Loading [MathJax]/jax/output/SVG/jax.js
Research article Special Issues

Color centers in YAG

  • Received: 31 May 2015 Accepted: 06 December 2015 Published: 16 December 2015
  • Yttrium aluminum garnet (Y3Al5O12, YAG) is one of the most important optical materials with many existing and potential future applications in laser, illumination, and scintillation. X-rays, g-rays, and UV light can induce ionization and significant changes in the valency of impurities and defects in YAG single crystals which may lead to the formation of color centers. In fact, the use of YAG crystals in laser and scintillation devices involves significant formation of color centers and requires full understanding for their characteristics and effects on the material properties. In this work, the formation and characteristics of color centers in undoped and rare-earth doped YAG single crystals was investigated mainly through optical absorption spectroscopy. An increase in the absorption over a broad range of wavelengths was observed in the as-grown sample after UV irradiation. F-centers and iron impurities in the as-grown undoped crystals were found to be responsible for the formation of color centers. However, air- or oxygen-anneal seems to be effective in suppressing most color centers in the crystals.

    Citation: Chris R. Varney, Farida A. Selim. Color centers in YAG[J]. AIMS Materials Science, 2015, 2(4): 560-572. doi: 10.3934/matersci.2015.4.560

    Related Papers:

    [1] Rashmi Murali, Sangeeta Malhotra, Debajit Palit, Krishnapada Sasmal . Socio-technical assessment of solar photovoltaic systems implemented for rural electrification in selected villages of Sundarbans region of India. AIMS Energy, 2015, 3(4): 612-634. doi: 10.3934/energy.2015.4.612
    [2] Pedro Neves, Morten Gleditsch, Cindy Bennet, Mathias Craig, Jon Sumanik-Leary . Assessment of locally manufactured small wind turbines as an appropriate technology for the electrification of the Caribbean Coast of Nicaragua. AIMS Energy, 2015, 3(1): 41-74. doi: 10.3934/energy.2015.1.41
    [3] Pugazenthi D, Gopal K Sarangi, Arabinda Mishra, Subhes C Bhattacharyya . Replication and scaling-up of isolated mini-grid type of off-grid interventions in India. AIMS Energy, 2016, 4(2): 222-255. doi: 10.3934/energy.2016.2.222
    [4] Jerome Mungwe, Stefano Mandelli, Emanuela Colombo . Community pico and micro hydropower for rural electrification: experiences from the mountain regions of Cameroon. AIMS Energy, 2016, 4(1): 190-205. doi: 10.3934/energy.2016.1.190
    [5] Matthew Dornan . Reforms for the expansion of electricity access and rural electrification in small island developing states. AIMS Energy, 2015, 3(3): 463-479. doi: 10.3934/energy.2015.3.463
    [6] Tilahun Nigussie, Wondwossen Bogale, Feyisa Bekele, Edessa Dribssa . Feasibility study for power generation using off- grid energy system from micro hydro-PV-diesel generator-battery for rural area of Ethiopia: The case of Melkey Hera village, Western Ethiopia. AIMS Energy, 2017, 5(4): 667-690. doi: 10.3934/energy.2017.4.667
    [7] Wesly Jean, Antonio C. P. Brasil Junior, Eugênia Cornils Monteiro da Silva . Smart grid systems infrastructures and distributed solar power generation in urban slums–A case study and energy policy in Rio de Janeiro. AIMS Energy, 2023, 11(3): 486-502. doi: 10.3934/energy.2023025
    [8] Ashebir Dingeto Hailu, Desta Kalbessa Kumsa . Ethiopia renewable energy potentials and current state. AIMS Energy, 2021, 9(1): 1-14. doi: 10.3934/energy.2021001
    [9] Kharisma Bani Adam, Jangkung Raharjo, Desri Kristina Silalahi, Bandiyah Sri Aprilia, IGPO Indra Wijaya . Integrative analysis of diverse hybrid power systems for sustainable energy in underdeveloped regions: A case study in Indonesia. AIMS Energy, 2024, 12(1): 304-320. doi: 10.3934/energy.2024015
    [10] Shi Yin, Yuan Yuan . Integrated assessment and influencing factor analysis of energy-economy-environment system in rural China. AIMS Energy, 2024, 12(6): 1173-1205. doi: 10.3934/energy.2024054
  • Yttrium aluminum garnet (Y3Al5O12, YAG) is one of the most important optical materials with many existing and potential future applications in laser, illumination, and scintillation. X-rays, g-rays, and UV light can induce ionization and significant changes in the valency of impurities and defects in YAG single crystals which may lead to the formation of color centers. In fact, the use of YAG crystals in laser and scintillation devices involves significant formation of color centers and requires full understanding for their characteristics and effects on the material properties. In this work, the formation and characteristics of color centers in undoped and rare-earth doped YAG single crystals was investigated mainly through optical absorption spectroscopy. An increase in the absorption over a broad range of wavelengths was observed in the as-grown sample after UV irradiation. F-centers and iron impurities in the as-grown undoped crystals were found to be responsible for the formation of color centers. However, air- or oxygen-anneal seems to be effective in suppressing most color centers in the crystals.


