Journal of Nuclear and Radiochemical Sciences, Vol. 17, pp , 2017

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1 Journl of Nuler n Riohemil Sienes, Vol. 17, pp , 2017 Mössuer Chrteriztion of Iron in Anient Burie Trees Exvte from the Foothills of Mt. Choki Shigeru Ymuhi, *, Ysuji Kurimoto, n Yoihi Ski Institute of Woo Tehnology, Akit Prefeturl University, Noshiro, Akit , Jpn Deprtment of Chemistry, Dio University, Ngoy, Aihi , Jpn Artiles Reeive August 18, 2017; Aepte Deemer 26, 2017; Pulishe online Jnury 25, 2018 The oxition numer n spin stte of Fe in smple of nient trees (umoregi trees) exvte from the foothills of Mt. Choki in Jpn were etermine from the 57 Fe Mössuer spetr. Moreover, si strutures of the Fe ompouns were investigte using Mössuer spetrosopy n omplementry nlytil tehniques. The umoregi woo smples were prepre from the trunks of four tree speies: Jpnese er n Jpnese zelkov whih were rown n rk green, respetively; n Jpnese ok n Jpnese hestnut whih were pure lk tone. Tretment with oxli i remove these hrteristi olors from the smples. Mössuer spetr were reore t 293 K n 78 K, n their sorption line-shpes were nlyze using urve-fitting metho. At 293 K n 78 K, the respetive isomer shifts of Fe were in the rnge of 0.21(3)-0.43(1) mm/s n 0.44(3)-0.53(1) mm/s, n the respetive qurupole splitting vlues were in the rnge of 0.62(6)-1.06(2) mm/s n 0.84(5)-1.07(1) mm/s. Although the resulting Mössuer prmeters onfirme tht Fe in the umoregi woo ws trivlent n its spin momentum numer ws 5/2 (i.e. high-spin stte), no hnges in spetrl shpe ue to prmgneti relxtion were oserve even t 78 K. From this omprehensive investigtion, it ws etermine tht Fe 3+ in Jpnese ok n Jpnese hestnut umoregi woo forms multinuler omplexes n hs some ifferenes in its first oorintion sphere from Fe 3+ in Jpnese er n Jpnese zelkov umoregi woo. Furthermore, it ws suggeste tht the moleulr struture of the Fe 3+ omplexes signifintly ffets the umoregi woo olor tone. 1. Introution The Jpnese term umoregi refers to nient trees urie or sumerge for long perio of time. In prtiulr, this term implies tht the trees, whih hve not een entirely enture ue to their isoltion from sunlight n oxygen, were urie or sumerge y nturl phenomen (e.g., lnslie, eris vlnhe, groun susienes) more thn severl hunre yers go. Umoregi generlly refers to the trunk of the nient trees. In English, og woo, fossil woo (su-fossil woo), n lignite hve een use s trnsltions for umoregi, however, they re not fully equivlent. This Jpnese term oes not elong to ny sientifi voulry n inlues some miguity. In this stuy, we efine umoregi woo s the trunk of n nient urie tree tht ontins neither ronize nor petrifie omponents, lthough nient trees re usully lle umoregi even if they hve unergone prtil roniztion. Most umoregi woo is rown or lk in olor, n sometimes eep green. Suffiiently stury umoregi woo n e use for onstrution n furniture, n they re tre s premium wooy mterils, euse their hrteristi olors or hues enhne their ommeril vlue. The olors re ue to hemil hnges in the woo omponents tht proee slowly over long perio of time. Umoregi trees hve een foun throughout Jpn, n the egree of enturtion in them ppers to e epenent on the tree speies n the uril onitions, inluing the uril time n the soil type. In the lst ee, Nrit n o-workers hve use hemil pprohes to exmine the essentil oils ontine in umoregi woo exvte in Jpn. 1-5 However, these stuies i not isuss the woo oloring *Corresponing uthor. E-mil: sigeru@iwt.kit-pu..jp, Fx: mehnisms. From stuies of iron-gll ink 6-10 n rk spots on timer ue to Fe ontmintion, it hs een reognize tht the hrteristi olor of umoregi woo rises from retions etween Fe n polyphenols suh s tnnin. Only two stuies 14, 15 on Fe in umoregi woo hve een reporte so fr, n they me no mention of the oloring mehnism, lthough they investigte the hemil sttes of Fe in the woo using Mössuer spetrosopy. Our im in this stuy is to etermine the oxition n spin stte of Fe in umoregi woo n to otin funmentl informtion out the moleulr struture of Fe-ontining hemil speies. Here, we use 57 Fe Mössuer spetrosopy n omplementry nlytil tehniques to exmine smples of umoregi woo otine from trees exvte from the foothills of Mt. Choki. 2. Experimentl 2.1. Umoregi n rw woo smples. The umoregi trees use in this stuy were exvte in 2015 from Nikho City in Akit Prefeture, Jpn, lote to the north-west of Mt. Choki. The exvtion site ws within onstrution re of the Nihonki-Tohoku Expresswy Nikho interhnge. It is oneivle tht lrge-sle lnslies ourre there n nturl forests on the north-west sie of Mt. Choki to the present ost of Nikho ity were overe with soil n stone , 17 yers go. The umoregi trees were Jpnese ok (OA; Querus setion Prinus, e.g. Querus serrt or Querus rispul), Jpnese hestnut (CH; Cstne rent), Jpnese er (CE; Cryptomeri jponi), n Jpnese zelkov (ZE; Zelkov serrt). Herefter, we refer to the tree trunks otine y removing 2018 The Jpn Soiety of Nuler n Riohemil Sienes Pulishe on We 01/25/2018

