The Relationship between Composition and Density in Binary Master Alloys for Titanium Dr. James W. Robison, Jr. and Scott M. Hawkins Reading Alloys, Inc. Abstract Each year we field several calls from consumers of master alloys asking how they can estimate the density of master alloys. Common approaches are weighted averages of elemental densities and mole-fraction averaging. As several lower-density titanium alloys are showing growth, there is accompanying interest in master alloys with lower density and often lower melting ranges. To address these issues, in this paper we examine the variation of measured densities as a function of composition for Al-V, Al-Cr, Al-Mo and Al-Nb alloys across the entire range of possible composition. We also compare the estimated densities obtained by the above approximations, and the composition-liquidus curve for each of the four binaries. It is hoped this information will be useful to the titanium industry. Introduction When people ask me about the relation between master alloy composition and density, they often are making some dubious assumptions about the behavior of alloys and metals, and about the most appropriate ways to estimate densities for new alloys or extrapolations from known alloys. The first questionable assumption is that binary alloys that form numerous relatively stable compounds are likely to be denser than the pure elements, because the compounds squeeze the atoms together more tightly. The following assumption is that a simple linear relation exists between the weight percentage of each element and the density of the alloy. Or, that such a relation exists between the atom fraction (i.e., mole fraction for a monatomic species) of each element and the alloy density. These assumptions can be addressed by considering an atom of a metallic element such as aluminum as a sphere of fixed diameter. The diameter and weight of such a sphere are different for each metallic element. How many spheres of a given diameter (and therefore, weight) can we stuff into a finite volume? In the eighteenth century the British navy explored this same question, but they used cannon balls and ships magazines. The conclusion was that for each diameter the maximum number of balls per unit volume was obtained by closely-packing the balls in what we today call hexagonal-close-packed (HCP) or facecentered-cubic (FCC) structures. In each structure the solids theoretically occupy 74% of the volume, while 26% is the volume of voids between balls. Any other arrangement has lower solids and greater voids. Aluminum is face-centered-cubic (i.e., maximum possible density), but vanadium, chromium, molybdenum and niobium are a lower-density form, bodycentered-cubic. The solids spheres in a theoretical body-centered-cubic structure occupy 68% of the volume, while 32% is void space. To combine two different ball sizes, such as 6 and 8, leads to lower percentages of solids and greater percentages of void space, unless one size
of balls was small enough to fit into the voids formed by the larger balls. Much later the great Linus Pauling expanded this work to crystallography, with what became known as Pauling s Rules of Packing. In applying this information to master alloy systems for the titanium industry, we are seeking to produce alloys with densities compatible with the titanium alloy in which they will be used, and with melting ranges that support rapid dissolution if not actual melting in the titanium alloy. The four alloys we are discussing today are used not only in high-titanium alloys, but also in lower-density, lower-melting alloys like Gamma Ti. How well do the estimates reflect the reality? Experimental Method At Reading Alloys we measure the density of our alloys using a simple volumedisplacement device called a pyncnometer, Figure 1. The values we obtain may not be as precise as those offered by more sophisticated instruments, but they are measurements of actual production alloys. The values we have obtained for our alloys are shown on the graphs that follow. Each point is the average of multiple determinations from different production lots. Figure 1. Typical Pyncnometer with working volume of 25 ml. Discussion The Al-V System Figure 