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2341:{\displaystyle \left({\begin{array}{c}B^{+}\\B^{-}\end{array}}\right)_{n}={\frac {1}{2\gamma _{n}}}\left({\begin{array}{cc}exp(-u_{n}L_{n})&0\\0&exp(u_{n}L_{n})\end{array}}\right)\left({\begin{array}{cc}\gamma _{n}+\gamma _{n+1}&\gamma _{n}-\gamma _{n+1}\\\gamma _{n}-\gamma _{n+1}&\gamma _{n}+\gamma _{n+1}\end{array}}\right)\left({\begin{array}{c}B^{+}\\B^{-}\end{array}}\right)_{n+1}}
3043:
of the diffusion of two adjacent metal blocks. An example would be a Ni-Cr-Pd-Pt-Rh-Ru diffusion multiple which would have diffusion zones of Ni-Cr, Ni-Pd, Ni-Pt and so on. In this way, many different materials can be tested at the same time. Lowest thermal conductivity for a thin film of solid, fully dense material (i.e. not porous) was also recently reported with measurements using this method.
66:
25:
128:
384:. Acoustic waves travel a few nanometers in a picosecond, where heat flows about a hundred nanometers in a second. Thus, lasers such as titanium sapphire (Ti:Al2O3) laser, with pulse width of ~200 fs, are used to monitor the characteristics of the interface. Other type of lasers include Yb:fiber, Yb:tungstate, Er:fiber, Nd:glass.
223:. This stress build in a localized region causes an acoustic strain pulse. At an interface, the pulse will be subjected to a transmittance/reflectance state, and the characteristics of the interface may be monitored with the reflected waves. A probe laser will detect the effects of the reflecting acoustic waves by sensing the
206:
materials (up to hundreds of nanometers thick), which have properties that vary greatly when compared to the same materials in bulk. The idea behind this technique is that once a material is heated up, the change in the reflectance of the surface can be utilized to derive the thermal properties. The
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Through this process of time-domain thermoreflectance, the thermal properties of many materials can be obtained. Common test setups include having multiple metal blocks connected together in a diffusion multiple, where once subjected to high temperatures various compounds can be created as a result
3050:
The data received from this process can then be compared to a thermal model, and the thermal conductivity and thermal conductance can then be derived. It is found that these two parameters can be derived independently based on the delay times, with short delay times (0.1 - .5 ns) resulting in the
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Once this test sample is obtained, time-domain thermoreflectance measurements can take place, with laser pulses of very short duration for both the pump and the probe lasers (<1 ps). The thermoreflected signal is then measured by a photodiode which is connected to a RF lock-in amplifier. The
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whose reference signal has the same frequency used to modulate the pump. The voltage output from the lock-in will be proportional to ΔR. Recording this signal as the optical delay line is changed provides a measurement of ΔR as a function of optical probe-pulse time delay.
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403:. The probe beam is then focused with a lens onto the same spot on the sample as the pulse. Both pump and probe have a spot size on the order of 10–50 μm. The reflected probe light is input to a high bandwidth photodetector. The output is fed into a
1959:
3029:
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Scott
Huxtable, David G. Cahill, Vincent Fauconnier, Jeffrey O. White, and Ji-Cheng Zhao, "Thermal conductivity imaging at micrometre-scale resolution for combinatorial studies of materials", Nature Materials 3 298-301 (2004),
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if the temperature is not very low (Ref B). Thus, this method is most efficient with the utilization of surface acoustic waves, and studies on investigation of this method toward lateral structures are being conducted.
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of the film. Usually, a typical magnitude value of the acoustic pulse will be small, and for long propagation nonlinear effects could become important. But propagation of such short duration pulses will suffer
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2522:(Λn: thermal conductivity of nth layer, Dn: thermal diffusivity of nth layer, Ln: thickness of nth layer) Using Eqs. (6) and (7), we can calculate the changes of temperature of a layered structure.
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608:
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signals that come out of the amplifier consist of an in phase and out of phase component, and the ratio of these allow thermal conductivity data to be measured for a specific delay time.
3154:
Catalin
Chiritescu, David G. Cahill, Ngoc Nguyen, David Johnson, Arun Bodapati, Pawel Keblinski, and Paul Zschack, "Ultralow Thermal Conductivity in Disordered, Layered WSe2 Crystals"
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X. Zheng, D. G. Cahill, P. Krasnochtchekov, R. S. Averback, and J.-C. Zhao, "High-throughput thermal conductivity measurements of nickel solid solutions and the applicability of the
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There is much room for error involved due to phase errors in the RF amplifier in addition to noise from the lasers. Typically, however, accuracy can be found to be within 8%.
