Shionoya, W.M. Yen, Eds., CRC Press, Boca Raton, U.S.A., 1999.

TE D

[27] D.K. Sardar, K.L. Nash, R.M. Yow, J.B. Gruber, Absorption intensities and emission cross section of intermanifold transition of Er3+ in Er3+:Y2O3 nanocrystals, J. Appl. Phys., 101 (2007) 113115.

[28] J.A. Capobianco, F. Ventrone, J.C. Boyer, A. Speghini, M. Bettinelli, Enhancement

EP

of red emission (4F9/2 → 4I15/2) via upconversion in bulk and nanocrystalline cubic Y2O3:Er3+, J. Phys. Chem. B 106 (2002) 1181-1187. [29] J. Zhang, S. Wang, L. An, M. Liu, L. Chen, Infrared to visible upconversion

AC C

luminescence in Er3+:Y2O3 transparent ceramics, J. Luminescence 122-123 (2007) 8-10. [30] S.F. Collins, G.W. Baxter, S.W. Wade, T. Sun, K.T.V. Grattan, Z.Y. Zhang, A.W. Palmer, Comparison of fluorescence-based temperature sensor schemes: Theoretical analysis and experimental validation, J. Appl. Phys. 84 (1998) 4649-4654. [31] J.I. Eldridge, M.D. Chambers, Fiber optic thermometer using Cr-doped GdAlO3 broadband emission decay, Meas. Sci. Technol. 26 (2015) 095202. [32] J.I. Eldridge, Single fiber temperature probe configuration using anti-Stokes luminescence from Cr:GdAlO3, Meas. Sci. Technol. 29 (2018) 065206. 27

ACCEPTED MANUSCRIPT

[33] J.I. Eldridge, S.W. Allison, T.P. Jenkins, S.L. Gollub, C.A. Hall, D.G. Walker, Surface temperature measurements from a stator vane doublet in a turbine afterburner flame using a YAG:Tm thermographic phosphor, Meas. Sci. Technol. 27 (2016) 125205.

exponential decay curves, Opt. Lasers Eng. 47 (2009) 75-79.

RI PT

[34] J. Brübach, J. Janicka, A. Dreizler, An algorithm for the characterization of multi-

[35] C. Knappe, K. Pfeiffer, M. Richter, M. Aldén, A library-based algorithm for

evaluation of luminescent decay curves by shape recognition in time domain phosphor thermometry, J. Therm. Anal. Calorim. 115 (2013) 545-554.

SC

[36] F. Abou Nada, C. Knappe, X. Xu, M. Richter, M. Aldén, Development of an

automatic routine for calibration of thermographic phosphors, Meas. Sci. Technol. 25

M AN U

(2014) 025201.

[37] W. Ryba-Romanowski, Effect of temperature and activator concentration on luminescence decay of erbium-doped tellurite glass, J. Luminescence 46 (1990) 163-172. [38] X. Chen, E. Ma, G. Liu, M. Yin, Excited-state dynamics of Er3+ in Gd2O3 nanocrystals, J. Phys. Chem. 111 (2007) 9638-9643.

[39] S. Kück, Recent development in laser crystals with 3d ions, in Optical Properties of

TE D

3d-Ions in Crystals: Spectroscopy and Crystal Field Analysis, N.M. Avram, M.G. Brik, Eds., Springer-Verlag Berlin Heidelberg, 2013. [40] J.R. Lakowicz, Principles of Fluorescence Spectroscopy, Kluwer Academic / Plenum Publishers, New York, 1999.

EP

[41] M.V. Abrashev, N.D. Todorov, J. Geshev, Raman spectra of R2O3 (R – rare earth) sesquioxides with C-type bixbyite crystal structure: A comparative study, J. Appl. Phys.

AC C

116 (2014) 103508.

[42] P.V. Dos Santos, M.T. de Araujo, A.S. Gouveia-Neto, J.A. Medeiros Neto, A.S.B. Sombra, Optical thermometry through infrared excited upconversion fluorescence emission in Er3+ - and Er3+–Yb3+-doped chalcogenide glasses, IEEE J. Quantum Electr. 35 (1999) 395-399.