2 24 J. Nul. Riohem. Si., Vol. 17, 2018 soil n rk from the exvte umoregi trees s umoregi woo. After rying t mient temperture for severl months, umoregi woo ws ut into m 3 loks. The trunk smples of OA (Querus serrt), CH, CE, n ZE, whih re moern speies, were prepre to ompre with umoregi woo smples. We refer to the trunks of the moern trees s rw woo Tretment with oxli i. Oxli i is wiely use s timer lehing gent for Fe ontmintion. It is generlly epte tht the lehing is ue to formtion of Fe oxltes inste of Fe tnntes, euse Fe oxltes exhiit yellow or ple-yellow hue, n hene we trete the umoregi woo with oxli i solution. The umoregi woo loks were ut into smller loks n rie in ir t 105 C for 24 hours in n eletri oven. The smll loks were immerse in queous oxli i solution (3 w/w%), n the glss eker holing the solution n loks ws susequently ple in vuum esitor. The internl pressure ws suffiiently reue using wter-jet pump, n the esitor ws sele for 3 hours. The loks were tken out from the solution n rie in ir for more thn 3 ys. Speil-gre oxli i ws otine from Wko Pure Chemil Inustries, Lt Preprtion of smple powers for spetrosopi nlyses. The smll loks of umoregi woo n rw woo were rushe to power using ermi ll mill. Woo power tht oul e psse through n 18.5-mesh-sieve ws use s smple for the spetrosopi mesurements. Soil ws ollete t the exvtion site of ZE umoregi tree. The soil ws groun in ermi mortr fter ir-rying, n the soil power ws nlyze y X-ry fluoresene spetrometry. Ymuhi 2.4. X-ry fluoresene spetrometry. Elements with tomi numers greter thn 11 in umoregi woo n soil smples were etermine y X-ry fluoresene spetrometry using ompt spetrometer (MESA-500, Hori, Lt.). Umoregi woo ( g) or soil (2.3 g) power ws ple in ylinril polytetrfluoroethylene ell with imeter of 20 mm. The smple hmer ws evute using n oilsele rotry vuum pump uring mesurements. X-ry irrition ws one t room temperture n the totl mesurement time ws 2000 s. The X-ry tue voltges were 15 kv (1000 s) n 50 kv (1000 s). Reltive mss perentges of elements to totl elements etete were estimte using stnrless funmentl prmeter metho 18, 19 from hrteristi X-ry intensities Infrre photoousti (IR-PA) spetrosopy. The IR-PA spetr were otine t 22±1 C using spetrometer (JIR7000W, JEOL, Lt.) equippe with n IR-PA spetrosopy moule (IR-PAS 1000, JEOL, Lt.). The spetr were otine from 300 umultions with spetrl resolution of. 4 m -1. A thin ell (imeter, 5 mm) ws fille with the woo power, n photoousti signls were ollete upon purging ell enh with He gs. The moving-mirror veloity ws fixe t 0.16 m/s. Cron lk ws use s referene Mössuer spetrosopy. 57 Fe Mössuer mesurements were rrie out in onventionl trnsmission moe on Mössuer spetrometer (Moel-222, Topologi System Co.) with 57 Co(Rh) soure (925 MBq). Mesurement tempertures were 293 K n 78 K n they were regulte using n Oxfor ryostt DN-1726 with n ITC-601 temperture ontroller. Curve fitting of the Mössuer spetr ws performe y nonliner lest-squres metho using the MossWinn 4.0Pre. progrm, ssuming tht ll spetr were ompose of oulet of Lorentzin-shpe peks. The isomer shift (IS) n Doppler veloity sle were lirte with respet to the sextet of α-fe t room temperture. The umoregi woo smple thiknesses of CE n the other three were. 43 mg/m 2 n. 30 mg/m 2, respetively, n these llowe us to isuss Mössuer sorption intensities semi-quntittively. 3. Results n Disussion 3.1. Umoregi woo olors n lehing with oxli i tretment. Figure 1 shows photos of the umoregi n rw woo smples, n the umoregi woo smples trete with Figure 1. Umoregi n rw woo smples, n umoregi woo smples trete with oxli i. The top row is umoregi woo (, CE;, ZE;, OA;, CH), the mile row is rw woo (, CE;, ZE;, OA;, CH), n the ottom row is umoregi woo trete with oxli i (, CE;, ZE;, OA;, CH).