146:
3100:
David G. Cahill, Wayne K. Ford, Kenneth E. Goodson, Gerald D. Mahan, Arun
Majudar, Humphrey J. Maris, Roberto Merlin, and Simon R. Phillpot. "Nanoscale thermal transport",
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1475:, while this change is measured by the changes in the reflected intensity of a probe laser beam. The probe laser beam measures a weighted average of the temperature
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G. Andrew
Antonelli, Bernard Perrin, Brian C. Daly, and David G. Cahill, "Characterization of mechanical and thermal properties using ultrafast optical metrology",
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reflectivity is measured with respect to time, and the data received can be matched to a model with coefficients that correspond to thermal properties.
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is the distance into the sample (Ref A). This temperature increase results in a strain that can be estimated by multiplying it with the linear
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The amount of strain is related to the optical laser pulse as follows. Take the localized temperature increase due to the laser,
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leading to a cross-polarized pump and probe. The pump beam is modulated on the order of a few megahertz by an acousto-optic or
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can be used to simplify the computation of the convolution of equation (1) with the distributions of the laser intensities.
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In a typical time-domain thermoreflectance experiment, the co-aligned laser beams have cylindrical symmetry, therefore the
3121:
Cahill, DG "Analysis of heat flow in layered structures for time-domain thermoreflectance" Rev Sci
Instrum 2007;75:5119,
1630:{\displaystyle \Delta T={\frac {4}{w_{1}^{2}}}\int _{0}^{\infty }\theta (r)exp\left(-{\frac {2r^{2}}{w_{1}^{2}}}\right)}
773:{\displaystyle G(k)=2\pi \int _{0}^{\infty }g(r)J_{0}(2\pi kr)r\,dr={\frac {1}{\Lambda (4\pi ^{2}k^{2}+q^{2})^{1/2}}}}
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2513:{\displaystyle u_{n}=(4\pi ^{2}k^{2}+q_{n}^{2})^{1/2},q_{n}^{2}={\frac {iw}{D_{n}}},\gamma _{n}=\Lambda _{n}u_{n}}
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To sense the piezo-optic effect of the reflected waves, fast monitoring is required due to the travel time of the
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2931:{\displaystyle Im=-i{\frac {dR}{dT}}\sum _{m=-M}^{M}(\Delta T(m/\tau +f)-\Delta T(m/\tau -f))exp(i2\pi mt/\tau )}
2724:{\displaystyle Re={\frac {dR}{dT}}\sum _{m=-M}^{M}(\Delta T(m/\tau +f)+\Delta T(m/\tau -f))exp(i2\pi mt/\tau )}
1811:{\displaystyle \Delta T=2\pi A\int _{0}^{\infty }G(k)exp(-\pi ^{2}k^{2}(\omega _{0}^{2}+\omega _{1}^{2})/2)kdk}
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The acquired data from time-domain thermoreflectance experiments are required to be compared with the model.
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3034:(Q: quality factor of the resonant circuit) This calculated Vf/V0 would be compared with the measured one.
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of a layered structure can be acquired. Instead of Eq. (2), Eq. (7) will be used for a layered structure.
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The output of the laser is split into pump and probe beams by a half-wave plate followed by a polarizing
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The technique of this method is based on the monitoring of acoustic waves that are generated with a
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582:(Λ: thermal conductivity of the solid, D: thermal diffusivity of the solid, r: radial coordinate)
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1954:{\displaystyle G(k)=({\frac {B_{1}^{+}+B_{1}^{-}}{B_{1}^{-}-B_{1}^{+}}}){\frac {1}{\gamma _{1}}}}
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219:. Localized heating of a material will create a localized temperature increase, which induces
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thermal conductivity and longer delay times (> 2ns) resulting in the thermal conductance.
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solution for a semi-infinite solid which is heated by a point source with angular frequency
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is a method by which the thermal properties of a material can be measured, most importantly
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Here g(r) is radially symmetric and by the definition of Hankel transform using Eq. (1),
3024:{\displaystyle {\frac {V_{f}(t)}{V_{0}}}={\frac {Q}{\sqrt {2}}}{\frac {\Delta R(t)}{R}}}
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Lab technique for measuring thermal properties through analyzing reflective properties
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and focused onto the sample with a lens. The probe is directed into an optical
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respectively. The surface is heated by the pump laser beam with the intensity
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The surface temperatures are measured due to the change in the reflectivity
1391:{\displaystyle \theta (r)=2\pi \int _{0}^{\infty }P(k)G(k)J_{0}(2\pi kr)kdk}
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329:{\displaystyle \Delta T(z)=(1-R){\frac {Q}{C(\zeta A)}}\exp(-z/\zeta ),}
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1015:{\displaystyle p(r)={\frac {2A}{\pi w_{0}^{2}}}exp(-2r^{2}/w_{0}^{2})}
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94:. Statements consisting only of original research should be removed.
