Special Researches in Physics

The special physical researches that have been conducted during the past several years in this office on the properties of waxes, investment materials and metals have been continued and have consisted, chiefly, during this year, in repeating the studies made previously to narrow the margin of former errors and to correct rather than to verify. We acknowledge the assistance particularly of Mr. Frank A. Fahrenwald, Professor Dayton C. Miller, Professor of Physics of Case School of Applied Science, Dr. Thomas J. Hill and Dr. George A. Shilling. Only a small part of the expense for these researches during this year have been met by the Commission. The results, however, are cheerfully given to them.

The coefficient of expansion of the waxes, as previously reported by the writer,1 has been checked over and the change in the coefficient, with the increase of temperature, or progressive increase in the rate of expansion, has been carefully noted and tabulated. Some waxes that have been put on the market more recently than the time of the original studies have been added to the list. By comparing the results in table No. 1 of this issue with table No. 2, page 271, of the previous article above referred to, you will note the great similarity in the readings, which indicate, chiefly, that the waxes with corresponding names and readings have practically the same formula as the samples secured in the open market some years ago. Several of the former waxes have been withdrawn from the market and several new ones are available.

A word of explanation will probably make the table more easily interpreted. All are familiar with the fact that pattern and impression waxes have a considerable range of temperature through which they may be moulded and worked, but which ranges vary with different formulas. The two columns of temperatures underneath the general heading of “Approximate Working Range” indicate respectively the lowest and highest temperatures, bounding the range through which that particular wax can be moulded. The center column indicates the change in linear dimension (which is one-third the volume change) which takes place between the lowest working range and room temperature in the wax in question. The second column from the reader’s right, while called expansion, expresses the same dimension changes for the additional range in temperature up to the maximum working temperature, and will be the same amount whether it is a cooling process or a heating process. The last column at the right expresses the difference, or the expansion, or contraction, taking place between the working limits of temperature. It will readily be noted that this dimension change within the working range varies from half of one per cent linear to two and one-fourth per cent linear, according to the wax. For those who are not familiar with the significance of this data and the enormous advantage or disadvantage it may be in the operations of making dental castings, we will review, briefly, the processes in which it is involved. When the wax pattern material is placed in the cavity at a temperature at which it is just plastic, see first column to the left, and is then removed from the cavity, either before or after being chilled, but finally brought to room temperature, 67° F. or 20° C., its dimension change will be indicated in the middle column. If the wax is invested in the moulding material, usually plaster and silica, at this temperature the dimension of the mould will be in error the amount of the contraction of the wax. If, however, it is still further chilled by being invested in a very cold investment, this error will be increased. On the other hand if it is invested in a very warm investment, comparable to the upper working range of the wax (see second last column) the pattern may be brought back to its original dimension and enlarged a definite per cent above it, in proportion to the formula of the wax and the temperature of the investment. (See the last column.)

Figure 1

 

Neglecting for the present the relatively small change in dimension that may be made in the investment material by heating it and passing to the process of putting the molten gold into the mould and allowing it to cool, we have with all investments (except stone hard investment materials, which may be strong enough to stretch the gold) a definite fixed contraction always present with the cooling gold, which amounts to 11.53% volume of 3.84% linear, from the time the gold is in the molten state until it is at room temperature; but of this 4.93% volume, or 1.64% linear, is due to change of state of the gold and occurs in a change of temperature of less than one degree, and which expresses itself as a fault or hollow in the side of the casting, which, however, need not appear, and does not, if fresh molten gold is permitted to pass into the form and take the place of this first contraction. The larger part of the contraction of the gold from its crystalizing point to normal temperature, amounted to 6.6% volume or 2.2% linear, is always present, even though its location is disturbed by holding the mass and stretching it.