2. Al-V Phase Diagram The aluminum-vanadium phase diagram, Figure 2, has two intermetallic compounds with melting points above 1200ºC, one at 55% V and one at about 39% V, so we might anticipate some variation in density in this composition range. This variation, if it exists, would not be predicted by either estimating technique. Using our hard-sphere model, one might expect the density to vary linearly with weight percentage from pure aluminum at 2.7 g/cm 3 to pure vanadium at 6.11 g/cm 3, as shown in Figure 3. We also might approximate the density by converting weight percentage to atom percentage (or atom fraction) and adding the atom fraction of each element times the density of the pure element. The formulas for this conversion are in Appendix A. Table 1 in Appendix A summarizes the calculated densities for alloys in the Al-V; Al-Cr; Al-Mo; and Al-Nb systems based on the atom fraction of each element in the alloy. The calculated densities for Al-V alloys are included in Figure 3. Note that the values are significantly lower for the 2
curve based on atom fraction than the curve (straight line) based on weighted averages of the elemental densities. g/cm 3 7 6 5 4 Measured Atom Fraction Weight Percent Density of Al-V Alloys The Al-Cr System The Al-Cr phase diagram, Figure 4, has only one intermetallic phase melting above 1200ºC, at approximately 56 weight per cent chromium, but six relatively stable intermetallic compounds ranging from 20 % to 83 % by weight. In Figure 5 the calculated densities based on both methods of estimation are shown as well as the results of our determination of actual densities, again from production heats with multiple samples. 3 2 0% 20% 40% 60% 80% 100% Wt % V Figure 3. Density of Al-V Alloys The experimental values are extremely close to the curve calculated using atom fractions, and there is no discernable deviation in the area of the previously identified stable compounds. In this case, the atom fraction method provides an excellent approximation of the density of the Al-V alloys. The weight-percent weighted average model is a very poor approximation. All of the measured data lie well below the linear estimate curve, and have no inflections. The lack of inflections indicates that rather than squeezing the atoms together the intermetallic compounds either have little effect or exacerbate the expansion of the lattice caused by interposing larger and smaller atoms, as predicted by the hard sphere model. Comparing figures 2 and 3, it is apparent that Al-V alloys with 40% to 50% vanadium have densities compatible with lower-density titanium alloys such as Gamma Ti, and the liquidus ranges also are compatible with the Gamma Ti alloys. g/cm 3 8 7 6 5 4 3 Figure 4. Al-Cr Phase Diagram Measured Atom Fraction Weight Percent Density of Al-Cr Alloys 2 0% 20% 40% 60% 80% 100% Wt % Cr Figure 5. Density of Al-Cr Alloys Clearly, the linear weighted-average model deviates too far from the measured values to be of use. In the Al-Cr system the 3
calculated densities based on atom fraction are not quite as good an approximation as in the Al-V case, but they probably are close enough for most applications. The maximum error is about 0.2 g/cm 3. 12 10 Density of Al-Mo Alloys Measured Atom Fraction Weight Percent From the melting ranges and densities of Figures 4 and 5, Al-Cr alloys with 40% Cr or greater would be suitable for use in lower density and lower melting titanium alloys. The Al-Mo System The Al-Mo system has multiple stable compounds, but only two are stable from above 1200ºC to room temperature. This system is shown in Figure 6, below. Once the weight percent molybdenum falls below approximately 55%, the only solid phase present at normal processing temperatures for titanium or Gamma-Ti alloys is Mo 3 Al 8. In the region from 0 to 55% molybdenum we might expect density increasing linearly with the fraction of (Mo 3 Al 8 ), but aluminum-rich alloys tend to segregate, so we have not reported experimental data, shown in Figure 7, in that range. The experimental data do support the atom fraction model as an excellent predictor of alloy density in this system. g/cm 3 8 6 4 2 0% 20% 40% 60% 80% 100% Wt % Mo Figure 7. Density of Al-Mo Alloys (45% Al-55% Mo contains ~2.5% Ti) The Al-Nb System Similar to the Al-Mo system, there are no stable phases in the aluminum-rich region below Al 3 Nb, at 53.4% Nb. The aluminumrich alloys tend to segregate, so our experimental data is focused on alloys with greater than 55% niobium. Once again, the experimental data are in close agreement with density predictions based on the atom fraction model, as shown in Figure 9. Figure 6. The Al-Mo Phase Diagram Figure 8. The Al-Nb Phase Diagram 4