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Then the distributions of temperature oscillations at the surface
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is the amplitude of the heat absorbed by the sample at frequency
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This last integral (6a) can be simplified to an integral over
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Modeling of data acquired in time-domain thermoreflectance
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may be utilized to achieve frequency of double or higher.
522:{\displaystyle g(r)={\frac {exp(-qr)}{(2\pi \Lambda r)}}}
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In the similar way, frequency domain solution for the
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may be too technical for most readers to understand
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783:Since the pump and probe beams used here have
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445:can be expressed by the following equation.
600:with a radially symmetric integral kernel)
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183:Learn how and when to remove this message
165:Learn how and when to remove this message
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110:Learn how and when to remove this message
351:is the specific heat (per unit volume),
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822:radius of the pump and probe beam are
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34:This article has multiple issues.
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1497:{\displaystyle \theta (r)}
1217:{\displaystyle \theta (r)}
386:Second-harmonic generation
3164:10.1126/science.1136494
1058:{\displaystyle \omega }
815:{\displaystyle 1/e^{2}}
438:{\displaystyle \omega }
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143:help improve it
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3102:J. Appl. Phys.
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393:beam splitter
389:
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378:acoustic wave
374:
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135:This article
133:
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73:This article
71:
62:
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56:
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47:
46:
41:
40:
35:
30:
21:
20:
3155:
3150:
3142:
3133:
3117:
3101:
3096:
3078:
3071:MRS Bulletin
3070:
3065:
3053:
3049:
3045:
3041:
3033:
2940:
2733:
2532:
2529:
2525:
2524:
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2349:
1963:
1832:
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1506:
1400:
1284:
1194:
1096:
1024:
907:
782:
605:
602:
591:
584:
581:
447:
420:
416:
415:
390:
375:
360:
359:length, and
352:
348:
344:
340:
338:
229:
217:pulsed laser
214:
195:
194:
179:
161:
155:January 2018
152:
136:
106:
97:
74:
50:
43:
37:
36:Please help
33:
3038:Application
3058:References
401:delay line
84:improve it
39:improve it
3001:Δ
2923:τ
2909:π
2879:−
2876:τ
2859:Δ
2856:−
2844:τ
2827:Δ
2811:−
2801:∑
2774:−
2750:Δ
2716:τ
2702:π
2672:−
2669:τ
2652:Δ
2637:τ
2620:Δ
2604:−
2594:∑
2549:Δ
2492:Λ
2479:γ
2377:π
2314:−
2263:γ
2250:γ
2232:γ
2228:−
2219:γ
2199:γ
2195:−
2186:γ
2168:γ
2155:γ
2063:−
2031:γ
1999:−
1941:γ
1911:−
1906:−
1889:−
1772:ω
1754:ω
1731:π
1727:−
1698:∞
1689:∫
1682:π
1670:Δ
1586:−
1560:θ
1555:∞
1546:∫
1514:Δ
1483:θ
1368:π
1323:∞
1314:∫
1310:π
1292:θ
1203:θ
1158:ω
1138:π
1134:−
1053:ω
974:−
941:π
718:π
708:Λ
677:π
644:∞
635:∫
631:π
508:Λ
505:π
485:−
433:ω
382:heat flow
318:ζ
307:−
301:
286:ζ
265:−
241:Δ
204:thin film
100:June 2008
88:verifying
45:talk page
3175:Category
3156:Science
1504:, i.e.
1441:, i.e.
1282:, i.e.
905:, i.e.
141:Please
82:Please
1192:. (4)
1025:where
787:, the
529:where
339:where
3031:(10)
1818:(6b)
1637:(6a)
2938:(9)
2731:(8)
1961:(7)
1398:(5)
1253:and
1022:(3)
849:and
780:(2)
579:(1)
421:The
380:and
3160:doi
3141:",
3123:doi
3106:doi
3085:doi
1094:is
298:exp
145:to
86:by
3177::
1660::
227:.
48:.
3162::
3125::
3112:.
3108::
3091:.