It is this large fixed error, due to the contraction of the gold after it leaves the molten state, which is the large embarrassment we have been seeking to find a solution for and which our practical results show the justification of. Since the contraction of the gold is a constant factor and of a definite amount, we may plan, systematically and definitely, to introduce an error that will precisely compensate or offset for the contraction of the gold; and whether we are so precise as to produce approximately the exact amount or not is not so important as that we work with sufficient intelligence and consistency as not to add to that fixed error, an additional amount which may even exceed that of the contracting gold, due to change in dimension of our wax pattern. We are not, in this observation, stating a new truth, or suggesting a new method or process, but reviewing briefly for clearness. For a more elaborate statement of this procedure see the article referred to above by the writer.1 Also one by Dr. C. S. Van Horn, Dental Cosmos, October 1911.2 It should be clear that, if possible, we should so handle our wax pattern as not to add its large dimension change to that of the gold’s fixed change, but, if possible, so thoroughly understand the wax with which we are working as to know what treatment to give it that would correct for the contraction of the gold. This could be read, with a little study for any of the waxes, directly from the figures in table figure No. 1 herewith, and also table No. 2 in the article above referred to. But for the convenience of the profession we have had the contents of these two tables, which include practically all the pattern waxes that we have been able to secure in the open market, placed in a graphic chart where at a glance we can see the fixed dimension change due to the contraction of the gold, and by the side of it the available dimension change that takes place in the various waxes, and which amount can largely, or in part, be added to, or subtracted from, the dimension change of the gold. These are shown in Figure No. 2, which is a very simple chart to read.

Figure 2

 

Since all the dimension changes are expressed in per cent, we have taken a column of each wax one hundred units long at room temperature of 67° F. or 20° C. A unit can be one inch or one hundredth of an inch, or any other dimension. To save space the long column is broken, showing only its two ends, the distance between lines A. and B. representing one hundred units of length. The dimension of a unit is shown on the scale to the left in which it is the distance from 100 to 101, etc. Also, the actual distance between lines A. & B. Each pair of double vertical lines represents one of the waxes, but a few are constituent or basic waxes used for making them. The elevation above the line A., which is labeled “Length at 67° F. or 20° C.” represents the expansion which occurs above that when the wax is heated to its low working range, represented in the shortest of the two columns, and to its high working range as shown in the longer column. The two columns at the extreme left marked 22 represent the dimension changes in gold. The long column represents the total dimension change in a column of gold one hundred units long between its molten state and room temperature, namely 3.84% linears. The heavy shorter column next to it represents the dimension change between its first crystaline form and room temperature, or 2.2% linear, and the difference between their lengths, the dimension change due to change of state from liquid to solid, namely, 1.64%. These two columns are marked gold. The names of the respective waxes are given below the base line and the columns are numbered above. The dotted line extending across the chart from the level of the shorter double blacked gold column to the point 102.2 on the scale indicates the amount of expansion that would require to be used with each wax if we were to just compensate for the fixed contraction of the gold. The names of the waxes from left to right are:

1. S. S. White Crown Sticky.
2. S. S. White Black.
3. Bird & Moyer Inlay.
4. Peck’s Inlay.
5. Price’s for Stone Model.
6. Standard Inlay.
7. Cleveland Dental Inlay (old formula).
8. Klewes Inlay.
9. Kerr’s Inlay.
10. Consolidated Inlay.
11. Caulk’s Inlay.
12. Security Inlay.
13. Taggart’s Crown Inlay.
14. Van Horn’s Inlay.
15. Japanese Insect.
16. Carnawba.
17. Ceracin.
18. Gum Damar.
19. Stearin.
20. Beeswax.
21. Paraffin.
22. Gold.

The Asterisk on Carnawba and Gum Damar indicates that their softening points, which are high, were not reached at the temperature used.

