Handbook Heat Treating (1991) WW Part 15 potx

• Billet is preheated in molten salt bath at 630 °C (1165 °F) and extruded • Extruded billet is machined into blank that is solution heat treated at 800 °C (1475 °F) for 8 h in vacuum and water quenched • Blank is aged at 385 °C (725 °F) for 4.5 h in argon and water quenched Example 2: U-0.75Ti. Bars of DU-0.75Ti alloy, 36 mm (1.4 in.) in diameter are to be heat treated to the following specifications: hardness, 38 to 44 HRC; minimum 0.2% yield strength, 725 MPa (105 ksi); minimum elongation, 12%; and maximum hydrogen content, 1 ppm. The procedure is to: • Cut extruded bar stock to length • Pickle in 1:1 nitric acid to remove copper sheath • Rinse and air dry • Place rods vertically in a basket • Solution treat 2 1 2 h at 850 °C (1560 °F) in a vacuum of 7 × 10 -3 Pa (5 × 10 -5 torr), or better • Quench into circulating water at 455 mm/ min (18 in./min) • Air dry • Age 16 h at 350 °C (660 °F) in an inert gas recirculating furnace Example 3: U-6Nb Alloy. A U-6 Nb alloy is to be formed into a hemisphere with the following mechanical properties: ultimate tensile strength, 770 MPa (112 ksi) min; yield strength at 0.2% offset, 360 to 485 MPa (52 to 70 ksi); and total elongation, 25% min. • Billet is preheated to 800 to 850 °C (1475 to 1560 °F) and forged • Forged billet is homogenized at 1000 °C (1830 °F) for 4 h in vacuum • Forged billet is preheated to 850 °C (1560 °F) in molten salt bath and cross rolled into plate • Plate is preheated in argon furnace to 850 °C (1560 °F) and formed into a hemisphere • Hemisphere is solution heat treated to 800 °C (1475 °F) for 1 to 2 h in vacuum and water quenched • Hemisphere is aged in argon at 200 °C (400 °F) for 2 h References cited in this section 5. K.H. Eckelmeyer, A.D. Romig Jr., and L.J. Weirick, The Effect of Quench Rate on the Microstructure, Mechanical Properties, and Corrosion Behavior of U-6 Wt. Pct. Nb, Met. Trans. A, Vol 15A, 1984, p 1319 6. K.H. Eckelmeyer and F.J. Zanner, The Effect of Aging on the Mechanical Behavior of U- 0.75 wt.% Ti and U-2.0 wt.% Mo, J. Nucl. Mater., Vol 62, 1976, p 37 7. G.H. Llewellyn, G.A. Aramayo, M. Siman- Tov, K.W. Childs, G.M. Ludtka, "Computer Simulation of Immersion of Uranium-0.75 wt.% Titanium Alloy Cylinders," Y- 2355, Martin Marietta Energy Systems, Inc., June 1986 8. G.H. Llewellyn, G.A. Aramayo, G.M. Ludtka, J.E. Park, M. Siman- Tov, "Experimental and Analytical Studies in Quenching Uranium-0.75% Titanium Alloy Cylinders," Y- 2397, Martin Marietta Energy Systems, Inc., Feb 1989 Licensing and Health and Safety Requirements Possession of more than 15 lb (6.8 kg) of depleted uranium in any form requires a license from the U.S. Nuclear Regulatory Commission. Title 10, Part 40, of Federal Regulations describes the steps necessary and the requirements to obtain such a license. In addition, all other local, state, and federal regulations are effective as applicable. The greatest potential source of contamination in the heat-treating area is uranium oxide. The area should be isolated from the remainder of the plant, and everyone entering should be required to wear disposable protective footwear. Smoking and eating should be restricted. Caution: The toxicity of depleted uranium if it enters the blood stream may result in poisoning similar to that caused by lead, arsenic, mercury, or any other heavy metal. A more detailed discussion about health and safety requirements is provided in Volume 2 of ASM Handbook, formerly 10th Edition Metals Handbook. The important fact to remember is that each new operation or procedure involving uranium alloys should be individually evaluated to determine the correct protective clothing and equipment, dosimetry, and handling requirements for that particular job. The prior processing history of the heat treatment