3087::
3017:R
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3010:t
3007:(
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2983:=
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2919:/
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2833:(
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2808:=
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2771:=
2768:]
2765:)
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2747:[
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2712:/
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2643:f
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2629:m
2626:(
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2617:(
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2607:M
2601:=
2598:m
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2570:=
2567:]
2564:)
2561:t
2558:(
2555:M
2552:R
2546:[
2543:e
2540:R
2506:n
2502:u
2496:n
2488:=
2483:n
2475:,
2468:n
2464:D
2459:w
2456:i
2450:=
2445:2
2440:n
2436:q
2432:,
2427:2
2423:/
2419:1
2415:)
2409:2
2404:n
2400:q
2396:+
2391:2
2387:k
2381:2
2373:4
2370:(
2367:=
2362:n
2358:u
2334:1
2331:+
2328:n
2323:)
2310:B
2300:+
2296:B
2288:(
2282:)
2273:1
2270:+
2267:n
2259:+
2254:n
2242:1
2239:+
2236:n
2223:n
2209:1
2206:+
2203:n
2190:n
2178:1
2175:+
2172:n
2164:+
2159:n
2147:(
2142:)
2135:)
2130:n
2126:L
2120:n
2116:u
2112:(
2109:p
2106:x
2103:e
2098:0
2091:0
2086:)
2081:n
2077:L
2071:n
2067:u
2060:(
2057:p
2054:x
2051:e
2044:(
2035:n
2027:2
2023:1
2018:=
2013:n
2008:)
1995:B
1985:+
1981:B
1973:(
1945:1
1937:1
1932:)
1924:+
1919:1
1915:B
1901:1
1897:B
1884:1
1880:B
1876:+
1871:+
1866:1
1862:B
1855:(
1852:=
1849:)
1846:k
1843:(
1840:G
1806:k
1803:d
1800:k
1797:)
1794:2
1790:/
1786:)
1781:2
1776:1
1768:+
1763:2
1758:0
1750:(
1745:2
1741:k
1735:2
1724:(
1721:p
1718:x
1715:e
1712:)
1709:k
1706:(
1703:G
1693:0
1685:A
1679:2
1676:=
1673:T
1648:k
1624:)
1616:2
1611:1
1607:w
1600:2
1596:r
1592:2
1582:(
1578:p
1575:x
1572:e
1569:)
1566:r
1563:(
1550:0
1538:2
1533:1
1529:w
1525:4
1520:=
1517:T
1492:)
1489:r
1486:(
1463:T
1460:d
1456:/
1452:R
1449:d
1429:T
1409:R
1386:k
1383:d
1380:k
1377:)
1374:r
1371:k
1365:2
1362:(
1357:0
1353:J
1349:)
1346:k
1343:(
1340:G
1337:)
1334:k
1331:(
1328:P
1318:0
1307:2
1304:=
1301:)
1298:r
1295:(
1270:)
1267:k
1264:(
1261:P
1241:)
1238:k
1235:(
1232:G
1212:)
1209:r
1206:(
1180:)
1177:2
1173:/
1167:2
1162:0
1152:2
1148:k
1142:2
1131:(
1128:p
1125:x
1122:e
1119:A
1116:=
1113:)
1110:k
1107:(
1104:P
1082:)
1079:r
1076:(
1073:p
1033:A
1010:)
1005:2
1000:0
996:w
991:/
985:2
981:r
977:2
971:(
968:p
965:x
962:e
954:2
949:0
945:w
936:A
933:2
927:=
924:)
921:r
918:(
915:p
893:)
890:r
887:(
884:p
862:1
858:w
835:0
831:w
808:2
804:e
799:/
795:1
763:2
759:/
755:1
751:)
745:2
741:q
737:+
732:2
728:k
722:2
714:4
711:(
704:1
699:=
696:r
693:d
689:r
686:)
683:r
680:k
674:2
671:(
666:0
662:J
658:)
655:r
652:(
649:g
639:0
628:2
625:=
622:)
619:k
616:(
613:G
567:)
564:d
560:/
556:w
553:i
550:(
547:=
542:2
538:q
514:)
511:r
502:2
499:(
494:)
491:r
488:q
482:(
479:p
476:x
473:e
467:=
464:)
461:r
458:(
455:g
361:z
353:A
349:C
345:Q
341:R
324:,
321:)
314:/
310:z
304:(
292:)
289:A
283:(
280:C
276:Q
271:)
268:R
262:1
259:(
256:=
253:)
250:z
247:(
244:T
186:)
180:(
168:)
162:(
157:)
153:(
139:.
113:)
107:(
102:)
98:(
80:.
55:)
51:(
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