In uence of grain size and grain boundaries on the properties of La 0.7 Sr 0.3 Co x Mn 12x O 3

Size: px
Start display at page:

Download "In uence of grain size and grain boundaries on the properties of La 0.7 Sr 0.3 Co x Mn 12x O 3"

Transcription

1 In uene of grin size nd grin oundries on the properties of L.7 Sr.3 Co x Mn x O 3 S. Ds, P. Chowdhury, *, T.K. Gundu Ro, D. Ds, D. Bhdur,1 Deprtment of Metllurgil Engineering nd Mterils Siene, Indin Institute of Tehnology, Bomy 476, Indi Regionl Sophistited Instrumenttion Center, Indin Institute of Tehnology, Bomy 476, Indi Astrt We hve synthesized L.7 Sr.3 Mn.9 Co.1 O 3 grnulr perovskites using ethylenediminetetreti id EDTA) s omplexing gent. The in uene of grin size nd grin oundry struture on the physil properties ws investigted. Our results show tht deresing grin size leds to lowering of the ferromgneti trnsition temperture, rodening of the trnsition, derese in mgnetiztion nd enhnement of resistivity nd mgnetoresistne t low tempertures. Also, eletron spin resonne linewidth nd g-vlue will derese. These results re explined y spin dependent sttering t the grin oundries nd wekening of mgneti intertion ner the surfe of grins, whih redues the internl eld in the system. Keywords: Mngnites; Resistivity; Mgnetoresistvity; Eletron spin resonne; Grin oundry 1. Introdution The in uene of the grin oundries or the grin size in mngnese perovskites on the mgneti nd mgnetotrnsport properties hs reently een investigted extensively [1,2]. One of the erliest reports on the effet of prtile size on the physil properties of mngnites ws y Mhesh et l. [3], where they hve vried the prtile size from.2 to 3. mm nd found signi nt hnges in the properties. It ws oserved y most of the reserhers tht the low temperture mgnetoresistne enhned sustntilly with the derese in grin size. Severl theoretil models hve een put forwrd to understnd the mehnism of inter-grin tunneling ondution. One of the rst models proposed y Hwng et l. [4] ws sed on the spin polrized tunneling SPT). In systems like mngnites, SPT my our, ut it is not neessrily the dominnt use of mgnetoresistne. Reently Zhng et l. [] hve studied the mgneti properties of LSMO systems nd proposed spin dependent intrgrnulr sttering in these systems. Aording to them, the intergrnulr sttering results from spin dependent surfe effet, relted to the differene in the mgneti struture etween the ore nd the surfe of the perovskite grins. This results in n enhned mgnetoresistne t low tempertures due to eld-indued hnge of interfil spin on gurtion. Previous eletron spin resonne ESR) studies on mngnities exhiiting olossl mgnetoresistne CMR) hve reported strong ESR lines oth in the prmgneti nd ferromgnetilly ordered phses [6]. Lrge vrition of the line prmeters like intensity nd linewidth were oserved s funtion of temperture. A rossover from ottleneked regime, where Mn 41 nd Mn 31 ions re strongly oupled, to n isotherml one ws proposed [7] to explin the oserved vrition of linewidth with temperture. In this ontext, ESR is n extremely useful tehnique to study mgneti orreltions on mirosopi level nd is well suited to the study of mngnites. In the present investigtions, we hve used low temperture sol±gel proessing to synthesize L.7 Sr.3 Co x Mn x O 3 LSCMO) with x ˆ :1;.3 nd. nd investigted the

2 692 Tle 1 Het tretment detils, revitions used for smples nd the estimted grin sizes Smple no. Dwell time h) Men grin size mm) LSMCO1..2 LSMCO1 2. LSMCO1.62 LSMCO1d 8.81 LSMCO1e 1.2 Mgnetistion (emu/gm) o C, 8 h 9 o C, h metl±insultor trnsition temperture through the resistivity mesurements. Mngnese nd olt ions re hemilly different with respet to ioni rdii nd eletroni on gurtions. Mn 31 t 3 2ge 1 g is Jhn Teller ion, wheres Co 31 n exist in high spin t 4 2ge 2 g nd low spin t 6 2ge g sttes. These my hve strong in uene on lttie distortion, mgneti exhnge s well s eletron trnsport ehvior. It is oserved tht the omposition with x ˆ :1is the est ompromise smple showing trnsition loser to room temperture with no hrmful effets on mgneti nd mgnetotrnsport properties. Thus, we hve investigted the in uene of the grin size on this prtiulr smple y sintering it t 9 8C for different dwell times. These smples were hrterized y X-ry diffrtion XRD), snning eletron mirosopy SEM), eletril resistivity, mgnetoresistne nd mgnetiztion mesurements. ESR 9 o C,. h experiments hve een rried out to further understnd the mgneti orreltions on mirosopi level. The results on the smple L.7 Sr.3 Mn.9 Co.1 O 3 LSCMO1) re presented in this pper. 2. Experimentl Temperture (K) Fig. 2. Vrition of mgnetiztion of LSMCO1 smples sintered t 9 8C for ). h, ) h, nd ) 8 h.. µ m Fig. 1. SEM of LSMCO1 smples sintered t 9 8C for ). h, ) 2 h, nd ) 8 h. Mngnite hving the formul L.7 Sr.3 Mn.9 Co.1 O 3 LSCMO1) hs een synthesized y mixing stoihiometri mounts of the individul metl nitrtes to form the trget omposition. One mole of this trget omposition ws mixed with 4 mol of itri id nd 3 mol of ethylene glyol nd heted t 8 8C until gel ws formed. To remove the orgni prts, the gel ws then heted t 3 8C. Differentil therml nlysis DTA) nd thermo-grvimetri nlysis TGA) studies of the preursor powders were done to estimte the lintion temperture. Bsed on this, the resultnt powder ws lined t 8 8C in ir for 2 h. The lined powder ws then pelletized nd sintered t 9 8C for., 2,, 8 nd h, respetively, to otin different grin size. The smples were hrterized y powder XRD Philips PW 1729) using Cu K rdition. SEM Cme SU 3) ws used to see the mirostruture. The mgnetiztion with temperture ws mesured using virting smple mgnetometer Oxford VSM). The temperture dependene of resistivity r T ) ws mesured y four-proe tehnique in the temperture rnge 1±3 K using losed yle refrigertor. Mgnetoresistivity mesurements hve een rried out from 3 to 8 K using liquid N 2 gs- ow ryostt. ESR experiments were rried out on Vrin Century series E-Line E-1 ESR spetrometer whih utilizes khz eld modultion.