3 Mössuer Chrteriztion of Iron in Anient Burie Trees Exvte J. Nul. Riohem. Si., Vol. 17, TABLE 1: Reltive mss perentge of elements in umoregi woo n soil smples Smple Element wt% Ash Mg Al Si P S Cl K C Mn Fe ontent % CE* umoregi - 2.0(1) 12.8(1) 0.2(1) - 0.3(2) 1.1(1) 39.9(2) 1.9(1) 41.2(2) 0.62 ZE* umoregi - 1.4(2) 22.4(2) 0.5(1) - 1.4(2) 1.0(1) 34.0(2) 0.1** 38.6(2) 1.38 OA* umoregi - 4.8(1) 11.7(1) (1) - 0.8** 14.4(1) 1.0** 53.7(1) 1.31 CH* umoregi - 0.7** 4.4** ** 21.5(1) 0.3** 72.1(1) 2.73 Soil*** 2.2** 11.6(1) 61.5(1) - 1.2** - 4.5** 4.2** 0.2** 13.3** - *CE, Jpnese er; ZE, Jpnese zelkov; OA, Jpnese ok; CH, Jpnese hestnut. **Stnr evition is less thn 0.1. ***Gry soil ws present t the exvtion site of the ZE umoregi tree. oxli i. In the top row, CE n ZE umoregi woo ppere s rown (khki) n rk green (olive green), respetively. Umoregi woo of OA n CH, whih elong to the fmily of Fgee, exhiite pure lk tone. Therefore, the olors of umoregi woo my vry with woo speies. By ompring with the rw woo shown in the mile row, we sw tht the woo olor hnge rstilly with the uril time, n the olor of umoregi woo ws unrelte to tht of the rw woo. The umoregi woo smples shown in Figure 1 were prepre out 15 months fter tree exvtion, n their Mössuer n IR-PA spetr were reore t roughly the sme time. The olor tones of CE n ZE umoregi woo h hnge to rown n rk green, respetively, immeitely fter the exvtion. However, we juge tht their olor tones slightly n grully eme eeper with time. As for OA n CH umoregi woo, no olor tone hnges with time oul e oserve y the nke eye. As mentione ove, lthough no stuies re ville on the oloring mehnism of umoregi woo se on immeite eviene, it is ommonly reognize tht the olor fetures of umoregi woo re ue minly to Fe ompouns interting with polyphenols suh s tnnin. This hs een eue from stuies of the historil ink (iron-gll ink) 6-10 or stins on timer use y Fe ontmintion The stins showe rk olors similr to those of umoregi woo. Moreover, it hs een reporte tht the rk stins our on timer owing to Cu, Cr, n Mn s well s Fe The ottom row shown in Figure 1 presents umoregi woo piees trete with oxli i whih were ut from the umoregi woo loks shown in the top row. In ll the umoregi woo piees, their hrteristi olors vnishe rmtilly through this tretment. The CE n ZE umoregi woo turne olors lose to those of their rw woo, n the pure lk tone fe wy from the OA n CH umoregi woo. From the ispperne of rk olor, we ntiipte tht the oloring mehnisms in umoregi woo were similr to those in timer use y Fe ontmintion Elements nlysis of umoregi woo n soil smples. Tle 1 summrizes the reltive mss perentge of elements from Mg to P in umoregi woo n soil smples ollete from the exvtion site. Tsuhiy et l. 23 reporte the ontent of minor elements in the woo n rk of vrious rw tree speies inluing CE, ZE, n OA using inutively ouple plsm emission spetrometry. Woo n rk re orgni mtter, n the mjor elements onstituting them re C, O, n H. Aoring to their stuy, K n C were mjor elements mong metls, exeeing 1000 mg/kg in more thn hlf of the woo smples. Mg, Si, n P were lssifie into seonry group mong the minor elements n their ontents rnge from ozens to severl hunre mg/kg. The Fe ontent in the woo smples ws uner 10 mg/kg n less thn Al n Sr. The umoregi woo h not een egre mrkely s mentione lter, n hene C, O, n H shoul lso e mjor elements. In ontrst, Fe ws mjor element in ll the umoregi woo smples mong the elements etete using X-ry fluoresene spetrometry, n, in prtiulr, the reltive mss perentge of Fe in CH umoregi woo ws more thn 70%. The elementl nlysis inite tht Fe ontent in the soil ws muh higher thn tht in the rw woo smples. Thus, it n e ssume tht Fe ws trnsferre from the soil to the umoregi woo uring the long uril perio. Other trnsition metls, whih re ple of using olor hnges in umoregi woo, were negligile exept for Mn. Although the ontents of Mn were lrger thn those of Cu, Ni, or P, prtiulrly in CE n OA umoregi woo, the reltive mss perentges of Mn were n orer of mgnitue lower thn those of Fe. Most C ontine in the umoregi