Influence of gas flow on thermal field and stress during growth of sapphire single crystal using Kyr

RARE METALS .Vol. 25 , Spec. Issue , Dec 2006 ,p. 260Influence of gas flow on thermal field and stress during growth ofsapphire single crystal using Kyropoulos methodLI Jinquan') ,SU Xiaoping') ,NA Myilatu') ,YANG Hail) ,LI Jjianmin') ,YU Yunqi?) ,and MI Jianjun2 )1 ) Beiing Guojing Infrared Optical Technology Co. ,Ltd. , General Research Institute for Non-ferrous Metals , Beijing100088 , China2 ) The 205 Research Institute of China W eapon Industry ,Xi'an 710065 , China( Received 2006-08-18 )Abstract : The professional modeling software package CrysVUn was employed to study the process of a largesapphire single crystal growth using Kyropoulos method. The infuence of gas pressure on thermal field , solid-liquid interface shape , gas velocity field and von Mises stress were studied for the first time. It is found that theroot of the seed melt when gas pressure equals to one atmosphere or more than one atmosphere , especially dur-ing the seeding period , this result is consistent with the experimental observation , and this paper presents threeways to solve this problem. The temperature gradient and stress decreases significantly as the gas pressure in-creases. The convexity of the solid-liquid interface slightly increases when the gas pressure increases. Numeri-cal analysis was used to optimize the hot zone design.Key words : gas convection ; thermal field ; von Mises stress ; sapphire single crystal ; numerical simulationfor analyzing processes that take place in the re-1. Introductionactor. In particular , the simulation allows evalua-ting such important parameters as temperatureSapphire single crystals are widely used in aand heat flux distributions in growing crystal andvariety of modern high-tech applications ，from .in other parts of the setup. .commercial and military optical systems to highLukanina et al.[ 4 ] had suggested a 3D nu-power laser components because of the favorablemerical model which had been developed on thecombination of excellent optical ，mechanical ,basis of the CGSim package for the simulation ofthermal and chemical characteristics[ 1-2 ] Theheat transfer in the furmace for growing large sap-high crystal perfection , low reactivity , and ap-phire crystals by horizontal directional crystalliza-propriate unit cell size make sapphire an excel-tion method ( HDC ). The model had been usedent substrate in the semiconductor industry forto improve the presented growth setup , to reduceblue light-emitting diodes and diode lasers[ 3 ]the energy losses , to control temperature gradi-Large columnar sapphire crystals can beents in the crystal , and to design a new HDCgrown by various techniques. A technique com-growth setup for the growth of corundum singlemonly used for growing sapphire single crystals iscrystals of larger size. The thermal fields at vari-the Kyropoulos method that provides the growth ofous positions of the crystal container and thehigh quality crystals of large size up to φ 300effct of various setup units and their design onmm. The growth occurs at very high temperaturesratre distrihution were analyzed.( the melting temperature is 2043 C ) 4 ] This中国煤化工IDAP to simulate the .practically eliminates a possibility of accurate ex-MYHCN M H Gss in a cyindrical cru-perimental investigations inside the hot area[ 5 ]cible , both the energy input and the energy out-So , the numerical simulation is an effective toolput were modeled under convection boundaryCorresponding新hr :LI Jinquan E-mail : spirsbstrate@ yahoo. com. cn .261LiJ e. etal. ,Infuence of gas lnow on spphire single crystal using Kyropoulos methodconditions. They found that the contact angle wastween the gas pressure and the thermal field ,sol-obtuse before the solid-melt interface touched theid-liquid interface shape , gas velocity field assidewall of the erucible , and that hot spots alwayswell as vonMisesStress during Kyropoulos sap-appeared. The efets of various thermal fields onphire crystal growth.the shape of interface and the increasing rate ofthe erystal size were investigated. Infuence of2. Modelingthe crucible geometry on the shape of the mel-Over two decades of development , modelingerystal interface was also studied. Brandon S. etis now an essential research field in crystalal.