3 693 Tle 2 Different prmeters otined for smples with vrying grin sizes Men grin size mm) T p K) T K) r 8 K) V m) r T p) V m) MR% 8 K) ± 348 ± Results nd disussion Smple prepred y ermi route sintered t 8C for 2 h) shows tetrgonl struture with lttie prmeter ˆ ˆ 3:893 A nd ˆ 11:2 A: On the other hnd, the smples prepred y sol±gel route, sintered t the sme temperture, shows ui struture with lttie prmeter ˆ ˆ ˆ 3:883 A: All the smples sintered t 9 8C for different dwell times given in Tle 1 show ui struture. The derese in the linewidth with inrese in dwell time ws oserved in the XRD pttern of the smples, whih indites n inrese in grin size. The grin size nd shpe of the smples were noted from the photogrphs of snning eletron mirosope Resistivity (Ω m) K Temperture (K) 22.3 K K Fig. 3. Vrition of resistivity nd mgnetoresistivty with tempertures for LSCMO1 smples sintered t 9 8C for different times: ). h, ) 2 h, ) h nd d) 8 h. d Mgnetoresistne(%) Fig. 1 )± )). As given in Tle 1, the grin size inreses from out.2 to 1.2 mm s the dwell time inreses from. to h. A typil vrition of mgnetiztion with temperture mesured t 2 koe for the three grin-size vried smples is shown in Fig. 2. The Curie temperture T ws tken from the in exion point of M±T urve nd is given in Tle 2. With derese in grin size, the vlue of M lowers. But the derese in mgnetiztion is firly lrge for smple LSMCO1 where the grin size is estimted round.2 mm. Seondly, T dereses signi ntly for this smple. There re similr reports in the literture. For exmple, Hung et l. [8] oserved suh trend of M with grin size in pure LSMO smples sintered t different tempertures. Iss et l. [9] nd Snhez et l. [] showed tht the spins eome hevily disordered t the grin oundry due to strin with lowering of the grin size, whih my result in redution of the vlue of M s nd T. Gupt et l. [11,] explined the vrition in properties with grin size s the re etion of mgneti disorder in the grin oundry region nd disorder indued nting of Mn spins ner the surfe of the grins. The depression in T in grin size vried smples studied here re onsistent with these pitures. Fig. 3 )± d) shows the temperture dependene of resistivity with nd without mgneti eld for smples sintered t 9 8C for different dwell times: ). h, ) 2 h, ) h nd d) 8 h. These gures lso show the vritions of MR with temperture. All the resistivity urves show only rod pek t temperture T p : The rod trnsition is hrteristi of the smll grin size. With the grin growth, the temperture T p shifts to higher temperture, wheres the mgnitude of resistivity redues y two orders of mgnitude. All the prmeters otined from mgneti nd mgnetotrnsport mesurements re given in Tle 2. The vlue of MR is mximum 2%) for the smple with smllest grin size. The mgneti inhomogenity t the grin oundries serves s strong sttering enters. The more the grin oundry region, the more should e the MR, s oserved in our present smples. Also, s the oundries of the grins onsist of more mgneti disorder thn the ores, the resistivity redues drstilly with the grin growth. For porous grnulr perovskite systems, Zhng et l. [] proposed tht the resistivity hs two ontriutions: 1) the