woo ws expete to hve een lrey present in the trees when they were urie. We note tht the reltive mss perentges of Al in the umoregi woo were muh less thn those of Fe espite the vlue of Al eing lose to tht of Fe in the soil smple. This might e expline s follows. In generl, Al 3+ shows mny similrities in hemil ehvior to Fe 3+ n ll of the Al ontine in the soil must e trivlent (Al 3+ ). However, our previous Mössuer mesurement revele tht the Fe 2+ /Fe 3+ rtio in the soil ws. 3/7, 24 n therefore Fe 2+ might trnsfer to umoregi woo more esily thn Fe 3+. Mjor elements of rw woo re C, O, n H, s mentione ove, n the sum of their ontents is out 99 %. These elements nnot e etete y X-ry fluoresene spetrometry. Thus, the reltive mss perentges shown in Tle 1 shoul e muh lrger thn the solute mss perentges. We opte simple lultion metho to estimte roughly the solute mss perentge of Fe in the umoregi woo smples. In prtiulr, ssuming tht only elements with tomi numers smller thn 11 were ompletely remove from sh y urning, we lulte the tenttive solute mss perentges of Fe se on Eq. (1): TP Fe = RP Fe A 1/100 (1) where TP Fe, RP Fe, n A re the tenttive solute mss perentge, reltive mss perentge, n sh ontent in perent unit, respetively. The sh ontents of CE, ZE, OA, n CH umoregi woo smples were 0.62, 1.38, 1.31, n 2.73%, respetively, s reporte in our previous work. 24 The TP Fe vlues otine from Eq. (1) of CE, ZE, OA, n CH umoregi woo smples were pproximtely 0.3, 0.5, 0.7, n 2%, respetively. Eq. (1) is n pproximte lultion euse metl elements shoul e ontine s oxies in sh. We expet, however, tht TP Fe otine from Eq. (1) is useful tool to estimte the hemil sttes of Fe in the umoregi woo.

4 26 J. Nul. Riohem. Si., Vol. 17, Infrre photoousti (IR-PA) spetrosopy. Figure 2 epits the IR-PA spetr over the m -1 rnge of the umoregi n rw woo smples. It is iffiult to otin fine IR spetrum from lk or rk-olore smples suh s egre woo n hrol using orinry tehniques euse of non-resonnt sorption. Photoousti spetrosopy is suitle tehnique to mesure the IR spetr of suh smples. For exmple, y mens of the IR-PA spetrosopi tehnique, we hve stuie the wethering of tropil woos, reveling tht this metho is useful tool to follow hemil hnges in funtionl groups, espeilly ronyl, roxyl, n phenyl groups. 25 As seen in Figure 2, the IR-PA spetrum of the umoregi woo smples ws nlogous to tht of the sme speies of rw woo exept for the regions of m -1 n m -1. We note tht there were no signifint spetrl ifferenes etween rw n umoregi woo smples in the virtionl ns ue to phenyl groups of lignin (1592 m -1 n 1503 m -1 ) 26, 27 n sturte yli groups of ellulose or hemiellulose ( m -1 n m -1, respetively). 26 Therefore, we oul ssume tht the egrtion of umoregi woo h not proeee rstilly uring the 2500-yer-uril of these trees. Remrkle spetrl ifferenes, however, ppere in two regions. A ro n roun 1740 m -1 ws ssigne minly to C=O strething virtions in roxyl 26 n unonjugte ronyl 28 groups, n the n intensity of umoregi woo ws muh less thn tht of rw woo. The n of strething virtions ttriute to onjugte C=O groups 28 ws etete t m -1, n its intensity in umoregi woo seeme to e slightly less thn in rw woo. Furthermore, it seeme tht the n intensities in the region of m -1 for the Reltive intensity Wvenumer /m 1 Figure 2. IR- PA spetr of rw n umoregi woo smples:, CE (rw woo);, CE (umoregi woo);, ZE (rw woo);, ZE (umoregi woo); e, OA (rw woo); f, OA (umoregi woo); g, CH (rw woo); h, CH (umoregi woo). e f g h Ymuhi umoregi woo smples exept for CE were smller thn those of the rw woo smples. Severl virtionl moes hve ns in this region n one of them will e strething virtion of C-O in roxyl groups. 26 Thus, the IR-PA spetr of the umoregi woo smples reinfore the suggestion tht some hemil hnges ourre in roxyl n/or ronyl groups uring the long uril perio. There re two possile hemil hnges. One is eomposition of the funtionl groups, n the other is the ourrene of hemil intertions etween the funtionl groups n their neighoring speies. If O toms inlue in the funtionl groups form hyrogen, ioni or oorinte ons, the ns t 1740 n 1650 m -1 woul e shifte to onsierly lower wvenumers. 