It will readily be seen from this chart that many of the waxes do not have sufficient change to offset or equal that of the contracting gold, while several others have more than is necessary if in any case it could all be utilized. Note particularly that several have relatively a small difference in dimension between their high and their low working range, which is clearly the part that can most easily be made use of. Others have a very large dimension change between these points. Let us for illustration apply the information in the chart to practical procedure. No. 1 is not a pattern wax, yet many dentists use it for taking impressions because of its great strength. If we were to take it from the cavity at its low working range and cool it to room temperature and invest at that temperature and cast, we will carry forward 1% contraction error to add to our 2.2% of the gold. If we heat this wax to try to put in an error of expansion to offset the gold’s contraction, we can only get half of one per cent above the dimension at which we removed it from the cavity. If we make the same tests with wax No. 2, we may either add two per cent to the error or we may take out 1½%, or even more, up to 3% if we use nearly all the available expansion. With No. 3 the difference between the dimensions at low and high working range is 2.4%, or more than enough to offset the gold contraction. If Nos. 2 or 3 were removed at a temperature near their high working range and invested in an ice water investment, a contraction error of over 3% could be carried forward to which that of the gold would be added, making a total of 5%. If, on the other hand, these same waxes could express, by their volume, the exact dimension of the cavity when they were at a temperature of 67° F. and could then be heated to their high working range and invested, they would produce a mould 3.5% larger than the cavity which, when the gold was cast into it and contracted its fixed 2.2%, would produce a cast still 1.3% larger than the cavity. These results can readily be produced, as will presently be shown. There is no doubt that many of the profession have been introducing an error with their wax, thereby increasing that of the contraction of the gold and probably not infrequently doubling it.

This would seem to be an ideal and simple way to correct for the fixed contraction of the gold and is, if the next distortion error is prevented from entering, which arises out of the elasticity of the wax. Figure No. 3 demonstrates this, as does also Figure No. 4. In Figure No. 3 we have two cast columns of gold both attached to the same sprue and hence from the time of investment they have had the same treatment. These two bars differ 18% in length, yet they were cast at once from wax patterns which were the same length. All waxes are more or less elastic when heated to their low working range. Any one can produce the error shown in Figure 3 as follows: Take two pieces, or bars, of inlay pattern wax (These were made from Cleveland Dental–their old formula), and place them in warm water and heat to the low working range. Take one of the bars out and stretch it, and while holding it plunge into cold water to chill, and thereby retain the elasticity. Then take the other piece and do the opposite by condensing it endwise and chilling. While cold, cut a piece one inch long from each and attach to a sprue. Mix the investment with water at the temperature of the high working range for the wax used and invest. When you last see the waxes they are the same length, but the warm investment releases their elasticity like the thawing of a frozen stretched rubber band. Each relaxes to its normal molecular state of rest without strain. The elongated one shortens and the shortened one elongates. It is true that these are extreme conditions; however, there is abundant evidence that in a considerable degree this error enters into much of our technic. We are liable to be misled and conclude that this is an extreme test and, therefore, not comparable to dental procedures, and particularly that it would be impossible to produce any considerable elastic distortion in the production of an MOD restoration.

 

Figure 3–Two similar wax bars placed in a warm investment and cast. A, Before heating. B, After heating.

 

Figure No. 4 clearly demonstrates that it is possible to very simply introduce this error in our ordinary technic, for all four of the MOD reproductions were cast at the same time, being attached to the same sprue, and all had precisely the same treatment and conditions except the elastic content of the wax. These patterns, when in the wax and attached to the sprue before investing in the warm investment, were uniform in size and shape, so much so that they could not be discerned one from another. It is particularly interesting to note that Nos. 1 and 2 had the wax put into the cavity by one technic, except that in No. 2 the elasticity was released, and Nos. 3 and 4 by another technic, except that No. 3 had the elasticity released. As you will readily see, No. 1 opened and No. 4 closed so much that they would not fit the form at all, while Nos. 2 and 3 fit very correctly. Before stating the difference in the technic of these two bars we should review the physical conditions obtaining in the compound MOD cavity. When a restoration is being made, for a simple occlusal cavity with all walls present, we have only to adapt to inside dimensions; and if our inlay is prepared with bevel margins, the fact that it has contracted does not prevent it going to place but simply gives it cavity surface freedom and allows it to settle in a little farther, unless it rides on the pulpal floor, which surface of the inlay can easily be ground. The fact that the gold has contracted makes the inlay enter the cavity more easily than if it had not. If, however, we must restore outside dimensions, only as for example a band surrounding a root or porcelain tooth, the same contraction prevents the gold from going to place by drawing it toward the wall at every point instead of away from it, as in the former case. This would be relieved by an expansion, and the surface freedom would be in proportion to that expansion. If our restoration is for conditions having both inside and outside dimensions, we immediately meet a new set of restrictions, for while an excess of contraction of our gold will give us cavity freedom on the inside dimensions, it brings embarrassment to the outside dimensions and an excess of expansion, while producing the desired freedom on the outside dimensions will embarrass the inside dimensions. We are required, therefore, in this case of restoration, to work with relative exactness or to introduce a technic that will increase our surface freedom on all surfaces. This can be accomplished by moving the pattern back and forth, in the cavity, thereby planing off as it were all surfaces and producing a free space on all surfaces. This can also be accomplished by compelling the wax to have an excessive shrinkage away from all margins which follow inside dimensions, and secure the required freedom for outside dimensions by the expansion of the mass. A suitable technic for this will be described later.