4 694 ρ sur (8 K) / ρ(8 Κ) w/D Grin size (µm) Grin size (µm) Intensity (Aritrry Units) g vlues Temperture (K) 2 Mgneti field (mt) Fig. 6. ESR spetr of the smple L.7 Sr.3 MnO 3 t tempertures: ) 2 8C, ) 6 8C nd )14 8C. Inset shows the vrition of g s funtion of tempertures for the sme smple. 4 Fig. 4. Grin size dependene of the interfil resistivity ontriution to totl resistivity r sur =r for grin size vried LSMCO1 smples. Inset shows the vrition of surfe volume frtion 6w/D with grin sizes. ody phse nd 2) the surfe phse. The surfe ontriution to resistivity with omptness hs een given y r sur ˆ fs r t where r t is the tunnel resistivity, f s is volume frtion oupied y the surfe nd is equl to 6w/D. Here, w is the verge thikness of the grin surfe nd D is the verge grin size. The vrition of r sur 8 K)/r 8 K) nd tht of 6w/D versus D is shown in Fig. 4. Here, r 8 K) is the ore resistivity nd hs een tken from the smples prepred y Intensity (Aritrry Units) g=2.277 Mgneti field mt H Fig.. Room temperture ESR spetr of the smples: ) LSMCO1, ) LSMCO1, ) LSMCO1, d) LSMCO1d nd e) LSMCO1e. d e 1 sol±gel nd sintered t 8C. r sur 8 K) is estimted from the differene etween the smple resistivity nd the ore resistivity [r 8 K)]. The verge thikness of the grin surfe is tken roughly s 2 nm s proposed y Zhng et l. [13]. Sine the surfe resistivity results from the sttering t the grin oundries, its mgnitude my e higher thn the ore resistivity. Therefore, s the surfe volume frtion 6w/D dereses with grin growth, the sttering t the oundries lso dereses resulting in redued r sur. Thus one should expet tht r sur /r nd 6w/D follow similr ehvior s lso reported y Zhng et l. [14]. The differene etween them in Fig. 4 n e ttriuted due to the omptness of grins s the sintering time inreses. Fig. shows the room temperture ESR spetr oserved in the smples LSMCO1, LSMCO1, LSMCO1, LSMCO1d nd LSMCO1e. In the system LSMCO1, single ESR line with gyromgneti ftor g, 2 is oserved t room temperture. With inresing grin size, the resonne line is oserved to shift to lower elds. The oserved ESR lines in LSMCO system hve to e exmined in the ontext of the ndings in L.7 Sr.3 MnO 3 system. Fig. 6 shows the ESR spetr of L.7 Sr.3 MnO 3 t 2, 6 nd 14 8C. The g vlue vrition, whih in effet re ets the resonne line position, is shown in the inset of Fig. 6. The g vlue is found to derese with inresing temperture nd remins onstnt ove the ferromgneti trnsition temperture of 8C oserved in L.7 Sr.3 MnO 3 system. Signi ntly high intensity ESR lines re oserved in doped mngnese perovskites investigted in the present study. Severl erlier investigtions hve onsidered the origin of the ESR signl in these perovskites [6,7]. These mngnese perovskites re mixed vlent systems ontining Mn 31 nd Mn 41 ions. Mn 31 3d 4 with S ˆ 2) exhiits lrge zero eld splitting nd strong spin±lttie relxtion [1] nd is unlikely to exhiit n ESR signl. On the other hnd, Mn 41 3d 3 with S ˆ 3=2), in n othedrl eld, hs wek spin lttie relxtion mking it oservle t room

5 69 temperture [16]. However, the Mn 41 ESR signl will e of lower intensity y ftor of out 7 less intense s ompred, for exmple, to the signl oserved in L.7 C.3 MnO 3 system) [6]. Hene, the intense signls seen t room temperture in the present system re inonsistent with either Mn 31 or Mn 41 ions. Oseroff et l. [6] were the rst to report the oservtion of n ESR signl in L x C x MnO 31d ompounds. The oserved strong ESR signls with unusul temperture dependene hs een ttriuted y them to omplex mgneti entity mde of olletion of Mn 31 nd Mn 41 ions. The present studies of the system L.7 Sr.3 Mn.9 Co.1 O 3, Mn 31 nd Mn 41 ions onstitute mjor omponent of mgneti ions. The oserved ESR signl in the present system rises lso from spin omplex formed y Mn 31 nd Mn 41 ions s in the system L x C x MnO 3 [6]. In our study on L.7 Sr.3 MnO 3, the pprent inrese in the g vlue elow T ould e due to n internl eld, whih rises from the onset of Mn±Mn exhnge. Within this frmework of oservtion, let us exmine the room temperture spetr oserved in smples with different grin sizes. It is found tht the g vlue generlly inreses in smples with lrge grin sizes. It thus ppers tht lrger grin size smples hve lrger internl elds, whih my e ttriuted to stronger Mn±Mn exhnge intertion. Mgnetiztion mesurements rried out in the present study on smples with different grin size support ESR oservtions. Mgnetiztion vlues re found to inrese with inrese in grin size. Smller grin size smples hve reltively lrger grin oundry region nd the disorder due to lrge strins present within the grin oundries n indue wekening of mgneti intertion etween Mn 31 nd Mn 41 ions. The wekening of the mgneti intertion is responsile for the suppression of T nd redution in mgnetiztion. 4. Conlusion The in uene of grin size on the mgnetotrnsport in L.7 Sr.3 Mn.9 Co.1 O 3 hs een investigted. The experimentl evidenes suh s mgnetiztion, resistivity, mgnetoresistne long with mirostruturl studies demonstrte tht spin dependent sttering t the grin oundry is responsile for low temperture mgnetoresistne. This enhnement in MR with derese in grin size is ttriuted to more re within the grin oundries. Progressive derese in linewidth nd g vlue of ESR signl with derese in grin size is inditive of redution of internl eld s is supported y mgnetiztion dt. For smller grins, lrger vlues of grin oundry region re ville, whih re ssoited with lrge strins disrupting the short-rnge mgneti intertion nd possily use nting of spins. This mehnism is presumly responsile for ll the oservtions of the mgneti nd mgneto trnsport ehvior. Aknowledgements The nnil support from Deprtment of Siene nd Tehnology, Government of Indi, is grtefully knowledged. Referenes [1] F. Dmmy, L.F. Cohen, J. Mmnus-Drisoll, R.S. Freits, L. Ghivelder, J. Mgn. Mgn. Mt ) L149. [2] L.E. Hueso, F. Rivdull, R.D. Snhez, D. Ceiro, C. Jrdon, J. Vzquez-Vzquez, M.A. Rivs, J. Mgn. Mgn. Mt ) 321. [3] R. Mhesh, R. Mhendirn, A.K. Ryhudhuri, C.N.R. Ro, Appl. Phys. Lett ) [4] H.Y. Hwng, S.W. Cheong, N.P. Ong, B. Btlogg, Phys. Rev. Lett ) 241. [] N. Zhng, W. Ding, W. Zhong, D. Xing, Y. Du, Phys. Rev. B ) [6] S.B. Oseroff, M. Torikhvili, J. Singley, S. Ali, S.W. Cheong, S. Shultz, Phys. Rev. B ) 621. [7] A. Shengely, Guo-Zhong, H. Keller, K.A. Muller, Phys. Rev. Lett ) 296. [8] Y.-H. Hung, Z.-G. Xu, C.-H. Yn, Z.-M. Wng, T. Zhu, C.- S. Lio, S. Go, G.-X. Xu, Solid Stte Commun ) 43. [9] S.P. Is, N.D. Mthur, J.E. Evets, M.G. Blmire, Appl. Phys. Lett ) 238. [] R.D. Snhez, J. Rivs, C. Vzquez-Vzquez, A. Lopez- Quintel, M.T. Cus, M. Tovr, S. Oseroff, Appl. Phys. Lett ) 134. [11] A. Gupt, G.Q. Gong, G. Xio, P.R. Dunome, P. Leoeur, P. Trouilloud, Y.Y. Wng, V.P. Drvid, J.Z. Sun, Phys. Rev. B ) R1629. [] A. Gupt, Clossl Mgnetoresistne, Chrge Ordering nd Relted Properties of Mngnese Oxides, World Sienti, Singpore, 1998 p [13] N. Zhng, S. Zhng, W. Ding, W. Zhong, Y. Du, Solid Stte Commun. 7 21) 417. [14] N. Zhng, W. Ding, W. Zhong, Phys. Lett. A ) 113. [1] A. Argm, B. Bleney, Eletron Prmgneti Resonne of Trnsition Ions, Clrendon press, Oxford, 197. [16] K.A. Muller, Phys. Rev. Lett ) 341.