    In 1997, Van Hamme [19,(H.2)] proved the following supercongruence: for any prime $ p\equiv 3\pmod 4 $,

    $ (p1)/2k=0(12)3kk!30(modp2), $ (1.1)

    where $ (a)_n = a(a+1)\cdots(a+n-1) $ is the rising factorial. It is easy to see that (1.1) is also true when the sum is over $ k $ from $ 0 $ to $ p-1 $, since $ (1/2)_k/k!\equiv 0\pmod{p} $ for $ (p-1)/2<k\leq p-1 $. Nowadays various generalizations of (1.1) can be found in [8,10,11,12,13,14,16,17]. For example, Liu [12] proved that, for any prime $ p\equiv 3\pmod{4} $ and positive integer $ m $,

    $ mp1k=0(12)3kk!30(modp2). $ (1.2)

    The first purpose of this paper is to prove the following $ q $-analogue of (1.2), which was originally conjectured by the author and Zudilin [10,Conjecture 2].

    Theorem 1.1. Let $ m $ and $ n $ be positive integers with $ n\equiv 3\pmod{4} $. Then

    $ mn1k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk0(modΦn(q)2), $ (1.3)
    $ [5pt]mn+(n1)/2k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk0(modΦn(q)2). $ (1.4)

    Here and in what follows, the $ q $-shifted factorial is defined by $ (a;q)_0 = 1 $ and $ (a;q)_n = (1-a)(1-aq)\cdots (1-aq^{n-1}) $ for $ n\geq 1 $, and the $ n $-th cyclotomic polynomial $ \Phi_n(q) $ is defined as

    $ Φn(q)=1kngcd(n,k)=1(qζk), $

    where $ \zeta $ is an $ n $-th primitive root of unity. Moreover, the $ q $-integer is given by $ [n] = [n]_q = 1+q+\cdots+q^{n-1} $.

    The $ m = 1 $ case of (1.3) was first conjectured by the author and Zudilin [9,Conjecture 4.13] and has already been proved by themselves in a recent paper [11]. For some other recent progress on $ q $-congruences, the reader may consult [2,3,4,5,6,7,8,10,15].

    In 2016, Swisher [18,(H.3) with $ r = 2 $] conjectured that, for primes $ p\equiv 3\pmod{4} $ and $ p>3 $,

    $ (p21)/2k=0(12)3kk!3p2(modp5), $ (1.5)

    The second purpose of this paper is to prove the following $ q $-congruences related to (1.5) modulo $ p^4 $.