samples is likewise important in this consideration since operations which change the state of the uranium, like casting, can make concerns about daughter-product beta radiation more important than normal low-level alpha radiation associated with depleted uranium. Annealing of Precious Metals Gaylord Smith, Inco Alloys International, Inc.; Al Robertson, Englehard Corporation Introduction THE PRECIOUS METAL GROUP consists of silver, gold, platinum, palladium, rhodium, iridium, ruthenium, and osmium. Significant production of wrought product forms is limited to the first four elements and their alloys. The last four elements become increasingly intractable or less ductile and consequently cannot be practically fabricated into engineering products. Because of the dissimilarities of the physical metallurgy of elements within the precious metal group, the annealing practice for each member of the group will be considered separately. For each element and its alloys, a brief description of the compositions, uses, annealing practices, and nominal annealing effects on key properties is given. Silver and Silver Alloys Consumption of silver and silver alloys in wrought product form is large and exceeds that of any other members of the precious metal group. Because of the extensive use of silver, data on annealing practice and the effects of annealing on mechanical properties are more available for silver than for the remainder of the precious metal group. Commercially Pure Fine Silver Commercially pure fine silver contains, by definition, at least 99.9% Ag. It is widely used in the electrical and electronics industries as contacts and conductors and in the chemical industry as linings for reactors and process/storage vessels, particularly caustic evaporators and crystallizers. Annealing Practice. Commercially pure fine silver is typically annealed between 300 and 350 °C (570 and 660 °F) following at least 50% cold work. However, data exists in the literature for annealing times up to 1.5 h at temperatures as high as 565 °C (1050 °F). Most annealing of silver, however, is done at approximately 500 °C (930 °F). Under extreme conditions of cold work, ultra-pure (99.99% pure) silver can recrystallize at temperatures as low as room temperature. Silver is typically annealed in air at temperatures below 350 °C (660 °F) without adverse effects. However, higher annealing temperatures (550 to 650 °C, or 1020 to 1200 °F) can result in oxygen adsorption due to the high solubility and diffusion rate (under 0.025 mm at >800 °C/h, or 1440 °F/h) of oxygen in silver. Very pure silver has a hardness of 25 HV after a hydrogen anneal at 650 °C (1200 °F) and 27 HV after annealing in air at the same temperature. Oxygen present in silver tends to react with impurities and has the beneficial effect of inhibiting grain growth. Silver containing oxygen will become embrittled when annealed in hydrogen. Hydrogen annealing of thin material sections of silver can cause the formation of blisters. This effect is similar to that known to occur when tough pitch copper, that is, copper refined in a reverberatory furnace to adjust the oxygen content to 0.2 to 0.5%, is annealed in hydrogen. Thus, deoxidized silver is essential where hydrogen annealing is practiced. Effect of Annealing Temperature on Mechanical Properties. The effect of annealing temperature on the tensile strength and elongation of wire cold drawn 49% prior to annealing is presented in Fig. 1. Ductility is maximized at approximately 370 °C (700 °F). Higher temperatures reduce ductility and ultimately increase tensile strength as grain growth and perhaps oxygen adsorption begin to adversely influence tensile properties. Comparable data are presented in Table 1 for commercially pure fine silver sheet, 0.81 mm (0.032 in.) thick. Data on the deep-drawing