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

Review Topic 14: Relationships between two numerical variables

Review Topic 14: Relationships between two numerical variables Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph

More information

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy

More information

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS IN-SITU PROBING OF DOMAIN POLING IN Bi 4 Ti 3 O 12 THIN FILMS BY OPTICAL SECOND HARMONIC GENERATION YANIV BARAD, VENKATRAMAN GOPALAN Mterils Reserh Lortory

More information

Lecture Notes No. 10

Lecture Notes No. 10 2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite

More information

Table of Content. c 1 / 5

Table of Content. c 1 / 5 Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................

More information

Processing and characterisation of Pr zircon pigment powder

Processing and characterisation of Pr zircon pigment powder Proessing nd hrteristion of Pr ziron pigment powder J. K. Kr* 1, R. Stevens 2 nd C. R. Bowen 2 Prseodymium ziron pigment powders were suessfully prepred t different lintion tempertures with sodium fluoride

More information

1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes.

1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes. 1 This question is out men ond enthlpies nd their use in the lultion of enthlpy hnges. Define men ond enthlpy s pplied to hlorine. Explin why the enthlpy of tomistion of hlorine is extly hlf the men ond

More information

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret

More information

Finite Element Simulation on Frictional and Brittle Preseismic fault slip

Finite Element Simulation on Frictional and Brittle Preseismic fault slip Finite Element Simultion on Fritionl nd Brittle Preseismi fult slip Zhishen Wu (1) Yun Go (1) Yutk Murkmi (2) (1) Deprtment of Urn & Civil Engineering. Irki University, Jpn (e-mil: zswu@ip.irki..jp; goyun@hs.irki..jp,

More information

Supplementary Figure 1 Supplementary Figure 2

Supplementary Figure 1 Supplementary Figure 2 Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully

More information

a) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points.

a) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points. Prole 3: Crnot Cyle of n Idel Gs In this prole, the strting pressure P nd volue of n idel gs in stte, re given he rtio R = / > of the volues of the sttes nd is given Finlly onstnt γ = 5/3 is given You

More information

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35. 0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression

More information

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

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light. 1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the

More information

22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:

22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of: 22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)

More information

Field Dependence of Magnetic Ordering in Kagomé-Staircase Compound Ni 3 V 2 O 8

Field Dependence of Magnetic Ordering in Kagomé-Staircase Compound Ni 3 V 2 O 8 University of Pennsylvni SholrlyCommons Deprtment of Physis Ppers Deprtment of Physis 7-25-2006 Field Dependene of Mgneti Ordering in Kgomé-Stirse Compound Ni 3 V 2 O 8 Mihel Kenzelmnn A. Brooks Hrris

More information

A Study on the Properties of Rational Triangles

A Study on the Properties of Rational Triangles Interntionl Journl of Mthemtis Reserh. ISSN 0976-5840 Volume 6, Numer (04), pp. 8-9 Interntionl Reserh Pulition House http://www.irphouse.om Study on the Properties of Rtionl Tringles M. Q. lm, M.R. Hssn

More information

Supporting Information. Observation of Excitonic Fine Structure in a 2D Transition Metal. Dichalcogenide Semiconductor

Supporting Information. Observation of Excitonic Fine Structure in a 2D Transition Metal. Dichalcogenide Semiconductor FWHM (ev) Normlized Intensity (. u.) Supporting Informtion Oservtion of Exitoni Fine Struture in 2D Trnsition Metl Dihlogenide Semiondutor Jingzhi Shng 1, Xionn Shen 1, Chunxio Cong 1, Nmphung Peimyoo

More information

Studies on Neon irradiated amorphous carbon using X-ray Diffraction. technique

Studies on Neon irradiated amorphous carbon using X-ray Diffraction. technique Studies on Neon irrdited morphous rbon using X-ry Diffrtion tehnique A.Srkr *, K. Dsgupt #, P. Brt *@, P. Mukherjee *, D. Sthiymoorthy # * Vrible Energy Cylotron Centre, 1/AF Bidhn Ngr, Kolkt 700 064,

More information

ANALYSIS AND MODELLING OF RAINFALL EVENTS

ANALYSIS AND MODELLING OF RAINFALL EVENTS Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.