    Theorem 1.2. Let $ n\equiv 3\pmod{4} $ be a positive integer. Modulo $ \Phi_n(q)^2\Phi_{n^2}(q)^2 $, we have

    $ (n21)/2k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk[n2]q2(q3;q4)(n21)/2(q5;q4)(n21)/2q(1n2)/2, $ (1.6)
    $ [5pt]n21k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk[n2]q2(q3;q4)(n21)/2(q5;q4)(n21)/2q(1n2)/2. $ (1.7)

    Let $ n = p\equiv 3\pmod{4} $ be a prime and take $ q\to1 $ in Theorem 1.2. Then $ \Phi_p(1) = \Phi_{p^2}(1) = p $, and

    $ limq1(q3;q4)(p21)/2(q5;q4)(p21)/2=(p21)/2k=14k14k+1=(34)(p21)/2(54)(p21)/2. $

    Therefore, we obtain the following conclusion.

    Corollary 1. Let $ p\equiv 3\pmod{4} $ be a prime. Then

    $ (p21)/2k=0(12)3kk!3p2(34)(p21)/2(54)(p21)/2(modp4), $ (1.8)
    $ [5pt]p21k=0(12)3kk!3p2(34)(p21)/2(54)(p21)/2(modp4). $ (1.9)

    Comparing (1.5) and (1.8), we would like to propose the following conjecture, which was recently confirmed by Wang and Pan [20].

    Conjecture 1. Let $ p\equiv 3\pmod{4} $ be a prime and $ r $ a positive integer. Then

    $ (p2r1)/2k=14k14k+11(modp2). $ (1.10)

    Note that the $ r = 1 $ case is equivalent to say that (1.5) is true modulo $ p^4 $.

    We need to use Watson's terminating $ _8\phi_7 $ transformation formula (see [1,Appendix (Ⅲ.18)] and [1,Section 2]):

    $ 8ϕ7[a,qa12,qa12,b,c,d,e,qna12,a12,aq/b,aq/c,aq/d,aq/e,aqn+1;q,a2qn+2bcde]=(aq;q)n(aq/de;q)n(aq/d;q)n(aq/e;q)n4ϕ3[aq/bc, d, e, qnaq/b,aq/c,deqn/a;q,q], $ (2.1)

    where the basic hypergeometric $ {}_{r+1}\phi_r $ series with $ r+1 $ upper parameters $ a_1, \dots, a_{r+1} $, $ r $ lower parameters $ b_1, \dots, b_r $, base $ q $ and argument $ z $ is defined as

    $ r+1ϕr[a1,a2,,ar+1b1,,br;q,z]:=k=0(a1;q)k(a2;q)k(ar+1;q)k(q;q)k(b1;q)k(br;q)kzk. $

    The left-hand side of (1.4) with $ m\geq 0 $ can be written as the following terminating $ _8\phi_7 $ series:

    $ 8ϕ7[q2,q5,q5,q2,q,q2,q4+(4m+2)n,q2(4m+2)nq,q,q4,q5,q4,q2(4m+2)n,q4+(4m+2)n;q4,q]. $ (2.2)

    By Watson's transformation formula (2.1) with $ q\mapsto q^4 $, $ a = b = d = q^2 $, $ c = q $, $ e = q^{4+(4m+2)n} $, and $ n\mapsto mn+(n-1)/2 $, we see that (2.2) is equal to

    $ (q6;q4)mn+(n1)/2(q(4m+2)n;q4)mn+(n1)/2(q4;q4)mn+(n1)/2(q2(4m+2)n;q4)mn+(n1)/2×4ϕ3[q3, q2,q4+(4m+2)n, q2(4m+2)nq4,q5,q6;q4,q4]. $ (2.3)