characteristics of commercially pure fine silver as a function of annealing temperature are given in Table 2. Annealing lowers Poisson's ratio to 0.37 from 0.39 for hard-drawn material. The most frequently reported room-temperature value for the elastic modulus of commercially pure fine silver is 71 GPa (10.3 × 10 6 psi). This value was determined on material strained 5% and then annealed 0.5 h at 350 °C (660 °F). Cold work and annealing temperature, as well as compositional variations, apparently can affect the elastic modulus. The shear modulus is reduced by annealing from the cold worked state from 26.9 GPa (3.90 × 10 6 psi) for hard-drawn material to 26.6 GPa (3.86 × 10 6 psi) for annealed commercially pure fine silver at 20 °C (68 °F). Table 1 Effect of annealing temperature on room- temperature tensile properties of commercially pure fine silver cold rolled 50% to 0.81 mm (0.032 in.) thickness Annealing condition (held 1 2 h) Tensile strength °C °F MPa ksi Elongation, % As rolled 50% 374 54.3 2.4 205 400 183 26.5 43.7 315 600 172 25.0 51.6 425 800 172 25.0 51.5 540 1000 166 24.1 50.3 650 1200 158 22.9 53.9 760 1400 155 22.5 48.4 Table 2 Cup depth at room temperature as a function of annealing temperature for comme rcially pure fine silver sheet 0.81 mm (0.032 in.) thick Annealing temperature Cup depth °C °F mm in. 95 200 3.56 0.140 205 400 7.65 0.301 315 600 8.33 0.328 425 800 8.43 0.332 540 1000 8.38 0.330 650 1200 8.41 0.331 760 1400 8.31 0.327 Source: Ref 2 Fig. 1 Tensile properties of commercially pure fine silver 2.3 mm (0.091 in.) diam wire Effect of Cold Work on Recovery and Recrystallization. Data for the onset of softening (recovery) for commercially pure fine silver as a function of the degree of cold rolling at 20 °C (68 °F) are shown in Table 3. Commercially pure fine silver that has been cold worked extensively, that is, greater than about 95%, can recrystallize at relatively low temperatures. The effect of small amounts of a second element has been found to measurably influence the recrystallization temperature under these conditions. A brief summary of these observations is given in Table 4. Because of the uncertainty of overall purity and whether the temperature given is the start or finish of recrystallization, these data are only indicative of a general trend. Table 3 Effect of cold work on the softening temperature of commercially pure fine silver Softening temperature Reduction by rolling at 20 °C (68 °F), % °C °F 10 250 480 50 100 210 90 65 150 Table 4 Effect of second elements on the recrystallization temperature of commercially pure fine silver that has been extensively cold worked Recrystallization temperature Element Nominal composition, wt% °C °F . . . . . . 150 300 Aluminum 0.200 190 370 Copper 0.012 200 390 Copper 0.037 175 350 Copper 0.303 230 450 Gold 0.100 110 230 Gold 0.200 110 230 Iron 0.035 110 230 Iron 0.055 20 70 Iron 0.065 20 70 Lead 0.059 145 290 Nickel 0.100 140 280 Palladium 0.100 110 230 Zinc 0.119 145 290 Source: Ref 4 Silver-Copper Alloys The most common silver-copper alloys are sterling silver (92.5% Ag minimum), coin silver (Ag-10% Cu), and the eutectic alloy containing 28.1% Cu. Sterling silver is normally alloyed only with copper because other elements have proved to be less effective hardeners. Sterling silver is typically used for flat and hollow tableware and in the manufacture of jewelry. Coin silver is used for coins and in certain electrical contacts where pure silver is deemed too soft and prone to pitting. Spring-type electrical contacts are made from the eutectic alloy. Effect of Annealing Temperature on Mechanical Properties. Figure 2 shows the effect of annealing temperature on the strength and elongation of cold drawn 2.3 mm (0.091 in.) diam sterling silver and eutectic alloy wire. Commercial silver-copper