29 It ws, however, iffiult to etermine from the IR-PA spetr whether suh shifts ourre Mössuer spetrosopy. Figures 3 n 4 show the Mössuer spetr of umoregi woo smples reore t 293 K n 78 K, respetively. The sorption intensities re sustntilly wek for lmost ll umoregi woo smples euse of the low Fe ontents (0.3 to 2 %) s esrie in Setion 3.2. Asorption lines in ll the Mössuer spetr onsiste of set of oulet lines, n no mgneti hyperfine splitting ws oserve even t 78 K. Tle 2 summrizes the Mössuer prmeters (IS; qurupole splitting, QS; n line with, LW) lulte y urve fitting. The LW vlues were slightly ut lerly lrger (~0.26 mm/s in the present work) ompre with orinry Fe ompouns. This enhnement of LW is expline lter. In ition, from Figures 3 n 4, the Mössuer sorption intensity ws onsiere to e in the following orer: CE < ZE < OA < CH, n this ws in greement with the orer of TP Fe (see Setion 3.2). The IS vlues of 0.21 to 0.43 mm/s t 293 K inite tht Fe in ll of the umoregi woo smples ws high-spin Fe 3+ or low-spin Fe The ssignment to high-spin Fe 2+ shoul e exlue, sine the IS n QS vlues t 293 K (Tle 2) rnge from 0.2 mm/s to 0.5 mm/s n from 0.6 mm/s to 1.1 mm/s, respetively, n they were muh smller thn those of most high-spin Fe 2+ ompouns. 33, 34 It seeme tht ll the IS n QS vlues t 293 K of Fe in the umoregi woo smples were within the shre rnges etween high-spin Fe 3+ n low-spin Fe , 34 However, the ssignment to low-spin Fe 2+ shoul lso e exlue, euse the umoregi woo n soil smples woul ontin little or no mounts of ligns inuing lrge lign fiel splitting suh s CN -, NO 2 -, or NH 3. Therefore, the Fe in the umoregi woo smples ws most likely to e highspin Fe 3+. However, the QS vlues were somewht lrger thn vlues typilly seen for high-spin Fe 3+ ompouns. The four types of umoregi woo were lssifie into two groups se on their IS n QS, s shown in Figure 5. Group 1 onsiste of CE n ZE, n Group 2 onsiste of OA n CH. IS n QS of Group 1 were signifintly smller thn those of Group 2. Moreover, the two groups iffere from eh other in olor; Group 1 smples were rown or rk green, while Group 2 smples were pure lk s seen in Figure 1. Hene, the first oorintion sphere of Fe in Group 1 woul e expete to e somewht ifferent from tht in Group 2, even though Fe in oth groups exists s high-spin Fe 3+ speies. Group 1 showe smll ut ler temperture-epenene for QS, lthough the QS vlues of Group 2 were inepenent of temperture. This suggeste tht Fe 3+ speies in Group 1 my unergo some struturl hnge from 293 K to 78 K, euse QS of high-spin Fe 3+ shows little or no tempertureepnene. 31 Moreover, the ifferenes in IS of Group 2 etween 293 K n 78 K were. 0.1 mm/s s shown in Tle 2, whih ws onsistent with the seon-orer Doppler shift. 30 However, the inreses in IS of Group 1 t 78 K were too lrge to e ounte for s the seon-orer Doppler shift lone,

5 Mössuer Chrteriztion of Iron in Anient Burie Trees Exvte J. Nul. Riohem. Si., Vol. 17, Reltive intensity /. u Reltive intensity /. u Doppler veloity / mm s 1 Figure 3. Mössuer spetr t 293 K of umoregi woo smples:, CE;, ZE;, OA; n, CH. Numerls in the spetr represent reltive mgnifition of intensity when the spetrum of CH is use s referene. The perent sorption intensity is out 0.8 % t the mximum for CH. 0 Doppler veloity / mm s 1 Figure 4. Mössuer spetr t 78 K of umoregi woo smples:, CE;, ZE;, OA; n, CH. Numerls in the spetr represent reltive mgnifition of intensity when the spetrum of CH is use s referene. The perent sorption intensity is out 1.6 % t the mximum for CH. TABLE 2: Mössuer prmeters of umoregi woo smples 1.2 Umoregi woo smple CE* ZE* OA* CH* Temp. IS** QS*** LW**** K mm s -1 mm s -1 mm s (3) 0.64(5) 0.66(8) (3) 0.84(5) 0.68(7) (3) 0.62(6) 0.82(15) (3) 0.88(4) 0.70(7) (1) 0.99(2) 0.60(3) (1) 0.98(1) 0.70(2) (1) 1.06(2) 0.70(3) (1) 1.07(1) 0.67(1) * CE, Jpnese er; ZE, Jpnese zelkov; OA, Jpnese ok; CH, Jpnese Chestnut. **Isomer shift, ***qurupole splitting, ****line with. Qurupole splitting / mm s ZE CE CH OA ZE CE OA CH n it ppere tht there ws some struturl hnge tking ple etween 293 K n 78 K. It is well reognize, t room temperture, tht IS is in the rnge of mm/s if oorinting toms to Fe 3+ form n otheron (six-oorinte struture), n in the rnge of mm/s if tetrheron (four-oorinte struture) is forme. 