[9 ] had examined the growth of eylindricalgrowth. Its impact is not only on the better un-sapphire single crystals numeically ，using aderstanding of fundamental phenomena , but alsoGSM system. They considered quasi-steady -stateon the much faster process improvement and in-solutions for the mel-crystal interface. The sensi-novation of erystal growth technologie[ 16] Twotivity of the thermal fields to the parameter valuesmathematical procedureswere implemented in thewas markedly dependent on the diameter of thesoftware system CrysVUN for global thermal simu-crucible. They found that the effect of the furnacelation of erystal growth processes. The forwardgradients on the interface in an intermediate sizesimulation can calculate the temperature distribu-crucible was larger than the interface in cruciblestion as long as the heater powers are given ,likewith diferent diamelers. Floricica Barvinschi etin experiments. The inverse simulation was ableal.[ 10 ] employed the finite element softwareto ealeulate the powers of an arbitrary number ofFIDAP to simulate the Verneuil process for theheaters in a erystal growth configuration in ordersapphire erystal growth. A steady-state numericalto obtain a prescribed temperature distribution inmodel of the Vermeuil growth process had beena growing crysta[ 17 ]built and gave resultls in qualitative agreementIn the present study，we employed thewith some experimental observations. Borodin A.standard K-epsilon gas turbulent model to simu-V.et al.[ 11 ] had simulated the pressure disti-late the gas convection using the inverse simula-bution eaused by a hydrodynamie stream of thetion in the numerical modeling , and set the tem-melt in meniscus and capillary regions to defineperature of the contolled point(0 ,0. 54 ) equaland analyze the forces that a erystal experiencesto 2316 K,i. e. , the solid-liquid interfaceduring the Stepanov ( EFG ) growth. The velocityshould pass through this point. To simplify thefields and the corresponding pressure distributionproblem , melt convection was not taken into ac-in the capillary and in the meniscus were de-count. Because the growth velocity was veryscribed by Stokes equations and the appropriatesmall ,generally from0.5-5 mm: hr' ,the pseu-class of functions.do-stationary assumption was used.Cenerally ,the fumace was charged with ar-Table 1 shows the thermo-physical of sap-gon asa protective gas during sapphire singlephire properties taken into account and some dif-erystal growth by Kyropoulos method. And gasferent non-dimensional numbers of the problem.pressure was an important parameter during Kyro-Argon physical data , including thermal difusivi-poulos- sapphire single erystal growth. Until now，ty ,specific heat and viscosity used in the simula-there are few researchers who have simulated thetion of gas convetion are list in Table 2.Kyropoulos process. The efet of the gas pres-中国煤化工simulatins of themalsure and flow on the Kyropoulos crystal growthMYHCNMH Gstress field was also cal-has not been considered. Hence , in the presentculated in the present study. The analysis of ther-study , we employ software CrysVUn[ 12-15 ]( amo-elastic stress in the crystal was quite impor-finitevolume code developed at the Fraunhofertant for predictions on the quality of sapphireInstute i币时数据n ) to study the correlation be-single erystal . The stress - strain relation for a262RARE METALS , Vol.25 , Spec. Issue , Dec 2006Table 1. Sapphire thermo-physical data usedDescriptionValueReferences'Thermal conductivity of crystal/( W. K-中. m-' )-27.4 + 590.57 * exp( -T/92.51 ) +24.49 * exp( -T/’ 6696.83 )+ 19.924 * ex( -7/6441.1 347 )Thermal conductivity of mel/( W. K' m~' ) 3.5[ 18]Melt point/K2316. [4]Emissivity0.9Latent heat/(J. kg-' )1.1 x10°[19]Transparency0.16 μm for crystal ;1-5 μm for meltTable 2. Argon physical data usedDensity/( kg° m-3 )5.222077e2/T[20]Thermal conductivity/( W. m-1. K-1 )-1.587964e-015*T* T* T* T + 1.050359e-011 * T* T* T-[21 ]2. 632101e-008 * T* T +5.576743e-005 * T +4.222052e-003Thermal difusivit/( m'. s-1 )1.553406e-018* T* T* T* T-1. 523237e-014*T*T* T +1. 233721e-010* T* T +5.101993e-008 * T-7. 696469e-006Specifie heat(小(kg" K)")5.2033e +002[22 ]Viscosity(kg: m”s~ ' )or(N. s) mi-1.007569e-018* T* T* T* T +8.881353e-015 * T* T* T-[ 223. 