alloys are typically annealed between 480 and 535 °C (900 and 1000 °F) followed by furnace cooling under protective atmosphere, which can result in some age hardening. Process annealing can be conducted at temperatures as high as 675 °C (1250 °F) usually in a steam atmosphere or salt bath. However, at the higher temperature, quenching is required for producing full softness. Alternating between oxidizing and reducing atmospheres during annealing is damaging to this alloy compositional range. Where light oxidation has occurred, pickling in a hot (approximately 50 °C, or 120 °F) sulfuric acid solution (5 to 10%) is suitable. Fig. 2 Tensile properties and electrical conductivity of silver- copper alloys. 2.3 mm (0.091 in.) diam wire, cold drawn (CD) 49% before annealing. (a) Sterling silver (92.5Ag-7.5Cu). (b) Eutectic alloy (72Ag-28Cu) Figure 3 records the nominal electrical resistivity of annealed as well as annealed/aged silver-copper wire as a function of copper content. The silver-copper alloys can be age hardened as depicted in Fig. 4. The solubility of copper in silver at 650 °C (1200 °F) is about 4% and at 730 °C (1350 °F) about 6%, thus sterling silver annealed at these temperatures is duplex with small amounts of the copper-rich phase scattered through the silver-rich matrix. Aging treatments cause precipitation of the copper-rich phase and, if prolonged, increase the electrical conductivity considerably. Coin silver will remain duplex after any annealing treatment, and ages in much the same manner as sterling silver. Both alloys respond to aging at 280 °C (535 °F) (Fig. 4). The mechanical properties of sterling silver and coin silver are virtually the same after the usual annealing treatment at about 650 °C (1200 °F) because the composition of the silver-rich phase is essentially the same. Alloys containing 20 to 30% Cu have much more of the copper-rich phase and show less age hardening. Fig. 3 Effect of copper content on the electrical resistivity of annealed silver- copper alloys and annealed/aged silver-copper alloys Fig. 4 Effect of copper content on properties of silver-copper alloys References cited in this section 1. A. Butts and C.D. Coxe, Ed., Silver: Economics, Metallurgy, and Use, R.E. Kriegier Publishing, 1967, p 141 2. A. Butts and C.D. Coxe, Ed., Silver: Economics, Metallurgy, and Use, R.E. Kriegier Publishing, 1967, p 144 3. A. Butts and C.D. Coxe, Ed., Silver: Economics, Metallurgy, and Use, R.E. Kriegier Publishing, 1967, p 149 4. A. Butts and C.D. Coxe, Ed., Silver: Economics, Metallurgy, and Use, R.E. Kriegier Publishing, 1967, p 148 Gold and Gold Alloys There are a number of types of pure and alloy gold systems of commercial significance each with different annealing practices. Included here will be annealing information on pure gold, color and white gold, gold-platinum, gold-palladium- iron, and cast and wrought gold alloys for dentistry. Pure Gold The usual grade of refined gold is 99.99% pure and is suitable for jewelry and dental applications. Coin gold contains 89.9 to 91.7% Au, with the balance being copper. Annealing Practice. Pure gold can be annealed in air at 305 °C (580 °F) to control grain size but it is usually not required because pure gold easily recrystallizes at room temperature. Wrought annealed pure gold has a room temperature tensile strength of 131 MPa (19 ksi), 45% elongation, and a hardness of 25 HB. The elastic modulus is 80 GPa (11.6 × 10 6 psi). Color Gold Alloys Most of the commercially important color gold alloys are based on the gold-silver-copper system although zinc and nickel are frequent modifiers. The composition of typical color gold alloys is given in Table 5. These alloys are used principally in jewelry; slip rings and bushings in electrical devices; and in dental applications. Table 5 Chemical