32 The IS of Fe 3+ in Group 2 umoregi woo smples ws in the former rnge, wheres the IS of Fe 3+ in Group 1 umoregi woo smples ws slightly less thn 0.3 mm/s. It is, however, known tht most Werner type Fe 3+ omplexes hve n otherl oorintion geometry, exept for hlogenoomplexes. On the other hn, for high-spin Fe 3+ speies, it hs een reporte tht QS rnges t room temperture orresponing to the six-oorinte n four-oorinte struture rnges re pproximtely mm/s n mm/s, respetively. 34 As liste in Tle 2, our QS vlues supporte the fining tht the oorintion numer of Fe 3+ in Group 2 umoregi woo smples ws six; however, they i not suggest oorintion Isomer shift / mm s 1 Figure 5. Isomer shift n qurupole splitting t 293 K ( ) n 78 K ( ) of Fe in umoregi woo smples. The re n shows the IS rnge for high-spin Fe 3+ t room temperture 32, 34, n the lue n shows tht t liqui nitrogen temperture estimte from the seonorer Doppler shift 30 on the sis of the former rnge. numer of Fe 3+ in Group 1 umoregi woo smples. Aoringly, the Fe 3+ in Group 2 umoregi woo is ertinly lote t the enter of n otheron struture. In ontrst, it is iffiult to etermine from Mössuer prmeters whether the first oorintion sphere of Fe 3+ in Group 1 umoregi woo is tetrherl or otherl struture. Severl stuies hve resse the retion etween Fe n polyphenols, n isusse the struture of polyphenol-fe omplexes. These stuies re ivie into two tegories. The first is reserh into the effets of polyphenols in woo on

6 28 J. Nul. Riohem. Si., Vol. 17, 2018 Fe orrosion Reserhers hve suppose tht two kins of mononuler Fe(III) omplexes one to tnnins s ientte lign re forme y the retion with tnnins extrte from woo, on the sis of Mössuer spetrosopi nlysis. The seon tegory is series of stuies of historil ink (iron-gll ink) From oth tegories, it shoul e note tht si struture for moel ompoun for glli i- Fe(III) omplex ws etermine using n X-ry iffrtion metho. 6, 37 The glli i-fe(iii) omplex hs polynuler strutures, n moleule of glli i forms three ons etween its three hyroxyl groups n two Fe toms, n helte on etween its roxyl group n nother Fe tom. Fe toms re lote t the enter of the otherl strutures. However, it will e very iffiult to etermine the struture of Fe ompouns ontine in the umoregi woo smples y X-ry iffrtion methos, euse Fe onentrtions re low n the rystls re mirosopil if Fe ompouns re rystllize. Our Mössuer t suggeste tht Fe speies in Group 2 umoregi woo h multinuler strutures for whih unit ontine two or more Fe toms, euse no hnges in spetrl shpe ue to prmgneti relxtion were oserve even t 78 K espite the presene of high-spin Fe 3+. However, it ws iffiult from our Mössuer spetrl t to etermine whether or not their moleulr strutures were nlogous to tht of the glli i-fe(iii) omplex. Prmgneti relxtion phenomen in Mössuer spetrosopy hve een interprete s the flutution of mgneti fiels proue y eletroni spins in prmgneti ompouns, n the flutution rte ereses s temperture ereses. This phenomenon is oservle in high-spin Fe 3+ n Eu 2+ whose oritl momentum vnishes (L 0) s hnges in Mössuer spetr. Well-resolve mgneti hyperfine splitting lerly ppers in Mössuer spetr when fully fixe mgneti fiel exists t Mössuer nulie. Menwhile, mgneti fiel hs no influene on Mössuer sorption line-shpe if its flututions re suffiiently fst. In oth ses, Mössuer spetr n e expresse s omintion of Lorentzin urves. However, t intermeite spin flutution rtes omprle to the Lrmor preession rte of the Mössuer nuleus, it is known tht the Mössuer sorption line-shpe eomes omplite through the relxtion effet n nnot e preisely pproximte with Lorentzin or Gussin urves. 