[43] H.C. Seat, J.H. Sharp, Er3+ + Yb3+-codoped Al2O3 crystal fibres for high-temperature sensing, Meas. Sci. Technol. 14 (2003) 279285.

28

ACCEPTED MANUSCRIPT

[44] X. Guo, H. Zhao, H. Song, E. Zhang, C. Combs, N. Clemens, X. Chen, K.K. Li, Y.K. Zou, H. Jiang, Upconverting phosphor thermometry for high temperature sensing capability, Sensors Transd. J. 13 (2011) 124-130. [45] W. Xu, X. Gao, L. Zheng, P. Wang, Z. Zhang, W. Cao, Optical thermometry

RI PT

through green upconversion emissions in Er3+/Yb3+-codoped CaWO4 phosphor, Appl. Phys. Exp. 5 (2012) 072201.

[46] G. Liu, L. Fu, Z. Gao, X. Yang, Z. Fu, Z. Wang, Y. Yang, Investigation into the

phosphors, RSC Adv. 5 (2015) 51820-51827.

SC

temperature sensing behavior of Yb3+ sensitized Er3+ doped Y2O3, YAG and LaAlO3

[47] H. Suo, C. Guo, T. Li, Broad-Scope thermometry based on dual-color modulation

M AN U

up-conversion phosphor Ba5Gd8Zn4O21:Er3+/Yb3+, J. Phys. Chem. 120 (2016) 2914-2924. [48] D. Manzani, J.F.S. Petruci, K. Nigoghossian, A.A. Cardoso, S.J.L. Ribeiro, A portable luminescent thermometer based on green upconversion emission of Er3+/Yb3+ co-doped tellurite glass, Nature Sci. Rep. 7 (2017) 41596.

[49] B.H. Henderson, R.H. Bartram, Crystal-Field Engineering of Solid-State Laser Materials, Cambridge University Press, 2000.

TE D

[50] M. Inokuti, F. Hirayama, Influence of energy transfer by the exchange mechanism on donor luminescence, J. Chem. Phys. 43 (1965) 1978-1989. [51] W.B. Gandrud, H.W. Moos, Rare-earth infrared lifetimes and exciton migration rates in trichloride crystals, J. Chem. Phys. 49 (1968) 2170-2182.

2314.

EP

[52] D.L. Huber, Fluorescence in the presence of traps, Phys. Rev. B 20 (1979) 2307-

[53] Y. Shen, M.D. Chambers, D.R. Clarke, Effects of dopants and excitation wavelength

AC C

on the temperature sensing of Ln3+-doped 7YSZ, Surf. Coat. Technol. 203 (2008) 456460.

[54] S.J. Skinner, J.P. Feist, I.J.E. Brooks, S. Seefeldt, A.L. Heyes, YAG:YSZ composites as potential thermographic phosphors for high temperature sensor application, Sensors Actuators B 136 (2009) 52-59. [55] B. Heeg, Precision of mono-exponential decay estimates from rapid lifetime determination in the presence of signal photon and background noise, Meas. Sci. Technol. 25 (2014) 105201. 29

ACCEPTED MANUSCRIPT

[56] D. Peng, Y. Liu, X. Zhao, K.C. Kim, Comparison of lifetime-based methods for 2D phosphor thermometry in high temperature environment, Meas. Sci. Technol. 27 (2016) 095201. [57] L.P. Goss, A.A. Smith, M.E. Post, Surface thermometry by laser-induced

RI PT

fluorescence, Rev. Sci. Instrum. 60 (1989) 3702-3706.

[58] M.R. Cates, S.W. Allison, S.L. Jaiswal, D.L. Beshears, YAG:Dy and YAG:Tm

fluorescence to 1700 °C, ISA 49th Int. Instrumentation Symposium, vol. 49 (2003) 389400.