More information

Generalization of 2-Corner Frequency Source Models Used in SMSIM

Generalization of 2-Corner Frequency Source Models Used in SMSIM Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville

More information

Iowa Training Systems Trial Snus Hill Winery Madrid, IA

Iowa Training Systems Trial Snus Hill Winery Madrid, IA Iow Trining Systems Tril Snus Hill Winery Mdrid, IA Din R. Cohrn nd Gil R. Nonneke Deprtment of Hortiulture, Iow Stte University Bkground nd Rtionle: Over the lst severl yers, five sttes hve een evluting

More information

Symmetrical Components 1

Symmetrical Components 1 Symmetril Components. Introdution These notes should e red together with Setion. of your text. When performing stedy-stte nlysis of high voltge trnsmission systems, we mke use of the per-phse equivlent

More information

On the Scale factor of the Universe and Redshift.

On the Scale factor of the Universe and Redshift. On the Sle ftor of the Universe nd Redshift. J. M. unter. john@grvity.uk.om ABSTRACT It is proposed tht there hs been longstnding misunderstnding of the reltionship between sle ftor of the universe nd

More information

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R /10/010 Question 1 1 mole of idel gs is rought to finl stte F y one of three proesses tht hve different initil sttes s shown in the figure. Wht is true for the temperture hnge etween initil nd finl sttes?

More information

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE V.S. Gordeev, G.A. Myskov Russin Federl Nuler Center All-Russi Sientifi Reserh Institute of Experimentl Physis (RFNC-VNIIEF)

More information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the

More information

Learning Partially Observable Markov Models from First Passage Times

Learning Partially Observable Markov Models from First Passage Times Lerning Prtilly Oservle Mrkov s from First Pssge s Jérôme Cllut nd Pierre Dupont Europen Conferene on Mhine Lerning (ECML) 8 Septemer 7 Outline. FPT in models nd sequenes. Prtilly Oservle Mrkov s (POMMs).

More information

Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface

Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface Engineering, 00,, 705-709 doi:0.436/eng.00.909 Published Online September 00 (http://www.sirp.org/journl/eng) Some Aspets of Non-Orthogonl Stgntion-Point Flow towrds Strething Surfe Abstrt Mothr Rez, Andi

More information

3.15 NMR spectroscopy Different types of NMR There are two main types of NMR 1. C 13 NMR 2. H (proton) NMR

3.15 NMR spectroscopy Different types of NMR There are two main types of NMR 1. C 13 NMR 2. H (proton) NMR .5 NMR spetrosopy Different types of NMR There re two min types of NMR. NMR. (proton) NMR There is only round % in orgni moleules ut modern NMR mhines re sensitive enough to give full spetr for The spetr

More information

Intermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths

Intermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths Intermedite Mth Cirles Wednesdy 17 Otoer 01 Geometry II: Side Lengths Lst week we disussed vrious ngle properties. As we progressed through the evening, we proved mny results. This week, we will look t

More information

8 THREE PHASE A.C. CIRCUITS

8 THREE PHASE A.C. CIRCUITS 8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),

More information

1.3 SCALARS AND VECTORS

1.3 SCALARS AND VECTORS Bridge Course Phy I PUC 24 1.3 SCLRS ND VECTORS Introdution: Physis is the study of nturl phenomen. The study of ny nturl phenomenon involves mesurements. For exmple, the distne etween the plnet erth nd

More information

University of Sioux Falls. MAT204/205 Calculus I/II

University of Sioux Falls. MAT204/205 Calculus I/II University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques

More information

CS 491G Combinatorial Optimization Lecture Notes

CS 491G Combinatorial Optimization Lecture Notes CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,

More information

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities Appendi Prtil dishrges. Reltionship Between Mesured nd Atul Dishrge Quntities A dishrging smple my e simply represented y the euilent iruit in Figure. The pplied lternting oltge V is inresed until the

More information

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. Two liner equtions in the sme two vriles re lled pir of liner equtions in two vriles. The most generl form of pir of liner equtions is x + y + 0 x + y + 0 where,,,,,,

More information

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte

More information

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and Leture 7: iffusion of Ions: Prt : oupled diffusion of tions nd nions s desried y Nernst-Plnk Eqution Tody s topis Continue to understnd the fundmentl kinetis prmeters of diffusion of ions within n eletrilly

More information

Discrete Structures Lecture 11

Discrete Structures Lecture 11 Introdution Good morning. In this setion we study funtions. A funtion is mpping from one set to nother set or, perhps, from one set to itself. We study the properties of funtions. A mpping my not e funtion.

More information

Supporting Information

Supporting Information tom-thik Interlyer Mde of VD-Grown Grphene Film on Seprtor for dvned thium-sulfur tteries Zhenzhen Du 1, hengkun Guo 2, njun Wng 3, jun Hu 1, Song Jin 1, Timing Zhng 1, Honghng Jin 1, Zhiki Qi 1, Sen Xin

More information

Supporting Information Mesoporous graphitic carbon nanodisks fabricated via catalytic carbonization of coordination polymers

Supporting Information Mesoporous graphitic carbon nanodisks fabricated via catalytic carbonization of coordination polymers Supporting Informtion Mesoporous grphiti ron nnodisks frited vi tlyti roniztion of oordintion polymers Pnpn Su, Ling Jing, Jio Zho, Jingwng Yn, Cn Li nd Qihu Yng Stte Key Lortory of Ctlysis, Dlin Institute

More information

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS AGRICULTURAL ENGINEERING VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS Ltvi University of Agriulture E-mil: ilze.pelee@llu.lv Astrt Use of solr energy inreses every

More information

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL Mhun Peng *, Lin Xie nd Leonrd J. Pietrfes Deprtment of Mrine, Erth nd Atmospheri

More information

H 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3.