    It is not difficult to see that there are exactly $ m+1 $ factors of the form $ 1-q^{an} $ ($ a $ is an integer) among the $ mn+(n-1)/2 $ factors of $ (q^6;q^4)_{mn+(n-1)/2} $. So are $ (q^{-(4m+2)n};q^4)_{mn+(n-1)/2} $. But there are only $ m $ factors of the form $ 1-q^{an} $ ($ a $ is an integer) in each of $ (q^4;q^4)_{mn+(n-1)/2} $ and $ (q^{2-(4m+2)n};q^4)_{mn+(n-1)/2} $. Since $ \Phi_n(q) $ is a factor of $ 1-q^N $ if and only if $ n $ divides $ N $, we conclude that the fraction before the $ _4\phi_3 $ series is congruent to $ 0 $ modulo $ \Phi_n(q)^2 $. Moreover, for any integer $ x $, let $ f_n(x) $ be the least non-negative integer $ k $ such that $ (q^x;q^4)_k\equiv 0 $ modulo $ \Phi_n(q) $. Since $ n\equiv 3\pmod{4} $, we have $ f_n(2) = (n+1)/2 $, $ f_n(3) = (n+1)/4 $, $ f_n(4) = n $, $ f_n(5) = (3n-1)/4 $, and $ f_n(6) = (n-1)/2 $. It follows that the denominator of the reduced form of the $ k $-th summand

    $ \frac{(q^3;q^4)_k (q^2;q^4)_k(q^{4+(4m+2)n};q^4)_k(q^{2-(4m+2)n};q^4)_k} {(q^4;q^4)_k^2(q^5;q^4)_k(q^6;q^4)_k}q^{4k} $

    in the $ _4\phi_3 $ summation is always relatively prime to $ \Phi_n(q) $ for any non-negative integer $ k $. This proves that (2.3) (i.e. (2.2)) is congruent to $ 0 $ modulo $ \Phi_n(q)^2 $, thus establishing (1.4) for $ m\geq 0 $.

    It is easy to see that $ (q^2;q^4)_k^3/(q^4;q^4)_k^3 $ is congruent to $ 0 $ modulo $ \Phi_n(q)^3 $ for $ mn+(n-1)/2<k\leq(m+1)n-1 $. Therefore, the $ q $-congruence (1.3) with $ m\mapsto m+1 $ follows from (1.4).

    The author and Zudilin [11,Theorem 1.1] proved that, for any positive odd integer $ n $,

    $ (n1)/2k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk[n]q2(q3;q4)(n1)/2(q5;q4)(n1)/2q(1n)/2(modΦn(q)2), $ (3.1)

    which is also true when the sum on the left-hand side of (3.1) is over $ k $ from $ 0 $ to $ n-1 $. Replacing $ n $ by $ n^2 $ in (3.1) and its equivalent form, we see that the $ q $-congruences (1.6) and (1.7) hold modulo $ \Phi_{n^2}(q)^2 $.

    It is easy to see that, for $ n\equiv 3\pmod{4} $,

    $ \dfrac{[n^2]_{q^2}(q^3;q^4)_{(n^2-1)/2}} {(q^5;q^4)_{(n^2-1)/2}} q^{(1-n^2)/2}\equiv 0\pmod{\Phi_n(q)^2} $

    because $ [n^2]_{q^2} = (1-q^{n^2})/(1-q^2) $ is divisible by $ \Phi_n(q) $, and $ (q^3;q^4)_{(n^2-1)/2} $ contains $ (n+1)/2 $ factors of the form $ 1-q^{an} $ ($ a $ is an integer), while $ (q^5;q^4)_{(n^2-1)/2} $ only has $ (n-1)/2 $ such factors. Meanwhile, by Theorem 1.1, the left-hand sides of (1.6) and (1.7) are both congruent to $ 0 $ modulo $ \Phi_n(q)^2 $ since $ (n^2-1)/2 = (n-1)n/2+(n-1)/2 $. This proves that the $ q $-congruences (1.6) and (1.7) also hold modulo $ \Phi_n(q)^2 $. Since the polynomials $ \Phi_n(q) $ and $ \Phi_{n^2}(q) $ are relatively prime, we finish the proof of the theorem.