SC

[59] G. Jovicic, L. Zigan, S. Will, A. Leipertz, Luminescence properties of the

thermographic phosphors Dy3+:YAG and Tm3+:YAG for the application in high

M AN U

temperature systems, Z. Phys. Chem. 229 (2015) 977-997.

[60] E. Hertle, L. Chepyga, M. Batentschuk, L. Zigan, Influence of codoping on the luminescence properties of YAG:Dy for high temperature phosphor thermometry, J. Luminescence 182 (2017) 200-207.

[61] M. Yu, G. Särner, C.C.M. Luijten, M. Richter, M. Aldén, R.S.G. Baert, L.P.H. de Goey, Survivability of thermographic phosphors (YAG:Dy) in a combustion

TE D

environment, Meas. Sci. Technol. 21 (2010) 037002.

[62] Y. Kalisky, The Physics and Engineering of Solid State Lasers, SPIE Press, Bellingham, U.S.A., 2006.

[63] M. Pollnau, Dynamics of solid-state coherent light sources, in Frontiers of Optical

EP

Spectroscopy: Investigating Extreme Physical Conditions with Advanced Optical Techniques, B. Di Bartolo, O. Forte, Eds., Kluwer Academic Publishers, Dordrecht, The

AC C

Netherlands, 2005.

30

ACCEPTED MANUSCRIPT

Table 1 Nonadjustable parameters obtained from literature for Y2O3:Er.

Reference

τ(4S3/2) = 1/W(4S3/2)

6.98 x 10-4 s

[12]

τ(2H11/2) = 1/W(2H11/2)

7.8 x 10-5 s

[12]

∆Ec

860 cm-1

[14]

∆E

2795 cm-1

[14]

phigh

5

[11]

ħωhigh

550 cm-1

RI PT

Value

SC

Parameter

AC C

EP

TE D

M AN U

[11]

31

ACCEPTED MANUSCRIPT

Table 2 Fitting parameter results from Eq. (12) fit to Y2O3:Er decay time versus temperature data. 95% confidence intervals in parentheses. W10 (s-1)

W20 (s-1)

plow

τ2 + τsingle

4753 (±58)

1.75 x 10-10 (±1.60 x 10-10)

18.8 (±0.3)

τ1 + τsingle

4672 (±88)

2.78 x 10-7 (±2.01 x 10-7)

16.7 (±0.3)

AC C

EP

TE D

M AN U

SC

RI PT

Data set

32

ACCEPTED MANUSCRIPT

Figure Captions Fig. 1. Electron energy level diagram for Er3+ in Y2O3 showing radiative (straight arrows) I15/2 → 2H11/2 transition.

Fig. 2. Setup for decay time versus temperature measurements.

RI PT

and nonradiative (wavy arrows) transitions occurring after excitation via hypersensitive 4

SC

Fig. 3. Room temperature excitation spectrum for Y2O3:Er. Emission at 564 nm. Final

M AN U

levels after excitation from 4I15/2 ground state are labeled.

Fig. 4. Temperature dependence of time-resolved (10 µs post-excitation pulse) emission spectra for Y2O3:Er. Excitation at 489 nm. Dashed vertical lines represents FWHM of 556 nm bandpass filter used for decay measurements.

Fig. 5. Lower temperature (a) and higher temperature (b) subset of luminescence decay

TE D

curves from Y2O3:Er. Excitation at 522 nm. Emission centered at 556 nm. Fig. 6. Luminescence decay curves at 575 °C for Y2O3:Er(0.1 mol%) and Y2O3:Er(0.8 mol%). Excitation at 522 nm. Emission centered at 556 nm. Dashed line indicates single

EP

exponential fit to Y2O3:Er(0.1 mol%) decay curve.