30 We previously reporte the Mössuer spetr of high-spin Fe n Eu 2+ 44, 45 ompouns n their frozen solutions, n inite tht the eletron-spin flutution rte ereses s the Fe-Fe or Eu-Eu istne inreses ue to less spin-spin ipole intertion. Speifilly, we experimentlly exmine the Mössuer line-shpes of tris(β-iketonto)fe(iii) 38, 39 n hexkis(lkylure)fe(iii) 42 omplexes, whih hve six-oorinte otherl struture in terms of the prmgneti relxtion effet. The Mössuer spetr of ll these omplexes showe n pprent single sorption line, ut the line h wings on oth sies n its line-shpe ws istintly non- Lorentzin. The ulkier the lign of the Fe omplex, the lrger the wings were. In other wors, the sorption lineshpe roene with inresing verge Fe-Fe istne in the omplexes. The sorption line t liqui nitrogen temperture (78K) exhiite more ovious roening ompre with tht t room temperture in eh omplex. Moreover, splittings ue to mgneti hyperfine strutures were oserve in the Mössuer spetr when Fe(III)() 3 (, CH 3 COCHCOCH - 3 ) omplexes were homogeneously isperse in 38, 40 frozen solutions. In ontrst, it ws onfirme tht the Mössuer sorption line-shpe of [(μ-ch 3 O)Fe(III)(pm) 2 ] 2 (pm, (CH 3 ) 3 COCHCOCH(CH 3 ) - 3 ), whih is inuler Fe omplex, shows no signifint hnges when isperse in frozen solution Ymuhi espite the ft tht the Fe 3+ in the omplex is in the high-spin stte n lote t the enter of n otherl struture. 46 This ws interprete s n inition tht the spin-spin ipole intertion ws hrly wekene y ispersion in frozen solution, euse the Fe-Fe istne in the inuler Fe omplex unit ws onstnt. Aoringly, the Mössuer sorption line of Fe in Group 2 umoregi woo smples shoul exhiit ro wings or some ifferenes from Lorentzin urves if the Fe 3+ speies were mononuler omplexes. The resons re s follows. (1) Fe 3+ speies in Group 2 umoregi woo ertinly hve six-oorinte otherl strutures. (2) Polyphenols, whih will e ulkier thn β-iketone n lkylure moleules, likely form hemil ons with Fe 3+ s ligns. In ition, the wings t 78 K shoul e roer n lrger thn those t 293 K. Nevertheless, neither wings nor ifferenes from Lorentzin urves were oserve in the Mössuer sorption of Fe in the umoregi woo smples n the sorption lines shown in Figures 3 n 4 were well expline y superposition of two ientil Lorentzin urves. The woo omponents with pyrogllol groups tht n form ross-linke strutures y n O-Fe-O-Fe-O on inlue severl polyphenols ontining tnnins. As result of the Mössuer spetrosopi mesurements, we onlue tht Fe 3+ forme multinuler omplexes with polyphenols in Group 2 umoregi woo. Furthermore, the lrge LW vlues llowe us to preit o-existene of two or more kins of Fe omplexes with similr strutures, n this preition ws pplile to Group 1 umoregi woo. On the other hn, the sene of prmgneti relxtion effet on the Mössuer sorption line-shpe oul not e esily epte s eviene tht Fe 3+ speies in Group 1 umoregi woo were multinuler omplexes, euse the oorintion toms to Fe 3+ my form tetrherl strutures. Our Mössuer spetrosopi t inite tht Fe 3+ speies in Group 1 umoregi woo iffer signifintly from those in Group 2 umoregi woo in terms of their moleulr struture, therey reinforing the suggestion tht the moleulr struture of Fe 3+ speies is n importnt ftor etermining the olor tone of the umoregi woo. Further stuy is neessry to unerstn ompletely the moleulr strutures of Fe 3+ speies in ifferent types of umoregi woo. 4. Conlusion The results of the Mössuer spetrosopi nlysis esrie here onfirme tht Fe in the umoregi woo smples h 3 5 eletron onfigurtion n its spin quntum numer (S) ws 5/2 (high-spin stte), n they inite tht the high-spin Fe 3+ speies in OA n CH umoregi woo smples exhiite otherl symmetry n oul e ttriute to multinuler ompouns. Moreover, the temperture-epenene of IS n QS suggeste tht some struturl hnges might our in Fe 3+ speies in CE n ZE umoregi woo smples etween 293 K n 78 K. Comprehensive investigtion of ll the experimentl results inite tht the Fe 3+ omplexes inlue polyphenols with pyrogllol groups s ligns, n suggeste tht their moleulr struture ws governing ftor for the umoregi woo olor tone. Aknowlegement We re grteful to the Nikho City Bor of Eution for the ontion of the umoregi woo smples.