 

Figure 4

 

Returning to the description of Figure No. 4, the wax material of the pattern, for both one and two, was introduced by taking a bar of the wax, after it had been kneaded with the fingers, and bending it like a horseshoe at its low working range, and in this way placing it in the cavity. The contained elastic strain tended to make the heals open outward when it was placed in the warm investment, which occurred in No. 1. No. 2 was treated in precisely the same way except that before it was removed from the cavity it had its elasticity released by placing a warm instrument, warm enough to melt the wax, into the mass of wax extended to what would be the gingival floor of the cavity, which released its elasticity. This is also accomplished by flooding the tooth or form with hot water after the wax has been inserted, which accomplished the double purpose, namely, of releasing the elasticity and by an excessive expansion makes some of the wax bulge out of the cavity, which should be scraped off instead of being pressed in after the temperature is reduced. Nos. 3 and 4, Figure 4, had the wax inserted by moulding it into a ball, and while at its low working range pressing the ball into the occlusal surface and into the mesial and distal chambers, which introduced into the wax an elastic strain, which tended to make the heals draw toward each other when all four were placed together in the warm investment. This is shown in No. 4. No 3 had identically the same treatment except that before the removal from the cavity its elasticity was released. Nos. 2 and 3, Figure 4, had, therefore, their elastic strain in opposite directions, as expressed in Nos. 1 and 4, but both are of closely the same size after casting and therefore their elastic strain must have been released. The contraction and distortion errors we are here studying become most embarrassing when we are making very complicated restorations, such as the casting of a crown base when it involves outside dimensions or MOD inlays, involving both inside and outside dimensions. It is probable, however, that few of the profession have appreciated how universally this embarrassment enters into our work. This has been most forcibly demonstrated in the past two years by the results of a series of tests made by different members of the profession, partly because of a premium that was offered by the writer of $150.00, which was placed in the hands of the Program Committee of the Cleveland Dental Society, to be given as three prizes for the first three members who would produce a cast restoration which would go to place within one-fiftieth of an inch. The judges were to consist of a committee of five, four of whom were to be dentists and one a Professor of Physics, which committee has done its work very patiently and efficiently. The form that was first provided consisted of a taper column one-fourth inch in diameter. The taper of the sides was to be one per cent per inch with respect to a common perpendicular. This form was expected to reproduce, approximately, the conditions that obtained when casting a gold base for a molar porcelain crown, where the gold extended over the bevel of the porcelain, as well as over a bevel on the roots, but where these bevels were one per cent to a common perpendicular. This condition provides for the reproducing of both an inside and outside dimension at the same time. As stated, the outside dimension, represented by the periphery of the root and the base of the porcelain, was represented by the taper column, the inside dimensions being the pulp chamber and post hole in the porcelain, were represented by surfaces on the inside of a ring. See Figure No. 5.