    Swisher's (H.3) conjecture also indicates that, for positive integer $ r $ and primes $ p\equiv 3\pmod{4} $ with $ p>3 $, we have

    $ (p2r1)/2k=0(12)3kk!3p2r(modp2r+3). $ (4.1)

    Motivated by (4.1), we shall give the following generalization of Theorem 1.2.

    Theorem 4.1. Let $ n $ and $ r $ be positive integers with $ n\equiv 3\pmod{4} $. Then, modulo $ \Phi_{n^{2r}}(q)^2\prod_{j = 1}^{r}\Phi_{n^{2j-1}}(q)^2 $, we have

    $ (n2r1)/2k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk[n2r]q2(q3;q4)(n2r1)/2(q5;q4)(n2r1)/2q(1n2r)/2, $ (4.2)
    $ [5pt]n2r1k=0(1+q4k+1)(q2;q4)3k(1+q)(q4;q4)3kqk[n2r]q2(q3;q4)(n2r1)/2(q5;q4)(n2r1)/2q(1n2r)/2. $ (4.3)

    Proof. Replacing $ n $ by $ n^{2r} $ in (3.1) and its equivalent form, we see that (4.2) and (4.3) are true modulo $ \Phi_{n^{2r}}(q)^2 $. Similarly as before, we can show that

    $ [n2r]q2(q3;q4)(n2r1)/2(q5;q4)(n2r1)/2q(1n2r)/20(modrj=1Φn2j1(q)2). $

    Further, by Theorem 1.1, we can easily deduce that the left-hand sides of (4.2) and (4.3) are also congruent to $ 0 $ modulo $ \prod_{j = 1}^{r}\Phi_{n^{2j-1}}(q)^2 $.

    Letting $ n = p\equiv 3\pmod{4} $ be a prime and taking $ q\to1 $ in Theorem 4.1, we are led to the following result.

    Corollary 2. Let $ p\equiv 3\pmod{4} $ be a prime and let $ r\geq 1 $. Then

    $ (p2r1)/2k=0(12)3kk!3p2r(34)(p2r1)/2(54)(p2r1)/2(modp2r+2), $ (4.4)
    $ [5pt]p2r1k=0(12)3kk!3p2r(34)(p2r1)/2(54)(p2r1)/2(modp2r+2). $ (4.5)

    In light of (1.10), the supercongruence (4.4) implies that (4.1) holds modulo $ p^{2r+2} $ for any odd prime $ p $.

    It is known that $ q $-analogues of supercongruences are usually not unique. See, for example, [2]. The author and Zudilin [10,Conjecture 1] also gave another $ q $-analogue of (1.2), which still remains open.

    Conjecture 2 (Guo and Zudilin). Let $ m $ and $ n $ be positive integers with $ n\equiv 3\pmod{4} $. Then

    $ mn1k=0(q;q2)2k(q2;q4)k(q2;q2)2k(q4;q4)kq2k0(modΦn(q)2),mn+(n1)/2k=0(q;q2)2k(q2;q4)k(q2;q2)2k(q4;q4)kq2k0(modΦn(q)2). $ (4.6)

    The author and Zudilin [10,Theorem 2] themselves have proved (4.6) for the $ m = 1 $ case. Motivated by Conjecture 2, we would like to give the following new conjectural $ q $-analogues of (1.8) and (1.9).

    Conjecture 3. Let $ n\equiv 3\pmod{4} $ be a positive integer. Modulo $ \Phi_n(q)^2\Phi_{n^2}(q)^2 $, we have

    $ (n21)/2k=0(q;q2)2k(q2;q4)k(q2;q2)2k(q4;q4)kq2k[n2](q3;q4)(n21)/2(q5;q4)(n21)/2,n21k=0(q;q2)2k(q2;q4)k(q2;q2)2k(q4;q4)kq2k[n2](q3;q4)(n21)/2(q5;q4)(n21)/2. $

    There are similar such new $ q $-analogues of (4.4) and (4.5). We omit them here and leave space for the reader's imagination.

