to produce a melt composition according to the present invention , a gallium raw material , a sodium raw material , and at least a barium raw material are mixed together to thereby melt the materials . as the gallium raw material , a simple substance metal of gallium or a gallium alloy ( for example , ga 4 na ) may be utilized , and the simple substance metal of gallium is preferable in terms of handling . as the sodium raw material , a simple substance metal of sodium or a sodium alloy ( for example , ga 4 na ) may be utilized , and the simple substance metal of sodium is preferable in terms of handling . barium , a simple substance metal of barium , a barium alloy ( for example , ba 8 ga 7 , baga 2 , baga 4 , ba 10 ga ), and a barium compound ( for example , ba 3 n 2 ) may be utilized , and the simple substance metal is preferable in terms of handling . mole fractions of gallium and sodium in the melt are not specifically limited . for example , when the amount of sodium is taken as 100 mol %, the number of moles of gallium is preferably 10 mol % or higher , more preferably 15 mol % or higher , and most preferably 20 mol % or higher . in addition , the number of moles of gallium is preferably 50 mol % or lower , and more preferably 40 mol % or lower . other than gallium , sodium and barium , a small amount of , for example , carbon , calcium , aluminum , indium , tin , zinc , bismuth , antimony , silicon , magnesium , and the like may be added to the melt . the material should be resistant to conditions of heating and pressurization intended for quality of material of a growth vessel in which the melt is caused to react . such a material includes a high - melting point metal such as tantalum metal , tungsten , or molybdenum ; an oxide such as alumina , sapphire , yttria , or yag ( y 3 al 5 o 12 ); a nitride ceramics such as aluminum nitride , titanium nitride , zirconium nitride , or boron nitride ; a refractory metal carbide such as tungsten carbide or tantalum carbide ; and a pyrolysate such as p - bn ( pyrolytic bn ) or p - gr ( pyrolytic graphite ). among the above - listed materials , the use of alumina is most preferable from a practical standpoint of growing a large gan single crystal of excellent crystallinity . in implementation of the present invention , a raw material mixture is melted under an atmosphere including , for example , at least nitrogen gas and / or ammonia to generate a melt . then , a predetermined condition for growing a single crystal is established . although such a condition is not specifically limited , it is preferable to define a total pressure of the atmosphere as being 3 to 200 mpa . in addition , a growth temperature is defined to be preferably 800 to 1200 ° c ., and more preferably 850 to 1000 ° c . gases other than nitrogen and ammonia in the atmosphere are not specifically limited , but may include preferably an inert gas , and particularly preferably argon , helium , and neon . the material of a growth substrate for epitaxially growing a gallium nitride crystal may include , but not limited to , a gan self - standing substrate ; sapphire ; an aln template ; a gan template ; a silicon single crystal ; a sic single crystal ; an mgo single crystal ; a spinelle ( mgal 2 o 4 ); lialo 2 ; ligao 2 ; and a perovskite - type composite oxide such as laalo 3 , lagao 3 , ndgao 3 , or the like . further , it is also possible to use a composite oxide having a cubic - system perovskite structure whose composition formula is [ a 1 - y ( sr 1 - x ba x ) y ][ al 1 - z ga z ] 1 - u . d u ] o 3 ( where a is a rare earth element , d is at least one element selected from a group of niobium and tantalum , y = 0 . 3 to 0 . 98 , x = 0 to 1 , z = 0 to 1 , u = 0 . 15 to 0 . 49 , and x + z = 0 . 1 to 2 ). still further , scam ( scalmgo 4 ) may be used . the aln template refers to those in which an aln single crystal epitaxial thin film is formed on a sapphire single crystal substrate . the gan template substrate refers to those in which a gan single crystal epitaxial thin film is formed on a sapphire substrate . a film thickness of the template may be appropriately determined as long as it is greater than a film thickness with which the template will undergo meltback at the start of growth . the aln template is more resistant to meltback as compared to the gan template . therefore , for example , the film thickness of the aln template may be 1 micron or more , while that of the gan template may be 3 micron or more . in a single crystal growth apparatus , an apparatus for heating the raw material mixture in order to generate the melt is not specifically limited . the apparatus may preferably be a hot isostatic press apparatus , while other atmosphere pressurized heating furnaces may be used . during production of the single crystal , for example , a plurality of heating elements 6 a , 6 b , and 6 c are vertically arranged as schematically shown in fig1 , and calorific values are independently controlled for each of the heating elements . in other words , multizone control is performed along a vertical direction . although it is generally difficult to control a temperature gradient in the vertical direction since internal temperature and pressure of the pressure vessel become high , temperature differences inside the melt can be optimally controlled by vertically arranging the plurality of heating elements and performing zone control for each of the heating elements . while causing each heating element to generate heat , a nitrogen containing atmosphere is fed through a gas tank 1 , a pressure controller 2 , and a pipe 3 into a growth vessel 7 in an atmosphere controlling container 4 , and heat and pressure are applied . as a result of the application of heat and pressure , all of mixture materials are melted inside the growth vessel to thereby generate the melt . here , as long as the predetermined condition for growing the single crystal is maintained , nitrogen is stably fed into the melt of growth materials , so that a single crystal film is grown on a seed crystal . the material of the heating elements includes , by way of illustration and not limited to , an alloy heating element such as an iron - chromium - aluminum system , a nickel - chromium system , or the like ; a refractory metal heating element such as platinum , molybdenum , tantalum , tungsten , or the like ; a non - metallic heating element such as silicon carbide , molybdenum silicide , carbon , or the like . in a glove box , 0 . 