composition of typical color gold alloys Nominal composition, wt% Alloy, k Color Au Cu Ag Zn 10 Yellow 41.7 43.8 5.5 9.0 10 Yellow 41.7 48.0 6.6 3.7 10 Yellow 41.7 40.8 11.7 5.8 10 Green 41.7 9.1 48.9 0.3 14 Yellow 58.3 31.3 4.0 6.4 14 Yellow 58.3 29.2 8.3 4.2 14 Yellow 58.3 39.7 10.0 2.0 14 Yellow 58.3 25.0 16.5 0.2 14 Yellow 58.3 16.8 24.8 0.1 14 Green 58.3 6.5 35.0 0.2 18 Yellow 75.0 10.0 15.0 . . . Annealing Practice. Typical annealing temperatures for the color gold alloys are in the range of 500 to 700 °C (930 to 1290 °F) depending on the exact composition. It is recommended that color gold alloys be quenched in water after annealing to avoid age hardening. This has the secondary effect of removing any oxide scale that may have formed during annealing in air. Commercially, most annealing of color gold alloys is done in a 7% H 2 -N 2 atmosphere with slow cooling instead of quenching. However, nickel-containing white gold alloys should be air cooled as quenching introduces high residual stress levels in these alloys. Aging of the two-phase alloys is customarily done at 260 to 315 °C (500 to 600 °F). Effect of Annealing and Aging on Hardness. Figure 5 depicts the effect of annealing, followed by quenching, on the hardness of the color gold alloys. Also shown is the effect of aging at 260 to 315 °C (500 to 600 °F) as a function of silver content. Age hardening temperatures can vary from between 100 °C (210 °F) and 425 °C (800 °F) depending upon the alloy that is being used. Aging times can vary from 5 min to 2 h, with increasing time associated with increasing strength and lower ductility. Longer aging times may result in overaging and subsequent decreasing hardness. In Fig. 5, note the lack of an aging response for the extremes of the silver content for the 10 and 14 k alloys, where k is karats. Fig. 5 Variation of hardness with silver content for gold-silver-copper alloys Gold Alloys in Dentistry A large number of alloys are used in dentistry in the form of wrought plate and wire, casting, and solder. These alloys require high strength and corrosion resistance. Both requirements are met by complex alloys of gold, platinum, palladium, silver, copper, and zinc. These alloys age harden readily. Typical compositional limits of wrought alloys are given in Table 6 and for cast alloys in Table 7. Table 6 Compositions and colors of wrought precious-metal alloys used in high-strength dental wires Composition (b) , % Alloy (a) Au Pt Pd Ag Cu Ni Zn Color 1 25-30 40-50 25-30 . . . . . . . . . . . . Platinum 2 54-60 14-18 1-8 7-11 11-14 1 max 2 max Platinum 3 45-50 8-12 20-25 5-8 7-12 . . . 1 max Platinum [...]... 845-870 155 0-1600 4145 815- 845 150 0 -155 0 4147 815- 845 150 0 -155 0 4150 815- 845 150 0 -155 0 4161 815- 845 150 0 -155 0 4337 815- 845 150 0 -155 0 4340 815- 845 150 0 -155 0 50B40 815- 845 150 0 -155 0 50B44 815- 845 150 0 -155 0 5046 815- 845 150 0 -155 0 50B46 815- 845 150 0 -155 0 50B50 800-845 1475 -155 0 50B60 800-845 1475 -155 0 5130 830-855 152 5 -157 5 5132 830-855 152 5 -157 5 5135 815- 845 150 0 -155 0 5140 815- 845 150 0 -155 0 5145 815- 845 150 0 -155 0... 154 1 815- 845 150 0 -155 0 154 8 815- 845 150 0 -155 0 155 2 815- 845 150 0 -155 0 156 6 855-885 157 5-1625 Alloy steels 1330 830-855 152 5 -157 5 1335 815- 845 150 0 -155 0 1340 815- 845 150 0 -155 0 1345 815- 845 150 0 -155 0 3140 815- 845 150 0 -155 0 4037 830-855 152 5 -157 5 4042 830-855 152 5 -157 5 4047 815- 855 150 0 -157 5 4063 800-845 1475 -155 0 4130 815- 870 150 0-1600 4135 845-870 155 0-1600 4137 845-870 155 0-1600 4140 845-870 155 0-1600... 790-830 1450 -152 5 4320 830-845 152 5 -155 0 4 615 815- 845 150 0 -155 0 4617 815- 845 150 0 -155 0 4620 815- 845 150 0 -155 0 4621 815- 845 150 0 -155 0 4626 815- 845 150 0 -155 0 4718 815- 845 150 0 -155 0 4720 815- 845 150 0 -155 0 4 815 800-830 1475 -152 5 4817 800-830 1475 -152 5 4820 800-830 1475 -152 5 8 115 845-870 155 0-1600 8 615 845-870 155 0-1600 8617 845-870 155 0-1600 8620 845-870 155 0-1600 8622 845-870 155 0-1600 8625 845-870 155 0-1600... 