H 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3. . Spetrosopy Mss spetrosopy igh resolution mss spetrometry n e used to determine the moleulr formul of ompound from the urte mss of the moleulr ion For exmple, the following moleulr formuls ll hve rough

More information

Particle-in-cell Simulations for the Effect of Magnetic Shielding and Channel Length on Cylindrical Hall Thruster

Particle-in-cell Simulations for the Effect of Magnetic Shielding and Channel Length on Cylindrical Hall Thruster Prtile-in-ell Simultions for the Effet of Mgneti Shielding nd Chnnel Length on Cylindril Hll Thruster IEPC-215-435 /ISTS-215-- 435 Presented t Joint Conferene of 3th Interntionl Symposium on Spe Tehnology

More information

Chapter 4rth LIQUIDS AND SOLIDS MCQs

Chapter 4rth LIQUIDS AND SOLIDS MCQs Chpter 4rth LIQUIDS AND SOLIDS MCQs Q.1 Ioni solis re hrterize y () low melting points () goo onutivity in soli stte () high vpour pressure () soluility in polr solvents Q.2 Amorphous solis. () hve shrp

More information

UV-Induced Self-Repairing Polydimethylsiloxane-Polyurethane (PDMS-PUR) Cu- Catalyzed Networks

UV-Induced Self-Repairing Polydimethylsiloxane-Polyurethane (PDMS-PUR) Cu- Catalyzed Networks Eletroni Supplementry Mteril (ESI) for Journl of Mterils Chemistry A. This journl is The Royl Soiety of Chemistry 2014 Supporting Online Mterils UV-Indued Self-Repiring Polydimethylsiloxne-Polyurethne

More information

The influence of 2,2 -dipyridyl on non-formaldehyde electroless copper plating

The influence of 2,2 -dipyridyl on non-formaldehyde electroless copper plating Eletrohimi At 9 () 1789 179 The influene of, -dipyridyl on non-formldehyde eletroless opper plting Jun Li, Hrley Hyden, Pul A. Kohl Shool of Chemil & Biomoleulr Engineering, Georgi Institute of Tehnology,

More information

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into

More information

T b a(f) [f ] +. P b a(f) = Conclude that if f is in AC then it is the difference of two monotone absolutely continuous functions.

T b a(f) [f ] +. P b a(f) = Conclude that if f is in AC then it is the difference of two monotone absolutely continuous functions. Rel Vribles, Fll 2014 Problem set 5 Solution suggestions Exerise 1. Let f be bsolutely ontinuous on [, b] Show tht nd T b (f) P b (f) f (x) dx [f ] +. Conlude tht if f is in AC then it is the differene

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Synthesis of metl oxide with roomtemperture photoreversile phse trnsition Shin-ichi Ohkoshi 1 *, Yoshihide Tsunouchi, 1 Tomoyuki Mtsud, 1 Kzuhito Hshimoto, 2 Asuk Nmi, 1 Fumiyoshi

More information

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò J Appl Eletrohem (009) 39:9 63 DOI 0.007/s0800-009-9797- ORIGINAL PAPER Cyli voltmmetry simultion t miroeletrode rrys with COMSOL Multiphysis Ò Alessndro Lvhi Æ U. Brdi Æ C. Borri Æ S. Cporli Æ A. Fossti

More information

AMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE

AMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE AMPERE 2000 th 30 CONGRESS AMPERE on Mgnetic Resonnce nd Relted Phenomen Lison, Portugl, 23-2 July 2000 Under the uspices of The GROUPEMENT AMPERE Edited y: A.F. MARTINS, A.G. FEIO nd J.G. MOURA Sponsoring

More information

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 orf, R.C., Wn,. T- Equivlent Networks The Eletril Engineering Hndook Ed. Rihrd C. orf Bo Rton: CRC Press LLC, 000 9 T P Equivlent Networks hen Wn University of Cliforni, vis Rihrd C. orf University of

More information

Chem Homework 11 due Monday, Apr. 28, 2014, 2 PM

Chem Homework 11 due Monday, Apr. 28, 2014, 2 PM Chem 44 - Homework due ondy, pr. 8, 4, P.. . Put this in eq 8.4 terms: E m = m h /m e L for L=d The degenery in the ring system nd the inresed sping per level (4x bigger) mkes the sping between the HOO

More information

ECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 7. Waveguides Part 4: Rectangular and Circular Waveguide

ECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 7. Waveguides Part 4: Rectangular and Circular Waveguide ECE 5317-6351 Mirowve Engineering Fll 01 Prof. Dvid R. Jkson Dept. of ECE Notes 7 Wveguides Prt 4: Retngulr nd Cirulr Wveguide 1 Retngulr Wveguide One of the erliest wveguides. Still ommon for high power

More information

4-cyanopentanoic acid dithiobenzoate (CPADB) was synthesized as reported by Y.

4-cyanopentanoic acid dithiobenzoate (CPADB) was synthesized as reported by Y. Eletroni upplementry Mteril (EI) for Journl of Mterils Chemistry B This journl is The Royl oiety of Chemistry 2012 ynthesis of 4-ynopentnoi id dithioenzote (CPADB). 4-ynopentnoi id dithioenzote (CPADB)

More information

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Effets of Applying Aumultor Strw in Soil on Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris under Cdmium Stress Jin Wng1,,

More information

Trigonometry Revision Sheet Q5 of Paper 2

Trigonometry Revision Sheet Q5 of Paper 2 Trigonometry Revision Sheet Q of Pper The Bsis - The Trigonometry setion is ll out tringles. We will normlly e given some of the sides or ngles of tringle nd we use formule nd rules to find the others.