    The author is grateful to the two anonymous referees for their careful readings of this paper.

    [1] Fox M (2010) Optical Properties of Solids, New York, NY: Oxford University Press.
    [2] Geller S (1967) Crystal chemistry of the garnets. Z Kristallogr 125: 1-47. doi: 10.1524/zkri.1967.125.125.1
    [3] Ashurov MKh, Rakov AF, Erzin RA (2001) Luminescence of defect centers in yttrium-aluminum garnet crystals. Solid State Commun 120: 491-494. doi: 10.1016/S0038-1098(01)00434-3
    [4] Bagdasarov KhS, Pasternak LB, Sevast'yanov BK (1977) Radiation color centers in Y3Al5O12:Cr3+ crystals. Sov J Quantum Elecron 7: 965-968. doi: 10.1070/QE1977v007n08ABEH012694
    [5] Bass M, Paladino AE (1967) Color centers in Yttrium Gallium Garnet and Yttrium Aluminum Garnet. J Appl Phys 38: 2706-2707. doi: 10.1063/1.1709988
    [6] Bernhard HJ (1978) Bound polarons in YAG crystals. Phys Status Solidi B 87: 213-219. doi: 10.1002/pssb.2220870125
    [7] Bunch JM (1977) Mollwo-Ivey relation between peak color-center absorption energy and average oxygen ion spacing in several oxides of group-II and -III metals. Phys Rev B 16: 724-725. doi: 10.1103/PhysRevB.16.724
    [8] Chakrabarti K (1988) Photobleaching and photoluminescence in neutron-irradiated YAG. J Phys Chem Solids 49: 1009-1011 doi: 10.1016/0022-3697(88)90146-1
    [9] Kaczmarek SM (1999) Role of the type of impurity in radiation influence on oxide compounds. Cryst Res Technol 34: 737-743.
    [10] Kovaleva NS, Ivanov AO, Dubrovina ÉP (1981) Relationship between formation of radiation color centers and growth defects in YAG:Nd crystals. Sov J Quantum Electron 11: 1485-1488 doi: 10.1070/QE1981v011n11ABEH008633
    [11] Masumoto T, Kuwano Y (1985) Effects of oxygen pressure on optical absorption of YAG. Jpn J Appl Phys 24: 546-551. doi: 10.1143/JJAP.24.546
    [12] Mori K (1977) Transient colour centres caused by UV light irradiation in yttrium aluminium garnet crystals. Phys Status Solidi A 42: 375-384. doi: 10.1002/pssa.2210420142
    [13] Pujats A, Springis M (2001) The F-type centers in YAG crystals. Radiat Eff Defects Solids 155: 65-69. doi: 10.1080/10420150108214094
    [14] Zorenko Y, Zorenko T, Voznyak T, et al. (2010) Luminescence of F+ and F centers in Al2O3-Y2O3 oxide compounds. IOP Conf Ser Mater Sci Eng 15: 012060
    [15] Lu L, Chen J, Wang W (2013) Wide bandgap Zn2GeO4 nanowires as photoanode for quantum dot sensitized solar cells. Appl Phys Lett 103: 123902. doi: 10.1063/1.4821541
    [16] Batygov SKh, Voron'ko YuK, Denker BI, et al. (1972) Color centers in Y3Al5O12 crystals. Sov Phy Solid State 14: 839-841.
    [17] Varney CR, Mackay DT, Reda SM, et al. (2012) On the optical properties of undoped and rare-earth-doped yttrium aluminum garnet single crystals. J Phys D Appl Phys 45: 015103. doi: 10.1088/0022-3727/45/1/015103
    [18] Varney CR, Reda SM, Mackay DT, et al. (2011) Strong visible and near infrared luminescence in undoped YAG single crystals. AIP Advances 1: 042170. doi: 10.1063/1.3671646
    [19] Varney CR (2012) Studies of trapping and luminescence phenomena in yttrium aluminum garnets [dissertation]. [Pullman (WA)]: Washington State University.