008134e-011 *T*T+7.512290-008* T+2.823345-006thermo-elastic anisotropic solid body was taken asdescribed by Lambropoulo[ 23-24 ]3. Results and discussionren C口2 cB 0γεn-d( T-Tm) \Because gas pressure has a direct impact onEp-a( T-T)temperature field and gas flow field , its a veryi3 Cn2 C23 0εn-a( T-Tm)important parameter during Kyropoulos processes(o(000c4八Enfor sapphire single crystal growth. To investigate(1)the effects of gas pressure , it had been changedHere a was the thermal expansion coefficient ,from0 to 10° Pa. Fig. 1 illustrates the tempera-Tm the reference temperature for the relaxed bodyture distribution and gas vector fields during theand εrπzn the strains. Cj were the elastic mate-initial Kyropoulos growth for different gas pres-rial constants in the Voigt notation. A very im-sure. There was no gas convection in vacuumportant scalar for the discussion of stress in solidsystems. For the lower gas pressure ,the gas ve-bodies , especially for crystal growth was the vonlocity was much slower and the gas flow was lessMises stress , which was computed from the dis-turbulent than the higher pressure , and its effectstinct stress components. In cylindrical coordi-on thermal fields were not obvious. The resultnates ,it was given byshows that the temperature fields change signifi-TMies =cantly when the pressure equals to or higher than(σπ -σ_y+(σnσy: (σge -σ。了+6r7。(2)105 Pa( about one atmosphere ). All the isother-中国煤化工the pesure equal toAs for sapphire single crystal , the stress coeff-MHCN MH G that the isothemals a-cient<[ 25 ]C =496x10° Pa ,C12 =164 x 10°bove the melt was close to the seed , the gas vec-Pa ,C3=115x10' Pa ,C33 =498x10° Pa ,C44tor fields show that the gas flow was moving up-=148 x10° Pa.ward ,and the flow was much more turbulent a-round the corner. With the increase of gas pres-Li J. Q. et al. , Influence of gas flow on sapphire single crystal using Kyropoulos method263sure , the isothermals which were higher than thewere higher than the melt point would be muchmelt point of sapphire were appearing in the re-closer to the seed , and because of many actualgions above the seed. When the gas pressure e-factors the gas velocity field should be unstablequaled to 106 Pa( Fig. 1( f)), the seed and theand fluctuant in a relatively large range duringisothermals of melt point were nearly touch withthe crystal growth experiments. This property ofeach other. It had a direct relationship with gasthe gas turbulent would greatly increase the possi-vector field , because tie temperature of argon gasbility of seed melting. It was noticeable that the :around the crucible was very high , and the gascorner between the water-cooling rod and the seedwould take heat flux with high temperature up-was orthogonal( Fig. 2( b)). We could find fromward.the gas vector fields in Fig. 2. That the gas con-Fig. 2 showed that the seed did not melt dur-vection strengthened around the corner , the heating the initial Kyropoulos growth , as the pressureexchange between the gas and the seed quickenedequaled to 105 Pa. But the melt-solid interfaceat the same time , and the gas transferred the heatwould move upward during the initial seedingof high energy to the seed ，which made theprocess , which meant that the isothermals whichroot of the seed easily melt during the initial(ab)(C)力SeedMeltd)e)(f中国煤化工Fig.1. Isothermals and gas flow vector fields for various.YHCNMHG:lds in the systems are Tmn=2316 K ,AT=1 K):( a)vacuum;( b)p=1x10* Pa;( c)p=1x10 Pa;( d)p=1 x105 Pa;( e)p=3 x 10*Pa;( f)p=1 x10° Pa.264RARE METALS , Vol.25 , Spec. Issue , Dec 2006witer-coling npdThe root of the seed melt during seedingSeed(a(bc)(dFig. 2. The root of the seed melted during initial seeding period at p = 10* Pa( a ) , the binding structure used atpresent( b ) , improved binding structure( c ) , and the seed was all right with the improved binding structure( d ).seeding period. This was consistent with the ex-tion in crystal and melt versus different gas pres-perimental observation( Fig. 2( a)).sure. All the curves intersected at the sameIt is very disadvantageous for the whole crys-point , which was the controlled point(0 ,0. 54 )tal growth process that the root of the seed meltedin the inverse simulation. The temperature distri-during seeding period. The experiments may bbution of the crystal was below this point , and theabortive due to awful condition of the seeds. Theparts above the point were the melt temperaturemelting of the seed root had direct relationshipdistribution. The slopes of these curves were re-with the gas turbulent around the orthogonal cor-garded as the axial temperature gradients. Its ob-ner. We should decrease the gas convection atvious that the temperature gradients decrease sig-the corner between the rod and the seed to avoidnificantly as the gas pressure increases.this problem. Hence , this paper brings forward34010 Pathree methods in the present study. 