Figure 5

 

A number of restorations were made for this form from different parts of the country. The conditions for securing the premiums required that the ring go to place over the outside dimensions and in the inside dimensions of this form to within one-fiftieth of an inch of its position when the pattern was made, for in making the pattern the taper column was drawn through it. This would be equivalent to the porcelain tooth going to place in its cast base when placed in the mouth so that the tooth of the opposite jaw, which had been in a normal occlusion at the time the impression was taken, would be not more than one-fifth of an inch from being in occlusion again. A brass plate represented the porcelain tooth in this form. The nearest that any of the restorations came to going to place on this form was one-half inch instead of one-fiftieth of an inch, because of the contraction around this taper column. Objection was made to this form, many dentists stating that they did not cast crown bases but that they could cast MOD fillings with accuracy. Others stated that they could cast half a ring, even if they could not cast a whole ring, that it was the hole that made the trouble. The explanations for the failures were varied and interesting. Accordingly, the form in which the tests would be made was changed to represent the conditions of an MOD filling, but unfortunately the mechanic got his dimensions large. The wax was put in from the side instead of the end of what would represent the mesial and distal chambers of the cavity. This form is shown in Figure No. 6.

Figure 6 

 

The surfaces representing the pulpal walls had a bevel to a common perpendicular of one per cent. The restorations made in this form did not go to place much better than those made for the previous form. Objection was made to this form on the ground that it was abnormally large and that the wax was put in from the side instead of the end. Accordingly, the third form was made, which reproduced, in a very hard steel, as nearly as possible, the actual condition obtaining in the molar tooth one-fourth inch in diameter with an MOD cavity, all walls of which had a taper of one per cent to a common perpendicular This instrument is shown in Figure No. 7.

Figure 7

 

It is interesting to note that no restorations were made in this form, under the conditions prescribed by the committee, which went nearly to place. The prime condition to secure the premiums required that the restoration go to place within one-fiftieth of an inch, under a pressure not exceeding five pounds. No restorations made in the test went even half way to place, and many would not enter the cavity. Had the contestants used the information that is contained in Figure No. 2, they probably could easily have secured the premiums, for many restorations have been made by following these directions, which were within the requirements. Figure No. 8 shows two rings made with each of three waxes shown on this list; namely, The Cleveland Dental, Klewe and Taggart. With each wax an effort was made to make two rings, one of which would be large and the other small, the latter produced by adding the error of the wax to the error of the gold, and the other, which was large, by subtracting the error of the wax from that of the gold. In other words, by introducing a correction. The three rings, Nos. 2, 4 and 6, shown on the bottom of the column in Figure No. 8 are all so large that they will pass readily over the base of the taper column, while the duplicate of each. Nos. 1, 3, 5, stop high on the column, as shown.

Figure 8

 

A large number of restorations have been made in the MOD form, which are so loose that they will rattle. The procedure is as follows: When we make an MOD pattern, and chill it in the cavity, the wax contracts and by being held takes on a condition of elastic strain. If this pattern is removed from the form or tooth, after being chilled, and we undertake to introduce an expansion sufficient to overcome the contraction of the gold, the warming of the pattern releases this elasticity, producing a distortion. If, however, we will remove this wax while it is warm and place it in cold water, producing its contraction without strain, it does not take on an elastic stress. It would, however, be too small to go back into position in the form or tooth. If, now, we will break it across the occlusal and while keeping it chilled, replace it in the form or tooth, we will have quite a wide crack between the broken surfaces. We will now take a wedge of new wax and force it into this opening, after softening the edges with a warm instrument. This will introduce enough new wax in that particular part which has to do with our outside dimensions, so that when the pattern is removed and invested in a warm investment, which temperature is dependent upon the formula of the pattern material, we will produce sufficient expansion of the mass of wax so that it will readily go over the outside dimensions. Care should be taken, however, to release the elasticity of the wax, as previously described, namely, by either flooding the tooth with hot water, prior to fracturing it across the occlusal surface, or by using a hot instrument, passing well up to the cervical floor of the cavity. Another method that answers well, instead of breaking the MOD pattern, is to cut it across the occlusal surface with a sharp knife in one or two places before chilling in the tooth, thereby allowing the contraction to express itself at the point of separation, and after producing the contraction insert additional wax as before. Rings can be made by this same method, which will introduce an expansion correction in the wax more than sufficient to compensate for the fixed contraction of the gold.