10 Density of Al-Nb Alloys as the previous four examples. The results are summarized in the table below. g/cm 3 9 8 7 6 5 4 3 Measured Atom Fraction Weight Percent For aluminum-zirconium and aluminumcobalt, the atom fraction method provides the closer approximation of the measured density, but for aluminum-silicon the two estimating techniques have negligible difference. However, in silicon-titanium, the measured density is much greater than either estimate. 2 0% 20% 40% 60% 80% 100% Figure 9 Wt % Nb The Density of Al-Nb Alloys We also looked at several other binary alloys to see if they followed the same trend While the atom fraction technique can provide good estimates of the actual alloy densities, a good measurement is the preferred option. Reading Alloys, Inc. would be glad to provide such measurements. Table 2 Density of Other Binary Alloys, grams/cm 3 Alloy, Weight % Wt % Estimate At. Fr. Estimate Measured 40Al-60Zr 5.24 3.89 4.20 50Al-50Co 5.80 4.69 4.29 50Al-50Si 2.51 2.52 2.41 53Si-47Ti 3.62 3.33 4.15 Conclusions 1. Estimating the density of binary Al-X alloys using the weight percentage technique is inaccurate and may lead to erroneous conclusions. 2. Estimating densities using the atom fraction technique provides excellent estimates for most of the alloys examined, and is more likely to lead to correct conclusions. 3. The pyncnometer is easy to use, quick, non-destructive, and simple. However, it requires careful use and does not work accurately on samples with internal voids, non-wetted cracks or powders. Acknowledgements The authors appreciate Reading Alloys allowing us to prepare and present this paper, the Reading Alloys Analytical Lab for performing the density measurements, and the ITA for their many kindnesses, and for offering us the opportunity to present this paper. 5
References All phase diagrams are from Binary Alloy Phase Diagrams, edited by T. B. Massalski, ASM, 1st ed., 1986 and 2 nd ed., 1990. Appendix A For Atom Fraction At. Fr. X = wt.% X at. wt. X wt at +.% X. wt. X 100 wt.% at. wt. Y X For Density estimated from Atom Fraction est. ( At. Fr. X ) ( Density ) + ( 1 At. Fr X ) ( Density ) Density =. purex purey Density (g/cm 3 ) Table 1 Calculated densities from Atom Fraction Wt % Al 100% 80% 60% 40% 20% 0% Balance V 2.70 3.10 3.59 4.21 5.02 6.11 Balance Cr 2.70 3.22 3.85 4.67 5.73 7.19 Balance Mo 2.70 3.19 3.89 4.93 6.68 10.22 Balance Nb 2.70 3.10 3.65 4.48 5.86 8.57 6
The Relationship between Composition and Density in Binary Master Alloys for Titanium Dr. James W. Robison, Jr. & Scott M. Hawkins Reading Alloys, Inc.
Pyncnometer
7 6 Density of Al-V Alloys Measured Atom Fraction Weight Percent 5 g/cm 3 4 3 2 0% 20% 40% 60% 80% 100% Wt % V
8 7 Density of Al-Cr Alloys Measured Atom Fraction Weight Percent 6 g/cm 3 5 4 3 2 0% 20% 40% 60% 80% 100% Wt % Cr
12 10 Density of Al-Mo Alloys Measured Atom Fraction Weight Percent 8 g/cm 3 6 4 2 0% 20% 40% 60% 80% 100% Wt % Mo
10 9 8 Density of Al-Nb Alloys Measured Atom Fraction Weight Percent 7 g/cm 3 6 5 4 3 2 0% 20% 40% 60% 80% 100% Wt % Nb
Density of Other Binary Alloys, in gr/cm 3 Alloy, Wt. % At. Fr. Measured Nominal Estimate Estimate 40Al-60Zr 524 5.24 389 3.89 42 4.2 50Al-50Co 5.80 4.69 4.29 50Al-50Si 2.51 2.52 2.41 53Si-47Ti 362 3.62 333 3.33 415 4.15
Conclusions: 1. The Weight-Percent density model is inaccurate in most situations and should be avoided. 2. The Atom-Fraction density model is a much better predictor of alloy density in many situations. 3. A Pyncnometer can provide quick and inexpensive density data dt on suitable itbl samples, but btith has limitations itti that must be considered. It may give erroneous results if the sample has internal voids, non-wetted cracks, or is a powder.