Electrical Conductivity Measurement of Oxides Melts

Transcription

1 Inrnaional Scinific Colloquium Modlling for Marial rocssing Riga Jun lcrical Conduciviy Masurmn of Oxids Mls I. ozniak A. chnkov A. Shaunov Absrac Nowihsanding on variy of xising procsss of ucion skull mling of oxids lcrical and hrmal propris of oxids mls ar pracically unknown. From h ohr hand liquid-phas synhsis of Hi-Tch oxids marials such as nw cramics monocrysals and glasss rquirs knowldg of mls propris up o 3700 K. Inasmuch as h main physical propry which influnc o h ml powr consumpion a ucion haing is lcrical conduciviy hn sudy of lcrical conduciviy mpraur dpndnc is ncssary. Th princl and chnical ralizaion of h lcrical conduciviy masurmn of mls ar prsnd. Th approach is basd on ucion mling in cold crucibl chnology and invrs lcromagnic problm soluion. Analysis of h mhod accuracy via inpu daa rrors is prsnd. For incrasing of Ill-posd problm soluion was usd ovr drminaion of s of quaions. Conduciviy of aluminum oxid mls for h mpraur up o 3223 K is shown oo. Inroducion Oxids and is combinaions form classs of major chnical marials which drmin sag of dvlopmn of nrgic mallurgy mchanical nginring communicaion and so on. Diffrn procsss of mling ar widly usd for oxids marials synhsis. Howvr ucion mling in cold crucibls is byond compar h bs chnology for producing high pur marials [1-3]. Mhod of ucion mling of oxids in cold crucibls is known mor han 40 yars. Bu usually asks of insallaions dsign and conrol of chnological procsss which provid producing of high-qualiy marials ar solving by mpirical mhods. From h ohr hand dficincy of rliabl daa abou lcro- and hrmophysical propris of oxids mls vrsus mpraur limis of using of modrn CA sysms [4]. Thrfor sudy of high mpraur mls propris in paricular lcrical conduciviy is acual ask. For invsigaion of ml conduciviy ar commonly usd conac mhods [5 6]. Bu all of hm hav ssnial limiaion by mpraur up o 2173 K whn i aks o work in air amosphr. To sudy of mls conduciviy wih mpraur up o 3700 K in air hr ar approachs which ar basd on non-conac mhods bu mos of hm is applid for mals [7-9]. Thr is amp o sima of lcrical conduciviy of oxids mls using paramrs of ucion mling in cold crucibl [2] bu suggsd hr approach rquirs masurmn of ucor powr facor and hrfor his lcrical conduciviy masur mhod dos no possss by wll accuracy. This prsn papr is h nx sag of laboraion of nonconac mhod for simaion of lcrical conduciviy of high mpraur mls [10-13]. Suggsd mhod is basd on ucion mling in cold crucibl chnology wih invrs soluion of lcromagnic 155

2 problm rlaiv of lcrical conduciviy. 1. Invrs problm chniqu Inducion mling in cold crucibl chnology provids rquird mpraur and chmical nonpolluing of h ml. A h sam im lcrical and hrmal paramrs of ucion sysm allow o judg abou ml conduciviy. On h bas of our xprinc powr losss ar mor availabl from masurmn chniqu poin of viw from hm. Thrfor invrs problm chniqu can us lcromagnic mahmaical modl of ucion sysm and concp of h powr balanc: Covr Shaf Quarz bo + cc + m + cov + sh = bo + cc πRi i + jω j j M ijds + jω k k S1 S A& 1 A& A& A& + + jω m µ 0 R R R z R ml 2. Accuracy of h mhod Crucibl Boom Inducor Fig. 1. Schm of h ucion sysm wr bo cov ( ) cc + ( M M ) 1 ik sh A& = 0 cov il ds = U& boom crucibl covr and shaf; cov (1) sh - calorimry powr in h bo cc m sh - lcrical losss in h boom; crucibl; covr; shaf and powr in h ml Fig. 1. Ohr symbols a (1) ar gnrally accpd. I was usd hr mahmaical modl on h bas of 2D ingrodiffrnial approach [14] bu i is possibl o us any availabl on. Fig. 2 illusras us soluion sarch a quaion sysm (1). Commonly h sysm (1) has wo dcisions (poins 1 and 2 s Fig. 2) whr hrmal balanc condiion is ralizd. To provid of on-valudnss soluion is addiionally usd ucor currn or powr losss valus as inpu daa. As far as his mhod is formulad as invrs problm soluion i aks o sima snsiiviy of dsird quaniy from inpu daa dviaion. Thus i nds o sima of accuracy of h lcrical conduciviy invsigaion mhod. Summarizd rror of h lcrical conduciviy invsigaion mhod includs rrors of invrs problm approach δ and mahmaical modlδ ma : δ = δ + δ. sum ma A h sam im rror of invrs problm approach is: ( δcal + δ gom ) W δ = 2 156