Inasmuch as ordinary dental MOD cavities are not prepared with walls so near parallel as one per cent to a common perpendicular, their wider bevel allows them to go more nearly to perfect seating before binding, and a less exacting technic will be sufficient to control the contraction of these cavities, which is as follows: Place the wax in the cavity at any desired temperature and after trimming and carving to form, warm thoroughly through, making it very soft by means of a stream of hot water. This will expand the wax, pushing the excess slightly out of the cavity, which will be recarved while hot. Next, place a threaded molybdenum or tungsten bar or wire into the occlusal mass of the wax and recarve, or cut through the occlusal and chill in the cavity and introduce more wax in the cut. Remove and invest in each case in a warm investment. The coefficient of expansion of molybdenum and tungsten is very much less than the gold, the former, being about one-fourth that of gold at normal temperature, and through the entire range of the melting of gold less than one-fifth.

A series of quantitative studies were made to ascertain the laws governing the elasticity of wax. It was found that the standard inlay waxes have an elastic content ranging 20, 30, 40, and 50 per cent, according to the treatment of the wax, and also that this elastic content tended to release itself if the wax was held for a sufficient length of time, amounting in some cases to days. Figure No. 9 gives a series of curves, showing the rate of release of elasticity of retained wax bars, due to molecular flow. The continuous lines represent tests with bent bars, the dotted lines compressed bars and the alternate line and dotted line stretched bars. 

 

Figure 9

 

This chart shows that with the various waxes and various treatments, the elastic content, though starting as high as fifty and forty per cent, drops to within ten per cent in twenty-four hours, and is practically gone in ten days. The numbers on the base line indicate the number of days during which the molecular flow is allowed to take place, and during which time the wax was retained in its bent position. It clearly is not possible for us to leave our wax patterns in the tooth for a day, or days, in order that the elastic stress may be released by a molecular flow, but it does answer the question why, when a wax pattern is made in the form and left in the form for days before being removed and then cast, it produces a better fitting inlay than if removed at once, unless the elastic content has been released by a quicker method, as by raising the temperature of the wax to the point at which it speedily releases it while the wax is still in the form or tooth. Figure No. 10 shows graphically the form in which the wax bars were bent and held for measuring their elastic stress. A represents the position of the wax bar with its base fastened securely in the angular groove. B shows the amount of bend put in the wax while at its low working temperature. C represents the amount of return, or elastic content, which takes place if the pressure is withdrawn and the temperature slightly raised, which, with all waxes, is large and with many amounting to forty and fifty per cent of the original bend.

 

Figure 10

 

The members of our profession will find great benefit and satisfaction in the placing of either staples, or a piece of straight tungsten or molybdenum, threaded or roughened, bars in their complicated patterns, which will control, largely, the warpage of the wax, due to elastic strain, and in a large measure will control the contraction of both the wax and the gold. They will also find it a great advantage to make themselves familiar with means for controlling and releasing the elasticity of the wax and thereby prevent its distressing distortions. We will strongly recommend that you study the coefficient of expansion of the wax you are using, if it is not shown on the chart in Figure No. 2, which contains all the waxes that could be obtained in the open market, make tests to determine its coefficient of expansion and endeavor to so manipulate it that you will make its dimension change compensate for the fixed contraction of your gold, and this without introducing the errors of the elasticity of the wax. We would recommend that you familiarize yourself with the information shown so graphically in Figure No. 4, which shows the errors and corrections all in one simple casting.

 

References Cited:

1. Price, Dental Cosmos, March 1911, “The Laws Determining the Behavior of Gold in Fusing and Casting.”
2. Dental Cosmos, October 1911, “Standardizing the Investment Process and Simplifying the Casting Process,” by C. S. Van Horn, D. D. S.