AC C

Fig. 7. Fitting window selection for luminescence decay curve from Y2O3:Er(0.1 mol%) at 1015 °C. Fitting window range determined by intensity-threshold crossings at 90% and 2% of initial intensity. Fit by biexponential (Eq. (11)) shown as dashed line. τ1 and τ2 values determined by fit are shown. Fig. 8. Temperature dependence of Y2O3:Er(0.1 mol%) luminescence decay times τsingle,

τ1, and τ2 from furnace calibration measurements. Solid line is a fit of Eq. (12) to a combined set of τsingle and τ2 values. Dashed line is a fit of Eq. (12) to a combined set of

τsingle and τ1 values. Decay time values between 600 and 850 °C were not included in fit. 33

ACCEPTED MANUSCRIPT

Fig. 9. Temperature dependence of total relaxation rate from thermally coupled 2H11/2 and 4

S3/2 energy levels of Y2O3:Er decomposed into radiative, high phonon energy

RI PT

multiphonon emission, and low phonon energy multiphonon emission rates.

Fig. 10. Comparison of time-resolved emission spectra from Y2O3:Er(0.1 mol%) at 971 °C obtained during early (solid line) and later (dashed line) portions of decay curve.

SC

Excitation at 489 nm. Specific time intervals during decay shown in inset.

Fig. 11. Temperature dependence of Srel for Y2O3:Er(0.1 mol%) decay time. Dashed line

AC C

EP

TE D

M AN U

indicates extrapolation beyond data range.

34

ACCEPTED MANUSCRIPT

20

16

4S 3/2

ΔE = 2795 cm-1

M AN U 4I

12

4I

TE D

10

4I

9/2

11/2

13/2

AC C

EP

Energy (103 cm-1)

14

6

9/2

SC

4F

8

ΔEc = 860 cm-1

RI PT

522 nm

18

547 nm

2H 11/2

4 2

4I

0

15/2 Fig. 1. Electron energy level diagram for in Y2O3 showing radiative (straight arrows) and nonradiative (wavy arrows) transitions occurring after excitation via hypersensitive 4I15/2 → 2H11/2 transition. Er3+

ACCEPTED MANUSCRIPT

RI PT

0.001

SC

Intensity (arb. units)

Intensity (V)

0.01

M AN U

0.0001 0E+00

2E-06

Time (s)

6E-06

4 µs gate delay 2 µs gate width

510

520

AC C

EP

TE D

0 µs gate delay 1.5 µs gate width

4E-06

530

540

550

560

570

Wavelength (nm) Fig. 10. Comparison of time-resolved emission spectra from Y2O3:Er(0.1 mol%) at 971 °C obtained during early (solid line) and later (dashed line) portions of decay curve. Excitation at 489 nm. Specific time intervals during decay shown in inset.

580

ACCEPTED MANUSCRIPT

1.2

RI PT

1.0

SC M AN U

0.6

EP

TE D

0.4 0.2

AC C

Srel (% K-1)

0.8

0.0 0

200

400

600

800

1000

1200

1400

Temperature (°C) Fig. 11. Temperature dependence of Srel for Y2O3:Er(0.1 mol%) decay time. Dashed line indicates extrapolation beyond data range.

1

ACCEPTED MANUSCRIPT

PMT

detection optics

Furnace

RI PT

collection fiber

collimator

collection optics

EP

oscilloscope

532 nm longpass

TE D

M AN U

SC

556/20 nm bandpass

Data acquisition

AC C

signal

trigger

laser synch

Fig. 2. Setup for decay time versus temperature measurements.

Y2O3:Er disk

2H

11/2 522 nm

11/2

379 nm

350

2H

390 nm

9/2

AC C

368 nm

EP

4G

TE D

M AN U

SC

Intensity (arb. units)

RI PT

ACCEPTED MANUSCRIPT

408 nm

400

4F 3/2, 5/2

526 nm 4F 7/2

489, 491, 493 nm

539 nm

455 nm

450 Wavelength (nm)

500

550

Fig. 3. Room temperature excitation spectrum for Y2O3:Er. Emission at 564 nm. Final levels after excitation from 4I15/2 ground state are labeled.