88 g ( 0 . 038 mol ) of metallic sodium , 1 g ( 0 . 014 mol ) ( 37 mol % with respect to 100 mol % of metallic sodium ) of metallic gallium , and 16 mg ( 0 . 27 mol % with respect to 100 mol % of metallic sodium ) of metallic barium were weighted . these raw materials were charged into an alumina crucible growth vessel having an inner diameter of φ17 mm . then , a seed crystal substrate was placed on a bottom part of the crucible growth vessel 1 . a gan template substrate measuring 10 mm per side was used as the seed crystal substrate . the substrate was horizontally placed on the bottom of the crucible growth vessel with a single crystal thin film of the template being faced upward . next , a crucible was set in the growth apparatus , which is pressurized to 3 . 5 mpa by means of nitrogen gas . the growth apparatus was kept at 870 ° c . for 100 hours to grow gan single crystals . at this time , for mixing the melt , a rocking furnace was used with an oscillation cycle was set to 10 rpm , while an oscillation angle was set to 15 degrees . after natural cooling to room temperature , the crucible growth vessel was removed from the growth apparatus , and treated in ethanol to thereby melt na and ba . subsequently , the crucible growth vessel was immersed in dilute hydrochloric acid to remove remaining ga , and the gan single crystals were drawn . the gan single crystals had a roughly hexagonal shape of approximately 12 mm × 12 mm , and were approximately 2 mm in thickness . the gan single crystals were almost transparent and colorless . neither cracks nor inclusion of other types of crystal macro defects were observed . a photograph of the gan single crystals is shown in fig2 . while irradiating the crystals with an ultraviolet lamp , only visible radiation was observed through an ultraviolet cut filter by means of a fluorescence microscope . the result of this observation is shown in fig3 . noticeable light emission is not seen . gan single crystals were grown in a manner similar to that of example 1 , except that instead of adding barium , 0 . 5 mol % of lithium was added with respect to 100 mol % of na . the obtained gan single crystals were almost identical in shape to the template , but slightly larger than the template . the dimensions of the crystals were approximately 11 mm × 11 mm and approximately 0 . 6 mm in thickness . the crystals were slightly brown , but transparent . neither cracks nor inclusion of other types of crystal macro defects were observed . fig4 shows a photograph of the gan single crystals . when the crystals were examined for impurity band emission by means of a fluorescence microscope as in the case of example 1 , emission of yellow - green light was observed ( fig5 ). gan single crystals were grown in the manner similar to that of example 1 , except that instead of adding ba , 0 . 27 mol % of sr was added with respect to 100 mol % of na . the obtained gan single crystals , which were almost identical in shape to the template but slightly larger than the template , had dimensions of approximately 11 mm × 11 mm and approximately 0 . 7 mm in thickness . the color was mostly gray other than an edge portion which was brown - tinted . neither cracks nor inclusion of other types of crystal macro defects were observed . a photograph of the crystals is shown in fig6 . when the crystals were similarly examined for impurity band emission by means of the fluorescence microscope , emission of yellow - green light was observed ( fig7 ). in addition , both the alumina crucible and a sapphire part of the gan template used as the seed substrate were slightly corroded . gan single crystals were grown in the manner similar to that of example 1 , except that instead of adding ba , 0 . 1 mol % of ca was added with respect to 100 mol % of na . the obtained gan single crystals were almost identical in shape to the template , but slightly larger than the template . the thickness was approximately 0 . 6 mm . although the color was mostly dark gray , the crystals were transparent . neither cracks nor inclusion of other types of crystal macro defects were found . a photograph of the gan single crystals is shown in fig8 . when the crystals were examined for impurity band emission by means of the fluorescence microscope as in the case of example 1 , emission of blue light was observed ( fig9 ). further , the alumina crucible was heavily corroded , and the thickness of the sapphire part of the gan template used as the seed substrate was thinned out . accordingly , it was confirmed that the sapphire part was dissolved . gan single crystals were grown in the manner similar to that of example 1 . however , a tungsten crucible was used in place of the alumina crucible . further , 0 . 66 g of nan 3 ( na : 0 . 010 mol ), 1 . 2 g of metallic ga ( ga : 0 . 017 mol ), and 16 mg of metallic ba ( ba : 0 . 117 mmol ) were used . when na is taken as 100 mol %, ga is 170 mol %, and ba is 1 . 17 mol %. the growth temperature was set to 750 ° c . no seed crystal was used . although microcrystals of gan having the size of approximately 1 mm were deposited on a wall surface of the crucible , the microcrystals were black and not transparent . although the specific embodiments of the present invention have been described , the present invention is not limited thereto , and various changes or modifications may be made in the invention without departing from the scope of the invention .