More information

Linear magnetoresistance due to multipleelectron scattering by low-mobility islands in an inhomogeneous conductor

Linear magnetoresistance due to multipleelectron scattering by low-mobility islands in an inhomogeneous conductor Reeived 2 Jun 212 Aepted 31 Aug 212 Pulished 2 Ot 212 DOI: 1.138/nomms216 Liner mgnetoresistne due to multipleeletron sttering y low-moility islnds in n inhomogeneous ondutor N.V. Kolov 1,2, N. Mori 3,

More information

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem. 27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we

More information

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply

More information

Behavior Composition in the Presence of Failure

Behavior Composition in the Presence of Failure Behvior Composition in the Presene of Filure Sestin Srdin RMIT University, Melourne, Austrli Fio Ptrizi & Giuseppe De Giomo Spienz Univ. Rom, Itly KR 08, Sept. 2008, Sydney Austrli Introdution There re

More information

Damping of Power System Oscillations using Unified Power Flow Controller (UPFC)

Damping of Power System Oscillations using Unified Power Flow Controller (UPFC) INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 73, DECEMBER 7-9, 47 of Power System Osilltions using Unified Power Flow Controller (UPFC) Neelim Tmey M. L. Kothri Astrt--This pper presents systemti pproh for

More information

Lecture 5: Crystal planes and Miller Indices

Lecture 5: Crystal planes and Miller Indices Leture Notes on Struture of Mtter y Mohmmd Jellur Rhmn, Deprtment of Physis, BUET, Dhk-000 Leture 5: Crystl plnes nd Miller Indies Index system for rystl diretions nd plnes Crystl diretions: Any lttie

More information

A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version

A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version A Lower Bound for the Length of Prtil Trnsversl in Ltin Squre, Revised Version Pooy Htmi nd Peter W. Shor Deprtment of Mthemtil Sienes, Shrif University of Tehnology, P.O.Bo 11365-9415, Tehrn, Irn Deprtment

More information

Spacetime and the Quantum World Questions Fall 2010

Spacetime and the Quantum World Questions Fall 2010 Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1

More information

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article Avilble online www.jopr.om Journl of Chemil nd Phrmeutil Reserh, 2013, 5(12):1283-1288 Reserh Artile ISSN : 0975-7384 CODEN(USA) : JCPRC5 Study on osion resistne of zin lloy oting of mehnil plting by eletrohemil

More information

Direct indirect character of the band gap in methylammonium lead iodide perovskite

Direct indirect character of the band gap in methylammonium lead iodide perovskite Direct indirect chrcter of the nd gp in methylmmonium led iodide perovskite Eline M. Hutter 1, Mrí C. Gélvez-Rued 1, Ann Osherov 2, Vldimir Bulović 2, Ferdinnd C. Grozem 1, Smuel D. Strnks 2,3*, nd Tom

More information

Two energy scales in the spin excitations of the high-temperature superconductor La 2 x Sr x CuO 4

Two energy scales in the spin excitations of the high-temperature superconductor La 2 x Sr x CuO 4 Two energy sles in the spin exittions of the high-temperture superondutor L x Sr x CuO 4 B. VIGNOLLE,S.M.HAYDEN *,D.F.MMORROW,, H. M. RØNNOW 4,B.LAKE 5,C.D.FROST AND T. G. PERRING H. H. Wills Physis Lortory,

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Nme Dte hpter 9 Mintining Mthemtil Profiieny Simplify the epression. 1. 500. 189 3. 5 4. 4 3 5. 11 5 6. 8 Solve the proportion. 9 3 14 7. = 8. = 9. 1 7 5 4 = 4 10. 0 6 = 11. 7 4 10 = 1. 5 9 15 3 = 5 +

More information

Übungen zur Theoretischen Physik Fa WS 17/18

Übungen zur Theoretischen Physik Fa WS 17/18 Krlsruher Institut für ehnologie Institut für heorie der Kondensierten Mterie Übungen zur heoretishen Physik F WS 17/18 Prof Dr A Shnirmn Bltt 4 PD Dr B Nrozhny Lösungsvorshlg 1 Nihtwehselwirkende Spins:

More information

8.3 THE HYPERBOLA OBJECTIVES

8.3 THE HYPERBOLA OBJECTIVES 8.3 THE HYPERBOLA OBJECTIVES 1. Define Hperol. Find the Stndrd Form of the Eqution of Hperol 3. Find the Trnsverse Ais 4. Find the Eentriit of Hperol 5. Find the Asmptotes of Hperol 6. Grph Hperol HPERBOLAS

More information

Energy corrugation in atomic-scale friction on graphite revisited by molecular dynamics simulations

Energy corrugation in atomic-scale friction on graphite revisited by molecular dynamics simulations At Meh. Sin. (6) ():6 6 DOI.7/s9-5-5-6 RESEARCH PAPER Energy orrugtion in tomi-sle frition on grphite revisited y moleulr dynmis simultions Xio-Yu Sun, Yi-Zhou Qi Wengen Ouyng Xi-Qio Feng, Qunyng Li, Reeived:

More information

Estimation of Sequence Components using Magnitude Information

Estimation of Sequence Components using Magnitude Information 6th NATIONAL POWER SYSTEMS CONFERENCE, 5th-7th DECEMBER, 2 47 Estimtion of Sequene Components using Mgnitude Informtion P.S. Ngendr ro nd Ssikirn Veknuru Deprtment of Eletril Engineering Indin Institute