3 wr δ cal - oal rror of calorimry; δ gom - masurmn rror of ucion sysm gomry and W - ransfr funcion of h invrs problm. This ransfr funcion is drm as: R ml H ml W = f δcal δl δgom ml H wr R ml - ml pool radius; ml - skin layr in h ml; H ml - ml pool dph; H - ucor high; δ l - rror of volag or currn masurmn. Th sysmaic rror valus and possibl nglcd losss which can aris as a rsul of imprfcion dsign of ral ucion sysm is prsnd a Tab. 1. rsnc of hardwar sysmaic rrors producs of possibl soluion aras Fig. 3. Analysis of invrs problm soluion snsiiviy via all inpu daa dviaions givs us dpndnc of invrs problm approach rror Fig. 4. Tab. 1. Grading of rrors K Sign rror % Flow mr 0.5 Thrmocoupl or rsisor mpraur snsor 0.25 Analog-o-digi convrr 0.1 Sysmaic rror of calorimry 0.85 Addiional nonrgisrd powr losss 1.2 Toal rror of calorimry δ cal 2.05 Masurmn rror of ucion sysm gomry δ 2.5 Invrs problm soluion on h bas of analyical lcromagnic mahmaical modl Numrical mahmaical modl Uniform of ml mpraur disribuion Toal rror of h mhod gom δ δ ma 5 10 no accound δ Rsuls analyss of our physical and numrical xprimns show ha powr sourcs in oxids ml ar disribud in ara wihou havy mpraur gradins. From h ohr hand buoyancy convcion dcrass h mpraur gradins oo and hs phnomna allows us o pu assumpion abou uniform lcrical conduciviy of oxids a h ml pool. sum Fig. 2. Sarch of soluion on h bas of hrmal balanc Fig. 3. Dcision rgion around poin 2 157

4 ml ml max 0.9 Ara of chnological procsss δ % ml ml max δ δ Ara of invsigaions Ml radius / Skin layr Fig. 4. Invrs problm soluion rror 3. Rsuls 10 5 For simaion of lcrical conduciviy valu of aluminium oxid ml sris ss wr don. Basic dimnsions of ucion sysms xprimnal daa and rsuls of numrical analysis r of ss ar prsnd in Tab. 2. Th valus of h ml lcrical conduciviy ar rlad o h mpraur on h ml surfac. Tab. 2. xprimnal and calculaions daa Basic * T m f U I cc + cov R ml δ dimnsions K MHz kv A kw kw (Ohm sum cm cm) -1 ml ±% H ml =11.1 R ml =7.6 H = R =11.0 W=3 H ml =5.0 R ml =3.30 H = R =12.6 W=4 H ml =7.20 R ml =2.65 H =6.50 R =4.70 W= * Brighnss mpraur (λ=0.65 µm). Rasoning from ha oxid aluminium ml is characrizd by ionic k of lcrical conduciviy and for h ovrhaing of h ml up o K abov h ml mpraur 158

5 numbr of charg carrirs as simpl ions is bcam much mor han complx on [15]. So i can b assumd ha h lcrical conduciviy is hrmally acivad and varis according o h quaion: RT whr 0 prxponnial facor R - h gas consan conduciviy and T - mpraur. Acivaion nrgy is drm as: d( ln( ) ) =. 1 d T = 0 (2) ( ) - acivaion nrgy of lcrical Fig. 5 shown ha acivaion nrgy = cons wih a fair accuracy. I allows us o f all cofficins a quaion (2) as h nx: 0 =243 Sm/cm; = J mol; R =8.314 J mol/k. Th whol s of daa includ h rsuls oba from h paricans on h hr sampls from h masurmns a hr mpraurs. Ths ss rsuls nd xponnial rlaion of lcrical rsusiviy of aluminium oxid ar plod in Fig. 6. ln() T K Sm/cm ρ Ohm cm ρ = xp(134496/8.314 T) y = x R2 = Fig. 5. Variaion of h ml lcrical conduciviy and is approximaiv rprsnaion by linar dpndnc 10 4 /T K Al2O3 ("supr pur" ) [4] Al2O3 ("pur" ) Fig. 6. lcrical rsisiviy of aluminium oxid diffrn puriy via mpraur T K CONCLUSION For simaion of lcrical conduciviy of oxids mls on h bas of ucion furnac wih cold crucibl h complx of hard and sofwar was dsignd. Nonconac invsigaion of mls lcrical conduciviy of oxids carbids nirids borids mals and so on in wid mpraur rang is advanag of h proposd mhod. This mhod can b applid o invsigaion of ml singular poins oo [16 17]. Rfrncs [1] rov Yu. B. Ranicov D. G. "Cold Crucibls" - M.: Mallurgy (Russian). [2] rov Yu. B. "Inducion mling of oxids" - M.: Mallurgy (Russian). [3] rov Yu. B. Kanav I. A."Inducion furnacs for mling of oxids" - L.: olyknica (Russian). [4] C. Gross W. Assmus A. Muizniks al. "owr Consumpion of skull Mling ar II: Numrical Calculaion of h Shap of h Moln Zon and Comparizon wih xprimn" // J. Crys. Rs. Tchnol vol. 34 pp