790- 815 1450 -150 0 1080 790- 815 1450 -150 0 1084 790- 815 1450 -150 0 1085 790- 815 1450 -150 0 1086 790- 815 1450 -150 0 1090 790- 815 1450 -150 0 1095 790- 815( a) 1450 -150 0(b) Free-cutting carbon steels 1137 830-855 152 5 -157 5 1138 815- 845 150 0 -155 0 1140 815- 845 150 0 -155 0 1141 800-845 1475 -155 0 1144 800-845 1475 -155 0 1145 800-845 1475 -155 0 1146 800-845 1475 -155 0 1151 800-845 1475 -155 0 153 6 815- 845 150 0 -155 0 154 1 815- 845... 150 0 -155 0 5147 800-845 1475 -155 0 5150 800-845 1475 -155 0 5155 800-845 1475 -155 0 5160 800-845 1475 -155 0 51B60 800-845 1475 -155 0 50100 775-800(c) 1425-1475(c) 51100 775-800(c) 1425-1475(c) 52100 775-800(c) 1425-1475(c) 6150 845-885 155 0-1625 81B45 815- 855 150 0 -157 5 8630 830-870 152 5-1600 8637 830-855 152 5 -157 5 8640 830-855 152 5 -157 5 8642 815- 855 150 0 -157 5 8645 815- 855 150 0 -157 5 86B45 815- 855 150 0 -157 5... 855-900 157 5-1650 1030 845-870 155 0-1600 1035 830-855 152 5 -157 5 1037 830-855 152 5 -157 5 1038(a) 830-855 152 5 -157 5 1039(a) 830-855 152 5 -157 5 1040(a) 830-855 152 5 -157 5 1042 800-845 1475 -155 0 1043(a) 800-845 1475 -155 0 1045(a) 800-845 1475 -155 0 1046(a) 800-845 1475 -155 0 1050(a) 800-845 1475 -155 0 1055 800-845 1475 -155 0 1060 800-845 1475 -155 0 1065 800-845 1475 -155 0 1070 800-845 1475 -155 0 1074 800-845 1475 -155 0... 815- 855 150 0 -157 5 8645 815- 855 150 0 -157 5 86B45 815- 855 150 0 -157 5 8650 815- 855 150 0 -157 5 8655 800-845 1475 -155 0 8660 800-845 1475 -155 0 8740 830-855 152 5 -157 5 8742 830-855 152 5 -157 5 9254 815- 900 150 0-1650 9255 815- 900 150 0-1650 9260 815- 900 150 0-1650 94B30 845-885 155 0-1625 94B40 845-885 155 0-1625 9840 830-855 152 5 -157 5 (a) Commonly used on parts where induction hardening is employed All steels from SAE 1030... 11 Q 95- 115 330-395 48-57 160-205 23-30 20-25 950-1000 1740-1830 11 A 115- 165 415- 565 60-82 200-400 29-58 6-20 950-1000 1740-1830 12 Q 130-160 415- 515 60-75 240-325 35-47 4-25 970-985 1600-1805 12 A 210-235 690-830 100-120 415- 635 60-92 1-6 870-985 1600-1805 13 Q 155 -175 460- 515 67-75 415- 485 60-70 4-6 1150 -1190 2100-2175 13 A 175-190 1150 -1190 2100-2175 14 Q 190-210 620-760 90-110 515- 585 75-85... Hardened Soft Hardened °C °F g/cm3 lb/in.3 1 14 -15 (f) 200-245 (f) 150 0 -153 0 2730-2790 16.9-17.6 0.611-0.636 2 12-22 5-10 150 -190 240-285 1005-1100 1840-2010 15. 0-18.5 0.542-0.668 3 8-10 7-9 210-230 250-270 1065-1120 1950-2050 15. 5 -15. 8 0.560-0.571 4 14-26 2-8 166-195 240-295 945-1 015 1730-1860 14.5 -15. 6 0.524-0.564 5 14-20 1-3 135-200 230-290 900-930 1650-1710 14.1 -15. 2 0.509-0.549 6 20-28 1-2 138-170 220-280... 760-790 1400-1450 1 015 760-790 1400-1450 1016 760-790 1400-1450 1017 760-790 1400-1450 1018 760-790 1400-1450 1019 760-790 1400-1450 1020 760-790 1400-1450 1022 760-790 1400-1450 151 3 760-790 1400-1450 151 8 760-790 1400-1450 152 2 760-790 1400-1450 152 4 760-790 1400-1450 152 5 760-790 1400-1450 152 6 760-790 1400-1450 152 7 760-790 1400-1450 Free-cutting carbon steels 1109 760-790 1400-1450 1 115 760-790 1400-1450 . 130-160 415- 515 60-75 240-325 35-47 4-25 970-985 1600-1805 12 A 210-235 690-830 100-120 415- 635 60-92 1-6 870-985 1600-1805 13 Q 155 -175 460- 515 67-75 415- 485 60-70 4-6 1150 -1190. 1065-1120 1950-2050 15. 5 -15. 8 0.560-0.571 4 14-26 2-8 166-195 240-295 945-1 015 1730-1860 14.5 -15. 6 0.524-0.564 5 14-20 1-3 135-200 230-290 900-930 1650-1710 14.1 -15. 2 0.509-0.549. 875-900 1610-1650 13.7-14.0 0.495-0.506 7 9-20 1-8 150 -225 180-270 940-1080 1725-1975 11.5 -15. 6 0. 415- 0.564 8 16-24 8 -15 150-200 235-270 1045-1075 1910-1970 10.7-11.2 0.387-0.405