More information

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions MEP: Demonstrtion Projet UNIT 4: Trigonometry UNIT 4 Trigonometry tivities tivities 4. Pythgors' Theorem 4.2 Spirls 4.3 linometers 4.4 Rdr 4.5 Posting Prels 4.6 Interloking Pipes 4.7 Sine Rule Notes nd

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

Chapter Gauss Quadrature Rule of Integration

Chapter Gauss Quadrature Rule of Integration Chpter 7. Guss Qudrture Rule o Integrtion Ater reding this hpter, you should e le to:. derive the Guss qudrture method or integrtion nd e le to use it to solve prolems, nd. use Guss qudrture method to

More information

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from

More information

GM1 Consolidation Worksheet

GM1 Consolidation Worksheet Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up

More information

ENERGY AND PACKING. Outline: MATERIALS AND PACKING. Crystal Structure

ENERGY AND PACKING. Outline: MATERIALS AND PACKING. Crystal Structure EERGY AD PACKIG Outline: Crstlline versus morphous strutures Crstl struture - Unit ell - Coordintion numer - Atomi pking ftor Crstl sstems on dense, rndom pking Dense, regulr pking tpil neighor ond energ

More information

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx Clulus Chet Sheet Integrls Definitions Definite Integrl: Suppose f ( ) is ontinuous Anti-Derivtive : An nti-derivtive of f ( ) on [, ]. Divide [, ] into n suintervls of is funtion, F( ), suh tht F = f.

More information

Fully Kinetic Simulations of Ion Beam Neutralization

Fully Kinetic Simulations of Ion Beam Neutralization Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion

More information

Section 4.4. Green s Theorem

Section 4.4. Green s Theorem The Clulus of Funtions of Severl Vriles Setion 4.4 Green s Theorem Green s theorem is n exmple from fmily of theorems whih onnet line integrls (nd their higher-dimensionl nlogues) with the definite integrls

More information

(h+ ) = 0, (3.1) s = s 0, (3.2)

(h+ ) = 0, (3.1) s = s 0, (3.2) Chpter 3 Nozzle Flow Qusistedy idel gs flow in pipes For the lrge vlues of the Reynolds number typilly found in nozzles, the flow is idel. For stedy opertion with negligible body fores the energy nd momentum

More information

Polynomials. Polynomials. Curriculum Ready ACMNA:

Polynomials. Polynomials. Curriculum Ready ACMNA: Polynomils Polynomils Curriulum Redy ACMNA: 66 www.mthletis.om Polynomils POLYNOMIALS A polynomil is mthemtil expression with one vrile whose powers re neither negtive nor frtions. The power in eh expression

More information

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint

More information

Lecture 1 - Introduction and Basic Facts about PDEs

Lecture 1 - Introduction and Basic Facts about PDEs * 18.15 - Introdution to PDEs, Fll 004 Prof. Gigliol Stffilni Leture 1 - Introdution nd Bsi Fts bout PDEs The Content of the Course Definition of Prtil Differentil Eqution (PDE) Liner PDEs VVVVVVVVVVVVVVVVVVVV

More information

arxiv: v1 [cond-mat.mtrl-sci] 26 Apr 2017

arxiv: v1 [cond-mat.mtrl-sci] 26 Apr 2017 Crystl nd Mgneti Strutures in Lyered, Trnsition Metl Dihlides nd Trihlides Mihel A. MGuire Mterils Siene nd Tehnology Division, Ok Ridge Ntionl Lortory, Ok Ridge, TN 37831 USA rxiv:1704.08225v1 [ond-mt.mtrl-si]

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION doi:1.138/nture1241 Figure S1., TEM imge of gold nnoprtiles.,, Chemil strutures of nioni itrte nd tioni polyurethne opolymer, respetively. Comment: Gold nnoprtiles were synthesized ording to slightly modified

More information

Appendix A: HVAC Equipment Efficiency Tables

Appendix A: HVAC Equipment Efficiency Tables Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER

More information

System Validation (IN4387) November 2, 2012, 14:00-17:00

System Validation (IN4387) November 2, 2012, 14:00-17:00 System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise

More information

#A42 INTEGERS 11 (2011) ON THE CONDITIONED BINOMIAL COEFFICIENTS

#A42 INTEGERS 11 (2011) ON THE CONDITIONED BINOMIAL COEFFICIENTS #A42 INTEGERS 11 (2011 ON THE CONDITIONED BINOMIAL COEFFICIENTS Liqun To Shool of Mthemtil Sienes, Luoyng Norml University, Luoyng, Chin lqto@lynuedun Reeived: 12/24/10, Revised: 5/11/11, Aepted: 5/16/11,

More information

The study of dual integral equations with generalized Legendre functions

The study of dual integral equations with generalized Legendre functions J. Mth. Anl. Appl. 34 (5) 75 733 www.elsevier.om/lote/jm The study of dul integrl equtions with generlized Legendre funtions B.M. Singh, J. Rokne,R.S.Dhliwl Deprtment of Mthemtis, The University of Clgry,

More information

Automatic Synthesis of New Behaviors from a Library of Available Behaviors

Automatic Synthesis of New Behaviors from a Library of Available Behaviors Automti Synthesis of New Behviors from Lirry of Aville Behviors Giuseppe De Giomo Università di Rom L Spienz, Rom, Itly degiomo@dis.unirom1.it Sestin Srdin RMIT University, Melourne, Austrli ssrdin@s.rmit.edu.u

More information

CALCULATING REACTING QUANTITIES

CALCULATING REACTING QUANTITIES MODULE 2 14 WORKSHEET WORKSHEET For multiple-hoie questions 1 5 irle the letter orresponding to the most orret nswer. 1 The lned eqution for the urning of utnol (C 4 H 9 OH) is given elow: C 4 H 9 OH(l)

More information