    [20] Reda SM, Varney CR, Selim FA (2012) Radio-luminescence and absence of trapping defects in Nd-doped YAG single crystals, Results in Physics 2, 123-126.
    [21] Fredrich-Thornton ST (2010) Nonlinear losses in single crystalline and ceramic Yb:YAG thin-disk lasers [dissertation]. [Hamburg (GER)]: University of Hamburg.
    [22] Guerassimova N, Dujardin C, Garnier N, et al. (2002) Charge-transfer luminescence and spectroscopic properties of Yb3+ in aluminum and gallium garnets. Nucl Instrum Methods Phys Res Sect A 486: 278-282. doi: 10.1016/S0168-9002(02)00718-0
    [23] Kamenskikh I, Dujardin C, Garnier N, et al. (2005) Temperature dependence of charge transfer and f-f luminescence of Yb3+ in garnets and YAP. J Phys Condens Matter 17: 5587-5594. doi: 10.1088/0953-8984/17/36/014
    [24] van Pieterson L, Heeroma M, de Heer E, et al. (2000) Charge transfer luminescence of Yb3+. J Lumin 91: 177-193. doi: 10.1016/S0022-2313(00)00214-3
    [25] Mackay DT, Varney CR, Buscher J, et al. (2012) Study of exciton dynamics in garnets by low temperature thermo-luminescence. J Appl Phys 112: 023522. doi: 10.1063/1.4739722
    [26] Selim FA, Varney CR, Tarun MC, et al. (2013) Positron lifetime measurements of hydrogen passivation of cation vacancies in yttrium aluminum oxide garnets. Phys Rev B 88: 174102. doi: 10.1103/PhysRevB.88.174102
    [27] Varney CR, Mackay DT, Pratt A, et al. (2012) Energy levels of exciton traps in yttrium aluminum garnet single crystals. J Appl Phys 111: 063505. doi: 10.1063/1.3693581
    [28] Varney CR, Selim FA (2014) Positron Lifetime Measurements of Vacancy Defects in Complex Oxides. Acta Phys Pol A 125: 764-766. doi: 10.12693/APhysPolA.125.764
    [29] Kuklja MM Pandey R (1999) Atomistic modeling of point defects in yttrium aluminum garnet crystals. J Am Ceram Soc 82: 2881-2886.
    [30] Kuklja MM (2000) Defects in yttrium aluminum perovskite and garnet crystals: atomistic study. J Phys Condens Matter 12: 2953-2967. doi: 10.1088/0953-8984/12/13/307
    [31] Zorenko Yu, Voloshinovskii A, Savchyn V, et al. (2007) Exciton and antisite defect-related luminescence in Lu3Al5O12 and Y3Al5O12 garnets. Phys Status Solidi B 244: 2180-2189. doi: 10.1002/pssb.200642431
    [32] Varney CR, Khamehchi MA, Ji J, et al. (2012) X-ray luminescence based spectrometer for investigation of scintillation properties. Rev Sci Instrum 83: 103112-103116. doi: 10.1063/1.4764772
  • This article has been cited by:

    1. Baseem Khan, Josep M. Guerrero, Sanjay Chaudhary, Juan C. Vasquez, Kenn H. B. Frederiksen, Ying Wu, A Review of Grid Code Requirements for the Integration of Renewable Energy Sources in Ethiopia, 2022, 15, 1996-1073, 5197, 10.3390/en15145197
    2. Mustafa Rahime, K.B. Rashitovich, Shir Agha Shahryar, Rafiqullah Hamdard, Yama Aseel, Development of Electric Network Impact on Socio-Economic of Ghazni Province, Republic of Afghanistan, 2024, 2, 2786-7447, 334, 10.59324/ejtas.2024.2(2).29
  • Reader Comments
  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(8408) PDF downloads(1445) Cited by(20)

Figures and Tables

Figures(7)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog