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  1. 1. Definition An investment can be described as a ceramic material which is suitable for forming a mold into which a metal or alloy is appropriately cast. The procedure for forming the mold is described as “investing” (wax pattern). Depending on the melting range of the alloy and the preference of the clinician, generally two types of investment: 1. Gypsum – bonded and 2. Phosphate – bonded investment are employed. - The gypsum based materials represent the type traditionally used for conventional gold alloys. - The phosphate based invest are designed purely for alloys used in the metal ceramic restoration. A 3rd type is the ethyl silicate bonded invest used periapically in the casting of R.P.D. with base metal alloys. According to ADA specification No.2 for casting investments for dental gold alloys are of three types of determined by whether the appliance is to be fabricated is fixed or removable and the method of obtaining the expansion required to compensate for the contraction of the molten gold alloy during solidification. 1
  2. 2. Type I – are used for the casting of inlays or crowns, and the compensation of casting shrinkage is principally by thermal expansion of the investment. Type II – are also used for the casting of inlays or crowns but major mode of compensation is by the hygroscopic expansion of the investment. Type III – are used in the construction of partial dentures with gold- alloys. Gypsum-Bonded Investment The essential ingredients are : 1. α-hemihydrate of gypsum and 2. A form of silica. α-hemihydrate gives greater strength to the material and acts as a binder to hold the other ingredients together and provide rigidity. Although depends on amount of binder – may contain 25% - 45% and is used for alloy with melting ranges below 1000°C (i.e., gold-containing). When heated to the required temperatures it shrinks considerably and frequently fractures all form shrink considerably after dehydration between 200°C and 400°C. A slight expansion then occur between 400°C and approximately 700°C, and then a large contraction occur. This is most likely carried by decomposition and sulfur gases such as sulfur dioxide are emitted 2
  3. 3. which contaminates the castings (with the sulfides of non habit allogest elements such as silver and copper). Thus not to be heated above 700°C. α-hemihydrate requires less mixing water and shrinks less. Silica Added to provide a refractory during the heating of the investment and to regulate the thermal expansion. It exists in an allotrophic form. 1. Quartz 2. Tridymite 3. Cristobalite and 4. Fused quartz. When heated a change in crystalline form occurs at a transition temperatures, characteristics of the particular form of silica. - When heated quartz invasion from a ‘low’ form α-quit to high form to quartz at 570°C. - Cristobalite undergoes – between 200°C-270°C from α –β cristobalite. - Tridymite – 117°C to 163°C. - α-allotropic form are stable only above the transition temperature, inversion to the lower form occur on cooking in each case. The density decrease as the α -changes to β -form resulting increase in volume. 3
  4. 4. Fused quartz is amorphous and glucobites in character exhibits inversion at any temperature below its fusion points has an extremely low coefficient of thermal expansion and is of little use in dental expansion. Quartz, cristobalite, or a combination of the two forms may be used in a dental investment. Modifiers Such as coloring matter reducing agents such as carbon powdered copper to provide a non-oxidizing atmosphere in the mold when the gold alloy is cast. Some of the added modifiers such as toxic acid and sodium chloride not only regulate setting expansion and the setting time, but also prevent most of the shrinkage of gypsum when it is heated above 300°C. Setting Time According ADA specifications No.2 for dental alloy casting, S.T. should not be shorter than 5 minutes nor longer than 25 minutes the modern inlay investments set initially in 9-18 minutes. Normal Setting Expansion A mixture of silica and gypsum hemihydrate results in setting expansion greater than that of the gypsum product when it is used alone. The silica 4
  5. 5. particles probably interfere with the inert washing and interlocking of the crystals as they form. Thus the thrust of the crystals is outward during growth and they increase expansion. ADA specification No.2 for type I invest permits maximum setting expansion in air of only 0.6%, that of modern invest is approximately 0.4%. The purpose of setting expansion is to aid in enlarging the mold to compensate partially for the casting shrinkage of the gold. The effectiveness of the setting expansion in enlarging the mold containing the wax pattern may be related to the thermal expansion of the pattern caused by the heat of reaction that occurs coincidentally with the setting of the investment. It follows from such a theory that the setting expansion and effective only to the extent that the exothermic heat is transmitted to the pattern. The amount of heat present depends on the gypsum content of the investment ; therefore the setting expansion of the invest with comparably high content of gypsum more effective in enlarging the mold than is a product with a lower gypsum content. Likewise manipulative conditions that increase the exothermic heat increase the effective setting expansion, (eg, the lower the water powder ratio for the investment, the greater is the effective setting expansion). 5
  6. 6. Other variables are: As the investment sets, it eventually gains sufficient strength to produce a dimensional change in the wax pattern as setting expansion occurs. The inner wall of the investment within a MOD wax pattern can actually force the proximal walls outward to a certain extent. If the pattern has a thin wall then the effective setting expansion, is somewhat greater than for a pattern with thicker walls because the investment can move the thinner wall more readily. Also the softer wax, the greater the effective setting expansion because the softer wax is more readily moved by the expanding investment. Hygroscopic Setting Expansion The hygroscopic setting expansion differs from the normal setting expansion in that it occurs when the gypsum product is allowed to set under or in contact with water and that it is greater in magnitude than the normal setting expansion. This is related to the additional crystal growth permitted and not to any differences in chemical reaction. In normal setting condition, the water around the particle is reduced by the hydration and the particle are brought more closely together by the surface tension action of the water. 6
  7. 7. In hygroscopic reaction the setting is taking place under water, the water of hydration is replaced and the distance between the particles remain same. As the crystals of dehydrate grow they contact each other and the setting expansion begins in normal setting reaction the crystals being inhibited become intermershed and entangled much sooner than those on hygroscopic reaction which grow much more freely during the early stage before the intermeshing finally prevents with further expansion, the hygroscopic setting expansion is one of the methods for expanding the casting mold to compensate for the casting shrinkage of the gold alloys. Commercial investments exhibit different amounts of wax expansion. ADA specification No.2 for such type II investments requires a minimum setting expansion in water of 1.2%, the wax expansion permitted is 2.2%. the factors controlling hygroscopic expansion. Effect of Composition Proportional to the silica content of the investment the fine the particle size of silica the greater hygroscopic expansion α-hemihydrate produce more with silica than pH. Should have enough binder with silica, at least 15% of binder is necessary to prevent and drying shrinkage. Effect of the Water / Powder Ratio (W:P) Higher the W:P ratio less the hygroscopic expansion. 7
  8. 8. Effect of Spatulation - Mixing time is reduced hygroscopic expansion decreased. - Older the inert lower is the setting expansion. Effect of Time of Investment The greater amount of hygroscopic expansion is observed if the immersion take place before the initial set, the longer the immersion of the investment in the water both is delayed beyond the time of the initial set of the invest. The lower is the hygroscopic expansion. The effect of confinement Both the normal and hygroscopic setting expansion are confined by exposing forces such as walls of the container in which the investment is placed on the walls of a wax pattern, the confining effect on the hygroscopic expansion is much more pronounced than the normal setting expansion. The increase in the effective setting expansion when the investment is immersed in a 38°C water bath is caused mainly by the softening of the wax pattern at the water bath temperature permitting an increase in effective setting expansion, softened conditions of wax reduces its confining effect on the expansion of the setting expansion. 8
  9. 9. Effect of the Amount of Added Water The magnitude of the hygroscopic setting expansion can be controlled by the amount of water than is added to the investment. Magnitude is in direct proportion to the amount of water added during the period until a maximum expansion occurs also further expansions to evident regardless of any amount of water added, the hygroscopic setting expansion is a continuation of the ordinary setting expansion because the immersion water replaces the water of hydration and thus prevents the confinement of the growing crystals by the surface tension of the excess water. Because of the diluent effect of the quartz particles the hygroscopic expansion in these invest is greater than that of the gypsum binder when used alone. The phenomenon is purely physical, the hemihydrate binder is not necessary for the hygroscopic expansion. Investment with other binder exhibit similar expansion when allowed to set under water. Expansion can be detected when water is poured into a vessel containing only small smooth quartz particles, the water is drawn between the particles by capillary action and thus causes the particles to separate, creating an expansion. Any water insoluble powder that is wettable can be mixed with hemihydrate and hygroscopic expansion results. The greater the amount of silica or inert filler the more easily the added water can diffuse thus the setting material and the greater is the expansion. 9
  10. 10. The term hygroscopic is a misnomer, although the added water may be drawn into the setting material by capillary action, the effect is not related to hygroscopy. On the basis of theory the hygroscopic expansion is a normal phenomenon as that which occurs during normal set expansions the terms have gained general acceptance by usage. Thermal Expansion The thermal expansions of a gypsum bonded investment is directly related to the amount of silica present and to the type of silica employed, the contraction of the gypsum is entirely balanced when the quartz content is immersed to 75%. The thermal expansion curves of the quartz is influenced by particle size of the quartz, the type of the gypsum binder and the resultant water powder ratio necessary to provide a workable mix. Much greater expansion occurs during the inversion of cristobalite, the normal contraction of the gypsum during heating is easily eliminated. The expansions occurs at a lower temperature because of the lower inversion temperature. Investments containing cristobalite expand earlier and to a greater extent than those containing quartz. 10
  11. 11. ADA specifications no.2 requires that the thermal expansion must be not (0-66%) less than 1% nor greater than 1.6%. Maximum thermal expansion is obtained at a temperature not higher than 700°C. W:P Ratio More water that is used in mixing the investment the less is the thermal expansion that is achieved during subsequent heating. Effect of Chemical Modifiers The addition of small amounts of sodium, potassium or libuim chlorides to the investments eliminates the contraction caused by the gypsum and increase the expansion without the presence of excessive silica. Strength The strength of the investment must be adequate to prevent fracture or chipping of the mold during heating and casting gold alloy. When the alloy is still quite hot and weak the investment and resist alloy shrinkage by strong and constant dimension. After burnout of the pattern (mold), the strength need be no greater than that required to resist the impact of the metals containing the mold. 11
  12. 12. ADA specifications no.2 the compressive strength for the inlay investments should not be less than 2.4 Mpa for gypsum. Other Gypsum Considerations Investments fineness affect the setting time, the surface roughness of the casting, a fine silica results in higher hygroscopic expansion. Porosity As the molten metal enters the mold, the air must be forced out ahead of it. If not a back pressure builds up to prevent the gold alloy from completely filling the mold, the common method for venting the mold is though pores of investment, the more gypsum crystals, the less is its porosity lower the hemihydrates content and the greater the amount of gauging water used to mix, the more porous it becomes. More uniform the particles size, the greater the porosity. Storage Phosphate Bonded Investment The rapid growth of use of metal ceramic restorations and the increased use of higher melting alloys have resulted in an increased use of phosphate or silica bonded investment. 12
  13. 13. Composition Consists of refractory fillers and binder, the filler is silica, in the form of cristobalite, quartz or a mixture of two – 80% concentration approximately. The purpose of silica is to provide high temperature thermal shock resistance and a high thermal expansion. The binder consists of magnesium oxide (basic) and a phosphate that is acid in nature. Originally phosphoric acid was used, but mono ammonium phosphate has replaced it, because it can be incorporated into the powdered investment. Newer gold-containing alloys and other alloys used for metal ceramic have higher melting temperature ranges and then contraction during solidification is also greater. This necessitate greater expansion, can be achieved by using colloidal silica suspensions with the phosphate investments, in place of water colloidal silica liquid suspension freeze, should be assessed before winter, freeze solid act low temperature. Some are made to be mixed with water, for predominantly base metal alloys, a 23% dilution of the colloidal silica is required. Carbon is often added to the powder to produce clear castings and facilitates the divesting of the casting from the mold, appropriate when the 13
  14. 14. casting alloys is gold not with silver containing and base metal alloys. It is believed carbon embrittles the alloys. Latest evidence palladium reacts with carbon if heated above 1504°C in this case investment without carbon should be used. Setting and Thermal Expansion There is a slight expansion during the reaction compared to gypsum products, and this can be increased considerably by using a colloidal silica solution instead of water. When phosphate investments are mixed with water this exhibit a shrinkage within essentially the same temperature range as gypsum inert (200°C-400°C). this contraction is practically eliminated when a colloidal silica solution replaces. (Some users of phosphate bonded) expansion can be decreased by the increasingly the liquid : powder reaction ratio also by decreasing the concentration of the special liquid or by they may use a combination of these methods. Working and Setting Time Phosphate investments are markedly affected by temperature. The normal the mix, the faster it sets the setting reaction itself gives off heat (this itself gives heat) and this further accelerates the rate of setting. 14
  15. 15. Increased mixing time and mixing efficiency results in a faster set and a greater rise in temperature. The ideal technique is to mix as long as possible yet have just enough time for investing. Mechanical mixing under vacuum is preferred. Ethyl-Silicate – Bonded Investments Involves more complicated and time consuming procedures involved. Used in the construction of the high fusing base metal palladium alloys. The binder is a silica gel, that reverts to silica cristobalite on heating. Several method may be used to produce the silica or silicic acid gel binder. When the pH of sodium silicate is lowered by the addition of an acid salt, a bonding silicic acid gel forms. The condition of magnesium oxide strengthen the gel. An aqueous suspension of colloidal silica can be converted to a gel by the addition of an accelerator, such as ammonium chloride. Another system for binder formation is based on ethyl silicate. A colloidal silicic acid is first formed by hydrolyzing ethyl silicate in the presence of hydrochloric acid, ethyl alcohol and water. The solution is then mixed with the quartz or cristobalite to which is added a small amount of finely powdered magnesium oxide to render the mixture alkaline. A coherent gel of polysilicic acid then forms accompanied by a shrinkage. The soft gel is dried at a temperature below 168°C. During the drying process, the gel losses alcohol and water to form a concentrated hard gel, a volumetric contraction accompanies 15
  16. 16. the drying which reduces the size of the mold. This contraction is known as “green shrinkage”, and it occurs in addition to the setting shrinkage. The gelation process is slow and time consuming certain types of amines can be added to the solution of ethyl silicate so that hydrolysis and gelation occurs simultaneously. The Sprue Former The purpose of a sprue former or sprue pin is to provide a channel through which molten alloy can reach the mold in an invested ring after the wax has been eliminated. With large restorations or prosthesis, such as removable partial denture frame works and fixed partial dentures, the sprue former are made of wax. For smaller casting metal pins can be used, plastic sprue forms are also available. The diameter and length of the sprue former depends to a larger extent on the 1. Type and size of the pattern, 2. The type of casting machine to be used, 3. And the dimensions of the flask ring in which the casting is to be made. Prefabricated sprue formers are available in a wide range of gauges or diameters sprue former gauge selection is often empirical, yet it is based on the following five general principles (Skinner’s). 16
  17. 17. • Select the gauge sprue former with a diameter that is approximately the same size as the thickest area of the wax pattern. If the pattern is small the sprue former must also be small because a large S.F. attached to a thin, delicate pattern could cause distortion. However, if the sprue former diameter is too small, this area will solidify before the casting itself and localized shrinkage porosity (“suck back” porosity) may develop. Reservoir sprues are used to help overcome this problem. • If possible, the sprue former should be attached to the portion of the pattern with the largest cross-sectional areas, it is best for the molten alloys to flow from a thick section to surrounding thin areas not the reverse. This minimizes the risk for turbulence. Porosity : Also, the sprue former orientation should minimize the risk of metal flow on to flat areas of the investment or small areas such as line angles. • The length of the sprue former should be long enough to be within 6 mm of the trailing end and yet short enough so the molten alloy doesn’t solidify before it fills the mold. • The type of sprue former selected influences the burnout technique used it is advisable to use a two-stage burnout technique, whenever plastic sprue 17
  18. 18. former or pattern are involved, to ensure complete carbon elimination because plastic sprues soften at temperature above the mounting point of inlay wax. • Patterns may be sprued either directly or indirectly. For direct spruing the sprue former provides a direct connection between the pattern area and the sprue base or crucible former area. In indirect spruing, a connector or reservoir bar is positioned between the pattern and the crucible former – commonly used for multiple single units and fixed partial dentures. Also several single limits can be sprued with multiple direct sprue. Reservoir should be added to a spruing network to prevent localized shrinkage porosity. When the molten alloy fills the heated casting ring, the pattern area should solidify first and reservoir lost. Because of its large mass of alloy and position in the heat centre of the ring, the reservoir remains molten to furnish liquid alloy into the mold as it solidifies. Resulting solidification shrinkage occurs in the reservoir bar and not in the restorations. Sprue Former Attachment 18
  19. 19. The sprue former connection in the wax pattern is generally flared (telescopic) for higher density gold alloy, but is often restricted for lower density alloys. Flaring act much in the same way as a reservoir, facilitating the entry of the fluid alloy into the pattern area. Sprue Former Position sprue former attachment is often a matter of individual judgement, based on the shape and form of the wax pattern. Some prefer at the occlusal surface, others choose sites such as a proximal wall or just below non functional cusp to minimize subsequent grinding of occlusal anatomy and contact areas, as indicated earlier the ideal area for the sprue former is the point of greatest bulk in the pattern to avoid distorting this areas of wax during attachment, and to permit a smooth flow of the alloy. Sprue Former Direction The sprue former should be directed away from thin or delicate parts of the pattern, because the molten metal may abrade or fracture investment in this area and result in a casting failure. It should not be attached at a right angle to a broad flat surface, this will lead to turbulence within the mold cavity and serve porosity in this region, if it 19
  20. 20. is sprued at a 45° angle to the proximal area a satisfactory casting can be obtained. Sprue Former Length Length depends on the length of the casting ring, if sprue is short, the resulting mould space may be far from the end of the casting ring that gases can not be adequately vented to permit the molten alloy to fill the ring completely (mould space), thus may result in the porosity. For gypsum bonded should be within 6mm of the open end of the ring, with the higher strong phosphate bonded investments position may be within 3- 4 mm of the top of the investment. For reproducibility of casting accuracy, the pattern should be placed as close to the center of the ring as possible. Wax Pattern Removal Sprue former should be attached with the pattern on the master die, provided the pattern can be removed directly in line with its path of withdrawal from the die. Preparation of the Master Die The most commonly used die materials are type-IV (dental stone, high strength) and type-V (dental stone, high strength, high expansion). 20
  21. 21. Relatively, inexpensive, easy to use and generally compatible with all impression materials. Type-IV stones have a setting expansion of 0.1% or less whereas the harder type-V stones expand as 0.3% this greater expansion is useful for compensation of the relatively large solidification shrinkage of base metal alloys. To increase the abrasion resistance several means including silver plating, coating the surface with cyanoacrylate and adding a die hardner to the gypsum. However each may also increase the die dimensions, thus reducing accuracy. Methods of Altering Die Dimensions To reduce the setting expansion of the type-IV die stone to less than 0.1% there by reducing diameter additional accelerator (potassium sulfate) and retarder (borax) can be added to the gauging water. To produce relief space for cement, die spacer can be used with a stone die, the most common die spacers are resins. Although proprietary point on liquids are sold for this purpose, model paint, colored nail polish or thermoplastic polymers dissolved in volatile solvents enjoy wide spread popularity. These spacers are applied in several coats to within 0.5mm of the preparation finish line to provide relief for the cement luting agent and to ensure complete seating of an otherwise precisely fitting casting. 21
  22. 22. Die Stone – Investment Combination In this technique (that has been developed) the die material and the investing medium have a comparable composition. A commercial gypsum bonded material, called divestments (whip mix corporation, Louisville KY) is mixed with a colloidal silica liquid. The die is made from this mix and the wax pattern constructed on it. Then the entire assembly (die and pattern) is inserted in a mixture of divestment and water thereby eliminating the possibility of distortion. Casting Ring Liners With the use of solid metal rings or casting flasks, the mold may actually become smaller rather than larger because of the reverse pressure resulting from the confinement of the setting expansion. This effect can be overcome by using a split ring on flexible rubber ring that permits the setting expansion of the investment. The most commonly used technique to provide investment expansion is to line the walls of the ring with ring liner. Traditionally, (earlier) asbestos was the material of choice, no longer be used because of its carcinogenic potential. Two types of non-asbestos ring liner used are aluminium silicate ceramic liner and a cellulose (paper) liner. 22
  23. 23. To ensure uniform expansion, the liner is cut to fit the inside diameter of the casting ring with no overlap. The cut liner is added in position with stick wax and then is used with a dry or wet, with a wet liner technique the liner ring is immersed in water for a time and the excess water is shaken away. Squeezing the liner should be avoided because this leads to variable amounts of water removal and uneven expansion. Ceramic liner doesn’t absorb water like a cellulose liner, its network of fibres can retain water on the surface. In the liner the absorbed water causes a semihygroscopic expansion as it is drawn into the investment during setting. A thicker liner material or two layers of liner provide even greater semihygroscopic expansion and also affect a more unrestricted normal setting expansion of the investment in any case, the thickness of the liner should not be less than approximately 1mm. The length of the liner remains a matter of controversy. If the liner is shorter than ring, the investment is confined at one or both end of the ring, the longitudinal setting and hygroscopic expansion are thereby restircted as (hygroscopic expansion are thereby restricted as) compared with the end where the liner is flush with the ends of the ring. The expansion of the investment is always greater in the unrestricted longitudinal direction than in the lateral direction that is toward the ring itself. Therefore it is desirable to reduce the expansion in the longitudinal direction. 23
  24. 24. Placing the liner somewhat shorter of the end of the ring tends to provide a more uniform expansion; thus there is less chance for distortion of the wax pattern and the mold. Investing Procedure The wax pattern should be cleaned of any debris, grease or oils. A commercial wax pattern cleaner or a diluted synthetic detergent is used. Any excess liquid is shaken off and the pattern is left to air dry while the investment is being prepared. The thin film of cleaner left on the pattern reduces the surface tension of the wax and permits better “wetting” of the investment to ensure complete coverage of the intricate portions of the pattern. While the wax pattern cleaner is air drying, the approximate amount of distilled water (gypsum investment) or colloidal silica special liquid (phosphate investment) is measured. The liquid is added to a clean dry mixing bowl, and the powder is gradually added to the liquid care should be taken to minimize air entrapment, mixing be started gently until all the powder has been wet, or the unmixed powder may inadvertantly be ejected from the bowl. Hand mixing is an option. It is far more common place to mechanically mix all casting investments under vacuum. 24
  25. 25. Vacuum Mixing Mechanical mixing under vacuum removes air bubbles created during mixing and excavators alloy potentially harmful gases produced during chemical reaction of the high heat investment. Once the mixing is completed, the pattern may be hand invested or vacuum invested. For investing by hand, the entire pattern is painted (inside and out) with a thin layer of investment. The casting ring is positioned on the crucible former, and the remainder of the investment is vibrated slowly into the ring, with vacuum investing, the same equipment used to mix the investment is employed to invest the pattern under vacuum. Amount of porosity in vacuum investment is reduced the texture of the cast surface is smoother with better detail reproduction and tensile strength also increases. In one study it has found 95% of vacuum invested castings were free of nodules where as 17% castings made in hand investment molds were entirely free of defects. Air bubbles that are remain in the mix, can be entraped on flat or concave surfaces that are not orientated suitably for air evacuation tilting the ring slightly aids in releasing these bubbles so they can rise to the surface. 25
  26. 26. Excessive vibration is to be avoided it can cause solids in investments to settle and may lead to free water illumination adjacent the wax pattern. Resulting surface roughness. Excessive vibration may also dislodge small pattern from the sprue former with miscast. If the hygroscopic technique is employed, the filled casting ring is immediately placed as 37°C water bath with crucible former side down. For high heat expansion, the invested ring is allowed to bench cool undisturbed for the time recommended by the manufacturers. Compensation for Shrinkage A number of factors influence the mold size: 1. two liners allows a greater setting and thermal expansion than does a single liner. 2. Setting thermal and hygroscopic expansion can be controlled to a certain extent by varying the liquid : powder ratio of the investment. 3. Lower the L:P ratio greater the potential for expansion, thinner mixes reduces the expansion. With some investment minor adjustments with L:P ratio is insignificant. There is a limit to which L:P can be altered if it is too thick, it can’t be applied to the pattern without distorting the pattern and producing air voids. If the mixture is too thin, a rough surface on the casting may result. 26
  27. 27. In controlling hygroscopic expansion along with L:P ratio can also be regulated either by reducing the time of immersion of the setting ivnestment or by controlling the amount of water to be added during the setting process. The longer the delay before immersion in the water bath, the less the hygroscopic expansion that occurs. Increasing the burnout temperature and the water bath temperature increases the expansion and vice versa. Controlled Water – Added Technique Another technique, in which the shrinkage compensation is controlled by the addition of water during the setting of the investment. Here the linear hygroscopic expansion increases directly with the amount of water added until a maximal expansion is attained. The compositions of investments in this technique ensure maximal expansion during immersion in water. The amount of hygroscopic expansion needed is then obtained by adding may enough water to provide the desired expansion. A soft, flexible rubber ring is employed instead of the usual asbestos lined metal ring. The pattern is invested as used, a specified. 27