6 [5] M.Consaninscu G. Jiianu M.Brichi C.Vuap M.Jlanu. ropris of som glass-cramics in moln and solid sa. Romanian acadmy Insiu of physical chmisry I.G.Murgulscu Spl.Indpndni 202 Buchars Romania. High mpraur Narial rocscc 6 (2002) p [6] A. Silnqa and B. Haugsdal. lcrical conduciviy masurmns of corrosiv liquids a high mpraurs. Dparmn of Chmisry Univrsiy oj Os Box Oslo Norway/Rv. Sci. Insrum. 64 (2) Fbruary [7] Yuu Ono Chng-Qing Zhng Francois G. Haml al. "xprimnal invsigaion on monioring and conrol of ucion haing procss for smi-solid alloys using h haing coil as snsor" // J. Mas. Sci. Tchnol vol. 13 pp [8] Won-Kyu Rhima) and Takhiko Ishikawa. Nonconac lcrical rsisiviy masurmn chniqu for moln mals. J ropulsion Laboraory California Insiu of Tchnology asadna California RVIW OF SCINTIFIC INSTRUMNTS VOLUM 69 NUMBR 10 OCTOBR [9] Gorg Loh.ofr. lcrical rsisiviy masurmn of liquid mals. Mas. Sci. Tchnol. 16 (2005) [10] ozniak A. chnkov. "Spcial ools for invsigaion and conrolling of ucion skull mling procsss". rocdings of h In. Colloq. "Modlling for Saving Rsourcs" // Riga Lavia May 2001 pp [11] I. ozniak A. chnkov. "An Approach of lcrical Conduciviy simaion of Tchnical Marials Mls" // 8 h In. Conf. on Microwav and High Frquncy Haing. Bayruh Grmany Spmbr [12] I.V. ozniak A.Yu. chnkov A.N. Shaunov. Inducion Furnac wih Cold Crucibl as a Tool for Invsigaion of High Tmpraur Mls. 9h KORAN-RUSSIAN INTRNATIONAL SYMOSIUM ON. Scinc & Tchnology / KORUS 2005 Jun 26 ~ July Novosibirsk Sa Tchnical Univrsiy Novosibirsk Russia. [13] I.V. ozniak A.Yu. chnkov A.N. Shaunov Yu.I. Blinov. Invrs chniqus for analyzing and conrol of cold crucibl ucion mling.rocdings of h In. Colloq. ACTUAL ROBLMS OF TH INDUCTION HATING (THORY&ALICATIONS) AIH-05. S.rsburg May [14] I. ozniak A. chnkov B. Nack and T. Bhrns. "Mahmaical Modlling and Invsigaion of Inducion Sysm wih Slid Crucibl" // rocdings of h In. Scin. Colloq. "Modlling for lcromagnic rocssing" Hannovr Grmany March pp [15] Bnly R. Jons T.. - J. Amr. Cram. Soc v p [16] Sung S. Kim Thomas H. Sandrs. "Thrmodynamic Modling of h Isomorphous has Diagrams in h Al 2 O 3 Cr 2 O 3 and V 2 O 3 Cr 2 O 3 Sysms" // J. Am. Cram. Soc. 84 [8] pp (2001). [17] Skrybin V. G. Novokhasky I.Usauk I. I. "Abou srucur rancformaion in ionic mls".// III All Russian conf. "Srucur and propris of mal and slag mls". ar. 3. "Invsigaion of slag mls". Svrdlovsk 1978 pp (Russian). Auhors h.d. ozniak Igor h.d. chnkov Andry Dl.-Ing. Shaunov Alxy lcrochnical Univrsiy rof. opov Sr S. rsburg - Russia Tl.: (812) mail: ivpozniak@mail.lch.ru aypchnkov@mail.lch.ru 160