7 Mössuer Chrteriztion of Iron in Anient Burie Trees Exvte J. Nul. Riohem. Si., Vol. 17, Referenes (1) H. Nrit, M. Ytgi, n T. Ohir, J. Essent. Oil Res. 18, 68(2006). (2) H. Nrit, n M. Ytgi, Org. Geohem. 37, 818 (2006). (3) H. Nrit, K. Huruht, S. Kug n M. Ytgi, Phytohem. 68, 587(2007). (4) H. Nrit, Mokuzi Kogyo 68, 330(2013). (5) H. Nrit, Woo Protetion 42, 62(2016). (6) C. H. Wunerlih, R. Weer, n G. Bergerhoff, Z. norg. llg. Chem. 598/599, 371(1991). (7) C. Krekel, Int. J. For. Do. Exm. 5, 54(1999). (8) B. Wgner, E. Bulsk, B. Sthl, M. Hek, n H. M. Ortner, Anl. Chim. At 527, 195(2004). (9) C. Burgu, V. Rouhon, P. Refit, n A. Wttiux, Appl. Phys. A92, 257(2008). (10) C. Cnevri, M. Delorenzi, C. Invernizzi, M. Lihelli, M. Mlgoi, T. Rovett, n M. Weththimuni, Woo Si. Tehnol. 50, 1057(2016). (11) W. Snermnn, n M. Lüthgens, Holz ls Roh-u. Wérkst. 11, 435(1953). (12) T. Kono, H. Uto, n M. Su, Mokuzi Gkkishi 2, 221(1956). (13) K. Tkenmi, Mokuzi Gkkishi 10, 22(1964). (14) S. Ymuhi, Y. Ski, n H. Aimi, J. Woo Si. 57, 549(2011). (15) U. Bürk, F. E. Wgner, n A. Lerf, Hyperfine Intert. 208, 105(2012). (16) H. Skuri, W. Kto, Y. Tkhshi, K. Suzuki, Y. Tkhshi, S. Gunji, n F. Tokni, Rioron 48, 401(2006). (17) S. Hyshi, So & Chisui 45, 80(2012). (18) A. Kir, n N. Roson, Reout No. 22, 19(2001). (19) W. T. Elm, R. B. Shen, B. Sruggs, n J. Niolosi, Av. X-ry Anl. 47, 104(2004). (20) J. Wehrmnn, Holz ls Roh-u. Wérkst. 15, 325(1957). (21) L. Plth, Holz ls Roh-u. Wérkst. 16, 357(1958). (22) K. Tkenmi, Mokuzi Gkkishi, 10, 30(1964). (23) Y. Tsuhiy, H. Shimogki, H. Ae, n A. Kgw, J. Woo Si. 56, 53(2010). (24) S. Ymuhi, Y. Kurimoto, n Y. Ski, J. Nul. Riohem. Si. 17, 1(2017). (25) S. Ymuhi, Y. Suiyni, Y. Immur, n S. Doi, J. Woo Si. 50, 433(2004). (26) A. J. Mihell, A. J. Wtson, n H. G. Higgins, Tppi 48, 520(1965). (27) U. M. Agrwl, J. D. MSweeny, n S. A. Rlph, J. Woo Chem. Teh. 31, 324(2011). (28) I. R. Lewis, N. W. Dniel, N. C. Chffin, Jr., n P. R. Griffiths, Spetrohim. At 50A, 1943(1994). (29) K. Nkmoto, Infrre n Rmn spetr of inorgni n oorintion ompouns Prt B: Applitions in oorintion, orgnometlli, n ioinorgni hemistry, A John Wiley & Sons, In., New Jersey, (2009). (30) P. Gütlih, E. Bill, n A. X. Trutwein, Mössuer spetrosopy n trnsition metl hemistry -Funmentls n pplitions-, Springer-Verlg, Berlin, (2011). (31) J. C. Trvis, The eletri fiel grient tensor, in: An introution to Mössuer spetrosopy E. L. My, Plenum Press, New York, (1971). (32) F. Menil, J. Phys. Chem. Solis, 46, 763(1985). (33) N. N. Greenwoo, n T. C. Gi, Mössuer spetrosopy, Chpmn n Hll Lt., Lonon, (1971). (34) R. E. Vnenerghe, n E. De Grve, Mössuer spetrosopy, Es. Y. Yoshi, n G. Lngouhe, Springer- Verlg, Berlin, (2013). (35) J. Gust, n J. Suwlski, Corrosion 50, 355(1994). (36) J. A. Jén, J. De Olí, n M. V. Roríguez, Hyperfine Intert. 202, 25(2011). (37) R. K. Feller, n A. K. Cheethm, Soli Stte Si. 8, 1121(2006). (38) Y. Ski, H. Nishioji, S. Ymuhi, n T. Toming, Riohem. Rionl. Lett. 53, 215(1982). (39) S. Ymuhi, Y. Ski, n T. Toming, Int. J. Appl. Rit. Isot. 34, 977(1983). (40) Y. Ski, H. Nishioji, n T. Toming, Riohim. At 36, 181(1984). (41) S. Ymuhi, Y. Ski, n T. Toming, Bull. Chem. So. Jpn. 58, 442(1985). (42) S. Ymuhi, Y. Ski, n T. Toming, J. Rionl. Nul. Chem. Lett. 119, 283(1987). (43) S. Ymuhi, Y. Ski, n T. Toming, J. Rionl. Nul. Chem. Lett. 146, 185(1990). (44) S. Ymuhi, Y. Mini, n T. Toming, J. Rionl. Nul. Chem. Lett. 93, 238(1985). (45) S. Ymuhi, T. Wtne, n T. Toming, Riohim. At 43, 51(1988). (46) S. Ymuhi, Mössuer spetrosopi stuy of mgneti relxtion in iron ompouns, The University of Tokyo, 1983, Mster s thesis.

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.

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