1

ACCEPTED MANUSCRIPT

2H

11/2

→ 4I15/2 385 °C

→ 4I15/2

Bandpass filter FWHM

RI PT

Intensity (arb. units)

1069 °C

4S 3/2

500

AC C

EP

TE D

M AN U

SC

21 °C 385 °C 1069 °C

520

21 °C 540

560

Wavelength (nm) Fig. 4. Temperature dependence of time-resolved (10 µs post-excitation pulse) emission spectra for Y2O3:Er. Excitation at 489 nm. Dashed vertical lines represents FWHM of 556 nm bandpass filter used for decay measurements.

1

ACCEPTED MANUSCRIPT

M AN U

SC

(a)

21 °C

EP

TE D

0.001

AC C

Intensity (V)

RI PT

0.01

480 °C

0.0001

0.0E+00

1.0E-04

91 °C 279 °C 2.0E-04

182 °C

3.0E-04

4.0E-04

Time (s) Fig. 5. Lower temperature (a) and higher temperature (b) subset of luminescence decay curves from Y2O3:Er. Excitation at 522 nm. Emission centered at 556 nm.

1

ACCEPTED MANUSCRIPT

M AN U

SC

(b)

0.001

1015 °C

TE D

Intensity (V)

RI PT

0.01

EP

1065 °C

AC C

1114 °C

1164 °C

0.0001 0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

Time (s) Fig. 5. Lower temperature (a) and higher temperature (b) subset of luminescence decay curves from Y2O3:Er. Excitation at 522 nm. Emission centered at 556 nm.

1

ACCEPTED MANUSCRIPT

SC M AN U

0.001

EP

TE D

Intensity (V)

RI PT

0.01

0.8 mol%

AC C

0.0001 0.0E+00

1.0E-05

2.0E-05

0.1 mol%

3.0E-05

4.0E-05

5.0E-05

6.0E-05

Time (s) Fig. 6. Luminescence decay curves at 575 °C for Y2O3:Er(0.1 mol%) and Y2O3:Er(0.8 mol%). Excitation at 522 nm. Emission centered at 556 nm. Dashed line indicates single exponential fit to Y2O3:Er(0.1 mol%) decay curve.

1

ACCEPTED MANUSCRIPT

M AN U

Intensity (V)

SC

1 = 0.47 µs 2 = 1.58 µs

RI PT

0.01000

TE D

0.00100

2% Imax

AC C

EP

90% Imax

0.00010

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

Time (s) Fig. 7. Fitting window selection for luminescence decay curve from Y2O3:Er(0.1 mol%) at 1015 °C. Fitting window range determined by intensity-threshold crossings at 90% and 2% of initial intensity. Fit by biexponential (Eq. (11)) shown as dashed line. 1 and 2 values determined by fit are shown.

ACCEPTED MANUSCRIPT

τ₁ data

RI PT

τ₁ fit τ₂ fit

M AN U

SC

1E-05

τ₂ data

TE D

1E-06

1E-07 0

AC C

EP

Decay Time (s)

τ singledata

data excluded from fit

1E-04

200

400

600

800

1000

1200

Temperature (°C) Fig. 8. Temperature dependence of Y2O3:Er(0.1 mol%) luminescence decay times single, 1, and 2 from furnace calibration measurements. Solid line is a fit of Eq. (12) to a combined set of single and 2 values. Dashed line is a fit of Eq. (12) to a combined set of single and 1 values. Decay time values between 600 and 850 °C were not included in fit.

1400

ACCEPTED MANUSCRIPT

1E+08 total

coupled radiative

RI PT

ħhigh multiphonon emission

1E+06

SC

ħlow multiphonon emission

M AN U

1E+05

TE D

1E+04

EP

1E+03 1E+02

AC C

Relaxation Rate (s-1)

1E+07

1E+01 0

200

400

600

800

1000

1200

1400

Temperature (°C) Fig. 9. Temperature dependence of total relaxation rate from thermally coupled 2H11/2 and 4S3/2 energy levels of Y2O3:Er decomposed into radiative, high phonon energy multiphonon emission, and low phonon energy multiphonon emission rates.