1 ) Increasing30-the space between the crucible , melt and the up-2330--p=10* Paper heat shield will lower the heat exchange between the gas and the seed. But the space should3202315-not be too large , or the function of the upper heatshield would be weakened. 2 ) Reducing the gaspressure is also an effective way to solve this2300+中国煤化工。problem.3 ) Improved the binding structurephire (melt & crystal)( Fig. 2( c)) , just changing the orthogonal angleYHCNMHGFig.3. Calculated temperature distribution in sap-to an obtuse angle. Experiments show that thephire melt & crystal of axis.problem was well solved( Fig. 2( d)).Fig.万市数据the axial temperature distribu-Li J. Q. et al. , Influence of gas flow on sapphire single crystal using Kyropoulos method265The vonMisesStress and thermal fields of the sap-by lower convexity at the interface , except for aphire single crystals are present in Fig.4. It cancertain orientation of the crystal seed[ 26 ] High-be clearly seen that all the melt-solid interfaceer quality crystals may be grown when there wasare convex. The convexity was defined byless convexity at the melt-solid interface. Fig. 4D= max Z/R(3 )shows that the shape of melt-solid interface is amax Z was the height of the interface in the z di-parabola when gas pressure equals to 10° Parection and R was the radius of the crystal. When( Fig.4( f)), but the shape is nearly a triangle inthe convexity equals to 1 ,it means that the shapevacuum systems. Hence , although the maximumof the melt-solid interface is hemispherical. Thevalues of the convexity does not change signifi-convexity of the interface is an important growthcantly with the variation of gas pressure ,the av-parameter that affects the quality of the crystal.erage convexity of the whole crystal slightly in-The formation of crystal facets can be preventedcreases as the pressure increases.b)(a)(c(d)()Fig.4. Infuence of gas pressure on temperature field and thermal stress σ( maximum of von Mises stress factor):( a)vacum;(b)p=1x10' Pa;(c)p=1x10* Pa;(d)p=1 x10° Pa;(e)p=3x10* Pa (f)p=1x10* Pa.百55-cracked using Verneuil method. .The maximumVon mises strcc vs. argon pressurestress mainly distributes in the region connectingwith the seed and the edge of the crystal during5-the seeding period( Fig.4 ). Fig. 5 ilustrates that0the von Mises stress decreases significantly whenthe gas pressure increases , but after the gas pres-叫sure equates to 3 X 10’Pa , the von Mises stressdecreases slightly.72↓887Pressurc/10* Pa4. ConclusionsFig.5. Effects of gas pressure on von Mises stress中国煤化Iressure on the thermalThe analysis of thermoelastic stress in theMYHCNM H Gce shape , gas veloeitycrystal was quite important for predictions on thefield and von Mises stress during the applicationquality of the grown material. Sapphire crystal ofof the Kyropoulos -sapphire single crystal growthbig stress罗绷堂,e. g. ,sapphire crystal easilywere investigated numerically using the CrysVUnRARE METALS , Vol.25 , Spec. Issuse ,Dec 2006266software. The results show that the root of thegometry onthe shape of the melt-crystal interfacecrystal using a heat ex-during gonhad sphiren crouad .i ,be2seed melt when gas pressure equals to one atmos-[9] Brandon s. ,and Gazit s. ,Interface shapes and ther.phere or more than one atmosphere , especiallymal fields during the gradient slification methodgrowth of sapphire single crystals. Journal of Crystalduring the seeding period , this result is consist-Grouth ,1996 ,167 :190.ent with the experimental observation. The melt-[ 10 ] Floricica Barvinschi , Jean-Louis Santaller ，ThieryDuffar ,et al.Molelling of Vemeuil process for theCostal Couth.ing of the seed root has direct relationship withsapphire erystal growth. Journal of Crystal Grouth，1999 ,198/199 :239. .the gas turbulent around the orthogonal cormer ,[11] Bordin A.V. , Borodin V. A. : and Zhdanov A.V.，Simulation of the pressure distribution in the melt forand this paper presents three ways to decrease thesapphire rbbon growth by the Stepanov( EFC )tech-gas convection at the corner between the rod andnique. Journal of Crystal Grovuth ,1999 ,198 :220.the seed. The experiment had validated that the[12] Kurz M. Pustai A. ,and MuMuller G. , Developmentof a new powerful conputer code CrysVUN+ + espe.cially designed for fast simulation of bulk crystalimproved binding structure could resolve it well ，growth processes. Poeedings of SPIE ,2003 ,5078.but the other two methods have not yet been con-[ 13] Kurz M. ,and MuK ler G. ,Control of thermal condi-tions during crystal growth by inverse modeling. Jour-firmed by comparing with experiments. 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